Tcl Source Code

    TclBN_s_mp_sub, /* 60 */
    TclBN_mp_init_set_int, /* 61 */
    TclBN_mp_set_int, /* 62 */
    TclBN_mp_cnt_lsb, /* 63 */
    TclBNInitBignumFromLong, /* 64 */
    TclBNInitBignumFromWideInt, /* 65 */
    TclBNInitBignumFromWideUInt, /* 66 */

};

static const TclStubHooks tclStubHooks = {
    &tclPlatStubs,
    &tclIntStubs,
    &tclIntPlatStubs
};

    TclBN_s_mp_sub, /* 60 */
    TclBN_mp_init_set_int, /* 61 */
    TclBN_mp_set_int, /* 62 */
    TclBN_mp_cnt_lsb, /* 63 */
    TclBNInitBignumFromLong, /* 64 */
    TclBNInitBignumFromWideInt, /* 65 */
    TclBNInitBignumFromWideUInt, /* 66 */
    TclBN_mp_expt_d_ex, /* 67 */
};

static const TclStubHooks tclStubHooks = {
    &tclPlatStubs,
    &tclIntStubs,
    &tclIntPlatStubs
};

}
declare 65 {
    void TclBNInitBignumFromWideInt(mp_int *bignum, Tcl_WideInt initVal)
}
declare 66 {
    void TclBNInitBignumFromWideUInt(mp_int *bignum, Tcl_WideUInt initVal)
}






# Local Variables:
# mode: tcl
# End:

}
declare 65 {
    void TclBNInitBignumFromWideInt(mp_int *bignum, Tcl_WideInt initVal)
}
declare 66 {
    void TclBNInitBignumFromWideUInt(mp_int *bignum, Tcl_WideUInt initVal)
}

# Added in libtommath 1.0
declare 67 {
    int TclBN_mp_expt_d_ex(mp_int *a, mp_digit b, mp_int *c, int fast)
}

# Local Variables:
# mode: tcl
# End:

#define mp_div TclBN_mp_div
#define mp_div_2 TclBN_mp_div_2
#define mp_div_2d TclBN_mp_div_2d
#define mp_div_3 TclBN_mp_div_3
#define mp_div_d TclBN_mp_div_d
#define mp_exch TclBN_mp_exch
#define mp_expt_d TclBN_mp_expt_d

#define mp_grow TclBN_mp_grow
#define mp_init TclBN_mp_init
#define mp_init_copy TclBN_mp_init_copy
#define mp_init_multi TclBN_mp_init_multi
#define mp_init_set TclBN_mp_init_set
#define mp_init_set_int TclBN_mp_init_set_int
#define mp_init_size TclBN_mp_init_size
................................................................................
EXTERN void		TclBNInitBignumFromLong(mp_int *bignum, long initVal);
/* 65 */
EXTERN void		TclBNInitBignumFromWideInt(mp_int *bignum,
				Tcl_WideInt initVal);
/* 66 */
EXTERN void		TclBNInitBignumFromWideUInt(mp_int *bignum,
				Tcl_WideUInt initVal);




typedef struct TclTomMathStubs {
    int magic;
    void *hooks;

    int (*tclBN_epoch) (void); /* 0 */
    int (*tclBN_revision) (void); /* 1 */
................................................................................
    int (*tclBN_s_mp_sub) (mp_int *a, mp_int *b, mp_int *c); /* 60 */
    int (*tclBN_mp_init_set_int) (mp_int *a, unsigned long i); /* 61 */
    int (*tclBN_mp_set_int) (mp_int *a, unsigned long i); /* 62 */
    int (*tclBN_mp_cnt_lsb) (const mp_int *a); /* 63 */
    void (*tclBNInitBignumFromLong) (mp_int *bignum, long initVal); /* 64 */
    void (*tclBNInitBignumFromWideInt) (mp_int *bignum, Tcl_WideInt initVal); /* 65 */
    void (*tclBNInitBignumFromWideUInt) (mp_int *bignum, Tcl_WideUInt initVal); /* 66 */

} TclTomMathStubs;

extern const TclTomMathStubs *tclTomMathStubsPtr;

#ifdef __cplusplus
}
#endif
................................................................................
	(tclTomMathStubsPtr->tclBN_mp_cnt_lsb) /* 63 */
#define TclBNInitBignumFromLong \
	(tclTomMathStubsPtr->tclBNInitBignumFromLong) /* 64 */
#define TclBNInitBignumFromWideInt \
	(tclTomMathStubsPtr->tclBNInitBignumFromWideInt) /* 65 */
#define TclBNInitBignumFromWideUInt \
	(tclTomMathStubsPtr->tclBNInitBignumFromWideUInt) /* 66 */



#endif /* defined(USE_TCL_STUBS) */

/* !END!: Do not edit above this line. */

#undef TCL_STORAGE_CLASS
#define TCL_STORAGE_CLASS DLLIMPORT

#endif /* _TCLINTDECLS */

#define mp_div TclBN_mp_div
#define mp_div_2 TclBN_mp_div_2
#define mp_div_2d TclBN_mp_div_2d
#define mp_div_3 TclBN_mp_div_3
#define mp_div_d TclBN_mp_div_d
#define mp_exch TclBN_mp_exch
#define mp_expt_d TclBN_mp_expt_d
#define mp_expt_d_ex TclBN_mp_expt_d_ex
#define mp_grow TclBN_mp_grow
#define mp_init TclBN_mp_init
#define mp_init_copy TclBN_mp_init_copy
#define mp_init_multi TclBN_mp_init_multi
#define mp_init_set TclBN_mp_init_set
#define mp_init_set_int TclBN_mp_init_set_int
#define mp_init_size TclBN_mp_init_size
................................................................................
EXTERN void		TclBNInitBignumFromLong(mp_int *bignum, long initVal);
/* 65 */
EXTERN void		TclBNInitBignumFromWideInt(mp_int *bignum,
				Tcl_WideInt initVal);
/* 66 */
EXTERN void		TclBNInitBignumFromWideUInt(mp_int *bignum,
				Tcl_WideUInt initVal);
/* 67 */
EXTERN int		TclBN_mp_expt_d_ex(mp_int *a, mp_digit b, mp_int *c,
				int fast);

typedef struct TclTomMathStubs {
    int magic;
    void *hooks;

    int (*tclBN_epoch) (void); /* 0 */
    int (*tclBN_revision) (void); /* 1 */
................................................................................
    int (*tclBN_s_mp_sub) (mp_int *a, mp_int *b, mp_int *c); /* 60 */
    int (*tclBN_mp_init_set_int) (mp_int *a, unsigned long i); /* 61 */
    int (*tclBN_mp_set_int) (mp_int *a, unsigned long i); /* 62 */
    int (*tclBN_mp_cnt_lsb) (const mp_int *a); /* 63 */
    void (*tclBNInitBignumFromLong) (mp_int *bignum, long initVal); /* 64 */
    void (*tclBNInitBignumFromWideInt) (mp_int *bignum, Tcl_WideInt initVal); /* 65 */
    void (*tclBNInitBignumFromWideUInt) (mp_int *bignum, Tcl_WideUInt initVal); /* 66 */
    int (*tclBN_mp_expt_d_ex) (mp_int *a, mp_digit b, mp_int *c, int fast); /* 67 */
} TclTomMathStubs;

extern const TclTomMathStubs *tclTomMathStubsPtr;

#ifdef __cplusplus
}
#endif
................................................................................
	(tclTomMathStubsPtr->tclBN_mp_cnt_lsb) /* 63 */
#define TclBNInitBignumFromLong \
	(tclTomMathStubsPtr->tclBNInitBignumFromLong) /* 64 */
#define TclBNInitBignumFromWideInt \
	(tclTomMathStubsPtr->tclBNInitBignumFromWideInt) /* 65 */
#define TclBNInitBignumFromWideUInt \
	(tclTomMathStubsPtr->tclBNInitBignumFromWideUInt) /* 66 */
#define TclBN_mp_expt_d_ex \
	(tclTomMathStubsPtr->tclBN_mp_expt_d_ex) /* 67 */

#endif /* defined(USE_TCL_STUBS) */

/* !END!: Do not edit above this line. */

#undef TCL_STORAGE_CLASS
#define TCL_STORAGE_CLASS DLLIMPORT

#endif /* _TCLINTDECLS */

LibTomMath is hereby released into the Public Domain.  







-- Tom St Denis

LibTomMath is licensed under DUAL licensing terms.

Choose and use the license of your needs.

[LICENSE #1]

LibTomMath is public domain.  As should all quality software be.

Tom St Denis

[/LICENSE #1]

[LICENSE #2]

            DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
                    Version 2, December 2004

 Copyright (C) 2004 Sam Hocevar <[email protected]>

 Everyone is permitted to copy and distribute verbatim or modified
 copies of this license document, and changing it is allowed as long
 as the name is changed.

            DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
   TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION

  0. You just DO WHAT THE FUCK YOU WANT TO. 

[/LICENSE #2]

This is makeindex, version 2.14 [02-Oct-2002] (kpathsea + Thai support).
Scanning input file bn.idx....done (79 entries accepted, 0 rejected).
Sorting entries....done (511 comparisons).
Generating output file bn.ind....done (82 lines written, 0 warnings).
Output written in bn.ind.
Transcript written in bn.ilg.

This is makeindex, version 2.15 [TeX Live 2013] (kpathsea + Thai support).
Scanning input file bn.idx....done (85 entries accepted, 0 rejected).
Sorting entries....done (554 comparisons).
Generating output file bn.ind....done (88 lines written, 0 warnings).
Output written in bn.ind.
Transcript written in bn.ilg.

\begin{theindex}

  \item mp\_add, \hyperpage{29}
  \item mp\_add\_d, \hyperpage{52}
  \item mp\_and, \hyperpage{29}
  \item mp\_clear, \hyperpage{11}
  \item mp\_clear\_multi, \hyperpage{12}
  \item mp\_cmp, \hyperpage{24}
  \item mp\_cmp\_d, \hyperpage{25}
  \item mp\_cmp\_mag, \hyperpage{23}
  \item mp\_div, \hyperpage{30}
  \item mp\_div\_2, \hyperpage{26}
  \item mp\_div\_2d, \hyperpage{28}
  \item mp\_div\_d, \hyperpage{52}
  \item mp\_dr\_reduce, \hyperpage{40}
  \item mp\_dr\_setup, \hyperpage{40}
  \item MP\_EQ, \hyperpage{22}
  \item mp\_error\_to\_string, \hyperpage{10}
  \item mp\_expt\_d, \hyperpage{43}

  \item mp\_exptmod, \hyperpage{43}
  \item mp\_exteuclid, \hyperpage{51}
  \item mp\_gcd, \hyperpage{51}
  \item mp\_get\_int, \hyperpage{20}


  \item mp\_grow, \hyperpage{16}
  \item MP\_GT, \hyperpage{22}
  \item mp\_init, \hyperpage{11}
  \item mp\_init\_copy, \hyperpage{13}
  \item mp\_init\_multi, \hyperpage{12}
  \item mp\_init\_set, \hyperpage{21}
  \item mp\_init\_set\_int, \hyperpage{21}
  \item mp\_init\_size, \hyperpage{14}
  \item mp\_int, \hyperpage{10}
  \item mp\_invmod, \hyperpage{52}
  \item mp\_jacobi, \hyperpage{52}
  \item mp\_lcm, \hyperpage{51}
  \item mp\_lshd, \hyperpage{28}
  \item MP\_LT, \hyperpage{22}
  \item MP\_MEM, \hyperpage{9}
  \item mp\_mod, \hyperpage{35}
  \item mp\_mod\_d, \hyperpage{52}
  \item mp\_montgomery\_calc\_normalization, \hyperpage{38}
  \item mp\_montgomery\_reduce, \hyperpage{37}
  \item mp\_montgomery\_setup, \hyperpage{37}
  \item mp\_mul, \hyperpage{31}
  \item mp\_mul\_2, \hyperpage{26}
  \item mp\_mul\_2d, \hyperpage{28}
  \item mp\_mul\_d, \hyperpage{52}
  \item mp\_n\_root, \hyperpage{44}
  \item mp\_neg, \hyperpage{29}
  \item MP\_NO, \hyperpage{9}
  \item MP\_OKAY, \hyperpage{9}
  \item mp\_or, \hyperpage{29}
  \item mp\_prime\_fermat, \hyperpage{45}
  \item mp\_prime\_is\_divisible, \hyperpage{45}
  \item mp\_prime\_is\_prime, \hyperpage{46}
  \item mp\_prime\_miller\_rabin, \hyperpage{45}
  \item mp\_prime\_next\_prime, \hyperpage{46}
  \item mp\_prime\_rabin\_miller\_trials, \hyperpage{46}
  \item mp\_prime\_random, \hyperpage{47}
  \item mp\_prime\_random\_ex, \hyperpage{47}
  \item mp\_radix\_size, \hyperpage{49}
  \item mp\_read\_radix, \hyperpage{49}
  \item mp\_read\_unsigned\_bin, \hyperpage{50}
  \item mp\_reduce, \hyperpage{36}
  \item mp\_reduce\_2k, \hyperpage{41}
  \item mp\_reduce\_2k\_setup, \hyperpage{41}
  \item mp\_reduce\_setup, \hyperpage{36}
  \item mp\_rshd, \hyperpage{28}
  \item mp\_set, \hyperpage{19}
  \item mp\_set\_int, \hyperpage{20}


  \item mp\_shrink, \hyperpage{15}
  \item mp\_sqr, \hyperpage{33}

  \item mp\_sub, \hyperpage{29}
  \item mp\_sub\_d, \hyperpage{52}
  \item mp\_to\_unsigned\_bin, \hyperpage{50}
  \item mp\_toradix, \hyperpage{49}
  \item mp\_unsigned\_bin\_size, \hyperpage{50}
  \item MP\_VAL, \hyperpage{9}
  \item mp\_xor, \hyperpage{29}
  \item MP\_YES, \hyperpage{9}

\end{theindex}

\begin{theindex}

  \item mp\_add, \hyperpage{24}
  \item mp\_add\_d, \hyperpage{44}
  \item mp\_and, \hyperpage{24}
  \item mp\_clear, \hyperpage{9}
  \item mp\_clear\_multi, \hyperpage{10}
  \item mp\_cmp, \hyperpage{19}
  \item mp\_cmp\_d, \hyperpage{20}
  \item mp\_cmp\_mag, \hyperpage{18}
  \item mp\_div, \hyperpage{24}
  \item mp\_div\_2, \hyperpage{22}
  \item mp\_div\_2d, \hyperpage{23}
  \item mp\_div\_d, \hyperpage{44}
  \item mp\_dr\_reduce, \hyperpage{33}
  \item mp\_dr\_setup, \hyperpage{33}
  \item MP\_EQ, \hyperpage{18}
  \item mp\_error\_to\_string, \hyperpage{7}
  \item mp\_expt\_d, \hyperpage{35}
  \item mp\_expt\_d\_ex, \hyperpage{35}
  \item mp\_exptmod, \hyperpage{35}
  \item mp\_exteuclid, \hyperpage{43}
  \item mp\_gcd, \hyperpage{43}
  \item mp\_get\_int, \hyperpage{16}
  \item mp\_get\_long, \hyperpage{17}
  \item mp\_get\_long\_long, \hyperpage{17}
  \item mp\_grow, \hyperpage{13}
  \item MP\_GT, \hyperpage{18}
  \item mp\_init, \hyperpage{8}
  \item mp\_init\_copy, \hyperpage{10}
  \item mp\_init\_multi, \hyperpage{10}
  \item mp\_init\_set, \hyperpage{17}
  \item mp\_init\_set\_int, \hyperpage{17}
  \item mp\_init\_size, \hyperpage{11}
  \item mp\_int, \hyperpage{8}
  \item mp\_invmod, \hyperpage{44}
  \item mp\_jacobi, \hyperpage{43}
  \item mp\_lcm, \hyperpage{43}
  \item mp\_lshd, \hyperpage{23}
  \item MP\_LT, \hyperpage{18}
  \item MP\_MEM, \hyperpage{7}
  \item mp\_mod, \hyperpage{29}
  \item mp\_mod\_d, \hyperpage{44}
  \item mp\_montgomery\_calc\_normalization, \hyperpage{31}
  \item mp\_montgomery\_reduce, \hyperpage{31}
  \item mp\_montgomery\_setup, \hyperpage{31}
  \item mp\_mul, \hyperpage{25}
  \item mp\_mul\_2, \hyperpage{22}
  \item mp\_mul\_2d, \hyperpage{23}
  \item mp\_mul\_d, \hyperpage{44}
  \item mp\_n\_root, \hyperpage{36}
  \item mp\_neg, \hyperpage{24}
  \item MP\_NO, \hyperpage{7}
  \item MP\_OKAY, \hyperpage{7}
  \item mp\_or, \hyperpage{24}
  \item mp\_prime\_fermat, \hyperpage{37}
  \item mp\_prime\_is\_divisible, \hyperpage{37}
  \item mp\_prime\_is\_prime, \hyperpage{38}
  \item mp\_prime\_miller\_rabin, \hyperpage{37}
  \item mp\_prime\_next\_prime, \hyperpage{38}
  \item mp\_prime\_rabin\_miller\_trials, \hyperpage{38}
  \item mp\_prime\_random, \hyperpage{38}
  \item mp\_prime\_random\_ex, \hyperpage{39}
  \item mp\_radix\_size, \hyperpage{41}
  \item mp\_read\_radix, \hyperpage{41}
  \item mp\_read\_unsigned\_bin, \hyperpage{42}
  \item mp\_reduce, \hyperpage{30}
  \item mp\_reduce\_2k, \hyperpage{34}
  \item mp\_reduce\_2k\_setup, \hyperpage{34}
  \item mp\_reduce\_setup, \hyperpage{29}
  \item mp\_rshd, \hyperpage{23}
  \item mp\_set, \hyperpage{15}
  \item mp\_set\_int, \hyperpage{16}
  \item mp\_set\_long, \hyperpage{17}
  \item mp\_set\_long\_long, \hyperpage{17}
  \item mp\_shrink, \hyperpage{12}
  \item mp\_sqr, \hyperpage{26}
  \item mp\_sqrtmod\_prime, \hyperpage{44}
  \item mp\_sub, \hyperpage{24}
  \item mp\_sub\_d, \hyperpage{44}
  \item mp\_to\_unsigned\_bin, \hyperpage{42}
  \item mp\_toradix, \hyperpage{41}
  \item mp\_unsigned\_bin\_size, \hyperpage{41}
  \item MP\_VAL, \hyperpage{7}
  \item mp\_xor, \hyperpage{24}
  \item MP\_YES, \hyperpage{7}

\end{theindex}

\newcommand{\emailaddr}[1]{\mbox{$<${#1}$>$}}
\def\twiddle{\raisebox{0.3ex}{\mbox{\tiny $\sim$}}}
\def\gap{\vspace{0.5ex}}
\makeindex
\begin{document}
\frontmatter
\pagestyle{empty}
\title{LibTomMath User Manual \\ v0.39}
\author{Tom St Denis \\ tomstdenis@iahu.ca}
\maketitle
This text, the library and the accompanying textbook are all hereby placed in the public domain.  This book has been 
formatted for B5 [176x250] paper using the \LaTeX{} {\em book} macro package.

\vspace{10cm}

\begin{flushright}Open Source.  Open Academia.  Open Minds.

\mbox{ }
................................................................................
\listoffigures
\mainmatter
\pagestyle{headings}
\chapter{Introduction}
\section{What is LibTomMath?}
LibTomMath is a library of source code which provides a series of efficient and carefully written functions for manipulating
large integer numbers.  It was written in portable ISO C source code so that it will build on any platform with a conforming
C compiler.  

In a nutshell the library was written from scratch with verbose comments to help instruct computer science students how
to implement ``bignum'' math.  However, the resulting code has proven to be very useful.  It has been used by numerous 
universities, commercial and open source software developers.  It has been used on a variety of platforms ranging from
Linux and Windows based x86 to ARM based Gameboys and PPC based MacOS machines.  

\section{License}
As of the v0.25 the library source code has been placed in the public domain with every new release.  As of the v0.28
release the textbook ``Implementing Multiple Precision Arithmetic'' has been placed in the public domain with every new
release as well.  This textbook is meant to compliment the project by providing a more solid walkthrough of the development
algorithms used in the library.

Since both\footnote{Note that the MPI files under mtest/ are copyrighted by Michael Fromberger.  They are not required to use LibTomMath.} are in the 
public domain everyone is entitled to do with them as they see fit.

\section{Building LibTomMath}

LibTomMath is meant to be very ``GCC friendly'' as it comes with a makefile well suited for GCC.  However, the library will
also build in MSVC, Borland C out of the box.  For any other ISO C compiler a makefile will have to be made by the end
developer.  

\subsection{Static Libraries}
To build as a static library for GCC issue the following
\begin{alltt}
make
\end{alltt}

command.  This will build the library and archive the object files in ``libtommath.a''.  Now you link against 
that and include ``tommath.h'' within your programs.  Alternatively to build with MSVC issue the following
\begin{alltt}
nmake -f makefile.msvc
\end{alltt}

This will build the library and archive the object files in ``tommath.lib''.  This has been tested with MSVC 
version 6.00 with service pack 5.  

\subsection{Shared Libraries}
To build as a shared library for GCC issue the following
\begin{alltt}
make -f makefile.shared
\end{alltt}
This requires the ``libtool'' package (common on most Linux/BSD systems).  It will build LibTomMath as both shared
and static then install (by default) into /usr/lib as well as install the header files in /usr/include.  The shared 
library (resource) will be called ``libtommath.la'' while the static library called ``libtommath.a''.  Generally 
you use libtool to link your application against the shared object.  

There is limited support for making a ``DLL'' in windows via the ``makefile.cygwin\_dll'' makefile.  It requires 
Cygwin to work with since it requires the auto-export/import functionality.  The resulting DLL and import library 
``libtommath.dll.a'' can be used to link LibTomMath dynamically to any Windows program using Cygwin.

\subsection{Testing}
To build the library and the test harness type

\begin{alltt}
make test
................................................................................
results.  ``mtest/mtest'' will generate test vectors using the MPI library by Michael Fromberger\footnote{A copy of MPI
is included in the package}.  Simply pipe mtest into test using

\begin{alltt}
mtest/mtest | test
\end{alltt}

If you do not have a ``/dev/urandom'' style RNG source you will have to write your own PRNG and simply pipe that into 
mtest.  For example, if your PRNG program is called ``myprng'' simply invoke

\begin{alltt}
myprng | mtest/mtest | test
\end{alltt}

This will output a row of numbers that are increasing.  Each column is a different test (such as addition, multiplication, etc)
that is being performed.  The numbers represent how many times the test was invoked.  If an error is detected the program
will exit with a dump of the relevent numbers it was working with.

\section{Build Configuration}
LibTomMath can configured at build time in three phases we shall call ``depends'', ``tweaks'' and ``trims''.  
Each phase changes how the library is built and they are applied one after another respectively.  

To make the system more powerful you can tweak the build process.  Classes are defined in the file
``tommath\_superclass.h''.  By default, the symbol ``LTM\_ALL'' shall be defined which simply 
instructs the system to build all of the functions.  This is how LibTomMath used to be packaged.  This will give you 
access to every function LibTomMath offers.

However, there are cases where such a build is not optional.  For instance, you want to perform RSA operations.  You 
don't need the vast majority of the library to perform these operations.  Aside from LTM\_ALL there is 
another pre--defined class ``SC\_RSA\_1'' which works in conjunction with the RSA from LibTomCrypt.  Additional 
classes can be defined base on the need of the user.

\subsection{Build Depends}
In the file tommath\_class.h you will see a large list of C ``defines'' followed by a series of ``ifdefs''
which further define symbols.  All of the symbols (technically they're macros $\ldots$) represent a given C source
file.  For instance, BN\_MP\_ADD\_C represents the file ``bn\_mp\_add.c''.  When a define has been enabled the
function in the respective file will be compiled and linked into the library.  Accordingly when the define
is absent the file will not be compiled and not contribute any size to the library.

You will also note that the header tommath\_class.h is actually recursively included (it includes itself twice).  
This is to help resolve as many dependencies as possible.  In the last pass the symbol LTM\_LAST will be defined.  
This is useful for ``trims''.

\subsection{Build Tweaks}
A tweak is an algorithm ``alternative''.  For example, to provide tradeoffs (usually between size and space).
They can be enabled at any pass of the configuration phase.

\begin{small}
................................................................................
\hline
\end{tabular}
\end{center}
\end{small}

\subsection{Build Trims}
A trim is a manner of removing functionality from a function that is not required.  For instance, to perform
RSA cryptography you only require exponentiation with odd moduli so even moduli support can be safely removed.  
Build trims are meant to be defined on the last pass of the configuration which means they are to be defined
only if LTM\_LAST has been defined.

\subsubsection{Moduli Related}
\begin{small}
\begin{center}
\begin{tabular}{|l|l|}
................................................................................
\hline \textbf{Restriction} & \textbf{Undefine} \\
\hline Moduli $\le 2560$ bits              & BN\_MP\_MONTGOMERY\_REDUCE\_C \\
                                           & BN\_S\_MP\_MUL\_DIGS\_C \\
                                           & BN\_S\_MP\_MUL\_HIGH\_DIGS\_C \\
                                           & BN\_S\_MP\_SQR\_C \\
\hline Polynomial Schmolynomial            & BN\_MP\_KARATSUBA\_MUL\_C \\
                                           & BN\_MP\_KARATSUBA\_SQR\_C \\
                                           & BN\_MP\_TOOM\_MUL\_C \\ 
                                           & BN\_MP\_TOOM\_SQR\_C \\

\hline
\end{tabular}
\end{center}
\end{small}


\section{Purpose of LibTomMath}
Unlike  GNU MP (GMP) Library, LIP, OpenSSL or various other commercial kits (Miracl), LibTomMath was not written with 
bleeding edge performance in mind.  First and foremost LibTomMath was written to be entirely open.  Not only is the 
source code public domain (unlike various other GPL/etc licensed code), not only is the code freely downloadable but the
source code is also accessible for computer science students attempting to learn ``BigNum'' or multiple precision
arithmetic techniques. 

LibTomMath was written to be an instructive collection of source code.  This is why there are many comments, only one
function per source file and often I use a ``middle-road'' approach where I don't cut corners for an extra 2\% speed
increase.

Source code alone cannot really teach how the algorithms work which is why I also wrote a textbook that accompanies
the library (beat that!).
................................................................................
\hline
\end{tabular}
\end{center}
\end{small}
\caption{LibTomMath Valuation}
\end{figure}

It may seem odd to compare LibTomMath to GnuPG since the math in GnuPG is only a small portion of the entire application. 
However, LibTomMath was written with cryptography in mind.  It provides essentially all of the functions a cryptosystem
would require when working with large integers.  

So it may feel tempting to just rip the math code out of GnuPG (or GnuMP where it was taken from originally) in your
own application but I think there are reasons not to.  While LibTomMath is slower than libraries such as GnuMP it is
not normally significantly slower.  On x86 machines the difference is normally a factor of two when performing modular
exponentiations.  It depends largely on the processor, compiler and the moduli being used.

Essentially the only time you wouldn't use LibTomMath is when blazing speed is the primary concern.  However,
on the other side of the coin LibTomMath offers you a totally free (public domain) well structured math library
that is very flexible, complete and performs well in resource contrained environments.  Fast RSA for example can
be performed with as little as 8KB of ram for data (again depending on build options).  

\chapter{Getting Started with LibTomMath}
\section{Building Programs}
In order to use LibTomMath you must include ``tommath.h'' and link against the appropriate library file (typically 
libtommath.a).  There is no library initialization required and the entire library is thread safe.

\section{Return Codes}
There are three possible return codes a function may return.

\index{MP\_OKAY}\index{MP\_YES}\index{MP\_NO}\index{MP\_VAL}\index{MP\_MEM}
\begin{figure}[here!]
................................................................................
to a string use the following function.

\index{mp\_error\_to\_string}
\begin{alltt}
char *mp_error_to_string(int code);
\end{alltt}

This will return a pointer to a string which describes the given error code.  It will not work for the return codes 
MP\_YES and MP\_NO.  

\section{Data Types}
The basic ``multiple precision integer'' type is known as the ``mp\_int'' within LibTomMath.  This data type is used to
organize all of the data required to manipulate the integer it represents.  Within LibTomMath it has been prototyped
as the following.

\index{mp\_int}
................................................................................
    int used, alloc, sign;
    mp_digit *dp;
\} mp_int;
\end{alltt}

Where ``mp\_digit'' is a data type that represents individual digits of the integer.  By default, an mp\_digit is the
ISO C ``unsigned long'' data type and each digit is $28-$bits long.  The mp\_digit type can be configured to suit other
platforms by defining the appropriate macros.  

All LTM functions that use the mp\_int type will expect a pointer to mp\_int structure.  You must allocate memory to
hold the structure itself by yourself (whether off stack or heap it doesn't matter).  The very first thing that must be
done to use an mp\_int is that it must be initialized.

\section{Function Organization}

................................................................................
mp_div(&a, &b, &a, &c);   /* a = [a/b], c = a mod b */
\end{alltt}

This allows operands to be re-used which can make programming simpler.

\section{Initialization}
\subsection{Single Initialization}
A single mp\_int can be initialized with the ``mp\_init'' function. 

\index{mp\_init}
\begin{alltt}
int mp_init (mp_int * a);
\end{alltt}

This function expects a pointer to an mp\_int structure and will initialize the members of the structure so the mp\_int
................................................................................
\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   if ((result = mp_init(&number)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* use the number */

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

\subsection{Single Free}
When you are finished with an mp\_int it is ideal to return the heap it used back to the system.  The following function 
provides this functionality.

\index{mp\_clear}
\begin{alltt}
void mp_clear (mp_int * a);
\end{alltt}

The function expects a pointer to a previously initialized mp\_int structure and frees the heap it uses.  It sets the 
pointer\footnote{The ``dp'' member.} within the mp\_int to \textbf{NULL} which is used to prevent double free situations. 
Is is legal to call mp\_clear() twice on the same mp\_int in a row.  

\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   if ((result = mp_init(&number)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* use the number */

   /* We're done with it. */
   mp_clear(&number);

   return EXIT_SUCCESS;
\}
................................................................................
\index{mp\_init\_multi} \index{mp\_clear\_multi}
\begin{alltt}
int mp_init_multi(mp_int *mp, ...);
\end{alltt}

It accepts a \textbf{NULL} terminated list of pointers to mp\_int structures.  It will attempt to initialize them all
at once.  If the function returns MP\_OKAY then all of the mp\_int variables are ready to use, otherwise none of them
are available for use.  A complementary mp\_clear\_multi() function allows multiple mp\_int variables to be free'd 
from the heap at the same time.  

\begin{small} \begin{alltt}
int main(void)
\{
   mp_int num1, num2, num3;
   int result;

   if ((result = mp_init_multi(&num1, 
                               &num2,
                               &num3, NULL)) != MP\_OKAY) \{      
      printf("Error initializing the numbers.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* use the numbers */

   /* We're done with them. */
   mp_clear_multi(&num1, &num2, &num3, NULL);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

\subsection{Other Initializers}
To initialized and make a copy of an mp\_int the mp\_init\_copy() function has been provided.  

\index{mp\_init\_copy}
\begin{alltt}
int mp_init_copy (mp_int * a, mp_int * b);
\end{alltt}

This function will initialize $a$ and make it a copy of $b$ if all goes well.
................................................................................
   mp_int num1, num2;
   int result;

   /* initialize and do work on num1 ... */

   /* We want a copy of num1 in num2 now */
   if ((result = mp_init_copy(&num2, &num1)) != MP_OKAY) \{
     printf("Error initializing the copy.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* now num2 is ready and contains a copy of num1 */

   /* We're done with them. */
   mp_clear_multi(&num1, &num2, NULL);

   return EXIT_SUCCESS;
\}
................................................................................

\index{mp\_init\_size}
\begin{alltt}
int mp_init_size (mp_int * a, int size);
\end{alltt}

The $size$ parameter must be greater than zero.  If the function succeeds the mp\_int $a$ will be initialized
to have $size$ digits (which are all initially zero).  

\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   /* we need a 60-digit number */
   if ((result = mp_init_size(&number, 60)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* use the number */

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

\section{Maintenance Functions}
................................................................................
\begin{alltt}
int mp_shrink (mp_int * a);
\end{alltt}

This will remove excess digits of the mp\_int $a$.  If the operation fails the mp\_int should be intact without the
excess digits being removed.  Note that you can use a shrunk mp\_int in further computations, however, such operations
will require heap operations which can be slow.  It is not ideal to shrink mp\_int variables that you will further
modify in the system (unless you are seriously low on memory).  

\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   if ((result = mp_init(&number)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* use the number [e.g. pre-computation]  */

   /* We're done with it for now. */
   if ((result = mp_shrink(&number)) != MP_OKAY) \{
      printf("Error shrinking the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* use it .... */


   /* we're done with it. */ 
   mp_clear(&number);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

\subsection{Adding additional digits}

Within the mp\_int structure are two parameters which control the limitations of the array of digits that represent
the integer the mp\_int is meant to equal.   The \textit{used} parameter dictates how many digits are significant, that is,
contribute to the value of the mp\_int.  The \textit{alloc} parameter dictates how many digits are currently available in
the array.  If you need to perform an operation that requires more digits you will have to mp\_grow() the mp\_int to
your desired size.  

\index{mp\_grow}
\begin{alltt}
int mp_grow (mp_int * a, int size);
\end{alltt}

This will grow the array of digits of $a$ to $size$.  If the \textit{alloc} parameter is already bigger than
................................................................................
\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   if ((result = mp_init(&number)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* use the number */

   /* We need to add 20 digits to the number  */
   if ((result = mp_grow(&number, number.alloc + 20)) != MP_OKAY) \{
      printf("Error growing the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}


   /* use the number */

   /* we're done with it. */ 
   mp_clear(&number);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

\chapter{Basic Operations}
\section{Small Constants}
Setting mp\_ints to small constants is a relatively common operation.  To accomodate these instances there are two
small constant assignment functions.  The first function is used to set a single digit constant while the second sets
an ISO C style ``unsigned long'' constant.  The reason for both functions is efficiency.  Setting a single digit is quick but the
domain of a digit can change (it's always at least $0 \ldots 127$).  

\subsection{Single Digit}

Setting a single digit can be accomplished with the following function.

\index{mp\_set}
\begin{alltt}
................................................................................
\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   if ((result = mp_init(&number)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* set the number to 5 */
   mp_set(&number, 5);

   /* we're done with it. */ 
   mp_clear(&number);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

\subsection{Long Constants}

To set a constant that is the size of an ISO C ``unsigned long'' and larger than a single digit the following function 
can be used.

\index{mp\_set\_int}
\begin{alltt}
int mp_set_int (mp_int * a, unsigned long b);
\end{alltt}

This will assign the value of the 32-bit variable $b$ to the mp\_int $a$.  Unlike mp\_set() this function will always
accept a 32-bit input regardless of the size of a single digit.  However, since the value may span several digits 
this function can fail if it runs out of heap memory.

To get the ``unsigned long'' copy of an mp\_int the following function can be used.

\index{mp\_get\_int}
\begin{alltt}
unsigned long mp_get_int (mp_int * a);
\end{alltt}

This will return the 32 least significant bits of the mp\_int $a$.  

\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   if ((result = mp_init(&number)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* set the number to 654321 (note this is bigger than 127) */
   if ((result = mp_set_int(&number, 654321)) != MP_OKAY) \{
      printf("Error setting the value of the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   printf("number == \%lu", mp_get_int(&number));

   /* we're done with it. */ 
   mp_clear(&number);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

This should output the following if the program succeeds.

\begin{alltt}
number == 654321
\end{alltt}





































\subsection{Initialize and Setting Constants}
To both initialize and set small constants the following two functions are available.
\index{mp\_init\_set} \index{mp\_init\_set\_int}
\begin{alltt}
int mp_init_set (mp_int * a, mp_digit b);
int mp_init_set_int (mp_int * a, unsigned long b);
\end{alltt}

Both functions work like the previous counterparts except they first mp\_init $a$ before setting the values.  

\begin{alltt}
int main(void)
\{
   mp_int number1, number2;
   int    result;

   /* initialize and set a single digit */
   if ((result = mp_init_set(&number1, 100)) != MP_OKAY) \{
      printf("Error setting number1: \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}             

   /* initialize and set a long */
   if ((result = mp_init_set_int(&number2, 1023)) != MP_OKAY) \{
      printf("Error setting number2: \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* display */
   printf("Number1, Number2 == \%lu, \%lu",
          mp_get_int(&number1), mp_get_int(&number2));
................................................................................
\hline
\end{tabular}
\end{center}
\caption{Comparison Codes for $a, b$}
\label{fig:CMP}
\end{figure}

In figure \ref{fig:CMP} two integers $a$ and $b$ are being compared.  In this case $a$ is said to be ``to the left'' of 
$b$.  

\subsection{Unsigned comparison}

An unsigned comparison considers only the digits themselves and not the associated \textit{sign} flag of the 
mp\_int structures.  This is analogous to an absolute comparison.  The function mp\_cmp\_mag() will compare two
mp\_int variables based on their digits only. 

\index{mp\_cmp\_mag}
\begin{alltt}
int mp_cmp_mag(mp_int * a, mp_int * b);
\end{alltt}
This will compare $a$ to $b$ placing $a$ to the left of $b$.  This function cannot fail and will return one of the
three compare codes listed in figure \ref{fig:CMP}.
................................................................................
\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number1, number2;
   int result;

   if ((result = mp_init_multi(&number1, &number2, NULL)) != MP_OKAY) \{
      printf("Error initializing the numbers.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* set the number1 to 5 */
   mp_set(&number1, 5);
  
   /* set the number2 to -6 */
   mp_set(&number2, 6);
   if ((result = mp_neg(&number2, &number2)) != MP_OKAY) \{
      printf("Error negating number2.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   switch(mp_cmp_mag(&number1, &number2)) \{
       case MP_GT:  printf("|number1| > |number2|"); break;
       case MP_EQ:  printf("|number1| = |number2|"); break;
       case MP_LT:  printf("|number1| < |number2|"); break;
   \}

   /* we're done with it. */ 
   mp_clear_multi(&number1, &number2, NULL);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

If this program\footnote{This function uses the mp\_neg() function which is discussed in section \ref{sec:NEG}.} completes 
successfully it should print the following.

\begin{alltt}
|number1| < |number2|
\end{alltt}

This is because $\vert -6 \vert = 6$ and obviously $5 < 6$.
................................................................................
\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number1, number2;
   int result;

   if ((result = mp_init_multi(&number1, &number2, NULL)) != MP_OKAY) \{
      printf("Error initializing the numbers.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* set the number1 to 5 */
   mp_set(&number1, 5);
  
   /* set the number2 to -6 */
   mp_set(&number2, 6);
   if ((result = mp_neg(&number2, &number2)) != MP_OKAY) \{
      printf("Error negating number2.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   switch(mp_cmp(&number1, &number2)) \{
       case MP_GT:  printf("number1 > number2"); break;
       case MP_EQ:  printf("number1 = number2"); break;
       case MP_LT:  printf("number1 < number2"); break;
   \}

   /* we're done with it. */ 
   mp_clear_multi(&number1, &number2, NULL);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

If this program\footnote{This function uses the mp\_neg() function which is discussed in section \ref{sec:NEG}.} completes 
successfully it should print the following.

\begin{alltt}
number1 > number2
\end{alltt}

\subsection{Single Digit}
................................................................................
To compare a single digit against an mp\_int the following function has been provided.

\index{mp\_cmp\_d}
\begin{alltt}
int mp_cmp_d(mp_int * a, mp_digit b);
\end{alltt}

This will compare $a$ to the left of $b$ using a signed comparison.  Note that it will always treat $b$ as 
positive.  This function is rather handy when you have to compare against small values such as $1$ (which often
comes up in cryptography).  The function cannot fail and will return one of the tree compare condition codes
listed in figure \ref{fig:CMP}.


\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   if ((result = mp_init(&number)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* set the number to 5 */
   mp_set(&number, 5);

   switch(mp_cmp_d(&number, 7)) \{
       case MP_GT:  printf("number > 7"); break;
       case MP_EQ:  printf("number = 7"); break;
       case MP_LT:  printf("number < 7"); break;
   \}

   /* we're done with it. */ 
   mp_clear(&number);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

If this program functions properly it will print out the following.
................................................................................

Logical operations are operations that can be performed either with simple shifts or boolean operators such as
AND, XOR and OR directly.  These operations are very quick.

\subsection{Multiplication by two}

Multiplications and divisions by any power of two can be performed with quick logical shifts either left or
right depending on the operation.  

When multiplying or dividing by two a special case routine can be used which are as follows.
\index{mp\_mul\_2} \index{mp\_div\_2}
\begin{alltt}
int mp_mul_2(mp_int * a, mp_int * b);
int mp_div_2(mp_int * a, mp_int * b);
\end{alltt}
................................................................................
\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   if ((result = mp_init(&number)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   /* set the number to 5 */
   mp_set(&number, 5);

   /* multiply by two */
   if ((result = mp\_mul\_2(&number, &number)) != MP_OKAY) \{
      printf("Error multiplying the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
   switch(mp_cmp_d(&number, 7)) \{
       case MP_GT:  printf("2*number > 7"); break;
       case MP_EQ:  printf("2*number = 7"); break;
       case MP_LT:  printf("2*number < 7"); break;
   \}

   /* now divide by two */
   if ((result = mp\_div\_2(&number, &number)) != MP_OKAY) \{
      printf("Error dividing the number.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
   switch(mp_cmp_d(&number, 7)) \{
       case MP_GT:  printf("2*number/2 > 7"); break;
       case MP_EQ:  printf("2*number/2 = 7"); break;
       case MP_LT:  printf("2*number/2 < 7"); break;
   \}

   /* we're done with it. */ 
   mp_clear(&number);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

If this program is successful it will print out the following text.

\begin{alltt}
2*number > 7
2*number/2 < 7
\end{alltt}



Since $10 > 7$ and $5 < 7$.  To multiply by a power of two the following function can be used.

\index{mp\_mul\_2d}
\begin{alltt}
int mp_mul_2d(mp_int * a, int b, mp_int * c);
\end{alltt}

This will multiply $a$ by $2^b$ and store the result in ``c''.  If the value of $b$ is less than or equal to 
zero the function will copy $a$ to ``c'' without performing any further actions.  


To divide by a power of two use the following.

\index{mp\_div\_2d}
\begin{alltt}
int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d);
\end{alltt}
Which will divide $a$ by $2^b$, store the quotient in ``c'' and the remainder in ``d'.  If $b \le 0$ then the
function simply copies $a$ over to ``c'' and zeroes $d$.  The variable $d$ may be passed as a \textbf{NULL}
value to signal that the remainder is not desired.


\subsection{Polynomial Basis Operations}

Strictly speaking the organization of the integers within the mp\_int structures is what is known as a 
``polynomial basis''.  This simply means a field element is stored by divisions of a radix.  For example, if
$f(x) = \sum_{i=0}^{k} y_ix^k$ for any vector $\vec y$ then the array of digits in $\vec y$ are said to be 
the polynomial basis representation of $z$ if $f(\beta) = z$ for a given radix $\beta$.  

To multiply by the polynomial $g(x) = x$ all you have todo is shift the digits of the basis left one place.  The
following function provides this operation.

\index{mp\_lshd}
\begin{alltt}
int mp_lshd (mp_int * a, int b);
................................................................................
\index{mp\_or} \index{mp\_and} \index{mp\_xor}
\begin{alltt}
int mp_or  (mp_int * a, mp_int * b, mp_int * c);
int mp_and (mp_int * a, mp_int * b, mp_int * c);
int mp_xor (mp_int * a, mp_int * b, mp_int * c);
\end{alltt}

Which compute $c = a \odot b$ where $\odot$ is one of OR, AND or XOR.  

\section{Addition and Subtraction}

To compute an addition or subtraction the following two functions can be used.

\index{mp\_add} \index{mp\_sub}
\begin{alltt}
................................................................................
Simple integer negation can be performed with the following.

\index{mp\_neg}
\begin{alltt}
int mp_neg (mp_int * a, mp_int * b);
\end{alltt}

Which assigns $-a$ to $b$.  

\subsection{Absolute}
Simple integer absolutes can be performed with the following.

\index{mp\_neg}
\begin{alltt}
int mp_abs (mp_int * a, mp_int * b);
\end{alltt}

Which assigns $\vert a \vert$ to $b$.  

\section{Integer Division and Remainder}
To perform a complete and general integer division with remainder use the following function.

\index{mp\_div}
\begin{alltt}
int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d);
\end{alltt}
                                                        
This divides $a$ by $b$ and stores the quotient in $c$ and $d$.  The signed quotient is computed such that 
$bc + d = a$.  Note that either of $c$ or $d$ can be set to \textbf{NULL} if their value is not required.  If 
$b$ is zero the function returns \textbf{MP\_VAL}.  


\chapter{Multiplication and Squaring}
\section{Multiplication}
A full signed integer multiplication can be performed with the following.
\index{mp\_mul}
\begin{alltt}
int mp_mul (mp_int * a, mp_int * b, mp_int * c);
\end{alltt}
Which assigns the full signed product $ab$ to $c$.  This function actually breaks into one of four cases which are 
specific multiplication routines optimized for given parameters.  First there are the Toom-Cook multiplications which
should only be used with very large inputs.  This is followed by the Karatsuba multiplications which are for moderate
sized inputs.  Then followed by the Comba and baseline multipliers.

Fortunately for the developer you don't really need to know this unless you really want to fine tune the system.  mp\_mul()
will determine on its own\footnote{Some tweaking may be required.} what routine to use automatically when it is called.

................................................................................
\begin{alltt}
int main(void)
\{
   mp_int number1, number2;
   int result;

   /* Initialize the numbers */
   if ((result = mp_init_multi(&number1, 
                               &number2, NULL)) != MP_OKAY) \{
      printf("Error initializing the numbers.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* set the terms */
   if ((result = mp_set_int(&number, 257)) != MP_OKAY) \{
      printf("Error setting number1.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
 
   if ((result = mp_set_int(&number2, 1023)) != MP_OKAY) \{
      printf("Error setting number2.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* multiply them */
   if ((result = mp_mul(&number1, &number2,
                        &number1)) != MP_OKAY) \{
      printf("Error multiplying terms.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* display */
   printf("number1 * number2 == \%lu", mp_get_int(&number1));

   /* free terms and return */
   mp_clear_multi(&number1, &number2, NULL);

   return EXIT_SUCCESS;
\}
\end{alltt}   

If this program succeeds it shall output the following.

\begin{alltt}
number1 * number2 == 262911
\end{alltt}

................................................................................
\index{mp\_sqr}
\begin{alltt}
int mp_sqr (mp_int * a, mp_int * b);
\end{alltt}

Will square $a$ and store it in $b$.  Like the case of multiplication there are four different squaring
algorithms all which can be called from mp\_sqr().  It is ideal to use mp\_sqr over mp\_mul when squaring terms because
of the speed difference.  

\section{Tuning Polynomial Basis Routines}

Both of the Toom-Cook and Karatsuba multiplication algorithms are faster than the traditional $O(n^2)$ approach that
the Comba and baseline algorithms use.  At $O(n^{1.464973})$ and $O(n^{1.584962})$ running times respectively they require 
considerably less work.  For example, a 10000-digit multiplication would take roughly 724,000 single precision
multiplications with Toom-Cook or 100,000,000 single precision multiplications with the standard Comba (a factor
of 138).

So why not always use Karatsuba or Toom-Cook?   The simple answer is that they have so much overhead that they're not
actually faster than Comba until you hit distinct  ``cutoff'' points.  For Karatsuba with the default configuration, 
GCC 3.3.1 and an Athlon XP processor the cutoff point is roughly 110 digits (about 70 for the Intel P4).  That is, at 
110 digits Karatsuba and Comba multiplications just about break even and for 110+ digits Karatsuba is faster.

Toom-Cook has incredible overhead and is probably only useful for very large inputs.  So far no known cutoff points 
exist and for the most part I just set the cutoff points very high to make sure they're not called.

A demo program in the ``etc/'' directory of the project called ``tune.c'' can be used to find the cutoff points.  This
can be built with GCC as follows

\begin{alltt}
make XXX
................................................................................

When the program is running it will output a series of measurements for different cutoff points.  It will first find
good Karatsuba squaring and multiplication points.  Then it proceeds to find Toom-Cook points.  Note that the Toom-Cook
tuning takes a very long time as the cutoff points are likely to be very high.

\chapter{Modular Reduction}

Modular reduction is process of taking the remainder of one quantity divided by another.  Expressed 
as (\ref{eqn:mod}) the modular reduction is equivalent to the remainder of $b$ divided by $c$.  

\begin{equation}
a \equiv b \mbox{ (mod }c\mbox{)}
\label{eqn:mod}
\end{equation}

Of particular interest to cryptography are reductions where $b$ is limited to the range $0 \le b < c^2$ since particularly 
fast reduction algorithms can be written for the limited range.  

Note that one of the four optimized reduction algorithms are automatically chosen in the modular exponentiation
algorithm mp\_exptmod when an appropriate modulus is detected.  

\section{Straight Division}
In order to effect an arbitrary modular reduction the following algorithm is provided.

\index{mp\_mod}
\begin{alltt}
int mp_mod(mp_int *a, mp_int *b, mp_int *c);
\end{alltt}

This reduces $a$ modulo $b$ and stores the result in $c$.  The sign of $c$ shall agree with the sign 
of $b$.  This algorithm accepts an input $a$ of any range and is not limited by $0 \le a < b^2$.

\section{Barrett Reduction}

Barrett reduction is a generic optimized reduction algorithm that requires pre--computation to achieve
a decent speedup over straight division.  First a $\mu$ value must be precomputed with the following function.

................................................................................

\begin{alltt}
int main(void)
\{
   mp_int   a, b, c, mu;
   int      result;

   /* initialize a,b to desired values, mp_init mu, 
    * c and set c to 1...we want to compute a^3 mod b 
    */

   /* get mu value */
   if ((result = mp_reduce_setup(&mu, b)) != MP_OKAY) \{
      printf("Error getting mu.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* square a to get c = a^2 */
   if ((result = mp_sqr(&a, &c)) != MP_OKAY) \{
      printf("Error squaring.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* now reduce `c' modulo b */
   if ((result = mp_reduce(&c, &b, &mu)) != MP_OKAY) \{
      printf("Error reducing.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
   
   /* multiply a to get c = a^3 */
   if ((result = mp_mul(&a, &c, &c)) != MP_OKAY) \{
      printf("Error reducing.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* now reduce `c' modulo b  */
   if ((result = mp_reduce(&c, &b, &mu)) != MP_OKAY) \{
      printf("Error reducing.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
  
   /* c now equals a^3 mod b */

   return EXIT_SUCCESS;
\}
\end{alltt} 

This program will calculate $a^3 \mbox{ mod }b$ if all the functions succeed.  

\section{Montgomery Reduction}

Montgomery is a specialized reduction algorithm for any odd moduli.  Like Barrett reduction a pre--computation
step is required.  This is accomplished with the following.

\index{mp\_montgomery\_setup}
\begin{alltt}
int mp_montgomery_setup(mp_int *a, mp_digit *mp);
\end{alltt}

For the given odd moduli $a$ the precomputation value is placed in $mp$.  The reduction is computed with the 
following.

\index{mp\_montgomery\_reduce}
\begin{alltt}
int mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
\end{alltt}
This reduces $a$ in place modulo $m$ with the pre--computed value $mp$.   $a$ must be in the range
$0 \le a < b^2$.

Montgomery reduction is faster than Barrett reduction for moduli smaller than the ``comba'' limit.  With the default
setup for instance, the limit is $127$ digits ($3556$--bits).   Note that this function is not limited to
$127$ digits just that it falls back to a baseline algorithm after that point.  

An important observation is that this reduction does not return $a \mbox{ mod }m$ but $aR^{-1} \mbox{ mod }m$ 
where $R = \beta^n$, $n$ is the n number of digits in $m$ and $\beta$ is radix used (default is $2^{28}$).  

To quickly calculate $R$ the following function was provided.

\index{mp\_montgomery\_calc\_normalization}
\begin{alltt}
int mp_montgomery_calc_normalization(mp_int *a, mp_int *b);
\end{alltt}
Which calculates $a = R$ for the odd moduli $b$ without using multiplication or division.  

The normal modus operandi for Montgomery reductions is to normalize the integers before entering the system.  For
example, to calculate $a^3 \mbox { mod }b$ using Montgomery reduction the value of $a$ can be normalized by
multiplying it by $R$.  Consider the following code snippet.

\begin{alltt}
int main(void)
\{
   mp_int   a, b, c, R;
   mp_digit mp;
   int      result;

   /* initialize a,b to desired values, 
    * mp_init R, c and set c to 1.... 
    */

   /* get normalization */
   if ((result = mp_montgomery_calc_normalization(&R, b)) != MP_OKAY) \{
      printf("Error getting norm.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* get mp value */
   if ((result = mp_montgomery_setup(&c, &mp)) != MP_OKAY) \{
      printf("Error setting up montgomery.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* normalize `a' so now a is equal to aR */
   if ((result = mp_mulmod(&a, &R, &b, &a)) != MP_OKAY) \{
      printf("Error computing aR.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* square a to get c = a^2R^2 */
   if ((result = mp_sqr(&a, &c)) != MP_OKAY) \{
      printf("Error squaring.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* now reduce `c' back down to c = a^2R^2 * R^-1 == a^2R */
   if ((result = mp_montgomery_reduce(&c, &b, mp)) != MP_OKAY) \{
      printf("Error reducing.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
   
   /* multiply a to get c = a^3R^2 */
   if ((result = mp_mul(&a, &c, &c)) != MP_OKAY) \{
      printf("Error reducing.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* now reduce `c' back down to c = a^3R^2 * R^-1 == a^3R */
   if ((result = mp_montgomery_reduce(&c, &b, mp)) != MP_OKAY) \{
      printf("Error reducing.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
   
   /* now reduce (again) `c' back down to c = a^3R * R^-1 == a^3 */
   if ((result = mp_montgomery_reduce(&c, &b, mp)) != MP_OKAY) \{
      printf("Error reducing.  \%s", 
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* c now equals a^3 mod b */

   return EXIT_SUCCESS;
\}
\end{alltt} 

This particular example does not look too efficient but it demonstrates the point of the algorithm.  By 
normalizing the inputs the reduced results are always of the form $aR$ for some variable $a$.  This allows
a single final reduction to correct for the normalization and the fast reduction used within the algorithm.

