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Overview
Comment:Merge trunk. Re-generate tclTomMath.h. Use faster exponentiation-function from libtommath 1.0 (in tclExecute.c).
Downloads: Tarball | ZIP archive | SQL archive
Timelines: family | ancestors | descendants | both | libtommath-1.0
Files: files | file ages | folders
SHA1: 1e2d716ec7638c034b23c1789210335dba37d7b5
User & Date: jan.nijtmans 2016-11-17 10:46:09
Context
2016-11-17
11:03
Bring in fix for mp_iseven().... almost missed that .... This should be given a dedicated test-cas... check-in: 04444b286a user: jan.nijtmans tags: libtommath-1.0
10:46
Merge trunk. Re-generate tclTomMath.h. Use faster exponentiation-function from libtommath 1.0 (in tc... check-in: 1e2d716ec7 user: jan.nijtmans tags: libtommath-1.0
09:33
Remove subdirectories of "libtommath", and various individual related files, not taking any part in ... check-in: 634ffe2b64 user: jan.nijtmans tags: trunk
2016-11-16
15:22
(experimental) Upgrade to libtommath 1.0 (actually by merging all changes between libtommath 0.42.0 ... check-in: d1210bac0b user: jan.nijtmans tags: libtommath-1.0
Changes
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*/config.cache
*/config.log
*/config.status
*/tclConfig.sh
*/tclsh*
*/tcltest*
*/versions.vc
















unix/autoMkindex.tcl
unix/dltest.marker
unix/tcl.pc
unix/tclIndex
unix/pkgs/*
win/pkgs/*
win/tcl.hpj






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*/config.cache
*/config.log
*/config.status
*/tclConfig.sh
*/tclsh*
*/tcltest*
*/versions.vc
libtommath/bn.ilg
libtommath/bn.ind
libtommath/pretty.build
libtommath/tommath.src
libtommath/*.pdf
libtommath/*.pl
libtommath/*.sh
libtommath/tombc/*
libtommath/pre_gen/*
libtommath/pics/*
libtommath/mtest/*
libtommath/logs/*
libtommath/etc/*
libtommath/demo/*
libtommath/*.out
libtommath/*.tex
unix/autoMkindex.tcl
unix/dltest.marker
unix/tcl.pc
unix/tclIndex
unix/pkgs/*
win/pkgs/*
win/tcl.hpj

Changes to generic/tclExecute.c.

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	    mp_clear(&big2);
	    Tcl_SetObjResult(interp, Tcl_NewStringObj(
		    "exponent too large", -1));
	    return GENERAL_ARITHMETIC_ERROR;
	}
	Tcl_TakeBignumFromObj(NULL, valuePtr, &big1);
	mp_init(&bigResult);
	mp_expt_d(&big1, big2.dp[0], &bigResult);
	mp_clear(&big1);
	mp_clear(&big2);
	BIG_RESULT(&bigResult);
    }

    case INST_ADD:
    case INST_SUB:






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	    mp_clear(&big2);
	    Tcl_SetObjResult(interp, Tcl_NewStringObj(
		    "exponent too large", -1));
	    return GENERAL_ARITHMETIC_ERROR;
	}
	Tcl_TakeBignumFromObj(NULL, valuePtr, &big1);
	mp_init(&bigResult);
	mp_expt_d_ex(&big1, big2.dp[0], &bigResult, 1);
	mp_clear(&big1);
	mp_clear(&big2);
	BIG_RESULT(&bigResult);
    }

    case INST_ADD:
    case INST_SUB:

Changes to generic/tclTomMath.h.

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 * 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, tom[email protected], http://math.libtomcrypt.com
 */
#ifndef BN_H_
#define BN_H_


#include "tclTomMathDecls.h"
#ifndef MODULE_SCOPE
#define MODULE_SCOPE extern
#endif



#ifndef MIN
#   define MIN(x,y) ((x)<(y)?(x):(y))
#endif

#ifndef MAX
#   define MAX(x,y) ((x)>(y)?(x):(y))
#endif

#ifdef __cplusplus
extern "C" {

/* C++ compilers don't like assigning void * to mp_digit * */
#define  OPT_CAST(x)  (x *)

#else

/* C on the other hand doesn't care */
#define  OPT_CAST(x)

#endif


/* detect 64-bit mode if possible */
#if defined(NEVER)  /* 128-bit ints fail in too many places */
#   if !(defined(MP_64BIT) && defined(MP_16BIT) && defined(MP_8BIT))
#	define MP_64BIT
#   endif
#endif

/* some default configurations.
 *
 * A "mp_digit" must be able to hold DIGIT_BIT + 1 bits
................................................................................
 * A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits
 *
 * At the very least a mp_digit must be able to hold 7 bits
 * [any size beyond that is ok provided it doesn't overflow the data type]
 */
#ifdef MP_8BIT
#ifndef MP_DIGIT_DECLARED
   typedef unsigned char      mp_digit;
#define MP_DIGIT_DECLARED
#endif
   typedef unsigned short     mp_word;




#elif defined(MP_16BIT)
#ifndef MP_DIGIT_DECLARED
   typedef unsigned short     mp_digit;

#define MP_DIGIT_DECLARED
#endif
   typedef unsigned long      mp_word;





#elif defined(MP_64BIT)
   /* for GCC only on supported platforms */
#ifndef CRYPT
   typedef unsigned long long ulong64;
   typedef signed long long   long64;
#endif

#ifndef MP_DIGIT_DECLARED
   typedef unsigned long      mp_digit;
#define MP_DIGIT_DECLARED
#endif



   typedef unsigned long      mp_word __attribute__ ((mode(TI)));






#  define DIGIT_BIT          60
#else
   /* this is the default case, 28-bit digits */
   
   /* this is to make porting into LibTomCrypt easier :-) */
#ifndef CRYPT
#  if defined(_MSC_VER) || defined(__BORLANDC__)
      typedef unsigned __int64   ulong64;
      typedef signed __int64     long64;
#  else
      typedef unsigned long long ulong64;
      typedef signed long long   long64;
#  endif
#endif

#ifndef MP_DIGIT_DECLARED
   typedef unsigned int      mp_digit;

#define MP_DIGIT_DECLARED
#endif
   typedef ulong64            mp_word;

#ifdef MP_31BIT   
   /* this is an extension that uses 31-bit digits */
#  define DIGIT_BIT          31
................................................................................
#else
   /* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */
#  define DIGIT_BIT          28
#  define MP_28BIT
#endif   
#endif

/* define heap macros */
#if 0 /* these are macros in tclTomMathDecls.h */
#ifndef CRYPT
   /* default to libc stuff */
#  ifndef XMALLOC
#     define XMALLOC  malloc
#     define XFREE    free
#     define XREALLOC realloc
#     define XCALLOC  calloc
#  else
      /* prototypes for our heap functions */
      extern void *XMALLOC(size_t n);
      extern void *XREALLOC(void *p, size_t n);
      extern void *XCALLOC(size_t n, size_t s);
      extern void XFREE(void *p);
#  endif
#endif
#endif


/* otherwise the bits per digit is calculated automatically from the size of a mp_digit */
#ifndef DIGIT_BIT
#   define DIGIT_BIT     ((int)((CHAR_BIT * sizeof(mp_digit) - 1)))  /* bits per digit */
#endif

#define MP_DIGIT_BIT     DIGIT_BIT
#define MP_MASK          ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
#define MP_DIGIT_MAX     MP_MASK

/* equalities */
................................................................................
#     define MP_PREC                 32     /* default digits of precision */
#  else
#     define MP_PREC                 8      /* default digits of precision */
#  endif
#endif

/* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */
#define MP_WARRAY               (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1))

/* the infamous mp_int structure */
#ifndef MP_INT_DECLARED
#define MP_INT_DECLARED
typedef struct mp_int mp_int;
#endif
struct mp_int {
................................................................................


#define USED(m)    ((m)->used)
#define DIGIT(m,k) ((m)->dp[(k)])
#define SIGN(m)    ((m)->sign)

/* error code to char* string */
/*
char *mp_error_to_string(int code);
*/

/* ---> init and deinit bignum functions <--- */
/* init a bignum */
/*
int mp_init(mp_int *a);
*/

................................................................................
/* init to a given number of digits */
/*
int mp_init_size(mp_int *a, int size);
*/

/* ---> Basic Manipulations <--- */
#define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
#define mp_iseven(a) (((a)->used == 0 || (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO)
#define mp_isodd(a)  (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO)


/* set to zero */
/*
void mp_zero(mp_int *a);
*/

/* set to a digit */
................................................................................
void mp_set(mp_int *a, mp_digit b);
*/

/* set a 32-bit const */
/*
int mp_set_int(mp_int *a, unsigned long b);
*/











/* get a 32-bit value */
unsigned long mp_get_int(mp_int * a);







/* initialize and set a digit */
/*
int mp_init_set (mp_int * a, mp_digit b);
*/

/* initialize and set 32-bit value */
................................................................................
int mp_init_copy(mp_int *a, mp_int *b);
*/

/* trim unused digits */
/*
void mp_clamp(mp_int *a);
*/











/* ---> digit manipulation <--- */

/* right shift by "b" digits */
/*
void mp_rshd(mp_int *a, int b);
*/

/* left shift by "b" digits */
/*
int mp_lshd(mp_int *a, int b);
*/

/* c = a / 2**b */
/*
int mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d);
*/

/* b = a/2 */
/*
int mp_div_2(mp_int *a, mp_int *b);
*/

/* c = a * 2**b */
/*
int mp_mul_2d(const mp_int *a, int b, mp_int *c);
*/

/* b = a*2 */
/*
int mp_mul_2(mp_int *a, mp_int *b);
*/

/* c = a mod 2**d */
/*
int mp_mod_2d(const mp_int *a, int b, mp_int *c);
*/

/* computes a = 2**b */
/*
int mp_2expt(mp_int *a, int b);
................................................................................
int mp_div_3(mp_int *a, mp_int *c, mp_digit *d);
*/

/* c = a**b */
/*
int mp_expt_d(mp_int *a, mp_digit b, mp_int *c);
*/




/* c = a mod b, 0 <= c < b  */
/*
int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c);
*/

/* ---> number theory <--- */
................................................................................
/* finds one of the b'th root of a, such that |c|**b <= |a|
 *
 * returns error if a < 0 and b is even
 */
/*
int mp_n_root(mp_int *a, mp_digit b, mp_int *c);
*/




/* special sqrt algo */
/*
int mp_sqrt(mp_int *arg, mp_int *ret);
*/






/* is number a square? */
/*
int mp_is_square(mp_int *arg, int *ret);
*/

/* computes the jacobi c = (a | n) (or Legendre if b is prime)  */
................................................................................
#  define PRIME_SIZE      31
#else
#  define PRIME_SIZE      256
#endif

/* table of first PRIME_SIZE primes */
#if defined(BUILD_tcl) || !defined(_WIN32)
MODULE_SCOPE const mp_digit ltm_prime_tab[];
#endif

/* result=1 if a is divisible by one of the first PRIME_SIZE primes */
/*
int mp_prime_is_divisible(mp_int *a, int *result);
*/

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

/* 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
 *
 */
................................................................................
/*
int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen);
*/
/*
int mp_radix_size(mp_int *a, int radix, int *size);
*/


/*
int mp_fread(mp_int *a, int radix, FILE *stream);
*/
/*
int mp_fwrite(mp_int *a, int radix, FILE *stream);
*/


#define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
#define mp_raw_size(mp)           mp_signed_bin_size(mp)
#define mp_toraw(mp, str)         mp_to_signed_bin((mp), (str))
#define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
#define mp_mag_size(mp)           mp_unsigned_bin_size(mp)
#define mp_tomag(mp, str)         mp_to_unsigned_bin((mp), (str))

#define mp_tobinary(M, S)  mp_toradix((M), (S), 2)
#define mp_tooctal(M, S)   mp_toradix((M), (S), 8)
#define mp_todecimal(M, S) mp_toradix((M), (S), 10)
#define mp_tohex(M, S)     mp_toradix((M), (S), 16)

/* lowlevel functions, do not call! */
/*

int s_mp_add(mp_int *a, mp_int *b, mp_int *c);
*/
/*
int s_mp_sub(mp_int *a, mp_int *b, mp_int *c);
*/
#define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
/*
int fast_s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
*/
/*
int s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
*/
/*
int fast_s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
*/
/*
int s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
*/
/*
int fast_s_mp_sqr(mp_int *a, mp_int *b);
*/
/*
int s_mp_sqr(mp_int *a, mp_int *b);
*/
/*
int mp_karatsuba_mul(mp_int *a, mp_int *b, mp_int *c);
*/
/*
int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c);
*/
/*
int mp_karatsuba_sqr(mp_int *a, mp_int *b);
*/
/*
int mp_toom_sqr(mp_int *a, mp_int *b);
*/
/*
int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c);
*/
/*
int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c);
*/
/*
int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
*/
/*
int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int mode);
*/
/*
int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int mode);
*/
/*
void bn_reverse(unsigned char *s, int len);
*/

#if defined(BUILD_tcl) || !defined(_WIN32)
MODULE_SCOPE const char *mp_s_rmap;
#endif

#ifdef __cplusplus
}
#endif




#endif






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 * 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://math.libtomcrypt.com
 */
#ifndef BN_H_
#define BN_H_

#include "tclInt.h"
#include "tclTomMathDecls.h"
#ifndef MODULE_SCOPE
#define MODULE_SCOPE extern
#endif











#ifdef __cplusplus
extern "C" {









#endif


/* detect 64-bit mode if possible */
#if defined(NEVER) /* 128-bit ints fail in too many places */
   #if !(defined(MP_32BIT) || defined(MP_16BIT) || defined(MP_8BIT))
      #define MP_64BIT
   #endif
#endif

/* some default configurations.
 *
 * A "mp_digit" must be able to hold DIGIT_BIT + 1 bits
................................................................................
 * A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits
 *
 * At the very least a mp_digit must be able to hold 7 bits
 * [any size beyond that is ok provided it doesn't overflow the data type]
 */
#ifdef MP_8BIT
#ifndef MP_DIGIT_DECLARED
   typedef uint8_t              mp_digit;
#define MP_DIGIT_DECLARED
#endif
   typedef uint16_t             mp_word;
#define MP_SIZEOF_MP_DIGIT      1
#ifdef DIGIT_BIT
#error You must not define DIGIT_BIT when using MP_8BIT
#endif
#elif defined(MP_16BIT)
#ifndef MP_DIGIT_DECLARED

   typedef uint16_t             mp_digit;
#define MP_DIGIT_DECLARED
#endif

   typedef uint32_t             mp_word;
#define MP_SIZEOF_MP_DIGIT      2
#ifdef DIGIT_BIT
#error You must not define DIGIT_BIT when using MP_16BIT
#endif
#elif defined(MP_64BIT)
   /* for GCC only on supported platforms */
#ifndef CRYPT
   typedef unsigned long long   ulong64;
   typedef signed long long     long64;
#endif

#ifndef MP_DIGIT_DECLARED
   typedef ulong64 mp_digit;
#define MP_DIGIT_DECLARED
#endif
#if defined(_WIN32)
   typedef unsigned __int128    mp_word;
#elif defined(__GNUC__)
   typedef unsigned long        mp_word __attribute__ ((mode(TI)));
#else
   /* it seems you have a problem
    * but we assume you can somewhere define your own uint128_t */
   typedef uint128_t            mp_word;
#endif

   #define DIGIT_BIT            60
#else
   /* this is the default case, 28-bit digits */

   /* this is to make porting into LibTomCrypt easier :-) */
#ifndef CRYPT




   typedef unsigned long long   ulong64;
   typedef signed long long     long64;
#endif


#ifndef MP_DIGIT_DECLARED

   typedef uint32_t             mp_digit;
#define MP_DIGIT_DECLARED
#endif
   typedef ulong64              mp_word;

#ifdef MP_31BIT
   /* this is an extension that uses 31-bit digits */
   #define DIGIT_BIT            31
................................................................................
#else
   /* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */
   #define DIGIT_BIT            28
   #define MP_28BIT
#endif
#endif

/* otherwise the bits per digit is calculated automatically from the size of a mp_digit */
#ifndef DIGIT_BIT
   #define DIGIT_BIT     (((CHAR_BIT * MP_SIZEOF_MP_DIGIT) - 1))  /* bits per digit */
   typedef uint_least32_t mp_min_u32;
#else
   typedef mp_digit mp_min_u32;
#endif

/* platforms that can use a better rand function */
#if defined(__FreeBSD__) || defined(__OpenBSD__) || defined(__NetBSD__) || defined(__DragonFly__)
    #define MP_USE_ALT_RAND 1
#endif

/* use arc4random on platforms that support it */
#ifdef MP_USE_ALT_RAND
    #define MP_GEN_RANDOM()    arc4random()
#else
    #define MP_GEN_RANDOM()    rand()





#endif

#define MP_DIGIT_BIT     DIGIT_BIT
#define MP_MASK          ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
#define MP_DIGIT_MAX     MP_MASK

/* equalities */
................................................................................
      #define MP_PREC                 32     /* default digits of precision */
   #else
      #define MP_PREC                 8      /* default digits of precision */
   #endif
#endif

/* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */
#define MP_WARRAY               (1 << (((sizeof(mp_word) * CHAR_BIT) - (2 * DIGIT_BIT)) + 1))

/* the infamous mp_int structure */
#ifndef MP_INT_DECLARED
#define MP_INT_DECLARED
typedef struct mp_int mp_int;
#endif
struct mp_int {
................................................................................


#define USED(m)    ((m)->used)
#define DIGIT(m,k) ((m)->dp[(k)])
#define SIGN(m)    ((m)->sign)

/* error code to char* string */

const char *mp_error_to_string(int code);


/* ---> init and deinit bignum functions <--- */
/* init a bignum */
/*
int mp_init(mp_int *a);
*/

................................................................................
/* init to a given number of digits */
/*
int mp_init_size(mp_int *a, int size);
*/

/* ---> Basic Manipulations <--- */
#define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
#define mp_iseven(a) ((((a)->used > 0) && (((a)->dp[0] & 1u) == 0u)) ? MP_YES : MP_NO)
#define mp_isodd(a)  ((((a)->used > 0) && (((a)->dp[0] & 1u) == 1u)) ? MP_YES : MP_NO)
#define mp_isneg(a)  (((a)->sign != MP_ZPOS) ? MP_YES : MP_NO)

/* set to zero */
/*
void mp_zero(mp_int *a);
*/

/* set to a digit */
................................................................................
void mp_set(mp_int *a, mp_digit b);
*/

/* set a 32-bit const */
/*
int mp_set_int(mp_int *a, unsigned long b);
*/

/* set a platform dependent unsigned long value */
/*
int mp_set_long(mp_int *a, unsigned long b);
*/

/* set a platform dependent unsigned long long value */
/*
int mp_set_long_long(mp_int *a, unsigned long long b);
*/

/* get a 32-bit value */
unsigned long mp_get_int(mp_int * a);

/* get a platform dependent unsigned long value */
unsigned long mp_get_long(mp_int * a);

/* get a platform dependent unsigned long long value */
unsigned long long mp_get_long_long(mp_int * a);

/* initialize and set a digit */
/*
int mp_init_set (mp_int * a, mp_digit b);
*/

/* initialize and set 32-bit value */
................................................................................
int mp_init_copy(mp_int *a, mp_int *b);
*/

/* trim unused digits */
/*
void mp_clamp(mp_int *a);
*/

/* import binary data */
/*
int mp_import(mp_int* rop, size_t count, int order, size_t size, int endian, size_t nails, const void* op);
*/

/* export binary data */
/*
int mp_export(void* rop, size_t* countp, int order, size_t size, int endian, size_t nails, mp_int* op);
*/

/* ---> digit manipulation <--- */

/* right shift by "b" digits */
/*
void mp_rshd(mp_int *a, int b);
*/

/* left shift by "b" digits */
/*
int mp_lshd(mp_int *a, int b);
*/

/* c = a / 2**b, implemented as c = a >> b */
/*
int mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d);
*/

/* b = a/2 */
/*
int mp_div_2(mp_int *a, mp_int *b);
*/

/* c = a * 2**b, implemented as c = a << b */
/*
int mp_mul_2d(const mp_int *a, int b, mp_int *c);
*/

/* b = a*2 */
/*
int mp_mul_2(mp_int *a, mp_int *b);
*/

/* c = a mod 2**b */
/*
int mp_mod_2d(const mp_int *a, int b, mp_int *c);
*/

/* computes a = 2**b */
/*
int mp_2expt(mp_int *a, int b);
................................................................................
int mp_div_3(mp_int *a, mp_int *c, mp_digit *d);
*/

/* c = a**b */
/*
int mp_expt_d(mp_int *a, mp_digit b, mp_int *c);
*/
/*
int mp_expt_d_ex (mp_int * a, mp_digit b, mp_int * c, int fast);
*/

/* c = a mod b, 0 <= c < b  */
/*
int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c);
*/

/* ---> number theory <--- */
................................................................................
/* finds one of the b'th root of a, such that |c|**b <= |a|
 *
 * returns error if a < 0 and b is even
 */
/*
int mp_n_root(mp_int *a, mp_digit b, mp_int *c);
*/
/*
int mp_n_root_ex (mp_int * a, mp_digit b, mp_int * c, int fast);
*/

/* special sqrt algo */
/*
int mp_sqrt(mp_int *arg, mp_int *ret);
*/

/* special sqrt (mod prime) */
/*
int mp_sqrtmod_prime(mp_int *arg, mp_int *prime, mp_int *ret);
*/

/* is number a square? */
/*
int mp_is_square(mp_int *arg, int *ret);
*/

/* computes the jacobi c = (a | n) (or Legendre if b is prime)  */
................................................................................
#  define PRIME_SIZE      31
#else
#  define PRIME_SIZE      256
#endif

/* table of first PRIME_SIZE primes */
#if defined(BUILD_tcl) || !defined(_WIN32)
MODULE_SCOPE const mp_digit ltm_prime_tab[PRIME_SIZE];
#endif

/* result=1 if a is divisible by one of the first PRIME_SIZE primes */
/*
int mp_prime_is_divisible(mp_int *a, int *result);
*/

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

/* 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
 *
 */
................................................................................
/*
int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen);
*/
/*
int mp_radix_size(mp_int *a, int radix, int *size);
*/

#ifndef LTM_NO_FILE
/*
int mp_fread(mp_int *a, int radix, FILE *stream);
*/
/*
int mp_fwrite(mp_int *a, int radix, FILE *stream);
*/
#endif

#define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
#define mp_raw_size(mp)           mp_signed_bin_size(mp)
#define mp_toraw(mp, str)         mp_to_signed_bin((mp), (str))
#define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
#define mp_mag_size(mp)           mp_unsigned_bin_size(mp)
#define mp_tomag(mp, str)         mp_to_unsigned_bin((mp), (str))

#define mp_tobinary(M, S)  mp_toradix((M), (S), 2)
#define mp_tooctal(M, S)   mp_toradix((M), (S), 8)
#define mp_todecimal(M, S) mp_toradix((M), (S), 10)
#define mp_tohex(M, S)     mp_toradix((M), (S), 16)

#ifdef __cplusplus

   }
#endif
























































#endif




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


Deleted libtommath/bn.ilg.

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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.
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\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}
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cannot compute difference between binary files

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\documentclass[b5paper]{book}
\usepackage{hyperref}
\usepackage{makeidx}
\usepackage{amssymb}
\usepackage{color}
\usepackage{alltt}
\usepackage{graphicx}
\usepackage{layout}
\def\union{\cup}
\def\intersect{\cap}
\def\getsrandom{\stackrel{\rm R}{\gets}}
\def\cross{\times}
\def\cat{\hspace{0.5em} \| \hspace{0.5em}}
\def\catn{$\|$}
\def\divides{\hspace{0.3em} | \hspace{0.3em}}
\def\nequiv{\not\equiv}
\def\approx{\raisebox{0.2ex}{\mbox{\small $\sim$}}}
\def\lcm{{\rm lcm}}
\def\gcd{{\rm gcd}}
\def\log{{\rm log}}
\def\ord{{\rm ord}}
\def\abs{{\mathit abs}}
\def\rep{{\mathit rep}}
\def\mod{{\mathit\ mod\ }}
\renewcommand{\pmod}[1]{\ ({\rm mod\ }{#1})}
\newcommand{\floor}[1]{\left\lfloor{#1}\right\rfloor}
\newcommand{\ceil}[1]{\left\lceil{#1}\right\rceil}
\def\Or{{\rm\ or\ }}
\def\And{{\rm\ and\ }}
\def\iff{\hspace{1em}\Longleftrightarrow\hspace{1em}}
\def\implies{\Rightarrow}
\def\undefined{{\rm ``undefined"}}
\def\Proof{\vspace{1ex}\noindent {\bf Proof:}\hspace{1em}}
\let\oldphi\phi
\def\phi{\varphi}
\def\Pr{{\rm Pr}}
\newcommand{\str}[1]{{\mathbf{#1}}}
\def\F{{\mathbb F}}
\def\N{{\mathbb N}}
\def\Z{{\mathbb Z}}
\def\R{{\mathbb R}}
\def\C{{\mathbb C}}
\def\Q{{\mathbb Q}}
\definecolor{DGray}{gray}{0.5}
\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 \\ [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{ }

Tom St Denis,

Ontario, Canada
\end{flushright}

\tableofcontents
\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
\end{alltt}

This will build the library, ``test'' and ``mtest/mtest''.  The ``test'' program will accept test vectors and verify the
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}
\begin{center}
\begin{tabular}{|l|l|}
\hline \textbf{Define} & \textbf{Purpose} \\
\hline BN\_MP\_DIV\_SMALL & Enables a slower, smaller and equally \\
                          & functional mp\_div() function \\
\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 Exponentiation with odd moduli only & BN\_S\_MP\_EXPTMOD\_C \\
                                           & BN\_MP\_REDUCE\_C \\
                                           & BN\_MP\_REDUCE\_SETUP\_C \\
                                           & BN\_S\_MP\_MUL\_HIGH\_DIGS\_C \\
                                           & BN\_FAST\_S\_MP\_MUL\_HIGH\_DIGS\_C \\
\hline Exponentiation with random odd moduli & (The above plus the following) \\
                                           & BN\_MP\_REDUCE\_2K\_C \\
                                           & BN\_MP\_REDUCE\_2K\_SETUP\_C \\
                                           & BN\_MP\_REDUCE\_IS\_2K\_C \\
                                           & BN\_MP\_DR\_IS\_MODULUS\_C \\
                                           & BN\_MP\_DR\_REDUCE\_C \\
                                           & BN\_MP\_DR\_SETUP\_C \\
\hline Modular inverse odd moduli only     & BN\_MP\_INVMOD\_SLOW\_C \\
\hline Modular inverse (both, smaller/slower) & BN\_FAST\_MP\_INVMOD\_C \\
\hline
\end{tabular}
\end{center}
\end{small}

\subsubsection{Operand Size 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!).

So you may be thinking ``should I use LibTomMath?'' and the answer is a definite maybe.  Let me tabulate what I think
are the pros and cons of LibTomMath by comparing it to the math routines from GnuPG\footnote{GnuPG v1.2.3 versus LibTomMath v0.28}.

\newpage\begin{figure}[here]
\begin{small}
\begin{center}
\begin{tabular}{|l|c|c|l|}
\hline \textbf{Criteria} & \textbf{Pro} & \textbf{Con} & \textbf{Notes} \\
\hline Few lines of code per file & X & & GnuPG $ = 300.9$, LibTomMath  $ = 71.97$ \\
\hline Commented function prototypes & X && GnuPG function names are cryptic. \\
\hline Speed && X & LibTomMath is slower.  \\
\hline Totally free & X & & GPL has unfavourable restrictions.\\
\hline Large function base & X & & GnuPG is barebones. \\
\hline Five modular reduction algorithms & X & & Faster modular exponentiation for a variety of moduli. \\
\hline Portable & X & & GnuPG requires configuration to build. \\
\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!]
\begin{center}
\begin{small}
\begin{tabular}{|l|l|}
\hline \textbf{Code} & \textbf{Meaning} \\
\hline MP\_OKAY & The function succeeded. \\
\hline MP\_VAL  & The function input was invalid. \\
\hline MP\_MEM  & Heap memory exhausted. \\
\hline &\\
\hline MP\_YES  & Response is yes. \\
\hline MP\_NO   & Response is no. \\
\hline
\end{tabular}
\end{small}
\end{center}
\caption{Return Codes}
\end{figure}

The last two codes listed are not actually ``return'ed'' by a function.  They are placed in an integer (the caller must
provide the address of an integer it can store to) which the caller can access.  To convert one of the three return codes
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}
\begin{alltt}
typedef struct  \{
    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}

The arithmetic functions of the library are all organized to have the same style prototype.  That is source operands
are passed on the left and the destination is on the right.  For instance,

\begin{alltt}
mp_add(&a, &b, &c);       /* c = a + b */
mp_mul(&a, &a, &c);       /* c = a * a */
mp_div(&a, &b, &c, &d);   /* c = [a/b], d = a mod b */
\end{alltt}

Another feature of the way the functions have been implemented is that source operands can be destination operands as well.
For instance,

\begin{alltt}
mp_add(&a, &b, &b);       /* b = a + b */
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
represents the default integer which is zero.  If the functions returns MP\_OKAY then the mp\_int is ready to be used
by the other LibTomMath functions.

\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;
\}
\end{alltt} \end{small}

\subsection{Multiple Initializations}
Certain algorithms require more than one large integer.  In these instances it is ideal to initialize all of the mp\_int
variables in an ``all or nothing'' fashion.  That is, they are either all initialized successfully or they are all
not initialized.

The  mp\_init\_multi() function provides this functionality.

\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.

\begin{small} \begin{alltt}
int main(void)
\{
   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;
\}
\end{alltt} \end{small}

Another less common initializer is mp\_init\_size() which allows the user to initialize an mp\_int with a given
default number of digits.  By default, all initializers allocate \textbf{MP\_PREC} digits.  This function lets
you override this behaviour.

\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}

\subsection{Reducing Memory Usage}
When an mp\_int is in a state where it won't be changed again\footnote{A Diffie-Hellman modulus for instance.} excess
digits can be removed to return memory to the heap with the mp\_shrink() function.

\index{mp\_shrink}
\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
$size$ the function will not do anything.

\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}
void mp_set (mp_int * a, mp_digit b);
\end{alltt}

This will zero the contents of $a$ and make it represent an integer equal to the value of $b$.  Note that this
function has a return type of \textbf{void}.  It cannot cause an error so it is safe to assume the function
succeeded.

\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));

   /* clear */
   mp_clear_multi(&number1, &number2, NULL);

   return EXIT_SUCCESS;
\}
\end{alltt}

If this program succeeds it shall output.
\begin{alltt}
Number1, Number2 == 100, 1023
\end{alltt}

\section{Comparisons}

Comparisons in LibTomMath are always performed in a ``left to right'' fashion.  There are three possible return codes
for any comparison.

\index{MP\_GT} \index{MP\_EQ} \index{MP\_LT}
\begin{figure}[here]
\begin{center}
\begin{tabular}{|c|c|}
\hline \textbf{Result Code} & \textbf{Meaning} \\
\hline MP\_GT & $a > b$ \\
\hline MP\_EQ & $a = b$ \\
\hline MP\_LT & $a < b$ \\
\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 $5 < 6$.

\subsection{Signed comparison}

To compare two mp\_int variables based on their signed value the mp\_cmp() function is provided.