For more details consider examining the file \textit{bn\_mp\_exptmod\_fast.c}.

\section{Restricted Dimminished Radix}

``Dimminished Radix'' reduction refers to reduction with respect to moduli that are ameniable to simple
digit shifting and small multiplications.  In this case the ``restricted'' variant refers to moduli of the
form $\beta^k - p$ for some $k \ge 0$ and $0 < p < \beta$ where $\beta$ is the radix (default to $2^{28}$).  

As in the case of Montgomery reduction there is a pre--computation phase required for a given modulus.

\index{mp\_dr\_setup}
\begin{alltt}
void mp_dr_setup(mp_int *a, mp_digit *d);
\end{alltt}
................................................................................

\index{mp\_dr\_reduce}
\begin{alltt}
int mp_dr_reduce(mp_int *a, mp_int *b, mp_digit mp);
\end{alltt}

This reduces $a$ in place modulo $b$ with the pre--computed value $mp$.  $b$ must be of a restricted
dimminished radix form and $a$ must be in the range $0 \le a < b^2$.  Dimminished radix reductions are 
much faster than both Barrett and Montgomery reductions as they have a much lower asymtotic running time.  

Since the moduli are restricted this algorithm is not particularly useful for something like Rabin, RSA or
BBS cryptographic purposes.  This reduction algorithm is useful for Diffie-Hellman and ECC where fixed
primes are acceptable.  

Note that unlike Montgomery reduction there is no normalization process.  The result of this function is
equal to the correct residue.

\section{Unrestricted Dimminshed Radix}

Unrestricted reductions work much like the restricted counterparts except in this case the moduli is of the 
form $2^k - p$ for $0 < p < \beta$.  In this sense the unrestricted reductions are more flexible as they 
can be applied to a wider range of numbers.  

\index{mp\_reduce\_2k\_setup}
\begin{alltt}
int mp_reduce_2k_setup(mp_int *a, mp_digit *d);
\end{alltt}

This will compute the required $d$ value for the given moduli $a$.  

\index{mp\_reduce\_2k}
\begin{alltt}
int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d);
\end{alltt}

This will reduce $a$ in place modulo $n$ with the pre--computed value $d$.  From my experience this routine is 
slower than mp\_dr\_reduce but faster for most moduli sizes than the Montgomery reduction.  

\chapter{Exponentiation}
\section{Single Digit Exponentiation}


















\index{mp\_expt\_d}
\begin{alltt}
int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
\end{alltt}
This computes $c = a^b$ using a simple binary left-to-right algorithm.  It is faster than repeated multiplications by 
$a$ for all values of $b$ greater than three.  

\section{Modular Exponentiation}
\index{mp\_exptmod}
\begin{alltt}
int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
\end{alltt}
This computes $Y \equiv G^X \mbox{ (mod }P\mbox{)}$ using a variable width sliding window algorithm.  This function
will automatically detect the fastest modular reduction technique to use during the operation.  For negative values of 
$X$ the operation is performed as $Y \equiv (G^{-1} \mbox{ mod }P)^{\vert X \vert} \mbox{ (mod }P\mbox{)}$ provided that 
$gcd(G, P) = 1$.

This function is actually a shell around the two internal exponentiation functions.  This routine will automatically
detect when Barrett, Montgomery, Restricted and Unrestricted Dimminished Radix based exponentiation can be used.  Generally
moduli of the a ``restricted dimminished radix'' form lead to the fastest modular exponentiations.  Followed by Montgomery
and the other two algorithms.

\section{Root Finding}
\index{mp\_n\_root}
\begin{alltt}
int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
\end{alltt}
This computes $c = a^{1/b}$ such that $c^b \le a$ and $(c+1)^b > a$.  The implementation of this function is not 
ideal for values of $b$ greater than three.  It will work but become very slow.  So unless you are working with very small
numbers (less than 1000 bits) I'd avoid $b > 3$ situations.  Will return a positive root only for even roots and return
a root with the sign of the input for odd roots.  For example, performing $4^{1/2}$ will return $2$ whereas $(-8)^{1/3}$ 
will return $-2$.  

This algorithm uses the ``Newton Approximation'' method and will converge on the correct root fairly quickly.  Since
the algorithm requires raising $a$ to the power of $b$ it is not ideal to attempt to find roots for large
values of $b$.  If particularly large roots are required then a factor method could be used instead.  For example,
$a^{1/16}$ is equivalent to $\left (a^{1/4} \right)^{1/4}$ or simply 
$\left ( \left ( \left ( a^{1/2} \right )^{1/2} \right )^{1/2} \right )^{1/2}$

\chapter{Prime Numbers}
\section{Trial Division}
\index{mp\_prime\_is\_divisible}
\begin{alltt}
int mp_prime_is_divisible (mp_int * a, int *result)
\end{alltt}
This will attempt to evenly divide $a$ by a list of primes\footnote{Default is the first 256 primes.} and store the 
outcome in ``result''.  That is if $result = 0$ then $a$ is not divisible by the primes, otherwise it is.  Note that 
if the function does not return \textbf{MP\_OKAY} the value in ``result'' should be considered undefined\footnote{Currently
the default is to set it to zero first.}.

\section{Fermat Test}
\index{mp\_prime\_fermat}
\begin{alltt}
int mp_prime_fermat (mp_int * a, mp_int * b, int *result)
................................................................................

\section{Miller-Rabin Test}
\index{mp\_prime\_miller\_rabin}
\begin{alltt}
int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
\end{alltt}
Performs a Miller-Rabin test to the base $b$ of $a$.  This test is much stronger than the Fermat test and is very hard to
fool (besides with Carmichael numbers).  If $a$ passes the test (therefore is probably prime) $result$ is set to one.  
Otherwise $result$ is set to zero.  

Note that is suggested that you use the Miller-Rabin test instead of the Fermat test since all of the failures of 
Miller-Rabin are a subset of the failures of the Fermat test.

\subsection{Required Number of Tests}
Generally to ensure a number is very likely to be prime you have to perform the Miller-Rabin with at least a half-dozen
or so unique bases.  However, it has been proven that the probability of failure goes down as the size of the input goes up.
This is why a simple function has been provided to help out.

\index{mp\_prime\_rabin\_miller\_trials}
\begin{alltt}
int mp_prime_rabin_miller_trials(int size)
\end{alltt}
This returns the number of trials required for a $2^{-96}$ (or lower) probability of failure for a given ``size'' expressed
in bits.  This comes in handy specially since larger numbers are slower to test.  For example, a 512-bit number would
require ten tests whereas a 1024-bit number would only require four tests. 

You should always still perform a trial division before a Miller-Rabin test though.

\section{Primality Testing}
\index{mp\_prime\_is\_prime}
\begin{alltt}
int mp_prime_is_prime (mp_int * a, int t, int *result)
\end{alltt}
This will perform a trial division followed by $t$ rounds of Miller-Rabin tests on $a$ and store the result in $result$.  
If $a$ passes all of the tests $result$ is set to one, otherwise it is set to zero.  Note that $t$ is bounded by 
$1 \le t < PRIME\_SIZE$ where $PRIME\_SIZE$ is the number of primes in the prime number table (by default this is $256$).

\section{Next Prime}
\index{mp\_prime\_next\_prime}
\begin{alltt}
int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
\end{alltt}
This finds the next prime after $a$ that passes mp\_prime\_is\_prime() with $t$ tests.  Set $bbs\_style$ to one if you 
want only the next prime congruent to $3 \mbox{ mod } 4$, otherwise set it to zero to find any next prime.  

\section{Random Primes}
\index{mp\_prime\_random}
\begin{alltt}
int mp_prime_random(mp_int *a, int t, int size, int bbs, 
                    ltm_prime_callback cb, void *dat)
\end{alltt}
This will find a prime greater than $256^{size}$ which can be ``bbs\_style'' or not depending on $bbs$ and must pass
$t$ rounds of tests.  The ``ltm\_prime\_callback'' is a typedef for 

\begin{alltt}
typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat);
\end{alltt}

Which is a function that must read $len$ bytes (and return the amount stored) into $dst$.  The $dat$ variable is simply
copied from the original input.  It can be used to pass RNG context data to the callback.  The function 
mp\_prime\_random() is more suitable for generating primes which must be secret (as in the case of RSA) since there 
is no skew on the least significant bits.

\textit{Note:}  As of v0.30 of the LibTomMath library this function has been deprecated.  It is still available
but users are encouraged to use the new mp\_prime\_random\_ex() function instead.

\subsection{Extended Generation}
\index{mp\_prime\_random\_ex}
\begin{alltt}
int mp_prime_random_ex(mp_int *a,    int t, 
                       int     size, int flags, 
                       ltm_prime_callback cb, void *dat);
\end{alltt}
This will generate a prime in $a$ using $t$ tests of the primality testing algorithms.  The variable $size$
specifies the bit length of the prime desired.  The variable $flags$ specifies one of several options available
(see fig. \ref{fig:primeopts}) which can be OR'ed together.  The callback parameters are used as in 
mp\_prime\_random().

\begin{figure}[here]
\begin{center}
\begin{small}
\begin{tabular}{|r|l|}
\hline \textbf{Flag}         & \textbf{Meaning} \\
................................................................................
to terminate the string.  Valid values of ``radix'' line in the range $[2, 64]$.  To determine the size (exact) required
by the conversion before storing any data use the following function.

\index{mp\_radix\_size}
\begin{alltt}
int mp_radix_size (mp_int * a, int radix, int *size)
\end{alltt}
This stores in ``size'' the number of characters (including space for the NUL terminator) required.  Upon error this 
function returns an error code and ``size'' will be zero.  

\subsection{From ASCII}
\index{mp\_read\_radix}
\begin{alltt}
int mp_read_radix (mp_int * a, char *str, int radix);
\end{alltt}
This will read the base-``radix'' NUL terminated string from ``str'' into $a$.  It will stop reading when it reads a
................................................................................
\begin{alltt}
int mp_signed_bin_size(mp_int *a);
int mp_read_signed_bin(mp_int *a, unsigned char *b, int c);
int mp_to_signed_bin(mp_int *a, unsigned char *b);
\end{alltt}
They operate essentially the same as the unsigned copies except they prefix the data with zero or non--zero
byte depending on the sign.  If the sign is zpos (e.g. not negative) the prefix is zero, otherwise the prefix
is non--zero.  

\chapter{Algebraic Functions}
\section{Extended Euclidean Algorithm}
\index{mp\_exteuclid}
\begin{alltt}
int mp_exteuclid(mp_int *a, mp_int *b, 
                 mp_int *U1, mp_int *U2, mp_int *U3);
\end{alltt}

This finds the triple U1/U2/U3 using the Extended Euclidean algorithm such that the following equation holds.

\begin{equation}
a \cdot U1 + b \cdot U2 = U3
\end{equation}

Any of the U1/U2/U3 paramters can be set to \textbf{NULL} if they are not desired.  

\section{Greatest Common Divisor}
\index{mp\_gcd}
\begin{alltt}
int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
\end{alltt}
This will compute the greatest common divisor of $a$ and $b$ and store it in $c$.
................................................................................
\index{mp\_jacobi}
\begin{alltt}
int mp_jacobi (mp_int * a, mp_int * p, int *c)
\end{alltt}
This will compute the Jacobi symbol for $a$ with respect to $p$.  If $p$ is prime this essentially computes the Legendre
symbol.  The result is stored in $c$ and can take on one of three values $\lbrace -1, 0, 1 \rbrace$.  If $p$ is prime
then the result will be $-1$ when $a$ is not a quadratic residue modulo $p$.  The result will be $0$ if $a$ divides $p$
and the result will be $1$ if $a$ is a quadratic residue modulo $p$.  






















\section{Modular Inverse}
\index{mp\_invmod}
\begin{alltt}
int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
\end{alltt}
Computes the multiplicative inverse of $a$ modulo $b$ and stores the result in $c$ such that $ac \equiv 1 \mbox{ (mod }b\mbox{)}$.

\newcommand{\emailaddr}[1]{\mbox{$<${#1}$>$}}
\def\twiddle{\raisebox{0.3ex}{\mbox{\tiny $\sim$}}}
\def\gap{\vspace{0.5ex}}
\makeindex
\begin{document}
\frontmatter
\pagestyle{empty}
\title{LibTomMath User Manual \\ v1.0.0}
\author{Tom St Denis \\ tstdenis[email protected]}
\maketitle
This text, the library and the accompanying textbook are all hereby placed in the public domain.  This book has been
formatted for B5 [176x250] paper using the \LaTeX{} {\em book} macro package.

\vspace{10cm}

\begin{flushright}Open Source.  Open Academia.  Open Minds.

\mbox{ }
................................................................................
\listoffigures
\mainmatter
\pagestyle{headings}
\chapter{Introduction}
\section{What is LibTomMath?}
LibTomMath is a library of source code which provides a series of efficient and carefully written functions for manipulating
large integer numbers.  It was written in portable ISO C source code so that it will build on any platform with a conforming
C compiler.

In a nutshell the library was written from scratch with verbose comments to help instruct computer science students how
to implement ``bignum'' math.  However, the resulting code has proven to be very useful.  It has been used by numerous
universities, commercial and open source software developers.  It has been used on a variety of platforms ranging from
Linux and Windows based x86 to ARM based Gameboys and PPC based MacOS machines.

\section{License}
As of the v0.25 the library source code has been placed in the public domain with every new release.  As of the v0.28
release the textbook ``Implementing Multiple Precision Arithmetic'' has been placed in the public domain with every new
release as well.  This textbook is meant to compliment the project by providing a more solid walkthrough of the development
algorithms used in the library.

Since both\footnote{Note that the MPI files under mtest/ are copyrighted by Michael Fromberger.  They are not required to use LibTomMath.} are in the
public domain everyone is entitled to do with them as they see fit.

\section{Building LibTomMath}

LibTomMath is meant to be very ``GCC friendly'' as it comes with a makefile well suited for GCC.  However, the library will
also build in MSVC, Borland C out of the box.  For any other ISO C compiler a makefile will have to be made by the end
developer.

\subsection{Static Libraries}
To build as a static library for GCC issue the following
\begin{alltt}
make
\end{alltt}

command.  This will build the library and archive the object files in ``libtommath.a''.  Now you link against
that and include ``tommath.h'' within your programs.  Alternatively to build with MSVC issue the following
\begin{alltt}
nmake -f makefile.msvc
\end{alltt}

This will build the library and archive the object files in ``tommath.lib''.  This has been tested with MSVC
version 6.00 with service pack 5.

\subsection{Shared Libraries}
To build as a shared library for GCC issue the following
\begin{alltt}
make -f makefile.shared
\end{alltt}
This requires the ``libtool'' package (common on most Linux/BSD systems).  It will build LibTomMath as both shared
and static then install (by default) into /usr/lib as well as install the header files in /usr/include.  The shared
library (resource) will be called ``libtommath.la'' while the static library called ``libtommath.a''.  Generally
you use libtool to link your application against the shared object.

There is limited support for making a ``DLL'' in windows via the ``makefile.cygwin\_dll'' makefile.  It requires
Cygwin to work with since it requires the auto-export/import functionality.  The resulting DLL and import library
``libtommath.dll.a'' can be used to link LibTomMath dynamically to any Windows program using Cygwin.

\subsection{Testing}
To build the library and the test harness type

\begin{alltt}
make test
................................................................................
results.  ``mtest/mtest'' will generate test vectors using the MPI library by Michael Fromberger\footnote{A copy of MPI
is included in the package}.  Simply pipe mtest into test using

\begin{alltt}
mtest/mtest | test
\end{alltt}

If you do not have a ``/dev/urandom'' style RNG source you will have to write your own PRNG and simply pipe that into
mtest.  For example, if your PRNG program is called ``myprng'' simply invoke

\begin{alltt}
myprng | mtest/mtest | test
\end{alltt}

This will output a row of numbers that are increasing.  Each column is a different test (such as addition, multiplication, etc)
that is being performed.  The numbers represent how many times the test was invoked.  If an error is detected the program
will exit with a dump of the relevent numbers it was working with.

\section{Build Configuration}
LibTomMath can configured at build time in three phases we shall call ``depends'', ``tweaks'' and ``trims''.
Each phase changes how the library is built and they are applied one after another respectively.

To make the system more powerful you can tweak the build process.  Classes are defined in the file
``tommath\_superclass.h''.  By default, the symbol ``LTM\_ALL'' shall be defined which simply
instructs the system to build all of the functions.  This is how LibTomMath used to be packaged.  This will give you
access to every function LibTomMath offers.

However, there are cases where such a build is not optional.  For instance, you want to perform RSA operations.  You
don't need the vast majority of the library to perform these operations.  Aside from LTM\_ALL there is
another pre--defined class ``SC\_RSA\_1'' which works in conjunction with the RSA from LibTomCrypt.  Additional
classes can be defined base on the need of the user.

\subsection{Build Depends}
In the file tommath\_class.h you will see a large list of C ``defines'' followed by a series of ``ifdefs''
which further define symbols.  All of the symbols (technically they're macros $\ldots$) represent a given C source
file.  For instance, BN\_MP\_ADD\_C represents the file ``bn\_mp\_add.c''.  When a define has been enabled the
function in the respective file will be compiled and linked into the library.  Accordingly when the define
is absent the file will not be compiled and not contribute any size to the library.

You will also note that the header tommath\_class.h is actually recursively included (it includes itself twice).
This is to help resolve as many dependencies as possible.  In the last pass the symbol LTM\_LAST will be defined.
This is useful for ``trims''.

\subsection{Build Tweaks}
A tweak is an algorithm ``alternative''.  For example, to provide tradeoffs (usually between size and space).
They can be enabled at any pass of the configuration phase.

\begin{small}
................................................................................
\hline
\end{tabular}
\end{center}
\end{small}

\subsection{Build Trims}
A trim is a manner of removing functionality from a function that is not required.  For instance, to perform
RSA cryptography you only require exponentiation with odd moduli so even moduli support can be safely removed.
Build trims are meant to be defined on the last pass of the configuration which means they are to be defined
only if LTM\_LAST has been defined.

\subsubsection{Moduli Related}
\begin{small}
\begin{center}
\begin{tabular}{|l|l|}
................................................................................
\hline \textbf{Restriction} & \textbf{Undefine} \\
\hline Moduli $\le 2560$ bits              & BN\_MP\_MONTGOMERY\_REDUCE\_C \\
                                           & BN\_S\_MP\_MUL\_DIGS\_C \\
                                           & BN\_S\_MP\_MUL\_HIGH\_DIGS\_C \\
                                           & BN\_S\_MP\_SQR\_C \\
\hline Polynomial Schmolynomial            & BN\_MP\_KARATSUBA\_MUL\_C \\
                                           & BN\_MP\_KARATSUBA\_SQR\_C \\
                                           & BN\_MP\_TOOM\_MUL\_C \\
                                           & BN\_MP\_TOOM\_SQR\_C \\

\hline
\end{tabular}
\end{center}
\end{small}


\section{Purpose of LibTomMath}
Unlike  GNU MP (GMP) Library, LIP, OpenSSL or various other commercial kits (Miracl), LibTomMath was not written with
bleeding edge performance in mind.  First and foremost LibTomMath was written to be entirely open.  Not only is the
source code public domain (unlike various other GPL/etc licensed code), not only is the code freely downloadable but the
source code is also accessible for computer science students attempting to learn ``BigNum'' or multiple precision
arithmetic techniques.

LibTomMath was written to be an instructive collection of source code.  This is why there are many comments, only one
function per source file and often I use a ``middle-road'' approach where I don't cut corners for an extra 2\% speed
increase.

Source code alone cannot really teach how the algorithms work which is why I also wrote a textbook that accompanies
the library (beat that!).
................................................................................
\hline
\end{tabular}
\end{center}
\end{small}
\caption{LibTomMath Valuation}
\end{figure}

It may seem odd to compare LibTomMath to GnuPG since the math in GnuPG is only a small portion of the entire application.
However, LibTomMath was written with cryptography in mind.  It provides essentially all of the functions a cryptosystem
would require when working with large integers.

So it may feel tempting to just rip the math code out of GnuPG (or GnuMP where it was taken from originally) in your
own application but I think there are reasons not to.  While LibTomMath is slower than libraries such as GnuMP it is
not normally significantly slower.  On x86 machines the difference is normally a factor of two when performing modular
exponentiations.  It depends largely on the processor, compiler and the moduli being used.

Essentially the only time you wouldn't use LibTomMath is when blazing speed is the primary concern.  However,
on the other side of the coin LibTomMath offers you a totally free (public domain) well structured math library
that is very flexible, complete and performs well in resource contrained environments.  Fast RSA for example can
be performed with as little as 8KB of ram for data (again depending on build options).

\chapter{Getting Started with LibTomMath}
\section{Building Programs}
In order to use LibTomMath you must include ``tommath.h'' and link against the appropriate library file (typically
libtommath.a).  There is no library initialization required and the entire library is thread safe.

\section{Return Codes}
There are three possible return codes a function may return.

\index{MP\_OKAY}\index{MP\_YES}\index{MP\_NO}\index{MP\_VAL}\index{MP\_MEM}
\begin{figure}[here!]
................................................................................
to a string use the following function.

\index{mp\_error\_to\_string}
\begin{alltt}
char *mp_error_to_string(int code);
\end{alltt}

This will return a pointer to a string which describes the given error code.  It will not work for the return codes
MP\_YES and MP\_NO.

\section{Data Types}
The basic ``multiple precision integer'' type is known as the ``mp\_int'' within LibTomMath.  This data type is used to
organize all of the data required to manipulate the integer it represents.  Within LibTomMath it has been prototyped
as the following.

\index{mp\_int}
................................................................................
    int used, alloc, sign;
    mp_digit *dp;
\} mp_int;
\end{alltt}

Where ``mp\_digit'' is a data type that represents individual digits of the integer.  By default, an mp\_digit is the
ISO C ``unsigned long'' data type and each digit is $28-$bits long.  The mp\_digit type can be configured to suit other
platforms by defining the appropriate macros.

All LTM functions that use the mp\_int type will expect a pointer to mp\_int structure.  You must allocate memory to
hold the structure itself by yourself (whether off stack or heap it doesn't matter).  The very first thing that must be
done to use an mp\_int is that it must be initialized.

\section{Function Organization}

................................................................................
mp_div(&a, &b, &a, &c);   /* a = [a/b], c = a mod b */
\end{alltt}

This allows operands to be re-used which can make programming simpler.

\section{Initialization}
\subsection{Single Initialization}
A single mp\_int can be initialized with the ``mp\_init'' function.

\index{mp\_init}
\begin{alltt}
int mp_init (mp_int * a);
\end{alltt}

This function expects a pointer to an mp\_int structure and will initialize the members of the structure so the mp\_int
................................................................................
\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   if ((result = mp_init(&number)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* use the number */

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

\subsection{Single Free}
When you are finished with an mp\_int it is ideal to return the heap it used back to the system.  The following function
provides this functionality.

\index{mp\_clear}
\begin{alltt}
void mp_clear (mp_int * a);
\end{alltt}

The function expects a pointer to a previously initialized mp\_int structure and frees the heap it uses.  It sets the
pointer\footnote{The ``dp'' member.} within the mp\_int to \textbf{NULL} which is used to prevent double free situations.
Is is legal to call mp\_clear() twice on the same mp\_int in a row.

\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   if ((result = mp_init(&number)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* use the number */

   /* We're done with it. */
   mp_clear(&number);

   return EXIT_SUCCESS;
\}
................................................................................
\index{mp\_init\_multi} \index{mp\_clear\_multi}
\begin{alltt}
int mp_init_multi(mp_int *mp, ...);
\end{alltt}

It accepts a \textbf{NULL} terminated list of pointers to mp\_int structures.  It will attempt to initialize them all
at once.  If the function returns MP\_OKAY then all of the mp\_int variables are ready to use, otherwise none of them
are available for use.  A complementary mp\_clear\_multi() function allows multiple mp\_int variables to be free'd
from the heap at the same time.

\begin{small} \begin{alltt}
int main(void)
\{
   mp_int num1, num2, num3;
   int result;

   if ((result = mp_init_multi(&num1,
                               &num2,
                               &num3, NULL)) != MP\_OKAY) \{
      printf("Error initializing the numbers.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* use the numbers */

   /* We're done with them. */
   mp_clear_multi(&num1, &num2, &num3, NULL);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

\subsection{Other Initializers}
To initialized and make a copy of an mp\_int the mp\_init\_copy() function has been provided.

\index{mp\_init\_copy}
\begin{alltt}
int mp_init_copy (mp_int * a, mp_int * b);
\end{alltt}

This function will initialize $a$ and make it a copy of $b$ if all goes well.
................................................................................
   mp_int num1, num2;
   int result;

   /* initialize and do work on num1 ... */

   /* We want a copy of num1 in num2 now */
   if ((result = mp_init_copy(&num2, &num1)) != MP_OKAY) \{
     printf("Error initializing the copy.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* now num2 is ready and contains a copy of num1 */

   /* We're done with them. */
   mp_clear_multi(&num1, &num2, NULL);

   return EXIT_SUCCESS;
\}
................................................................................

\index{mp\_init\_size}
\begin{alltt}
int mp_init_size (mp_int * a, int size);
\end{alltt}

The $size$ parameter must be greater than zero.  If the function succeeds the mp\_int $a$ will be initialized
to have $size$ digits (which are all initially zero).

\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   /* we need a 60-digit number */
   if ((result = mp_init_size(&number, 60)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* use the number */

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

\section{Maintenance Functions}
................................................................................
\begin{alltt}
int mp_shrink (mp_int * a);
\end{alltt}

This will remove excess digits of the mp\_int $a$.  If the operation fails the mp\_int should be intact without the
excess digits being removed.  Note that you can use a shrunk mp\_int in further computations, however, such operations
will require heap operations which can be slow.  It is not ideal to shrink mp\_int variables that you will further
modify in the system (unless you are seriously low on memory).

\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   if ((result = mp_init(&number)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* use the number [e.g. pre-computation]  */

   /* We're done with it for now. */
   if ((result = mp_shrink(&number)) != MP_OKAY) \{
      printf("Error shrinking the number.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* use it .... */


   /* we're done with it. */
   mp_clear(&number);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

\subsection{Adding additional digits}

Within the mp\_int structure are two parameters which control the limitations of the array of digits that represent
the integer the mp\_int is meant to equal.   The \textit{used} parameter dictates how many digits are significant, that is,
contribute to the value of the mp\_int.  The \textit{alloc} parameter dictates how many digits are currently available in
the array.  If you need to perform an operation that requires more digits you will have to mp\_grow() the mp\_int to
your desired size.

\index{mp\_grow}
\begin{alltt}
int mp_grow (mp_int * a, int size);
\end{alltt}

This will grow the array of digits of $a$ to $size$.  If the \textit{alloc} parameter is already bigger than
................................................................................
\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   if ((result = mp_init(&number)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* use the number */

   /* We need to add 20 digits to the number  */
   if ((result = mp_grow(&number, number.alloc + 20)) != MP_OKAY) \{
      printf("Error growing the number.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}


   /* use the number */

   /* we're done with it. */
   mp_clear(&number);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

\chapter{Basic Operations}
\section{Small Constants}
Setting mp\_ints to small constants is a relatively common operation.  To accomodate these instances there are two
small constant assignment functions.  The first function is used to set a single digit constant while the second sets
an ISO C style ``unsigned long'' constant.  The reason for both functions is efficiency.  Setting a single digit is quick but the
domain of a digit can change (it's always at least $0 \ldots 127$).

\subsection{Single Digit}

Setting a single digit can be accomplished with the following function.

\index{mp\_set}
\begin{alltt}
................................................................................
\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   if ((result = mp_init(&number)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* set the number to 5 */
   mp_set(&number, 5);

   /* we're done with it. */
   mp_clear(&number);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

\subsection{Long Constants}

To set a constant that is the size of an ISO C ``unsigned long'' and larger than a single digit the following function
can be used.

\index{mp\_set\_int}
\begin{alltt}
int mp_set_int (mp_int * a, unsigned long b);
\end{alltt}

This will assign the value of the 32-bit variable $b$ to the mp\_int $a$.  Unlike mp\_set() this function will always
accept a 32-bit input regardless of the size of a single digit.  However, since the value may span several digits
this function can fail if it runs out of heap memory.

To get the ``unsigned long'' copy of an mp\_int the following function can be used.

\index{mp\_get\_int}
\begin{alltt}
unsigned long mp_get_int (mp_int * a);
\end{alltt}

This will return the 32 least significant bits of the mp\_int $a$.

\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   if ((result = mp_init(&number)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* set the number to 654321 (note this is bigger than 127) */
   if ((result = mp_set_int(&number, 654321)) != MP_OKAY) \{
      printf("Error setting the value of the number.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   printf("number == \%lu", mp_get_int(&number));

   /* we're done with it. */
   mp_clear(&number);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

This should output the following if the program succeeds.

\begin{alltt}
number == 654321
\end{alltt}

\subsection{Long Constants - platform dependant}

\index{mp\_set\_long}
\begin{alltt}
int mp_set_long (mp_int * a, unsigned long b);
\end{alltt}

This will assign the value of the platform-dependant sized variable $b$ to the mp\_int $a$.

To get the ``unsigned long'' copy of an mp\_int the following function can be used.

\index{mp\_get\_long}
\begin{alltt}
unsigned long mp_get_long (mp_int * a);
\end{alltt}

This will return the least significant bits of the mp\_int $a$ that fit into an ``unsigned long''.

\subsection{Long Long Constants}

\index{mp\_set\_long\_long}
\begin{alltt}
int mp_set_long_long (mp_int * a, unsigned long long b);
\end{alltt}

This will assign the value of the 64-bit variable $b$ to the mp\_int $a$.

To get the ``unsigned long long'' copy of an mp\_int the following function can be used.

\index{mp\_get\_long\_long}
\begin{alltt}
unsigned long long mp_get_long_long (mp_int * a);
\end{alltt}

This will return the 64 least significant bits of the mp\_int $a$.

\subsection{Initialize and Setting Constants}
To both initialize and set small constants the following two functions are available.
\index{mp\_init\_set} \index{mp\_init\_set\_int}
\begin{alltt}
int mp_init_set (mp_int * a, mp_digit b);
int mp_init_set_int (mp_int * a, unsigned long b);
\end{alltt}

Both functions work like the previous counterparts except they first mp\_init $a$ before setting the values.

\begin{alltt}
int main(void)
\{
   mp_int number1, number2;
   int    result;

   /* initialize and set a single digit */
   if ((result = mp_init_set(&number1, 100)) != MP_OKAY) \{
      printf("Error setting number1: \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* initialize and set a long */
   if ((result = mp_init_set_int(&number2, 1023)) != MP_OKAY) \{
      printf("Error setting number2: \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* display */
   printf("Number1, Number2 == \%lu, \%lu",
          mp_get_int(&number1), mp_get_int(&number2));
................................................................................
\hline
\end{tabular}
\end{center}
\caption{Comparison Codes for $a, b$}
\label{fig:CMP}
\end{figure}

In figure \ref{fig:CMP} two integers $a$ and $b$ are being compared.  In this case $a$ is said to be ``to the left'' of
$b$.

\subsection{Unsigned comparison}

An unsigned comparison considers only the digits themselves and not the associated \textit{sign} flag of the
mp\_int structures.  This is analogous to an absolute comparison.  The function mp\_cmp\_mag() will compare two
mp\_int variables based on their digits only.

\index{mp\_cmp\_mag}
\begin{alltt}
int mp_cmp_mag(mp_int * a, mp_int * b);
\end{alltt}
This will compare $a$ to $b$ placing $a$ to the left of $b$.  This function cannot fail and will return one of the
three compare codes listed in figure \ref{fig:CMP}.
................................................................................
\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number1, number2;
   int result;

   if ((result = mp_init_multi(&number1, &number2, NULL)) != MP_OKAY) \{
      printf("Error initializing the numbers.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* set the number1 to 5 */
   mp_set(&number1, 5);

   /* set the number2 to -6 */
   mp_set(&number2, 6);
   if ((result = mp_neg(&number2, &number2)) != MP_OKAY) \{
      printf("Error negating number2.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   switch(mp_cmp_mag(&number1, &number2)) \{
       case MP_GT:  printf("|number1| > |number2|"); break;
       case MP_EQ:  printf("|number1| = |number2|"); break;
       case MP_LT:  printf("|number1| < |number2|"); break;
   \}

   /* we're done with it. */
   mp_clear_multi(&number1, &number2, NULL);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

If this program\footnote{This function uses the mp\_neg() function which is discussed in section \ref{sec:NEG}.} completes
successfully it should print the following.

\begin{alltt}
|number1| < |number2|
\end{alltt}

This is because $\vert -6 \vert = 6$ and obviously $5 < 6$.
................................................................................
\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number1, number2;
   int result;

   if ((result = mp_init_multi(&number1, &number2, NULL)) != MP_OKAY) \{
      printf("Error initializing the numbers.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* set the number1 to 5 */
   mp_set(&number1, 5);

   /* set the number2 to -6 */
   mp_set(&number2, 6);
   if ((result = mp_neg(&number2, &number2)) != MP_OKAY) \{
      printf("Error negating number2.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   switch(mp_cmp(&number1, &number2)) \{
       case MP_GT:  printf("number1 > number2"); break;
       case MP_EQ:  printf("number1 = number2"); break;
       case MP_LT:  printf("number1 < number2"); break;
   \}

   /* we're done with it. */
   mp_clear_multi(&number1, &number2, NULL);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

If this program\footnote{This function uses the mp\_neg() function which is discussed in section \ref{sec:NEG}.} completes
successfully it should print the following.

\begin{alltt}
number1 > number2
\end{alltt}

\subsection{Single Digit}
................................................................................
To compare a single digit against an mp\_int the following function has been provided.

\index{mp\_cmp\_d}
\begin{alltt}
int mp_cmp_d(mp_int * a, mp_digit b);
\end{alltt}

This will compare $a$ to the left of $b$ using a signed comparison.  Note that it will always treat $b$ as
positive.  This function is rather handy when you have to compare against small values such as $1$ (which often
comes up in cryptography).  The function cannot fail and will return one of the tree compare condition codes
listed in figure \ref{fig:CMP}.


\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   if ((result = mp_init(&number)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* set the number to 5 */
   mp_set(&number, 5);

   switch(mp_cmp_d(&number, 7)) \{
       case MP_GT:  printf("number > 7"); break;
       case MP_EQ:  printf("number = 7"); break;
       case MP_LT:  printf("number < 7"); break;
   \}

   /* we're done with it. */
   mp_clear(&number);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

If this program functions properly it will print out the following.
................................................................................

Logical operations are operations that can be performed either with simple shifts or boolean operators such as
AND, XOR and OR directly.  These operations are very quick.

\subsection{Multiplication by two}

Multiplications and divisions by any power of two can be performed with quick logical shifts either left or
right depending on the operation.

When multiplying or dividing by two a special case routine can be used which are as follows.
\index{mp\_mul\_2} \index{mp\_div\_2}
\begin{alltt}
int mp_mul_2(mp_int * a, mp_int * b);
int mp_div_2(mp_int * a, mp_int * b);
\end{alltt}
................................................................................
\begin{small} \begin{alltt}
int main(void)
\{
   mp_int number;
   int result;

   if ((result = mp_init(&number)) != MP_OKAY) \{
      printf("Error initializing the number.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* set the number to 5 */
   mp_set(&number, 5);

   /* multiply by two */
   if ((result = mp\_mul\_2(&number, &number)) != MP_OKAY) \{
      printf("Error multiplying the number.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
   switch(mp_cmp_d(&number, 7)) \{
       case MP_GT:  printf("2*number > 7"); break;
       case MP_EQ:  printf("2*number = 7"); break;
       case MP_LT:  printf("2*number < 7"); break;
   \}

   /* now divide by two */
   if ((result = mp\_div\_2(&number, &number)) != MP_OKAY) \{
      printf("Error dividing the number.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}
   switch(mp_cmp_d(&number, 7)) \{
       case MP_GT:  printf("2*number/2 > 7"); break;
       case MP_EQ:  printf("2*number/2 = 7"); break;
       case MP_LT:  printf("2*number/2 < 7"); break;
   \}

   /* we're done with it. */
   mp_clear(&number);

   return EXIT_SUCCESS;
\}
\end{alltt} \end{small}

If this program is successful it will print out the following text.

\begin{alltt}
2*number > 7
2*number/2 < 7
\end{alltt}

Since $10 > 7$ and $5 < 7$.

To multiply by a power of two the following function can be used.

\index{mp\_mul\_2d}
\begin{alltt}
int mp_mul_2d(mp_int * a, int b, mp_int * c);
\end{alltt}

This will multiply $a$ by $2^b$ and store the result in ``c''.  If the value of $b$ is less than or equal to
zero the function will copy $a$ to ``c'' without performing any further actions.  The multiplication itself
is implemented as a right-shift operation of $a$ by $b$ bits.

To divide by a power of two use the following.

\index{mp\_div\_2d}
\begin{alltt}
int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d);
\end{alltt}
Which will divide $a$ by $2^b$, store the quotient in ``c'' and the remainder in ``d'.  If $b \le 0$ then the
function simply copies $a$ over to ``c'' and zeroes $d$.  The variable $d$ may be passed as a \textbf{NULL}
value to signal that the remainder is not desired.  The division itself is implemented as a left-shift
operation of $a$ by $b$ bits.

\subsection{Polynomial Basis Operations}

Strictly speaking the organization of the integers within the mp\_int structures is what is known as a
``polynomial basis''.  This simply means a field element is stored by divisions of a radix.  For example, if
$f(x) = \sum_{i=0}^{k} y_ix^k$ for any vector $\vec y$ then the array of digits in $\vec y$ are said to be
the polynomial basis representation of $z$ if $f(\beta) = z$ for a given radix $\beta$.

To multiply by the polynomial $g(x) = x$ all you have todo is shift the digits of the basis left one place.  The
following function provides this operation.

\index{mp\_lshd}
\begin{alltt}
int mp_lshd (mp_int * a, int b);
................................................................................
\index{mp\_or} \index{mp\_and} \index{mp\_xor}
\begin{alltt}
int mp_or  (mp_int * a, mp_int * b, mp_int * c);
int mp_and (mp_int * a, mp_int * b, mp_int * c);
int mp_xor (mp_int * a, mp_int * b, mp_int * c);
\end{alltt}

Which compute $c = a \odot b$ where $\odot$ is one of OR, AND or XOR.

\section{Addition and Subtraction}

To compute an addition or subtraction the following two functions can be used.

\index{mp\_add} \index{mp\_sub}
\begin{alltt}
................................................................................
Simple integer negation can be performed with the following.

\index{mp\_neg}
\begin{alltt}
int mp_neg (mp_int * a, mp_int * b);
\end{alltt}

Which assigns $-a$ to $b$.

\subsection{Absolute}
Simple integer absolutes can be performed with the following.

\index{mp\_neg}
\begin{alltt}
int mp_abs (mp_int * a, mp_int * b);
\end{alltt}

Which assigns $\vert a \vert$ to $b$.

\section{Integer Division and Remainder}
To perform a complete and general integer division with remainder use the following function.

\index{mp\_div}
\begin{alltt}
int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d);
\end{alltt}

This divides $a$ by $b$ and stores the quotient in $c$ and $d$.  The signed quotient is computed such that
$bc + d = a$.  Note that either of $c$ or $d$ can be set to \textbf{NULL} if their value is not required.  If
$b$ is zero the function returns \textbf{MP\_VAL}.


\chapter{Multiplication and Squaring}
\section{Multiplication}
A full signed integer multiplication can be performed with the following.
\index{mp\_mul}
\begin{alltt}
int mp_mul (mp_int * a, mp_int * b, mp_int * c);
\end{alltt}
Which assigns the full signed product $ab$ to $c$.  This function actually breaks into one of four cases which are
specific multiplication routines optimized for given parameters.  First there are the Toom-Cook multiplications which
should only be used with very large inputs.  This is followed by the Karatsuba multiplications which are for moderate
sized inputs.  Then followed by the Comba and baseline multipliers.

Fortunately for the developer you don't really need to know this unless you really want to fine tune the system.  mp\_mul()
will determine on its own\footnote{Some tweaking may be required.} what routine to use automatically when it is called.

................................................................................
\begin{alltt}
int main(void)
\{
   mp_int number1, number2;
   int result;

   /* Initialize the numbers */
   if ((result = mp_init_multi(&number1,
                               &number2, NULL)) != MP_OKAY) \{
      printf("Error initializing the numbers.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* set the terms */
   if ((result = mp_set_int(&number, 257)) != MP_OKAY) \{
      printf("Error setting number1.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   if ((result = mp_set_int(&number2, 1023)) != MP_OKAY) \{
      printf("Error setting number2.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* multiply them */
   if ((result = mp_mul(&number1, &number2,
                        &number1)) != MP_OKAY) \{
      printf("Error multiplying terms.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* display */
   printf("number1 * number2 == \%lu", mp_get_int(&number1));

   /* free terms and return */
   mp_clear_multi(&number1, &number2, NULL);

   return EXIT_SUCCESS;
\}
\end{alltt}

If this program succeeds it shall output the following.

\begin{alltt}
number1 * number2 == 262911
\end{alltt}

................................................................................
\index{mp\_sqr}
\begin{alltt}
int mp_sqr (mp_int * a, mp_int * b);
\end{alltt}

Will square $a$ and store it in $b$.  Like the case of multiplication there are four different squaring
algorithms all which can be called from mp\_sqr().  It is ideal to use mp\_sqr over mp\_mul when squaring terms because
of the speed difference.

\section{Tuning Polynomial Basis Routines}

Both of the Toom-Cook and Karatsuba multiplication algorithms are faster than the traditional $O(n^2)$ approach that
the Comba and baseline algorithms use.  At $O(n^{1.464973})$ and $O(n^{1.584962})$ running times respectively they require
considerably less work.  For example, a 10000-digit multiplication would take roughly 724,000 single precision
multiplications with Toom-Cook or 100,000,000 single precision multiplications with the standard Comba (a factor
of 138).

So why not always use Karatsuba or Toom-Cook?   The simple answer is that they have so much overhead that they're not
actually faster than Comba until you hit distinct  ``cutoff'' points.  For Karatsuba with the default configuration,
GCC 3.3.1 and an Athlon XP processor the cutoff point is roughly 110 digits (about 70 for the Intel P4).  That is, at
110 digits Karatsuba and Comba multiplications just about break even and for 110+ digits Karatsuba is faster.

Toom-Cook has incredible overhead and is probably only useful for very large inputs.  So far no known cutoff points
exist and for the most part I just set the cutoff points very high to make sure they're not called.

A demo program in the ``etc/'' directory of the project called ``tune.c'' can be used to find the cutoff points.  This
can be built with GCC as follows

\begin{alltt}
make XXX
................................................................................

When the program is running it will output a series of measurements for different cutoff points.  It will first find
good Karatsuba squaring and multiplication points.  Then it proceeds to find Toom-Cook points.  Note that the Toom-Cook
tuning takes a very long time as the cutoff points are likely to be very high.

\chapter{Modular Reduction}

Modular reduction is process of taking the remainder of one quantity divided by another.  Expressed
as (\ref{eqn:mod}) the modular reduction is equivalent to the remainder of $b$ divided by $c$.

\begin{equation}
a \equiv b \mbox{ (mod }c\mbox{)}
\label{eqn:mod}
\end{equation}

Of particular interest to cryptography are reductions where $b$ is limited to the range $0 \le b < c^2$ since particularly
fast reduction algorithms can be written for the limited range.

Note that one of the four optimized reduction algorithms are automatically chosen in the modular exponentiation
algorithm mp\_exptmod when an appropriate modulus is detected.

\section{Straight Division}
In order to effect an arbitrary modular reduction the following algorithm is provided.

\index{mp\_mod}
\begin{alltt}
int mp_mod(mp_int *a, mp_int *b, mp_int *c);
\end{alltt}

This reduces $a$ modulo $b$ and stores the result in $c$.  The sign of $c$ shall agree with the sign
of $b$.  This algorithm accepts an input $a$ of any range and is not limited by $0 \le a < b^2$.

\section{Barrett Reduction}

Barrett reduction is a generic optimized reduction algorithm that requires pre--computation to achieve
a decent speedup over straight division.  First a $\mu$ value must be precomputed with the following function.

................................................................................

\begin{alltt}
int main(void)
\{
   mp_int   a, b, c, mu;
   int      result;

   /* initialize a,b to desired values, mp_init mu,
    * c and set c to 1...we want to compute a^3 mod b
    */

   /* get mu value */
   if ((result = mp_reduce_setup(&mu, b)) != MP_OKAY) \{
      printf("Error getting mu.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* square a to get c = a^2 */
   if ((result = mp_sqr(&a, &c)) != MP_OKAY) \{
      printf("Error squaring.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* now reduce `c' modulo b */
   if ((result = mp_reduce(&c, &b, &mu)) != MP_OKAY) \{
      printf("Error reducing.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* multiply a to get c = a^3 */
   if ((result = mp_mul(&a, &c, &c)) != MP_OKAY) \{
      printf("Error reducing.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* now reduce `c' modulo b  */
   if ((result = mp_reduce(&c, &b, &mu)) != MP_OKAY) \{
      printf("Error reducing.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* c now equals a^3 mod b */

   return EXIT_SUCCESS;
\}
\end{alltt}

This program will calculate $a^3 \mbox{ mod }b$ if all the functions succeed.

\section{Montgomery Reduction}

Montgomery is a specialized reduction algorithm for any odd moduli.  Like Barrett reduction a pre--computation
step is required.  This is accomplished with the following.

\index{mp\_montgomery\_setup}
\begin{alltt}
int mp_montgomery_setup(mp_int *a, mp_digit *mp);
\end{alltt}

For the given odd moduli $a$ the precomputation value is placed in $mp$.  The reduction is computed with the
following.

\index{mp\_montgomery\_reduce}
\begin{alltt}
int mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
\end{alltt}
This reduces $a$ in place modulo $m$ with the pre--computed value $mp$.   $a$ must be in the range
$0 \le a < b^2$.

Montgomery reduction is faster than Barrett reduction for moduli smaller than the ``comba'' limit.  With the default
setup for instance, the limit is $127$ digits ($3556$--bits).   Note that this function is not limited to
$127$ digits just that it falls back to a baseline algorithm after that point.

An important observation is that this reduction does not return $a \mbox{ mod }m$ but $aR^{-1} \mbox{ mod }m$
where $R = \beta^n$, $n$ is the n number of digits in $m$ and $\beta$ is radix used (default is $2^{28}$).

To quickly calculate $R$ the following function was provided.

\index{mp\_montgomery\_calc\_normalization}
\begin{alltt}
int mp_montgomery_calc_normalization(mp_int *a, mp_int *b);
\end{alltt}
Which calculates $a = R$ for the odd moduli $b$ without using multiplication or division.

The normal modus operandi for Montgomery reductions is to normalize the integers before entering the system.  For
example, to calculate $a^3 \mbox { mod }b$ using Montgomery reduction the value of $a$ can be normalized by
multiplying it by $R$.  Consider the following code snippet.

\begin{alltt}
int main(void)
\{
   mp_int   a, b, c, R;
   mp_digit mp;
   int      result;

   /* initialize a,b to desired values,
    * mp_init R, c and set c to 1....
    */

   /* get normalization */
   if ((result = mp_montgomery_calc_normalization(&R, b)) != MP_OKAY) \{
      printf("Error getting norm.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* get mp value */
   if ((result = mp_montgomery_setup(&c, &mp)) != MP_OKAY) \{
      printf("Error setting up montgomery.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* normalize `a' so now a is equal to aR */
   if ((result = mp_mulmod(&a, &R, &b, &a)) != MP_OKAY) \{
      printf("Error computing aR.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* square a to get c = a^2R^2 */
   if ((result = mp_sqr(&a, &c)) != MP_OKAY) \{
      printf("Error squaring.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* now reduce `c' back down to c = a^2R^2 * R^-1 == a^2R */
   if ((result = mp_montgomery_reduce(&c, &b, mp)) != MP_OKAY) \{
      printf("Error reducing.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* multiply a to get c = a^3R^2 */
   if ((result = mp_mul(&a, &c, &c)) != MP_OKAY) \{
      printf("Error reducing.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* now reduce `c' back down to c = a^3R^2 * R^-1 == a^3R */
   if ((result = mp_montgomery_reduce(&c, &b, mp)) != MP_OKAY) \{
      printf("Error reducing.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* now reduce (again) `c' back down to c = a^3R * R^-1 == a^3 */
   if ((result = mp_montgomery_reduce(&c, &b, mp)) != MP_OKAY) \{
      printf("Error reducing.  \%s",
             mp_error_to_string(result));
      return EXIT_FAILURE;
   \}

   /* c now equals a^3 mod b */

   return EXIT_SUCCESS;
\}
\end{alltt}

This particular example does not look too efficient but it demonstrates the point of the algorithm.  By
normalizing the inputs the reduced results are always of the form $aR$ for some variable $a$.  This allows
a single final reduction to correct for the normalization and the fast reduction used within the algorithm.

For more details consider examining the file \textit{bn\_mp\_exptmod\_fast.c}.

\section{Restricted Dimminished Radix}

``Dimminished Radix'' reduction refers to reduction with respect to moduli that are ameniable to simple
digit shifting and small multiplications.  In this case the ``restricted'' variant refers to moduli of the
form $\beta^k - p$ for some $k \ge 0$ and $0 < p < \beta$ where $\beta$ is the radix (default to $2^{28}$).

As in the case of Montgomery reduction there is a pre--computation phase required for a given modulus.

\index{mp\_dr\_setup}
\begin{alltt}
void mp_dr_setup(mp_int *a, mp_digit *d);
\end{alltt}
................................................................................

\index{mp\_dr\_reduce}
\begin{alltt}
int mp_dr_reduce(mp_int *a, mp_int *b, mp_digit mp);
\end{alltt}

This reduces $a$ in place modulo $b$ with the pre--computed value $mp$.  $b$ must be of a restricted
dimminished radix form and $a$ must be in the range $0 \le a < b^2$.  Dimminished radix reductions are
much faster than both Barrett and Montgomery reductions as they have a much lower asymtotic running time.

Since the moduli are restricted this algorithm is not particularly useful for something like Rabin, RSA or
BBS cryptographic purposes.  This reduction algorithm is useful for Diffie-Hellman and ECC where fixed
primes are acceptable.

Note that unlike Montgomery reduction there is no normalization process.  The result of this function is
equal to the correct residue.

\section{Unrestricted Dimminshed Radix}

Unrestricted reductions work much like the restricted counterparts except in this case the moduli is of the
form $2^k - p$ for $0 < p < \beta$.  In this sense the unrestricted reductions are more flexible as they
can be applied to a wider range of numbers.

\index{mp\_reduce\_2k\_setup}
\begin{alltt}
int mp_reduce_2k_setup(mp_int *a, mp_digit *d);
\end{alltt}

This will compute the required $d$ value for the given moduli $a$.

\index{mp\_reduce\_2k}
\begin{alltt}
int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d);
\end{alltt}

This will reduce $a$ in place modulo $n$ with the pre--computed value $d$.  From my experience this routine is
slower than mp\_dr\_reduce but faster for most moduli sizes than the Montgomery reduction.

\chapter{Exponentiation}
\section{Single Digit Exponentiation}
\index{mp\_expt\_d\_ex}
\begin{alltt}
int mp_expt_d_ex (mp_int * a, mp_digit b, mp_int * c, int fast)
\end{alltt}
This function computes $c = a^b$.

With parameter \textit{fast} set to $0$ the old version of the algorithm is used,
when \textit{fast} is $1$, a faster but not statically timed version of the algorithm is used.

The old version uses a simple binary left-to-right algorithm.
It is faster than repeated multiplications by $a$ for all values of $b$ greater than three.

The new version uses a binary right-to-left algorithm.

The difference between the old and the new version is that the old version always
executes $DIGIT\_BIT$ iterations. The new algorithm executes only $n$ iterations
where $n$ is equal to the position of the highest bit that is set in $b$.

\index{mp\_expt\_d}
\begin{alltt}
int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
\end{alltt}
mp\_expt\_d(a, b, c) is a wrapper function to mp\_expt\_d\_ex(a, b, c, 0).


\section{Modular Exponentiation}
\index{mp\_exptmod}
\begin{alltt}
int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
\end{alltt}
This computes $Y \equiv G^X \mbox{ (mod }P\mbox{)}$ using a variable width sliding window algorithm.  This function
will automatically detect the fastest modular reduction technique to use during the operation.  For negative values of
$X$ the operation is performed as $Y \equiv (G^{-1} \mbox{ mod }P)^{\vert X \vert} \mbox{ (mod }P\mbox{)}$ provided that
$gcd(G, P) = 1$.

This function is actually a shell around the two internal exponentiation functions.  This routine will automatically
detect when Barrett, Montgomery, Restricted and Unrestricted Dimminished Radix based exponentiation can be used.  Generally
moduli of the a ``restricted dimminished radix'' form lead to the fastest modular exponentiations.  Followed by Montgomery
and the other two algorithms.

\section{Root Finding}
\index{mp\_n\_root}
\begin{alltt}
int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
\end{alltt}
This computes $c = a^{1/b}$ such that $c^b \le a$ and $(c+1)^b > a$.  The implementation of this function is not
ideal for values of $b$ greater than three.  It will work but become very slow.  So unless you are working with very small
numbers (less than 1000 bits) I'd avoid $b > 3$ situations.  Will return a positive root only for even roots and return
a root with the sign of the input for odd roots.  For example, performing $4^{1/2}$ will return $2$ whereas $(-8)^{1/3}$
will return $-2$.

This algorithm uses the ``Newton Approximation'' method and will converge on the correct root fairly quickly.  Since
the algorithm requires raising $a$ to the power of $b$ it is not ideal to attempt to find roots for large
values of $b$.  If particularly large roots are required then a factor method could be used instead.  For example,
$a^{1/16}$ is equivalent to $\left (a^{1/4} \right)^{1/4}$ or simply
$\left ( \left ( \left ( a^{1/2} \right )^{1/2} \right )^{1/2} \right )^{1/2}$

\chapter{Prime Numbers}
\section{Trial Division}
\index{mp\_prime\_is\_divisible}
\begin{alltt}
int mp_prime_is_divisible (mp_int * a, int *result)
\end{alltt}
This will attempt to evenly divide $a$ by a list of primes\footnote{Default is the first 256 primes.} and store the
outcome in ``result''.  That is if $result = 0$ then $a$ is not divisible by the primes, otherwise it is.  Note that
if the function does not return \textbf{MP\_OKAY} the value in ``result'' should be considered undefined\footnote{Currently
the default is to set it to zero first.}.

\section{Fermat Test}
\index{mp\_prime\_fermat}
\begin{alltt}
int mp_prime_fermat (mp_int * a, mp_int * b, int *result)
................................................................................

\section{Miller-Rabin Test}
\index{mp\_prime\_miller\_rabin}
\begin{alltt}
int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
\end{alltt}
Performs a Miller-Rabin test to the base $b$ of $a$.  This test is much stronger than the Fermat test and is very hard to
fool (besides with Carmichael numbers).  If $a$ passes the test (therefore is probably prime) $result$ is set to one.
Otherwise $result$ is set to zero.

Note that is suggested that you use the Miller-Rabin test instead of the Fermat test since all of the failures of
Miller-Rabin are a subset of the failures of the Fermat test.

\subsection{Required Number of Tests}
Generally to ensure a number is very likely to be prime you have to perform the Miller-Rabin with at least a half-dozen
or so unique bases.  However, it has been proven that the probability of failure goes down as the size of the input goes up.
This is why a simple function has been provided to help out.

\index{mp\_prime\_rabin\_miller\_trials}
\begin{alltt}
int mp_prime_rabin_miller_trials(int size)
\end{alltt}
This returns the number of trials required for a $2^{-96}$ (or lower) probability of failure for a given ``size'' expressed
in bits.  This comes in handy specially since larger numbers are slower to test.  For example, a 512-bit number would
require ten tests whereas a 1024-bit number would only require four tests.

You should always still perform a trial division before a Miller-Rabin test though.

\section{Primality Testing}
\index{mp\_prime\_is\_prime}
\begin{alltt}
int mp_prime_is_prime (mp_int * a, int t, int *result)
\end{alltt}
This will perform a trial division followed by $t$ rounds of Miller-Rabin tests on $a$ and store the result in $result$.
If $a$ passes all of the tests $result$ is set to one, otherwise it is set to zero.  Note that $t$ is bounded by
$1 \le t < PRIME\_SIZE$ where $PRIME\_SIZE$ is the number of primes in the prime number table (by default this is $256$).

\section{Next Prime}
\index{mp\_prime\_next\_prime}
\begin{alltt}
int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
\end{alltt}
This finds the next prime after $a$ that passes mp\_prime\_is\_prime() with $t$ tests.  Set $bbs\_style$ to one if you
want only the next prime congruent to $3 \mbox{ mod } 4$, otherwise set it to zero to find any next prime.

\section{Random Primes}
\index{mp\_prime\_random}
\begin{alltt}
int mp_prime_random(mp_int *a, int t, int size, int bbs,
                    ltm_prime_callback cb, void *dat)
\end{alltt}
This will find a prime greater than $256^{size}$ which can be ``bbs\_style'' or not depending on $bbs$ and must pass
$t$ rounds of tests.  The ``ltm\_prime\_callback'' is a typedef for

\begin{alltt}
typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat);
\end{alltt}

Which is a function that must read $len$ bytes (and return the amount stored) into $dst$.  The $dat$ variable is simply
copied from the original input.  It can be used to pass RNG context data to the callback.  The function
mp\_prime\_random() is more suitable for generating primes which must be secret (as in the case of RSA) since there
is no skew on the least significant bits.

\textit{Note:}  As of v0.30 of the LibTomMath library this function has been deprecated.  It is still available
but users are encouraged to use the new mp\_prime\_random\_ex() function instead.

\subsection{Extended Generation}
\index{mp\_prime\_random\_ex}
\begin{alltt}
int mp_prime_random_ex(mp_int *a,    int t,
                       int     size, int flags,
                       ltm_prime_callback cb, void *dat);
\end{alltt}
This will generate a prime in $a$ using $t$ tests of the primality testing algorithms.  The variable $size$
specifies the bit length of the prime desired.  The variable $flags$ specifies one of several options available
(see fig. \ref{fig:primeopts}) which can be OR'ed together.  The callback parameters are used as in
mp\_prime\_random().

\begin{figure}[here]
\begin{center}
\begin{small}
\begin{tabular}{|r|l|}
\hline \textbf{Flag}         & \textbf{Meaning} \\
................................................................................
to terminate the string.  Valid values of ``radix'' line in the range $[2, 64]$.  To determine the size (exact) required
by the conversion before storing any data use the following function.

\index{mp\_radix\_size}
\begin{alltt}
int mp_radix_size (mp_int * a, int radix, int *size)
\end{alltt}
This stores in ``size'' the number of characters (including space for the NUL terminator) required.  Upon error this
function returns an error code and ``size'' will be zero.

\subsection{From ASCII}
\index{mp\_read\_radix}
\begin{alltt}
int mp_read_radix (mp_int * a, char *str, int radix);
\end{alltt}
This will read the base-``radix'' NUL terminated string from ``str'' into $a$.  It will stop reading when it reads a
................................................................................
\begin{alltt}
int mp_signed_bin_size(mp_int *a);
int mp_read_signed_bin(mp_int *a, unsigned char *b, int c);
int mp_to_signed_bin(mp_int *a, unsigned char *b);
\end{alltt}
They operate essentially the same as the unsigned copies except they prefix the data with zero or non--zero
byte depending on the sign.  If the sign is zpos (e.g. not negative) the prefix is zero, otherwise the prefix
is non--zero.

\chapter{Algebraic Functions}
\section{Extended Euclidean Algorithm}
\index{mp\_exteuclid}
\begin{alltt}
int mp_exteuclid(mp_int *a, mp_int *b,
                 mp_int *U1, mp_int *U2, mp_int *U3);
\end{alltt}

This finds the triple U1/U2/U3 using the Extended Euclidean algorithm such that the following equation holds.

\begin{equation}
a \cdot U1 + b \cdot U2 = U3
\end{equation}

Any of the U1/U2/U3 paramters can be set to \textbf{NULL} if they are not desired.

\section{Greatest Common Divisor}
\index{mp\_gcd}
\begin{alltt}
int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
\end{alltt}
This will compute the greatest common divisor of $a$ and $b$ and store it in $c$.
................................................................................
\index{mp\_jacobi}
\begin{alltt}
int mp_jacobi (mp_int * a, mp_int * p, int *c)
\end{alltt}
This will compute the Jacobi symbol for $a$ with respect to $p$.  If $p$ is prime this essentially computes the Legendre
symbol.  The result is stored in $c$ and can take on one of three values $\lbrace -1, 0, 1 \rbrace$.  If $p$ is prime
then the result will be $-1$ when $a$ is not a quadratic residue modulo $p$.  The result will be $0$ if $a$ divides $p$
and the result will be $1$ if $a$ is a quadratic residue modulo $p$.

\section{Modular square root}
\index{mp\_sqrtmod\_prime}
\begin{alltt}
int mp_sqrtmod_prime(mp_int *n, mp_int *p, mp_int *r)
\end{alltt}

This will solve the modular equatioon $r^2 = n \mod p$ where $p$ is a prime number greater than 2 (odd prime).
The result is returned in the third argument $r$, the function returns \textbf{MP\_OKAY} on success,
other return values indicate failure.

The implementation is split for two different cases:

1. if $p \mod 4 == 3$ we apply \href{http://cacr.uwaterloo.ca/hac/}{Handbook of Applied Cryptography algorithm 3.36} and compute $r$ directly as
$r = n^{(p+1)/4} \mod p$

2. otherwise we use \href{https://en.wikipedia.org/wiki/Tonelli-Shanks_algorithm}{Tonelli-Shanks algorithm}

The function does not check the primality of parameter $p$ thus it is up to the caller to assure that this parameter
is a prime number. When $p$ is a composite the function behaviour is undefined, it may even return a false-positive
\textbf{MP\_OKAY}.

\section{Modular Inverse}
\index{mp\_invmod}
\begin{alltt}
int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
\end{alltt}
Computes the multiplicative inverse of $a$ modulo $b$ and stores the result in $c$ such that $ac \equiv 1 \mbox{ (mod }b\mbox{)}$.

#include <tommath.h>
#ifdef BN_ERROR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

static const struct {
     int code;
     char *msg;
} msgs[] = {
     { MP_OKAY, "Successful" },
     { MP_MEM,  "Out of heap" },
     { MP_VAL,  "Value out of range" }
};

/* return a char * string for a given code */
char *mp_error_to_string(int code)
{
   int x;

   /* scan the lookup table for the given message */
   for (x = 0; x < (int)(sizeof(msgs) / sizeof(msgs[0])); x++) {
       if (msgs[x].code == code) {
          return msgs[x].msg;
................................................................................
   }

   /* generic reply for invalid code */
   return "Invalid error code";
}

#endif

#include <tommath_private.h>
#ifdef BN_ERROR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

static const struct {
     int code;
     const char *msg;
} msgs[] = {
     { MP_OKAY, "Successful" },
     { MP_MEM,  "Out of heap" },
     { MP_VAL,  "Value out of range" }
};

/* return a char * string for a given code */
const char *mp_error_to_string(int code)
{
   int x;

   /* scan the lookup table for the given message */
   for (x = 0; x < (int)(sizeof(msgs) / sizeof(msgs[0])); x++) {
       if (msgs[x].code == code) {
          return msgs[x].msg;
................................................................................
   }

   /* generic reply for invalid code */
   return "Invalid error code";
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_FAST_MP_INVMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* computes the modular inverse via binary extended euclidean algorithm, 
 * that is c = 1/a mod b 
 *
 * Based on slow invmod except this is optimized for the case where b is 
 * odd as per HAC Note 14.64 on pp. 610
................................................................................
 */
int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int  x, y, u, v, B, D;
  int     res, neg;

  /* 2. [modified] b must be odd   */
  if (mp_iseven (b) == 1) {
    return MP_VAL;
  }

  /* init all our temps */
  if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
     return res;
  }
................................................................................
  if ((res = mp_copy (&y, &v)) != MP_OKAY) {
    goto LBL_ERR;
  }
  mp_set (&D, 1);

top:
  /* 4.  while u is even do */
  while (mp_iseven (&u) == 1) {
    /* 4.1 u = u/2 */
    if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
      goto LBL_ERR;
    }
    /* 4.2 if B is odd then */
    if (mp_isodd (&B) == 1) {
      if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
        goto LBL_ERR;
      }
    }
    /* B = B/2 */
    if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* 5.  while v is even do */
  while (mp_iseven (&v) == 1) {
    /* 5.1 v = v/2 */
    if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
      goto LBL_ERR;
    }
    /* 5.2 if D is odd then */
    if (mp_isodd (&D) == 1) {
      /* D = (D-x)/2 */
      if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
        goto LBL_ERR;
      }
    }
    /* D = D/2 */
    if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
................................................................................

    if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* if not zero goto step 4 */
  if (mp_iszero (&u) == 0) {
    goto top;
  }

  /* now a = C, b = D, gcd == g*v */

  /* if v != 1 then there is no inverse */
  if (mp_cmp_d (&v, 1) != MP_EQ) {
................................................................................
  c->sign = neg;
  res = MP_OKAY;

LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
  return res;
}
#endif

#include <tommath_private.h>
#ifdef BN_FAST_MP_INVMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* computes the modular inverse via binary extended euclidean algorithm, 
 * that is c = 1/a mod b 
 *
 * Based on slow invmod except this is optimized for the case where b is 
 * odd as per HAC Note 14.64 on pp. 610
................................................................................
 */
int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int  x, y, u, v, B, D;
  int     res, neg;

  /* 2. [modified] b must be odd   */
  if (mp_iseven (b) == MP_YES) {
    return MP_VAL;
  }

  /* init all our temps */
  if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
     return res;
  }
................................................................................
  if ((res = mp_copy (&y, &v)) != MP_OKAY) {
    goto LBL_ERR;
  }
  mp_set (&D, 1);

top:
  /* 4.  while u is even do */
  while (mp_iseven (&u) == MP_YES) {
    /* 4.1 u = u/2 */
    if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
      goto LBL_ERR;
    }
    /* 4.2 if B is odd then */
    if (mp_isodd (&B) == MP_YES) {
      if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
        goto LBL_ERR;
      }
    }
    /* B = B/2 */
    if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* 5.  while v is even do */
  while (mp_iseven (&v) == MP_YES) {
    /* 5.1 v = v/2 */
    if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
      goto LBL_ERR;
    }
    /* 5.2 if D is odd then */
    if (mp_isodd (&D) == MP_YES) {
      /* D = (D-x)/2 */
      if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
        goto LBL_ERR;
      }
    }
    /* D = D/2 */
    if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
................................................................................

    if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* if not zero goto step 4 */
  if (mp_iszero (&u) == MP_NO) {
    goto top;
  }

  /* now a = C, b = D, gcd == g*v */

  /* if v != 1 then there is no inverse */
  if (mp_cmp_d (&v, 1) != MP_EQ) {
................................................................................
  c->sign = neg;
  res = MP_OKAY;

LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* computes xR**-1 == x (mod N) via Montgomery Reduction
 *
 * This is an optimized implementation of montgomery_reduce
 * which uses the comba method to quickly calculate the columns of the
 * reduction.
................................................................................
  int     ix, res, olduse;
  mp_word W[MP_WARRAY];

  /* get old used count */
  olduse = x->used;

  /* grow a as required */
  if (x->alloc < n->used + 1) {
    if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
      return res;
    }
  }

  /* first we have to get the digits of the input into
   * an array of double precision words W[...]
   */
  {
    register mp_word *_W;
    register mp_digit *tmpx;

    /* alias for the W[] array */
    _W   = W;

    /* alias for the digits of  x*/
    tmpx = x->dp;

    /* copy the digits of a into W[0..a->used-1] */
    for (ix = 0; ix < x->used; ix++) {
      *_W++ = *tmpx++;
    }

    /* zero the high words of W[a->used..m->used*2] */
    for (; ix < n->used * 2 + 1; ix++) {
      *_W++ = 0;
    }
  }

  /* now we proceed to zero successive digits
   * from the least significant upwards
   */
................................................................................
  for (ix = 0; ix < n->used; ix++) {
    /* mu = ai * m' mod b
     *
     * We avoid a double precision multiplication (which isn't required)
     * by casting the value down to a mp_digit.  Note this requires
     * that W[ix-1] have  the carry cleared (see after the inner loop)
     */
    register mp_digit mu;
    mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);

    /* a = a + mu * m * b**i
     *
     * This is computed in place and on the fly.  The multiplication
     * by b**i is handled by offseting which columns the results
     * are added to.
................................................................................
     * column since the Montgomery reduction requires digits of the
     * result (so far) [see above] to work.  This is
     * handled by fixing up one carry after the inner loop.  The
     * carry fixups are done in order so after these loops the
     * first m->used words of W[] have the carries fixed
     */
    {
      register int iy;
      register mp_digit *tmpn;
      register mp_word *_W;

      /* alias for the digits of the modulus */
      tmpn = n->dp;

      /* Alias for the columns set by an offset of ix */
      _W = W + ix;

................................................................................
  }

  /* now we have to propagate the carries and
   * shift the words downward [all those least
   * significant digits we zeroed].
   */
  {
    register mp_digit *tmpx;
    register mp_word *_W, *_W1;

    /* nox fix rest of carries */

    /* alias for current word */
    _W1 = W + ix;

    /* alias for next word, where the carry goes */
    _W = W + ++ix;

    for (; ix <= n->used * 2 + 1; ix++) {
      *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
    }

    /* copy out, A = A/b**n
     *
     * The result is A/b**n but instead of converting from an
     * array of mp_word to mp_digit than calling mp_rshd
................................................................................

    /* alias for destination word */
    tmpx = x->dp;

    /* alias for shifted double precision result */
    _W = W + n->used;

    for (ix = 0; ix < n->used + 1; ix++) {
      *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
    }

    /* zero oldused digits, if the input a was larger than
     * m->used+1 we'll have to clear the digits
     */
    for (; ix < olduse; ix++) {
................................................................................
  /* if A >= m then A = A - m */
  if (mp_cmp_mag (x, n) != MP_LT) {
    return s_mp_sub (x, n, x);
  }
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* computes xR**-1 == x (mod N) via Montgomery Reduction
 *
 * This is an optimized implementation of montgomery_reduce
 * which uses the comba method to quickly calculate the columns of the
 * reduction.
................................................................................
  int     ix, res, olduse;
  mp_word W[MP_WARRAY];

  /* get old used count */
  olduse = x->used;

  /* grow a as required */
  if (x->alloc < (n->used + 1)) {
    if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
      return res;
    }
  }

  /* first we have to get the digits of the input into
   * an array of double precision words W[...]
   */
  {
    mp_word *_W;
    mp_digit *tmpx;

    /* alias for the W[] array */
    _W   = W;

    /* alias for the digits of  x*/
    tmpx = x->dp;

    /* copy the digits of a into W[0..a->used-1] */
    for (ix = 0; ix < x->used; ix++) {
      *_W++ = *tmpx++;
    }

    /* zero the high words of W[a->used..m->used*2] */
    for (; ix < ((n->used * 2) + 1); ix++) {
      *_W++ = 0;
    }
  }

  /* now we proceed to zero successive digits
   * from the least significant upwards
   */
................................................................................
  for (ix = 0; ix < n->used; ix++) {
    /* mu = ai * m' mod b
     *
     * We avoid a double precision multiplication (which isn't required)
     * by casting the value down to a mp_digit.  Note this requires
     * that W[ix-1] have  the carry cleared (see after the inner loop)
     */
    mp_digit mu;
    mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);

    /* a = a + mu * m * b**i
     *
     * This is computed in place and on the fly.  The multiplication
     * by b**i is handled by offseting which columns the results
     * are added to.
................................................................................
     * column since the Montgomery reduction requires digits of the
     * result (so far) [see above] to work.  This is
     * handled by fixing up one carry after the inner loop.  The
     * carry fixups are done in order so after these loops the
     * first m->used words of W[] have the carries fixed
     */
    {
      int iy;
      mp_digit *tmpn;
      mp_word *_W;

      /* alias for the digits of the modulus */
      tmpn = n->dp;

      /* Alias for the columns set by an offset of ix */
      _W = W + ix;

................................................................................
  }

  /* now we have to propagate the carries and
   * shift the words downward [all those least
   * significant digits we zeroed].
   */
  {
    mp_digit *tmpx;
    mp_word *_W, *_W1;

    /* nox fix rest of carries */

    /* alias for current word */
    _W1 = W + ix;

    /* alias for next word, where the carry goes */
    _W = W + ++ix;

    for (; ix <= ((n->used * 2) + 1); ix++) {
      *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
    }

    /* copy out, A = A/b**n
     *
     * The result is A/b**n but instead of converting from an
     * array of mp_word to mp_digit than calling mp_rshd
................................................................................

    /* alias for destination word */
    tmpx = x->dp;

    /* alias for shifted double precision result */
    _W = W + n->used;

    for (ix = 0; ix < (n->used + 1); ix++) {
      *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
    }

    /* zero oldused digits, if the input a was larger than
     * m->used+1 we'll have to clear the digits
     */
    for (; ix < olduse; ix++) {
................................................................................
  /* if A >= m then A = A - m */
  if (mp_cmp_mag (x, n) != MP_LT) {
    return s_mp_sub (x, n, x);
  }
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_FAST_S_MP_MUL_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* Fast (comba) multiplier
 *
 * This is the fast column-array [comba] multiplier.  It is 
 * designed to compute the columns of the product first 
 * then handle the carries afterwards.  This has the effect 
................................................................................
 * Based on Algorithm 14.12 on pp.595 of HAC.
 *
 */
int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
{
  int     olduse, res, pa, ix, iz;
  mp_digit W[MP_WARRAY];
  register mp_word  _W;

  /* grow the destination as required */
  if (c->alloc < digs) {
    if ((res = mp_grow (c, digs)) != MP_OKAY) {
      return res;
    }
  }
................................................................................
      }

      /* store term */
      W[ix] = ((mp_digit)_W) & MP_MASK;

      /* make next carry */
      _W = _W >> ((mp_word)DIGIT_BIT);
 }

  /* setup dest */
  olduse  = c->used;
  c->used = pa;

  {
    register mp_digit *tmpc;
    tmpc = c->dp;
    for (ix = 0; ix < pa+1; ix++) {
      /* now extract the previous digit [below the carry] */
      *tmpc++ = W[ix];
    }

    /* clear unused digits [that existed in the old copy of c] */
    for (; ix < olduse; ix++) {
      *tmpc++ = 0;
    }
  }
  mp_clamp (c);
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_FAST_S_MP_MUL_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* Fast (comba) multiplier
 *
 * This is the fast column-array [comba] multiplier.  It is 
 * designed to compute the columns of the product first 
 * then handle the carries afterwards.  This has the effect 
................................................................................
 * Based on Algorithm 14.12 on pp.595 of HAC.
 *
 */
int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
{
  int     olduse, res, pa, ix, iz;
  mp_digit W[MP_WARRAY];
  mp_word  _W;

  /* grow the destination as required */
  if (c->alloc < digs) {
    if ((res = mp_grow (c, digs)) != MP_OKAY) {
      return res;
    }
  }
................................................................................
      }

      /* store term */
      W[ix] = ((mp_digit)_W) & MP_MASK;

      /* make next carry */
      _W = _W >> ((mp_word)DIGIT_BIT);
  }

  /* setup dest */
  olduse  = c->used;
  c->used = pa;

  {
    mp_digit *tmpc;
    tmpc = c->dp;
    for (ix = 0; ix < (pa + 1); ix++) {
      /* now extract the previous digit [below the carry] */
      *tmpc++ = W[ix];
    }

    /* clear unused digits [that existed in the old copy of c] */
    for (; ix < olduse; ix++) {
      *tmpc++ = 0;
    }
  }
  mp_clamp (c);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* this is a modified version of fast_s_mul_digs that only produces
 * output digits *above* digs.  See the comments for fast_s_mul_digs
 * to see how it works.
 *
 * This is used in the Barrett reduction since for one of the multiplications
................................................................................
  }
  
  /* setup dest */
  olduse  = c->used;
  c->used = pa;

  {
    register mp_digit *tmpc;

    tmpc = c->dp + digs;
    for (ix = digs; ix < pa; ix++) {
      /* now extract the previous digit [below the carry] */
      *tmpc++ = W[ix];
    }

................................................................................
      *tmpc++ = 0;
    }
  }
  mp_clamp (c);
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* this is a modified version of fast_s_mul_digs that only produces
 * output digits *above* digs.  See the comments for fast_s_mul_digs
 * to see how it works.
 *
 * This is used in the Barrett reduction since for one of the multiplications
................................................................................
  }
  
  /* setup dest */
  olduse  = c->used;
  c->used = pa;

  {
    mp_digit *tmpc;

    tmpc = c->dp + digs;
    for (ix = digs; ix < pa; ix++) {
      /* now extract the previous digit [below the carry] */
      *tmpc++ = W[ix];
    }

................................................................................
      *tmpc++ = 0;
    }
  }
  mp_clamp (c);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_FAST_S_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* the jist of squaring...
 * you do like mult except the offset of the tmpx [one that 
 * starts closer to zero] can't equal the offset of tmpy.  
 * So basically you set up iy like before then you min it with
 * (ty-tx) so that it never happens.  You double all those 
................................................................................
       */
      iy = MIN(a->used-tx, ty+1);

      /* now for squaring tx can never equal ty 
       * we halve the distance since they approach at a rate of 2x
       * and we have to round because odd cases need to be executed
       */
      iy = MIN(iy, (ty-tx+1)>>1);

      /* execute loop */
      for (iz = 0; iz < iy; iz++) {
         _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
      }

      /* double the inner product and add carry */
................................................................................
      *tmpb++ = 0;
    }
  }
  mp_clamp (b);
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_FAST_S_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* the jist of squaring...
 * you do like mult except the offset of the tmpx [one that 
 * starts closer to zero] can't equal the offset of tmpy.  
 * So basically you set up iy like before then you min it with
 * (ty-tx) so that it never happens.  You double all those 
................................................................................
       */
      iy = MIN(a->used-tx, ty+1);

      /* now for squaring tx can never equal ty 
       * we halve the distance since they approach at a rate of 2x
       * and we have to round because odd cases need to be executed
       */
      iy = MIN(iy, ((ty-tx)+1)>>1);

      /* execute loop */
      for (iz = 0; iz < iy; iz++) {
         _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
      }

      /* double the inner product and add carry */
................................................................................
      *tmpb++ = 0;
    }
  }
  mp_clamp (b);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_2EXPT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* computes a = 2**b 
 *
 * Simple algorithm which zeroes the int, grows it then just sets one bit
 * as required.
 */
................................................................................
{
  int     res;

  /* zero a as per default */
  mp_zero (a);

  /* grow a to accomodate the single bit */
  if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) {
    return res;
  }

  /* set the used count of where the bit will go */
  a->used = b / DIGIT_BIT + 1;

  /* put the single bit in its place */
  a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);

  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_2EXPT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* computes a = 2**b 
 *
 * Simple algorithm which zeroes the int, grows it then just sets one bit
 * as required.
 */
................................................................................
{
  int     res;

  /* zero a as per default */
  mp_zero (a);

  /* grow a to accomodate the single bit */
  if ((res = mp_grow (a, (b / DIGIT_BIT) + 1)) != MP_OKAY) {
    return res;
  }

  /* set the used count of where the bit will go */
  a->used = (b / DIGIT_BIT) + 1;

  /* put the single bit in its place */
  a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);

  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_ABS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* b = |a| 
 *
 * Simple function copies the input and fixes the sign to positive
 */
int
................................................................................

  /* force the sign of b to positive */
  b->sign = MP_ZPOS;

  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_ABS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* b = |a| 
 *
 * Simple function copies the input and fixes the sign to positive
 */
int
................................................................................

  /* force the sign of b to positive */
  b->sign = MP_ZPOS;

  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_ADD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* high level addition (handles signs) */
int mp_add (mp_int * a, mp_int * b, mp_int * c)
{
  int     sa, sb, res;

................................................................................
      res = s_mp_sub (a, b, c);
    }
  }
  return res;
}

#endif

#include <tommath_private.h>
#ifdef BN_MP_ADD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* high level addition (handles signs) */
int mp_add (mp_int * a, mp_int * b, mp_int * c)
{
  int     sa, sb, res;

................................................................................
      res = s_mp_sub (a, b, c);
    }
  }
  return res;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_ADD_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* single digit addition */
int
mp_add_d (mp_int * a, mp_digit b, mp_int * c)
{
  int     res, ix, oldused;
  mp_digit *tmpa, *tmpc, mu;

  /* grow c as required */
  if (c->alloc < a->used + 1) {
     if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
        return res;
     }
  }

  /* if a is negative and |a| >= b, call c = |a| - b */
  if (a->sign == MP_NEG && (a->used > 1 || a->dp[0] >= b)) {
     /* temporarily fix sign of a */
     a->sign = MP_ZPOS;

     /* c = |a| - b */
     res = mp_sub_d(a, b, c);

     /* fix signs  */
................................................................................
  }
  mp_clamp(c);

  return MP_OKAY;
}

#endif

#include <tommath_private.h>
#ifdef BN_MP_ADD_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* single digit addition */
int
mp_add_d (mp_int * a, mp_digit b, mp_int * c)
{
  int     res, ix, oldused;
  mp_digit *tmpa, *tmpc, mu;

  /* grow c as required */
  if (c->alloc < (a->used + 1)) {
     if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
        return res;
     }
  }

  /* if a is negative and |a| >= b, call c = |a| - b */
  if ((a->sign == MP_NEG) && ((a->used > 1) || (a->dp[0] >= b))) {
     /* temporarily fix sign of a */
     a->sign = MP_ZPOS;

     /* c = |a| - b */
     res = mp_sub_d(a, b, c);

     /* fix signs  */
................................................................................
  }
  mp_clamp(c);

  return MP_OKAY;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_ADDMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* d = a + b (mod c) */
int
mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
  int     res;
................................................................................
    return res;
  }
  res = mp_mod (&t, c, d);
  mp_clear (&t);
  return res;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_ADDMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* d = a + b (mod c) */
int
mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
  int     res;
................................................................................
    return res;
  }
  res = mp_mod (&t, c, d);
  mp_clear (&t);
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_AND_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* AND two ints together */
int
mp_and (mp_int * a, mp_int * b, mp_int * c)
{
  int     res, ix, px;
................................................................................

  mp_clamp (&t);
  mp_exch (c, &t);
  mp_clear (&t);
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_AND_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* AND two ints together */
int
mp_and (mp_int * a, mp_int * b, mp_int * c)
{
  int     res, ix, px;
................................................................................

  mp_clamp (&t);
  mp_exch (c, &t);
  mp_clear (&t);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_CLAMP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* trim unused digits 
 *
 * This is used to ensure that leading zero digits are
 * trimed and the leading "used" digit will be non-zero
 * Typically very fast.  Also fixes the sign if there
................................................................................
 */
void
mp_clamp (mp_int * a)
{
  /* decrease used while the most significant digit is
   * zero.
   */
  while (a->used > 0 && a->dp[a->used - 1] == 0) {
    --(a->used);
  }

  /* reset the sign flag if used == 0 */
  if (a->used == 0) {
    a->sign = MP_ZPOS;
  }
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_CLAMP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* trim unused digits 
 *
 * This is used to ensure that leading zero digits are
 * trimed and the leading "used" digit will be non-zero
 * Typically very fast.  Also fixes the sign if there
................................................................................
 */
void
mp_clamp (mp_int * a)
{
  /* decrease used while the most significant digit is
   * zero.
   */
  while ((a->used > 0) && (a->dp[a->used - 1] == 0)) {
    --(a->used);
  }

  /* reset the sign flag if used == 0 */
  if (a->used == 0) {
    a->sign = MP_ZPOS;
  }
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_CLEAR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* clear one (frees)  */
void
mp_clear (mp_int * a)
{
  int i;
................................................................................
    /* reset members to make debugging easier */
    a->dp    = NULL;
    a->alloc = a->used = 0;
    a->sign  = MP_ZPOS;
  }
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_CLEAR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* clear one (frees)  */
void
mp_clear (mp_int * a)
{
  int i;
................................................................................
    /* reset members to make debugging easier */
    a->dp    = NULL;
    a->alloc = a->used = 0;
    a->sign  = MP_ZPOS;
  }
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_CLEAR_MULTI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */
#include <stdarg.h>

void mp_clear_multi(mp_int *mp, ...) 
{
    mp_int* next_mp = mp;
    va_list args;
................................................................................
    while (next_mp != NULL) {
        mp_clear(next_mp);
        next_mp = va_arg(args, mp_int*);
    }
    va_end(args);
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_CLEAR_MULTI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */
#include <stdarg.h>

void mp_clear_multi(mp_int *mp, ...) 
{
    mp_int* next_mp = mp;
    va_list args;
................................................................................
    while (next_mp != NULL) {
        mp_clear(next_mp);
        next_mp = va_arg(args, mp_int*);
    }
    va_end(args);
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_CMP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* compare two ints (signed)*/
int
mp_cmp (const mp_int * a, const mp_int * b)
{
  /* compare based on sign */
................................................................................
     /* if negative compare opposite direction */
     return mp_cmp_mag(b, a);
  } else {
     return mp_cmp_mag(a, b);
  }
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_CMP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* compare two ints (signed)*/
int
mp_cmp (const mp_int * a, const mp_int * b)
{
  /* compare based on sign */
................................................................................
     /* if negative compare opposite direction */
     return mp_cmp_mag(b, a);
  } else {
     return mp_cmp_mag(a, b);
  }
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_CMP_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* compare a digit */
int mp_cmp_d(const mp_int * a, mp_digit b)
{
  /* compare based on sign */
  if (a->sign == MP_NEG) {
................................................................................
  } else if (a->dp[0] < b) {
    return MP_LT;
  } else {
    return MP_EQ;
  }
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_CMP_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* compare a digit */
int mp_cmp_d(const mp_int * a, mp_digit b)
{
  /* compare based on sign */
  if (a->sign == MP_NEG) {
................................................................................
  } else if (a->dp[0] < b) {
    return MP_LT;
  } else {
    return MP_EQ;
  }
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_CMP_MAG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* compare maginitude of two ints (unsigned) */
int mp_cmp_mag (const mp_int * a, const mp_int * b)
{
  int     n;
  mp_digit *tmpa, *tmpb;
................................................................................
    if (*tmpa < *tmpb) {
      return MP_LT;
    }
  }
  return MP_EQ;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_CMP_MAG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* compare maginitude of two ints (unsigned) */
int mp_cmp_mag (const mp_int * a, const mp_int * b)
{
  int     n;
  mp_digit *tmpa, *tmpb;
................................................................................
    if (*tmpa < *tmpb) {
      return MP_LT;
    }
  }
  return MP_EQ;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_CNT_LSB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

static const int lnz[16] = { 
   4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
};

/* Counts the number of lsbs which are zero before the first zero bit */
int mp_cnt_lsb(const mp_int *a)
{
   int x;
   mp_digit q, qq;

   /* easy out */
   if (mp_iszero(a) == 1) {
      return 0;
   }

   /* scan lower digits until non-zero */
   for (x = 0; x < a->used && a->dp[x] == 0; x++);
   q = a->dp[x];
   x *= DIGIT_BIT;

   /* now scan this digit until a 1 is found */
   if ((q & 1) == 0) {
      do {
         qq  = q & 15;
................................................................................
         q >>= 4;
      } while (qq == 0);
   }
   return x;
}

#endif

#include <tommath_private.h>
#ifdef BN_MP_CNT_LSB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

static const int lnz[16] = { 
   4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
};

/* Counts the number of lsbs which are zero before the first zero bit */
int mp_cnt_lsb(const mp_int *a)
{
   int x;
   mp_digit q, qq;

   /* easy out */
   if (mp_iszero(a) == MP_YES) {
      return 0;
   }

   /* scan lower digits until non-zero */
   for (x = 0; (x < a->used) && (a->dp[x] == 0); x++) {}
   q = a->dp[x];
   x *= DIGIT_BIT;

   /* now scan this digit until a 1 is found */
   if ((q & 1) == 0) {
      do {
         qq  = q & 15;
................................................................................
         q >>= 4;
      } while (qq == 0);
   }
   return x;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_COPY_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* copy, b = a */
int
mp_copy (const mp_int * a, mp_int * b)
{
  int     res, n;
................................................................................
     if ((res = mp_grow (b, a->used)) != MP_OKAY) {
        return res;
     }
  }

  /* zero b and copy the parameters over */
  {
    register mp_digit *tmpa, *tmpb;

    /* pointer aliases */

    /* source */
    tmpa = a->dp;

    /* destination */
................................................................................

  /* copy used count and sign */
  b->used = a->used;
  b->sign = a->sign;
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_COPY_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* copy, b = a */
int
mp_copy (const mp_int * a, mp_int * b)
{
  int     res, n;
................................................................................
     if ((res = mp_grow (b, a->used)) != MP_OKAY) {
        return res;
     }
  }

  /* zero b and copy the parameters over */
  {
    mp_digit *tmpa, *tmpb;

    /* pointer aliases */

    /* source */
    tmpa = a->dp;

    /* destination */
................................................................................

  /* copy used count and sign */
  b->used = a->used;
  b->sign = a->sign;
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_COUNT_BITS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* returns the number of bits in an int */
int
mp_count_bits (const mp_int * a)
{
  int     r;
................................................................................
  while (q > ((mp_digit) 0)) {
    ++r;
    q >>= ((mp_digit) 1);
  }
  return r;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_COUNT_BITS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* returns the number of bits in an int */
int
mp_count_bits (const mp_int * a)
{
  int     r;
................................................................................
  while (q > ((mp_digit) 0)) {
    ++r;
    q >>= ((mp_digit) 1);
  }
  return r;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_DIV_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

#ifdef BN_MP_DIV_SMALL

/* slower bit-bang division... also smaller */
int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
   mp_int ta, tb, tq, q;
   int    res, n, n2;

  /* is divisor zero ? */
  if (mp_iszero (b) == 1) {
    return MP_VAL;
  }

  /* if a < b then q=0, r = a */
  if (mp_cmp_mag (a, b) == MP_LT) {
    if (d != NULL) {
      res = mp_copy (a, d);
................................................................................
      res = MP_OKAY;
    }
    if (c != NULL) {
      mp_zero (c);
    }
    return res;
  }
	
  /* init our temps */
  if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) {
     return res;
  }


  mp_set(&tq, 1);
  n = mp_count_bits(a) - mp_count_bits(b);
  if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
      ((res = mp_abs(b, &tb)) != MP_OKAY) || 
      ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
      ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
      goto LBL_ERR;
  }

  while (n-- >= 0) {
     if (mp_cmp(&tb, &ta) != MP_GT) {
................................................................................
         ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
           goto LBL_ERR;
     }
  }

  /* now q == quotient and ta == remainder */
  n  = a->sign;
  n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
  if (c != NULL) {
     mp_exch(c, &q);
     c->sign  = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
  }
  if (d != NULL) {
     mp_exch(d, &ta);
     d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
................................................................................
LBL_ERR:
   mp_clear_multi(&ta, &tb, &tq, &q, NULL);
   return res;
}

#else

/* integer signed division. 
 * c*b + d == a [e.g. a/b, c=quotient, d=remainder]
 * HAC pp.598 Algorithm 14.20
 *
 * Note that the description in HAC is horribly 
 * incomplete.  For example, it doesn't consider 
 * the case where digits are removed from 'x' in 
 * the inner loop.  It also doesn't consider the 
 * case that y has fewer than three digits, etc..
 *
 * The overall algorithm is as described as 
 * 14.20 from HAC but fixed to treat these cases.
*/
int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
  mp_int  q, x, y, t1, t2;
  int     res, n, t, i, norm, neg;

  /* is divisor zero ? */
  if (mp_iszero (b) == 1) {
    return MP_VAL;
  }

  /* if a < b then q=0, r = a */
  if (mp_cmp_mag (a, b) == MP_LT) {
    if (d != NULL) {
      res = mp_copy (a, d);
................................................................................

  /* step 3. for i from n down to (t + 1) */
  for (i = n; i >= (t + 1); i--) {
    if (i > x.used) {
      continue;
    }

    /* step 3.1 if xi == yt then set q{i-t-1} to b-1, 
     * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
    if (x.dp[i] == y.dp[t]) {
      q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
    } else {
      mp_word tmp;
      tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
      tmp |= ((mp_word) x.dp[i - 1]);
      tmp /= ((mp_word) y.dp[t]);
      if (tmp > (mp_word) MP_MASK)
        tmp = MP_MASK;

      q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
    }

    /* while (q{i-t-1} * (yt * b + y{t-1})) > 
             xi * b**2 + xi-1 * b + xi-2 
     
       do q{i-t-1} -= 1; 
    */
    q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK;

    do {
      q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK;


      /* find left hand */
      mp_zero (&t1);
      t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
      t1.dp[1] = y.dp[t];
      t1.used = 2;
      if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) {
        goto LBL_Y;
      }

      /* find right hand */
      t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
      t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
      t2.dp[2] = x.dp[i];
      t2.used = 3;
    } while (mp_cmp_mag(&t1, &t2) == MP_GT);

    /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
    if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) {
      goto LBL_Y;
    }

    if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
      goto LBL_Y;
    }

    if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
      goto LBL_Y;
    }

    /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
    if (x.sign == MP_NEG) {
      if ((res = mp_copy (&y, &t1)) != MP_OKAY) {
        goto LBL_Y;
      }
      if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
        goto LBL_Y;
      }
      if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
        goto LBL_Y;
      }

      q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
    }
  }

  /* now q is the quotient and x is the remainder 
   * [which we have to normalize] 
   */
  
  /* get sign before writing to c */
  x.sign = x.used == 0 ? MP_ZPOS : a->sign;

  if (c != NULL) {
    mp_clamp (&q);
    mp_exch (&q, c);
    c->sign = neg;
  }

  if (d != NULL) {
    mp_div_2d (&x, norm, &x, NULL);


    mp_exch (&x, d);
  }

  res = MP_OKAY;

LBL_Y:mp_clear (&y);
LBL_X:mp_clear (&x);
................................................................................
LBL_Q:mp_clear (&q);
  return res;
}

#endif

#endif

#include <tommath_private.h>
#ifdef BN_MP_DIV_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

#ifdef BN_MP_DIV_SMALL

/* slower bit-bang division... also smaller */
int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
   mp_int ta, tb, tq, q;
   int    res, n, n2;

  /* is divisor zero ? */
  if (mp_iszero (b) == MP_YES) {
    return MP_VAL;
  }

  /* if a < b then q=0, r = a */
  if (mp_cmp_mag (a, b) == MP_LT) {
    if (d != NULL) {
      res = mp_copy (a, d);
................................................................................
      res = MP_OKAY;
    }
    if (c != NULL) {
      mp_zero (c);
    }
    return res;
  }

  /* init our temps */
  if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL)) != MP_OKAY) {
     return res;
  }


  mp_set(&tq, 1);
  n = mp_count_bits(a) - mp_count_bits(b);
  if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
      ((res = mp_abs(b, &tb)) != MP_OKAY) ||
      ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
      ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
      goto LBL_ERR;
  }

  while (n-- >= 0) {
     if (mp_cmp(&tb, &ta) != MP_GT) {
................................................................................
         ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
           goto LBL_ERR;
     }
  }

  /* now q == quotient and ta == remainder */
  n  = a->sign;
  n2 = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
  if (c != NULL) {
     mp_exch(c, &q);
     c->sign  = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
  }
  if (d != NULL) {
     mp_exch(d, &ta);
     d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
................................................................................
LBL_ERR:
   mp_clear_multi(&ta, &tb, &tq, &q, NULL);
   return res;
}

#else

/* integer signed division.
 * c*b + d == a [e.g. a/b, c=quotient, d=remainder]
 * HAC pp.598 Algorithm 14.20
 *
 * Note that the description in HAC is horribly
 * incomplete.  For example, it doesn't consider
 * the case where digits are removed from 'x' in
 * the inner loop.  It also doesn't consider the
 * case that y has fewer than three digits, etc..
 *
 * The overall algorithm is as described as
 * 14.20 from HAC but fixed to treat these cases.
*/
int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
  mp_int  q, x, y, t1, t2;
  int     res, n, t, i, norm, neg;

  /* is divisor zero ? */
  if (mp_iszero (b) == MP_YES) {
    return MP_VAL;
  }

  /* if a < b then q=0, r = a */
  if (mp_cmp_mag (a, b) == MP_LT) {
    if (d != NULL) {
      res = mp_copy (a, d);
................................................................................

  /* step 3. for i from n down to (t + 1) */
  for (i = n; i >= (t + 1); i--) {
    if (i > x.used) {
      continue;
    }

    /* step 3.1 if xi == yt then set q{i-t-1} to b-1,
     * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
    if (x.dp[i] == y.dp[t]) {
      q.dp[(i - t) - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
    } else {
      mp_word tmp;
      tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
      tmp |= ((mp_word) x.dp[i - 1]);
      tmp /= ((mp_word) y.dp[t]);
      if (tmp > (mp_word) MP_MASK) {
        tmp = MP_MASK;
      }
      q.dp[(i - t) - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
    }

    /* while (q{i-t-1} * (yt * b + y{t-1})) >
             xi * b**2 + xi-1 * b + xi-2

       do q{i-t-1} -= 1;
    */

    q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] + 1) & MP_MASK;
    do {

      q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] - 1) & MP_MASK;

      /* find left hand */
      mp_zero (&t1);
      t1.dp[0] = ((t - 1) < 0) ? 0 : y.dp[t - 1];
      t1.dp[1] = y.dp[t];
      t1.used = 2;
      if ((res = mp_mul_d (&t1, q.dp[(i - t) - 1], &t1)) != MP_OKAY) {
        goto LBL_Y;
      }

      /* find right hand */
      t2.dp[0] = ((i - 2) < 0) ? 0 : x.dp[i - 2];
      t2.dp[1] = ((i - 1) < 0) ? 0 : x.dp[i - 1];
      t2.dp[2] = x.dp[i];
      t2.used = 3;
    } while (mp_cmp_mag(&t1, &t2) == MP_GT);

    /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
    if ((res = mp_mul_d (&y, q.dp[(i - t) - 1], &t1)) != MP_OKAY) {
      goto LBL_Y;
    }

    if ((res = mp_lshd (&t1, (i - t) - 1)) != MP_OKAY) {
      goto LBL_Y;
    }

    if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
      goto LBL_Y;
    }

    /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
    if (x.sign == MP_NEG) {
      if ((res = mp_copy (&y, &t1)) != MP_OKAY) {
        goto LBL_Y;
      }
      if ((res = mp_lshd (&t1, (i - t) - 1)) != MP_OKAY) {
        goto LBL_Y;
      }
      if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
        goto LBL_Y;
      }

      q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] - 1UL) & MP_MASK;
    }
  }

  /* now q is the quotient and x is the remainder
   * [which we have to normalize]
   */

  /* get sign before writing to c */
  x.sign = (x.used == 0) ? MP_ZPOS : a->sign;

  if (c != NULL) {
    mp_clamp (&q);
    mp_exch (&q, c);
    c->sign = neg;
  }

  if (d != NULL) {
    if ((res = mp_div_2d (&x, norm, &x, NULL)) != MP_OKAY) {
      goto LBL_Y;
    }
    mp_exch (&x, d);
  }

  res = MP_OKAY;

LBL_Y:mp_clear (&y);
LBL_X:mp_clear (&x);
................................................................................
LBL_Q:mp_clear (&q);
  return res;
}

#endif

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_DIV_2_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* b = a/2 */
int mp_div_2(mp_int * a, mp_int * b)
{
  int     x, res, oldused;

................................................................................
      return res;
    }
  }

  oldused = b->used;
  b->used = a->used;
  {
    register mp_digit r, rr, *tmpa, *tmpb;

    /* source alias */
    tmpa = a->dp + b->used - 1;

    /* dest alias */
    tmpb = b->dp + b->used - 1;

................................................................................
    }
  }
  b->sign = a->sign;
  mp_clamp (b);
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_DIV_2_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* b = a/2 */
int mp_div_2(mp_int * a, mp_int * b)
{
  int     x, res, oldused;

................................................................................
      return res;
    }
  }

  oldused = b->used;
  b->used = a->used;
  {
    mp_digit r, rr, *tmpa, *tmpb;

    /* source alias */
    tmpa = a->dp + b->used - 1;

    /* dest alias */
    tmpb = b->dp + b->used - 1;

................................................................................
    }
  }
  b->sign = a->sign;
  mp_clamp (b);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_DIV_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* shift right by a certain bit count (store quotient in c, optional remainder in d) */
int mp_div_2d (const mp_int * a, int b, mp_int * c, mp_int * d)
{
  mp_digit D, r, rr;
  int     x, res;
................................................................................
  if (b >= (int)DIGIT_BIT) {
    mp_rshd (c, b / DIGIT_BIT);
  }

  /* shift any bit count < DIGIT_BIT */
  D = (mp_digit) (b % DIGIT_BIT);
  if (D != 0) {
    register mp_digit *tmpc, mask, shift;

    /* mask */
    mask = (((mp_digit)1) << D) - 1;

    /* shift for lsb */
    shift = DIGIT_BIT - D;

................................................................................
  if (d != NULL) {
    mp_exch (&t, d);
  }
  mp_clear (&t);
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_DIV_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* shift right by a certain bit count (store quotient in c, optional remainder in d) */
int mp_div_2d (const mp_int * a, int b, mp_int * c, mp_int * d)
{
  mp_digit D, r, rr;
  int     x, res;
................................................................................
  if (b >= (int)DIGIT_BIT) {
    mp_rshd (c, b / DIGIT_BIT);
  }

  /* shift any bit count < DIGIT_BIT */
  D = (mp_digit) (b % DIGIT_BIT);
  if (D != 0) {
    mp_digit *tmpc, mask, shift;

    /* mask */
    mask = (((mp_digit)1) << D) - 1;

    /* shift for lsb */
    shift = DIGIT_BIT - D;

................................................................................
  if (d != NULL) {
    mp_exch (&t, d);
  }
  mp_clear (&t);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_DIV_3_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* divide by three (based on routine from MPI and the GMP manual) */
int
mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
{
  mp_int   q;
................................................................................
  }
  mp_clear(&q);
  
  return res;
}

#endif

#include <tommath_private.h>
#ifdef BN_MP_DIV_3_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* divide by three (based on routine from MPI and the GMP manual) */
int
mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
{
  mp_int   q;
................................................................................
  }
  mp_clear(&q);
  
  return res;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_DIV_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

static int s_is_power_of_two(mp_digit b, int *p)
{
   int x;

   /* quick out - if (b & (b-1)) isn't zero, b isn't a power of two */
   if ((b==0) || (b & (b-1))) {
       return 0;
   }
   for (x = 1; x < DIGIT_BIT; x++) {
      if (b == (((mp_digit)1)<<x)) {
         *p = x;
         return 1;
      }
................................................................................

  /* cannot divide by zero */
  if (b == 0) {
     return MP_VAL;
  }

  /* quick outs */
  if (b == 1 || mp_iszero(a) == 1) {
     if (d != NULL) {
        *d = 0;
     }
     if (c != NULL) {
        return mp_copy(a, c);
     }
     return MP_OKAY;
................................................................................
  }
  mp_clear(&q);
  
  return res;
}

#endif

#include <tommath_private.h>
#ifdef BN_MP_DIV_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

static int s_is_power_of_two(mp_digit b, int *p)
{
   int x;

   /* quick out - if (b & (b-1)) isn't zero, b isn't a power of two */
   if ((b == 0) || ((b & (b-1)) != 0)) {
       return 0;
   }
   for (x = 1; x < DIGIT_BIT; x++) {
      if (b == (((mp_digit)1)<<x)) {
         *p = x;
         return 1;
      }
................................................................................