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

This will compare $a$ to the left of $b$.  It will first compare the signs of the two mp\_int variables.  If they
differ it will return immediately based on their signs.  If the signs are equal then it will compare the digits
individually.  This function will return one of the compare conditions 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(&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.

\begin{alltt}
number < 7
\end{alltt}

\section{Logical Operations}

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}

The former will assign twice $a$ to $b$ while the latter will assign half $a$ to $b$.  These functions are fast
since the shift counts and maskes are hardcoded into the routines.

\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);
\end{alltt}

This will multiply $a$ in place by $x^b$ which is equivalent to shifting the digits left $b$ places and inserting zeroes
in the least significant digits.  Similarly to divide by a power of $x$ the following function is provided.

\index{mp\_rshd}
\begin{alltt}
void mp_rshd (mp_int * a, int b)
\end{alltt}
This will divide $a$ in place by $x^b$ and discard the remainder.  This function cannot fail as it performs the operations
in place and no new digits are required to complete it.

\subsection{AND, OR and XOR Operations}

While AND, OR and XOR operations are not typical ``bignum functions'' they can be useful in several instances.  The
three functions are prototyped as follows.

\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}
int mp_add (mp_int * a, mp_int * b, mp_int * c);
int mp_sub (mp_int * a, mp_int * b, mp_int * c)
\end{alltt}

Which perform $c = a \odot b$ where $\odot$ is one of signed addition or subtraction.  The operations are fully sign
aware.

\section{Sign Manipulation}
\subsection{Negation}
\label{sec:NEG}
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}

\section{Squaring}
Since squaring can be performed faster than multiplication it is performed it's own function instead of just using
mp\_mul().

\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
\end{alltt}
Where ``XXX'' is one of the following entries from the table \ref{fig:tuning}.

\begin{figure}[here]
\begin{center}
\begin{small}
\begin{tabular}{|l|l|}
\hline \textbf{Value of XXX} & \textbf{Meaning} \\
\hline tune & Builds portable tuning application \\
\hline tune86 & Builds x86 (pentium and up) program for COFF \\
\hline tune86c & Builds x86 program for Cygwin \\
\hline tune86l & Builds x86 program for Linux (ELF format) \\
\hline
\end{tabular}
\end{small}
\end{center}
\caption{Build Names for Tuning Programs}
\label{fig:tuning}
\end{figure}

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.

\index{mp\_reduce\_setup}
\begin{alltt}
int mp_reduce_setup(mp_int *a, mp_int *b);
\end{alltt}

Given a modulus in $b$ this produces the required $\mu$ value in $a$.  For any given modulus this only has to
be computed once.  Modular reduction can now be performed with the following.

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

This will reduce $a$ in place modulo $b$ with the precomputed $\mu$ value in $c$.  $a$ must be in the range
$0 \le a < b^2$.

\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}

This computes the value required for the modulus $a$ and stores it in $d$.  This function cannot fail
and does not return any error codes.  After the pre--computation a reduction can be performed with the
following.

\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)
\end{alltt}
Performs a Fermat primality test to the base $b$.  That is it computes $b^a \mbox{ mod }a$ and tests whether the value is
equal to $b$ or not.  If the values are equal then $a$ is probably prime and $result$ is set to one.  Otherwise $result$
is set to zero.

\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} \\
\hline LTM\_PRIME\_BBS       & Make the prime congruent to $3$ modulo $4$ \\
\hline LTM\_PRIME\_SAFE      & Make a prime $p$ such that $(p - 1)/2$ is also prime. \\
                             & This option implies LTM\_PRIME\_BBS as well. \\
\hline LTM\_PRIME\_2MSB\_OFF & Makes sure that the bit adjacent to the most significant bit \\
                             & Is forced to zero.  \\
\hline LTM\_PRIME\_2MSB\_ON  & Makes sure that the bit adjacent to the most significant bit \\
                             & Is forced to one. \\
\hline
\end{tabular}
\end{small}
\end{center}
\caption{Primality Generation Options}
\label{fig:primeopts}
\end{figure}

\chapter{Input and Output}
\section{ASCII Conversions}
\subsection{To ASCII}
\index{mp\_toradix}
\begin{alltt}
int mp_toradix (mp_int * a, char *str, int radix);
\end{alltt}
This still store $a$ in ``str'' as a base-``radix'' string of ASCII chars.  This function appends a NUL character
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
character it does not recognize (which happens to include th NUL char... imagine that...).  A single leading $-$ sign
can be used to denote a negative number.

\section{Binary Conversions}

Converting an mp\_int to and from binary is another keen idea.

\index{mp\_unsigned\_bin\_size}
\begin{alltt}
int mp_unsigned_bin_size(mp_int *a);
\end{alltt}

This will return the number of bytes (octets) required to store the unsigned copy of the integer $a$.

\index{mp\_to\_unsigned\_bin}
\begin{alltt}
int mp_to_unsigned_bin(mp_int *a, unsigned char *b);
\end{alltt}
This will store $a$ into the buffer $b$ in big--endian format.  Fortunately this is exactly what DER (or is it ASN?)
requires.  It does not store the sign of the integer.

\index{mp\_read\_unsigned\_bin}
\begin{alltt}
int mp_read_unsigned_bin(mp_int *a, unsigned char *b, int c);
\end{alltt}
This will read in an unsigned big--endian array of bytes (octets) from $b$ of length $c$ into $a$.  The resulting
integer $a$ will always be positive.

For those who acknowledge the existence of negative numbers (heretic!) there are ``signed'' versions of the
previous functions.

\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 $c$.

\section{Least Common Multiple}
\index{mp\_lcm}
\begin{alltt}
int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
\end{alltt}
This will compute the least common multiple of $a$ and $b$ and store it in $c$.

\section{Jacobi Symbol}
\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 $ac \equiv 1 \mbox{ (mod }b\mbox{)}$.

\section{Single Digit Functions}

For those using small numbers (\textit{snicker snicker}) there are several ``helper'' functions

\index{mp\_add\_d} \index{mp\_sub\_d} \index{mp\_mul\_d} \index{mp\_div\_d} \index{mp\_mod\_d}
\begin{alltt}
int mp_add_d(mp_int *a, mp_digit b, mp_int *c);
int mp_sub_d(mp_int *a, mp_digit b, mp_int *c);
int mp_mul_d(mp_int *a, mp_digit b, mp_int *c);
int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d);
int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c);
\end{alltt}

These work like the full mp\_int capable variants except the second parameter $b$ is a mp\_digit.  These
functions fairly handy if you have to work with relatively small numbers since you will not have to allocate
an entire mp\_int to store a number like $1$ or $2$.

\input{bn.ind}

\end{document}
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Added libtommath/bn_mp_export.c.
















































































































































































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#include <tommath_private.h>
#ifdef BN_MP_EXPORT_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].com, http://libtom.org
 */

/* based on gmp's mpz_export.
 * see http://gmplib.org/manual/Integer-Import-and-Export.html
 */
int mp_export(void* rop, size_t* countp, int order, size_t size, 
                                int endian, size_t nails, mp_int* op) {
	int result;
	size_t odd_nails, nail_bytes, i, j, bits, count;
	unsigned char odd_nail_mask;

	mp_int t;

	if ((result = mp_init_copy(&t, op)) != MP_OKAY) {
		return result;
	}

	if (endian == 0) {
		union {
			unsigned int i;
			char c[4];
		} lint;
		lint.i = 0x01020304;

		endian = (lint.c[0] == 4) ? -1 : 1;
	}

	odd_nails = (nails % 8);
	odd_nail_mask = 0xff;
	for (i = 0; i < odd_nails; ++i) {
		odd_nail_mask ^= (1 << (7 - i));
	}
	nail_bytes = nails / 8;

	bits = mp_count_bits(&t);
	count = (bits / ((size * 8) - nails)) + (((bits % ((size * 8) - nails)) != 0) ? 1 : 0);

	for (i = 0; i < count; ++i) {
		for (j = 0; j < size; ++j) {
			unsigned char* byte = (
				(unsigned char*)rop + 
				(((order == -1) ? i : ((count - 1) - i)) * size) +
				((endian == -1) ? j : ((size - 1) - j))
			);

			if (j >= (size - nail_bytes)) {
				*byte = 0;
				continue;
			}

			*byte = (unsigned char)((j == ((size - nail_bytes) - 1)) ? (t.dp[0] & odd_nail_mask) : (t.dp[0] & 0xFF));

			if ((result = mp_div_2d(&t, ((j == ((size - nail_bytes) - 1)) ? (8 - odd_nails) : 8), &t, NULL)) != MP_OKAY) {
				mp_clear(&t);
				return result;
			}
		}
	}

	mp_clear(&t);

	if (countp != NULL) {
		*countp = count;
	}

	return MP_OKAY;
}

#endif

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

Added libtommath/bn_mp_get_long.c.


















































































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#include <tommath_private.h>
#ifdef BN_MP_GET_LONG_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
 */

/* get the lower unsigned long of an mp_int, platform dependent */
unsigned long mp_get_long(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);

#if (ULONG_MAX != 0xffffffffuL) || (DIGIT_BIT < 32)
  while (--i >= 0) {
    res = (res << DIGIT_BIT) | DIGIT(a,i);
  }
#endif
  return res;
}
#endif

Added libtommath/bn_mp_get_long_long.c.


















































































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#include <tommath_private.h>
#ifdef BN_MP_GET_LONG_LONG_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
 */

/* get the lower unsigned long long of an mp_int, platform dependent */
unsigned long long mp_get_long_long (mp_int * a)
{
  int i;
  unsigned long 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 long) * CHAR_BIT) + DIGIT_BIT - 1) / DIGIT_BIT)) - 1;

  /* get most significant digit of result */
  res = DIGIT(a,i);

#if DIGIT_BIT < 64
  while (--i >= 0) {
    res = (res << DIGIT_BIT) | DIGIT(a,i);
  }
#endif
  return res;
}
#endif

Added libtommath/bn_mp_import.c.


















































































































































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#include <tommath_private.h>
#ifdef BN_MP_IMPORT_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
 */

/* based on gmp's mpz_import.
 * see http://gmplib.org/manual/Integer-Import-and-Export.html
 */
int mp_import(mp_int* rop, size_t count, int order, size_t size, 
                            int endian, size_t nails, const void* op) {
	int result;
	size_t odd_nails, nail_bytes, i, j;
	unsigned char odd_nail_mask;

	mp_zero(rop);

	if (endian == 0) {
		union {
			unsigned int i;
			char c[4];
		} lint;
		lint.i = 0x01020304;

		endian = (lint.c[0] == 4) ? -1 : 1;
	}

	odd_nails = (nails % 8);
	odd_nail_mask = 0xff;
	for (i = 0; i < odd_nails; ++i) {
		odd_nail_mask ^= (1 << (7 - i));
	}
	nail_bytes = nails / 8;

	for (i = 0; i < count; ++i) {
		for (j = 0; j < (size - nail_bytes); ++j) {
			unsigned char byte = *(
					(unsigned char*)op + 
					(((order == 1) ? i : ((count - 1) - i)) * size) +
					((endian == 1) ? (j + nail_bytes) : (((size - 1) - j) - nail_bytes))
				);

			if (
				(result = mp_mul_2d(rop, ((j == 0) ? (8 - odd_nails) : 8), rop)) != MP_OKAY) {
				return result;
			}

			rop->dp[0] |= (j == 0) ? (byte & odd_nail_mask) : byte;
			rop->used  += 1;
		}
	}

	mp_clamp(rop);

	return MP_OKAY;
}

#endif

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

Added libtommath/bn_mp_n_root_ex.c.








































































































































































































































































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#include <tommath_private.h>
#ifdef BN_MP_N_ROOT_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
 */

/* 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_ex (mp_int * a, mp_digit b, mp_int * c, int fast)
{
  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_ex (&t1, b - 1, &t3, fast)) != 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_ex (&t1, b, &t2, fast)) != 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

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

Added libtommath/bn_mp_set_long.c.
















































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#include <tommath_private.h>
#ifdef BN_MP_SET_LONG_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
 */

/* set a platform dependent unsigned long int */
MP_SET_XLONG(mp_set_long, unsigned long)
#endif

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

Added libtommath/bn_mp_set_long_long.c.
















































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#include <tommath_private.h>
#ifdef BN_MP_SET_LONG_LONG_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
 */

/* set a platform dependent unsigned long long int */
MP_SET_XLONG(mp_set_long_long, unsigned long long)
#endif

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

Changes to libtommath/bn_mp_sqrt.c.

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#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
<







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#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

Added libtommath/bn_mp_sqrtmod_prime.c.
























































































































































































































































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#include <tommath_private.h>
#ifdef BN_MP_SQRTMOD_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 is free for all purposes without any express
 * guarantee it works.
 */

/* Tonelli-Shanks algorithm
 * https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm
 * https://gmplib.org/list-archives/gmp-discuss/2013-April/005300.html
 *
 */

int mp_sqrtmod_prime(mp_int *n, mp_int *prime, mp_int *ret)
{
  int res, legendre;
  mp_int t1, C, Q, S, Z, M, T, R, two;
  mp_digit i;

  /* first handle the simple cases */
  if (mp_cmp_d(n, 0) == MP_EQ) {
    mp_zero(ret);
    return MP_OKAY;
  }
  if (mp_cmp_d(prime, 2) == MP_EQ)                              return MP_VAL; /* prime must be odd */
  if ((res = mp_jacobi(n, prime, &legendre)) != MP_OKAY)        return res;
  if (legendre == -1)                                           return MP_VAL; /* quadratic non-residue mod prime */

  if ((res = mp_init_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL)) != MP_OKAY) {
	return res;
  }

  /* SPECIAL CASE: if prime mod 4 == 3
   * compute directly: res = n^(prime+1)/4 mod prime
   * Handbook of Applied Cryptography algorithm 3.36
   */
  if ((res = mp_mod_d(prime, 4, &i)) != MP_OKAY)                goto cleanup;
  if (i == 3) {
    if ((res = mp_add_d(prime, 1, &t1)) != MP_OKAY)             goto cleanup;
    if ((res = mp_div_2(&t1, &t1)) != MP_OKAY)                  goto cleanup;
    if ((res = mp_div_2(&t1, &t1)) != MP_OKAY)                  goto cleanup;
    if ((res = mp_exptmod(n, &t1, prime, ret)) != MP_OKAY)      goto cleanup;
    res = MP_OKAY;
    goto cleanup;
  }

  /* NOW: Tonelli-Shanks algorithm */

  /* factor out powers of 2 from prime-1, defining Q and S as: prime-1 = Q*2^S */
  if ((res = mp_copy(prime, &Q)) != MP_OKAY)                    goto cleanup;
  if ((res = mp_sub_d(&Q, 1, &Q)) != MP_OKAY)                   goto cleanup;
  /* Q = prime - 1 */
  mp_zero(&S);
  /* S = 0 */
  while (mp_iseven(&Q) != MP_NO) {
    if ((res = mp_div_2(&Q, &Q)) != MP_OKAY)                    goto cleanup;
    /* Q = Q / 2 */
    if ((res = mp_add_d(&S, 1, &S)) != MP_OKAY)                 goto cleanup;
    /* S = S + 1 */
  }

  /* find a Z such that the Legendre symbol (Z|prime) == -1 */
  if ((res = mp_set_int(&Z, 2)) != MP_OKAY)                     goto cleanup;
  /* Z = 2 */
  while(1) {
    if ((res = mp_jacobi(&Z, prime, &legendre)) != MP_OKAY)     goto cleanup;
    if (legendre == -1) break;
    if ((res = mp_add_d(&Z, 1, &Z)) != MP_OKAY)                 goto cleanup;
    /* Z = Z + 1 */
  }

  if ((res = mp_exptmod(&Z, &Q, prime, &C)) != MP_OKAY)         goto cleanup;
  /* C = Z ^ Q mod prime */
  if ((res = mp_add_d(&Q, 1, &t1)) != MP_OKAY)                  goto cleanup;
  if ((res = mp_div_2(&t1, &t1)) != MP_OKAY)                    goto cleanup;
  /* t1 = (Q + 1) / 2 */
  if ((res = mp_exptmod(n, &t1, prime, &R)) != MP_OKAY)         goto cleanup;
  /* R = n ^ ((Q + 1) / 2) mod prime */
  if ((res = mp_exptmod(n, &Q, prime, &T)) != MP_OKAY)          goto cleanup;
  /* T = n ^ Q mod prime */
  if ((res = mp_copy(&S, &M)) != MP_OKAY)                       goto cleanup;
  /* M = S */
  if ((res = mp_set_int(&two, 2)) != MP_OKAY)                   goto cleanup;

  res = MP_VAL;
  while (1) {
    if ((res = mp_copy(&T, &t1)) != MP_OKAY)                    goto cleanup;
    i = 0;
    while (1) {
      if (mp_cmp_d(&t1, 1) == MP_EQ) break;
      if ((res = mp_exptmod(&t1, &two, prime, &t1)) != MP_OKAY) goto cleanup;
      i++;
    }
    if (i == 0) {
      if ((res = mp_copy(&R, ret)) != MP_OKAY)                  goto cleanup;
      res = MP_OKAY;
      goto cleanup;
    }
    if ((res = mp_sub_d(&M, i, &t1)) != MP_OKAY)                goto cleanup;
    if ((res = mp_sub_d(&t1, 1, &t1)) != MP_OKAY)               goto cleanup;
    if ((res = mp_exptmod(&two, &t1, prime, &t1)) != MP_OKAY)   goto cleanup;
    /* t1 = 2 ^ (M - i - 1) */
    if ((res = mp_exptmod(&C, &t1, prime, &t1)) != MP_OKAY)     goto cleanup;
    /* t1 = C ^ (2 ^ (M - i - 1)) mod prime */
    if ((res = mp_sqrmod(&t1, prime, &C)) != MP_OKAY)           goto cleanup;
    /* C = (t1 * t1) mod prime */
    if ((res = mp_mulmod(&R, &t1, prime, &R)) != MP_OKAY)       goto cleanup;
    /* R = (R * t1) mod prime */
    if ((res = mp_mulmod(&T, &C, prime, &T)) != MP_OKAY)        goto cleanup;
    /* T = (T * C) mod prime */
    mp_set(&M, i);
    /* M = i */
  }

cleanup:
  mp_clear_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL);
  return res;
}

#endif

Deleted libtommath/booker.pl.