  /* cannot divide by zero */
  if (b == 0) {
     return MP_VAL;
  }

  /* quick outs */
  if ((b == 1) || (mp_iszero(a) == MP_YES)) {
     if (d != NULL) {
        *d = 0;
     }
     if (c != NULL) {
        return mp_copy(a, c);
     }
     return MP_OKAY;
................................................................................
  }
  mp_clear(&q);
  
  return res;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_DR_IS_MODULUS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* determines if a number is a valid DR modulus */
int mp_dr_is_modulus(mp_int *a)
{
   int ix;

................................................................................
          return 0;
       }
   }
   return 1;
}

#endif

#include <tommath_private.h>
#ifdef BN_MP_DR_IS_MODULUS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* determines if a number is a valid DR modulus */
int mp_dr_is_modulus(mp_int *a)
{
   int ix;

................................................................................
          return 0;
       }
   }
   return 1;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_DR_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
 *
 * Based on algorithm from the paper
 *
 * "Generating Efficient Primes for Discrete Log Cryptosystems"
................................................................................
  mp_word  r;
  mp_digit mu, *tmpx1, *tmpx2;

  /* m = digits in modulus */
  m = n->used;

  /* ensure that "x" has at least 2m digits */
  if (x->alloc < m + m) {
    if ((err = mp_grow (x, m + m)) != MP_OKAY) {
      return err;
    }
  }

/* top of loop, this is where the code resumes if
 * another reduction pass is required.
................................................................................
  tmpx2 = x->dp + m;

  /* set carry to zero */
  mu = 0;

  /* compute (x mod B**m) + k * [x/B**m] inline and inplace */
  for (i = 0; i < m; i++) {
      r         = ((mp_word)*tmpx2++) * ((mp_word)k) + *tmpx1 + mu;
      *tmpx1++  = (mp_digit)(r & MP_MASK);
      mu        = (mp_digit)(r >> ((mp_word)DIGIT_BIT));
  }

  /* set final carry */
  *tmpx1++ = mu;

................................................................................
  /* clamp, sub and return */
  mp_clamp (x);

  /* if x >= n then subtract and reduce again
   * Each successive "recursion" makes the input smaller and smaller.
   */
  if (mp_cmp_mag (x, n) != MP_LT) {
    s_mp_sub(x, n, x);


    goto top;
  }
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_DR_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
 *
 * Based on algorithm from the paper
 *
 * "Generating Efficient Primes for Discrete Log Cryptosystems"
................................................................................
  mp_word  r;
  mp_digit mu, *tmpx1, *tmpx2;

  /* m = digits in modulus */
  m = n->used;

  /* ensure that "x" has at least 2m digits */
  if (x->alloc < (m + m)) {
    if ((err = mp_grow (x, m + m)) != MP_OKAY) {
      return err;
    }
  }

/* top of loop, this is where the code resumes if
 * another reduction pass is required.
................................................................................
  tmpx2 = x->dp + m;

  /* set carry to zero */
  mu = 0;

  /* compute (x mod B**m) + k * [x/B**m] inline and inplace */
  for (i = 0; i < m; i++) {
      r         = (((mp_word)*tmpx2++) * (mp_word)k) + *tmpx1 + mu;
      *tmpx1++  = (mp_digit)(r & MP_MASK);
      mu        = (mp_digit)(r >> ((mp_word)DIGIT_BIT));
  }

  /* set final carry */
  *tmpx1++ = mu;

................................................................................
  /* clamp, sub and return */
  mp_clamp (x);

  /* if x >= n then subtract and reduce again
   * Each successive "recursion" makes the input smaller and smaller.
   */
  if (mp_cmp_mag (x, n) != MP_LT) {
    if ((err = s_mp_sub(x, n, x)) != MP_OKAY) {
      return err;
    }
    goto top;
  }
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_DR_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* determines the setup value */
void mp_dr_setup(mp_int *a, mp_digit *d)
{
   /* the casts are required if DIGIT_BIT is one less than
    * the number of bits in a mp_digit [e.g. DIGIT_BIT==31]
    */
   *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) - 
        ((mp_word)a->dp[0]));
}

#endif

#include <tommath_private.h>
#ifdef BN_MP_DR_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* determines the setup value */
void mp_dr_setup(mp_int *a, mp_digit *d)
{
   /* the casts are required if DIGIT_BIT is one less than
    * the number of bits in a mp_digit [e.g. DIGIT_BIT==31]
    */
   *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) - 
        ((mp_word)a->dp[0]));
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_EXCH_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* swap the elements of two integers, for cases where you can't simply swap the 
 * mp_int pointers around
 */
void
mp_exch (mp_int * a, mp_int * b)
................................................................................
  mp_int  t;

  t  = *a;
  *a = *b;
  *b = t;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_EXCH_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* swap the elements of two integers, for cases where you can't simply swap the 
 * mp_int pointers around
 */
void
mp_exch (mp_int * a, mp_int * b)
................................................................................
  mp_int  t;

  t  = *a;
  *a = *b;
  *b = t;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_EXPT_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* calculate c = a**b  using a square-multiply algorithm */
int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
{
  int     res, x;
  mp_int  g;

  if ((res = mp_init_copy (&g, a)) != MP_OKAY) {
    return res;
  }




  /* set initial result */
  mp_set (c, 1);

  for (x = 0; x < (int) DIGIT_BIT; x++) {
    /* square */
    if ((res = mp_sqr (c, c)) != MP_OKAY) {
      mp_clear (&g);
      return res;
    }

    /* if the bit is set multiply */
    if ((b & (mp_digit) (((mp_digit)1) << (DIGIT_BIT - 1))) != 0) {
      if ((res = mp_mul (c, &g, c)) != MP_OKAY) {
         mp_clear (&g);
         return res;
      }
    }

    /* shift to next bit */
    b <<= 1;
  }

  mp_clear (&g);
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_EXPT_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* wrapper function for mp_expt_d_ex() */
int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
{
  return mp_expt_d_ex(a, b, c, 0);

}



#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath_private.h>
#ifdef BN_MP_EXPT_D_EX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* calculate c = a**b  using a square-multiply algorithm */
int mp_expt_d_ex (mp_int * a, mp_digit b, mp_int * c, int fast)
{
  int     res;
  unsigned int x;

  mp_int  g;

  if ((res = mp_init_copy (&g, a)) != MP_OKAY) {
    return res;
  }

  /* set initial result */
  mp_set (c, 1);

  if (fast != 0) {
    while (b > 0) {
      /* if the bit is set multiply */
      if ((b & 1) != 0) {
        if ((res = mp_mul (c, &g, c)) != MP_OKAY) {
          mp_clear (&g);
          return res;
        }
      }

      /* square */
      if (b > 1) {
        if ((res = mp_sqr (&g, &g)) != MP_OKAY) {
          mp_clear (&g);
          return res;
        }
      }

      /* shift to next bit */
      b >>= 1;
    }
  }
  else {
    for (x = 0; x < DIGIT_BIT; x++) {
      /* square */
      if ((res = mp_sqr (c, c)) != MP_OKAY) {
        mp_clear (&g);
        return res;
      }

      /* if the bit is set multiply */
      if ((b & (mp_digit) (((mp_digit)1) << (DIGIT_BIT - 1))) != 0) {
        if ((res = mp_mul (c, &g, c)) != MP_OKAY) {
           mp_clear (&g);
           return res;
        }
      }

      /* shift to next bit */
      b <<= 1;
    }
  } /* if ... else */

  mp_clear (&g);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_EXPTMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */


/* this is a shell function that calls either the normal or Montgomery
 * exptmod functions.  Originally the call to the montgomery code was
 * embedded in the normal function but that wasted alot of stack space
 * for nothing (since 99% of the time the Montgomery code would be called)
................................................................................
  if (dr == 0) {
     dr = mp_reduce_is_2k(P) << 1;
  }
#endif
    
  /* if the modulus is odd or dr != 0 use the montgomery method */
#ifdef BN_MP_EXPTMOD_FAST_C
  if (mp_isodd (P) == 1 || dr !=  0) {
    return mp_exptmod_fast (G, X, P, Y, dr);
  } else {
#endif
#ifdef BN_S_MP_EXPTMOD_C
    /* otherwise use the generic Barrett reduction technique */
    return s_mp_exptmod (G, X, P, Y, 0);
#else
................................................................................
#endif
#ifdef BN_MP_EXPTMOD_FAST_C
  }
#endif
}

#endif

#include <tommath_private.h>
#ifdef BN_MP_EXPTMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */


/* this is a shell function that calls either the normal or Montgomery
 * exptmod functions.  Originally the call to the montgomery code was
 * embedded in the normal function but that wasted alot of stack space
 * for nothing (since 99% of the time the Montgomery code would be called)
................................................................................
  if (dr == 0) {
     dr = mp_reduce_is_2k(P) << 1;
  }
#endif
    
  /* if the modulus is odd or dr != 0 use the montgomery method */
#ifdef BN_MP_EXPTMOD_FAST_C
  if ((mp_isodd (P) == MP_YES) || (dr !=  0)) {
    return mp_exptmod_fast (G, X, P, Y, dr);
  } else {
#endif
#ifdef BN_S_MP_EXPTMOD_C
    /* otherwise use the generic Barrett reduction technique */
    return s_mp_exptmod (G, X, P, Y, 0);
#else
................................................................................
#endif
#ifdef BN_MP_EXPTMOD_FAST_C
  }
#endif
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_EXPTMOD_FAST_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
 *
 * Uses a left-to-right k-ary sliding window to compute the modular exponentiation.
 * The value of k changes based on the size of the exponent.
 *
................................................................................
#else
     err = MP_VAL;
     goto LBL_M;
#endif

     /* automatically pick the comba one if available (saves quite a few calls/ifs) */
#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
     if (((P->used * 2 + 1) < MP_WARRAY) &&
          P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
        redux = fast_mp_montgomery_reduce;
     } else 
#endif
     {
#ifdef BN_MP_MONTGOMERY_REDUCE_C
        /* use slower baseline Montgomery method */
        redux = mp_montgomery_reduce;
................................................................................
    buf <<= (mp_digit)1;

    /* if the bit is zero and mode == 0 then we ignore it
     * These represent the leading zero bits before the first 1 bit
     * in the exponent.  Technically this opt is not required but it
     * does lower the # of trivial squaring/reductions used
     */
    if (mode == 0 && y == 0) {
      continue;
    }

    /* if the bit is zero and mode == 1 then we square */
    if (mode == 1 && y == 0) {
      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
        goto LBL_RES;
      }
      if ((err = redux (&res, P, mp)) != MP_OKAY) {
        goto LBL_RES;
      }
      continue;
................................................................................
      bitcpy = 0;
      bitbuf = 0;
      mode   = 1;
    }
  }

  /* if bits remain then square/multiply */
  if (mode == 2 && bitcpy > 0) {
    /* square then multiply if the bit is set */
    for (x = 0; x < bitcpy; x++) {
      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
        goto LBL_RES;
      }
      if ((err = redux (&res, P, mp)) != MP_OKAY) {
        goto LBL_RES;
................................................................................
  mp_clear(&M[1]);
  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
    mp_clear (&M[x]);
  }
  return err;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_EXPTMOD_FAST_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
 *
 * Uses a left-to-right k-ary sliding window to compute the modular exponentiation.
 * The value of k changes based on the size of the exponent.
 *
................................................................................
#else
     err = MP_VAL;
     goto LBL_M;
#endif

     /* automatically pick the comba one if available (saves quite a few calls/ifs) */
#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
     if ((((P->used * 2) + 1) < MP_WARRAY) &&
          (P->used < (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) {
        redux = fast_mp_montgomery_reduce;
     } else 
#endif
     {
#ifdef BN_MP_MONTGOMERY_REDUCE_C
        /* use slower baseline Montgomery method */
        redux = mp_montgomery_reduce;
................................................................................
    buf <<= (mp_digit)1;

    /* if the bit is zero and mode == 0 then we ignore it
     * These represent the leading zero bits before the first 1 bit
     * in the exponent.  Technically this opt is not required but it
     * does lower the # of trivial squaring/reductions used
     */
    if ((mode == 0) && (y == 0)) {
      continue;
    }

    /* if the bit is zero and mode == 1 then we square */
    if ((mode == 1) && (y == 0)) {
      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
        goto LBL_RES;
      }
      if ((err = redux (&res, P, mp)) != MP_OKAY) {
        goto LBL_RES;
      }
      continue;
................................................................................
      bitcpy = 0;
      bitbuf = 0;
      mode   = 1;
    }
  }

  /* if bits remain then square/multiply */
  if ((mode == 2) && (bitcpy > 0)) {
    /* square then multiply if the bit is set */
    for (x = 0; x < bitcpy; x++) {
      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
        goto LBL_RES;
      }
      if ((err = redux (&res, P, mp)) != MP_OKAY) {
        goto LBL_RES;
................................................................................
  mp_clear(&M[1]);
  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
    mp_clear (&M[x]);
  }
  return err;
}
#endif


/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_EXTEUCLID_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* Extended euclidean algorithm of (a, b) produces 
   a*u1 + b*u2 = u3
 */
int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
{
   mp_int u1,u2,u3,v1,v2,v3,t1,t2,t3,q,tmp;
   int err;

................................................................................
       if ((err = mp_copy(&t1, &v1)) != MP_OKAY)                                  { goto _ERR; }
       if ((err = mp_copy(&t2, &v2)) != MP_OKAY)                                  { goto _ERR; }
       if ((err = mp_copy(&t3, &v3)) != MP_OKAY)                                  { goto _ERR; }
   }

   /* make sure U3 >= 0 */
   if (u3.sign == MP_NEG) {
      mp_neg(&u1, &u1);
      mp_neg(&u2, &u2);
      mp_neg(&u3, &u3);
   }

   /* copy result out */
   if (U1 != NULL) { mp_exch(U1, &u1); }
   if (U2 != NULL) { mp_exch(U2, &u2); }
   if (U3 != NULL) { mp_exch(U3, &u3); }

   err = MP_OKAY;
_ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
   return err;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_EXTEUCLID_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* Extended euclidean algorithm of (a, b) produces
   a*u1 + b*u2 = u3
 */
int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
{
   mp_int u1,u2,u3,v1,v2,v3,t1,t2,t3,q,tmp;
   int err;

................................................................................
       if ((err = mp_copy(&t1, &v1)) != MP_OKAY)                                  { goto _ERR; }
       if ((err = mp_copy(&t2, &v2)) != MP_OKAY)                                  { goto _ERR; }
       if ((err = mp_copy(&t3, &v3)) != MP_OKAY)                                  { goto _ERR; }
   }

   /* make sure U3 >= 0 */
   if (u3.sign == MP_NEG) {
       if ((err = mp_neg(&u1, &u1)) != MP_OKAY)                                   { goto _ERR; }
       if ((err = mp_neg(&u2, &u2)) != MP_OKAY)                                   { goto _ERR; }
       if ((err = mp_neg(&u3, &u3)) != MP_OKAY)                                   { goto _ERR; }
   }

   /* copy result out */
   if (U1 != NULL) { mp_exch(U1, &u1); }
   if (U2 != NULL) { mp_exch(U2, &u2); }
   if (U3 != NULL) { mp_exch(U3, &u3); }

   err = MP_OKAY;
_ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
   return err;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_FREAD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* read a bigint from a file stream in ASCII */
int mp_fread(mp_int *a, int radix, FILE *stream)
{
   int err, ch, neg, y;
   
................................................................................
      a->sign = neg;
   }
   
   return MP_OKAY;
}

#endif

#include <tommath_private.h>
#ifdef BN_MP_FREAD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* read a bigint from a file stream in ASCII */
int mp_fread(mp_int *a, int radix, FILE *stream)
{
   int err, ch, neg, y;
   
................................................................................
      a->sign = neg;
   }
   
   return MP_OKAY;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_FWRITE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

int mp_fwrite(mp_int *a, int radix, FILE *stream)
{
   char *buf;
   int err, len, x;
   
................................................................................
   }
   
   XFREE (buf);
   return MP_OKAY;
}

#endif

#include <tommath_private.h>
#ifdef BN_MP_FWRITE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

int mp_fwrite(mp_int *a, int radix, FILE *stream)
{
   char *buf;
   int err, len, x;
   
................................................................................
   }
   
   XFREE (buf);
   return MP_OKAY;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_GCD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* Greatest Common Divisor using the binary method */
int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int  u, v;
  int     k, u_lsb, v_lsb, res;
................................................................................

  if (v_lsb != k) {
     if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) {
        goto LBL_V;
     }
  }

  while (mp_iszero(&v) == 0) {
     /* make sure v is the largest */
     if (mp_cmp_mag(&u, &v) == MP_GT) {
        /* swap u and v to make sure v is >= u */
        mp_exch(&u, &v);
     }
     
     /* subtract smallest from largest */
................................................................................
  c->sign = MP_ZPOS;
  res = MP_OKAY;
LBL_V:mp_clear (&u);
LBL_U:mp_clear (&v);
  return res;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_GCD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* Greatest Common Divisor using the binary method */
int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int  u, v;
  int     k, u_lsb, v_lsb, res;
................................................................................

  if (v_lsb != k) {
     if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) {
        goto LBL_V;
     }
  }

  while (mp_iszero(&v) == MP_NO) {
     /* make sure v is the largest */
     if (mp_cmp_mag(&u, &v) == MP_GT) {
        /* swap u and v to make sure v is >= u */
        mp_exch(&u, &v);
     }
     
     /* subtract smallest from largest */
................................................................................
  c->sign = MP_ZPOS;
  res = MP_OKAY;
LBL_V:mp_clear (&u);
LBL_U:mp_clear (&v);
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_GET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* get the lower 32-bits of an mp_int */
unsigned long mp_get_int(mp_int * a) 
{
  int i;
  unsigned long res;

  if (a->used == 0) {
     return 0;
  }

  /* get number of digits of the lsb we have to read */
  i = MIN(a->used,(int)((sizeof(unsigned long)*CHAR_BIT+DIGIT_BIT-1)/DIGIT_BIT))-1;

  /* get most significant digit of result */
  res = DIGIT(a,i);
   
  while (--i >= 0) {
    res = (res << DIGIT_BIT) | DIGIT(a,i);
  }

  /* force result to 32-bits always so it is consistent on non 32-bit platforms */
  return res & 0xFFFFFFFFUL;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_GET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* get the lower 32-bits of an mp_int */
unsigned long mp_get_int(mp_int * a)
{
  int i;
  mp_min_u32 res;

  if (a->used == 0) {
     return 0;
  }

  /* get number of digits of the lsb we have to read */
  i = MIN(a->used,(int)(((sizeof(unsigned long) * CHAR_BIT) + DIGIT_BIT - 1) / DIGIT_BIT)) - 1;

  /* get most significant digit of result */
  res = DIGIT(a,i);

  while (--i >= 0) {
    res = (res << DIGIT_BIT) | DIGIT(a,i);
  }

  /* force result to 32-bits always so it is consistent on non 32-bit platforms */
  return res & 0xFFFFFFFFUL;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_GROW_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* grow as required */
int mp_grow (mp_int * a, int size)
{
  int     i;
  mp_digit *tmp;
................................................................................
    for (; i < a->alloc; i++) {
      a->dp[i] = 0;
    }
  }
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_GROW_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* grow as required */
int mp_grow (mp_int * a, int size)
{
  int     i;
  mp_digit *tmp;
................................................................................
    for (; i < a->alloc; i++) {
      a->dp[i] = 0;
    }
  }
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_INIT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* init a new mp_int */
int mp_init (mp_int * a)
{
  int i;

................................................................................
  a->used  = 0;
  a->alloc = MP_PREC;
  a->sign  = MP_ZPOS;

  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_INIT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* init a new mp_int */
int mp_init (mp_int * a)
{
  int i;

................................................................................
  a->used  = 0;
  a->alloc = MP_PREC;
  a->sign  = MP_ZPOS;

  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_INIT_COPY_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* creates "a" then copies b into it */
int mp_init_copy (mp_int * a, mp_int * b)
{
  int     res;

  if ((res = mp_init (a)) != MP_OKAY) {
    return res;
  }
  return mp_copy (b, a);
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_INIT_COPY_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* creates "a" then copies b into it */
int mp_init_copy (mp_int * a, mp_int * b)
{
  int     res;

  if ((res = mp_init_size (a, b->used)) != MP_OKAY) {
    return res;
  }
  return mp_copy (b, a);
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_INIT_MULTI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */
#include <stdarg.h>

int mp_init_multi(mp_int *mp, ...) 
{
    mp_err res = MP_OKAY;      /* Assume ok until proven otherwise */
    int n = 0;                 /* Number of ok inits */
................................................................................
            
            /* end the current list */
            va_end(args);
            
            /* now start cleaning up */            
            cur_arg = mp;
            va_start(clean_args, mp);
            while (n--) {
                mp_clear(cur_arg);
                cur_arg = va_arg(clean_args, mp_int*);
            }
            va_end(clean_args);
            res = MP_MEM;
            break;
        }
................................................................................
        cur_arg = va_arg(args, mp_int*);
    }
    va_end(args);
    return res;                /* Assumed ok, if error flagged above. */
}

#endif

#include <tommath_private.h>
#ifdef BN_MP_INIT_MULTI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */
#include <stdarg.h>

int mp_init_multi(mp_int *mp, ...) 
{
    mp_err res = MP_OKAY;      /* Assume ok until proven otherwise */
    int n = 0;                 /* Number of ok inits */
................................................................................
            
            /* end the current list */
            va_end(args);
            
            /* now start cleaning up */            
            cur_arg = mp;
            va_start(clean_args, mp);
            while (n-- != 0) {
                mp_clear(cur_arg);
                cur_arg = va_arg(clean_args, mp_int*);
            }
            va_end(clean_args);
            res = MP_MEM;
            break;
        }
................................................................................
        cur_arg = va_arg(args, mp_int*);
    }
    va_end(args);
    return res;                /* Assumed ok, if error flagged above. */
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_INIT_SET_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* initialize and set a digit */
int mp_init_set (mp_int * a, mp_digit b)
{
  int err;
  if ((err = mp_init(a)) != MP_OKAY) {
     return err;
  }
  mp_set(a, b);
  return err;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_INIT_SET_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* initialize and set a digit */
int mp_init_set (mp_int * a, mp_digit b)
{
  int err;
  if ((err = mp_init(a)) != MP_OKAY) {
     return err;
  }
  mp_set(a, b);
  return err;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_INIT_SET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* initialize and set a digit */
int mp_init_set_int (mp_int * a, unsigned long b)
{
  int err;
  if ((err = mp_init(a)) != MP_OKAY) {
     return err;
  }
  return mp_set_int(a, b);
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_INIT_SET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* initialize and set a digit */
int mp_init_set_int (mp_int * a, unsigned long b)
{
  int err;
  if ((err = mp_init(a)) != MP_OKAY) {
     return err;
  }
  return mp_set_int(a, b);
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_INIT_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* init an mp_init for a given size */
int mp_init_size (mp_int * a, int size)
{
  int x;

................................................................................
  for (x = 0; x < size; x++) {
      a->dp[x] = 0;
  }

  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_INIT_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* init an mp_init for a given size */
int mp_init_size (mp_int * a, int size)
{
  int x;

................................................................................
  for (x = 0; x < size; x++) {
      a->dp[x] = 0;
  }

  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_INVMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* hac 14.61, pp608 */
int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
{
  /* b cannot be negative */
  if (b->sign == MP_NEG || mp_iszero(b) == 1) {
    return MP_VAL;
  }

#ifdef BN_FAST_MP_INVMOD_C
  /* if the modulus is odd we can use a faster routine instead */
  if (mp_isodd (b) == 1) {
    return fast_mp_invmod (a, b, c);
  }
#endif

#ifdef BN_MP_INVMOD_SLOW_C
  return mp_invmod_slow(a, b, c);
#endif

  return MP_VAL;

}
#endif

#include <tommath_private.h>
#ifdef BN_MP_INVMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* hac 14.61, pp608 */
int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
{
  /* b cannot be negative */
  if ((b->sign == MP_NEG) || (mp_iszero(b) == MP_YES)) {
    return MP_VAL;
  }

#ifdef BN_FAST_MP_INVMOD_C
  /* if the modulus is odd we can use a faster routine instead */
  if (mp_isodd (b) == MP_YES) {
    return fast_mp_invmod (a, b, c);
  }
#endif

#ifdef BN_MP_INVMOD_SLOW_C
  return mp_invmod_slow(a, b, c);
#else

  return MP_VAL;
#endif
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_INVMOD_SLOW_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* hac 14.61, pp608 */
int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int  x, y, u, v, A, B, C, D;
  int     res;

  /* b cannot be negative */
  if (b->sign == MP_NEG || mp_iszero(b) == 1) {
    return MP_VAL;
  }

  /* init temps */
  if ((res = mp_init_multi(&x, &y, &u, &v, 
                           &A, &B, &C, &D, NULL)) != MP_OKAY) {
     return res;
................................................................................
      goto LBL_ERR;
  }
  if ((res = mp_copy (b, &y)) != MP_OKAY) {
    goto LBL_ERR;
  }

  /* 2. [modified] if x,y are both even then return an error! */
  if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
    res = MP_VAL;
    goto LBL_ERR;
  }

  /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
  if ((res = mp_copy (&x, &u)) != MP_OKAY) {
    goto LBL_ERR;
................................................................................
    goto LBL_ERR;
  }
  mp_set (&A, 1);
  mp_set (&D, 1);

top:
  /* 4.  while u is even do */
  while (mp_iseven (&u) == 1) {
    /* 4.1 u = u/2 */
    if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
      goto LBL_ERR;
    }
    /* 4.2 if A or B is odd then */
    if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) {
      /* A = (A+y)/2, B = (B-x)/2 */
      if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
         goto LBL_ERR;
      }
      if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
         goto LBL_ERR;
      }
................................................................................
    }
    if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* 5.  while v is even do */
  while (mp_iseven (&v) == 1) {
    /* 5.1 v = v/2 */
    if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
      goto LBL_ERR;
    }
    /* 5.2 if C or D is odd then */
    if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) {
      /* C = (C+y)/2, D = (D-x)/2 */
      if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
         goto LBL_ERR;
      }
      if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
         goto LBL_ERR;
      }
................................................................................

    if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* if not zero goto step 4 */
  if (mp_iszero (&u) == 0)
    goto top;

  /* now a = C, b = D, gcd == g*v */

  /* if v != 1 then there is no inverse */
  if (mp_cmp_d (&v, 1) != MP_EQ) {
    res = MP_VAL;
................................................................................
  /* C is now the inverse */
  mp_exch (&C, c);
  res = MP_OKAY;
LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
  return res;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_INVMOD_SLOW_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* hac 14.61, pp608 */
int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int  x, y, u, v, A, B, C, D;
  int     res;

  /* b cannot be negative */
  if ((b->sign == MP_NEG) || (mp_iszero(b) == MP_YES)) {
    return MP_VAL;
  }

  /* init temps */
  if ((res = mp_init_multi(&x, &y, &u, &v, 
                           &A, &B, &C, &D, NULL)) != MP_OKAY) {
     return res;
................................................................................
      goto LBL_ERR;
  }
  if ((res = mp_copy (b, &y)) != MP_OKAY) {
    goto LBL_ERR;
  }

  /* 2. [modified] if x,y are both even then return an error! */
  if ((mp_iseven (&x) == MP_YES) && (mp_iseven (&y) == MP_YES)) {
    res = MP_VAL;
    goto LBL_ERR;
  }

  /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
  if ((res = mp_copy (&x, &u)) != MP_OKAY) {
    goto LBL_ERR;
................................................................................
    goto LBL_ERR;
  }
  mp_set (&A, 1);
  mp_set (&D, 1);

top:
  /* 4.  while u is even do */
  while (mp_iseven (&u) == MP_YES) {
    /* 4.1 u = u/2 */
    if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
      goto LBL_ERR;
    }
    /* 4.2 if A or B is odd then */
    if ((mp_isodd (&A) == MP_YES) || (mp_isodd (&B) == MP_YES)) {
      /* A = (A+y)/2, B = (B-x)/2 */
      if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
         goto LBL_ERR;
      }
      if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
         goto LBL_ERR;
      }
................................................................................
    }
    if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* 5.  while v is even do */
  while (mp_iseven (&v) == MP_YES) {
    /* 5.1 v = v/2 */
    if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
      goto LBL_ERR;
    }
    /* 5.2 if C or D is odd then */
    if ((mp_isodd (&C) == MP_YES) || (mp_isodd (&D) == MP_YES)) {
      /* C = (C+y)/2, D = (D-x)/2 */
      if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
         goto LBL_ERR;
      }
      if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
         goto LBL_ERR;
      }
................................................................................

    if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* if not zero goto step 4 */
  if (mp_iszero (&u) == MP_NO)
    goto top;

  /* now a = C, b = D, gcd == g*v */

  /* if v != 1 then there is no inverse */
  if (mp_cmp_d (&v, 1) != MP_EQ) {
    res = MP_VAL;
................................................................................
  /* C is now the inverse */
  mp_exch (&C, c);
  res = MP_OKAY;
LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_IS_SQUARE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* Check if remainders are possible squares - fast exclude non-squares */
static const char rem_128[128] = {
 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
................................................................................
     goto ERR;
  }
  r = mp_get_int(&t);
  /* Check for other prime modules, note it's not an ERROR but we must
   * free "t" so the easiest way is to goto ERR.  We know that res
   * is already equal to MP_OKAY from the mp_mod call 
   */ 
  if ( (1L<<(r%11)) & 0x5C4L )             goto ERR;
  if ( (1L<<(r%13)) & 0x9E4L )             goto ERR;
  if ( (1L<<(r%17)) & 0x5CE8L )            goto ERR;
  if ( (1L<<(r%19)) & 0x4F50CL )           goto ERR;
  if ( (1L<<(r%23)) & 0x7ACCA0L )          goto ERR;
  if ( (1L<<(r%29)) & 0xC2EDD0CL )         goto ERR;
  if ( (1L<<(r%31)) & 0x6DE2B848L )        goto ERR;

  /* Final check - is sqr(sqrt(arg)) == arg ? */
  if ((res = mp_sqrt(arg,&t)) != MP_OKAY) {
     goto ERR;
  }
  if ((res = mp_sqr(&t,&t)) != MP_OKAY) {
     goto ERR;
................................................................................
  }

  *ret = (mp_cmp_mag(&t,arg) == MP_EQ) ? MP_YES : MP_NO;
ERR:mp_clear(&t);
  return res;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_IS_SQUARE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* Check if remainders are possible squares - fast exclude non-squares */
static const char rem_128[128] = {
 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
................................................................................
     goto ERR;
  }
  r = mp_get_int(&t);
  /* Check for other prime modules, note it's not an ERROR but we must
   * free "t" so the easiest way is to goto ERR.  We know that res
   * is already equal to MP_OKAY from the mp_mod call 
   */ 
  if (((1L<<(r%11)) & 0x5C4L) != 0L)       goto ERR;
  if (((1L<<(r%13)) & 0x9E4L) != 0L)       goto ERR;
  if (((1L<<(r%17)) & 0x5CE8L) != 0L)      goto ERR;
  if (((1L<<(r%19)) & 0x4F50CL) != 0L)     goto ERR;
  if (((1L<<(r%23)) & 0x7ACCA0L) != 0L)    goto ERR;
  if (((1L<<(r%29)) & 0xC2EDD0CL) != 0L)   goto ERR;
  if (((1L<<(r%31)) & 0x6DE2B848L) != 0L)  goto ERR;

  /* Final check - is sqr(sqrt(arg)) == arg ? */
  if ((res = mp_sqrt(arg,&t)) != MP_OKAY) {
     goto ERR;
  }
  if ((res = mp_sqr(&t,&t)) != MP_OKAY) {
     goto ERR;
................................................................................
  }

  *ret = (mp_cmp_mag(&t,arg) == MP_EQ) ? MP_YES : MP_NO;
ERR:mp_clear(&t);
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_JACOBI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* computes the jacobi c = (a | n) (or Legendre if n is prime)
 * HAC pp. 73 Algorithm 2.149


 */
int mp_jacobi (mp_int * a, mp_int * p, int *c)
{
  mp_int  a1, p1;
  int     k, s, r, res;
  mp_digit residue;






  /* if p <= 0 return MP_VAL */
  if (mp_cmp_d(p, 0) != MP_GT) {
     return MP_VAL;
  }

  /* step 1.  if a == 0, return 0 */
  if (mp_iszero (a) == 1) {




    *c = 0;

    return MP_OKAY;
  }

  /* step 2.  if a == 1, return 1 */
  if (mp_cmp_d (a, 1) == MP_EQ) {
    *c = 1;
    return MP_OKAY;
  }
................................................................................
  }

  /* step 4.  if e is even set s=1 */
  if ((k & 1) == 0) {
    s = 1;
  } else {
    /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
    residue = p->dp[0] & 7;

    if (residue == 1 || residue == 7) {
      s = 1;
    } else if (residue == 3 || residue == 5) {
      s = -1;
    }
  }

  /* step 5.  if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
  if ( ((p->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) {
    s = -s;
  }

  /* if a1 == 1 we're done */
  if (mp_cmp_d (&a1, 1) == MP_EQ) {
    *c = s;
  } else {
    /* n1 = n mod a1 */
    if ((res = mp_mod (p, &a1, &p1)) != MP_OKAY) {
      goto LBL_P1;
    }
    if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) {
      goto LBL_P1;
    }
    *c = s * r;
  }
................................................................................
  /* done */
  res = MP_OKAY;
LBL_P1:mp_clear (&p1);
LBL_A1:mp_clear (&a1);
  return res;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_JACOBI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* computes the jacobi c = (a | n) (or Legendre if n is prime)
 * HAC pp. 73 Algorithm 2.149
 * HAC is wrong here, as the special case of (0 | 1) is not
 * handled correctly.
 */
int mp_jacobi (mp_int * a, mp_int * n, int *c)
{
  mp_int  a1, p1;
  int     k, s, r, res;
  mp_digit residue;

  /* if a < 0 return MP_VAL */
  if (mp_isneg(a) == MP_YES) {
     return MP_VAL;
  }

  /* if n <= 0 return MP_VAL */
  if (mp_cmp_d(n, 0) != MP_GT) {
     return MP_VAL;
  }

  /* step 1. handle case of a == 0 */
  if (mp_iszero (a) == MP_YES) {
     /* special case of a == 0 and n == 1 */
     if (mp_cmp_d (n, 1) == MP_EQ) {
       *c = 1;
     } else {
       *c = 0;
     }
     return MP_OKAY;
  }

  /* step 2.  if a == 1, return 1 */
  if (mp_cmp_d (a, 1) == MP_EQ) {
    *c = 1;
    return MP_OKAY;
  }
................................................................................
  }

  /* step 4.  if e is even set s=1 */
  if ((k & 1) == 0) {
    s = 1;
  } else {
    /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
    residue = n->dp[0] & 7;

    if ((residue == 1) || (residue == 7)) {
      s = 1;
    } else if ((residue == 3) || (residue == 5)) {
      s = -1;
    }
  }

  /* step 5.  if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
  if ( ((n->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) {
    s = -s;
  }

  /* if a1 == 1 we're done */
  if (mp_cmp_d (&a1, 1) == MP_EQ) {
    *c = s;
  } else {
    /* n1 = n mod a1 */
    if ((res = mp_mod (n, &a1, &p1)) != MP_OKAY) {
      goto LBL_P1;
    }
    if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) {
      goto LBL_P1;
    }
    *c = s * r;
  }
................................................................................
  /* done */
  res = MP_OKAY;
LBL_P1:mp_clear (&p1);
LBL_A1:mp_clear (&a1);
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_KARATSUBA_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* c = |a| * |b| using Karatsuba Multiplication using 
 * three half size multiplications
 *
 * Let B represent the radix [e.g. 2**DIGIT_BIT] and 
 * let n represent half of the number of digits in 
................................................................................

  /* now shift the digits */
  x0.used = y0.used = B;
  x1.used = a->used - B;
  y1.used = b->used - B;

  {
    register int x;
    register mp_digit *tmpa, *tmpb, *tmpx, *tmpy;

    /* we copy the digits directly instead of using higher level functions
     * since we also need to shift the digits
     */
    tmpa = a->dp;
    tmpb = b->dp;

................................................................................
Y0:mp_clear (&y0);
X1:mp_clear (&x1);
X0:mp_clear (&x0);
ERR:
  return err;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_KARATSUBA_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* c = |a| * |b| using Karatsuba Multiplication using 
 * three half size multiplications
 *
 * Let B represent the radix [e.g. 2**DIGIT_BIT] and 
 * let n represent half of the number of digits in 
................................................................................

  /* now shift the digits */
  x0.used = y0.used = B;
  x1.used = a->used - B;
  y1.used = b->used - B;

  {
    int x;
    mp_digit *tmpa, *tmpb, *tmpx, *tmpy;

    /* we copy the digits directly instead of using higher level functions
     * since we also need to shift the digits
     */
    tmpa = a->dp;
    tmpb = b->dp;

................................................................................
Y0:mp_clear (&y0);
X1:mp_clear (&x1);
X0:mp_clear (&x0);
ERR:
  return err;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_KARATSUBA_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* Karatsuba squaring, computes b = a*a using three 
 * half size squarings
 *
 * See comments of karatsuba_mul for details.  It 
 * is essentially the same algorithm but merely 
................................................................................
    goto T1;
  if (mp_init_size (&x0x0, B * 2) != MP_OKAY)
    goto T2;
  if (mp_init_size (&x1x1, (a->used - B) * 2) != MP_OKAY)
    goto X0X0;

  {
    register int x;
    register mp_digit *dst, *src;

    src = a->dp;

    /* now shift the digits */
    dst = x0.dp;
    for (x = 0; x < B; x++) {
      *dst++ = *src++;
................................................................................
T1:mp_clear (&t1);
X1:mp_clear (&x1);
X0:mp_clear (&x0);
ERR:
  return err;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_KARATSUBA_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* Karatsuba squaring, computes b = a*a using three 
 * half size squarings
 *
 * See comments of karatsuba_mul for details.  It 
 * is essentially the same algorithm but merely 
................................................................................
    goto T1;
  if (mp_init_size (&x0x0, B * 2) != MP_OKAY)
    goto T2;
  if (mp_init_size (&x1x1, (a->used - B) * 2) != MP_OKAY)
    goto X0X0;

  {
    int x;
    mp_digit *dst, *src;

    src = a->dp;

    /* now shift the digits */
    dst = x0.dp;
    for (x = 0; x < B; x++) {
      *dst++ = *src++;
................................................................................
T1:mp_clear (&t1);
X1:mp_clear (&x1);
X0:mp_clear (&x0);
ERR:
  return err;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_LCM_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* computes least common multiple as |a*b|/(a, b) */
int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
{
  int     res;
  mp_int  t1, t2;
................................................................................
  c->sign = MP_ZPOS;

LBL_T:
  mp_clear_multi (&t1, &t2, NULL);
  return res;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_LCM_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* computes least common multiple as |a*b|/(a, b) */
int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
{
  int     res;
  mp_int  t1, t2;
................................................................................
  c->sign = MP_ZPOS;

LBL_T:
  mp_clear_multi (&t1, &t2, NULL);
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_LSHD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* shift left a certain amount of digits */
int mp_lshd (mp_int * a, int b)
{
  int     x, res;

  /* if its less than zero return */
  if (b <= 0) {
    return MP_OKAY;
  }

  /* grow to fit the new digits */
  if (a->alloc < a->used + b) {
     if ((res = mp_grow (a, a->used + b)) != MP_OKAY) {
       return res;
     }
  }

  {
    register mp_digit *top, *bottom;

    /* increment the used by the shift amount then copy upwards */
    a->used += b;

    /* top */
    top = a->dp + a->used - 1;

    /* base */
    bottom = a->dp + a->used - 1 - b;

    /* much like mp_rshd this is implemented using a sliding window
     * except the window goes the otherway around.  Copying from
     * the bottom to the top.  see bn_mp_rshd.c for more info.
     */
    for (x = a->used - 1; x >= b; x--) {
      *top-- = *bottom--;
................................................................................
    for (x = 0; x < b; x++) {
      *top++ = 0;
    }
  }
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_LSHD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* shift left a certain amount of digits */
int mp_lshd (mp_int * a, int b)
{
  int     x, res;

  /* if its less than zero return */
  if (b <= 0) {
    return MP_OKAY;
  }

  /* grow to fit the new digits */
  if (a->alloc < (a->used + b)) {
     if ((res = mp_grow (a, a->used + b)) != MP_OKAY) {
       return res;
     }
  }

  {
    mp_digit *top, *bottom;

    /* increment the used by the shift amount then copy upwards */
    a->used += b;

    /* top */
    top = a->dp + a->used - 1;

    /* base */
    bottom = (a->dp + a->used - 1) - b;

    /* much like mp_rshd this is implemented using a sliding window
     * except the window goes the otherway around.  Copying from
     * the bottom to the top.  see bn_mp_rshd.c for more info.
     */
    for (x = a->used - 1; x >= b; x--) {
      *top-- = *bottom--;
................................................................................
    for (x = 0; x < b; x++) {
      *top++ = 0;
    }
  }
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_MOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* c = a mod b, 0 <= c < b */
int
mp_mod (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int  t;
  int     res;

  if ((res = mp_init (&t)) != MP_OKAY) {
................................................................................
  }

  if ((res = mp_div (a, b, NULL, &t)) != MP_OKAY) {
    mp_clear (&t);
    return res;
  }

  if (t.sign != b->sign) {
    res = mp_add (b, &t, c);
  } else {
    res = MP_OKAY;
    mp_exch (&t, c);


  }

  mp_clear (&t);
  return res;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_MOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* c = a mod b, 0 <= c < b if b > 0, b < c <= 0 if b < 0 */
int
mp_mod (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int  t;
  int     res;

  if ((res = mp_init (&t)) != MP_OKAY) {
................................................................................
  }

  if ((res = mp_div (a, b, NULL, &t)) != MP_OKAY) {
    mp_clear (&t);
    return res;
  }

  if ((mp_iszero(&t) != MP_NO) || (t.sign == b->sign)) {


    res = MP_OKAY;
    mp_exch (&t, c);
  } else {
    res = mp_add (b, &t, c);
  }

  mp_clear (&t);
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_MOD_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* calc a value mod 2**b */
int
mp_mod_2d (const mp_int * a, int b, mp_int * c)
{
  int     x, res;
................................................................................

  /* copy */
  if ((res = mp_copy (a, c)) != MP_OKAY) {
    return res;
  }

  /* zero digits above the last digit of the modulus */
  for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++) {
    c->dp[x] = 0;
  }
  /* clear the digit that is not completely outside/inside the modulus */
  c->dp[b / DIGIT_BIT] &=
    (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1));
  mp_clamp (c);
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_MOD_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* calc a value mod 2**b */
int
mp_mod_2d (const mp_int * a, int b, mp_int * c)
{
  int     x, res;
................................................................................

  /* copy */
  if ((res = mp_copy (a, c)) != MP_OKAY) {
    return res;
  }

  /* zero digits above the last digit of the modulus */
  for (x = (b / DIGIT_BIT) + (((b % DIGIT_BIT) == 0) ? 0 : 1); x < c->used; x++) {
    c->dp[x] = 0;
  }
  /* clear the digit that is not completely outside/inside the modulus */
  c->dp[b / DIGIT_BIT] &=
    (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1));
  mp_clamp (c);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_MOD_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

int
mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
{
  return mp_div_d(a, b, NULL, c);
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_MOD_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

int
mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
{
  return mp_div_d(a, b, NULL, c);
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/*
 * shifts with subtractions when the result is greater than b.
 *
 * The method is slightly modified to shift B unconditionally upto just under
 * the leading bit of b.  This saves alot of multiple precision shifting.
................................................................................
{
  int     x, bits, res;

  /* how many bits of last digit does b use */
  bits = mp_count_bits (b) % DIGIT_BIT;

  if (b->used > 1) {
     if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
        return res;
     }
  } else {
     mp_set(a, 1);
     bits = 1;
  }

................................................................................
      }
    }
  }

  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/*
 * shifts with subtractions when the result is greater than b.
 *
 * The method is slightly modified to shift B unconditionally upto just under
 * the leading bit of b.  This saves alot of multiple precision shifting.
................................................................................
{
  int     x, bits, res;

  /* how many bits of last digit does b use */
  bits = mp_count_bits (b) % DIGIT_BIT;

  if (b->used > 1) {
     if ((res = mp_2expt (a, ((b->used - 1) * DIGIT_BIT) + bits - 1)) != MP_OKAY) {
        return res;
     }
  } else {
     mp_set(a, 1);
     bits = 1;
  }

................................................................................
      }
    }
  }

  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_MONTGOMERY_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* computes xR**-1 == x (mod N) via Montgomery Reduction */
int
mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
{
  int     ix, res, digs;
................................................................................

  /* can the fast reduction [comba] method be used?
   *
   * Note that unlike in mul you're safely allowed *less*
   * than the available columns [255 per default] since carries
   * are fixed up in the inner loop.
   */
  digs = n->used * 2 + 1;
  if ((digs < MP_WARRAY) &&
      n->used <
      (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
    return fast_mp_montgomery_reduce (x, n, rho);
  }

  /* grow the input as required */
  if (x->alloc < digs) {
    if ((res = mp_grow (x, digs)) != MP_OKAY) {
      return res;
................................................................................
     *
     * The value of rho must be precalculated via
     * montgomery_setup() such that
     * it equals -1/n0 mod b this allows the
     * following inner loop to reduce the
     * input one digit at a time
     */
    mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK);

    /* a = a + mu * m * b**i */
    {
      register int iy;
      register mp_digit *tmpn, *tmpx, u;
      register mp_word r;

      /* alias for digits of the modulus */
      tmpn = n->dp;

      /* alias for the digits of x [the input] */
      tmpx = x->dp + ix;

      /* set the carry to zero */
      u = 0;

      /* Multiply and add in place */
      for (iy = 0; iy < n->used; iy++) {
        /* compute product and sum */
        r       = ((mp_word)mu) * ((mp_word)*tmpn++) +
                  ((mp_word) u) + ((mp_word) * tmpx);

        /* get carry */
        u       = (mp_digit)(r >> ((mp_word) DIGIT_BIT));

        /* fix digit */
        *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
      }
      /* At this point the ix'th digit of x should be zero */


      /* propagate carries upwards as required*/
      while (u) {
        *tmpx   += u;
        u        = *tmpx >> DIGIT_BIT;
        *tmpx++ &= MP_MASK;
      }
    }
  }

................................................................................
  if (mp_cmp_mag (x, n) != MP_LT) {
    return s_mp_sub (x, n, x);
  }

  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_MONTGOMERY_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* computes xR**-1 == x (mod N) via Montgomery Reduction */
int
mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
{
  int     ix, res, digs;
................................................................................

  /* can the fast reduction [comba] method be used?
   *
   * Note that unlike in mul you're safely allowed *less*
   * than the available columns [255 per default] since carries
   * are fixed up in the inner loop.
   */
  digs = (n->used * 2) + 1;
  if ((digs < MP_WARRAY) &&
      (n->used <
      (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) {
    return fast_mp_montgomery_reduce (x, n, rho);
  }

  /* grow the input as required */
  if (x->alloc < digs) {
    if ((res = mp_grow (x, digs)) != MP_OKAY) {
      return res;
................................................................................
     *
     * The value of rho must be precalculated via
     * montgomery_setup() such that
     * it equals -1/n0 mod b this allows the
     * following inner loop to reduce the
     * input one digit at a time
     */
    mu = (mp_digit) (((mp_word)x->dp[ix] * (mp_word)rho) & MP_MASK);

    /* a = a + mu * m * b**i */
    {
      int iy;
      mp_digit *tmpn, *tmpx, u;
      mp_word r;

      /* alias for digits of the modulus */
      tmpn = n->dp;

      /* alias for the digits of x [the input] */
      tmpx = x->dp + ix;

      /* set the carry to zero */
      u = 0;

      /* Multiply and add in place */
      for (iy = 0; iy < n->used; iy++) {
        /* compute product and sum */
        r       = ((mp_word)mu * (mp_word)*tmpn++) +
                   (mp_word) u + (mp_word) *tmpx;

        /* get carry */
        u       = (mp_digit)(r >> ((mp_word) DIGIT_BIT));

        /* fix digit */
        *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
      }
      /* At this point the ix'th digit of x should be zero */


      /* propagate carries upwards as required*/
      while (u != 0) {
        *tmpx   += u;
        u        = *tmpx >> DIGIT_BIT;
        *tmpx++ &= MP_MASK;
      }
    }
  }

................................................................................
  if (mp_cmp_mag (x, n) != MP_LT) {
    return s_mp_sub (x, n, x);
  }

  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_MONTGOMERY_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* setups the montgomery reduction stuff */
int
mp_montgomery_setup (mp_int * n, mp_digit * rho)
{
  mp_digit x, b;
................................................................................
  b = n->dp[0];

  if ((b & 1) == 0) {
    return MP_VAL;
  }

  x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
  x *= 2 - b * x;               /* here x*a==1 mod 2**8 */
#if !defined(MP_8BIT)
  x *= 2 - b * x;               /* here x*a==1 mod 2**16 */
#endif
#if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
  x *= 2 - b * x;               /* here x*a==1 mod 2**32 */
#endif
#ifdef MP_64BIT
  x *= 2 - b * x;               /* here x*a==1 mod 2**64 */
#endif

  /* rho = -1/m mod b */
  *rho = (unsigned long)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;

  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_MONTGOMERY_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* setups the montgomery reduction stuff */
int
mp_montgomery_setup (mp_int * n, mp_digit * rho)
{
  mp_digit x, b;
................................................................................
  b = n->dp[0];

  if ((b & 1) == 0) {
    return MP_VAL;
  }

  x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
  x *= 2 - (b * x);             /* here x*a==1 mod 2**8 */
#if !defined(MP_8BIT)
  x *= 2 - (b * x);             /* here x*a==1 mod 2**16 */
#endif
#if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
  x *= 2 - (b * x);             /* here x*a==1 mod 2**32 */
#endif
#ifdef MP_64BIT
  x *= 2 - (b * x);             /* here x*a==1 mod 2**64 */
#endif

  /* rho = -1/m mod b */
  *rho = (mp_digit)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;

  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* high level multiplication (handles sign) */
int mp_mul (mp_int * a, mp_int * b, mp_int * c)
{
  int     res, neg;
  neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
................................................................................
     * have less than MP_WARRAY digits and the number of 
     * digits won't affect carry propagation
     */
    int     digs = a->used + b->used + 1;

#ifdef BN_FAST_S_MP_MUL_DIGS_C
    if ((digs < MP_WARRAY) &&
        MIN(a->used, b->used) <= 
        (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
      res = fast_s_mp_mul_digs (a, b, c, digs);
    } else 
#endif

#ifdef BN_S_MP_MUL_DIGS_C
      res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
#else
      res = MP_VAL;
#endif

  }
  c->sign = (c->used > 0) ? neg : MP_ZPOS;
  return res;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* high level multiplication (handles sign) */
int mp_mul (mp_int * a, mp_int * b, mp_int * c)
{
  int     res, neg;
  neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
................................................................................
     * have less than MP_WARRAY digits and the number of 
     * digits won't affect carry propagation
     */
    int     digs = a->used + b->used + 1;

#ifdef BN_FAST_S_MP_MUL_DIGS_C
    if ((digs < MP_WARRAY) &&
        (MIN(a->used, b->used) <= 
         (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) {
      res = fast_s_mp_mul_digs (a, b, c, digs);
    } else 
#endif
    {
#ifdef BN_S_MP_MUL_DIGS_C
      res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
#else
      res = MP_VAL;
#endif
    }
  }
  c->sign = (c->used > 0) ? neg : MP_ZPOS;
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_MUL_2_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* b = a*2 */
int mp_mul_2(mp_int * a, mp_int * b)
{
  int     x, res, oldused;

  /* grow to accomodate result */
  if (b->alloc < a->used + 1) {
    if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) {
      return res;
    }
  }

  oldused = b->used;
  b->used = a->used;

  {
    register mp_digit r, rr, *tmpa, *tmpb;

    /* alias for source */
    tmpa = a->dp;
    
    /* alias for dest */
    tmpb = b->dp;

................................................................................
      *tmpb++ = 0;
    }
  }
  b->sign = a->sign;
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_MUL_2_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* b = a*2 */
int mp_mul_2(mp_int * a, mp_int * b)
{
  int     x, res, oldused;

  /* grow to accomodate result */
  if (b->alloc < (a->used + 1)) {
    if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) {
      return res;
    }
  }

  oldused = b->used;
  b->used = a->used;

  {
    mp_digit r, rr, *tmpa, *tmpb;

    /* alias for source */
    tmpa = a->dp;
    
    /* alias for dest */
    tmpb = b->dp;

................................................................................
      *tmpb++ = 0;
    }
  }
  b->sign = a->sign;
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_MUL_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* shift left by a certain bit count */
int mp_mul_2d (const mp_int * a, int b, mp_int * c)
{
  mp_digit d;
  int      res;
................................................................................
  /* copy */
  if (a != c) {
     if ((res = mp_copy (a, c)) != MP_OKAY) {
       return res;
     }
  }

  if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) {
     if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) {
       return res;
     }
  }

  /* shift by as many digits in the bit count */
  if (b >= (int)DIGIT_BIT) {
    if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) {
................................................................................
      return res;
    }
  }

  /* shift any bit count < DIGIT_BIT */
  d = (mp_digit) (b % DIGIT_BIT);
  if (d != 0) {
    register mp_digit *tmpc, shift, mask, r, rr;
    register int x;

    /* bitmask for carries */
    mask = (((mp_digit)1) << d) - 1;

    /* shift for msbs */
    shift = DIGIT_BIT - d;

................................................................................
       c->dp[(c->used)++] = r;
    }
  }
  mp_clamp (c);
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_MUL_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* shift left by a certain bit count */
int mp_mul_2d (const mp_int * a, int b, mp_int * c)
{
  mp_digit d;
  int      res;
................................................................................
  /* copy */
  if (a != c) {
     if ((res = mp_copy (a, c)) != MP_OKAY) {
       return res;
     }
  }

  if (c->alloc < (int)(c->used + (b / DIGIT_BIT) + 1)) {
     if ((res = mp_grow (c, c->used + (b / DIGIT_BIT) + 1)) != MP_OKAY) {
       return res;
     }
  }

  /* shift by as many digits in the bit count */
  if (b >= (int)DIGIT_BIT) {
    if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) {
................................................................................
      return res;
    }
  }

  /* shift any bit count < DIGIT_BIT */
  d = (mp_digit) (b % DIGIT_BIT);
  if (d != 0) {
    mp_digit *tmpc, shift, mask, r, rr;
    int x;

    /* bitmask for carries */
    mask = (((mp_digit)1) << d) - 1;

    /* shift for msbs */
    shift = DIGIT_BIT - d;

................................................................................
       c->dp[(c->used)++] = r;
    }
  }
  mp_clamp (c);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_MUL_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* multiply by a digit */
int
mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
{
  mp_digit u, *tmpa, *tmpc;
  mp_word  r;
  int      ix, res, olduse;

  /* make sure c is big enough to hold a*b */
  if (c->alloc < a->used + 1) {
    if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) {
      return res;
    }
  }

  /* get the original destinations used count */
  olduse = c->used;
................................................................................

  /* zero carry */
  u = 0;

  /* compute columns */
  for (ix = 0; ix < a->used; ix++) {
    /* compute product and carry sum for this term */
    r       = ((mp_word) u) + ((mp_word)*tmpa++) * ((mp_word)b);

    /* mask off higher bits to get a single digit */
    *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));

    /* send carry into next iteration */
    u       = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
  }
................................................................................
  /* set used count */
  c->used = a->used + 1;
  mp_clamp(c);

  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_MUL_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* multiply by a digit */
int
mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
{
  mp_digit u, *tmpa, *tmpc;
  mp_word  r;
  int      ix, res, olduse;

  /* make sure c is big enough to hold a*b */
  if (c->alloc < (a->used + 1)) {
    if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) {
      return res;
    }
  }

  /* get the original destinations used count */
  olduse = c->used;
................................................................................

  /* zero carry */
  u = 0;

  /* compute columns */
  for (ix = 0; ix < a->used; ix++) {
    /* compute product and carry sum for this term */
    r       = (mp_word)u + ((mp_word)*tmpa++ * (mp_word)b);

    /* mask off higher bits to get a single digit */
    *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));

    /* send carry into next iteration */
    u       = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
  }
................................................................................
  /* set used count */
  c->used = a->used + 1;
  mp_clamp(c);

  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_MULMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* d = a * b (mod c) */
int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
  int     res;
  mp_int  t;
................................................................................
    return res;
  }
  res = mp_mod (&t, c, d);
  mp_clear (&t);
  return res;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_MULMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* d = a * b (mod c) */
int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
  int     res;
  mp_int  t;
................................................................................
    return res;
  }
  res = mp_mod (&t, c, d);
  mp_clear (&t);
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_N_ROOT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* find the n'th root of an integer 
 *
 * Result found such that (c)**b <= a and (c+1)**b > a 
 *
 * This algorithm uses Newton's approximation 
 * x[i+1] = x[i] - f(x[i])/f'(x[i]) 
 * which will find the root in log(N) time where 
 * each step involves a fair bit.  This is not meant to 
 * find huge roots [square and cube, etc].
 */
int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
{
  mp_int  t1, t2, t3;
  int     res, neg;

  /* input must be positive if b is even */
  if ((b & 1) == 0 && a->sign == MP_NEG) {
    return MP_VAL;
  }

  if ((res = mp_init (&t1)) != MP_OKAY) {
    return res;
  }

  if ((res = mp_init (&t2)) != MP_OKAY) {
    goto LBL_T1;
  }

  if ((res = mp_init (&t3)) != MP_OKAY) {
    goto LBL_T2;
  }

  /* if a is negative fudge the sign but keep track */
  neg     = a->sign;
  a->sign = MP_ZPOS;

  /* t2 = 2 */
  mp_set (&t2, 2);

  do {
    /* t1 = t2 */
    if ((res = mp_copy (&t2, &t1)) != MP_OKAY) {
      goto LBL_T3;
    }

    /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
    
    /* t3 = t1**(b-1) */
    if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) {   
      goto LBL_T3;
    }

    /* numerator */
    /* t2 = t1**b */
    if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) {    
      goto LBL_T3;
    }

    /* t2 = t1**b - a */
    if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) {  
      goto LBL_T3;
    }

    /* denominator */
    /* t3 = t1**(b-1) * b  */
    if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) {    
      goto LBL_T3;
    }

    /* t3 = (t1**b - a)/(b * t1**(b-1)) */
    if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) {  
      goto LBL_T3;
    }

    if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) {
      goto LBL_T3;
    }
  }  while (mp_cmp (&t1, &t2) != MP_EQ);

  /* result can be off by a few so check */
  for (;;) {
    if ((res = mp_expt_d (&t1, b, &t2)) != MP_OKAY) {
      goto LBL_T3;
    }

    if (mp_cmp (&t2, a) == MP_GT) {
      if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
         goto LBL_T3;
      }
    } else {
      break;
    }
  }

  /* reset the sign of a first */
  a->sign = neg;

  /* set the result */
  mp_exch (&t1, c);

  /* set the sign of the result */
  c->sign = neg;

  res = MP_OKAY;

LBL_T3:mp_clear (&t3);
LBL_T2:mp_clear (&t2);
LBL_T1:mp_clear (&t1);
  return res;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_N_ROOT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* wrapper function for mp_n_root_ex()

 * computes c = (a)**(1/b) such that (c)**b <= a and (c+1)**b > a






 */
int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
{
  return mp_n_root_ex(a, b, c, 0);

}































































































#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_NEG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* b = -a */
int mp_neg (const mp_int * a, mp_int * b)
{
  int     res;
  if (a != b) {
................................................................................
  } else {
     b->sign = MP_ZPOS;
  }

  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_NEG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* b = -a */
int mp_neg (const mp_int * a, mp_int * b)
{
  int     res;
  if (a != b) {
................................................................................
  } else {
     b->sign = MP_ZPOS;
  }

  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_OR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* OR two ints together */
int mp_or (mp_int * a, mp_int * b, mp_int * c)
{
  int     res, ix, px;
  mp_int  t, *x;
................................................................................
  }
  mp_clamp (&t);
  mp_exch (c, &t);
  mp_clear (&t);
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_OR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* OR two ints together */
int mp_or (mp_int * a, mp_int * b, mp_int * c)
{
  int     res, ix, px;
  mp_int  t, *x;
................................................................................
  }
  mp_clamp (&t);
  mp_exch (c, &t);
  mp_clear (&t);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_PRIME_FERMAT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* performs one Fermat test.
 * 
 * If "a" were prime then b**a == b (mod a) since the order of
 * the multiplicative sub-group would be phi(a) = a-1.  That means
 * it would be the same as b**(a mod (a-1)) == b**1 == b (mod a).
................................................................................
  }

  err = MP_OKAY;
LBL_T:mp_clear (&t);
  return err;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_PRIME_FERMAT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* performs one Fermat test.
 * 
 * If "a" were prime then b**a == b (mod a) since the order of
 * the multiplicative sub-group would be phi(a) = a-1.  That means
 * it would be the same as b**(a mod (a-1)) == b**1 == b (mod a).
................................................................................
  }

  err = MP_OKAY;
LBL_T:mp_clear (&t);
  return err;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_PRIME_IS_DIVISIBLE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* determines if an integers is divisible by one 
 * of the first PRIME_SIZE primes or not
 *
 * sets result to 0 if not, 1 if yes
 */
................................................................................
      return MP_OKAY;
    }
  }

  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_PRIME_IS_DIVISIBLE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* determines if an integers is divisible by one 
 * of the first PRIME_SIZE primes or not
 *
 * sets result to 0 if not, 1 if yes
 */
................................................................................
      return MP_OKAY;
    }
  }

  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_PRIME_IS_PRIME_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* performs a variable number of rounds of Miller-Rabin
 *
 * Probability of error after t rounds is no more than

 *
................................................................................
  mp_int  b;
  int     ix, err, res;

  /* default to no */
  *result = MP_NO;

  /* valid value of t? */
  if (t <= 0 || t > PRIME_SIZE) {
    return MP_VAL;
  }

  /* is the input equal to one of the primes in the table? */
  for (ix = 0; ix < PRIME_SIZE; ix++) {
      if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) {
         *result = 1;
................................................................................

  /* passed the test */
  *result = MP_YES;
LBL_B:mp_clear (&b);
  return err;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_PRIME_IS_PRIME_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* performs a variable number of rounds of Miller-Rabin
 *
 * Probability of error after t rounds is no more than

 *
................................................................................
  mp_int  b;
  int     ix, err, res;

  /* default to no */
  *result = MP_NO;

  /* valid value of t? */
  if ((t <= 0) || (t > PRIME_SIZE)) {
    return MP_VAL;
  }

  /* is the input equal to one of the primes in the table? */
  for (ix = 0; ix < PRIME_SIZE; ix++) {
      if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) {
         *result = 1;
................................................................................

  /* passed the test */
  *result = MP_YES;
LBL_B:mp_clear (&b);
  return err;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_PRIME_MILLER_RABIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* Miller-Rabin test of "a" to the base of "b" as described in 
 * HAC pp. 139 Algorithm 4.24
 *
 * Sets result to 0 if definitely composite or 1 if probably prime.
 * Randomly the chance of error is no more than 1/4 and often 
................................................................................
    goto LBL_R;
  }
  if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) {
    goto LBL_Y;
  }

  /* if y != 1 and y != n1 do */
  if (mp_cmp_d (&y, 1) != MP_EQ && mp_cmp (&y, &n1) != MP_EQ) {
    j = 1;
    /* while j <= s-1 and y != n1 */
    while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) {
      if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) {
         goto LBL_Y;
      }

      /* if y == 1 then composite */
      if (mp_cmp_d (&y, 1) == MP_EQ) {
         goto LBL_Y;
................................................................................
  *result = MP_YES;
LBL_Y:mp_clear (&y);
LBL_R:mp_clear (&r);
LBL_N1:mp_clear (&n1);
  return err;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_PRIME_MILLER_RABIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* Miller-Rabin test of "a" to the base of "b" as described in 
 * HAC pp. 139 Algorithm 4.24
 *
 * Sets result to 0 if definitely composite or 1 if probably prime.
 * Randomly the chance of error is no more than 1/4 and often 
................................................................................
    goto LBL_R;
  }
  if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) {
    goto LBL_Y;
  }

  /* if y != 1 and y != n1 do */
  if ((mp_cmp_d (&y, 1) != MP_EQ) && (mp_cmp (&y, &n1) != MP_EQ)) {
    j = 1;
    /* while j <= s-1 and y != n1 */
    while ((j <= (s - 1)) && (mp_cmp (&y, &n1) != MP_EQ)) {
      if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) {
         goto LBL_Y;
      }

      /* if y == 1 then composite */
      if (mp_cmp_d (&y, 1) == MP_EQ) {
         goto LBL_Y;
................................................................................
  *result = MP_YES;
LBL_Y:mp_clear (&y);
LBL_R:mp_clear (&r);
LBL_N1:mp_clear (&n1);
  return err;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_PRIME_NEXT_PRIME_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* finds the next prime after the number "a" using "t" trials
 * of Miller-Rabin.
 *
 * bbs_style = 1 means the prime must be congruent to 3 mod 4
 */
int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
{
   int      err, res, x, y;
   mp_digit res_tab[PRIME_SIZE], step, kstep;
   mp_int   b;

   /* ensure t is valid */
   if (t <= 0 || t > PRIME_SIZE) {
      return MP_VAL;
   }

   /* force positive */
   a->sign = MP_ZPOS;

   /* simple algo if a is less than the largest prime in the table */
................................................................................

   if (bbs_style == 1) {
      /* if a mod 4 != 3 subtract the correct value to make it so */
      if ((a->dp[0] & 3) != 3) {
         if ((err = mp_sub_d(a, (a->dp[0] & 3) + 1, a)) != MP_OKAY) { return err; };
      }
   } else {
      if (mp_iseven(a) == 1) {
         /* force odd */
         if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) {
            return err;
         }
      }
   }

................................................................................
             }

             /* set flag if zero */
             if (res_tab[x] == 0) {
                y = 1;
             }
         }
      } while (y == 1 && step < ((((mp_digit)1)<<DIGIT_BIT) - kstep));

      /* add the step */
      if ((err = mp_add_d(a, step, a)) != MP_OKAY) {
         goto LBL_ERR;
      }

      /* if didn't pass sieve and step == MAX then skip test */
      if (y == 1 && step >= ((((mp_digit)1)<<DIGIT_BIT) - kstep)) {
         continue;
      }

      /* is this prime? */
      for (x = 0; x < t; x++) {
          mp_set(&b, ltm_prime_tab[x]);
          if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
................................................................................
   err = MP_OKAY;
LBL_ERR:
   mp_clear(&b);
   return err;
}

#endif

#include <tommath_private.h>
#ifdef BN_MP_PRIME_NEXT_PRIME_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* finds the next prime after the number "a" using "t" trials
 * of Miller-Rabin.
 *
 * bbs_style = 1 means the prime must be congruent to 3 mod 4
 */
int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
{
   int      err, res = MP_NO, x, y;
   mp_digit res_tab[PRIME_SIZE], step, kstep;
   mp_int   b;

   /* ensure t is valid */
   if ((t <= 0) || (t > PRIME_SIZE)) {
      return MP_VAL;
   }

   /* force positive */
   a->sign = MP_ZPOS;

   /* simple algo if a is less than the largest prime in the table */
................................................................................

   if (bbs_style == 1) {
      /* if a mod 4 != 3 subtract the correct value to make it so */
      if ((a->dp[0] & 3) != 3) {
         if ((err = mp_sub_d(a, (a->dp[0] & 3) + 1, a)) != MP_OKAY) { return err; };
      }
   } else {
      if (mp_iseven(a) == MP_YES) {
         /* force odd */
         if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) {
            return err;
         }
      }
   }

................................................................................
             }

             /* set flag if zero */
             if (res_tab[x] == 0) {
                y = 1;
             }
         }
      } while ((y == 1) && (step < ((((mp_digit)1) << DIGIT_BIT) - kstep)));

      /* add the step */
      if ((err = mp_add_d(a, step, a)) != MP_OKAY) {
         goto LBL_ERR;
      }

      /* if didn't pass sieve and step == MAX then skip test */
      if ((y == 1) && (step >= ((((mp_digit)1) << DIGIT_BIT) - kstep))) {
         continue;
      }

      /* is this prime? */
      for (x = 0; x < t; x++) {
          mp_set(&b, ltm_prime_tab[x]);
          if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
................................................................................
   err = MP_OKAY;
LBL_ERR:
   mp_clear(&b);
   return err;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */


static const struct {
   int k, t;
} sizes[] = {
{   128,    28 },
................................................................................
       }
   }
   return sizes[x-1].t + 1;
}


#endif

#include <tommath_private.h>
#ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */


static const struct {
   int k, t;
} sizes[] = {
{   128,    28 },
................................................................................
       }
   }
   return sizes[x-1].t + 1;
}


#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_PRIME_RANDOM_EX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* makes a truly random prime of a given size (bits),
 *
 * Flags are as follows:
 * 
 *   LTM_PRIME_BBS      - make prime congruent to 3 mod 4
 *   LTM_PRIME_SAFE     - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)
 *   LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero
 *   LTM_PRIME_2MSB_ON  - make the 2nd highest bit one
 *
 * You have to supply a callback which fills in a buffer with random bytes.  "dat" is a parameter you can
 * have passed to the callback (e.g. a state or something).  This function doesn't use "dat" itself
 * so it can be NULL
 *
 */
................................................................................
/* This is possibly the mother of all prime generation functions, muahahahahaha! */
int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat)
{
   unsigned char *tmp, maskAND, maskOR_msb, maskOR_lsb;
   int res, err, bsize, maskOR_msb_offset;

   /* sanity check the input */
   if (size <= 1 || t <= 0) {
      return MP_VAL;
   }

   /* LTM_PRIME_SAFE implies LTM_PRIME_BBS */
   if (flags & LTM_PRIME_SAFE) {
      flags |= LTM_PRIME_BBS;
   }

   /* calc the byte size */
   bsize = (size>>3) + ((size&7)?1:0);

   /* we need a buffer of bsize bytes */
................................................................................

   /* calc the maskAND value for the MSbyte*/
   maskAND = ((size&7) == 0) ? 0xFF : (0xFF >> (8 - (size & 7)));

   /* calc the maskOR_msb */
   maskOR_msb        = 0;
   maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0;
   if (flags & LTM_PRIME_2MSB_ON) {
      maskOR_msb       |= 0x80 >> ((9 - size) & 7);
   }  

   /* get the maskOR_lsb */
   maskOR_lsb         = 1;
   if (flags & LTM_PRIME_BBS) {
      maskOR_lsb     |= 3;
   }

   do {
      /* read the bytes */
      if (cb(tmp, bsize, dat) != bsize) {
         err = MP_VAL;
................................................................................

      /* is it prime? */
      if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY)           { goto error; }
      if (res == MP_NO) {  
         continue;
      }

      if (flags & LTM_PRIME_SAFE) {
         /* see if (a-1)/2 is prime */
         if ((err = mp_sub_d(a, 1, a)) != MP_OKAY)                    { goto error; }
         if ((err = mp_div_2(a, a)) != MP_OKAY)                       { goto error; }
 
         /* is it prime? */
         if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY)        { goto error; }
      }
   } while (res == MP_NO);

   if (flags & LTM_PRIME_SAFE) {
      /* restore a to the original value */
      if ((err = mp_mul_2(a, a)) != MP_OKAY)                          { goto error; }
      if ((err = mp_add_d(a, 1, a)) != MP_OKAY)                       { goto error; }
   }

   err = MP_OKAY;
error:
   XFREE(tmp);
   return err;
}


#endif

#include <tommath_private.h>
#ifdef BN_MP_PRIME_RANDOM_EX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* makes a truly random prime of a given size (bits),
 *
 * Flags are as follows:
 * 
 *   LTM_PRIME_BBS      - make prime congruent to 3 mod 4
 *   LTM_PRIME_SAFE     - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)

 *   LTM_PRIME_2MSB_ON  - make the 2nd highest bit one
 *
 * You have to supply a callback which fills in a buffer with random bytes.  "dat" is a parameter you can
 * have passed to the callback (e.g. a state or something).  This function doesn't use "dat" itself
 * so it can be NULL
 *
 */
................................................................................
/* This is possibly the mother of all prime generation functions, muahahahahaha! */
int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat)
{
   unsigned char *tmp, maskAND, maskOR_msb, maskOR_lsb;
   int res, err, bsize, maskOR_msb_offset;

   /* sanity check the input */
   if ((size <= 1) || (t <= 0)) {
      return MP_VAL;
   }

   /* LTM_PRIME_SAFE implies LTM_PRIME_BBS */
   if ((flags & LTM_PRIME_SAFE) != 0) {
      flags |= LTM_PRIME_BBS;
   }

   /* calc the byte size */
   bsize = (size>>3) + ((size&7)?1:0);

   /* we need a buffer of bsize bytes */
................................................................................

   /* calc the maskAND value for the MSbyte*/
   maskAND = ((size&7) == 0) ? 0xFF : (0xFF >> (8 - (size & 7)));

   /* calc the maskOR_msb */
   maskOR_msb        = 0;
   maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0;
   if ((flags & LTM_PRIME_2MSB_ON) != 0) {
      maskOR_msb       |= 0x80 >> ((9 - size) & 7);
   }  

   /* get the maskOR_lsb */
   maskOR_lsb         = 1;
   if ((flags & LTM_PRIME_BBS) != 0) {
      maskOR_lsb     |= 3;
   }

   do {
      /* read the bytes */
      if (cb(tmp, bsize, dat) != bsize) {
         err = MP_VAL;
................................................................................

      /* is it prime? */
      if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY)           { goto error; }
      if (res == MP_NO) {  
         continue;
      }

      if ((flags & LTM_PRIME_SAFE) != 0) {
         /* see if (a-1)/2 is prime */
         if ((err = mp_sub_d(a, 1, a)) != MP_OKAY)                    { goto error; }
         if ((err = mp_div_2(a, a)) != MP_OKAY)                       { goto error; }
 
         /* is it prime? */
         if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY)        { goto error; }
      }
   } while (res == MP_NO);

   if ((flags & LTM_PRIME_SAFE) != 0) {
      /* restore a to the original value */
      if ((err = mp_mul_2(a, a)) != MP_OKAY)                          { goto error; }
      if ((err = mp_add_d(a, 1, a)) != MP_OKAY)                       { goto error; }
   }

   err = MP_OKAY;
error:
   XFREE(tmp);
   return err;
}


#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_RADIX_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* returns size of ASCII reprensentation */
int mp_radix_size (mp_int * a, int radix, int *size)
{
  int     res, digs;
  mp_int  t;
  mp_digit d;

  *size = 0;

  /* special case for binary */
  if (radix == 2) {
    *size = mp_count_bits (a) + (a->sign == MP_NEG ? 1 : 0) + 1;
    return MP_OKAY;
  }

  /* make sure the radix is in range */
  if (radix < 2 || radix > 64) {

    return MP_VAL;
  }

  if (mp_iszero(a) == MP_YES) {
    *size = 2;
    return MP_OKAY;
  }







  /* digs is the digit count */
  digs = 0;

  /* if it's negative add one for the sign */
  if (a->sign == MP_NEG) {
    ++digs;
................................................................................
  } else {
      *size = 3;
  }
  return MP_OKAY;
}

#endif

#include <tommath_private.h>
#ifdef BN_MP_RADIX_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* returns size of ASCII reprensentation */
int mp_radix_size (mp_int * a, int radix, int *size)
{
  int     res, digs;
  mp_int  t;
  mp_digit d;

  *size = 0;







  /* make sure the radix is in range */

  if ((radix < 2) || (radix > 64)) {
    return MP_VAL;
  }

  if (mp_iszero(a) == MP_YES) {
    *size = 2;
    return MP_OKAY;
  }

  /* special case for binary */
  if (radix == 2) {
    *size = mp_count_bits (a) + ((a->sign == MP_NEG) ? 1 : 0) + 1;
    return MP_OKAY;
  }

  /* digs is the digit count */
  digs = 0;

  /* if it's negative add one for the sign */
  if (a->sign == MP_NEG) {
    ++digs;
................................................................................
  } else {
      *size = 3;
  }
  return MP_OKAY;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_RADIX_SMAP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* chars used in radix conversions */
const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
#endif

#include <tommath_private.h>
#ifdef BN_MP_RADIX_SMAP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* chars used in radix conversions */
const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_RAND_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* makes a pseudo-random int of a given size */
int
mp_rand (mp_int * a, int digits)
{
  int     res;
................................................................................
  mp_zero (a);
  if (digits <= 0) {
    return MP_OKAY;
  }

  /* first place a random non-zero digit */
  do {
    d = ((mp_digit) abs (rand ())) & MP_MASK;
  } while (d == 0);

  if ((res = mp_add_d (a, d, a)) != MP_OKAY) {
    return res;
  }

  while (--digits > 0) {
    if ((res = mp_lshd (a, 1)) != MP_OKAY) {
      return res;
    }

    if ((res = mp_add_d (a, ((mp_digit) abs (rand ())), a)) != MP_OKAY) {
      return res;
    }
  }

  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_RAND_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* makes a pseudo-random int of a given size */
int
mp_rand (mp_int * a, int digits)
{
  int     res;
................................................................................
  mp_zero (a);
  if (digits <= 0) {
    return MP_OKAY;
  }

  /* first place a random non-zero digit */
  do {
    d = ((mp_digit) abs (MP_GEN_RANDOM())) & MP_MASK;
  } while (d == 0);

  if ((res = mp_add_d (a, d, a)) != MP_OKAY) {
    return res;
  }

  while (--digits > 0) {
    if ((res = mp_lshd (a, 1)) != MP_OKAY) {
      return res;
    }

    if ((res = mp_add_d (a, ((mp_digit) abs (MP_GEN_RANDOM())), a)) != MP_OKAY) {
      return res;
    }
  }

  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_READ_RADIX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* read a string [ASCII] in a given radix */
int mp_read_radix (mp_int * a, const char *str, int radix)
{
  int     y, res, neg;
  char    ch;

  /* zero the digit bignum */
  mp_zero(a);

  /* make sure the radix is ok */
  if (radix < 2 || radix > 64) {
    return MP_VAL;
  }

  /* if the leading digit is a 
   * minus set the sign to negative. 
   */
  if (*str == '-') {
................................................................................
    neg = MP_ZPOS;
  }

  /* set the integer to the default of zero */
  mp_zero (a);
  
  /* process each digit of the string */
  while (*str) {
    /* if the radix < 36 the conversion is case insensitive
     * this allows numbers like 1AB and 1ab to represent the same  value
     * [e.g. in hex]
     */
    ch = (char) ((radix < 36) ? toupper ((unsigned char) *str) : *str);
    for (y = 0; y < 64; y++) {
      if (ch == mp_s_rmap[y]) {
         break;
      }
    }

    /* if the char was found in the map 
................................................................................

  if ( *str != '\0' ) {
      mp_zero( a );
      return MP_VAL;
  }

  /* set the sign only if a != 0 */
  if (mp_iszero(a) != 1) {
     a->sign = neg;
  }
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_READ_RADIX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* read a string [ASCII] in a given radix */
int mp_read_radix (mp_int * a, const char *str, int radix)
{
  int     y, res, neg;
  char    ch;

  /* zero the digit bignum */
  mp_zero(a);

  /* make sure the radix is ok */
  if ((radix < 2) || (radix > 64)) {
    return MP_VAL;
  }

  /* if the leading digit is a 
   * minus set the sign to negative. 
   */
  if (*str == '-') {
................................................................................
    neg = MP_ZPOS;
  }

  /* set the integer to the default of zero */
  mp_zero (a);
  
  /* process each digit of the string */
  while (*str != '\0') {
    /* if the radix <= 36 the conversion is case insensitive
     * this allows numbers like 1AB and 1ab to represent the same  value
     * [e.g. in hex]
     */
    ch = (radix <= 36) ? (char)toupper((unsigned char)*str) : *str;
    for (y = 0; y < 64; y++) {
      if (ch == mp_s_rmap[y]) {
         break;
      }
    }

    /* if the char was found in the map 
................................................................................

  if ( *str != '\0' ) {
      mp_zero( a );
      return MP_VAL;
  }

  /* set the sign only if a != 0 */
  if (mp_iszero(a) != MP_YES) {
     a->sign = neg;
  }
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_READ_SIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* read signed bin, big endian, first byte is 0==positive or 1==negative */
int mp_read_signed_bin (mp_int * a, const unsigned char *b, int c)
{
  int     res;

................................................................................
  } else {
     a->sign = MP_NEG;
  }

  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_READ_SIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* read signed bin, big endian, first byte is 0==positive or 1==negative */
int mp_read_signed_bin (mp_int * a, const unsigned char *b, int c)
{
  int     res;

................................................................................
  } else {
     a->sign = MP_NEG;
  }

  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_READ_UNSIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* reads a unsigned char array, assumes the msb is stored first [big endian] */
int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c)
{
  int     res;

................................................................................
  /* read the bytes in */
  while (c-- > 0) {
    if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) {
      return res;
    }

#ifndef MP_8BIT
      a->dp[0] |= *b++;
      a->used += 1;
#else
      a->dp[0] = (*b & MP_MASK);
      a->dp[1] |= ((*b++ >> 7U) & 1);
      a->used += 2;
#endif
  }
  mp_clamp (a);
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_READ_UNSIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* reads a unsigned char array, assumes the msb is stored first [big endian] */
int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c)
{
  int     res;

................................................................................
  /* read the bytes in */
  while (c-- > 0) {
    if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) {
      return res;
    }

#ifndef MP_8BIT
    a->dp[0] |= *b++;
    a->used += 1;
#else
    a->dp[0] = (*b & MP_MASK);
    a->dp[1] |= ((*b++ >> 7U) & 1);
    a->used += 2;
#endif
  }
  mp_clamp (a);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* reduces x mod m, assumes 0 < x < m**2, mu is 
 * precomputed via mp_reduce_setup.
 * From HAC pp.604 Algorithm 14.42
 */
int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
{
  mp_int  q;
  int     res, um = m->used;
................................................................................

  /* q = x */
  if ((res = mp_init_copy (&q, x)) != MP_OKAY) {
    return res;
  }

  /* q1 = x / b**(k-1)  */
  mp_rshd (&q, um - 1);         

  /* according to HAC this optimization is ok */
  if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
    if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
      goto CLEANUP;
    }
  } else {
#ifdef BN_S_MP_MUL_HIGH_DIGS_C
    if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
      goto CLEANUP;
    }
#elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
    if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
      goto CLEANUP;
    }
#else 
    { 
      res = MP_VAL;
      goto CLEANUP;
    }
#endif
  }

  /* q3 = q2 / b**(k+1) */
  mp_rshd (&q, um + 1);         

  /* x = x mod b**(k+1), quick (no division) */
  if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
    goto CLEANUP;
  }

  /* q = q * m mod b**(k+1), quick (no division) */
................................................................................

  /* Back off if it's too big */
  while (mp_cmp (x, m) != MP_LT) {
    if ((res = s_mp_sub (x, m, x)) != MP_OKAY) {
      goto CLEANUP;
    }
  }
  
CLEANUP:
  mp_clear (&q);

  return res;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* reduces x mod m, assumes 0 < x < m**2, mu is
 * precomputed via mp_reduce_setup.
 * From HAC pp.604 Algorithm 14.42
 */
int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
{
  mp_int  q;
  int     res, um = m->used;
................................................................................

  /* q = x */
  if ((res = mp_init_copy (&q, x)) != MP_OKAY) {
    return res;
  }

  /* q1 = x / b**(k-1)  */
  mp_rshd (&q, um - 1);

  /* according to HAC this optimization is ok */
  if (((mp_digit) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
    if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
      goto CLEANUP;
    }
  } else {
#ifdef BN_S_MP_MUL_HIGH_DIGS_C
    if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
      goto CLEANUP;
    }
#elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
    if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
      goto CLEANUP;
    }
#else
    {
      res = MP_VAL;
      goto CLEANUP;
    }
#endif
  }

  /* q3 = q2 / b**(k+1) */
  mp_rshd (&q, um + 1);

  /* x = x mod b**(k+1), quick (no division) */
  if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
    goto CLEANUP;
  }

  /* q = q * m mod b**(k+1), quick (no division) */
................................................................................

  /* Back off if it's too big */
  while (mp_cmp (x, m) != MP_LT) {
    if ((res = s_mp_sub (x, m, x)) != MP_OKAY) {
      goto CLEANUP;
    }
  }

CLEANUP:
  mp_clear (&q);

  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_REDUCE_2K_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* reduces a modulo n where n is of the form 2**p - d */
int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d)
{
   mp_int q;
   int    p, res;
   
   if ((res = mp_init(&q)) != MP_OKAY) {
      return res;
   }
   
   p = mp_count_bits(n);    
top:
   /* q = a/2**p, a = a mod 2**p */
   if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
      goto ERR;
   }
   
   if (d != 1) {
      /* q = q * d */
      if ((res = mp_mul_d(&q, d, &q)) != MP_OKAY) { 
         goto ERR;
      }
   }
   
   /* a = a + q */
   if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
      goto ERR;
   }
   
   if (mp_cmp_mag(a, n) != MP_LT) {
      s_mp_sub(a, n, a);


      goto top;
   }
   
ERR:
   mp_clear(&q);
   return res;
}

#endif

#include <tommath_private.h>
#ifdef BN_MP_REDUCE_2K_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* reduces a modulo n where n is of the form 2**p - d */
int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d)
{
   mp_int q;
   int    p, res;

   if ((res = mp_init(&q)) != MP_OKAY) {
      return res;
   }

   p = mp_count_bits(n);
top:
   /* q = a/2**p, a = a mod 2**p */
   if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
      goto ERR;
   }

   if (d != 1) {
      /* q = q * d */
      if ((res = mp_mul_d(&q, d, &q)) != MP_OKAY) {
         goto ERR;
      }
   }

   /* a = a + q */
   if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
      goto ERR;
   }

   if (mp_cmp_mag(a, n) != MP_LT) {
      if ((res = s_mp_sub(a, n, a)) != MP_OKAY) {
         goto ERR;
      }
      goto top;
   }

ERR:
   mp_clear(&q);
   return res;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_REDUCE_2K_L_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* reduces a modulo n where n is of the form 2**p - d 
   This differs from reduce_2k since "d" can be larger
   than a single digit.
*/
int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d)
{
   mp_int q;
   int    p, res;
   
   if ((res = mp_init(&q)) != MP_OKAY) {
      return res;
   }
   
   p = mp_count_bits(n);    
top:
   /* q = a/2**p, a = a mod 2**p */
   if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
      goto ERR;
   }
   
   /* q = q * d */
   if ((res = mp_mul(&q, d, &q)) != MP_OKAY) { 
      goto ERR;
   }
   
   /* a = a + q */
   if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
      goto ERR;
   }
   
   if (mp_cmp_mag(a, n) != MP_LT) {
      s_mp_sub(a, n, a);


      goto top;
   }
   
ERR:
   mp_clear(&q);
   return res;
}

#endif

#include <tommath_private.h>
#ifdef BN_MP_REDUCE_2K_L_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* reduces a modulo n where n is of the form 2**p - d
   This differs from reduce_2k since "d" can be larger
   than a single digit.
*/
int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d)
{
   mp_int q;
   int    p, res;

   if ((res = mp_init(&q)) != MP_OKAY) {
      return res;
   }

   p = mp_count_bits(n);
top:
   /* q = a/2**p, a = a mod 2**p */
   if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
      goto ERR;
   }

   /* q = q * d */
   if ((res = mp_mul(&q, d, &q)) != MP_OKAY) {
      goto ERR;
   }

   /* a = a + q */
   if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
      goto ERR;
   }

   if (mp_cmp_mag(a, n) != MP_LT) {
      if ((res = s_mp_sub(a, n, a)) != MP_OKAY) {
         goto ERR;
      }
      goto top;
   }

ERR:
   mp_clear(&q);
   return res;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_REDUCE_2K_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* determines the setup value */
int mp_reduce_2k_setup(mp_int *a, mp_digit *d)
{
   int res, p;
   mp_int tmp;
................................................................................
   }
   
   *d = tmp.dp[0];
   mp_clear(&tmp);
   return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_REDUCE_2K_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* determines the setup value */
int mp_reduce_2k_setup(mp_int *a, mp_digit *d)
{
   int res, p;
   mp_int tmp;
................................................................................
   }
   
   *d = tmp.dp[0];
   mp_clear(&tmp);
   return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_REDUCE_2K_SETUP_L_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* determines the setup value */
int mp_reduce_2k_setup_l(mp_int *a, mp_int *d)
{
   int    res;
   mp_int tmp;
................................................................................
   }
   
ERR:
   mp_clear(&tmp);
   return res;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_REDUCE_2K_SETUP_L_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* determines the setup value */
int mp_reduce_2k_setup_l(mp_int *a, mp_int *d)
{
   int    res;
   mp_int tmp;
................................................................................
   }
   
ERR:
   mp_clear(&tmp);
   return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_REDUCE_IS_2K_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* determines if mp_reduce_2k can be used */
int mp_reduce_is_2k(mp_int *a)
{
   int ix, iy, iw;
   mp_digit iz;
................................................................................
          }
      }
   }
   return MP_YES;
}

#endif

#include <tommath_private.h>
#ifdef BN_MP_REDUCE_IS_2K_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* determines if mp_reduce_2k can be used */
int mp_reduce_is_2k(mp_int *a)
{
   int ix, iy, iw;
   mp_digit iz;
................................................................................
          }
      }
   }
   return MP_YES;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_REDUCE_IS_2K_L_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* determines if reduce_2k_l can be used */
int mp_reduce_is_2k_l(mp_int *a)
{
   int ix, iy;
   
................................................................................
      return (iy >= (a->used/2)) ? MP_YES : MP_NO;
      
   }
   return MP_NO;
}

#endif

#include <tommath_private.h>
#ifdef BN_MP_REDUCE_IS_2K_L_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* determines if reduce_2k_l can be used */
int mp_reduce_is_2k_l(mp_int *a)
{
   int ix, iy;
   
................................................................................
      return (iy >= (a->used/2)) ? MP_YES : MP_NO;
      
   }
   return MP_NO;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_REDUCE_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* pre-calculate the value required for Barrett reduction
 * For a given modulus "b" it calulates the value required in "a"
 */
int mp_reduce_setup (mp_int * a, mp_int * b)
{
................................................................................
  
  if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
    return res;
  }
  return mp_div (a, b, a, NULL);
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_REDUCE_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* pre-calculate the value required for Barrett reduction
 * For a given modulus "b" it calulates the value required in "a"
 */
int mp_reduce_setup (mp_int * a, mp_int * b)
{
................................................................................
  
  if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
    return res;
  }
  return mp_div (a, b, a, NULL);
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_RSHD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* shift right a certain amount of digits */
void mp_rshd (mp_int * a, int b)
{
  int     x;

................................................................................
  /* if b > used then simply zero it and return */
  if (a->used <= b) {
    mp_zero (a);
    return;
  }

  {
    register mp_digit *bottom, *top;

    /* shift the digits down */

    /* bottom */
    bottom = a->dp;

    /* top [offset into digits] */
................................................................................
    }
  }
  
  /* remove excess digits */
  a->used -= b;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_RSHD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* shift right a certain amount of digits */
void mp_rshd (mp_int * a, int b)
{
  int     x;

................................................................................
  /* if b > used then simply zero it and return */
  if (a->used <= b) {
    mp_zero (a);
    return;
  }

  {
    mp_digit *bottom, *top;

    /* shift the digits down */

    /* bottom */
    bottom = a->dp;

    /* top [offset into digits] */
................................................................................
    }
  }
  
  /* remove excess digits */
  a->used -= b;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_SET_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* set to a digit */
void mp_set (mp_int * a, mp_digit b)
{
  mp_zero (a);
  a->dp[0] = b & MP_MASK;
  a->used  = (a->dp[0] != 0) ? 1 : 0;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_SET_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* set to a digit */
void mp_set (mp_int * a, mp_digit b)
{
  mp_zero (a);
  a->dp[0] = b & MP_MASK;
  a->used  = (a->dp[0] != 0) ? 1 : 0;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_SET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* set a 32-bit const */
int mp_set_int (mp_int * a, unsigned long b)
{
  int     x, res;

................................................................................
    /* ensure that digits are not clamped off */
    a->used += 1;
  }
  mp_clamp (a);
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_SET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* set a 32-bit const */
int mp_set_int (mp_int * a, unsigned long b)
{
  int     x, res;

................................................................................
    /* ensure that digits are not clamped off */
    a->used += 1;
  }
  mp_clamp (a);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_SHRINK_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* shrink a bignum */
int mp_shrink (mp_int * a)
{
  mp_digit *tmp;
  int used = 1;
  
  if(a->used > 0)
    used = a->used;

  
  if (a->alloc != used) {
    if ((tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * used)) == NULL) {
      return MP_MEM;
    }
    a->dp    = tmp;
    a->alloc = used;
  }
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_SHRINK_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* shrink a bignum */
int mp_shrink (mp_int * a)
{
  mp_digit *tmp;
  int used = 1;
  
  if(a->used > 0) {
    used = a->used;
  }
  
  if (a->alloc != used) {
    if ((tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * used)) == NULL) {
      return MP_MEM;
    }
    a->dp    = tmp;
    a->alloc = used;
  }
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_SIGNED_BIN_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* get the size for an signed equivalent */
int mp_signed_bin_size (mp_int * a)
{
  return 1 + mp_unsigned_bin_size (a);
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_SIGNED_BIN_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* get the size for an signed equivalent */
int mp_signed_bin_size (mp_int * a)
{
  return 1 + mp_unsigned_bin_size (a);
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* computes b = a*a */
int
mp_sqr (mp_int * a, mp_int * b)
{
  int     res;
................................................................................
  /* use Toom-Cook? */
  if (a->used >= TOOM_SQR_CUTOFF) {
    res = mp_toom_sqr(a, b);
  /* Karatsuba? */
  } else 
#endif
#ifdef BN_MP_KARATSUBA_SQR_C
if (a->used >= KARATSUBA_SQR_CUTOFF) {
    res = mp_karatsuba_sqr (a, b);
  } else 
#endif
  {
#ifdef BN_FAST_S_MP_SQR_C
    /* can we use the fast comba multiplier? */
    if ((a->used * 2 + 1) < MP_WARRAY && 
         a->used < 
         (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) {
      res = fast_s_mp_sqr (a, b);
    } else
#endif

#ifdef BN_S_MP_SQR_C
      res = s_mp_sqr (a, b);
#else
      res = MP_VAL;
#endif

  }
  b->sign = MP_ZPOS;
  return res;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* computes b = a*a */
int
mp_sqr (mp_int * a, mp_int * b)
{
  int     res;
................................................................................
  /* use Toom-Cook? */
  if (a->used >= TOOM_SQR_CUTOFF) {
    res = mp_toom_sqr(a, b);
  /* Karatsuba? */
  } else 
#endif
#ifdef BN_MP_KARATSUBA_SQR_C
  if (a->used >= KARATSUBA_SQR_CUTOFF) {
    res = mp_karatsuba_sqr (a, b);
  } else 
#endif
  {
#ifdef BN_FAST_S_MP_SQR_C
    /* can we use the fast comba multiplier? */
    if ((((a->used * 2) + 1) < MP_WARRAY) &&
         (a->used <
         (1 << (((sizeof(mp_word) * CHAR_BIT) - (2 * DIGIT_BIT)) - 1)))) {
      res = fast_s_mp_sqr (a, b);
    } else
#endif
    {
#ifdef BN_S_MP_SQR_C
      res = s_mp_sqr (a, b);
#else
      res = MP_VAL;
#endif
    }
  }
  b->sign = MP_ZPOS;
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_SQRMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* c = a * a (mod b) */
int
mp_sqrmod (mp_int * a, mp_int * b, mp_int * c)
{
  int     res;
................................................................................
    return res;
  }
  res = mp_mod (&t, b, c);
  mp_clear (&t);
  return res;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_SQRMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* c = a * a (mod b) */
int
mp_sqrmod (mp_int * a, mp_int * b, mp_int * c)
{
  int     res;
................................................................................
    return res;
  }
  res = mp_mod (&t, b, c);
  mp_clear (&t);
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>

#ifdef BN_MP_SQRT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
................................................................................
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

#ifndef NO_FLOATING_POINT
#include <math.h>
#endif

/* this function is less generic than mp_n_root, simpler and faster */
................................................................................

E1: mp_clear(&t2);
E2: mp_clear(&t1);
  return res;
}

#endif

#include <tommath_private.h>

#ifdef BN_MP_SQRT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
................................................................................
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

#ifndef NO_FLOATING_POINT
#include <math.h>
#endif

/* this function is less generic than mp_n_root, simpler and faster */
................................................................................

E1: mp_clear(&t2);
E2: mp_clear(&t1);
  return res;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_SUB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* high level subtraction (handles signs) */
int
mp_sub (mp_int * a, mp_int * b, mp_int * c)
{
  int     sa, sb, res;
................................................................................
      res = s_mp_sub (b, a, c);
    }
  }
  return res;
}

#endif

#include <tommath_private.h>
#ifdef BN_MP_SUB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* high level subtraction (handles signs) */
int
mp_sub (mp_int * a, mp_int * b, mp_int * c)
{
  int     sa, sb, res;
................................................................................
      res = s_mp_sub (b, a, c);
    }
  }
  return res;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_SUB_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* single digit subtraction */
int
mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
{
  mp_digit *tmpa, *tmpc, mu;
  int       res, ix, oldused;

  /* grow c as required */
  if (c->alloc < a->used + 1) {
     if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
        return res;
     }
  }

  /* if a is negative just do an unsigned
   * addition [with fudged signs]
................................................................................

  /* setup regs */
  oldused = c->used;
  tmpa    = a->dp;
  tmpc    = c->dp;

  /* if a <= b simply fix the single digit */
  if ((a->used == 1 && a->dp[0] <= b) || a->used == 0) {
     if (a->used == 1) {
        *tmpc++ = b - *tmpa;
     } else {
        *tmpc++ = b;
     }
     ix      = 1;

................................................................................
  } else {
     /* positive/size */
     c->sign = MP_ZPOS;
     c->used = a->used;

     /* subtract first digit */
     *tmpc    = *tmpa++ - b;
     mu       = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
     *tmpc++ &= MP_MASK;

     /* handle rest of the digits */
     for (ix = 1; ix < a->used; ix++) {
        *tmpc    = *tmpa++ - mu;
        mu       = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
        *tmpc++ &= MP_MASK;
     }
  }

  /* zero excess digits */
  while (ix++ < oldused) {
     *tmpc++ = 0;
  }
  mp_clamp(c);
  return MP_OKAY;
}

#endif

#include <tommath_private.h>
#ifdef BN_MP_SUB_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* single digit subtraction */
int
mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
{
  mp_digit *tmpa, *tmpc, mu;
  int       res, ix, oldused;

  /* grow c as required */
  if (c->alloc < (a->used + 1)) {
     if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
        return res;
     }
  }

  /* if a is negative just do an unsigned
   * addition [with fudged signs]
................................................................................

  /* setup regs */
  oldused = c->used;
  tmpa    = a->dp;
  tmpc    = c->dp;

  /* if a <= b simply fix the single digit */
  if (((a->used == 1) && (a->dp[0] <= b)) || (a->used == 0)) {
     if (a->used == 1) {
        *tmpc++ = b - *tmpa;
     } else {
        *tmpc++ = b;
     }
     ix      = 1;

................................................................................
  } else {
     /* positive/size */
     c->sign = MP_ZPOS;
     c->used = a->used;

     /* subtract first digit */
     *tmpc    = *tmpa++ - b;
     mu       = *tmpc >> ((sizeof(mp_digit) * CHAR_BIT) - 1);
     *tmpc++ &= MP_MASK;

     /* handle rest of the digits */
     for (ix = 1; ix < a->used; ix++) {
        *tmpc    = *tmpa++ - mu;
        mu       = *tmpc >> ((sizeof(mp_digit) * CHAR_BIT) - 1);
        *tmpc++ &= MP_MASK;
     }
  }

  /* zero excess digits */
  while (ix++ < oldused) {
     *tmpc++ = 0;
  }
  mp_clamp(c);
  return MP_OKAY;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_SUBMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* d = a - b (mod c) */
int
mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
  int     res;
................................................................................
    return res;
  }
  res = mp_mod (&t, c, d);
  mp_clear (&t);
  return res;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_SUBMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* d = a - b (mod c) */
int
mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
  int     res;
................................................................................
    return res;
  }
  res = mp_mod (&t, c, d);
  mp_clear (&t);
  return res;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_TO_SIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* store in signed [big endian] format */
int mp_to_signed_bin (mp_int * a, unsigned char *b)
{
  int     res;

  if ((res = mp_to_unsigned_bin (a, b + 1)) != MP_OKAY) {
    return res;
  }
  b[0] = (unsigned char) ((a->sign == MP_ZPOS) ? 0 : 1);
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_TO_SIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* store in signed [big endian] format */
int mp_to_signed_bin (mp_int * a, unsigned char *b)
{
  int     res;

  if ((res = mp_to_unsigned_bin (a, b + 1)) != MP_OKAY) {
    return res;
  }
  b[0] = (a->sign == MP_ZPOS) ? (unsigned char)0 : (unsigned char)1;
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_TO_SIGNED_BIN_N_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* store in signed [big endian] format */
int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
{
   if (*outlen < (unsigned long)mp_signed_bin_size(a)) {
      return MP_VAL;
   }
   *outlen = mp_signed_bin_size(a);
   return mp_to_signed_bin(a, b);
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_TO_SIGNED_BIN_N_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* store in signed [big endian] format */
int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
{
   if (*outlen < (unsigned long)mp_signed_bin_size(a)) {
      return MP_VAL;
   }
   *outlen = mp_signed_bin_size(a);
   return mp_to_signed_bin(a, b);
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_TO_UNSIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* store in unsigned [big endian] format */
int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
{
  int     x, res;
  mp_int  t;

  if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
    return res;
  }

  x = 0;
  while (mp_iszero (&t) == 0) {
#ifndef MP_8BIT
      b[x++] = (unsigned char) (t.dp[0] & 255);
#else
      b[x++] = (unsigned char) (t.dp[0] | ((t.dp[1] & 0x01) << 7));
#endif
    if ((res = mp_div_2d (&t, 8, &t, NULL)) != MP_OKAY) {
      mp_clear (&t);
................................................................................
    }
  }
  bn_reverse (b, x);
  mp_clear (&t);
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_TO_UNSIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* store in unsigned [big endian] format */
int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
{
  int     x, res;
  mp_int  t;

  if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
    return res;
  }

  x = 0;
  while (mp_iszero (&t) == MP_NO) {
#ifndef MP_8BIT
      b[x++] = (unsigned char) (t.dp[0] & 255);
#else
      b[x++] = (unsigned char) (t.dp[0] | ((t.dp[1] & 0x01) << 7));
#endif
    if ((res = mp_div_2d (&t, 8, &t, NULL)) != MP_OKAY) {
      mp_clear (&t);
................................................................................
    }
  }
  bn_reverse (b, x);
  mp_clear (&t);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_TO_UNSIGNED_BIN_N_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* store in unsigned [big endian] format */
int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
{
   if (*outlen < (unsigned long)mp_unsigned_bin_size(a)) {
      return MP_VAL;
   }
   *outlen = mp_unsigned_bin_size(a);
   return mp_to_unsigned_bin(a, b);
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_TO_UNSIGNED_BIN_N_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* store in unsigned [big endian] format */
int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
{
   if (*outlen < (unsigned long)mp_unsigned_bin_size(a)) {
      return MP_VAL;
   }
   *outlen = mp_unsigned_bin_size(a);
   return mp_to_unsigned_bin(a, b);
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_TOOM_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* multiplication using the Toom-Cook 3-way algorithm 
 *
 * Much more complicated than Karatsuba but has a lower 
 * asymptotic running time of O(N**1.464).  This algorithm is 
 * only particularly useful on VERY large inputs 
 * (we're talking 1000s of digits here...).
*/
int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
{
    mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
    int res, B;
        
    /* init temps */
    if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, 
                             &a0, &a1, &a2, &b0, &b1, 
                             &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) {
       return res;
    }
    
    /* B */
    B = MIN(a->used, b->used) / 3;
    
    /* a = a2 * B**2 + a1 * B + a0 */
    if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
       goto ERR;
    }

    if ((res = mp_copy(a, &a1)) != MP_OKAY) {
       goto ERR;
    }
    mp_rshd(&a1, B);
    mp_mod_2d(&a1, DIGIT_BIT * B, &a1);



    if ((res = mp_copy(a, &a2)) != MP_OKAY) {
       goto ERR;
    }
    mp_rshd(&a2, B*2);
    
    /* b = b2 * B**2 + b1 * B + b0 */
    if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) {
       goto ERR;
    }

    if ((res = mp_copy(b, &b1)) != MP_OKAY) {
       goto ERR;
    }
    mp_rshd(&b1, B);
    mp_mod_2d(&b1, DIGIT_BIT * B, &b1);

    if ((res = mp_copy(b, &b2)) != MP_OKAY) {
       goto ERR;
    }
    mp_rshd(&b2, B*2);
    
    /* w0 = a0*b0 */
    if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) {
       goto ERR;
    }
    
    /* w4 = a2 * b2 */
    if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) {
       goto ERR;
    }
    
    /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
    if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    
    if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    
    if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) {
       goto ERR;
    }
    
    /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
    if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    
    if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    
    if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) {
       goto ERR;
    }
    

    /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
    if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
       goto ERR;
................................................................................
    }
    if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) {
       goto ERR;
    }
    
    /* now solve the matrix 
    
       0  0  0  0  1
       1  2  4  8  16
       1  1  1  1  1
       16 8  4  2  1
       1  0  0  0  0
       
       using 12 subtractions, 4 shifts, 
              2 small divisions and 1 small multiplication 
     */
     
     /* r1 - r4 */
     if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
        goto ERR;
     }
     /* r3 - r0 */
     if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
        goto ERR;
     }
     /* r1/2 */
     if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
        goto ERR;
     }
     /* r3/2 */
     if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
        goto ERR;
     }
     /* r2 - r0 - r4 */
     if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
        goto ERR;
     }
     /* r1 - r2 */
     if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
        goto ERR;
     }
     /* r3 - r2 */
     if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
        goto ERR;
     }
     /* r1 - 8r0 */
     if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
        goto ERR;
     }
     /* r3 - 8r4 */
     if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
        goto ERR;
     }
     /* 3r2 - r1 - r3 */
     if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
        goto ERR;
     }
     /* r1 - r2 */
     if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
        goto ERR;
     }
     /* r3 - r2 */
     if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
        goto ERR;
     }
     /* r1/3 */
     if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
        goto ERR;
     }
     /* r3/3 */
     if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
        goto ERR;
     }
     
     /* at this point shift W[n] by B*n */
     if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
        goto ERR;
     }     
     
     if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) {
        goto ERR;
     }     
     
ERR:
     mp_clear_multi(&w0, &w1, &w2, &w3, &w4, 
                    &a0, &a1, &a2, &b0, &b1, 
                    &b2, &tmp1, &tmp2, NULL);
     return res;
}     
     
#endif

#include <tommath_private.h>
#ifdef BN_MP_TOOM_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* multiplication using the Toom-Cook 3-way algorithm
 *
 * Much more complicated than Karatsuba but has a lower
 * asymptotic running time of O(N**1.464).  This algorithm is
 * only particularly useful on VERY large inputs
 * (we're talking 1000s of digits here...).
*/
int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
{
    mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
    int res, B;

    /* init temps */
    if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4,
                             &a0, &a1, &a2, &b0, &b1,
                             &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) {
       return res;
    }

    /* B */
    B = MIN(a->used, b->used) / 3;

    /* a = a2 * B**2 + a1 * B + a0 */
    if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
       goto ERR;
    }

    if ((res = mp_copy(a, &a1)) != MP_OKAY) {
       goto ERR;
    }
    mp_rshd(&a1, B);
    if ((res = mp_mod_2d(&a1, DIGIT_BIT * B, &a1)) != MP_OKAY) {
       goto ERR;
    }

    if ((res = mp_copy(a, &a2)) != MP_OKAY) {
       goto ERR;
    }
    mp_rshd(&a2, B*2);

    /* b = b2 * B**2 + b1 * B + b0 */
    if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) {
       goto ERR;
    }

    if ((res = mp_copy(b, &b1)) != MP_OKAY) {
       goto ERR;
    }
    mp_rshd(&b1, B);
    (void)mp_mod_2d(&b1, DIGIT_BIT * B, &b1);

    if ((res = mp_copy(b, &b2)) != MP_OKAY) {
       goto ERR;
    }
    mp_rshd(&b2, B*2);

    /* w0 = a0*b0 */
    if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) {
       goto ERR;
    }

    /* w4 = a2 * b2 */
    if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) {
       goto ERR;
    }