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#!/bin/perl
#
#Used to prepare the book "tommath.src" for LaTeX by pre-processing it into a .tex file
#
#Essentially you write the "tommath.src" as normal LaTex except where you want code snippets you put
#
#EXAM,file
#
#This preprocessor will then open "file" and insert it as a verbatim copy.
#
#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;
   }
}
close(IN);

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;
      }
      $totlines = $line;
      print OUT "\\end{alltt}\n\\end{small}\n";
      close(SRC);
      print "$inline lines\n";
      $wroteline += 2;
   } elsif ($_ =~ 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 = $foundline2;
        } elsif ($found1 == 1 && $found2 == 1) {
           $found = 1;
           if (($foundline1 - $parms[0]) <= ($parms[0] - $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 == 3) {
                     $str = "chapter three";
                  } elsif ($a == 4) {
                     $str = "chapter four";
                  } elsif ($a == 5) {
                     $str = "chapter five";
                  } elsif ($a == 6) {
                     $str = "chapter six";
                  } elsif ($a == 7) {
                     $str = "chapter seven";
                  } elsif ($a == 8) {
                     $str = "chapter eight";
                  } elsif ($a == 9) {
                     $str = "chapter nine";
                  } elsif ($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] . "~";
         }
      }
      print OUT $_;
      ++$wroteline;
   } elsif ($_ =~ m/FIGU/) {
      # FIGU,file,caption
      chomp($_);
      @m = split(",", $_);
      print OUT "\\begin{center}\n\\begin{figure}[here]\n\\includegraphics{pics/$m[1]$graph}\n";
      print OUT "\\caption{$m[2]}\n\\label{pic:$m[1]}\n\\end{figure}\n\\end{center}\n";
      $wroteline += 4;
   } else {
      print OUT $_;
      ++$wroteline;
   }
}
print "Read $readline lines, wrote $wroteline lines\n";

close (OUT);
close (IN);

system('perl -pli -e "s/\s*$//" tommath.tex');
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<




















































































































































































































































































































































































































































































































































Deleted libtommath/demo/demo.c.

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#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) {
      lfsr = ((lfsr << 1) ^ 0x8000001BUL) & 0xFFFFFFFFUL;
      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);
   printf("a == %s\n", buf);
   mp_toradix_n(&a, buf, 10, 4);
   printf("a == %s\n", buf);
   mp_toradix_n(&a, buf, 10, 30);
   printf("a == %s\n", buf);


#if 0
   for (;;) {
      fgets(buf, sizeof(buf), stdin);
      mp_read_radix(&a, buf, 10);
      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;
   TOOM_SQR_CUTOFF = TOOM_MUL_CUTOFF = 16;

   for (;;) {
      /* randomly clear and re-init one variable, this has the affect of triming the alloc space */
      switch (abs(rand()) % 7) {
      case 0:
	 mp_clear(&a);
	 mp_init(&a);
	 break;
      case 1:
	 mp_clear(&b);
	 mp_init(&b);
	 break;
      case 2:
	 mp_clear(&c);
	 mp_init(&c);
	 break;
      case 3:
	 mp_clear(&d);
	 mp_init(&d);
	 break;
      case 4:
	 mp_clear(&e);
	 mp_init(&e);
	 break;
      case 5:
	 mp_clear(&f);
	 mp_init(&f);
	 break;
      case 6:
	 break;			/* don't clear any */
      }


      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;
}

/* $Source$ */
/* $Revision$ */
/* $Date$ */
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Deleted libtommath/demo/timing.c.

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#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);
   mp_toradix(a, buf, 64);
   printf("%s\n", buf);
}

static void draw(mp_int * a)
{
   ndraw(a, "");
}


unsigned long lfsr = 0xAAAAAAAAUL;

int lbit(void)
{
   if (lfsr & 0x80000000UL) {
      lfsr = ((lfsr << 1) ^ 0x8000001BUL) & 0xFFFFFFFFUL;
      return 1;
   } else {
      lfsr <<= 1;
      return 0;
   }
}

/* 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

   // Microsoft and Intel Windows compilers
#elif defined _M_IX86
   __asm rdtsc
#elif defined _M_AMD64
   return __rdtsc();
#elif defined _M_IA64
#if defined __INTEL_COMPILER
#include <ia64intrin.h>
#endif
   return __getReg(3116);
#else
#error need rdtsc function for this build
#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 {
	 gg = TIMFUNC();
	 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();
	 DO(mp_sub(&a, &b, &c));
	 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 {
	    gg = TIMFUNC();
	    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",
	 /* 2K moduli mersenne primes */
	 "6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151",
	 "531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728127",
	 "10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729087",
	 "1475979915214180235084898622737381736312066145333169775147771216478570297878078949377407337049389289382748507531496480477281264838760259191814463365330269540496961201113430156902396093989090226259326935025281409614983499388222831448598601834318536230923772641390209490231836446899608210795482963763094236630945410832793769905399982457186322944729636418890623372171723742105636440368218459649632948538696905872650486914434637457507280441823676813517852099348660847172579408422316678097670224011990280170474894487426924742108823536808485072502240519452587542875349976558572670229633962575212637477897785501552646522609988869914013540483809865681250419497686697771007",
	 "259117086013202627776246767922441530941818887553125427303974923161874019266586362086201209516800483406550695241733194177441689509238807017410377709597512042313066624082916353517952311186154862265604547691127595848775610568757931191017711408826252153849035830401185072116424747461823031471398340229288074545677907941037288235820705892351068433882986888616658650280927692080339605869308790500409503709875902119018371991620994002568935113136548829739112656797303241986517250116412703509705427773477972349821676443446668383119322540099648994051790241624056519054483690809616061625743042361721863339415852426431208737266591962061753535748892894599629195183082621860853400937932839420261866586142503251450773096274235376822938649407127700846077124211823080804139298087057504713825264571448379371125032081826126566649084251699453951887789613650248405739378594599444335231188280123660406262468609212150349937584782292237144339628858485938215738821232393687046160677362909315071",
	 "190797007524439073807468042969529173669356994749940177394741882673528979787005053706368049835514900244303495954950709725762186311224148828811920216904542206960744666169364221195289538436845390250168663932838805192055137154390912666527533007309292687539092257043362517857366624699975402375462954490293259233303137330643531556539739921926201438606439020075174723029056838272505051571967594608350063404495977660656269020823960825567012344189908927956646011998057988548630107637380993519826582389781888135705408653045219655801758081251164080554609057468028203308718724654081055323215860189611391296030471108443146745671967766308925858547271507311563765171008318248647110097614890313562856541784154881743146033909602737947385055355960331855614540900081456378659068370317267696980001187750995491090350108417050917991562167972281070161305972518044872048331306383715094854938415738549894606070722584737978176686422134354526989443028353644037187375385397838259511833166416134323695660367676897722287918773420968982326089026150031515424165462111337527431154890666327374921446276833564519776797633875503548665093914556482031482248883127023777039667707976559857333357013727342079099064400455741830654320379350833236245819348824064783585692924881021978332974949906122664421376034687815350484991",

	 /* DR moduli */
	 "14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203368612079",
	 "101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411688900243039",
	 "736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140821797602431",
	 "38564998830736521417281865696453025806593491967131023221754800625044118265468851210705360385717536794615180260494208076605798671660719333199513807806252394423283413430106003596332513246682903994829528690198205120921557533726473585751382193953592127439965050261476810842071573684505878854588706623484573925925903505747545471088867712185004135201289273405614415899438276535626346098904241020877974002916168099951885406379295536200413493190419727789712076165162175783",
	 "542189391331696172661670440619180536749994166415993334151601745392193484590296600979602378676624808129613777993466242203025054573692562689251250471628358318743978285860720148446448885701001277560572526947619392551574490839286458454994488665744991822837769918095117129546414124448777033941223565831420390846864429504774477949153794689948747680362212954278693335653935890352619041936727463717926744868338358149568368643403037768649616778526013610493696186055899318268339432671541328195724261329606699831016666359440874843103020666106568222401047720269951530296879490444224546654729111504346660859907296364097126834834235287147",
	 "1487259134814709264092032648525971038895865645148901180585340454985524155135260217788758027400478312256339496385275012465661575576202252063145698732079880294664220579764848767704076761853197216563262660046602703973050798218246170835962005598561669706844469447435461092542265792444947706769615695252256130901271870341005768912974433684521436211263358097522726462083917939091760026658925757076733484173202927141441492573799914240222628795405623953109131594523623353044898339481494120112723445689647986475279242446083151413667587008191682564376412347964146113898565886683139407005941383669325997475076910488086663256335689181157957571445067490187939553165903773554290260531009121879044170766615232300936675369451260747671432073394867530820527479172464106442450727640226503746586340279816318821395210726268291535648506190714616083163403189943334431056876038286530365757187367147446004855912033137386225053275419626102417236133948503",
	 "1095121115716677802856811290392395128588168592409109494900178008967955253005183831872715423151551999734857184538199864469605657805519106717529655044054833197687459782636297255219742994736751541815269727940751860670268774903340296040006114013971309257028332849679096824800250742691718610670812374272414086863715763724622797509437062518082383056050144624962776302147890521249477060215148275163688301275847155316042279405557632639366066847442861422164832655874655824221577849928863023018366835675399949740429332468186340518172487073360822220449055340582568461568645259954873303616953776393853174845132081121976327462740354930744487429617202585015510744298530101547706821590188733515880733527449780963163909830077616357506845523215289297624086914545378511082534229620116563260168494523906566709418166011112754529766183554579321224940951177394088465596712620076240067370589036924024728375076210477267488679008016579588696191194060127319035195370137160936882402244399699172017835144537488486396906144217720028992863941288217185353914991583400421682751000603596655790990815525126154394344641336397793791497068253936771017031980867706707490224041075826337383538651825493679503771934836094655802776331664261631740148281763487765852746577808019633679",

	 /* generic unrestricted moduli */
	 "17933601194860113372237070562165128350027320072176844226673287945873370751245439587792371960615073855669274087805055507977323024886880985062002853331424203",
	 "2893527720709661239493896562339544088620375736490408468011883030469939904368086092336458298221245707898933583190713188177399401852627749210994595974791782790253946539043962213027074922559572312141181787434278708783207966459019479487",
	 "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();
	    b.used += 1;
	 }
	 mp_sub_d(&a, 1, &c);
	 mp_mod(&b, &c, &b);
	 mp_set(&c, 3);
	 rr = 0;
	 tt = -1;
	 do {
	    gg = TIMFUNC();
	    DO(mp_exptmod(&c, &b, &a, &d));
	    gg = (TIMFUNC() - gg) >> 1;
	    if (tt > gg)
	       tt = gg;
	 } while (++rr < 10);
	 mp_sub_d(&a, 1, &e);
	 mp_sub(&e, &b, &b);
	 mp_exptmod(&c, &b, &a, &e);	/* c^(p-1-b) mod a */
	 mp_mulmod(&e, &d, &a, &d);	/* c^b * c^(p-1-b) == c^p-1 == 1 */
	 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);
      } while (mp_cmp_d(&c, 1) != MP_EQ);

      rr = 0;
      tt = -1;
      do {
	 gg = TIMFUNC();
	 DO(mp_invmod(&b, &a, &c));
	 gg = (TIMFUNC() - gg) >> 1;
	 if (tt > gg)
	    tt = gg;
      } while (++rr < 1000);
      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;
}

/* $Source$ */
/* $Revision$ */
/* $Date$ */
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Deleted libtommath/dep.pl.

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#!/usr/bin/perl 
#
# Walk through source, add labels and make classes
#
#use strict;

my %deplist;

#open class file and write preamble 
open(CLASS, ">tommath_class.h") or die "Couldn't open tommath_class.h for writing\n";
print CLASS "#if !(defined(LTM1) && defined(LTM2) && defined(LTM3))\n#if defined(LTM2)\n#define LTM3\n#endif\n#if defined(LTM1)\n#define LTM2\n#endif\n#define LTM1\n\n#if defined(LTM_ALL)\n";

foreach my $filename (glob "bn*.c") {
   my $define = $filename;

print "Processing $filename\n";

   # convert filename to upper case so we can use it as a define 
   $define =~ tr/[a-z]/[A-Z]/;
   $define =~ tr/\./_/;
   print CLASS "#define $define\n";

   # now copy text and apply #ifdef as required 
   my $apply = 0;
   open(SRC, "<$filename");
   open(OUT, ">tmp");

   # first line will be the #ifdef
   my $line = <SRC>;
   if ($line =~ /include/) {
      print OUT $line;
   } else {
      print OUT "#include <tommath.h>\n#ifdef $define\n$line";
      $apply = 1;
   }
   while (<SRC>) {
      if (!($_ =~ /tommath\.h/)) {
         print OUT $_;
      }
   }
   if ($apply == 1) {
      print OUT "#endif\n";
   }
   close SRC;
   close OUT;

   unlink($filename);
   rename("tmp", $filename);
}
print CLASS "#endif\n\n";

# now do classes 

foreach my $filename (glob "bn*.c") {
   open(SRC, "<$filename") or die "Can't open source file!\n"; 

   # convert filename to upper case so we can use it as a define 
   $filename =~ tr/[a-z]/[A-Z]/;
   $filename =~ tr/\./_/;

   print CLASS "#if defined($filename)\n";
   my $list = $filename;

   # 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 . "," . $a;
          }
      }
   }
   @deplist{$filename} = $list;

   print CLASS "#endif\n\n";
   close SRC;
}

print CLASS "#ifdef LTM3\n#define LTM_LAST\n#endif\n#include <tommath_superclass.h>\n#include <tommath_class.h>\n#else\n#define LTM_LAST\n#endif\n";
close CLASS;

#now let's make a cool call graph... 

open(OUT,">callgraph.txt");
$indent = 0;
foreach (keys %deplist) {
   $list = "";
   draw_func(@deplist{$_});
   print OUT "\n\n";
}
close(OUT);

sub draw_func()
{
   my @funcs = split(",", $_[0]);
   if ($list =~ /@funcs[0]/) {
      return;
   } else {
      $list = $list . @funcs[0];
   }
   if ($indent == 0) { }
   elsif ($indent >= 1) { print OUT "|   " x ($indent - 1) . "+--->"; }
   print OUT @funcs[0] . "\n";   
   shift @funcs;
      my $temp = $list;
   foreach my $i (@funcs) {
      ++$indent;
      draw_func(@deplist{$i});
      --$indent;
   }
      $list = $temp;
}


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Deleted libtommath/etc/2kprime.1.