    /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
    if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
       goto ERR;
    }

    if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) {
       goto ERR;
    }

    if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) {
       goto ERR;
    }

    /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
    if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
       goto ERR;
    }

    if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
       goto ERR;
    }

    if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) {
       goto ERR;
    }


    /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
    if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
       goto ERR;
................................................................................
    }
    if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) {
       goto ERR;
    }

    /* now solve the matrix

       0  0  0  0  1
       1  2  4  8  16
       1  1  1  1  1
       16 8  4  2  1
       1  0  0  0  0

       using 12 subtractions, 4 shifts,
              2 small divisions and 1 small multiplication
     */

    /* r1 - r4 */
    if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
       goto ERR;
    }
    /* r3 - r0 */
    if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
       goto ERR;
    }
    /* r1/2 */
    if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
       goto ERR;
    }
    /* r3/2 */
    if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
       goto ERR;
    }
    /* r2 - r0 - r4 */
    if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
       goto ERR;
    }
    /* r1 - r2 */
    if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
       goto ERR;
    }
    /* r3 - r2 */
    if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
       goto ERR;
    }
    /* r1 - 8r0 */
    if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
       goto ERR;
    }
    /* r3 - 8r4 */
    if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
       goto ERR;
    }
    /* 3r2 - r1 - r3 */
    if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
       goto ERR;
    }
    /* r1 - r2 */
    if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
       goto ERR;
    }
    /* r3 - r2 */
    if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
       goto ERR;
    }
    /* r1/3 */
    if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
       goto ERR;
    }
    /* r3/3 */
    if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
       goto ERR;
    }

    /* at this point shift W[n] by B*n */
    if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
       goto ERR;
    }

    if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) {
       goto ERR;
    }

ERR:
    mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
                   &a0, &a1, &a2, &b0, &b1,
                   &b2, &tmp1, &tmp2, NULL);
    return res;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_TOOM_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* squaring using Toom-Cook 3-way algorithm */
int
mp_toom_sqr(mp_int *a, mp_int *b)
{
    mp_int w0, w1, w2, w3, w4, tmp1, a0, a1, a2;
................................................................................
       goto ERR;
    }

    if ((res = mp_copy(a, &a1)) != MP_OKAY) {
       goto ERR;
    }
    mp_rshd(&a1, B);
    mp_mod_2d(&a1, DIGIT_BIT * B, &a1);



    if ((res = mp_copy(a, &a2)) != MP_OKAY) {
       goto ERR;
    }
    mp_rshd(&a2, B*2);

    /* w0 = a0*a0 */
................................................................................
       1  1  1  1  1
       16 8  4  2  1
       1  0  0  0  0

       using 12 subtractions, 4 shifts, 2 small divisions and 1 small multiplication.
     */

     /* r1 - r4 */
     if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
        goto ERR;
     }
     /* r3 - r0 */
     if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
        goto ERR;
     }
     /* r1/2 */
     if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
        goto ERR;
     }
     /* r3/2 */
     if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
        goto ERR;
     }
     /* r2 - r0 - r4 */
     if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
        goto ERR;
     }
     /* r1 - r2 */
     if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
        goto ERR;
     }
     /* r3 - r2 */
     if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
        goto ERR;
     }
     /* r1 - 8r0 */
     if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
        goto ERR;
     }
     /* r3 - 8r4 */
     if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
        goto ERR;
     }
     /* 3r2 - r1 - r3 */
     if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
        goto ERR;
     }
     /* r1 - r2 */
     if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
        goto ERR;
     }
     /* r3 - r2 */
     if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
        goto ERR;
     }
     /* r1/3 */
     if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
        goto ERR;
     }
     /* r3/3 */
     if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
        goto ERR;
     }

     /* at this point shift W[n] by B*n */
     if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
        goto ERR;
     }

     if ((res = mp_add(&w0, &w1, b)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
        goto ERR;
     }
     if ((res = mp_add(&tmp1, b, b)) != MP_OKAY) {
        goto ERR;
     }

ERR:
     mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL);
     return res;
}

#endif

#include <tommath_private.h>
#ifdef BN_MP_TOOM_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* squaring using Toom-Cook 3-way algorithm */
int
mp_toom_sqr(mp_int *a, mp_int *b)
{
    mp_int w0, w1, w2, w3, w4, tmp1, a0, a1, a2;
................................................................................
       goto ERR;
    }

    if ((res = mp_copy(a, &a1)) != MP_OKAY) {
       goto ERR;
    }
    mp_rshd(&a1, B);
    if ((res = mp_mod_2d(&a1, DIGIT_BIT * B, &a1)) != MP_OKAY) {
       goto ERR;
    }

    if ((res = mp_copy(a, &a2)) != MP_OKAY) {
       goto ERR;
    }
    mp_rshd(&a2, B*2);

    /* w0 = a0*a0 */
................................................................................
       1  1  1  1  1
       16 8  4  2  1
       1  0  0  0  0

       using 12 subtractions, 4 shifts, 2 small divisions and 1 small multiplication.
     */

    /* r1 - r4 */
    if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
       goto ERR;
    }
    /* r3 - r0 */
    if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
       goto ERR;
    }
    /* r1/2 */
    if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
       goto ERR;
    }
    /* r3/2 */
    if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
       goto ERR;
    }
    /* r2 - r0 - r4 */
    if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
       goto ERR;
    }
    /* r1 - r2 */
    if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
       goto ERR;
    }
    /* r3 - r2 */
    if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
       goto ERR;
    }
    /* r1 - 8r0 */
    if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
       goto ERR;
    }
    /* r3 - 8r4 */
    if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
       goto ERR;
    }
    /* 3r2 - r1 - r3 */
    if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
       goto ERR;
    }
    /* r1 - r2 */
    if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
       goto ERR;
    }
    /* r3 - r2 */
    if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
       goto ERR;
    }
    /* r1/3 */
    if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
       goto ERR;
    }
    /* r3/3 */
    if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
       goto ERR;
    }

    /* at this point shift W[n] by B*n */
    if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
       goto ERR;
    }

    if ((res = mp_add(&w0, &w1, b)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
       goto ERR;
    }
    if ((res = mp_add(&tmp1, b, b)) != MP_OKAY) {
       goto ERR;
    }

ERR:
    mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL);
    return res;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_TORADIX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* stores a bignum as a ASCII string in a given radix (2..64) */
int mp_toradix (mp_int * a, char *str, int radix)
{
  int     res, digs;
  mp_int  t;
  mp_digit d;
  char   *_s = str;

  /* check range of the radix */
  if (radix < 2 || radix > 64) {
    return MP_VAL;
  }

  /* quick out if its zero */
  if (mp_iszero(a) == 1) {
     *str++ = '0';
     *str = '\0';
     return MP_OKAY;
  }

  if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
    return res;
................................................................................
  if (t.sign == MP_NEG) {
    ++_s;
    *str++ = '-';
    t.sign = MP_ZPOS;
  }

  digs = 0;
  while (mp_iszero (&t) == 0) {
    if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
      mp_clear (&t);
      return res;
    }
    *str++ = mp_s_rmap[d];
    ++digs;
  }
................................................................................
  *str = '\0';

  mp_clear (&t);
  return MP_OKAY;
}

#endif

#include <tommath_private.h>
#ifdef BN_MP_TORADIX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* stores a bignum as a ASCII string in a given radix (2..64) */
int mp_toradix (mp_int * a, char *str, int radix)
{
  int     res, digs;
  mp_int  t;
  mp_digit d;
  char   *_s = str;

  /* check range of the radix */
  if ((radix < 2) || (radix > 64)) {
    return MP_VAL;
  }

  /* quick out if its zero */
  if (mp_iszero(a) == MP_YES) {
     *str++ = '0';
     *str = '\0';
     return MP_OKAY;
  }

  if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
    return res;
................................................................................
  if (t.sign == MP_NEG) {
    ++_s;
    *str++ = '-';
    t.sign = MP_ZPOS;
  }

  digs = 0;
  while (mp_iszero (&t) == MP_NO) {
    if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
      mp_clear (&t);
      return res;
    }
    *str++ = mp_s_rmap[d];
    ++digs;
  }
................................................................................
  *str = '\0';

  mp_clear (&t);
  return MP_OKAY;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_TORADIX_N_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* stores a bignum as a ASCII string in a given radix (2..64) 
 *
 * Stores upto maxlen-1 chars and always a NULL byte 
 */
int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen)
................................................................................
{
  int     res, digs;
  mp_int  t;
  mp_digit d;
  char   *_s = str;

  /* check range of the maxlen, radix */
  if (maxlen < 2 || radix < 2 || radix > 64) {
    return MP_VAL;
  }

  /* quick out if its zero */
  if (mp_iszero(a) == MP_YES) {
     *str++ = '0';
     *str = '\0';
................................................................................
    t.sign = MP_ZPOS;
 
    /* subtract a char */
    --maxlen;
  }

  digs = 0;
  while (mp_iszero (&t) == 0) {
    if (--maxlen < 1) {
       /* no more room */
       break;
    }
    if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
      mp_clear (&t);
      return res;
................................................................................
  *str = '\0';

  mp_clear (&t);
  return MP_OKAY;
}

#endif

#include <tommath_private.h>
#ifdef BN_MP_TORADIX_N_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* stores a bignum as a ASCII string in a given radix (2..64) 
 *
 * Stores upto maxlen-1 chars and always a NULL byte 
 */
int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen)
................................................................................
{
  int     res, digs;
  mp_int  t;
  mp_digit d;
  char   *_s = str;

  /* check range of the maxlen, radix */
  if ((maxlen < 2) || (radix < 2) || (radix > 64)) {
    return MP_VAL;
  }

  /* quick out if its zero */
  if (mp_iszero(a) == MP_YES) {
     *str++ = '0';
     *str = '\0';
................................................................................
    t.sign = MP_ZPOS;
 
    /* subtract a char */
    --maxlen;
  }

  digs = 0;
  while (mp_iszero (&t) == MP_NO) {
    if (--maxlen < 1) {
       /* no more room */
       break;
    }
    if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
      mp_clear (&t);
      return res;
................................................................................
  *str = '\0';

  mp_clear (&t);
  return MP_OKAY;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_UNSIGNED_BIN_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* get the size for an unsigned equivalent */
int mp_unsigned_bin_size (mp_int * a)
{
  int     size = mp_count_bits (a);
  return (size / 8 + ((size & 7) != 0 ? 1 : 0));
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_UNSIGNED_BIN_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* get the size for an unsigned equivalent */
int mp_unsigned_bin_size (mp_int * a)
{
  int     size = mp_count_bits (a);
  return (size / 8) + (((size & 7) != 0) ? 1 : 0);
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_XOR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* XOR two ints together */
int
mp_xor (mp_int * a, mp_int * b, mp_int * c)
{
  int     res, ix, px;
................................................................................
  }
  mp_clamp (&t);
  mp_exch (c, &t);
  mp_clear (&t);
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_XOR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* XOR two ints together */
int
mp_xor (mp_int * a, mp_int * b, mp_int * c)
{
  int     res, ix, px;
................................................................................
  }
  mp_clamp (&t);
  mp_exch (c, &t);
  mp_clear (&t);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_MP_ZERO_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* set to zero */
void mp_zero (mp_int * a)
{
  int       n;
  mp_digit *tmp;
................................................................................

  tmp = a->dp;
  for (n = 0; n < a->alloc; n++) {
     *tmp++ = 0;
  }
}
#endif

#include <tommath_private.h>
#ifdef BN_MP_ZERO_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* set to zero */
void mp_zero (mp_int * a)
{
  int       n;
  mp_digit *tmp;
................................................................................

  tmp = a->dp;
  for (n = 0; n < a->alloc; n++) {
     *tmp++ = 0;
  }
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_PRIME_TAB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */
const mp_digit ltm_prime_tab[] = {
  0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
  0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
  0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
  0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F,
#ifndef MP_8BIT
................................................................................
  0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3,
  0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7,
  0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623,
  0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
#endif
};
#endif

#include <tommath_private.h>
#ifdef BN_PRIME_TAB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */
const mp_digit ltm_prime_tab[] = {
  0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
  0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
  0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
  0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F,
#ifndef MP_8BIT
................................................................................
  0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3,
  0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7,
  0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623,
  0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
#endif
};
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_REVERSE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* reverse an array, used for radix code */
void
bn_reverse (unsigned char *s, int len)
{
  int     ix, iy;
................................................................................
    s[ix] = s[iy];
    s[iy] = t;
    ++ix;
    --iy;
  }
}
#endif

#include <tommath_private.h>
#ifdef BN_REVERSE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* reverse an array, used for radix code */
void
bn_reverse (unsigned char *s, int len)
{
  int     ix, iy;
................................................................................
    s[ix] = s[iy];
    s[iy] = t;
    ++ix;
    --iy;
  }
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_S_MP_ADD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* low level addition, based on HAC pp.594, Algorithm 14.7 */
int
s_mp_add (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int *x;
................................................................................
  } else {
    min = a->used;
    max = b->used;
    x = b;
  }

  /* init result */
  if (c->alloc < max + 1) {
    if ((res = mp_grow (c, max + 1)) != MP_OKAY) {
      return res;
    }
  }

  /* get old used digit count and set new one */
  olduse = c->used;
  c->used = max + 1;

  {
    register mp_digit u, *tmpa, *tmpb, *tmpc;
    register int i;

    /* alias for digit pointers */

    /* first input */
    tmpa = a->dp;

    /* second input */
................................................................................
    }
  }

  mp_clamp (c);
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_S_MP_ADD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* low level addition, based on HAC pp.594, Algorithm 14.7 */
int
s_mp_add (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int *x;
................................................................................
  } else {
    min = a->used;
    max = b->used;
    x = b;
  }

  /* init result */
  if (c->alloc < (max + 1)) {
    if ((res = mp_grow (c, max + 1)) != MP_OKAY) {
      return res;
    }
  }

  /* get old used digit count and set new one */
  olduse = c->used;
  c->used = max + 1;

  {
    mp_digit u, *tmpa, *tmpb, *tmpc;
    int i;

    /* alias for digit pointers */

    /* first input */
    tmpa = a->dp;

    /* second input */
................................................................................
    }
  }

  mp_clamp (c);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_S_MP_EXPTMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */
#ifdef MP_LOW_MEM
   #define TAB_SIZE 32
#else
   #define TAB_SIZE 256
#endif

................................................................................
    buf <<= (mp_digit)1;

    /* if the bit is zero and mode == 0 then we ignore it
     * These represent the leading zero bits before the first 1 bit
     * in the exponent.  Technically this opt is not required but it
     * does lower the # of trivial squaring/reductions used
     */
    if (mode == 0 && y == 0) {
      continue;
    }

    /* if the bit is zero and mode == 1 then we square */
    if (mode == 1 && y == 0) {
      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
        goto LBL_RES;
      }
      if ((err = redux (&res, P, &mu)) != MP_OKAY) {
        goto LBL_RES;
      }
      continue;
................................................................................
      bitcpy = 0;
      bitbuf = 0;
      mode   = 1;
    }
  }

  /* if bits remain then square/multiply */
  if (mode == 2 && bitcpy > 0) {
    /* square then multiply if the bit is set */
    for (x = 0; x < bitcpy; x++) {
      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
        goto LBL_RES;
      }
      if ((err = redux (&res, P, &mu)) != MP_OKAY) {
        goto LBL_RES;
................................................................................
  mp_clear(&M[1]);
  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
    mp_clear (&M[x]);
  }
  return err;
}
#endif

#include <tommath_private.h>
#ifdef BN_S_MP_EXPTMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */
#ifdef MP_LOW_MEM
   #define TAB_SIZE 32
#else
   #define TAB_SIZE 256
#endif

................................................................................
    buf <<= (mp_digit)1;

    /* if the bit is zero and mode == 0 then we ignore it
     * These represent the leading zero bits before the first 1 bit
     * in the exponent.  Technically this opt is not required but it
     * does lower the # of trivial squaring/reductions used
     */
    if ((mode == 0) && (y == 0)) {
      continue;
    }

    /* if the bit is zero and mode == 1 then we square */
    if ((mode == 1) && (y == 0)) {
      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
        goto LBL_RES;
      }
      if ((err = redux (&res, P, &mu)) != MP_OKAY) {
        goto LBL_RES;
      }
      continue;
................................................................................
      bitcpy = 0;
      bitbuf = 0;
      mode   = 1;
    }
  }

  /* if bits remain then square/multiply */
  if ((mode == 2) && (bitcpy > 0)) {
    /* square then multiply if the bit is set */
    for (x = 0; x < bitcpy; x++) {
      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
        goto LBL_RES;
      }
      if ((err = redux (&res, P, &mu)) != MP_OKAY) {
        goto LBL_RES;
................................................................................
  mp_clear(&M[1]);
  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
    mp_clear (&M[x]);
  }
  return err;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_S_MP_MUL_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* multiplies |a| * |b| and only computes upto digs digits of result
 * HAC pp. 595, Algorithm 14.12  Modified so you can control how 
 * many digits of output are created.
 */
int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
................................................................................
  int     res, pa, pb, ix, iy;
  mp_digit u;
  mp_word r;
  mp_digit tmpx, *tmpt, *tmpy;

  /* can we use the fast multiplier? */
  if (((digs) < MP_WARRAY) &&
      MIN (a->used, b->used) < 
          (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
    return fast_s_mp_mul_digs (a, b, c, digs);
  }

  if ((res = mp_init_size (&t, digs)) != MP_OKAY) {
    return res;
  }
  t.used = digs;
................................................................................
    
    /* an alias for the digits of b */
    tmpy = b->dp;

    /* compute the columns of the output and propagate the carry */
    for (iy = 0; iy < pb; iy++) {
      /* compute the column as a mp_word */
      r       = ((mp_word)*tmpt) +
                ((mp_word)tmpx) * ((mp_word)*tmpy++) +
                ((mp_word) u);

      /* the new column is the lower part of the result */
      *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));

      /* get the carry word from the result */
      u       = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
    }
    /* set carry if it is placed below digs */
    if (ix + iy < digs) {
      *tmpt = u;
    }
  }

  mp_clamp (&t);
  mp_exch (&t, c);

  mp_clear (&t);
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_S_MP_MUL_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* multiplies |a| * |b| and only computes upto digs digits of result
 * HAC pp. 595, Algorithm 14.12  Modified so you can control how 
 * many digits of output are created.
 */
int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
................................................................................
  int     res, pa, pb, ix, iy;
  mp_digit u;
  mp_word r;
  mp_digit tmpx, *tmpt, *tmpy;

  /* can we use the fast multiplier? */
  if (((digs) < MP_WARRAY) &&
      (MIN (a->used, b->used) < 
          (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) {
    return fast_s_mp_mul_digs (a, b, c, digs);
  }

  if ((res = mp_init_size (&t, digs)) != MP_OKAY) {
    return res;
  }
  t.used = digs;
................................................................................
    
    /* an alias for the digits of b */
    tmpy = b->dp;

    /* compute the columns of the output and propagate the carry */
    for (iy = 0; iy < pb; iy++) {
      /* compute the column as a mp_word */
      r       = (mp_word)*tmpt +
                ((mp_word)tmpx * (mp_word)*tmpy++) +
                (mp_word)u;

      /* the new column is the lower part of the result */
      *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));

      /* get the carry word from the result */
      u       = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
    }
    /* set carry if it is placed below digs */
    if ((ix + iy) < digs) {
      *tmpt = u;
    }
  }

  mp_clamp (&t);
  mp_exch (&t, c);

  mp_clear (&t);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_S_MP_MUL_HIGH_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* multiplies |a| * |b| and does not compute the lower digs digits
 * [meant to get the higher part of the product]
 */
int
s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
................................................................................
  mp_digit u;
  mp_word r;
  mp_digit tmpx, *tmpt, *tmpy;

  /* can we use the fast multiplier? */
#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
  if (((a->used + b->used + 1) < MP_WARRAY)
      && MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
    return fast_s_mp_mul_high_digs (a, b, c, digs);
  }
#endif

  if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) {
    return res;
  }
................................................................................
    tmpt = &(t.dp[digs]);

    /* alias for where to read the right hand side from */
    tmpy = b->dp + (digs - ix);

    for (iy = digs - ix; iy < pb; iy++) {
      /* calculate the double precision result */
      r       = ((mp_word)*tmpt) +
                ((mp_word)tmpx) * ((mp_word)*tmpy++) +
                ((mp_word) u);

      /* get the lower part */
      *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));

      /* carry the carry */
      u       = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
    }
................................................................................
  }
  mp_clamp (&t);
  mp_exch (&t, c);
  mp_clear (&t);
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_S_MP_MUL_HIGH_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* multiplies |a| * |b| and does not compute the lower digs digits
 * [meant to get the higher part of the product]
 */
int
s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
................................................................................
  mp_digit u;
  mp_word r;
  mp_digit tmpx, *tmpt, *tmpy;

  /* can we use the fast multiplier? */
#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
  if (((a->used + b->used + 1) < MP_WARRAY)
      && (MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) {
    return fast_s_mp_mul_high_digs (a, b, c, digs);
  }
#endif

  if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) {
    return res;
  }
................................................................................
    tmpt = &(t.dp[digs]);

    /* alias for where to read the right hand side from */
    tmpy = b->dp + (digs - ix);

    for (iy = digs - ix; iy < pb; iy++) {
      /* calculate the double precision result */
      r       = (mp_word)*tmpt +
                ((mp_word)tmpx * (mp_word)*tmpy++) +
                (mp_word)u;

      /* get the lower part */
      *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));

      /* carry the carry */
      u       = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
    }
................................................................................
  }
  mp_clamp (&t);
  mp_exch (&t, c);
  mp_clear (&t);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_S_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
int s_mp_sqr (mp_int * a, mp_int * b)
{
  mp_int  t;
  int     res, ix, iy, pa;
  mp_word r;
  mp_digit u, tmpx, *tmpt;

  pa = a->used;
  if ((res = mp_init_size (&t, 2*pa + 1)) != MP_OKAY) {
    return res;
  }

  /* default used is maximum possible size */
  t.used = 2*pa + 1;

  for (ix = 0; ix < pa; ix++) {
    /* first calculate the digit at 2*ix */
    /* calculate double precision result */
    r = ((mp_word) t.dp[2*ix]) +
        ((mp_word)a->dp[ix])*((mp_word)a->dp[ix]);

    /* store lower part in result */
    t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK));

    /* get the carry */
    u           = (mp_digit)(r >> ((mp_word) DIGIT_BIT));

    /* left hand side of A[ix] * A[iy] */
    tmpx        = a->dp[ix];

    /* alias for where to store the results */
    tmpt        = t.dp + (2*ix + 1);
    
    for (iy = ix + 1; iy < pa; iy++) {
      /* first calculate the product */
      r       = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);

      /* now calculate the double precision result, note we use
       * addition instead of *2 since it's easier to optimize
................................................................................

  mp_clamp (&t);
  mp_exch (&t, b);
  mp_clear (&t);
  return MP_OKAY;
}
#endif

#include <tommath_private.h>
#ifdef BN_S_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
int s_mp_sqr (mp_int * a, mp_int * b)
{
  mp_int  t;
  int     res, ix, iy, pa;
  mp_word r;
  mp_digit u, tmpx, *tmpt;

  pa = a->used;
  if ((res = mp_init_size (&t, (2 * pa) + 1)) != MP_OKAY) {
    return res;
  }

  /* default used is maximum possible size */
  t.used = (2 * pa) + 1;

  for (ix = 0; ix < pa; ix++) {
    /* first calculate the digit at 2*ix */
    /* calculate double precision result */
    r = (mp_word)t.dp[2*ix] +
        ((mp_word)a->dp[ix] * (mp_word)a->dp[ix]);

    /* store lower part in result */
    t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK));

    /* get the carry */
    u           = (mp_digit)(r >> ((mp_word) DIGIT_BIT));

    /* left hand side of A[ix] * A[iy] */
    tmpx        = a->dp[ix];

    /* alias for where to store the results */
    tmpt        = t.dp + ((2 * ix) + 1);
    
    for (iy = ix + 1; iy < pa; iy++) {
      /* first calculate the product */
      r       = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);

      /* now calculate the double precision result, note we use
       * addition instead of *2 since it's easier to optimize
................................................................................

  mp_clamp (&t);
  mp_exch (&t, b);
  mp_clear (&t);
  return MP_OKAY;
}
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BN_S_MP_SUB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
int
s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
{
  int     olduse, res, min, max;
................................................................................
      return res;
    }
  }
  olduse = c->used;
  c->used = max;

  {
    register mp_digit u, *tmpa, *tmpb, *tmpc;
    register int i;

    /* alias for digit pointers */
    tmpa = a->dp;
    tmpb = b->dp;
    tmpc = c->dp;

    /* set carry to zero */
    u = 0;
    for (i = 0; i < min; i++) {
      /* T[i] = A[i] - B[i] - U */
      *tmpc = *tmpa++ - *tmpb++ - u;

      /* U = carry bit of T[i]
       * Note this saves performing an AND operation since
       * if a carry does occur it will propagate all the way to the
       * MSB.  As a result a single shift is enough to get the carry
       */
      u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));

      /* Clear carry from T[i] */
      *tmpc++ &= MP_MASK;
    }

    /* now copy higher words if any, e.g. if A has more digits than B  */
    for (; i < max; i++) {
      /* T[i] = A[i] - U */
      *tmpc = *tmpa++ - u;

      /* U = carry bit of T[i] */
      u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));

      /* Clear carry from T[i] */
      *tmpc++ &= MP_MASK;
    }

    /* clear digits above used (since we may not have grown result above) */
    for (i = c->used; i < olduse; i++) {
................................................................................
  }

  mp_clamp (c);
  return MP_OKAY;
}

#endif

#include <tommath_private.h>
#ifdef BN_S_MP_SUB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
int
s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
{
  int     olduse, res, min, max;
................................................................................
      return res;
    }
  }
  olduse = c->used;
  c->used = max;

  {
    mp_digit u, *tmpa, *tmpb, *tmpc;
    int i;

    /* alias for digit pointers */
    tmpa = a->dp;
    tmpb = b->dp;
    tmpc = c->dp;

    /* set carry to zero */
    u = 0;
    for (i = 0; i < min; i++) {
      /* T[i] = A[i] - B[i] - U */
      *tmpc = (*tmpa++ - *tmpb++) - u;

      /* U = carry bit of T[i]
       * Note this saves performing an AND operation since
       * if a carry does occur it will propagate all the way to the
       * MSB.  As a result a single shift is enough to get the carry
       */
      u = *tmpc >> ((mp_digit)((CHAR_BIT * sizeof(mp_digit)) - 1));

      /* Clear carry from T[i] */
      *tmpc++ &= MP_MASK;
    }

    /* now copy higher words if any, e.g. if A has more digits than B  */
    for (; i < max; i++) {
      /* T[i] = A[i] - U */
      *tmpc = *tmpa++ - u;

      /* U = carry bit of T[i] */
      u = *tmpc >> ((mp_digit)((CHAR_BIT * sizeof(mp_digit)) - 1));

      /* Clear carry from T[i] */
      *tmpc++ &= MP_MASK;
    }

    /* clear digits above used (since we may not have grown result above) */
    for (i = c->used; i < olduse; i++) {
................................................................................
  }

  mp_clamp (c);
  return MP_OKAY;
}

#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#ifdef BNCORE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
 */

/* Known optimal configurations

 CPU                    /Compiler     /MUL CUTOFF/SQR CUTOFF
-------------------------------------------------------------
 Intel P4 Northwood     /GCC v3.4.1   /        88/       128/LTM 0.32 ;-)
................................................................................

int     KARATSUBA_MUL_CUTOFF = 80,      /* Min. number of digits before Karatsuba multiplication is used. */
        KARATSUBA_SQR_CUTOFF = 120,     /* Min. number of digits before Karatsuba squaring is used. */
        
        TOOM_MUL_CUTOFF      = 350,      /* no optimal values of these are known yet so set em high */
        TOOM_SQR_CUTOFF      = 400; 
#endif

#include <tommath_private.h>
#ifdef BNCORE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
 */

/* Known optimal configurations

 CPU                    /Compiler     /MUL CUTOFF/SQR CUTOFF
-------------------------------------------------------------
 Intel P4 Northwood     /GCC v3.4.1   /        88/       128/LTM 0.32 ;-)
................................................................................

int     KARATSUBA_MUL_CUTOFF = 80,      /* Min. number of digits before Karatsuba multiplication is used. */
        KARATSUBA_SQR_CUTOFF = 120,     /* Min. number of digits before Karatsuba squaring is used. */
        
        TOOM_MUL_CUTOFF      = 350,      /* no optimal values of these are known yet so set em high */
        TOOM_SQR_CUTOFF      = 400; 
#endif

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#Tom St Denis

#get graphics type
if (shift =~ /PDF/) {
   $graph = "";
} else {
   $graph = ".ps";
}   

open(IN,"<tommath.src") or die "Can't open source file";
open(OUT,">tommath.tex") or die "Can't open destination file";

print "Scanning for sections\n";
$chapter = $section = $subsection = 0;
$x = 0;
while (<IN>) {
   print ".";
   if (!(++$x % 80)) { print "\n"; }
   #update the headings 
   if (~($_ =~ /\*/)) {
      if ($_ =~ /\\chapter{.+}/) {
          ++$chapter;
          $section = $subsection = 0;
      } elsif ($_ =~ /\\section{.+}/) {
          ++$section;
          $subsection = 0;
      } elsif ($_ =~ /\\subsection{.+}/) {
          ++$subsection;
      }
   }      

   if ($_ =~ m/MARK/) {
      @m = split(",",$_);
      chomp(@m[1]);
      $index1{@m[1]} = $chapter;
      $index2{@m[1]} = $section;
      $index3{@m[1]} = $subsection;
................................................................................
open(IN,"<tommath.src") or die "Can't open source file";
$readline = $wroteline = 0;
$srcline = 0;

while (<IN>) {
   ++$readline;
   ++$srcline;
   
   if ($_ =~ m/MARK/) {
   } elsif ($_ =~ m/EXAM/ || $_ =~ m/LIST/) {
      if ($_ =~ m/EXAM/) {
         $skipheader = 1;
      } else {
         $skipheader = 0;
      }
      
      # EXAM,file
      chomp($_);
      @m = split(",",$_);
      open(SRC,"<$m[1]") or die "Error:$srcline:Can't open source file $m[1]";
      
      print "$srcline:Inserting $m[1]:";
      
      $line = 0;
      $tmp = $m[1];
      $tmp =~ s/_/"\\_"/ge;
      print OUT "\\vspace{+3mm}\\begin{small}\n\\hspace{-5.1mm}{\\bf File}: $tmp\n\\vspace{-3mm}\n\\begin{alltt}\n";
      $wroteline += 5;
      
      if ($skipheader == 1) {
         # scan till next end of comment, e.g. skip license 
         while (<SRC>) {
            $text[$line++] = $_;
            last if ($_ =~ /math\.libtomcrypt\.org/);
         }
         <SRC>;   
      }
      
      $inline = 0;
      while (<SRC>) {
      next if ($_ =~ /\$Source/);
      next if ($_ =~ /\$Revision/);
      next if ($_ =~ /\$Date/);
         $text[$line++] = $_;
         ++$inline;
         chomp($_);
         $_ =~ s/\t/"    "/ge;
         $_ =~ s/{/"^{"/ge;
         $_ =~ s/}/"^}"/ge;
         $_ =~ s/\\/'\symbol{92}'/ge;
         $_ =~ s/\^/"\\"/ge;
           
         printf OUT ("%03d   ", $line);
         for ($x = 0; $x < length($_); $x++) {
             print OUT chr(vec($_, $x, 8));
             if ($x == 75) { 
                 print OUT "\n      ";
                 ++$wroteline;
             }
         }
         print OUT "\n";
         ++$wroteline;
      }
................................................................................
      $wroteline += 2;
   } elsif ($_ =~ m/@\d+,[email protected]/) {
     # line contains [number,text]
     # e.g. @14,for (ix = 0)@
     $txt = $_;
     while ($txt =~ m/@\d+,[email protected]/) {
        @m = split("@",$txt);      # splits into text, one, two
        @parms = split(",",$m[1]);  # splits one,two into two elements 
                
        # now search from $parms[0] down for $parms[1] 
        $found1 = 0;
        $found2 = 0;
        for ($i = $parms[0]; $i < $totlines && $found1 == 0; $i++) {
           if ($text[$i] =~ m/\Q$parms[1]\E/) {
              $foundline1 = $i + 1;
              $found1 = 1;
           }
        }
        
        # now search backwards
        for ($i = $parms[0] - 1; $i >= 0 && $found2 == 0; $i--) {
           if ($text[$i] =~ m/\Q$parms[1]\E/) {
              $foundline2 = $i + 1;
              $found2 = 1;
           }
        }
        
        # now use the closest match or the first if tied
        if ($found1 == 1 && $found2 == 0) {
           $found = 1;
           $foundline = $foundline1;
        } elsif ($found1 == 0 && $found2 == 1) {
           $found = 1;
           $foundline = $foundline2;
................................................................................
              $foundline = $foundline1;
           } else {
              $foundline = $foundline2;
           }
        } else {
           $found = 0;
        }
                      
        # if found replace 
        if ($found == 1) {
           $delta = $parms[0] - $foundline;
           print "Found replacement tag for \"$parms[1]\" on line $srcline which refers to line $foundline (delta $delta)\n";
           $_ =~ s/@\Q$m[1]\[email protected]/$foundline/;
        } else {
           print "ERROR:  The tag \"$parms[1]\" on line $srcline was not found in the most recently parsed source!\n";
        }
        
        # remake the rest of the line 
        $cnt = @m;
        $txt = "";
        for ($i = 2; $i < $cnt; $i++) {
            $txt = $txt . $m[$i] . "@";
        }
     }
     print OUT $_;
     ++$wroteline;
   } elsif ($_ =~ /~.+~/) {
      # line contains a ~text~ pair used to refer to indexing :-)
      $txt = $_;
      while ($txt =~ /~.+~/) {
         @m = split("~", $txt);
         
         # word is the second position
         $word = @m[1];
         $a = $index1{$word};
         $b = $index2{$word};
         $c = $index3{$word};
         
         # if chapter (a) is zero it wasn't found
         if ($a == 0) {
            print "ERROR: the tag \"$word\" on line $srcline was not found previously marked.\n";
         } else {
            # format the tag as x, x.y or x.y.z depending on the values
            $str = $a;
            $str = $str . ".$b" if ($b != 0);
            $str = $str . ".$c" if ($c != 0);
            
            if ($b == 0 && $c == 0) {
               # its a chapter
               if ($a <= 10) {
                  if ($a == 1) {
                     $str = "chapter one";
                  } elsif ($a == 2) {
                     $str = "chapter two";
................................................................................
                  } elsif ($a == 10) {
                     $str = "chapter ten";
                  }
               } else {
                  $str = "chapter " . $str;
               }
            } else {
               $str = "section " . $str     if ($b != 0 && $c == 0);            
               $str = "sub-section " . $str if ($b != 0 && $c != 0);
            }
            
            #substitute
            $_ =~ s/~\Q$word\E~/$str/;
            
            print "Found replacement tag for marker \"$word\" on line $srcline which refers to $str\n";
         }
         
         # remake rest of the line
         $cnt = @m;
         $txt = "";
         for ($i = 2; $i < $cnt; $i++) {
             $txt = $txt . $m[$i] . "~";
         }
      }
................................................................................
      ++$wroteline;
   }
}
print "Read $readline lines, wrote $wroteline lines\n";

close (OUT);
close (IN);

#Tom St Denis

#get graphics type
if (shift =~ /PDF/) {
   $graph = "";
} else {
   $graph = ".ps";
}

open(IN,"<tommath.src") or die "Can't open source file";
open(OUT,">tommath.tex") or die "Can't open destination file";

print "Scanning for sections\n";
$chapter = $section = $subsection = 0;
$x = 0;
while (<IN>) {
   print ".";
   if (!(++$x % 80)) { print "\n"; }
   #update the headings
   if (~($_ =~ /\*/)) {
      if ($_ =~ /\\chapter\{.+}/) {
          ++$chapter;
          $section = $subsection = 0;
      } elsif ($_ =~ /\\section\{.+}/) {
          ++$section;
          $subsection = 0;
      } elsif ($_ =~ /\\subsection\{.+}/) {
          ++$subsection;
      }
   }

   if ($_ =~ m/MARK/) {
      @m = split(",",$_);
      chomp(@m[1]);
      $index1{@m[1]} = $chapter;
      $index2{@m[1]} = $section;
      $index3{@m[1]} = $subsection;
................................................................................
open(IN,"<tommath.src") or die "Can't open source file";
$readline = $wroteline = 0;
$srcline = 0;

while (<IN>) {
   ++$readline;
   ++$srcline;

   if ($_ =~ m/MARK/) {
   } elsif ($_ =~ m/EXAM/ || $_ =~ m/LIST/) {
      if ($_ =~ m/EXAM/) {
         $skipheader = 1;
      } else {
         $skipheader = 0;
      }

      # EXAM,file
      chomp($_);
      @m = split(",",$_);
      open(SRC,"<$m[1]") or die "Error:$srcline:Can't open source file $m[1]";

      print "$srcline:Inserting $m[1]:";

      $line = 0;
      $tmp = $m[1];
      $tmp =~ s/_/"\\_"/ge;
      print OUT "\\vspace{+3mm}\\begin{small}\n\\hspace{-5.1mm}{\\bf File}: $tmp\n\\vspace{-3mm}\n\\begin{alltt}\n";
      $wroteline += 5;

      if ($skipheader == 1) {
         # scan till next end of comment, e.g. skip license
         while (<SRC>) {
            $text[$line++] = $_;
            last if ($_ =~ /libtom\.org/);
         }
         <SRC>;
      }

      $inline = 0;
      while (<SRC>) {
      next if ($_ =~ /\$Source/);
      next if ($_ =~ /\$Revision/);
      next if ($_ =~ /\$Date/);
         $text[$line++] = $_;
         ++$inline;
         chomp($_);
         $_ =~ s/\t/"    "/ge;
         $_ =~ s/{/"^{"/ge;
         $_ =~ s/}/"^}"/ge;
         $_ =~ s/\\/'\symbol{92}'/ge;
         $_ =~ s/\^/"\\"/ge;

         printf OUT ("%03d   ", $line);
         for ($x = 0; $x < length($_); $x++) {
             print OUT chr(vec($_, $x, 8));
             if ($x == 75) {
                 print OUT "\n      ";
                 ++$wroteline;
             }
         }
         print OUT "\n";
         ++$wroteline;
      }
................................................................................
      $wroteline += 2;
   } elsif ($_ =~ m/@\d+,[email protected]/) {
     # line contains [number,text]
     # e.g. @14,for (ix = 0)@
     $txt = $_;
     while ($txt =~ m/@\d+,[email protected]/) {
        @m = split("@",$txt);      # splits into text, one, two
        @parms = split(",",$m[1]);  # splits one,two into two elements

        # now search from $parms[0] down for $parms[1]
        $found1 = 0;
        $found2 = 0;
        for ($i = $parms[0]; $i < $totlines && $found1 == 0; $i++) {
           if ($text[$i] =~ m/\Q$parms[1]\E/) {
              $foundline1 = $i + 1;
              $found1 = 1;
           }
        }

        # now search backwards
        for ($i = $parms[0] - 1; $i >= 0 && $found2 == 0; $i--) {
           if ($text[$i] =~ m/\Q$parms[1]\E/) {
              $foundline2 = $i + 1;
              $found2 = 1;
           }
        }

        # now use the closest match or the first if tied
        if ($found1 == 1 && $found2 == 0) {
           $found = 1;
           $foundline = $foundline1;
        } elsif ($found1 == 0 && $found2 == 1) {
           $found = 1;
           $foundline = $foundline2;
................................................................................
              $foundline = $foundline1;
           } else {
              $foundline = $foundline2;
           }
        } else {
           $found = 0;
        }

        # if found replace
        if ($found == 1) {
           $delta = $parms[0] - $foundline;
           print "Found replacement tag for \"$parms[1]\" on line $srcline which refers to line $foundline (delta $delta)\n";
           $_ =~ s/@\Q$m[1]\[email protected]/$foundline/;
        } else {
           print "ERROR:  The tag \"$parms[1]\" on line $srcline was not found in the most recently parsed source!\n";
        }

        # remake the rest of the line
        $cnt = @m;
        $txt = "";
        for ($i = 2; $i < $cnt; $i++) {
            $txt = $txt . $m[$i] . "@";
        }
     }
     print OUT $_;
     ++$wroteline;
   } elsif ($_ =~ /~.+~/) {
      # line contains a ~text~ pair used to refer to indexing :-)
      $txt = $_;
      while ($txt =~ /~.+~/) {
         @m = split("~", $txt);

         # word is the second position
         $word = @m[1];
         $a = $index1{$word};
         $b = $index2{$word};
         $c = $index3{$word};

         # if chapter (a) is zero it wasn't found
         if ($a == 0) {
            print "ERROR: the tag \"$word\" on line $srcline was not found previously marked.\n";
         } else {
            # format the tag as x, x.y or x.y.z depending on the values
            $str = $a;
            $str = $str . ".$b" if ($b != 0);
            $str = $str . ".$c" if ($c != 0);

            if ($b == 0 && $c == 0) {
               # its a chapter
               if ($a <= 10) {
                  if ($a == 1) {
                     $str = "chapter one";
                  } elsif ($a == 2) {
                     $str = "chapter two";
................................................................................
                  } elsif ($a == 10) {
                     $str = "chapter ten";
                  }
               } else {
                  $str = "chapter " . $str;
               }
            } else {
               $str = "section " . $str     if ($b != 0 && $c == 0);
               $str = "sub-section " . $str if ($b != 0 && $c != 0);
            }

            #substitute
            $_ =~ s/~\Q$word\E~/$str/;

            print "Found replacement tag for marker \"$word\" on line $srcline which refers to $str\n";
         }

         # remake rest of the line
         $cnt = @m;
         $txt = "";
         for ($i = 2; $i < $cnt; $i++) {
             $txt = $txt . $m[$i] . "~";
         }
      }
................................................................................
      ++$wroteline;
   }
}
print "Read $readline lines, wrote $wroteline lines\n";

close (OUT);
close (IN);

system('perl -pli -e "s/\s*$//" tommath.tex');

July 23rd, 2010
v0.42.0
       -- Fix for mp_prime_next_prime() bug when checking generated prime
       -- allow mp_shrink to shrink initialized, but empty MPI's
       -- Added project and solution files for Visual Studio 2005 and Visual Studio 2008. 

March 10th, 2007
v0.41  -- Wolfgang Ehrhardt suggested a quick fix to mp_div_d() which makes the detection of powers of two quicker. 
       -- [CRI] Added libtommath.dsp for Visual C++ users.

December 24th, 2006
v0.40  -- Updated makefile to properly support LIBNAME
       -- Fixed bug in fast_s_mp_mul_high_digs() which overflowed (line 83), thanks Valgrind!

April 4th, 2006
................................................................................
       -- "mm" from sci.crypt pointed out that my mp_gcd was sub-optimal (I also updated and corrected the book)
       -- updated some of the @@ tags in tommath.src to reflect source changes.
       -- updated email and url info in all source files

Jan 26th, 2006
v0.38  -- broken makefile.shared fixed
       -- removed some carry stores that were not required [updated text]
       
November 18th, 2005
v0.37  -- [Don Porter] reported on a TCL list [HEY SEND ME BUGREPORTS ALREADY!!!] that mp_add_d() would compute -0 with some inputs.  Fixed.
       -- [[email protected]] reported the makefile.bcc was messed up.  Fixed.
       -- [Kevin Kenny] reported some issues with mp_toradix_n().  Now it doesn't require a min of 3 chars of output.  
       -- Made the make command renamable.  Wee

August 1st, 2005
v0.36  -- LTM_PRIME_2MSB_ON was fixed and the "OFF" flag was removed.
       -- [Peter LaDow] found a typo in the XREALLOC macro
       -- [Peter LaDow] pointed out that mp_read_(un)signed_bin should have "const" on the input
       -- Ported LTC patch to fix the prime_random_ex() function to get the bitsize correct [and the maskOR flags]
       -- Kevin Kenny pointed out a stray //
       -- David Hulton pointed out a typo in the textbook [mp_montgomery_setup() pseudo-code]
       -- Neal Hamilton (Elliptic Semiconductor) pointed out that my Karatsuba notation was backwards and that I could use 
          unsigned operations in the routine.  
       -- Paul Schmidt pointed out a linking error in mp_exptmod() when BN_S_MP_EXPTMOD_C is undefined (and another for read_radix)
       -- Updated makefiles to be way more flexible

March 12th, 2005
v0.35  -- Stupid XOR function missing line again... oops.
       -- Fixed bug in invmod not handling negative inputs correctly [Wolfgang Ehrhardt]
       -- Made exteuclid always give positive u3 output...[ Wolfgang Ehrhardt ]
       -- [Wolfgang Ehrhardt] Suggested a fix for mp_reduce() which avoided underruns.  ;-)
       -- mp_rand() would emit one too many digits and it was possible to get a 0 out of it ... oops
       -- Added montgomery to the testing to make sure it handles 1..10 digit moduli correctly
       -- Fixed bug in comba that would lead to possible erroneous outputs when "pa < digs" 
       -- Fixed bug in mp_toradix_size for "0" [Kevin Kenny]
       -- Updated chapters 1-5 of the textbook ;-) It now talks about the new comba code!

February 12th, 2005
v0.34  -- Fixed two more small errors in mp_prime_random_ex()
       -- Fixed overflow in mp_mul_d() [Kevin Kenny]
       -- Added mp_to_(un)signed_bin_n() functions which do bounds checking for ya [and report the size]
       -- Added "large" diminished radix support.  Speeds up things like DSA where the moduli is of the form 2^k - P for some P < 2^(k/2) or so
          Actually is faster than Montgomery on my AMD64 (and probably much faster on a P4)
       -- Updated the manual a bit
       -- Ok so I haven't done the textbook work yet... My current freelance gig has landed me in France till the 
          end of Feb/05.  Once I get back I'll have tons of free time and I plan to go to town on the book.
          As of this release the API will freeze.  At least until the book catches up with all the changes.  I welcome
          bug reports but new algorithms will have to wait.

December 23rd, 2004
v0.33  -- Fixed "small" variant for mp_div() which would munge with negative dividends...
       -- Fixed bug in mp_prime_random_ex() which would set the most significant byte to zero when
................................................................................
       -- Made the makefiles easier to configure the group/user that ltm will install as
       -- Fixed "final carry" bug in comba multipliers. (Volkan Ceylan)
       -- Matt Johnston pointed out a missing semi-colon in mp_exptmod

October 29th, 2004
v0.32  -- Added "makefile.shared" for shared object support
       -- Added more to the build options/configs in the manual
       -- Started the Depends framework, wrote dep.pl to scan deps and 
          produce "callgraph.txt" ;-)
       -- Wrote SC_RSA_1 which will enable close to the minimum required to perform
          RSA on 32-bit [or 64-bit] platforms with LibTomCrypt
       -- Merged in the small/slower mp_div replacement.  You can now toggle which
          you want to use as your mp_div() at build time.  Saves roughly 8KB or so.
       -- Renamed a few files and changed some comments to make depends system work better.
          (No changes to function names)
       -- Merged in new Combas that perform 2 reads per inner loop instead of the older 
          3reads/2writes per inner loop of the old code.  Really though if you want speed
          learn to use TomsFastMath ;-)

August 9th, 2004
v0.31  -- "profiled" builds now :-) new timings for Intel Northwoods
       -- Added "pretty" build target
       -- Update mp_init() to actually assign 0's instead of relying on calloc()
................................................................................
          is only accurate to byte lengths).  See the new LTM_PRIME_* flags ;-)
       -- Alex Polushin contributed an optimized mp_sqrt() as well as mp_get_int() and mp_is_square().
          I've cleaned them all up to be a little more consistent [along with one bug fix] for this release.
       -- Added mp_init_set and mp_init_set_int to initialize and set small constants with one function
          call.
       -- Removed /etclib directory [um LibTomPoly deprecates this].
       -- Fixed mp_mod() so the sign of the result agrees with the sign of the modulus.
       ++ N.B.  My semester is almost up so expect updates to the textbook to be posted to the libtomcrypt.org 
          website.  

Jan 25th, 2004
v0.29  ++ Note: "Henrik" from the v0.28 changelog refers to Henrik Goldman ;-)
       -- Added fix to mp_shrink to prevent a realloc when used == 0 [e.g. realloc zero bytes???]
       -- Made the mp_prime_rabin_miller_trials() function internal table smaller and also
          set the minimum number of tests to two (sounds a bit safer).
       -- Added a mp_exteuclid() which computes the extended euclidean algorithm.

Feb 5th, 2016
v1.0.0
       -- Bump to 1.0.0
       -- Dirkjan Bussink provided a faster version of mp_expt_d()
       -- Moritz Lenz contributed a fix to mp_mod()
          and provided mp_get_long() and mp_set_long()
       -- Fixed bugs in mp_read_radix(), mp_radix_size
          Thanks to shameister, Gerhard R,
       -- Christopher Brown provided mp_export() and mp_import()
       -- Improvements in the code of mp_init_copy()
          Thanks to ramkumarkoppu,
       -- lomereiter provided mp_balance_mul()
       -- Alexander Boström from the heimdal project contributed patches to
          mp_prime_next_prime() and mp_invmod() and added a mp_isneg() macro
       -- Fix build issues for Linux x32 ABI
       -- Added mp_get_long_long() and mp_set_long_long()
       -- Carlin provided a patch to use arc4random() instead of rand()
          on platforms where it is supported
       -- Karel Miko provided mp_sqrtmod_prime()


July 23rd, 2010
v0.42.0
       -- Fix for mp_prime_next_prime() bug when checking generated prime
       -- allow mp_shrink to shrink initialized, but empty MPI's
       -- Added project and solution files for Visual Studio 2005 and Visual Studio 2008.

March 10th, 2007
v0.41  -- Wolfgang Ehrhardt suggested a quick fix to mp_div_d() which makes the detection of powers of two quicker.
       -- [CRI] Added libtommath.dsp for Visual C++ users.

December 24th, 2006
v0.40  -- Updated makefile to properly support LIBNAME
       -- Fixed bug in fast_s_mp_mul_high_digs() which overflowed (line 83), thanks Valgrind!

April 4th, 2006
................................................................................
       -- "mm" from sci.crypt pointed out that my mp_gcd was sub-optimal (I also updated and corrected the book)
       -- updated some of the @@ tags in tommath.src to reflect source changes.
       -- updated email and url info in all source files

Jan 26th, 2006
v0.38  -- broken makefile.shared fixed
       -- removed some carry stores that were not required [updated text]

November 18th, 2005
v0.37  -- [Don Porter] reported on a TCL list [HEY SEND ME BUGREPORTS ALREADY!!!] that mp_add_d() would compute -0 with some inputs.  Fixed.
       -- [[email protected]] reported the makefile.bcc was messed up.  Fixed.
       -- [Kevin Kenny] reported some issues with mp_toradix_n().  Now it doesn't require a min of 3 chars of output.
       -- Made the make command renamable.  Wee

August 1st, 2005
v0.36  -- LTM_PRIME_2MSB_ON was fixed and the "OFF" flag was removed.
       -- [Peter LaDow] found a typo in the XREALLOC macro
       -- [Peter LaDow] pointed out that mp_read_(un)signed_bin should have "const" on the input
       -- Ported LTC patch to fix the prime_random_ex() function to get the bitsize correct [and the maskOR flags]
       -- Kevin Kenny pointed out a stray //
       -- David Hulton pointed out a typo in the textbook [mp_montgomery_setup() pseudo-code]
       -- Neal Hamilton (Elliptic Semiconductor) pointed out that my Karatsuba notation was backwards and that I could use
          unsigned operations in the routine.
       -- Paul Schmidt pointed out a linking error in mp_exptmod() when BN_S_MP_EXPTMOD_C is undefined (and another for read_radix)
       -- Updated makefiles to be way more flexible

March 12th, 2005
v0.35  -- Stupid XOR function missing line again... oops.
       -- Fixed bug in invmod not handling negative inputs correctly [Wolfgang Ehrhardt]
       -- Made exteuclid always give positive u3 output...[ Wolfgang Ehrhardt ]
       -- [Wolfgang Ehrhardt] Suggested a fix for mp_reduce() which avoided underruns.  ;-)
       -- mp_rand() would emit one too many digits and it was possible to get a 0 out of it ... oops
       -- Added montgomery to the testing to make sure it handles 1..10 digit moduli correctly
       -- Fixed bug in comba that would lead to possible erroneous outputs when "pa < digs"
       -- Fixed bug in mp_toradix_size for "0" [Kevin Kenny]
       -- Updated chapters 1-5 of the textbook ;-) It now talks about the new comba code!

February 12th, 2005
v0.34  -- Fixed two more small errors in mp_prime_random_ex()
       -- Fixed overflow in mp_mul_d() [Kevin Kenny]
       -- Added mp_to_(un)signed_bin_n() functions which do bounds checking for ya [and report the size]
       -- Added "large" diminished radix support.  Speeds up things like DSA where the moduli is of the form 2^k - P for some P < 2^(k/2) or so
          Actually is faster than Montgomery on my AMD64 (and probably much faster on a P4)
       -- Updated the manual a bit
       -- Ok so I haven't done the textbook work yet... My current freelance gig has landed me in France till the
          end of Feb/05.  Once I get back I'll have tons of free time and I plan to go to town on the book.
          As of this release the API will freeze.  At least until the book catches up with all the changes.  I welcome
          bug reports but new algorithms will have to wait.