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256-bits (k = 36113) = 115792089237316195423570985008687907853269984665640564039457584007913129603823
512-bits (k = 38117) = 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006045979
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Deleted libtommath/etc/2kprime.c.

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/* Makes safe primes of a 2k nature */
#include <tommath.h>
#include <time.h>

int sizes[] = {256, 512, 768, 1024, 1536, 2048, 3072, 4096};

int main(void)
{
   char buf[2000];
   int x, y;
   mp_int q, p;
   FILE *out;
   clock_t t1;
   mp_digit z;
   
   mp_init_multi(&q, &p, NULL);
   
   out = fopen("2kprime.1", "w");
   for (x = 0; x < (int)(sizeof(sizes) / sizeof(sizes[0])); x++) {
   top:
       mp_2expt(&q, sizes[x]);
       mp_add_d(&q, 3, &q);
       z = -3;
       
       t1 = clock();
       for(;;) {
         mp_sub_d(&q, 4, &q);
         z += 4;

         if (z > MP_MASK) {
            printf("No primes of size %d found\n", sizes[x]);
            break;
         }
         
         if (clock() - t1 > CLOCKS_PER_SEC) { 
            printf("."); fflush(stdout);
//            sleep((clock() - t1 + CLOCKS_PER_SEC/2)/CLOCKS_PER_SEC);
            t1 = clock();
         }
         
         /* quick test on q */
         mp_prime_is_prime(&q, 1, &y);
         if (y == 0) {
            continue;
         }

         /* find (q-1)/2 */
         mp_sub_d(&q, 1, &p);
         mp_div_2(&p, &p);
         mp_prime_is_prime(&p, 3, &y);
         if (y == 0) {
            continue;
         }

         /* test on q */
         mp_prime_is_prime(&q, 3, &y);
         if (y == 0) {
            continue;
         }

         break;
       }
       
       if (y == 0) {
          ++sizes[x];
          goto top;
       }
       
       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;
}   
       
         
            
            
          

/* $Source$ */
/* $Revision$ */
/* $Date$ */
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Deleted libtommath/etc/drprime.c.

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/* Makes safe primes of a DR nature */
#include <tommath.h>

int sizes[] = { 1+256/DIGIT_BIT, 1+512/DIGIT_BIT, 1+768/DIGIT_BIT, 1+1024/DIGIT_BIT, 1+2048/DIGIT_BIT, 1+4096/DIGIT_BIT };
int main(void)
{
   int res, x, y;
   char buf[4096];
   FILE *out;
   mp_int a, b;
   
   mp_init(&a);
   mp_init(&b);
   
   out = fopen("drprimes.txt", "w");
   for (x = 0; x < (int)(sizeof(sizes)/sizeof(sizes[0])); x++) {
   top:
       printf("Seeking a %d-bit safe prime\n", sizes[x] * DIGIT_BIT);
       mp_grow(&a, sizes[x]);
       mp_zero(&a);
       for (y = 1; y < sizes[x]; y++) {
           a.dp[y] = MP_MASK;
       }
       
       /* make a DR modulus */
       a.dp[0] = -1;
       a.used = sizes[x];
       
       /* now loop */
       res = 0;
       for (;;) { 
          a.dp[0] += 4;
          if (a.dp[0] >= MP_MASK) break;
          mp_prime_is_prime(&a, 1, &res);
          if (res == 0) continue;
          printf("."); fflush(stdout);
          mp_sub_d(&a, 1, &b);
          mp_div_2(&b, &b);
          mp_prime_is_prime(&b, 3, &res);  
          if (res == 0) continue;
          mp_prime_is_prime(&a, 3, &res);
          if (res == 1) break;
	}
        
        if (res != 1) {
           printf("Error not DR modulus\n"); sizes[x] += 1; goto top;
        } else {
           mp_toradix(&a, buf, 10);
           printf("\n\np == %s\n\n", buf);
           fprintf(out, "%d-bit prime:\np == %s\n\n", mp_count_bits(&a), buf); fflush(out);
        }           
   }
   fclose(out);
   
   mp_clear(&a);
   mp_clear(&b);
   
   return 0;
}


/* $Source$ */
/* $Revision$ */
/* $Date$ */
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Deleted libtommath/etc/drprimes.28.

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DR safe primes for 28-bit digits.

224-bit prime:
p == 26959946667150639794667015087019630673637144422540572481103341844143

532-bit prime:
p == 14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203368691747

784-bit prime:
p == 101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411688900243039

1036-bit prime:
p == 736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140821798437127

1540-bit prime:
p == 38564998830736521417281865696453025806593491967131023221754800625044118265468851210705360385717536794615180260494208076605798671660719333199513807806252394423283413430106003596332513246682903994829528690198205120921557533726473585751382193953592127439965050261476810842071573684505878854588706623484573925925903505747545471088867712185004135201289273405614415899438276535626346098904241020877974002916168099951885406379295536200413493190419727789712076165162175783

2072-bit prime:
p == 542189391331696172661670440619180536749994166415993334151601745392193484590296600979602378676624808129613777993466242203025054573692562689251250471628358318743978285860720148446448885701001277560572526947619392551574490839286458454994488665744991822837769918095117129546414124448777033941223565831420390846864429504774477949153794689948747680362212954278693335653935890352619041936727463717926744868338358149568368643403037768649616778526013610493696186055899318268339432671541328195724261329606699831016666359440874843103020666106568222401047720269951530296879490444224546654729111504346660859907296364097126834834235287147

3080-bit prime:
p == 1487259134814709264092032648525971038895865645148901180585340454985524155135260217788758027400478312256339496385275012465661575576202252063145698732079880294664220579764848767704076761853197216563262660046602703973050798218246170835962005598561669706844469447435461092542265792444947706769615695252256130901271870341005768912974433684521436211263358097522726462083917939091760026658925757076733484173202927141441492573799914240222628795405623953109131594523623353044898339481494120112723445689647986475279242446083151413667587008191682564376412347964146113898565886683139407005941383669325997475076910488086663256335689181157957571445067490187939553165903773554290260531009121879044170766615232300936675369451260747671432073394867530820527479172464106442450727640226503746586340279816318821395210726268291535648506190714616083163403189943334431056876038286530365757187367147446004855912033137386225053275419626102417236133948503

4116-bit prime:
p == 1095121115716677802856811290392395128588168592409109494900178008967955253005183831872715423151551999734857184538199864469605657805519106717529655044054833197687459782636297255219742994736751541815269727940751860670268774903340296040006114013971309257028332849679096824800250742691718610670812374272414086863715763724622797509437062518082383056050144624962776302147890521249477060215148275163688301275847155316042279405557632639366066847442861422164832655874655824221577849928863023018366835675399949740429332468186340518172487073360822220449055340582568461568645259954873303616953776393853174845132081121976327462740354930744487429617202585015510744298530101547706821590188733515880733527449780963163909830077616357506845523215289297624086914545378511082534229620116563260168494523906566709418166011112754529766183554579321224940951177394088465596712620076240067370589036924024728375076210477267488679008016579588696191194060127319035195370137160936882402244399699172017835144537488486396906144217720028992863941288217185353914991583400421682751000603596655790990815525126154394344641336397793791497068253936771017031980867706707490224041075826337383538651825493679503771934836094655802776331664261631740148281763487765852746577808019633679
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Deleted libtommath/etc/drprimes.txt.

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300-bit prime:
p == 2037035976334486086268445688409378161051468393665936250636140449354381298610415201576637819

540-bit prime:
p == 3599131035634557106248430806148785487095757694641533306480604458089470064537190296255232548883112685719936728506816716098566612844395439751206810991770626477344739

780-bit prime:
p == 6359114106063703798370219984742410466332205126109989319225557147754704702203399726411277962562135973685197744935448875852478791860694279747355800678568677946181447581781401213133886609947027230004277244697462656003655947791725966271167

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Deleted libtommath/etc/makefile.

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CFLAGS += -Wall -W -Wshadow -O3 -fomit-frame-pointer -funroll-loops -I../

# default lib name (requires install with root)
# LIBNAME=-ltommath

# libname when you can't install the lib with install
LIBNAME=../libtommath.a

#provable primes
pprime: pprime.o
	$(CC) pprime.o $(LIBNAME) -o pprime

# portable [well requires clock()] tuning app
tune: tune.o
	$(CC) tune.o $(LIBNAME) -o tune
	
# same app but using RDTSC for higher precision [requires 80586+], coff based gcc installs [e.g. ming, cygwin, djgpp]
tune86: tune.c
	nasm -f coff timer.asm
	$(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o  $(LIBNAME) -o tune86
	
# for cygwin
tune86c: tune.c
	nasm -f gnuwin32 timer.asm
	$(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o  $(LIBNAME) -o tune86

#make tune86 for linux or any ELF format
tune86l: tune.c
	nasm -f elf -DUSE_ELF timer.asm
	$(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86l
        
# spits out mersenne primes
mersenne: mersenne.o
	$(CC) mersenne.o $(LIBNAME) -o mersenne

# fines DR safe primes for the given config
drprime: drprime.o
	$(CC) drprime.o $(LIBNAME) -o drprime
	
# fines 2k safe primes for the given config
2kprime: 2kprime.o
	$(CC) 2kprime.o $(LIBNAME) -o 2kprime

mont: mont.o
	$(CC) mont.o $(LIBNAME) -o mont

        
clean:
	rm -f *.log *.o *.obj *.exe pprime tune mersenne drprime tune86 tune86l mont 2kprime pprime.dat \
         *.da *.dyn *.dpi *~
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Deleted libtommath/etc/makefile.icc.

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CC = icc

CFLAGS += -I../

# optimize for SPEED
#
# -mcpu= can be pentium, pentiumpro (covers PII through PIII) or pentium4
# -ax?   specifies make code specifically for ? but compatible with IA-32
# -x?    specifies compile solely for ? [not specifically IA-32 compatible]
#
# where ? is 
#   K - PIII
#   W - first P4 [Williamette]
#   N - P4 Northwood
#   P - P4 Prescott
#   B - Blend of P4 and PM [mobile]
#
# Default to just generic max opts
CFLAGS += -O3 -xP -ip

# default lib name (requires install with root)
# LIBNAME=-ltommath

# libname when you can't install the lib with install
LIBNAME=../libtommath.a

#provable primes
pprime: pprime.o
	$(CC) pprime.o $(LIBNAME) -o pprime

# portable [well requires clock()] tuning app
tune: tune.o
	$(CC) tune.o $(LIBNAME) -o tune
	
# same app but using RDTSC for higher precision [requires 80586+], coff based gcc installs [e.g. ming, cygwin, djgpp]
tune86: tune.c
	nasm -f coff timer.asm
	$(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o  $(LIBNAME) -o tune86
	
# for cygwin
tune86c: tune.c
	nasm -f gnuwin32 timer.asm
	$(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o  $(LIBNAME) -o tune86

#make tune86 for linux or any ELF format
tune86l: tune.c
	nasm -f elf -DUSE_ELF timer.asm
	$(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86l
        
# spits out mersenne primes
mersenne: mersenne.o
	$(CC) mersenne.o $(LIBNAME) -o mersenne

# fines DR safe primes for the given config
drprime: drprime.o
	$(CC) drprime.o $(LIBNAME) -o drprime
	
# fines 2k safe primes for the given config
2kprime: 2kprime.o
	$(CC) 2kprime.o $(LIBNAME) -o 2kprime

mont: mont.o
	$(CC) mont.o $(LIBNAME) -o mont

        
clean:
	rm -f *.log *.o *.obj *.exe pprime tune mersenne drprime tune86 tune86l mont 2kprime pprime.dat *.il
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Deleted libtommath/etc/makefile.msvc.

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#MSVC Makefile
#
#Tom St Denis

CFLAGS = /I../ /Ox /DWIN32 /W3

pprime: pprime.obj
	cl pprime.obj ../tommath.lib 

mersenne: mersenne.obj
	cl mersenne.obj ../tommath.lib
	
tune: tune.obj
	cl tune.obj ../tommath.lib

mont: mont.obj
	cl mont.obj ../tommath.lib
	
drprime: drprime.obj
	cl drprime.obj ../tommath.lib

2kprime: 2kprime.obj
	cl 2kprime.obj ../tommath.lib
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Deleted libtommath/etc/mersenne.c.

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/* Finds Mersenne primes using the Lucas-Lehmer test 
 *
 * Tom St Denis, [email protected]
 */
#include <time.h>
#include <tommath.h>

int
is_mersenne (long s, int *pp)
{
  mp_int  n, u;
  int     res, k;
  
  *pp = 0;

  if ((res = mp_init (&n)) != MP_OKAY) {
    return res;
  }

  if ((res = mp_init (&u)) != MP_OKAY) {
    goto LBL_N;
  }

  /* n = 2^s - 1 */
  if ((res = mp_2expt(&n, s)) != MP_OKAY) {
     goto LBL_MU;
  }
  if ((res = mp_sub_d (&n, 1, &n)) != MP_OKAY) {
    goto LBL_MU;
  }

  /* set u=4 */
  mp_set (&u, 4);

  /* for k=1 to s-2 do */
  for (k = 1; k <= s - 2; k++) {
    /* u = u^2 - 2 mod n */
    if ((res = mp_sqr (&u, &u)) != MP_OKAY) {
      goto LBL_MU;
    }
    if ((res = mp_sub_d (&u, 2, &u)) != MP_OKAY) {
      goto LBL_MU;
    }

    /* make sure u is positive */
    while (u.sign == MP_NEG) {
      if ((res = mp_add (&u, &n, &u)) != MP_OKAY) {
         goto LBL_MU;
      }
    }

    /* reduce */
    if ((res = mp_reduce_2k (&u, &n, 1)) != MP_OKAY) {
      goto LBL_MU;
    }
  }

  /* if u == 0 then its prime */
  if (mp_iszero (&u) == 1) {
    mp_prime_is_prime(&n, 8, pp);
  if (*pp != 1) printf("FAILURE\n");
  }

  res = MP_OKAY;
LBL_MU:mp_clear (&u);
LBL_N:mp_clear (&n);
  return res;
}

/* square root of a long < 65536 */
long
i_sqrt (long x)
{
  long    x1, x2;

  x2 = 16;
  do {
    x1 = x2;
    x2 = x1 - ((x1 * x1) - x) / (2 * x1);
  } while (x1 != x2);

  if (x1 * x1 > x) {
    --x1;
  }

  return x1;
}

/* is the long prime by brute force */
int
isprime (long k)
{
  long    y, z;

  y = i_sqrt (k);
  for (z = 2; z <= y; z++) {
    if ((k % z) == 0)
      return 0;
  }
  return 1;
}


int
main (void)
{
  int     pp;
  long    k;
  clock_t tt;

  k = 3;

  for (;;) {
    /* start time */
    tt = clock ();

    /* test if 2^k - 1 is prime */
    if (is_mersenne (k, &pp) != MP_OKAY) {
      printf ("Whoa error\n");
      return -1;
    }

    if (pp == 1) {
      /* count time */
      tt = clock () - tt;

      /* display if prime */
      printf ("2^%-5ld - 1 is prime, test took %ld ticks\n", k, tt);
    }

    /* goto next odd exponent */
    k += 2;

    /* but make sure its prime */
    while (isprime (k) == 0) {
      k += 2;
    }
  }
  return 0;
}

/* $Source$ */
/* $Revision$ */
/* $Date$ */
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Deleted libtommath/etc/mont.c.