December 23rd, 2004
v0.33  -- Fixed "small" variant for mp_div() which would munge with negative dividends...
       -- Fixed bug in mp_prime_random_ex() which would set the most significant byte to zero when
................................................................................
       -- Made the makefiles easier to configure the group/user that ltm will install as
       -- Fixed "final carry" bug in comba multipliers. (Volkan Ceylan)
       -- Matt Johnston pointed out a missing semi-colon in mp_exptmod

October 29th, 2004
v0.32  -- Added "makefile.shared" for shared object support
       -- Added more to the build options/configs in the manual
       -- Started the Depends framework, wrote dep.pl to scan deps and
          produce "callgraph.txt" ;-)
       -- Wrote SC_RSA_1 which will enable close to the minimum required to perform
          RSA on 32-bit [or 64-bit] platforms with LibTomCrypt
       -- Merged in the small/slower mp_div replacement.  You can now toggle which
          you want to use as your mp_div() at build time.  Saves roughly 8KB or so.
       -- Renamed a few files and changed some comments to make depends system work better.
          (No changes to function names)
       -- Merged in new Combas that perform 2 reads per inner loop instead of the older
          3reads/2writes per inner loop of the old code.  Really though if you want speed
          learn to use TomsFastMath ;-)

August 9th, 2004
v0.31  -- "profiled" builds now :-) new timings for Intel Northwoods
       -- Added "pretty" build target
       -- Update mp_init() to actually assign 0's instead of relying on calloc()
................................................................................
          is only accurate to byte lengths).  See the new LTM_PRIME_* flags ;-)
       -- Alex Polushin contributed an optimized mp_sqrt() as well as mp_get_int() and mp_is_square().
          I've cleaned them all up to be a little more consistent [along with one bug fix] for this release.
       -- Added mp_init_set and mp_init_set_int to initialize and set small constants with one function
          call.
       -- Removed /etclib directory [um LibTomPoly deprecates this].
       -- Fixed mp_mod() so the sign of the result agrees with the sign of the modulus.
       ++ N.B.  My semester is almost up so expect updates to the textbook to be posted to the libtomcrypt.org
          website.

Jan 25th, 2004
v0.29  ++ Note: "Henrik" from the v0.28 changelog refers to Henrik Goldman ;-)
       -- Added fix to mp_shrink to prevent a realloc when used == 0 [e.g. realloc zero bytes???]
       -- Made the mp_prime_rabin_miller_trials() function internal table smaller and also
          set the minimum number of tests to two (sounds a bit safer).
       -- Added a mp_exteuclid() which computes the extended euclidean algorithm.

#include <time.h>

#ifdef IOWNANATHLON
#include <unistd.h>
#define SLEEP sleep(4)
#else
#define SLEEP
#endif























#include "tommath.h"

void ndraw(mp_int * a, char *name)
{
   char buf[16000];

   printf("%s: ", name);
   mp_toradix(a, buf, 10);
   printf("%s\n", buf);


}


static void draw(mp_int * a)
{
   ndraw(a, "");
}



unsigned long lfsr = 0xAAAAAAAAUL;

int lbit(void)
{
   if (lfsr & 0x80000000UL) {
................................................................................
      return 1;
   } else {
      lfsr <<= 1;
      return 0;
   }
}




int myrng(unsigned char *dst, int len, void *dat)
{
   int x;











   for (x = 0; x < len; x++)
      dst[x] = rand() & 0xFF;






   return len;
}










































char cmd[4096], buf[4096];
int main(void)
{
   mp_int a, b, c, d, e, f;



   unsigned long expt_n, add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n,
      gcd_n, lcm_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n, t;


   unsigned rr;
   int i, n, err, cnt, ix, old_kara_m, old_kara_s;

   mp_digit mp;






   mp_init(&a);
   mp_init(&b);
   mp_init(&c);
   mp_init(&d);
   mp_init(&e);
   mp_init(&f);


   srand(time(NULL));











































































































#if 0






















































































































































   // test montgomery 
   printf("Testing montgomery...\n");
   for (i = 1; i < 10; i++) {


      printf("Testing digit size: %d\n", i);

      for (n = 0; n < 1000; n++) {
         mp_rand(&a, i);
         a.dp[0] |= 1;

         // let's see if R is right
         mp_montgomery_calc_normalization(&b, &a);
         mp_montgomery_setup(&a, &mp);

         // now test a random reduction 
         for (ix = 0; ix < 100; ix++) {
             mp_rand(&c, 1 + abs(rand()) % (2*i));
             mp_copy(&c, &d);
             mp_copy(&c, &e);

             mp_mod(&d, &a, &d);
             mp_montgomery_reduce(&c, &a, mp);
             mp_mulmod(&c, &b, &a, &c);

             if (mp_cmp(&c, &d) != MP_EQ) { 
printf("d = e mod a, c = e MOD a\n");
mp_todecimal(&a, buf); printf("a = %s\n", buf);
mp_todecimal(&e, buf); printf("e = %s\n", buf);
mp_todecimal(&d, buf); printf("d = %s\n", buf);
mp_todecimal(&c, buf); printf("c = %s\n", buf);
printf("compare no compare!\n"); exit(EXIT_FAILURE); }
         }
      }
   }
   printf("done\n");



   // test mp_get_int
   printf("Testing: mp_get_int\n");
   for (i = 0; i < 1000; ++i) {
      t = ((unsigned long) rand() * rand() + 1) & 0xFFFFFFFF;
      mp_set_int(&a, t);
      if (t != mp_get_int(&a)) {
	 printf("mp_get_int() bad result!\n");
	 return 1;


      }
   }
   mp_set_int(&a, 0);
   if (mp_get_int(&a) != 0) {
      printf("mp_get_int() bad result!\n");
      return 1;
   }
   mp_set_int(&a, 0xffffffff);
   if (mp_get_int(&a) != 0xffffffff) {
      printf("mp_get_int() bad result!\n");
      return 1;
   }
   // test mp_sqrt
   printf("Testing: mp_sqrt\n");
   for (i = 0; i < 1000; ++i) {
      printf("%6d\r", i);
      fflush(stdout);
      n = (rand() & 15) + 1;
      mp_rand(&a, n);
      if (mp_sqrt(&a, &b) != MP_OKAY) {
	 printf("mp_sqrt() error!\n");
	 return 1;
      }
      mp_n_root(&a, 2, &a);
      if (mp_cmp_mag(&b, &a) != MP_EQ) {
	 printf("mp_sqrt() bad result!\n");
	 return 1;
      }
   }

   printf("\nTesting: mp_is_square\n");
   for (i = 0; i < 1000; ++i) {
      printf("%6d\r", i);
      fflush(stdout);

      /* test mp_is_square false negatives */
      n = (rand() & 7) + 1;
      mp_rand(&a, n);
      mp_sqr(&a, &a);
      if (mp_is_square(&a, &n) != MP_OKAY) {
	 printf("fn:mp_is_square() error!\n");
	 return 1;
      }
      if (n == 0) {
	 printf("fn:mp_is_square() bad result!\n");
	 return 1;
      }

      /* test for false positives */
      mp_add_d(&a, 1, &a);
      if (mp_is_square(&a, &n) != MP_OKAY) {
	 printf("fp:mp_is_square() error!\n");
	 return 1;
      }
      if (n == 1) {
	 printf("fp:mp_is_square() bad result!\n");
	 return 1;
      }

   }
   printf("\n\n");

   /* test for size */
   for (ix = 10; ix < 128; ix++) {
      printf("Testing (not safe-prime): %9d bits    \r", ix);
      fflush(stdout);
      err =
	 mp_prime_random_ex(&a, 8, ix,
			    (rand() & 1) ? LTM_PRIME_2MSB_OFF :
			    LTM_PRIME_2MSB_ON, myrng, NULL);
      if (err != MP_OKAY) {
	 printf("failed with err code %d\n", err);
	 return EXIT_FAILURE;
      }
      if (mp_count_bits(&a) != ix) {
	 printf("Prime is %d not %d bits!!!\n", mp_count_bits(&a), ix);
	 return EXIT_FAILURE;
      }
   }

   for (ix = 16; ix < 128; ix++) {
      printf("Testing (   safe-prime): %9d bits    \r", ix);
      fflush(stdout);
      err =
	 mp_prime_random_ex(&a, 8, ix,
			    ((rand() & 1) ? LTM_PRIME_2MSB_OFF :
			     LTM_PRIME_2MSB_ON) | LTM_PRIME_SAFE, myrng,
			    NULL);
      if (err != MP_OKAY) {
	 printf("failed with err code %d\n", err);
	 return EXIT_FAILURE;
      }
      if (mp_count_bits(&a) != ix) {
	 printf("Prime is %d not %d bits!!!\n", mp_count_bits(&a), ix);
	 return EXIT_FAILURE;
      }
      /* let's see if it's really a safe prime */
      mp_sub_d(&a, 1, &a);
      mp_div_2(&a, &a);
      mp_prime_is_prime(&a, 8, &cnt);
      if (cnt != MP_YES) {
	 printf("sub is not prime!\n");
	 return EXIT_FAILURE;
      }
   }

   printf("\n\n");

   mp_read_radix(&a, "123456", 10);
   mp_toradix_n(&a, buf, 10, 3);
................................................................................
      mp_prime_next_prime(&a, 5, 1);
      mp_toradix(&a, buf, 10);
      printf("%s, %lu\n", buf, a.dp[0] & 3);
   }
#endif

   /* test mp_cnt_lsb */
   printf("testing mp_cnt_lsb...\n");
   mp_set(&a, 1);
   for (ix = 0; ix < 1024; ix++) {
      if (mp_cnt_lsb(&a) != ix) {
	 printf("Failed at %d, %d\n", ix, mp_cnt_lsb(&a));
	 return 0;
      }
      mp_mul_2(&a, &a);
   }

/* test mp_reduce_2k */
   printf("Testing mp_reduce_2k...\n");
   for (cnt = 3; cnt <= 128; ++cnt) {
      mp_digit tmp;

      mp_2expt(&a, cnt);
      mp_sub_d(&a, 2, &a);	/* a = 2**cnt - 2 */


      printf("\nTesting %4d bits", cnt);
      printf("(%d)", mp_reduce_is_2k(&a));
      mp_reduce_2k_setup(&a, &tmp);
      printf("(%d)", tmp);

      for (ix = 0; ix < 1000; ix++) {
	 if (!(ix & 127)) {
	    printf(".");
	    fflush(stdout);
	 }
	 mp_rand(&b, (cnt / DIGIT_BIT + 1) * 2);
	 mp_copy(&c, &b);
	 mp_mod(&c, &a, &c);
	 mp_reduce_2k(&b, &a, 2);
	 if (mp_cmp(&c, &b)) {
	    printf("FAILED\n");
	    exit(0);

	 }
      }
   }

/* test mp_div_3  */
   printf("Testing mp_div_3...\n");
   mp_set(&d, 3);
   for (cnt = 0; cnt < 10000;) {
      mp_digit r1, r2;

      if (!(++cnt & 127))

	 printf("%9d\r", cnt);


      mp_rand(&a, abs(rand()) % 128 + 1);
      mp_div(&a, &d, &b, &e);
      mp_div_3(&a, &c, &r2);

      if (mp_cmp(&b, &c) || mp_cmp_d(&e, r2)) {
	 printf("\n\nmp_div_3 => Failure\n");
      }
   }
   printf("\n\nPassed div_3 testing\n");

/* test the DR reduction */
   printf("testing mp_dr_reduce...\n");
   for (cnt = 2; cnt < 32; cnt++) {
      printf("%d digit modulus\n", cnt);
      mp_grow(&a, cnt);
      mp_zero(&a);
      for (ix = 1; ix < cnt; ix++) {
	 a.dp[ix] = MP_MASK;
      }
      a.used = cnt;
      a.dp[0] = 3;

      mp_rand(&b, cnt - 1);
      mp_copy(&b, &c);

      rr = 0;
      do {
	 if (!(rr & 127)) {
	    printf("%9lu\r", rr);
	    fflush(stdout);
	 }
	 mp_sqr(&b, &b);
	 mp_add_d(&b, 1, &b);
	 mp_copy(&b, &c);

	 mp_mod(&b, &a, &b);
	 mp_dr_reduce(&c, &a, (((mp_digit) 1) << DIGIT_BIT) - a.dp[0]);


	 if (mp_cmp(&b, &c) != MP_EQ) {
	    printf("Failed on trial %lu\n", rr);
	    exit(-1);


	 }
      } while (++rr < 500);
      printf("Passed DR test for %d digits\n", cnt);

   }

#endif


/* test the mp_reduce_2k_l code */
#if 0
#if 0
/* first load P with 2^1024 - 0x2A434 B9FDEC95 D8F9D550 FFFFFFFF FFFFFFFF */
   mp_2expt(&a, 1024);
   mp_read_radix(&b, "2A434B9FDEC95D8F9D550FFFFFFFFFFFFFFFF", 16);
   mp_sub(&a, &b, &a);
#elif 1
/*  p = 2^2048 - 0x1 00000000 00000000 00000000 00000000 4945DDBF 8EA2A91D 5776399B B83E188F  */
   mp_2expt(&a, 2048);
   mp_read_radix(&b,
		 "1000000000000000000000000000000004945DDBF8EA2A91D5776399BB83E188F",
		 16);
   mp_sub(&a, &b, &a);


#endif

   mp_todecimal(&a, buf);
   printf("p==%s\n", buf);
/* now mp_reduce_is_2k_l() should return */
   if (mp_reduce_is_2k_l(&a) != 1) {
      printf("mp_reduce_is_2k_l() return 0, should be 1\n");
      return EXIT_FAILURE;
   }
   mp_reduce_2k_setup_l(&a, &d);
   /* now do a million square+1 to see if it varies */
   mp_rand(&b, 64);
   mp_mod(&b, &a, &b);
   mp_copy(&b, &c);
   printf("testing mp_reduce_2k_l...");
   fflush(stdout);
   for (cnt = 0; cnt < (1UL << 20); cnt++) {
      mp_sqr(&b, &b);
      mp_add_d(&b, 1, &b);
      mp_reduce_2k_l(&b, &a, &d);
      mp_sqr(&c, &c);
      mp_add_d(&c, 1, &c);
      mp_mod(&c, &a, &c);
      if (mp_cmp(&b, &c) != MP_EQ) {
	 printf("mp_reduce_2k_l() failed at step %lu\n", cnt);
	 mp_tohex(&b, buf);
	 printf("b == %s\n", buf);
	 mp_tohex(&c, buf);
	 printf("c == %s\n", buf);
	 return EXIT_FAILURE;
      }
   }
   printf("...Passed\n");


#endif

   div2_n = mul2_n = inv_n = expt_n = lcm_n = gcd_n = add_n =
      sub_n = mul_n = div_n = sqr_n = mul2d_n = div2d_n = cnt = add_d_n =
      sub_d_n = 0;

   /* force KARA and TOOM to enable despite cutoffs */
   KARATSUBA_SQR_CUTOFF = KARATSUBA_MUL_CUTOFF = 8;
................................................................................
      }


      printf
	 ("%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu ",
	  add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n, gcd_n, lcm_n,
	  expt_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n);
      fgets(cmd, 4095, stdin);
      cmd[strlen(cmd) - 1] = 0;
      printf("%s  ]\r", cmd);
      fflush(stdout);
      if (!strcmp(cmd, "mul2d")) {
	 ++mul2d_n;
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&a, buf, 64);
	 fgets(buf, 4095, stdin);
	 sscanf(buf, "%d", &rr);
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&b, buf, 64);

	 mp_mul_2d(&a, rr, &a);
	 a.sign = b.sign;
	 if (mp_cmp(&a, &b) != MP_EQ) {
	    printf("mul2d failed, rr == %d\n", rr);
	    draw(&a);
	    draw(&b);
	    return 0;
	 }
      } else if (!strcmp(cmd, "div2d")) {
	 ++div2d_n;
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&a, buf, 64);
	 fgets(buf, 4095, stdin);
	 sscanf(buf, "%d", &rr);
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&b, buf, 64);

	 mp_div_2d(&a, rr, &a, &e);
	 a.sign = b.sign;
	 if (a.used == b.used && a.used == 0) {
	    a.sign = b.sign = MP_ZPOS;
	 }
	 if (mp_cmp(&a, &b) != MP_EQ) {
	    printf("div2d failed, rr == %d\n", rr);
	    draw(&a);
	    draw(&b);
	    return 0;
	 }
      } else if (!strcmp(cmd, "add")) {
	 ++add_n;
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&a, buf, 64);
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&b, buf, 64);
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&c, buf, 64);
	 mp_copy(&a, &d);
	 mp_add(&d, &b, &d);
	 if (mp_cmp(&c, &d) != MP_EQ) {
	    printf("add %lu failure!\n", add_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    draw(&d);
	    return 0;
	 }

	 /* test the sign/unsigned storage functions */

	 rr = mp_signed_bin_size(&c);
	 mp_to_signed_bin(&c, (unsigned char *) cmd);
	 memset(cmd + rr, rand() & 255, sizeof(cmd) - rr);
	 mp_read_signed_bin(&d, (unsigned char *) cmd, rr);
	 if (mp_cmp(&c, &d) != MP_EQ) {
	    printf("mp_signed_bin failure!\n");
	    draw(&c);
	    draw(&d);
	    return 0;
	 }


	 rr = mp_unsigned_bin_size(&c);
	 mp_to_unsigned_bin(&c, (unsigned char *) cmd);
	 memset(cmd + rr, rand() & 255, sizeof(cmd) - rr);
	 mp_read_unsigned_bin(&d, (unsigned char *) cmd, rr);
	 if (mp_cmp_mag(&c, &d) != MP_EQ) {
	    printf("mp_unsigned_bin failure!\n");
	    draw(&c);
	    draw(&d);
	    return 0;
	 }

      } else if (!strcmp(cmd, "sub")) {
	 ++sub_n;
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&a, buf, 64);
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&b, buf, 64);
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&c, buf, 64);
	 mp_copy(&a, &d);
	 mp_sub(&d, &b, &d);
	 if (mp_cmp(&c, &d) != MP_EQ) {
	    printf("sub %lu failure!\n", sub_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    draw(&d);
	    return 0;
	 }
      } else if (!strcmp(cmd, "mul")) {
	 ++mul_n;
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&a, buf, 64);
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&b, buf, 64);
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&c, buf, 64);
	 mp_copy(&a, &d);
	 mp_mul(&d, &b, &d);
	 if (mp_cmp(&c, &d) != MP_EQ) {
	    printf("mul %lu failure!\n", mul_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    draw(&d);
	    return 0;
	 }
      } else if (!strcmp(cmd, "div")) {
	 ++div_n;
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&a, buf, 64);
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&b, buf, 64);
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&c, buf, 64);
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&d, buf, 64);

	 mp_div(&a, &b, &e, &f);
	 if (mp_cmp(&c, &e) != MP_EQ || mp_cmp(&d, &f) != MP_EQ) {
	    printf("div %lu %d, %d, failure!\n", div_n, mp_cmp(&c, &e),
		   mp_cmp(&d, &f));
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    draw(&d);
	    draw(&e);
	    draw(&f);
	    return 0;
	 }

      } else if (!strcmp(cmd, "sqr")) {
	 ++sqr_n;
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&a, buf, 64);
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&b, buf, 64);
	 mp_copy(&a, &c);
	 mp_sqr(&c, &c);
	 if (mp_cmp(&b, &c) != MP_EQ) {
	    printf("sqr %lu failure!\n", sqr_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    return 0;
	 }
      } else if (!strcmp(cmd, "gcd")) {
	 ++gcd_n;
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&a, buf, 64);
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&b, buf, 64);
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&c, buf, 64);
	 mp_copy(&a, &d);
	 mp_gcd(&d, &b, &d);
	 d.sign = c.sign;
	 if (mp_cmp(&c, &d) != MP_EQ) {
	    printf("gcd %lu failure!\n", gcd_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    draw(&d);
	    return 0;
	 }
      } else if (!strcmp(cmd, "lcm")) {
	 ++lcm_n;
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&a, buf, 64);
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&b, buf, 64);
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&c, buf, 64);
	 mp_copy(&a, &d);
	 mp_lcm(&d, &b, &d);
	 d.sign = c.sign;
	 if (mp_cmp(&c, &d) != MP_EQ) {
	    printf("lcm %lu failure!\n", lcm_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    draw(&d);
	    return 0;
	 }
      } else if (!strcmp(cmd, "expt")) {
	 ++expt_n;
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&a, buf, 64);
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&b, buf, 64);
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&c, buf, 64);
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&d, buf, 64);
	 mp_copy(&a, &e);
	 mp_exptmod(&e, &b, &c, &e);
	 if (mp_cmp(&d, &e) != MP_EQ) {
	    printf("expt %lu failure!\n", expt_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    draw(&d);
	    draw(&e);
	    return 0;
	 }
      } else if (!strcmp(cmd, "invmod")) {
	 ++inv_n;
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&a, buf, 64);
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&b, buf, 64);
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&c, buf, 64);
	 mp_invmod(&a, &b, &d);
	 mp_mulmod(&d, &a, &b, &e);
	 if (mp_cmp_d(&e, 1) != MP_EQ) {
	    printf("inv [wrong value from MPI?!] failure\n");
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    draw(&d);

	    mp_gcd(&a, &b, &e);
	    draw(&e);
	    return 0;
	 }

      } else if (!strcmp(cmd, "div2")) {
	 ++div2_n;
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&a, buf, 64);
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&b, buf, 64);
	 mp_div_2(&a, &c);
	 if (mp_cmp(&c, &b) != MP_EQ) {
	    printf("div_2 %lu failure\n", div2_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    return 0;
	 }
      } else if (!strcmp(cmd, "mul2")) {
	 ++mul2_n;
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&a, buf, 64);
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&b, buf, 64);
	 mp_mul_2(&a, &c);
	 if (mp_cmp(&c, &b) != MP_EQ) {
	    printf("mul_2 %lu failure\n", mul2_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    return 0;
	 }
      } else if (!strcmp(cmd, "add_d")) {
	 ++add_d_n;
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&a, buf, 64);
	 fgets(buf, 4095, stdin);
	 sscanf(buf, "%d", &ix);
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&b, buf, 64);
	 mp_add_d(&a, ix, &c);
	 if (mp_cmp(&b, &c) != MP_EQ) {
	    printf("add_d %lu failure\n", add_d_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    printf("d == %d\n", ix);
	    return 0;
	 }
      } else if (!strcmp(cmd, "sub_d")) {
	 ++sub_d_n;
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&a, buf, 64);
	 fgets(buf, 4095, stdin);
	 sscanf(buf, "%d", &ix);
	 fgets(buf, 4095, stdin);
	 mp_read_radix(&b, buf, 64);
	 mp_sub_d(&a, ix, &c);
	 if (mp_cmp(&b, &c) != MP_EQ) {
	    printf("sub_d %lu failure\n", sub_d_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    printf("d == %d\n", ix);
	    return 0;
	 }



      }
   }

   return 0;
}

#include <string.h>
#include <time.h>

#ifdef IOWNANATHLON
#include <unistd.h>
#define SLEEP sleep(4)
#else
#define SLEEP
#endif

/*
 * Configuration
 */
#ifndef LTM_DEMO_TEST_VS_MTEST
#define LTM_DEMO_TEST_VS_MTEST 1
#endif

#ifndef LTM_DEMO_TEST_REDUCE_2K_L
/* This test takes a moment so we disable it by default, but it can be:
 * 0 to disable testing
 * 1 to make the test with P = 2^1024 - 0x2A434 B9FDEC95 D8F9D550 FFFFFFFF FFFFFFFF
 * 2 to make the test with P = 2^2048 - 0x1 00000000 00000000 00000000 00000000 4945DDBF 8EA2A91D 5776399B B83E188F
 */
#define LTM_DEMO_TEST_REDUCE_2K_L 0
#endif

#ifdef LTM_DEMO_REAL_RAND
#define LTM_DEMO_RAND_SEED  time(NULL)
#else
#define LTM_DEMO_RAND_SEED  23
#endif

#include "tommath.h"

void ndraw(mp_int * a, char *name)
{
   char buf[16000];

   printf("%s: ", name);
   mp_toradix(a, buf, 10);
   printf("%s\n", buf);
   mp_toradix(a, buf, 16);
   printf("0x%s\n", buf);
}

#if LTM_DEMO_TEST_VS_MTEST
static void draw(mp_int * a)
{
   ndraw(a, "");
}
#endif


unsigned long lfsr = 0xAAAAAAAAUL;

int lbit(void)
{
   if (lfsr & 0x80000000UL) {
................................................................................
      return 1;
   } else {
      lfsr <<= 1;
      return 0;
   }
}

#if defined(LTM_DEMO_REAL_RAND) && !defined(_WIN32)
static FILE* fd_urandom;
#endif
int myrng(unsigned char *dst, int len, void *dat)
{
   int x;
   (void)dat;
#if defined(LTM_DEMO_REAL_RAND)
   if (!fd_urandom) {
#if !defined(_WIN32)
      fprintf(stderr, "\nno /dev/urandom\n");
#endif
   }
   else {
      return fread(dst, 1, len, fd_urandom);
   }
#endif
   for (x = 0; x < len; ) {

      unsigned int r = (unsigned int)rand();
      do {
         dst[x++] = r & 0xFF;
         r >>= 8;
      } while((r != 0) && (x < len));
   }
   return len;
}

#if LTM_DEMO_TEST_VS_MTEST != 0
static void _panic(int l)
{
  fprintf(stderr, "\n%d: fgets failed\n", l);
  exit(EXIT_FAILURE);
}
#endif

mp_int a, b, c, d, e, f;

static void _cleanup(void)
{
  mp_clear_multi(&a, &b, &c, &d, &e, &f, NULL);
  printf("\n");

#ifdef LTM_DEMO_REAL_RAND
  if(fd_urandom)
     fclose(fd_urandom);
#endif
}
struct mp_sqrtmod_prime_st {
   unsigned long p;
   unsigned long n;
   mp_digit r;
};
struct mp_sqrtmod_prime_st sqrtmod_prime[] = {
      { 5, 14, 3 },
      { 7, 9, 4 },
      { 113, 2, 62 }
};
struct mp_jacobi_st {
   unsigned long n;
   int c[16];
};
struct mp_jacobi_st jacobi[] = {
      { 3, {  1, -1,  0,  1, -1,  0,  1, -1,  0,  1, -1,  0,  1, -1,  0,  1 } },
      { 5, {  0,  1, -1, -1,  1,  0,  1, -1, -1,  1,  0,  1, -1, -1,  1,  0 } },
      { 7, {  1, -1,  1, -1, -1,  0,  1,  1, -1,  1, -1, -1,  0,  1,  1, -1 } },
      { 9, { -1,  1,  0,  1,  1,  0,  1,  1,  0,  1,  1,  0,  1,  1,  0,  1 } },
};

char cmd[4096], buf[4096];
int main(void)
{

   unsigned rr;
   int cnt, ix;
#if LTM_DEMO_TEST_VS_MTEST
   unsigned long expt_n, add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n,
      gcd_n, lcm_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n;
   char* ret;
#else
   unsigned long s, t;

   unsigned long long q, r;
   mp_digit mp;
   int i, n, err, should;
#endif

   if (mp_init_multi(&a, &b, &c, &d, &e, &f, NULL)!= MP_OKAY)
     return EXIT_FAILURE;







   atexit(_cleanup);


#if defined(LTM_DEMO_REAL_RAND)
   if (!fd_urandom) {
      fd_urandom = fopen("/dev/urandom", "r");
      if (!fd_urandom) {
#if !defined(_WIN32)
         fprintf(stderr, "\ncould not open /dev/urandom\n");
#endif
      }
   }
#endif
   srand(LTM_DEMO_RAND_SEED);

#ifdef MP_8BIT
   printf("Digit size 8 Bit \n");
#endif
#ifdef MP_16BIT
   printf("Digit size 16 Bit \n");
#endif
#ifdef MP_32BIT
   printf("Digit size 32 Bit \n");
#endif
#ifdef MP_64BIT
   printf("Digit size 64 Bit \n");
#endif
   printf("Size of mp_digit: %u\n", (unsigned int)sizeof(mp_digit));
   printf("Size of mp_word: %u\n", (unsigned int)sizeof(mp_word));
   printf("DIGIT_BIT: %d\n", DIGIT_BIT);
   printf("MP_PREC: %d\n", MP_PREC);

#if LTM_DEMO_TEST_VS_MTEST == 0
   // trivial stuff
   mp_set_int(&a, 5);
   mp_neg(&a, &b);
   if (mp_cmp(&a, &b) != MP_GT) {
      return EXIT_FAILURE;
   }
   if (mp_cmp(&b, &a) != MP_LT) {
      return EXIT_FAILURE;
   }
   mp_neg(&a, &a);
   if (mp_cmp(&b, &a) != MP_EQ) {
      return EXIT_FAILURE;
   }
   mp_abs(&a, &b);
   if (mp_isneg(&b) != MP_NO) {
      return EXIT_FAILURE;
   }
   mp_add_d(&a, 1, &b);
   mp_add_d(&a, 6, &b);


   mp_set_int(&a, 0);
   mp_set_int(&b, 1);
   if ((err = mp_jacobi(&a, &b, &i)) != MP_OKAY) {
      printf("Failed executing mp_jacobi(0 | 1) %s.\n", mp_error_to_string(err));
      return EXIT_FAILURE;
   }
   if (i != 1) {
      printf("Failed trivial mp_jacobi(0 | 1) %d != 1\n", i);
      return EXIT_FAILURE;
   }
   for (cnt = 0; cnt < (int)(sizeof(jacobi)/sizeof(jacobi[0])); ++cnt) {
      mp_set_int(&b, jacobi[cnt].n);
      /* only test positive values of a */
      for (n = -5; n <= 10; ++n) {
         mp_set_int(&a, abs(n));
         should = MP_OKAY;
         if (n < 0) {
            mp_neg(&a, &a);
            /* Until #44 is fixed the negative a's must fail */
            should = MP_VAL;
         }
         if ((err = mp_jacobi(&a, &b, &i)) != should) {
            printf("Failed executing mp_jacobi(%d | %lu) %s.\n", n, jacobi[cnt].n, mp_error_to_string(err));
            return EXIT_FAILURE;
         }
         if (err == MP_OKAY && i != jacobi[cnt].c[n + 5]) {
            printf("Failed trivial mp_jacobi(%d | %lu) %d != %d\n", n, jacobi[cnt].n, i, jacobi[cnt].c[n + 5]);
            return EXIT_FAILURE;
         }
      }
   }

   // test mp_get_int
   printf("\n\nTesting: mp_get_int");
   for (i = 0; i < 1000; ++i) {
      t = ((unsigned long) rand () * rand () + 1) & 0xFFFFFFFF;
      mp_set_int (&a, t);
      if (t != mp_get_int (&a)) {
         printf ("\nmp_get_int() bad result!");
         return EXIT_FAILURE;
      }
   }
   mp_set_int(&a, 0);
   if (mp_get_int(&a) != 0) {
      printf("\nmp_get_int() bad result!");
      return EXIT_FAILURE;
   }
   mp_set_int(&a, 0xffffffff);
   if (mp_get_int(&a) != 0xffffffff) {
      printf("\nmp_get_int() bad result!");
      return EXIT_FAILURE;
   }

   printf("\n\nTesting: mp_get_long\n");
   for (i = 0; i < (int)(sizeof(unsigned long)*CHAR_BIT) - 1; ++i) {
      t = (1ULL << (i+1)) - 1;
      if (!t)
         t = -1;
      printf(" t = 0x%lx i = %d\r", t, i);
      do {
         if (mp_set_long(&a, t) != MP_OKAY) {
            printf("\nmp_set_long() error!");
            return EXIT_FAILURE;
         }
         s = mp_get_long(&a);
         if (s != t) {
            printf("\nmp_get_long() bad result! 0x%lx != 0x%lx", s, t);
            return EXIT_FAILURE;
         }
         t <<= 1;
      } while(t);
   }

   printf("\n\nTesting: mp_get_long_long\n");
   for (i = 0; i < (int)(sizeof(unsigned long long)*CHAR_BIT) - 1; ++i) {
      r = (1ULL << (i+1)) - 1;
      if (!r)
         r = -1;
      printf(" r = 0x%llx i = %d\r", r, i);
      do {
         if (mp_set_long_long(&a, r) != MP_OKAY) {
            printf("\nmp_set_long_long() error!");
            return EXIT_FAILURE;
         }
         q = mp_get_long_long(&a);
         if (q != r) {
            printf("\nmp_get_long_long() bad result! 0x%llx != 0x%llx", q, r);
            return EXIT_FAILURE;
         }
         r <<= 1;
      } while(r);
   }

   // test mp_sqrt
   printf("\n\nTesting: mp_sqrt\n");
   for (i = 0; i < 1000; ++i) {
      printf ("%6d\r", i);
      fflush (stdout);
      n = (rand () & 15) + 1;
      mp_rand (&a, n);
      if (mp_sqrt (&a, &b) != MP_OKAY) {
         printf ("\nmp_sqrt() error!");
         return EXIT_FAILURE;
      }
      mp_n_root_ex (&a, 2, &c, 0);
      mp_n_root_ex (&a, 2, &d, 1);
      if (mp_cmp_mag (&c, &d) != MP_EQ) {
         printf ("\nmp_n_root_ex() bad result!");
         return EXIT_FAILURE;
      }
      if (mp_cmp_mag (&b, &c) != MP_EQ) {
         printf ("mp_sqrt() bad result!\n");
         return EXIT_FAILURE;
      }
   }

   printf("\n\nTesting: mp_is_square\n");
   for (i = 0; i < 1000; ++i) {
      printf ("%6d\r", i);
      fflush (stdout);

      /* test mp_is_square false negatives */
      n = (rand () & 7) + 1;
      mp_rand (&a, n);
      mp_sqr (&a, &a);
      if (mp_is_square (&a, &n) != MP_OKAY) {
         printf ("\nfn:mp_is_square() error!");
         return EXIT_FAILURE;
      }
      if (n == 0) {
         printf ("\nfn:mp_is_square() bad result!");
         return EXIT_FAILURE;
      }

      /* test for false positives */
      mp_add_d (&a, 1, &a);
      if (mp_is_square (&a, &n) != MP_OKAY) {
         printf ("\nfp:mp_is_square() error!");
         return EXIT_FAILURE;
      }
      if (n == 1) {
         printf ("\nfp:mp_is_square() bad result!");
         return EXIT_FAILURE;
      }

   }
   printf("\n\n");

   // r^2 = n (mod p)
   for (i = 0; i < (int)(sizeof(sqrtmod_prime)/sizeof(sqrtmod_prime[0])); ++i) {
      mp_set_int(&a, sqrtmod_prime[i].p);
      mp_set_int(&b, sqrtmod_prime[i].n);
      if (mp_sqrtmod_prime(&b, &a, &c) != MP_OKAY) {
         printf("Failed executing %d. mp_sqrtmod_prime\n", (i+1));
         return EXIT_FAILURE;
      }
      if (mp_cmp_d(&c, sqrtmod_prime[i].r) != MP_EQ) {
         printf("Failed %d. trivial mp_sqrtmod_prime\n", (i+1));
         ndraw(&c, "r");
         return EXIT_FAILURE;
      }
   }

   /* test for size */
   for (ix = 10; ix < 128; ix++) {
      printf ("Testing (not safe-prime): %9d bits    \r", ix);
      fflush (stdout);
      err = mp_prime_random_ex (&a, 8, ix,
                                (rand () & 1) ? 0 : LTM_PRIME_2MSB_ON, myrng,
                                NULL);
      if (err != MP_OKAY) {
         printf ("failed with err code %d\n", err);
         return EXIT_FAILURE;
      }
      if (mp_count_bits (&a) != ix) {
         printf ("Prime is %d not %d bits!!!\n", mp_count_bits (&a), ix);
         return EXIT_FAILURE;
      }
   }
   printf("\n");

   for (ix = 16; ix < 128; ix++) {
      printf ("Testing (    safe-prime): %9d bits    \r", ix);
      fflush (stdout);
      err = mp_prime_random_ex (
            &a, 8, ix, ((rand () & 1) ? 0 : LTM_PRIME_2MSB_ON) | LTM_PRIME_SAFE,
            myrng, NULL);
      if (err != MP_OKAY) {
         printf ("failed with err code %d\n", err);
         return EXIT_FAILURE;
      }
      if (mp_count_bits (&a) != ix) {
         printf ("Prime is %d not %d bits!!!\n", mp_count_bits (&a), ix);
         return EXIT_FAILURE;
      }
      /* let's see if it's really a safe prime */
      mp_sub_d (&a, 1, &a);
      mp_div_2 (&a, &a);
      mp_prime_is_prime (&a, 8, &cnt);
      if (cnt != MP_YES) {
         printf ("sub is not prime!\n");
         return EXIT_FAILURE;
      }
   }

   printf("\n\n");

   // test montgomery
   printf("Testing: montgomery...\n");
   for (i = 1; i <= 10; i++) {
      if (i == 10)
         i = 1000;
      printf(" digit size: %2d\r", i);
      fflush(stdout);
      for (n = 0; n < 1000; n++) {
         mp_rand(&a, i);
         a.dp[0] |= 1;

         // let's see if R is right
         mp_montgomery_calc_normalization(&b, &a);
         mp_montgomery_setup(&a, &mp);

         // now test a random reduction
         for (ix = 0; ix < 100; ix++) {
             mp_rand(&c, 1 + abs(rand()) % (2*i));
             mp_copy(&c, &d);
             mp_copy(&c, &e);

             mp_mod(&d, &a, &d);
             mp_montgomery_reduce(&c, &a, mp);
             mp_mulmod(&c, &b, &a, &c);

             if (mp_cmp(&c, &d) != MP_EQ) {
printf("d = e mod a, c = e MOD a\n");
mp_todecimal(&a, buf); printf("a = %s\n", buf);
mp_todecimal(&e, buf); printf("e = %s\n", buf);
mp_todecimal(&d, buf); printf("d = %s\n", buf);
mp_todecimal(&c, buf); printf("c = %s\n", buf);
printf("compare no compare!\n"); return EXIT_FAILURE; }




             /* only one big montgomery reduction */
             if (i > 10)
             {








                n = 1000;
                ix = 100;
             }
         }





































































































      }
   }

   printf("\n\n");

   mp_read_radix(&a, "123456", 10);
   mp_toradix_n(&a, buf, 10, 3);
................................................................................
      mp_prime_next_prime(&a, 5, 1);
      mp_toradix(&a, buf, 10);
      printf("%s, %lu\n", buf, a.dp[0] & 3);
   }
#endif

   /* test mp_cnt_lsb */
   printf("\n\nTesting: mp_cnt_lsb");
   mp_set(&a, 1);
   for (ix = 0; ix < 1024; ix++) {
      if (mp_cnt_lsb (&a) != ix) {
         printf ("Failed at %d, %d\n", ix, mp_cnt_lsb (&a));
         return EXIT_FAILURE;
      }
      mp_mul_2 (&a, &a);
   }

/* test mp_reduce_2k */
   printf("\n\nTesting: mp_reduce_2k\n");
   for (cnt = 3; cnt <= 128; ++cnt) {
      mp_digit tmp;

      mp_2expt (&a, cnt);
      mp_sub_d (&a, 2, &a); /* a = 2**cnt - 2 */


      printf ("\r %4d bits", cnt);
      printf ("(%d)", mp_reduce_is_2k (&a));
      mp_reduce_2k_setup (&a, &tmp);

      printf ("(%lu)", (unsigned long) tmp);
      for (ix = 0; ix < 1000; ix++) {
         if (!(ix & 127)) {
            printf (".");
            fflush (stdout);
         }
         mp_rand (&b, (cnt / DIGIT_BIT + 1) * 2);
         mp_copy (&c, &b);
         mp_mod (&c, &a, &c);
         mp_reduce_2k (&b, &a, 2);
         if (mp_cmp (&c, &b)) {
            printf ("FAILED\n");

            return EXIT_FAILURE;
         }
      }
   }

/* test mp_div_3  */
   printf("\n\nTesting: mp_div_3...\n");
   mp_set(&d, 3);
   for (cnt = 0; cnt < 10000;) {
      mp_digit r2;

      if (!(++cnt & 127))
      {
        printf("%9d\r", cnt);
        fflush(stdout);
      }
      mp_rand(&a, abs(rand()) % 128 + 1);
      mp_div(&a, &d, &b, &e);
      mp_div_3(&a, &c, &r2);

      if (mp_cmp(&b, &c) || mp_cmp_d(&e, r2)) {
	 printf("\nmp_div_3 => Failure\n");
      }
   }
   printf("\nPassed div_3 testing");

/* test the DR reduction */
   printf("\n\nTesting: mp_dr_reduce...\n");
   for (cnt = 2; cnt < 32; cnt++) {
      printf ("\r%d digit modulus", cnt);
      mp_grow (&a, cnt);
      mp_zero (&a);
      for (ix = 1; ix < cnt; ix++) {
         a.dp[ix] = MP_MASK;
      }
      a.used = cnt;
      a.dp[0] = 3;

      mp_rand (&b, cnt - 1);
      mp_copy (&b, &c);

      rr = 0;
      do {
         if (!(rr & 127)) {
            printf (".");
            fflush (stdout);
         }
         mp_sqr (&b, &b);
         mp_add_d (&b, 1, &b);
         mp_copy (&b, &c);

         mp_mod (&b, &a, &b);
         mp_dr_setup(&a, &mp),
         mp_dr_reduce (&c, &a, mp);

         if (mp_cmp (&b, &c) != MP_EQ) {
            printf ("Failed on trial %u\n", rr);

            return EXIT_FAILURE;
         }

      } while (++rr < 500);
      printf (" passed");
      fflush (stdout);
   }



#if LTM_DEMO_TEST_REDUCE_2K_L
/* test the mp_reduce_2k_l code */
#if LTM_DEMO_TEST_REDUCE_2K_L == 1

/* first load P with 2^1024 - 0x2A434 B9FDEC95 D8F9D550 FFFFFFFF FFFFFFFF */
   mp_2expt(&a, 1024);
   mp_read_radix(&b, "2A434B9FDEC95D8F9D550FFFFFFFFFFFFFFFF", 16);
   mp_sub(&a, &b, &a);
#elif LTM_DEMO_TEST_REDUCE_2K_L == 2
/*  p = 2^2048 - 0x1 00000000 00000000 00000000 00000000 4945DDBF 8EA2A91D 5776399B B83E188F  */
   mp_2expt(&a, 2048);
   mp_read_radix(&b,
		 "1000000000000000000000000000000004945DDBF8EA2A91D5776399BB83E188F",
		 16);
   mp_sub(&a, &b, &a);
#else
#error oops
#endif

   mp_todecimal(&a, buf);
   printf("\n\np==%s\n", buf);
/* now mp_reduce_is_2k_l() should return */
   if (mp_reduce_is_2k_l(&a) != 1) {
      printf("mp_reduce_is_2k_l() return 0, should be 1\n");
      return EXIT_FAILURE;
   }
   mp_reduce_2k_setup_l(&a, &d);
   /* now do a million square+1 to see if it varies */
   mp_rand(&b, 64);
   mp_mod(&b, &a, &b);
   mp_copy(&b, &c);
   printf("Testing: mp_reduce_2k_l...");
   fflush(stdout);
   for (cnt = 0; cnt < (int)(1UL << 20); cnt++) {
      mp_sqr(&b, &b);
      mp_add_d(&b, 1, &b);
      mp_reduce_2k_l(&b, &a, &d);
      mp_sqr(&c, &c);
      mp_add_d(&c, 1, &c);
      mp_mod(&c, &a, &c);
      if (mp_cmp(&b, &c) != MP_EQ) {
	 printf("mp_reduce_2k_l() failed at step %d\n", cnt);
	 mp_tohex(&b, buf);
	 printf("b == %s\n", buf);
	 mp_tohex(&c, buf);
	 printf("c == %s\n", buf);
	 return EXIT_FAILURE;
      }
   }
   printf("...Passed\n");
#endif /* LTM_DEMO_TEST_REDUCE_2K_L */

#else

   div2_n = mul2_n = inv_n = expt_n = lcm_n = gcd_n = add_n =
      sub_n = mul_n = div_n = sqr_n = mul2d_n = div2d_n = cnt = add_d_n =
      sub_d_n = 0;

   /* force KARA and TOOM to enable despite cutoffs */
   KARATSUBA_SQR_CUTOFF = KARATSUBA_MUL_CUTOFF = 8;
................................................................................
      }


      printf
	 ("%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu ",
	  add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n, gcd_n, lcm_n,
	  expt_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n);
      ret=fgets(cmd, 4095, stdin); if(!ret){_panic(__LINE__);}
      cmd[strlen(cmd) - 1] = 0;
      printf("%-6s ]\r", cmd);
      fflush(stdout);
      if (!strcmp(cmd, "mul2d")) {
	 ++mul2d_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 sscanf(buf, "%d", &rr);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);

	 mp_mul_2d(&a, rr, &a);
	 a.sign = b.sign;
	 if (mp_cmp(&a, &b) != MP_EQ) {
	    printf("mul2d failed, rr == %d\n", rr);
	    draw(&a);
	    draw(&b);
	    return EXIT_FAILURE;
	 }
      } else if (!strcmp(cmd, "div2d")) {
	 ++div2d_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 sscanf(buf, "%d", &rr);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);

	 mp_div_2d(&a, rr, &a, &e);
	 a.sign = b.sign;
	 if (a.used == b.used && a.used == 0) {
	    a.sign = b.sign = MP_ZPOS;
	 }
	 if (mp_cmp(&a, &b) != MP_EQ) {
	    printf("div2d failed, rr == %d\n", rr);
	    draw(&a);
	    draw(&b);
	    return EXIT_FAILURE;
	 }
      } else if (!strcmp(cmd, "add")) {
	 ++add_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&c, buf, 64);
	 mp_copy(&a, &d);
	 mp_add(&d, &b, &d);
	 if (mp_cmp(&c, &d) != MP_EQ) {
	    printf("add %lu failure!\n", add_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    draw(&d);
	    return EXIT_FAILURE;
	 }

	 /* test the sign/unsigned storage functions */

	 rr = mp_signed_bin_size(&c);
	 mp_to_signed_bin(&c, (unsigned char *) cmd);
	 memset(cmd + rr, rand() & 255, sizeof(cmd) - rr);
	 mp_read_signed_bin(&d, (unsigned char *) cmd, rr);
	 if (mp_cmp(&c, &d) != MP_EQ) {
	    printf("mp_signed_bin failure!\n");
	    draw(&c);
	    draw(&d);
	    return EXIT_FAILURE;
	 }


	 rr = mp_unsigned_bin_size(&c);
	 mp_to_unsigned_bin(&c, (unsigned char *) cmd);
	 memset(cmd + rr, rand() & 255, sizeof(cmd) - rr);
	 mp_read_unsigned_bin(&d, (unsigned char *) cmd, rr);
	 if (mp_cmp_mag(&c, &d) != MP_EQ) {
	    printf("mp_unsigned_bin failure!\n");
	    draw(&c);
	    draw(&d);
	    return EXIT_FAILURE;
	 }

      } else if (!strcmp(cmd, "sub")) {
	 ++sub_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&c, buf, 64);
	 mp_copy(&a, &d);
	 mp_sub(&d, &b, &d);
	 if (mp_cmp(&c, &d) != MP_EQ) {
	    printf("sub %lu failure!\n", sub_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    draw(&d);
	    return EXIT_FAILURE;
	 }
      } else if (!strcmp(cmd, "mul")) {
	 ++mul_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&c, buf, 64);
	 mp_copy(&a, &d);
	 mp_mul(&d, &b, &d);
	 if (mp_cmp(&c, &d) != MP_EQ) {
	    printf("mul %lu failure!\n", mul_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    draw(&d);
	    return EXIT_FAILURE;
	 }
      } else if (!strcmp(cmd, "div")) {
	 ++div_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&c, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&d, buf, 64);

	 mp_div(&a, &b, &e, &f);
	 if (mp_cmp(&c, &e) != MP_EQ || mp_cmp(&d, &f) != MP_EQ) {
	    printf("div %lu %d, %d, failure!\n", div_n, mp_cmp(&c, &e),
		   mp_cmp(&d, &f));
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    draw(&d);
	    draw(&e);
	    draw(&f);
	    return EXIT_FAILURE;
	 }

      } else if (!strcmp(cmd, "sqr")) {
	 ++sqr_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 mp_copy(&a, &c);
	 mp_sqr(&c, &c);
	 if (mp_cmp(&b, &c) != MP_EQ) {
	    printf("sqr %lu failure!\n", sqr_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    return EXIT_FAILURE;
	 }
      } else if (!strcmp(cmd, "gcd")) {
	 ++gcd_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&c, buf, 64);
	 mp_copy(&a, &d);
	 mp_gcd(&d, &b, &d);
	 d.sign = c.sign;
	 if (mp_cmp(&c, &d) != MP_EQ) {
	    printf("gcd %lu failure!\n", gcd_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    draw(&d);
	    return EXIT_FAILURE;
	 }
      } else if (!strcmp(cmd, "lcm")) {
	 ++lcm_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&c, buf, 64);
	 mp_copy(&a, &d);
	 mp_lcm(&d, &b, &d);
	 d.sign = c.sign;
	 if (mp_cmp(&c, &d) != MP_EQ) {
	    printf("lcm %lu failure!\n", lcm_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    draw(&d);
	    return EXIT_FAILURE;
	 }
      } else if (!strcmp(cmd, "expt")) {
	 ++expt_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&c, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&d, buf, 64);
	 mp_copy(&a, &e);
	 mp_exptmod(&e, &b, &c, &e);
	 if (mp_cmp(&d, &e) != MP_EQ) {
	    printf("expt %lu failure!\n", expt_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    draw(&d);
	    draw(&e);
	    return EXIT_FAILURE;
	 }
      } else if (!strcmp(cmd, "invmod")) {
	 ++inv_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&c, buf, 64);
	 mp_invmod(&a, &b, &d);
	 mp_mulmod(&d, &a, &b, &e);
	 if (mp_cmp_d(&e, 1) != MP_EQ) {
	    printf("inv [wrong value from MPI?!] failure\n");
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    draw(&d);
	    draw(&e);
	    mp_gcd(&a, &b, &e);
	    draw(&e);
	    return EXIT_FAILURE;
	 }

      } else if (!strcmp(cmd, "div2")) {
	 ++div2_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 mp_div_2(&a, &c);
	 if (mp_cmp(&c, &b) != MP_EQ) {
	    printf("div_2 %lu failure\n", div2_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    return EXIT_FAILURE;
	 }
      } else if (!strcmp(cmd, "mul2")) {
	 ++mul2_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 mp_mul_2(&a, &c);
	 if (mp_cmp(&c, &b) != MP_EQ) {
	    printf("mul_2 %lu failure\n", mul2_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    return EXIT_FAILURE;
	 }
      } else if (!strcmp(cmd, "add_d")) {
	 ++add_d_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 sscanf(buf, "%d", &ix);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 mp_add_d(&a, ix, &c);
	 if (mp_cmp(&b, &c) != MP_EQ) {
	    printf("add_d %lu failure\n", add_d_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    printf("d == %d\n", ix);
	    return EXIT_FAILURE;
	 }
      } else if (!strcmp(cmd, "sub_d")) {
	 ++sub_d_n;
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&a, buf, 64);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 sscanf(buf, "%d", &ix);
	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
	 mp_read_radix(&b, buf, 64);
	 mp_sub_d(&a, ix, &c);
	 if (mp_cmp(&b, &c) != MP_EQ) {
	    printf("sub_d %lu failure\n", sub_d_n);
	    draw(&a);
	    draw(&b);
	    draw(&c);
	    printf("d == %d\n", ix);
	    return EXIT_FAILURE;
	 }
      } else if (!strcmp(cmd, "exit")) {
         printf("\nokay, exiting now\n");
         break;
      }
   }
#endif
   return 0;
}

/* $Source$ */
/* $Revision$ */
/* $Date$ */

#include <tommath.h>
#include <time.h>


ulong64 _tt;

#ifdef IOWNANATHLON
#include <unistd.h>
#define SLEEP sleep(4)
#else
#define SLEEP
#endif








void ndraw(mp_int * a, char *name)
{
   char buf[4096];

   printf("%s: ", name);
................................................................................
}

/* RDTSC from Scott Duplichan */
static ulong64 TIMFUNC(void)
{
#if defined __GNUC__
#if defined(__i386__) || defined(__x86_64__)
   unsigned long long a;
   __asm__ __volatile__("rdtsc\nmovl %%eax,%0\nmovl %%edx,4+%0\n"::
			"m"(a):"%eax", "%edx");
   return a;


#else /* gcc-IA64 version */
   unsigned long result;
   __asm__ __volatile__("mov %0=ar.itc":"=r"(result)::"memory");

   while (__builtin_expect((int) result == -1, 0))
      __asm__ __volatile__("mov %0=ar.itc":"=r"(result)::"memory");

................................................................................
#endif
}

#define DO(x) x; x;
//#define DO4(x) DO2(x); DO2(x);
//#define DO8(x) DO4(x); DO4(x);
//#define DO(x)  DO8(x); DO8(x);













int main(void)
{
   ulong64 tt, gg, CLK_PER_SEC;
   FILE *log, *logb, *logc, *logd;
   mp_int a, b, c, d, e, f;
   int n, cnt, ix, old_kara_m, old_kara_s;
   unsigned rr;

   mp_init(&a);
   mp_init(&b);
   mp_init(&c);
   mp_init(&d);
   mp_init(&e);
   mp_init(&f);

   srand(time(NULL));


   /* temp. turn off TOOM */
   TOOM_MUL_CUTOFF = TOOM_SQR_CUTOFF = 100000;

   CLK_PER_SEC = TIMFUNC();
   sleep(1);
   CLK_PER_SEC = TIMFUNC() - CLK_PER_SEC;

   printf("CLK_PER_SEC == %llu\n", CLK_PER_SEC);
   goto exptmod;
   log = fopen("logs/add.log", "w");
   for (cnt = 8; cnt <= 128; cnt += 8) {
      SLEEP;
      mp_rand(&a, cnt);
      mp_rand(&b, cnt);
      rr = 0;
      tt = -1;
      do {
................................................................................
	 DO(mp_add(&a, &b, &c));
	 gg = (TIMFUNC() - gg) >> 1;
	 if (tt > gg)
	    tt = gg;
      } while (++rr < 100000);
      printf("Adding\t\t%4d-bit => %9llu/sec, %9llu cycles\n",
	     mp_count_bits(&a), CLK_PER_SEC / tt, tt);
      fprintf(log, "%d %9llu\n", cnt * DIGIT_BIT, tt);
      fflush(log);
   }
   fclose(log);

   log = fopen("logs/sub.log", "w");
   for (cnt = 8; cnt <= 128; cnt += 8) {
      SLEEP;
      mp_rand(&a, cnt);
      mp_rand(&b, cnt);
      rr = 0;
      tt = -1;
      do {
................................................................................
	 gg = (TIMFUNC() - gg) >> 1;
	 if (tt > gg)
	    tt = gg;
      } while (++rr < 100000);

      printf("Subtracting\t\t%4d-bit => %9llu/sec, %9llu cycles\n",
	     mp_count_bits(&a), CLK_PER_SEC / tt, tt);
      fprintf(log, "%d %9llu\n", cnt * DIGIT_BIT, tt);
      fflush(log);
   }
   fclose(log);

   /* do mult/square twice, first without karatsuba and second with */
 multtest:
   old_kara_m = KARATSUBA_MUL_CUTOFF;
   old_kara_s = KARATSUBA_SQR_CUTOFF;



   for (ix = 0; ix < 2; ix++) {
      printf("With%s Karatsuba\n", (ix == 0) ? "out" : "");

      KARATSUBA_MUL_CUTOFF = (ix == 0) ? 9999 : old_kara_m;
      KARATSUBA_SQR_CUTOFF = (ix == 0) ? 9999 : old_kara_s;



      log = fopen((ix == 0) ? "logs/mult.log" : "logs/mult_kara.log", "w");
      for (cnt = 4; cnt <= 10240 / DIGIT_BIT; cnt += 2) {
	 SLEEP;
	 mp_rand(&a, cnt);
	 mp_rand(&b, cnt);
	 rr = 0;
	 tt = -1;
	 do {
................................................................................
	    DO(mp_mul(&a, &b, &c));
	    gg = (TIMFUNC() - gg) >> 1;
	    if (tt > gg)
	       tt = gg;
	 } while (++rr < 100);
	 printf("Multiplying\t%4d-bit => %9llu/sec, %9llu cycles\n",
		mp_count_bits(&a), CLK_PER_SEC / tt, tt);
	 fprintf(log, "%d %9llu\n", mp_count_bits(&a), tt);
	 fflush(log);
      }
      fclose(log);

      log = fopen((ix == 0) ? "logs/sqr.log" : "logs/sqr_kara.log", "w");
      for (cnt = 4; cnt <= 10240 / DIGIT_BIT; cnt += 2) {
	 SLEEP;
	 mp_rand(&a, cnt);
	 rr = 0;
	 tt = -1;
	 do {
	    gg = TIMFUNC();
................................................................................
	    DO(mp_sqr(&a, &b));
	    gg = (TIMFUNC() - gg) >> 1;
	    if (tt > gg)
	       tt = gg;
	 } while (++rr < 100);
	 printf("Squaring\t%4d-bit => %9llu/sec, %9llu cycles\n",
		mp_count_bits(&a), CLK_PER_SEC / tt, tt);
	 fprintf(log, "%d %9llu\n", mp_count_bits(&a), tt);
	 fflush(log);
      }
      fclose(log);

   }
 exptmod:

   {
      char *primes[] = {
	 /* 2K large moduli */
	 "179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586239334100047359817950870678242457666208137217",
	 "32317006071311007300714876688669951960444102669715484032130345427524655138867890893197201411522913463688717960921898019494119559150490921095088152386448283120630877367300996091750197750389652106796057638384067568276792218642619756161838094338476170470581645852036305042887575891541065808607552399123930385521914333389668342420684974786564569494856176035326322058077805659331026192708460314150258592864177116725943603718461857357598351152301645904403697613233287231227125684710820209725157101726931323469678542580656697935045997268352998638099733077152121140120031150424541696791951097529546801429027668869927491725169",
	 "1044388881413152506691752710716624382579964249047383780384233483283953907971557456848826811934997558340890106714439262837987573438185793607263236087851365277945956976543709998340361590134383718314428070011855946226376318839397712745672334684344586617496807908705803704071284048740118609114467977783598029006686938976881787785946905630190260940599579453432823469303026696443059025015972399867714215541693835559885291486318237914434496734087811872639496475100189041349008417061675093668333850551032972088269550769983616369411933015213796825837188091833656751221318492846368125550225998300412344784862595674492194617023806505913245610825731835380087608622102834270197698202313169017678006675195485079921636419370285375124784014907159135459982790513399611551794271106831134090584272884279791554849782954323534517065223269061394905987693002122963395687782878948440616007412945674919823050571642377154816321380631045902916136926708342856440730447899971901781465763473223850267253059899795996090799469201774624817718449867455659250178329070473119433165550807568221846571746373296884912819520317457002440926616910874148385078411929804522981857338977648103126085902995208257421855249796721729039744118165938433694823325696642096892124547425283",
................................................................................
	 "347743159439876626079252796797422223177535447388206607607181663903045907591201940478223621722118173270898487582987137708656414344685816179420855160986340457973820182883508387588163122354089264395604796675278966117567294812714812796820596564876450716066283126720010859041484786529056457896367683122960411136319",
	 "47266428956356393164697365098120418976400602706072312735924071745438532218237979333351774907308168340693326687317443721193266215155735814510792148768576498491199122744351399489453533553203833318691678263241941706256996197460424029012419012634671862283532342656309677173602509498417976091509154360039893165037637034737020327399910409885798185771003505320583967737293415979917317338985837385734747478364242020380416892056650841470869294527543597349250299539682430605173321029026555546832473048600327036845781970289288898317888427517364945316709081173840186150794397479045034008257793436817683392375274635794835245695887",
	 "436463808505957768574894870394349739623346440601945961161254440072143298152040105676491048248110146278752857839930515766167441407021501229924721335644557342265864606569000117714935185566842453630868849121480179691838399545644365571106757731317371758557990781880691336695584799313313687287468894148823761785582982549586183756806449017542622267874275103877481475534991201849912222670102069951687572917937634467778042874315463238062009202992087620963771759666448266532858079402669920025224220613419441069718482837399612644978839925207109870840278194042158748845445131729137117098529028886770063736487420613144045836803985635654192482395882603511950547826439092832800532152534003936926017612446606135655146445620623395788978726744728503058670046885876251527122350275750995227",
	 "11424167473351836398078306042624362277956429440521137061889702611766348760692206243140413411077394583180726863277012016602279290144126785129569474909173584789822341986742719230331946072730319555984484911716797058875905400999504305877245849119687509023232790273637466821052576859232452982061831009770786031785669030271542286603956118755585683996118896215213488875253101894663403069677745948305893849505434201763745232895780711972432011344857521691017896316861403206449421332243658855453435784006517202894181640562433575390821384210960117518650374602256601091379644034244332285065935413233557998331562749140202965844219336298970011513882564935538704289446968322281451907487362046511461221329799897350993370560697505809686438782036235372137015731304779072430260986460269894522159103008260495503005267165927542949439526272736586626709581721032189532726389643625590680105784844246152702670169304203783072275089194754889511973916207",
	 "1214855636816562637502584060163403830270705000634713483015101384881871978446801224798536155406895823305035467591632531067547890948695117172076954220727075688048751022421198712032848890056357845974246560748347918630050853933697792254955890439720297560693579400297062396904306270145886830719309296352765295712183040773146419022875165382778007040109957609739589875590885701126197906063620133954893216612678838507540777138437797705602453719559017633986486649523611975865005712371194067612263330335590526176087004421363598470302731349138773205901447704682181517904064735636518462452242791676541725292378925568296858010151852326316777511935037531017413910506921922450666933202278489024521263798482237150056835746454842662048692127173834433089016107854491097456725016327709663199738238442164843147132789153725513257167915555162094970853584447993125488607696008169807374736711297007473812256272245489405898470297178738029484459690836250560495461579533254473316340608217876781986188705928270735695752830825527963838355419762516246028680280988020401914551825487349990306976304093109384451438813251211051597392127491464898797406789175453067960072008590614886532333015881171367104445044718144312416815712216611576221546455968770801413440778423979",
	 NULL
      };
      log = fopen("logs/expt.log", "w");
      logb = fopen("logs/expt_dr.log", "w");
      logc = fopen("logs/expt_2k.log", "w");
      logd = fopen("logs/expt_2kl.log", "w");
      for (n = 0; primes[n]; n++) {
	 SLEEP;
	 mp_read_radix(&a, primes[n], 10);
	 mp_zero(&b);
	 for (rr = 0; rr < (unsigned) mp_count_bits(&a); rr++) {
	    mp_mul_2(&b, &b);
	    b.dp[0] |= lbit();
................................................................................
	 if (mp_cmp_d(&d, 1)) {
	    printf("Different (%d)!!!\n", mp_count_bits(&a));
	    draw(&d);
	    exit(0);
	 }
	 printf("Exponentiating\t%4d-bit => %9llu/sec, %9llu cycles\n",
		mp_count_bits(&a), CLK_PER_SEC / tt, tt);
	 fprintf(n < 4 ? logd : (n < 9) ? logc : (n < 16) ? logb : log,
		 "%d %9llu\n", mp_count_bits(&a), tt);
      }
   }
   fclose(log);
   fclose(logb);
   fclose(logc);
   fclose(logd);

   log = fopen("logs/invmod.log", "w");
   for (cnt = 4; cnt <= 128; cnt += 4) {
      SLEEP;
      mp_rand(&a, cnt);
      mp_rand(&b, cnt);

      do {
	 mp_add_d(&b, 1, &b);
	 mp_gcd(&a, &b, &c);
................................................................................
      mp_mulmod(&b, &c, &a, &d);
      if (mp_cmp_d(&d, 1) != MP_EQ) {
	 printf("Failed to invert\n");
	 return 0;
      }
      printf("Inverting mod\t%4d-bit => %9llu/sec, %9llu cycles\n",
	     mp_count_bits(&a), CLK_PER_SEC / tt, tt);
      fprintf(log, "%d %9llu\n", cnt * DIGIT_BIT, tt);
   }
   fclose(log);

   return 0;
}

#include <tommath.h>
#include <time.h>
#include <unistd.h>

ulong64 _tt;

#ifdef IOWNANATHLON
#include <unistd.h>
#define SLEEP sleep(4)
#else
#define SLEEP
#endif

#ifdef LTM_TIMING_REAL_RAND
#define LTM_TIMING_RAND_SEED  time(NULL)
#else
#define LTM_TIMING_RAND_SEED  23
#endif


void ndraw(mp_int * a, char *name)
{
   char buf[4096];

   printf("%s: ", name);
................................................................................
}

/* RDTSC from Scott Duplichan */
static ulong64 TIMFUNC(void)
{
#if defined __GNUC__
#if defined(__i386__) || defined(__x86_64__)
  /* version from http://www.mcs.anl.gov/~kazutomo/rdtsc.html
   * the old code always got a warning issued by gcc, clang did not complain...
   */
  unsigned hi, lo;
  __asm__ __volatile__ ("rdtsc" : "=a"(lo), "=d"(hi));
  return ((ulong64)lo)|( ((ulong64)hi)<<32);
#else /* gcc-IA64 version */
   unsigned long result;
   __asm__ __volatile__("mov %0=ar.itc":"=r"(result)::"memory");

   while (__builtin_expect((int) result == -1, 0))
      __asm__ __volatile__("mov %0=ar.itc":"=r"(result)::"memory");

................................................................................
#endif
}

#define DO(x) x; x;
//#define DO4(x) DO2(x); DO2(x);
//#define DO8(x) DO4(x); DO4(x);
//#define DO(x)  DO8(x); DO8(x);

#ifdef TIMING_NO_LOGS
#define FOPEN(a, b)     NULL
#define FPRINTF(a,b,c,d)
#define FFLUSH(a)
#define FCLOSE(a)       (void)(a)
#else
#define FOPEN(a,b)       fopen(a,b)
#define FPRINTF(a,b,c,d) fprintf(a,b,c,d)
#define FFLUSH(a)        fflush(a)
#define FCLOSE(a)        fclose(a)
#endif

int main(void)
{
   ulong64 tt, gg, CLK_PER_SEC;
   FILE *log, *logb, *logc, *logd;
   mp_int a, b, c, d, e, f;
   int n, cnt, ix, old_kara_m, old_kara_s, old_toom_m, old_toom_s;
   unsigned rr;

   mp_init(&a);
   mp_init(&b);
   mp_init(&c);
   mp_init(&d);
   mp_init(&e);
   mp_init(&f);

   srand(LTM_TIMING_RAND_SEED);





   CLK_PER_SEC = TIMFUNC();
   sleep(1);
   CLK_PER_SEC = TIMFUNC() - CLK_PER_SEC;

   printf("CLK_PER_SEC == %llu\n", CLK_PER_SEC);

   log = FOPEN("logs/add.log", "w");
   for (cnt = 8; cnt <= 128; cnt += 8) {
      SLEEP;
      mp_rand(&a, cnt);
      mp_rand(&b, cnt);
      rr = 0;
      tt = -1;
      do {
................................................................................
	 DO(mp_add(&a, &b, &c));
	 gg = (TIMFUNC() - gg) >> 1;
	 if (tt > gg)
	    tt = gg;
      } while (++rr < 100000);
      printf("Adding\t\t%4d-bit => %9llu/sec, %9llu cycles\n",
	     mp_count_bits(&a), CLK_PER_SEC / tt, tt);
      FPRINTF(log, "%d %9llu\n", cnt * DIGIT_BIT, tt);
      FFLUSH(log);
   }
   FCLOSE(log);

   log = FOPEN("logs/sub.log", "w");
   for (cnt = 8; cnt <= 128; cnt += 8) {
      SLEEP;
      mp_rand(&a, cnt);
      mp_rand(&b, cnt);
      rr = 0;
      tt = -1;
      do {
................................................................................
	 gg = (TIMFUNC() - gg) >> 1;
	 if (tt > gg)
	    tt = gg;
      } while (++rr < 100000);

      printf("Subtracting\t\t%4d-bit => %9llu/sec, %9llu cycles\n",
	     mp_count_bits(&a), CLK_PER_SEC / tt, tt);
      FPRINTF(log, "%d %9llu\n", cnt * DIGIT_BIT, tt);
      FFLUSH(log);
   }
   FCLOSE(log);

   /* do mult/square twice, first without karatsuba and second with */

   old_kara_m = KARATSUBA_MUL_CUTOFF;
   old_kara_s = KARATSUBA_SQR_CUTOFF;
   /* currently toom-cook cut-off is too high to kick in, so we just use the karatsuba values */
   old_toom_m = old_kara_m;
   old_toom_s = old_kara_m;
   for (ix = 0; ix < 3; ix++) {
      printf("With%s Karatsuba, With%s Toom\n", (ix == 0) ? "out" : "", (ix == 1) ? "out" : "");

      KARATSUBA_MUL_CUTOFF = (ix == 1) ? old_kara_m : 9999;
      KARATSUBA_SQR_CUTOFF = (ix == 1) ? old_kara_s : 9999;
      TOOM_MUL_CUTOFF = (ix == 2) ? old_toom_m : 9999;
      TOOM_SQR_CUTOFF = (ix == 2) ? old_toom_s : 9999;

      log = FOPEN((ix == 0) ? "logs/mult.log" : (ix == 1) ? "logs/mult_kara.log" : "logs/mult_toom.log", "w");
      for (cnt = 4; cnt <= 10240 / DIGIT_BIT; cnt += 2) {
	 SLEEP;
	 mp_rand(&a, cnt);
	 mp_rand(&b, cnt);
	 rr = 0;
	 tt = -1;
	 do {
................................................................................
	    DO(mp_mul(&a, &b, &c));
	    gg = (TIMFUNC() - gg) >> 1;
	    if (tt > gg)
	       tt = gg;
	 } while (++rr < 100);
	 printf("Multiplying\t%4d-bit => %9llu/sec, %9llu cycles\n",
		mp_count_bits(&a), CLK_PER_SEC / tt, tt);
	 FPRINTF(log, "%d %9llu\n", mp_count_bits(&a), tt);
	 FFLUSH(log);
      }
      FCLOSE(log);

      log = FOPEN((ix == 0) ? "logs/sqr.log" : (ix == 1) ? "logs/sqr_kara.log" : "logs/sqr_toom.log", "w");
      for (cnt = 4; cnt <= 10240 / DIGIT_BIT; cnt += 2) {
	 SLEEP;
	 mp_rand(&a, cnt);
	 rr = 0;
	 tt = -1;
	 do {
	    gg = TIMFUNC();
................................................................................
	    DO(mp_sqr(&a, &b));
	    gg = (TIMFUNC() - gg) >> 1;
	    if (tt > gg)
	       tt = gg;
	 } while (++rr < 100);
	 printf("Squaring\t%4d-bit => %9llu/sec, %9llu cycles\n",
		mp_count_bits(&a), CLK_PER_SEC / tt, tt);
	 FPRINTF(log, "%d %9llu\n", mp_count_bits(&a), tt);
	 FFLUSH(log);
      }
      FCLOSE(log);

   }


   {
      char *primes[] = {
	 /* 2K large moduli */
	 "179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586239334100047359817950870678242457666208137217",
	 "32317006071311007300714876688669951960444102669715484032130345427524655138867890893197201411522913463688717960921898019494119559150490921095088152386448283120630877367300996091750197750389652106796057638384067568276792218642619756161838094338476170470581645852036305042887575891541065808607552399123930385521914333389668342420684974786564569494856176035326322058077805659331026192708460314150258592864177116725943603718461857357598351152301645904403697613233287231227125684710820209725157101726931323469678542580656697935045997268352998638099733077152121140120031150424541696791951097529546801429027668869927491725169",
	 "1044388881413152506691752710716624382579964249047383780384233483283953907971557456848826811934997558340890106714439262837987573438185793607263236087851365277945956976543709998340361590134383718314428070011855946226376318839397712745672334684344586617496807908705803704071284048740118609114467977783598029006686938976881787785946905630190260940599579453432823469303026696443059025015972399867714215541693835559885291486318237914434496734087811872639496475100189041349008417061675093668333850551032972088269550769983616369411933015213796825837188091833656751221318492846368125550225998300412344784862595674492194617023806505913245610825731835380087608622102834270197698202313169017678006675195485079921636419370285375124784014907159135459982790513399611551794271106831134090584272884279791554849782954323534517065223269061394905987693002122963395687782878948440616007412945674919823050571642377154816321380631045902916136926708342856440730447899971901781465763473223850267253059899795996090799469201774624817718449867455659250178329070473119433165550807568221846571746373296884912819520317457002440926616910874148385078411929804522981857338977648103126085902995208257421855249796721729039744118165938433694823325696642096892124547425283",
................................................................................
	 "347743159439876626079252796797422223177535447388206607607181663903045907591201940478223621722118173270898487582987137708656414344685816179420855160986340457973820182883508387588163122354089264395604796675278966117567294812714812796820596564876450716066283126720010859041484786529056457896367683122960411136319",
	 "47266428956356393164697365098120418976400602706072312735924071745438532218237979333351774907308168340693326687317443721193266215155735814510792148768576498491199122744351399489453533553203833318691678263241941706256996197460424029012419012634671862283532342656309677173602509498417976091509154360039893165037637034737020327399910409885798185771003505320583967737293415979917317338985837385734747478364242020380416892056650841470869294527543597349250299539682430605173321029026555546832473048600327036845781970289288898317888427517364945316709081173840186150794397479045034008257793436817683392375274635794835245695887",
	 "436463808505957768574894870394349739623346440601945961161254440072143298152040105676491048248110146278752857839930515766167441407021501229924721335644557342265864606569000117714935185566842453630868849121480179691838399545644365571106757731317371758557990781880691336695584799313313687287468894148823761785582982549586183756806449017542622267874275103877481475534991201849912222670102069951687572917937634467778042874315463238062009202992087620963771759666448266532858079402669920025224220613419441069718482837399612644978839925207109870840278194042158748845445131729137117098529028886770063736487420613144045836803985635654192482395882603511950547826439092832800532152534003936926017612446606135655146445620623395788978726744728503058670046885876251527122350275750995227",
	 "11424167473351836398078306042624362277956429440521137061889702611766348760692206243140413411077394583180726863277012016602279290144126785129569474909173584789822341986742719230331946072730319555984484911716797058875905400999504305877245849119687509023232790273637466821052576859232452982061831009770786031785669030271542286603956118755585683996118896215213488875253101894663403069677745948305893849505434201763745232895780711972432011344857521691017896316861403206449421332243658855453435784006517202894181640562433575390821384210960117518650374602256601091379644034244332285065935413233557998331562749140202965844219336298970011513882564935538704289446968322281451907487362046511461221329799897350993370560697505809686438782036235372137015731304779072430260986460269894522159103008260495503005267165927542949439526272736586626709581721032189532726389643625590680105784844246152702670169304203783072275089194754889511973916207",
	 "1214855636816562637502584060163403830270705000634713483015101384881871978446801224798536155406895823305035467591632531067547890948695117172076954220727075688048751022421198712032848890056357845974246560748347918630050853933697792254955890439720297560693579400297062396904306270145886830719309296352765295712183040773146419022875165382778007040109957609739589875590885701126197906063620133954893216612678838507540777138437797705602453719559017633986486649523611975865005712371194067612263330335590526176087004421363598470302731349138773205901447704682181517904064735636518462452242791676541725292378925568296858010151852326316777511935037531017413910506921922450666933202278489024521263798482237150056835746454842662048692127173834433089016107854491097456725016327709663199738238442164843147132789153725513257167915555162094970853584447993125488607696008169807374736711297007473812256272245489405898470297178738029484459690836250560495461579533254473316340608217876781986188705928270735695752830825527963838355419762516246028680280988020401914551825487349990306976304093109384451438813251211051597392127491464898797406789175453067960072008590614886532333015881171367104445044718144312416815712216611576221546455968770801413440778423979",
	 NULL
      };
      log = FOPEN("logs/expt.log", "w");
      logb = FOPEN("logs/expt_dr.log", "w");
      logc = FOPEN("logs/expt_2k.log", "w");
      logd = FOPEN("logs/expt_2kl.log", "w");
      for (n = 0; primes[n]; n++) {
	 SLEEP;
	 mp_read_radix(&a, primes[n], 10);
	 mp_zero(&b);
	 for (rr = 0; rr < (unsigned) mp_count_bits(&a); rr++) {
	    mp_mul_2(&b, &b);
	    b.dp[0] |= lbit();
................................................................................
	 if (mp_cmp_d(&d, 1)) {
	    printf("Different (%d)!!!\n", mp_count_bits(&a));
	    draw(&d);
	    exit(0);
	 }
	 printf("Exponentiating\t%4d-bit => %9llu/sec, %9llu cycles\n",
		mp_count_bits(&a), CLK_PER_SEC / tt, tt);
	 FPRINTF(n < 4 ? logd : (n < 9) ? logc : (n < 16) ? logb : log,
		 "%d %9llu\n", mp_count_bits(&a), tt);
      }
   }
   FCLOSE(log);
   FCLOSE(logb);
   FCLOSE(logc);
   FCLOSE(logd);

   log = FOPEN("logs/invmod.log", "w");
   for (cnt = 4; cnt <= 32; cnt += 4) {
      SLEEP;
      mp_rand(&a, cnt);
      mp_rand(&b, cnt);

      do {
	 mp_add_d(&b, 1, &b);
	 mp_gcd(&a, &b, &c);
................................................................................
      mp_mulmod(&b, &c, &a, &d);
      if (mp_cmp_d(&d, 1) != MP_EQ) {
	 printf("Failed to invert\n");
	 return 0;
      }
      printf("Inverting mod\t%4d-bit => %9llu/sec, %9llu cycles\n",
	     mp_count_bits(&a), CLK_PER_SEC / tt, tt);
      FPRINTF(log, "%d %9llu\n", cnt * DIGIT_BIT, tt);
   }
   FCLOSE(log);

   return 0;
}

/* $Source$ */
/* $Revision$ */
/* $Date$ */

   # scan for mp_* and make classes
   while (<SRC>) {
      my $line = $_;
      while ($line =~ m/(fast_)*(s_)*mp\_[a-z_0-9]*/) {
          $line = $';
          # now $& is the match, we want to skip over LTM keywords like
          # mp_int, mp_word, mp_digit
          if (!($& eq "mp_digit") && !($& eq "mp_word") && !($& eq "mp_int")) {
             my $a = $&;
             $a =~ tr/[a-z]/[A-Z]/;
             $a = "BN_" . $a . "_C";
             if (!($list =~ /$a/)) {
                print CLASS "   #define $a\n";
             }
             $list = $list . "," . $a;

   # scan for mp_* and make classes
   while (<SRC>) {
      my $line = $_;
      while ($line =~ m/(fast_)*(s_)*mp\_[a-z_0-9]*/) {
          $line = $';
          # now $& is the match, we want to skip over LTM keywords like
          # mp_int, mp_word, mp_digit
          if (!($& eq "mp_digit") && !($& eq "mp_word") && !($& eq "mp_int") && !($& eq "mp_min_u32")) {
             my $a = $&;
             $a =~ tr/[a-z]/[A-Z]/;
             $a = "BN_" . $a . "_C";
             if (!($list =~ /$a/)) {
                print CLASS "   #define $a\n";
             }
             $list = $list . "," . $a;

       mp_toradix(&q, buf, 10);
       printf("\n\n%d-bits (k = %lu) = %s\n", sizes[x], z, buf);
       fprintf(out, "%d-bits (k = %lu) = %s\n", sizes[x], z, buf); fflush(out);
   }
   
   return 0;
}   

       mp_toradix(&q, buf, 10);
       printf("\n\n%d-bits (k = %lu) = %s\n", sizes[x], z, buf);
       fprintf(out, "%d-bits (k = %lu) = %s\n", sizes[x], z, buf); fflush(out);
   }
   
   return 0;
}   
       
         
            
            
          

/* $Source$ */
/* $Revision$ */
/* $Date$ */

   fclose(out);
   
   mp_clear(&a);
   mp_clear(&b);
   
   return 0;
}

   fclose(out);
   
   mp_clear(&a);
   mp_clear(&b);
   
   return 0;
}


/* $Source$ */
/* $Revision$ */
/* $Date$ */

    /* but make sure its prime */
    while (isprime (k) == 0) {
      k += 2;
    }
  }
  return 0;
}

    /* but make sure its prime */
    while (isprime (k) == 0) {
      k += 2;
    }
  }
  return 0;
}

/* $Source$ */
/* $Revision$ */
/* $Date$ */

           }
       }
       printf("PASSED\n");
    }
    
    return 0;
}

           }
       }
       printf("PASSED\n");
    }
    
    return 0;
}






/* $Source$ */
/* $Revision$ */
/* $Date$ */

  mp_toradix (&p, buf, 10);
  printf ("P == %s\n", buf);
  mp_toradix (&q, buf, 10);
  printf ("Q == %s\n", buf);

  return 0;
}

  mp_toradix (&p, buf, 10);
  printf ("P == %s\n", buf);
  mp_toradix (&q, buf, 10);
  printf ("Q == %s\n", buf);

  return 0;
}

/* $Source$ */
/* $Revision$ */
/* $Date$ */

 *
 * Tom St Denis, [email protected]
 */
#include <tommath.h>
#include <time.h>

/* how many times todo each size mult.  Depends on your computer.  For slow computers
 * this can be low like 5 or 10.  For fast [re: Athlon] should be 25 - 50 or so 
 */
#define TIMES (1UL<<14UL)



/* RDTSC from Scott Duplichan */
static ulong64 TIMFUNC (void)
   {
   #if defined __GNUC__
      #if defined(__i386__) || defined(__x86_64__)



         unsigned long long a;
         __asm__ __volatile__ ("rdtsc\nmovl %%eax,%0\nmovl %%edx,4+%0\n"::"m"(a):"%eax","%edx");
         return a;

      #else /* gcc-IA64 version */
         unsigned long result;
         __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory");
         while (__builtin_expect ((int) result == -1, 0))
         __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory");
         return result;
      #endif
................................................................................
      return __getReg (3116);
   #else
     #error need rdtsc function for this build
   #endif
   }


#ifndef X86_TIMER

/* generic ISO C timer */
ulong64 LBL_T;
void t_start(void) { LBL_T = TIMFUNC(); }
ulong64 t_read(void) { return TIMFUNC() - LBL_T; }

#else
extern void t_start(void);
................................................................................
  mp_init (&a);
  mp_init (&b);
  mp_init (&c);

  mp_rand (&a, size);
  mp_rand (&b, size);

  if (s == 1) { 
      KARATSUBA_MUL_CUTOFF = size;
  } else {
      KARATSUBA_MUL_CUTOFF = 100000;
  }

  t_start();
  for (x = 0; x < TIMES; x++) {
................................................................................
  ulong64 t1;

  mp_init (&a);
  mp_init (&b);

  mp_rand (&a, size);

  if (s == 1) { 
      KARATSUBA_SQR_CUTOFF = size;
  } else {
      KARATSUBA_SQR_CUTOFF = 100000;
  }

  t_start();
  for (x = 0; x < TIMES; x++) {
................................................................................

int
main (void)
{
  ulong64 t1, t2;
  int x, y;

  for (x = 8; ; x += 2) { 
     t1 = time_mult(x, 0);
     t2 = time_mult(x, 1);
     printf("%d: %9llu %9llu, %9llu\n", x, t1, t2, t2 - t1);
     if (t2 < t1) break;
  }
  y = x;

  for (x = 8; ; x += 2) { 
     t1 = time_sqr(x, 0);
     t2 = time_sqr(x, 1);
     printf("%d: %9llu %9llu, %9llu\n", x, t1, t2, t2 - t1);
     if (t2 < t1) break;
  }
  printf("KARATSUBA_MUL_CUTOFF = %d\n", y);
  printf("KARATSUBA_SQR_CUTOFF = %d\n", x);

  return 0;
}

 *
 * Tom St Denis, [email protected]
 */
#include <tommath.h>
#include <time.h>

/* how many times todo each size mult.  Depends on your computer.  For slow computers
 * this can be low like 5 or 10.  For fast [re: Athlon] should be 25 - 50 or so
 */
#define TIMES (1UL<<14UL)

#ifndef X86_TIMER

/* RDTSC from Scott Duplichan */
static ulong64 TIMFUNC (void)
   {
   #if defined __GNUC__
      #if defined(__i386__) || defined(__x86_64__)
        /* version from http://www.mcs.anl.gov/~kazutomo/rdtsc.html
         * the old code always got a warning issued by gcc, clang did not complain...
         */
        unsigned hi, lo;
        __asm__ __volatile__ ("rdtsc" : "=a"(lo), "=d"(hi));

        return ((ulong64)lo)|( ((ulong64)hi)<<32);
      #else /* gcc-IA64 version */
         unsigned long result;
         __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory");
         while (__builtin_expect ((int) result == -1, 0))
         __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory");
         return result;
      #endif
................................................................................
      return __getReg (3116);
   #else
     #error need rdtsc function for this build
   #endif
   }




/* generic ISO C timer */
ulong64 LBL_T;
void t_start(void) { LBL_T = TIMFUNC(); }
ulong64 t_read(void) { return TIMFUNC() - LBL_T; }

#else
extern void t_start(void);
................................................................................
  mp_init (&a);
  mp_init (&b);
  mp_init (&c);

  mp_rand (&a, size);
  mp_rand (&b, size);

  if (s == 1) {
      KARATSUBA_MUL_CUTOFF = size;
  } else {
      KARATSUBA_MUL_CUTOFF = 100000;
  }

  t_start();
  for (x = 0; x < TIMES; x++) {
................................................................................
  ulong64 t1;

  mp_init (&a);
  mp_init (&b);

  mp_rand (&a, size);

  if (s == 1) {
      KARATSUBA_SQR_CUTOFF = size;
  } else {
      KARATSUBA_SQR_CUTOFF = 100000;
  }

  t_start();
  for (x = 0; x < TIMES; x++) {
................................................................................

int
main (void)
{
  ulong64 t1, t2;
  int x, y;

  for (x = 8; ; x += 2) {
     t1 = time_mult(x, 0);
     t2 = time_mult(x, 1);
     printf("%d: %9llu %9llu, %9llu\n", x, t1, t2, t2 - t1);
     if (t2 < t1) break;
  }
  y = x;

  for (x = 8; ; x += 2) {
     t1 = time_sqr(x, 0);
     t2 = time_sqr(x, 1);
     printf("%d: %9llu %9llu, %9llu\n", x, t1, t2, t2 - t1);
     if (t2 < t1) break;
  }
  printf("KARATSUBA_MUL_CUTOFF = %d\n", y);
  printf("KARATSUBA_SQR_CUTOFF = %d\n", x);

  return 0;
}

/* $Source$ */
/* $Revision$ */
/* $Date$ */

   print OUT "/* Start: $filename */\n";
   print OUT while <SRC>;
   print OUT "\n/* End: $filename */\n\n";
   close SRC or die "Error closing $filename after reading: $!";
}
print OUT "\n/* EOF */\n";
close OUT or die "Error closing mpi.c after writing: $!";

   print OUT "/* Start: $filename */\n";
   print OUT while <SRC>;
   print OUT "\n/* End: $filename */\n\n";
   close SRC or die "Error closing $filename after reading: $!";
}
print OUT "\n/* EOF */\n";
close OUT or die "Error closing mpi.c after writing: $!";

system('perl -pli -e "s/\s*$//" mpi.c');

#Makefile for GCC
#
#Tom St Denis

#version of library 
VERSION=0.42.0

CFLAGS  +=  -I./ -Wall -W -Wshadow -Wsign-compare

ifndef MAKE
   MAKE=make
endif

ifndef IGNORE_SPEED

#for speed 
CFLAGS += -O3 -funroll-loops

#for size 
#CFLAGS += -Os

#x86 optimizations [should be valid for any GCC install though]
CFLAGS  += -fomit-frame-pointer

#debug
#CFLAGS += -g3

endif

#install as this user
ifndef INSTALL_GROUP
   GROUP=wheel

else
   GROUP=$(INSTALL_GROUP)

endif

ifndef INSTALL_USER
   USER=root
else
   USER=$(INSTALL_USER)



endif


#default files to install
ifndef LIBNAME
   LIBNAME=libtommath.a
endif

default: ${LIBNAME}


HEADERS=tommath.h tommath_class.h tommath_superclass.h


#LIBPATH-The directory for libtommath to be installed to.
#INCPATH-The directory to install the header files for libtommath.
#DATAPATH-The directory to install the pdf docs.
DESTDIR=
LIBPATH=/usr/lib
INCPATH=/usr/include
DATAPATH=/usr/share/doc/libtommath/pdf


OBJECTS=bncore.o bn_mp_init.o bn_mp_clear.o bn_mp_exch.o bn_mp_grow.o bn_mp_shrink.o \
bn_mp_clamp.o bn_mp_zero.o  bn_mp_set.o bn_mp_set_int.o bn_mp_init_size.o bn_mp_copy.o \
bn_mp_init_copy.o bn_mp_abs.o bn_mp_neg.o bn_mp_cmp_mag.o bn_mp_cmp.o bn_mp_cmp_d.o \
bn_mp_rshd.o bn_mp_lshd.o bn_mp_mod_2d.o bn_mp_div_2d.o bn_mp_mul_2d.o bn_mp_div_2.o \
bn_mp_mul_2.o bn_s_mp_add.o bn_s_mp_sub.o bn_fast_s_mp_mul_digs.o bn_s_mp_mul_digs.o \


bn_fast_s_mp_mul_high_digs.o bn_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_s_mp_sqr.o \
bn_mp_add.o bn_mp_sub.o bn_mp_karatsuba_mul.o bn_mp_mul.o bn_mp_karatsuba_sqr.o \
bn_mp_sqr.o bn_mp_div.o bn_mp_mod.o bn_mp_add_d.o bn_mp_sub_d.o bn_mp_mul_d.o \
bn_mp_div_d.o bn_mp_mod_d.o bn_mp_expt_d.o bn_mp_addmod.o bn_mp_submod.o \
bn_mp_mulmod.o bn_mp_sqrmod.o bn_mp_gcd.o bn_mp_lcm.o bn_fast_mp_invmod.o bn_mp_invmod.o \
bn_mp_reduce.o bn_mp_montgomery_setup.o bn_fast_mp_montgomery_reduce.o bn_mp_montgomery_reduce.o \
bn_mp_exptmod_fast.o bn_mp_exptmod.o bn_mp_2expt.o bn_mp_n_root.o bn_mp_jacobi.o bn_reverse.o \
bn_mp_count_bits.o bn_mp_read_unsigned_bin.o bn_mp_read_signed_bin.o bn_mp_to_unsigned_bin.o \
bn_mp_to_signed_bin.o bn_mp_unsigned_bin_size.o bn_mp_signed_bin_size.o  \
bn_mp_xor.o bn_mp_and.o bn_mp_or.o bn_mp_rand.o bn_mp_montgomery_calc_normalization.o \
bn_mp_prime_is_divisible.o bn_prime_tab.o bn_mp_prime_fermat.o bn_mp_prime_miller_rabin.o \
bn_mp_prime_is_prime.o bn_mp_prime_next_prime.o bn_mp_dr_reduce.o \


bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \
bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \
bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \
bn_mp_reduce_2k_l.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_2k_setup_l.o \
bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \

bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \
bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \







bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o \






bn_mp_to_signed_bin_n.o bn_mp_to_unsigned_bin_n.o





$(LIBNAME):  $(OBJECTS)
	$(AR) $(ARFLAGS) [email protected] $(OBJECTS)
	ranlib [email protected]


#make a profiled library (takes a while!!!)
#
# This will build the library with profile generation
# then run the test demo and rebuild the library.
# 
# So far I've seen improvements in the MP math
profiled:
	make CFLAGS="$(CFLAGS) -fprofile-arcs -DTESTING" timing
	./ltmtest
	rm -f *.a *.o ltmtest
	make CFLAGS="$(CFLAGS) -fbranch-probabilities"

#make a single object profiled library 
profiled_single:
	perl gen.pl
	$(CC) $(CFLAGS) -fprofile-arcs -DTESTING -c mpi.c -o mpi.o
	$(CC) $(CFLAGS) -DTESTING -DTIMER demo/timing.c mpi.o -o ltmtest
	./ltmtest
	rm -f *.o ltmtest
	$(CC) $(CFLAGS) -fbranch-probabilities -DTESTING -c mpi.c -o mpi.o
	$(AR) $(ARFLAGS) $(LIBNAME) mpi.o
	ranlib $(LIBNAME)	

install: $(LIBNAME)
	install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(LIBPATH)
	install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(INCPATH)
	install -g $(GROUP) -o $(USER) $(LIBNAME) $(DESTDIR)$(LIBPATH)
	install -g $(GROUP) -o $(USER) $(HEADERS) $(DESTDIR)$(INCPATH)

test: $(LIBNAME) demo/demo.o
	$(CC) $(CFLAGS) demo/demo.o $(LIBNAME) -o test
	




mtest: test	
	cd mtest ; $(CC) $(CFLAGS) mtest.c -o mtest
        
timing: $(LIBNAME)
	$(CC) $(CFLAGS) -DTIMER demo/timing.c $(LIBNAME) -o ltmtest




# makes the LTM book DVI file, requires tetex, perl and makeindex [part of tetex I think]
docdvi: tommath.src
	cd pics ; MAKE=${MAKE} ${MAKE} 
	echo "hello" > tommath.ind
	perl booker.pl
	latex tommath > /dev/null
	latex tommath > /dev/null
	makeindex tommath
	latex tommath > /dev/null

# poster, makes the single page PDF poster
poster: poster.tex









	pdflatex poster


	rm -f poster.aux poster.log 

# makes the LTM book PDF file, requires tetex, cleans up the LaTeX temp files
docs:   docdvi
	dvipdf tommath
	rm -f tommath.log tommath.aux tommath.dvi tommath.idx tommath.toc tommath.lof tommath.ind tommath.ilg
	cd pics ; MAKE=${MAKE} ${MAKE} clean
	
#LTM user manual
mandvi: bn.tex









	echo "hello" > bn.ind
	latex bn > /dev/null
	latex bn > /dev/null
	makeindex bn
	latex bn > /dev/null

#LTM user manual [pdf]
manual:	mandvi
	pdflatex bn >/dev/null


	rm -f bn.aux bn.dvi bn.log bn.idx bn.lof bn.out bn.toc

pretty: 
	perl pretty.build

clean:
	rm -f *.bat *.pdf *.o *.a *.obj *.lib *.exe *.dll etclib/*.o demo/demo.o test ltmtest mpitest mtest/mtest mtest/mtest.exe \
        *.idx *.toc *.log *.aux *.dvi *.lof *.ind *.ilg *.ps *.log *.s mpi.c *.da *.dyn *.dpi tommath.tex `find . -type f | grep [~] | xargs` *.lo *.la
	rm -rf .libs
	cd etc ; MAKE=${MAKE} ${MAKE} clean
	cd pics ; MAKE=${MAKE} ${MAKE} clean

#zipup the project (take that!)
no_oops: clean
	cd .. ; cvs commit 
	echo Scanning for scratch/dirty files
	find . -type f | grep -v CVS | xargs -n 1 bash mess.sh

zipup: clean manual poster docs


	perl gen.pl ; mv mpi.c pre_gen/ ; \




	cd .. ; rm -rf ltm* libtommath-$(VERSION) ; mkdir libtommath-$(VERSION) ; \


	cp -R ./libtommath/* ./libtommath-$(VERSION)/ ; \

	tar -c libtommath-$(VERSION)/* | bzip2 -9vvc > ltm-$(VERSION).tar.bz2 ; \
	zip -9 -r ltm-$(VERSION).zip libtommath-$(VERSION)/* ; \
	mv -f ltm* ~ ; rm -rf libtommath-$(VERSION)

#Makefile for GCC
#
#Tom St Denis

ifeq ($V,1)



























silent=
else

[email protected]
endif





%.o: %.c
ifneq ($V,1)
	@echo "   * ${CC} [email protected]"
endif
	${silent} ${CC} -c ${CFLAGS} $^ -o [email protected]

#default files to install
ifndef LIBNAME
   LIBNAME=libtommath.a
endif


coverage: LIBNAME:=-Wl,--whole-archive $(LIBNAME)  -Wl,--no-whole-archive


include makefile.include








LCOV_ARGS=--directory .






#START_INS
OBJECTS=bncore.o bn_error.o bn_fast_mp_invmod.o bn_fast_mp_montgomery_reduce.o bn_fast_s_mp_mul_digs.o \
bn_fast_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_mp_2expt.o bn_mp_abs.o bn_mp_add.o bn_mp_add_d.o \











bn_mp_addmod.o bn_mp_and.o bn_mp_clamp.o bn_mp_clear.o bn_mp_clear_multi.o bn_mp_cmp.o bn_mp_cmp_d.o \
bn_mp_cmp_mag.o bn_mp_cnt_lsb.o bn_mp_copy.o bn_mp_count_bits.o bn_mp_div_2.o bn_mp_div_2d.o bn_mp_div_3.o \
bn_mp_div.o bn_mp_div_d.o bn_mp_dr_is_modulus.o bn_mp_dr_reduce.o bn_mp_dr_setup.o bn_mp_exch.o \




bn_mp_export.o bn_mp_expt_d.o bn_mp_expt_d_ex.o bn_mp_exptmod.o bn_mp_exptmod_fast.o bn_mp_exteuclid.o \
bn_mp_fread.o bn_mp_fwrite.o bn_mp_gcd.o bn_mp_get_int.o bn_mp_get_long.o bn_mp_get_long_long.o \


bn_mp_grow.o bn_mp_import.o bn_mp_init.o bn_mp_init_copy.o bn_mp_init_multi.o bn_mp_init_set.o \
bn_mp_init_set_int.o bn_mp_init_size.o bn_mp_invmod.o bn_mp_invmod_slow.o bn_mp_is_square.o \
bn_mp_jacobi.o bn_mp_karatsuba_mul.o bn_mp_karatsuba_sqr.o bn_mp_lcm.o bn_mp_lshd.o bn_mp_mod_2d.o \
bn_mp_mod.o bn_mp_mod_d.o bn_mp_montgomery_calc_normalization.o bn_mp_montgomery_reduce.o \
bn_mp_montgomery_setup.o bn_mp_mul_2.o bn_mp_mul_2d.o bn_mp_mul.o bn_mp_mul_d.o bn_mp_mulmod.o bn_mp_neg.o \
bn_mp_n_root.o bn_mp_n_root_ex.o bn_mp_or.o bn_mp_prime_fermat.o bn_mp_prime_is_divisible.o \
bn_mp_prime_is_prime.o bn_mp_prime_miller_rabin.o bn_mp_prime_next_prime.o \
bn_mp_prime_rabin_miller_trials.o bn_mp_prime_random_ex.o bn_mp_radix_size.o bn_mp_radix_smap.o \
bn_mp_rand.o bn_mp_read_radix.o bn_mp_read_signed_bin.o bn_mp_read_unsigned_bin.o bn_mp_reduce_2k.o \
bn_mp_reduce_2k_l.o bn_mp_reduce_2k_setup.o bn_mp_reduce_2k_setup_l.o bn_mp_reduce.o \
bn_mp_reduce_is_2k.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_setup.o bn_mp_rshd.o bn_mp_set.o bn_mp_set_int.o \
bn_mp_set_long.o bn_mp_set_long_long.o bn_mp_shrink.o bn_mp_signed_bin_size.o bn_mp_sqr.o bn_mp_sqrmod.o \
bn_mp_sqrt.o bn_mp_sqrtmod_prime.o bn_mp_sub.o bn_mp_sub_d.o bn_mp_submod.o bn_mp_toom_mul.o \
bn_mp_toom_sqr.o bn_mp_toradix.o bn_mp_toradix_n.o bn_mp_to_signed_bin.o bn_mp_to_signed_bin_n.o \
bn_mp_to_unsigned_bin.o bn_mp_to_unsigned_bin_n.o bn_mp_unsigned_bin_size.o bn_mp_xor.o bn_mp_zero.o \
bn_prime_tab.o bn_reverse.o bn_s_mp_add.o bn_s_mp_exptmod.o bn_s_mp_mul_digs.o bn_s_mp_mul_high_digs.o \
bn_s_mp_sqr.o bn_s_mp_sub.o

#END_INS

$(LIBNAME):  $(OBJECTS)
	$(AR) $(ARFLAGS) [email protected] $(OBJECTS)

	$(RANLIB) [email protected]

#make a profiled library (takes a while!!!)
#
# This will build the library with profile generation
# then run the test demo and rebuild the library.
#
# So far I've seen improvements in the MP math
profiled:
	make CFLAGS="$(CFLAGS) -fprofile-arcs -DTESTING" timing
	./ltmtest
	rm -f *.a *.o ltmtest
	make CFLAGS="$(CFLAGS) -fbranch-probabilities"

#make a single object profiled library
profiled_single:
	perl gen.pl
	$(CC) $(CFLAGS) -fprofile-arcs -DTESTING -c mpi.c -o mpi.o
	$(CC) $(CFLAGS) -DTESTING -DTIMER demo/timing.c mpi.o -lgcov -o ltmtest
	./ltmtest
	rm -f *.o ltmtest
	$(CC) $(CFLAGS) -fbranch-probabilities -DTESTING -c mpi.c -o mpi.o
	$(AR) $(ARFLAGS) $(LIBNAME) mpi.o
	ranlib $(LIBNAME)

install: $(LIBNAME)
	install -d $(DESTDIR)$(LIBPATH)
	install -d $(DESTDIR)$(INCPATH)
	install -m 644 $(LIBNAME) $(DESTDIR)$(LIBPATH)
	install -m 644 $(HEADERS_PUB) $(DESTDIR)$(INCPATH)

test: $(LIBNAME) demo/demo.o
	$(CC) $(CFLAGS) demo/demo.o $(LIBNAME) $(LFLAGS) -o test

test_standalone: $(LIBNAME) demo/demo.o
	$(CC) $(CFLAGS) demo/demo.o $(LIBNAME) $(LFLAGS) -o test

.PHONY: mtest
mtest:
	cd mtest ; $(CC) $(CFLAGS) -O0 mtest.c $(LFLAGS) -o mtest

timing: $(LIBNAME)
	$(CC) $(CFLAGS) -DTIMER demo/timing.c $(LIBNAME) $(LFLAGS) -o ltmtest

coveralls: coverage
	cpp-coveralls

# makes the LTM book DVI file, requires tetex, perl and makeindex [part of tetex I think]
docdvi: tommath.src
	cd pics ; MAKE=${MAKE} ${MAKE}
	echo "hello" > tommath.ind
	perl booker.pl
	latex tommath > /dev/null
	latex tommath > /dev/null
	makeindex tommath
	latex tommath > /dev/null

# poster, makes the single page PDF poster
poster: poster.tex
	cp poster.tex poster.bak
	touch --reference=poster.tex poster.bak
	(printf "%s" "\def\fixedpdfdate{"; date +'D:%Y%m%d%H%M%S%:z' -d @$$(stat --format=%Y poster.tex) | sed "s/:\([0-9][0-9]\)$$/'\1'}/g") > poster-deterministic.tex
	printf "%s\n" "\pdfinfo{" >> poster-deterministic.tex
	printf "%s\n" "  /CreationDate (\fixedpdfdate)" >> poster-deterministic.tex
	printf "%s\n}\n" "  /ModDate (\fixedpdfdate)" >> poster-deterministic.tex
	cat poster.tex >> poster-deterministic.tex
	mv poster-deterministic.tex poster.tex
	touch --reference=poster.bak poster.tex
	pdflatex poster
	sed -b -i 's,^/ID \[.*\]$$,/ID [<0> <0>],g' poster.pdf
	mv poster.bak poster.tex
	rm -f poster.aux poster.log poster.out

# makes the LTM book PDF file, requires tetex, cleans up the LaTeX temp files
docs:   docdvi
	dvipdf tommath
	rm -f tommath.log tommath.aux tommath.dvi tommath.idx tommath.toc tommath.lof tommath.ind tommath.ilg
	cd pics ; MAKE=${MAKE} ${MAKE} clean

#LTM user manual
mandvi: bn.tex
	cp bn.tex bn.bak
	touch --reference=bn.tex bn.bak
	(printf "%s" "\def\fixedpdfdate{"; date +'D:%Y%m%d%H%M%S%:z' -d @$$(stat --format=%Y bn.tex) | sed "s/:\([0-9][0-9]\)$$/'\1'}/g") > bn-deterministic.tex
	printf "%s\n" "\pdfinfo{" >> bn-deterministic.tex
	printf "%s\n" "  /CreationDate (\fixedpdfdate)" >> bn-deterministic.tex
	printf "%s\n}\n" "  /ModDate (\fixedpdfdate)" >> bn-deterministic.tex
	cat bn.tex >> bn-deterministic.tex
	mv bn-deterministic.tex bn.tex
	touch --reference=bn.bak bn.tex
	echo "hello" > bn.ind
	latex bn > /dev/null
	latex bn > /dev/null
	makeindex bn
	latex bn > /dev/null

#LTM user manual [pdf]
manual:	mandvi
	pdflatex bn >/dev/null
	sed -b -i 's,^/ID \[.*\]$$,/ID [<0> <0>],g' bn.pdf
	mv bn.bak bn.tex
	rm -f bn.aux bn.dvi bn.log bn.idx bn.lof bn.out bn.toc

pretty:
	perl pretty.build








#\zipup the project (take that!)
no_oops: clean
	cd .. ; cvs commit
	echo Scanning for scratch/dirty files
	find . -type f | grep -v CVS | xargs -n 1 bash mess.sh


.PHONY: pre_gen
pre_gen:
	perl gen.pl
	sed -e 's/[[:blank:]]*$$//' mpi.c > pre_gen/mpi.c
	rm mpi.c

zipup:
	rm -rf ../libtommath-$(VERSION) \
		&& rm -f ../ltm-$(VERSION).zip ../ltm-$(VERSION).zip.asc ../ltm-$(VERSION).tar.xz ../ltm-$(VERSION).tar.xz.asc
	git archive HEAD --prefix=libtommath-$(VERSION)/ > ../libtommath-$(VERSION).tar
	cd .. ; tar xf libtommath-$(VERSION).tar
	MAKE=${MAKE} ${MAKE} -C ../libtommath-$(VERSION) clean manual poster docs
	tar -c ../libtommath-$(VERSION)/* | xz -9 > ../ltm-$(VERSION).tar.xz
	find ../libtommath-$(VERSION)/ -type f -exec unix2dos -q {} \;
	cd .. ; zip -9r ltm-$(VERSION).zip libtommath-$(VERSION)
	gpg -b -a ../ltm-$(VERSION).tar.xz && gpg -b -a ../ltm-$(VERSION).zip

new_file:
	bash updatemakes.sh
	perl dep.pl