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/* tests the montgomery routines */
#include <tommath.h>

int main(void)
{
   mp_int modulus, R, p, pp;
   mp_digit mp;
   long x, y;

   srand(time(NULL));
   mp_init_multi(&modulus, &R, &p, &pp, NULL);

   /* loop through various sizes */
   for (x = 4; x < 256; x++) {
       printf("DIGITS == %3ld...", x); fflush(stdout);
       
       /* make up the odd modulus */
       mp_rand(&modulus, x);
       modulus.dp[0] |= 1;
       
       /* now find the R value */
       mp_montgomery_calc_normalization(&R, &modulus);
       mp_montgomery_setup(&modulus, &mp);
       
       /* now run through a bunch tests */
       for (y = 0; y < 1000; y++) {
           mp_rand(&p, x/2);        /* p = random */
           mp_mul(&p, &R, &pp);     /* pp = R * p */
           mp_montgomery_reduce(&pp, &modulus, mp);
           
           /* should be equal to p */
           if (mp_cmp(&pp, &p) != MP_EQ) {
              printf("FAILURE!\n");
              exit(-1);
           }
       }
       printf("PASSED\n");
    }
    
    return 0;
}






/* $Source$ */
/* $Revision$ */
/* $Date$ */
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Deleted libtommath/etc/pprime.c.

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/* Generates provable primes
 *
 * See http://gmail.com:8080/papers/pp.pdf for more info.
 *
 * Tom St Denis, [email protected], http://tom.gmail.com
 */
#include <time.h>
#include "tommath.h"

int   n_prime;
FILE *primes;

/* fast square root */
static  mp_digit
i_sqrt (mp_word x)
{
  mp_word x1, x2;

  x2 = x;
  do {
    x1 = x2;
    x2 = x1 - ((x1 * x1) - x) / (2 * x1);
  } while (x1 != x2);

  if (x1 * x1 > x) {
    --x1;
  }

  return x1;
}


/* generates a prime digit */
static void gen_prime (void)
{
  mp_digit r, x, y, next;
  FILE *out;

  out = fopen("pprime.dat", "wb");

  /* write first set of primes */
  r = 3; fwrite(&r, 1, sizeof(mp_digit), out);
  r = 5; fwrite(&r, 1, sizeof(mp_digit), out);
  r = 7; fwrite(&r, 1, sizeof(mp_digit), out);
  r = 11; fwrite(&r, 1, sizeof(mp_digit), out);
  r = 13; fwrite(&r, 1, sizeof(mp_digit), out);
  r = 17; fwrite(&r, 1, sizeof(mp_digit), out);
  r = 19; fwrite(&r, 1, sizeof(mp_digit), out);
  r = 23; fwrite(&r, 1, sizeof(mp_digit), out);
  r = 29; fwrite(&r, 1, sizeof(mp_digit), out);
  r = 31; fwrite(&r, 1, sizeof(mp_digit), out);

  /* get square root, since if 'r' is composite its factors must be < than this */
  y = i_sqrt (r);
  next = (y + 1) * (y + 1);

  for (;;) {
  do {
    r += 2;			/* next candidate */
    r &= MP_MASK;
    if (r < 31) break;

    /* update sqrt ? */
    if (next <= r) {
      ++y;
      next = (y + 1) * (y + 1);
    }

    /* loop if divisible by 3,5,7,11,13,17,19,23,29  */
    if ((r % 3) == 0) {
      x = 0;
      continue;
    }
    if ((r % 5) == 0) {
      x = 0;
      continue;
    }
    if ((r % 7) == 0) {
      x = 0;
      continue;
    }
    if ((r % 11) == 0) {
      x = 0;
      continue;
    }
    if ((r % 13) == 0) {
      x = 0;
      continue;
    }
    if ((r % 17) == 0) {
      x = 0;
      continue;
    }
    if ((r % 19) == 0) {
      x = 0;
      continue;
    }
    if ((r % 23) == 0) {
      x = 0;
      continue;
    }
    if ((r % 29) == 0) {
      x = 0;
      continue;
    }

    /* now check if r is divisible by x + k={1,7,11,13,17,19,23,29} */
    for (x = 30; x <= y; x += 30) {
      if ((r % (x + 1)) == 0) {
	x = 0;
	break;
      }
      if ((r % (x + 7)) == 0) {
	x = 0;
	break;
      }
      if ((r % (x + 11)) == 0) {
	x = 0;
	break;
      }
      if ((r % (x + 13)) == 0) {
	x = 0;
	break;
      }
      if ((r % (x + 17)) == 0) {
	x = 0;
	break;
      }
      if ((r % (x + 19)) == 0) {
	x = 0;
	break;
      }
      if ((r % (x + 23)) == 0) {
	x = 0;
	break;
      }
      if ((r % (x + 29)) == 0) {
	x = 0;
	break;
      }
    }
  } while (x == 0);
  if (r > 31) { fwrite(&r, 1, sizeof(mp_digit), out); printf("%9d\r", r); fflush(stdout); }
  if (r < 31) break;
  }

  fclose(out);
}

void load_tab(void)
{
   primes = fopen("pprime.dat", "rb");
   if (primes == NULL) {
      gen_prime();
      primes = fopen("pprime.dat", "rb");
   }
   fseek(primes, 0, SEEK_END);
   n_prime = ftell(primes) / sizeof(mp_digit);
}

mp_digit prime_digit(void)
{
   int n;
   mp_digit d;

   n = abs(rand()) % n_prime;
   fseek(primes, n * sizeof(mp_digit), SEEK_SET);
   fread(&d, 1, sizeof(mp_digit), primes);
   return d;
}


/* makes a prime of at least k bits */
int
pprime (int k, int li, mp_int * p, mp_int * q)
{
  mp_int  a, b, c, n, x, y, z, v;
  int     res, ii;
  static const mp_digit bases[] = { 2, 3, 5, 7, 11, 13, 17, 19 };

  /* single digit ? */
  if (k <= (int) DIGIT_BIT) {
    mp_set (p, prime_digit ());
    return MP_OKAY;
  }

  if ((res = mp_init (&c)) != MP_OKAY) {
    return res;
  }

  if ((res = mp_init (&v)) != MP_OKAY) {
    goto LBL_C;
  }

  /* product of first 50 primes */
  if ((res =
       mp_read_radix (&v,
		      "19078266889580195013601891820992757757219839668357012055907516904309700014933909014729740190",
		      10)) != MP_OKAY) {
    goto LBL_V;
  }

  if ((res = mp_init (&a)) != MP_OKAY) {
    goto LBL_V;
  }

  /* set the prime */
  mp_set (&a, prime_digit ());

  if ((res = mp_init (&b)) != MP_OKAY) {
    goto LBL_A;
  }

  if ((res = mp_init (&n)) != MP_OKAY) {
    goto LBL_B;
  }

  if ((res = mp_init (&x)) != MP_OKAY) {
    goto LBL_N;
  }

  if ((res = mp_init (&y)) != MP_OKAY) {
    goto LBL_X;
  }

  if ((res = mp_init (&z)) != MP_OKAY) {
    goto LBL_Y;
  }

  /* now loop making the single digit */
  while (mp_count_bits (&a) < k) {
    fprintf (stderr, "prime has %4d bits left\r", k - mp_count_bits (&a));
    fflush (stderr);
  top:
    mp_set (&b, prime_digit ());

    /* now compute z = a * b * 2 */
    if ((res = mp_mul (&a, &b, &z)) != MP_OKAY) {	/* z = a * b */
      goto LBL_Z;
    }

    if ((res = mp_copy (&z, &c)) != MP_OKAY) {	/* c = a * b */
      goto LBL_Z;
    }

    if ((res = mp_mul_2 (&z, &z)) != MP_OKAY) {	/* z = 2 * a * b */
      goto LBL_Z;
    }

    /* n = z + 1 */
    if ((res = mp_add_d (&z, 1, &n)) != MP_OKAY) {	/* n = z + 1 */
      goto LBL_Z;
    }

    /* check (n, v) == 1 */
    if ((res = mp_gcd (&n, &v, &y)) != MP_OKAY) {	/* y = (n, v) */
      goto LBL_Z;
    }

    if (mp_cmp_d (&y, 1) != MP_EQ)
      goto top;

    /* now try base x=bases[ii]  */
    for (ii = 0; ii < li; ii++) {
      mp_set (&x, bases[ii]);

      /* compute x^a mod n */
      if ((res = mp_exptmod (&x, &a, &n, &y)) != MP_OKAY) {	/* y = x^a mod n */
	goto LBL_Z;
      }

      /* if y == 1 loop */
      if (mp_cmp_d (&y, 1) == MP_EQ)
	continue;

      /* now x^2a mod n */
      if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) {	/* y = x^2a mod n */
	goto LBL_Z;
      }

      if (mp_cmp_d (&y, 1) == MP_EQ)
	continue;

      /* compute x^b mod n */
      if ((res = mp_exptmod (&x, &b, &n, &y)) != MP_OKAY) {	/* y = x^b mod n */
	goto LBL_Z;
      }

      /* if y == 1 loop */
      if (mp_cmp_d (&y, 1) == MP_EQ)
	continue;

      /* now x^2b mod n */
      if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) {	/* y = x^2b mod n */
	goto LBL_Z;
      }

      if (mp_cmp_d (&y, 1) == MP_EQ)
	continue;

      /* compute x^c mod n == x^ab mod n */
      if ((res = mp_exptmod (&x, &c, &n, &y)) != MP_OKAY) {	/* y = x^ab mod n */
	goto LBL_Z;
      }

      /* if y == 1 loop */
      if (mp_cmp_d (&y, 1) == MP_EQ)
	continue;

      /* now compute (x^c mod n)^2 */
      if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) {	/* y = x^2ab mod n */
	goto LBL_Z;
      }

      /* y should be 1 */
      if (mp_cmp_d (&y, 1) != MP_EQ)
	continue;
      break;
    }

    /* no bases worked? */
    if (ii == li)
      goto top;

{
   char buf[4096];

   mp_toradix(&n, buf, 10);
   printf("Certificate of primality for:\n%s\n\n", buf);
   mp_toradix(&a, buf, 10);
   printf("A == \n%s\n\n", buf);
   mp_toradix(&b, buf, 10);
   printf("B == \n%s\n\nG == %d\n", buf, bases[ii]);
   printf("----------------------------------------------------------------\n");
}

    /* a = n */
    mp_copy (&n, &a);
  }

  /* get q to be the order of the large prime subgroup */
  mp_sub_d (&n, 1, q);
  mp_div_2 (q, q);
  mp_div (q, &b, q, NULL);

  mp_exch (&n, p);

  res = MP_OKAY;
LBL_Z:mp_clear (&z);
LBL_Y:mp_clear (&y);
LBL_X:mp_clear (&x);
LBL_N:mp_clear (&n);
LBL_B:mp_clear (&b);
LBL_A:mp_clear (&a);
LBL_V:mp_clear (&v);
LBL_C:mp_clear (&c);
  return res;
}


int
main (void)
{
  mp_int  p, q;
  char    buf[4096];
  int     k, li;
  clock_t t1;

  srand (time (NULL));
  load_tab();

  printf ("Enter # of bits: \n");
  fgets (buf, sizeof (buf), stdin);
  sscanf (buf, "%d", &k);

  printf ("Enter number of bases to try (1 to 8):\n");
  fgets (buf, sizeof (buf), stdin);
  sscanf (buf, "%d", &li);


  mp_init (&p);
  mp_init (&q);

  t1 = clock ();
  pprime (k, li, &p, &q);
  t1 = clock () - t1;

  printf ("\n\nTook %ld ticks, %d bits\n", t1, mp_count_bits (&p));

  mp_toradix (&p, buf, 10);
  printf ("P == %s\n", buf);
  mp_toradix (&q, buf, 10);
  printf ("Q == %s\n", buf);

  return 0;
}

/* $Source$ */
/* $Revision$ */
/* $Date$ */
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Deleted libtommath/etc/prime.1024.

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Enter # of bits: 
Enter number of bases to try (1 to 8):
Certificate of primality for:
36360080703173363

A == 
89963569

B == 
202082249

G == 2
----------------------------------------------------------------
Certificate of primality for:
4851595597739856136987139

A == 
36360080703173363

B == 
66715963

G == 2
----------------------------------------------------------------
Certificate of primality for:
19550639734462621430325731591027

A == 
4851595597739856136987139

B == 
2014867

G == 2
----------------------------------------------------------------
Certificate of primality for:
10409036141344317165691858509923818734539

A == 
19550639734462621430325731591027

B == 
266207047

G == 2
----------------------------------------------------------------
Certificate of primality for:
1049829549988285012736475602118094726647504414203

A == 
10409036141344317165691858509923818734539

B == 
50428759

G == 2
----------------------------------------------------------------
Certificate of primality for:
77194737385528288387712399596835459931920358844586615003

A == 
1049829549988285012736475602118094726647504414203

B == 
36765367

G == 2
----------------------------------------------------------------
Certificate of primality for:
35663756695365208574443215955488689578374232732893628896541201763

A == 
77194737385528288387712399596835459931920358844586615003

B == 
230998627

G == 2
----------------------------------------------------------------
Certificate of primality for:
16711831463502165169495622246023119698415848120292671294127567620396469803

A == 
35663756695365208574443215955488689578374232732893628896541201763

B == 
234297127

G == 2
----------------------------------------------------------------
Certificate of primality for:
6163534781560285962890718925972249753147470953579266394395432475622345597103528739

A == 
16711831463502165169495622246023119698415848120292671294127567620396469803

B == 
184406323

G == 2
----------------------------------------------------------------
Certificate of primality for:
814258256205243497704094951432575867360065658372158511036259934640748088306764553488803787

A == 
6163534781560285962890718925972249753147470953579266394395432475622345597103528739

B == 
66054487

G == 2
----------------------------------------------------------------
Certificate of primality for:
176469695533271657902814176811660357049007467856432383037590673407330246967781451723764079581998187

A == 
814258256205243497704094951432575867360065658372158511036259934640748088306764553488803787

B == 
108362239

G == 2
----------------------------------------------------------------
Certificate of primality for:
44924492859445516541759485198544012102424796403707253610035148063863073596051272171194806669756971406400419

A == 
176469695533271657902814176811660357049007467856432383037590673407330246967781451723764079581998187

B == 
127286707

G == 2
----------------------------------------------------------------
Certificate of primality for:
20600996927219343383225424320134474929609459588323857796871086845924186191561749519858600696159932468024710985371059

A == 
44924492859445516541759485198544012102424796403707253610035148063863073596051272171194806669756971406400419

B == 
229284691

G == 2
----------------------------------------------------------------
Certificate of primality for:
6295696427695493110141186605837397185848992307978456138112526915330347715236378041486547994708748840844217371233735072572979

A == 
20600996927219343383225424320134474929609459588323857796871086845924186191561749519858600696159932468024710985371059

B == 
152800771

G == 2
----------------------------------------------------------------
Certificate of primality for:
3104984078042317488749073016454213579257792635142218294052134804187631661145261015102617582090263808696699966840735333252107678792123

A == 
6295696427695493110141186605837397185848992307978456138112526915330347715236378041486547994708748840844217371233735072572979

B == 
246595759

G == 2
----------------------------------------------------------------
Certificate of primality for:
26405175827665701256325699315126705508919255051121452292124404943796947287968603975320562847910946802396632302209435206627913466015741799499

A == 
3104984078042317488749073016454213579257792635142218294052134804187631661145261015102617582090263808696699966840735333252107678792123

B == 
4252063

G == 2
----------------------------------------------------------------
Certificate of primality for:
11122146237908413610034600609460545703591095894418599759742741406628055069007082998134905595800236452010905900391505454890446585211975124558601770163

A == 
26405175827665701256325699315126705508919255051121452292124404943796947287968603975320562847910946802396632302209435206627913466015741799499

B == 
210605419

G == 2
----------------------------------------------------------------
Certificate of primality for:
1649861642047798890580354082088712649911849362201343649289384923147797960364736011515757482030049342943790127685185806092659832129486307035500638595572396187

A == 
11122146237908413610034600609460545703591095894418599759742741406628055069007082998134905595800236452010905900391505454890446585211975124558601770163

B == 
74170111

G == 2
----------------------------------------------------------------
Certificate of primality for:
857983367126266717607389719637086684134462613006415859877666235955788392464081914127715967940968197765042399904117392707518175220864852816390004264107201177394565363

A == 
1649861642047798890580354082088712649911849362201343649289384923147797960364736011515757482030049342943790127685185806092659832129486307035500638595572396187

B == 
260016763

G == 2
----------------------------------------------------------------
Certificate of primality for:
175995909353623703257072120479340610010337144085688850745292031336724691277374210929188442230237711063783727092685448718515661641054886101716698390145283196296702450566161283

A == 
857983367126266717607389719637086684134462613006415859877666235955788392464081914127715967940968197765042399904117392707518175220864852816390004264107201177394565363

B == 
102563707

G == 2
----------------------------------------------------------------
Certificate of primality for:
48486002551155667224487059713350447239190772068092630563272168418880661006593537218144160068395218642353495339720640699721703003648144463556291315694787862009052641640656933232794283

A == 
175995909353623703257072120479340610010337144085688850745292031336724691277374210929188442230237711063783727092685448718515661641054886101716698390145283196296702450566161283

B == 
137747527

G == 2
----------------------------------------------------------------
Certificate of primality for:
13156468011529105025061495011938518171328604045212410096476697450506055664012861932372156505805788068791146986282263016790631108386790291275939575123375304599622623328517354163964228279867403

A == 
48486002551155667224487059713350447239190772068092630563272168418880661006593537218144160068395218642353495339720640699721703003648144463556291315694787862009052641640656933232794283

B == 
135672847

G == 2
----------------------------------------------------------------
Certificate of primality for:
6355194692790533601105154341731997464407930009404822926832136060319955058388106456084549316415200519472481147942263916585428906582726749131479465958107142228236909665306781538860053107680830113869123

A == 
13156468011529105025061495011938518171328604045212410096476697450506055664012861932372156505805788068791146986282263016790631108386790291275939575123375304599622623328517354163964228279867403

B == 
241523587

G == 2
----------------------------------------------------------------
Certificate of primality for:
3157116676535430302794438027544146642863331358530722860333745617571010460905857862561870488000265751138954271040017454405707755458702044884023184574412221802502351503929935224995314581932097706874819348858083

A == 
6355194692790533601105154341731997464407930009404822926832136060319955058388106456084549316415200519472481147942263916585428906582726749131479465958107142228236909665306781538860053107680830113869123

B == 
248388667

G == 2
----------------------------------------------------------------
Certificate of primality for:
390533129219992506725320633489467713907837370444962163378727819939092929448752905310115311180032249230394348337568973177802874166228132778126338883671958897238722734394783244237133367055422297736215754829839364158067

A == 
3157116676535430302794438027544146642863331358530722860333745617571010460905857862561870488000265751138954271040017454405707755458702044884023184574412221802502351503929935224995314581932097706874819348858083

B == 
61849651

G == 2
----------------------------------------------------------------
Certificate of primality for:
48583654555070224891047847050732516652910250240135992225139515777200432486685999462997073444468380434359929499498804723793106565291183220444221080449740542884172281158126259373095216435009661050109711341419005972852770440739

A == 
390533129219992506725320633489467713907837370444962163378727819939092929448752905310115311180032249230394348337568973177802874166228132778126338883671958897238722734394783244237133367055422297736215754829839364158067

B == 
62201707

G == 2
----------------------------------------------------------------
Certificate of primality for:
25733035251905120039135866524384525138869748427727001128764704499071378939227862068500633813538831598776578372709963673670934388213622433800015759585470542686333039614931682098922935087822950084908715298627996115185849260703525317419

A == 
48583654555070224891047847050732516652910250240135992225139515777200432486685999462997073444468380434359929499498804723793106565291183220444221080449740542884172281158126259373095216435009661050109711341419005972852770440739

B == 
264832231

G == 2
----------------------------------------------------------------
Certificate of primality for:
2804594464939948901906623499531073917980499195397462605359913717827014360538186518540781517129548650937632008683280555602633122170458773895504894807182664540529077836857897972175530148107545939211339044386106111633510166695386323426241809387

A == 
25733035251905120039135866524384525138869748427727001128764704499071378939227862068500633813538831598776578372709963673670934388213622433800015759585470542686333039614931682098922935087822950084908715298627996115185849260703525317419

B == 
54494047

G == 2
----------------------------------------------------------------
Certificate of primality for:
738136612083433720096707308165797114449914259256979340471077690416567237592465306112484843530074782721390528773594351482384711900456440808251196845265132086486672447136822046628407467459921823150600138073268385534588238548865012638209515923513516547

A == 
2804594464939948901906623499531073917980499195397462605359913717827014360538186518540781517129548650937632008683280555602633122170458773895504894807182664540529077836857897972175530148107545939211339044386106111633510166695386323426241809387

B == 
131594179

G == 2
----------------------------------------------------------------
Certificate of primality for:
392847529056126766528615419937165193421166694172790666626558750047057558168124866940509180171236517681470100877687445134633784815352076138790217228749332398026714192707447855731679485746120589851992221508292976900578299504461333767437280988393026452846013683

A == 
738136612083433720096707308165797114449914259256979340471077690416567237592465306112484843530074782721390528773594351482384711900456440808251196845265132086486672447136822046628407467459921823150600138073268385534588238548865012638209515923513516547

B == 
266107603

G == 2
----------------------------------------------------------------
Certificate of primality for:
168459393231883505975876919268398655632763956627405508859662408056221544310200546265681845397346956580604208064328814319465940958080244889692368602591598503944015835190587740756859842792554282496742843600573336023639256008687581291233481455395123454655488735304365627

A == 
392847529056126766528615419937165193421166694172790666626558750047057558168124866940509180171236517681470100877687445134633784815352076138790217228749332398026714192707447855731679485746120589851992221508292976900578299504461333767437280988393026452846013683

B == 
214408111

G == 2
----------------------------------------------------------------
Certificate of primality for:
14865774288636941404884923981945833072113667565310054952177860608355263252462409554658728941191929400198053290113492910272458441655458514080123870132092365833472436407455910185221474386718838138135065780840839893113912689594815485706154461164071775481134379794909690501684643

A == 
168459393231883505975876919268398655632763956627405508859662408056221544310200546265681845397346956580604208064328814319465940958080244889692368602591598503944015835190587740756859842792554282496742843600573336023639256008687581291233481455395123454655488735304365627

B == 
44122723

G == 2
----------------------------------------------------------------
Certificate of primality for:
1213301773203241614897109856134894783021668292000023984098824423682568173639394290886185366993108292039068940333907505157813934962357206131450244004178619265868614859794316361031904412926604138893775068853175215502104744339658944443630407632290152772487455298652998368296998719996019

A == 
14865774288636941404884923981945833072113667565310054952177860608355263252462409554658728941191929400198053290113492910272458441655458514080123870132092365833472436407455910185221474386718838138135065780840839893113912689594815485706154461164071775481134379794909690501684643

B == 
40808563

G == 2
----------------------------------------------------------------
Certificate of primality for:
186935245989515158127969129347464851990429060640910951266513740972248428651109062997368144722015290092846666943896556191257222521203647606911446635194198213436423080005867489516421559330500722264446765608763224572386410155413161172707802334865729654109050873820610813855041667633843601286843

A == 
1213301773203241614897109856134894783021668292000023984098824423682568173639394290886185366993108292039068940333907505157813934962357206131450244004178619265868614859794316361031904412926604138893775068853175215502104744339658944443630407632290152772487455298652998368296998719996019

B == 
77035759

G == 2
----------------------------------------------------------------
Certificate of primality for:
83142661079751490510739960019112406284111408348732592580459037404394946037094409915127399165633756159385609671956087845517678367844901424617866988187132480585966721962585586730693443536100138246516868613250009028187662080828012497191775172228832247706080044971423654632146928165751885302331924491683

A == 
186935245989515158127969129347464851990429060640910951266513740972248428651109062997368144722015290092846666943896556191257222521203647606911446635194198213436423080005867489516421559330500722264446765608763224572386410155413161172707802334865729654109050873820610813855041667633843601286843

B == 
222383587

G == 2
----------------------------------------------------------------
Certificate of primality for:
3892354773803809855317742245039794448230625839512638747643814927766738642436392673485997449586432241626440927010641564064764336402368634186618250134234189066179771240232458249806850838490410473462391401438160528157981942499581634732706904411807195259620779379274017704050790865030808501633772117217899534443

A == 
83142661079751490510739960019112406284111408348732592580459037404394946037094409915127399165633756159385609671956087845517678367844901424617866988187132480585966721962585586730693443536100138246516868613250009028187662080828012497191775172228832247706080044971423654632146928165751885302331924491683

B == 
23407687

G == 2
----------------------------------------------------------------
Certificate of primality for:
1663606652988091811284014366560171522582683318514519379924950390627250155440313691226744227787921928894551755219495501365555370027257568506349958010457682898612082048959464465369892842603765280317696116552850664773291371490339084156052244256635115997453399761029567033971998617303988376172539172702246575225837054723

A == 
3892354773803809855317742245039794448230625839512638747643814927766738642436392673485997449586432241626440927010641564064764336402368634186618250134234189066179771240232458249806850838490410473462391401438160528157981942499581634732706904411807195259620779379274017704050790865030808501633772117217899534443

B == 
213701827

G == 2
----------------------------------------------------------------


Took 33057 ticks, 1048 bits
P == 1663606652988091811284014366560171522582683318514519379924950390627250155440313691226744227787921928894551755219495501365555370027257568506349958010457682898612082048959464465369892842603765280317696116552850664773291371490339084156052244256635115997453399761029567033971998617303988376172539172702246575225837054723
Q == 3892354773803809855317742245039794448230625839512638747643814927766738642436392673485997449586432241626440927010641564064764336402368634186618250134234189066179771240232458249806850838490410473462391401438160528157981942499581634732706904411807195259620779379274017704050790865030808501633772117217899534443
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Deleted libtommath/etc/prime.512.

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Enter # of bits: 
Enter number of bases to try (1 to 8):
Certificate of primality for:
85933926807634727

A == 
253758023

B == 
169322581

G == 5
----------------------------------------------------------------
Certificate of primality for:
23930198825086241462113799

A == 
85933926807634727

B == 
139236037

G == 11
----------------------------------------------------------------
Certificate of primality for:
6401844647261612602378676572510019

A == 
23930198825086241462113799

B == 
133760791

G == 2
----------------------------------------------------------------
Certificate of primality for:
269731366027728777712034888684015329354259

A == 
6401844647261612602378676572510019

B == 
21066691

G == 2
----------------------------------------------------------------
Certificate of primality for:
37942338209025571690075025099189467992329684223707

A == 
269731366027728777712034888684015329354259

B == 
70333567

G == 2
----------------------------------------------------------------
Certificate of primality for:
15306904714258982484473490774101705363308327436988160248323

A == 
37942338209025571690075025099189467992329684223707

B == 
201712723

G == 2
----------------------------------------------------------------
Certificate of primality for:
1616744757018513392810355191503853040357155275733333124624513530099

A == 
15306904714258982484473490774101705363308327436988160248323

B == 
52810963

G == 2
----------------------------------------------------------------
Certificate of primality for:
464222094814208047161771036072622485188658077940154689939306386289983787983

A == 
1616744757018513392810355191503853040357155275733333124624513530099

B == 
143566909

G == 5
----------------------------------------------------------------
Certificate of primality for:
187429931674053784626487560729643601208757374994177258429930699354770049369025096447

A == 
464222094814208047161771036072622485188658077940154689939306386289983787983

B == 
201875281

G == 5
----------------------------------------------------------------
Certificate of primality for:
100579220846502621074093727119851331775052664444339632682598589456666938521976625305832917563

A == 
187429931674053784626487560729643601208757374994177258429930699354770049369025096447

B == 
268311523

G == 2
----------------------------------------------------------------
Certificate of primality for:
1173616081309758475197022137833792133815753368965945885089720153370737965497134878651384030219765163

A == 
100579220846502621074093727119851331775052664444339632682598589456666938521976625305832917563

B == 
5834287

G == 2
----------------------------------------------------------------
Certificate of primality for:
191456913489905913185935197655672585713573070349044195411728114905691721186574907738081340754373032735283623

A == 
1173616081309758475197022137833792133815753368965945885089720153370737965497134878651384030219765163

B == 
81567097

G == 5
----------------------------------------------------------------
Certificate of primality for:
57856530489201750164178576399448868489243874083056587683743345599898489554401618943240901541005080049321706789987519

A == 
191456913489905913185935197655672585713573070349044195411728114905691721186574907738081340754373032735283623

B == 
151095433

G == 7
----------------------------------------------------------------
Certificate of primality for:
13790529750452576698109671710773784949185621244122040804792403407272729038377767162233653248852099545134831722512085881814803

A == 
57856530489201750164178576399448868489243874083056587683743345599898489554401618943240901541005080049321706789987519

B == 
119178679

G == 2
----------------------------------------------------------------
Certificate of primality for:
7075985989000817742677547821106534174334812111605018857703825637170140040509067704269696198231266351631132464035671858077052876058979

A == 
13790529750452576698109671710773784949185621244122040804792403407272729038377767162233653248852099545134831722512085881814803

B == 
256552363

G == 2
----------------------------------------------------------------
Certificate of primality for:
1227273006232588072907488910282307435921226646895131225407452056677899411162892829564455154080310937471747140942360789623819327234258162420463

A == 
7075985989000817742677547821106534174334812111605018857703825637170140040509067704269696198231266351631132464035671858077052876058979

B == 
86720989

G == 5
----------------------------------------------------------------
Certificate of primality for:
446764896913554613686067036908702877942872355053329937790398156069936255759889884246832779737114032666318220500106499161852193765380831330106375235763

A == 
1227273006232588072907488910282307435921226646895131225407452056677899411162892829564455154080310937471747140942360789623819327234258162420463

B == 
182015287

G == 2
----------------------------------------------------------------
Certificate of primality for:
5290203010849586596974953717018896543907195901082056939587768479377028575911127944611236020459652034082251335583308070846379514569838984811187823420951275243

A == 
446764896913554613686067036908702877942872355053329937790398156069936255759889884246832779737114032666318220500106499161852193765380831330106375235763

B == 
5920567

G == 2
----------------------------------------------------------------


Took 3454 ticks, 521 bits
P == 5290203010849586596974953717018896543907195901082056939587768479377028575911127944611236020459652034082251335583308070846379514569838984811187823420951275243
Q == 446764896913554613686067036908702877942872355053329937790398156069936255759889884246832779737114032666318220500106499161852193765380831330106375235763
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Deleted libtommath/etc/timer.asm.

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; x86 timer in NASM
;
; Tom St Denis, [email protected]
[bits 32]
[section .data]
time dd 0, 0

[section .text]

%ifdef USE_ELF
[global t_start]
t_start:
%else
[global _t_start]
_t_start:
%endif
   push edx
   push eax
   rdtsc
   mov [time+0],edx
   mov [time+4],eax
   pop eax
   pop edx
   ret
   
%ifdef USE_ELF
[global t_read]
t_read:
%else
[global _t_read]
_t_read:
%endif
   rdtsc
   sub eax,[time+4]
   sbb edx,[time+0]
   ret
   
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Deleted libtommath/etc/tune.c.

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/* Tune the Karatsuba parameters
 *
 * 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

   // Microsoft and Intel Windows compilers
   #elif defined _M_IX86
     __asm rdtsc
   #elif defined _M_AMD64
     return __rdtsc ();
   #elif defined _M_IA64
     #if defined __INTEL_COMPILER
       #include <ia64intrin.h>
     #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);
extern ulong64 t_read(void);
#endif

ulong64 time_mult(int size, int s)
{
  unsigned long     x;
  mp_int  a, b, c;
  ulong64 t1;

  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++) {
      mp_mul(&a,&b,&c);
  }
  t1 = t_read();
  mp_clear (&a);
  mp_clear (&b);
  mp_clear (&c);
  return t1;
}

ulong64 time_sqr(int size, int s)
{
  unsigned long     x;
  mp_int  a, b;
  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++) {
      mp_sqr(&a,&b);
  }
  t1 = t_read();
  mp_clear (&a);
  mp_clear (&b);
  return t1;
}

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;
}

/* $Source$ */
/* $Revision$ */
/* $Date$ */
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Deleted libtommath/gen.pl.

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#!/usr/bin/perl -w
#
# Generates a "single file" you can use to quickly
# add the whole source without any makefile troubles
#
use strict;

open( OUT, ">mpi.c" ) or die "Couldn't open mpi.c for writing: $!";
foreach my $filename (glob "bn*.c") {
   open( SRC, "<$filename" ) or die "Couldn't open $filename for reading: $!";
   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');
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Deleted libtommath/logs/README.

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To use the pretty graphs you have to first build/run the ltmtest from the root directory of the package.  
Todo this type 

make timing ; ltmtest

in the root.  It will run for a while [about ten minutes on most PCs] and produce a series of .log files in logs/.

After doing that run "gnuplot graphs.dem" to make the PNGs.  If you managed todo that all so far just open index.html to view
them all :-)

Have fun

Tom
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Deleted libtommath/logs/add.log.

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480        87
960       111
1440       135
1920       159
2400       200
2880       224
3360       248
3840       272
4320       296
4800       320
5280       344
5760       368
6240       392
6720       416
7200       440
7680       464
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Deleted libtommath/logs/addsub.png.

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Deleted libtommath/logs/expt.log.

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513   1435869
769   3544970
1025   7791638
2049  46902238
2561  85334899
3073 141451412
4097 308770310
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Deleted libtommath/logs/expt.png.

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Deleted libtommath/logs/expt_2k.log.

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607   2109225
1279  10148314
2203  34126877
3217  82716424
4253 161569606
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Deleted libtommath/logs/expt_2kl.log.

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1024   7705271
2048  34286851
4096 165207491
521   1618631
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Deleted libtommath/logs/expt_dr.log.

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532   1928550
784   3763908
1036   7564221
1540  16566059
2072  32283784
3080  79851565
4116 157843530
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Deleted libtommath/logs/graphs.dem.

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set terminal png
set size 1.75
set ylabel "Cycles per Operation"
set xlabel "Operand size (bits)"

set output "addsub.png"
plot 'add.log' smooth bezier title "Addition", 'sub.log' smooth bezier title "Subtraction"

set output "mult.png"
plot 'sqr.log' smooth bezier title "Squaring (without Karatsuba)", 'sqr_kara.log' smooth bezier title "Squaring (Karatsuba)", 'mult.log' smooth bezier title "Multiplication (without Karatsuba)", 'mult_kara.log' smooth bezier title "Multiplication (Karatsuba)"

set output "expt.png"
plot 'expt.log' smooth bezier title "Exptmod (Montgomery)", 'expt_dr.log' smooth bezier title "Exptmod (Dimminished Radix)", 'expt_2k.log' smooth bezier title "Exptmod (2k Reduction)"

set output "invmod.png"
plot 'invmod.log' smooth bezier title "Modular Inverse"

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Deleted libtommath/logs/index.html.

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<html>
<head>
<title>LibTomMath Log Plots</title>
</head>
<body>

<h1>Addition and Subtraction</h1>
<center><img src=addsub.png></center>
<hr>

<h1>Multipliers</h1>
<center><img src=mult.png></center>
<hr>

<h1>Exptmod</h1>
<center><img src=expt.png></center>
<hr>

<h1>Modular Inverse</h1>
<center><img src=invmod.png></center>
<hr>

</body>
</html>
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Deleted libtommath/logs/mult.log.

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271       555
390       855
508      1161
631      1605
749      2117
871      2687
991      3329
1108      4084
1231      4786
1351      5624
1470      6392
1586      7364
1710      8218
1830      9255
1951     10217
2067     11461
2191     12463
2308     13677
2430     14800
2551     16232
2671     17460
2791     18899
2902     20247
3028     21902
3151     23240
3267     24927
3391     26441
3511     28277
3631     29838
3749     31751
3869     33673
3989     35431
4111     37518
4231     39426
4349     41504
4471     43567
4591     45786
4711     47876
4831     50299
4951     52427
5071     54785
5189     57241
5307     59730
5431     62194
5551     64761
5670     67322
5789     70073
5907     72663
6030     75437
6151     78242
6268     81202
6389     83948
6509     86985
6631     89903
6747     93184
6869     96044
6991     99286
7109    102395
7229    105917
7351    108940
7470    112490
7589    115702
7711    119508
7831    122632
7951    126410
8071    129808
8190    133895
8311    137146
8431    141218
8549    144732
8667    149131
8790    152462
8911    156754
9030    160479
9149    165138
9271    168601
9391    173185
9511    176988
9627    181976
9751    185539
9870    190388
9991    194335
10110    199605
10228    203298
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Deleted libtommath/logs/mult.png.

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Deleted libtommath/logs/mult_kara.log.

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271       560
391       870
511      1159
631      1605
750      2111
871      2737
991      3361
1111      4054
1231      4778
1351      5600
1471      6404
1591      7323
1710      8255
1831      9239
1948     10257
2070     11397
2190     12531
2308     13665
2429     14870
2550     16175
2671     17539
2787     18879
2911     20350
3031     21807
3150     23415
3270     24897
3388     26567
3511     28205
3627     30076
3751     31744
3869     33657
3991     35425
4111     37522
4229     39363
4351     41503
4470     43491
4590     45827
4711     47795
4828     50166
4951     52318
5070     54911
5191     57036
5308     58237
5431     60248
5551     62678
5671     64786
5791     67294
5908     69343
6031     71607
6151     74166
6271     76590
6391     78734
6511     81175
6631     83742
6750     86403
6868     88873
6990     91150
7110     94211
7228     96922
7351     99445
7469    102216
7589    104968
7711    108113
7827    110758
7950    113714
8071    116511
8186    119643
8310    122679
8425    125581
8551    128715
8669    131778
8788    135116
8910    138138
9031    141628
9148    144754
9268    148367
9391    151551
9511    155033
9631    158652
9751    162125
9871    165248
9988    168627
10111    172427
10231    176412
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265       562
389       882
509      1207
631      1572
750      1990
859      2433
991      2894
1109      3555
1230      4228
1350      5018
1471      5805
1591      6579
1709      7415
1829      8329
1949      9225
2071     10139
2188     11239
2309     12178
2431     13212
2551     14294
2671     15551
2791     16512
2911     17718
3030     18876
3150     20259
3270     21374
3391     22650
3511     23948
3631     25493
3750     26756
3870     28225
3989     29705
4110     31409
4230     32834
4351     34327
4471     35818
4591     37636
4711     39228
4830     40868
4949     42393
5070     44541
5191     46269
5310     48162
5429     49728
5548     51985
5671     53948
5791     55885
5910     57584
6031     60082
6150     62239
6270     64309
6390     66014
6511     68766
6631     71012
6750     73172
6871     74952
6991     77909
7111     80371
7231     82666
7351     84531
7469     87698
7589     90318
7711    225384
7830    232428
7950    240009
8070    246522
8190    253662
8310    260961
8431    269253
8549    275743
8671    283769
8789    290811
8911    300034
9030    306873
9149    315085
9270    323944
9390    332390
9508    337519
9631    348986
9749    356904
9871    367013
9989    373831
10108    381033
10230    393475
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Deleted libtommath/logs/sqr_kara.log.

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271       560
388       878
511      1179
629      1625
751      1988
871      2423
989      2896
1111      3561
1231      4209
1350      5015
1470      5804
1591      6556
1709      7420
1831      8263
1951      9173
2070     10153
2191     11229
2310     12167
2431     13211
2550     14309
2671     15524
2788     16525
2910     17712
3028     18822
3148     20220
3271     21343
3391     22652
3511     23944
3630     25485
3750     26778
3868     28201
3990     29653
4111     31393
4225     32841
4350     34328
4471     35786
4590     37652
4711     39245
4830     40876
4951     42433
5068     44547
5191     46321
5311     48140
5430     49727
5550     52034
5671     53954
5791     55921
5908     57597
6031     60084
6148     62226
6270     64295
6390     66045
6511     68779
6629     71003
6751     73169
6871     74992
6991     77895
7110     80376
7231     82628
7351     84468
7470     87664
7591     90284
7711     91352
7828     93995
7950     96276
8071     98691
8190    101256
8308    103631
8431    105222
8550    108343
8671    110281
8787    112764
8911    115397
9031    117690
9151    120266
9271    122715
9391    124624
9510    127937
9630    130313
9750    132914
9871    136129
9991    138517
10108    141525
10231    144225
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Deleted libtommath/logs/sub.log.

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480        94
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1440       140
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3360       253
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Deleted libtommath/mess.sh.

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#!/bin/bash
if cvs log $1 >/dev/null 2>/dev/null; then exit 0; else echo "$1 shouldn't be here" ; exit 1; fi


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Deleted libtommath/mtest/logtab.h.

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const float s_logv_2[] = {
   0.000000000, 0.000000000, 1.000000000, 0.630929754, 	/*  0  1  2  3 */
   0.500000000, 0.430676558, 0.386852807, 0.356207187, 	/*  4  5  6  7 */
   0.333333333, 0.315464877, 0.301029996, 0.289064826, 	/*  8  9 10 11 */
   0.278942946, 0.270238154, 0.262649535, 0.255958025, 	/* 12 13 14 15 */
   0.250000000, 0.244650542, 0.239812467, 0.235408913, 	/* 16 17 18 19 */
   0.231378213, 0.227670249, 0.224243824, 0.221064729, 	/* 20 21 22 23 */
   0.218104292, 0.215338279, 0.212746054, 0.210309918, 	/* 24 25 26 27 */
   0.208014598, 0.205846832, 0.203795047, 0.201849087, 	/* 28 29 30 31 */
   0.200000000, 0.198239863, 0.196561632, 0.194959022, 	/* 32 33 34 35 */
   0.193426404, 0.191958720, 0.190551412, 0.189200360, 	/* 36 37 38 39 */
   0.187901825, 0.186652411, 0.185449023, 0.184288833, 	/* 40 41 42 43 */
   0.183169251, 0.182087900, 0.181042597, 0.180031327, 	/* 44 45 46 47 */
   0.179052232, 0.178103594, 0.177183820, 0.176291434, 	/* 48 49 50 51 */
   0.175425064, 0.174583430, 0.173765343, 0.172969690, 	/* 52 53 54 55 */
   0.172195434, 0.171441601, 0.170707280, 0.169991616, 	/* 56 57 58 59 */
   0.169293808, 0.168613099, 0.167948779, 0.167300179, 	/* 60 61 62 63 */
   0.166666667
};


/* $Source$ */
/* $Revision$ */
/* $Date$ */
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Deleted libtommath/mtest/mpi-config.h.

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/* Default configuration for MPI library */
/* $Id$ */

#ifndef MPI_CONFIG_H_
#define MPI_CONFIG_H_

/*
  For boolean options, 
  0 = no
  1 = yes

  Other options are documented individually.

 */

#ifndef MP_IOFUNC
#define MP_IOFUNC     0  /* include mp_print() ?                */
#endif

#ifndef MP_MODARITH
#define MP_MODARITH   1  /* include modular arithmetic ?        */
#endif

#ifndef MP_NUMTH
#define MP_NUMTH      1  /* include number theoretic functions? */
#endif

#ifndef MP_LOGTAB
#define MP_LOGTAB     1  /* use table of logs instead of log()? */
#endif

#ifndef MP_MEMSET
#define MP_MEMSET     1  /* use memset() to zero buffers?       */
#endif

#ifndef MP_MEMCPY
#define MP_MEMCPY     1  /* use memcpy() to copy buffers?       */
#endif

#ifndef MP_CRYPTO
#define MP_CRYPTO     1  /* erase memory on free?               */
#endif

#ifndef MP_ARGCHK
/*
  0 = no parameter checks
  1 = runtime checks, continue execution and return an error to caller
  2 = assertions; dump core on parameter errors
 */
#define MP_ARGCHK     2  /* how to check input arguments        */
#endif

#ifndef MP_DEBUG
#define MP_DEBUG      0  /* print diagnostic output?            */
#endif

#ifndef MP_DEFPREC
#define MP_DEFPREC    64 /* default precision, in digits        */
#endif

#ifndef MP_MACRO
#define MP_MACRO      1  /* use macros for frequent calls?      */
#endif

#ifndef MP_SQUARE
#define MP_SQUARE     1  /* use separate squaring code?         */
#endif

#ifndef MP_PTAB_SIZE
/*
  When building mpprime.c, we build in a table of small prime
  values to use for primality testing.  The more you include,
  the more space they take up.  See primes.c for the possible
  values (currently 16, 32, 64, 128, 256, and 6542)
 */
#define MP_PTAB_SIZE  128  /* how many built-in primes?         */
#endif

#ifndef MP_COMPAT_MACROS
#define MP_COMPAT_MACROS 1   /* define compatibility macros?    */
#endif

#endif /* ifndef MPI_CONFIG_H_ */


/* crc==3287762869, version==2, Sat Feb 02 06:43:53 2002 */

/* $Source$ */
/* $Revision$ */
/* $Date$ */
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/* Type definitions generated by 'types.pl' */
typedef char               mp_sign;
typedef unsigned short     mp_digit;  /* 2 byte type */
typedef unsigned int       mp_word;   /* 4 byte type */
typedef unsigned int       mp_size;
typedef int                mp_err;

#define MP_DIGIT_BIT       (CHAR_BIT*sizeof(mp_digit))
#define MP_DIGIT_MAX       USHRT_MAX
#define MP_WORD_BIT        (CHAR_BIT*sizeof(mp_word))
#define MP_WORD_MAX        UINT_MAX

#define MP_DIGIT_SIZE      2
#define DIGIT_FMT          "%04X"
#define RADIX              (MP_DIGIT_MAX+1)


/* $Source$ */
/* $Revision$ */
/* $Date$ */
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/*
    mpi.c

    by Michael J. Fromberger <[email protected]>
    Copyright (C) 1998 Michael J. Fromberger, All Rights Reserved

    Arbitrary precision integer arithmetic library

    $Id$
 */

#include "mpi.h"
#include <stdlib.h>
#include <string.h>
#include <ctype.h>

#if MP_DEBUG
#include <stdio.h>

#define DIAG(T,V) {fprintf(stderr,T);mp_print(V,stderr);fputc('\n',stderr);}
#else
#define DIAG(T,V)
#endif

/*
   If MP_LOGTAB is not defined, use the math library to compute the
   logarithms on the fly.  Otherwise, use the static table below.
   Pick which works best for your system.
 */
#if MP_LOGTAB

/* {{{ s_logv_2[] - log table for 2 in various bases */

/*
  A table of the logs of 2 for various bases (the 0 and 1 entries of
  this table are meaningless and should not be referenced).

  This table is used to compute output lengths for the mp_toradix()
  function.  Since a number n in radix r takes up about log_r(n)
  digits, we estimate the output size by taking the least integer
  greater than log_r(n), where:

  log_r(n) = log_2(n) * log_r(2)

  This table, therefore, is a table of log_r(2) for 2 <= r <= 36,
  which are the output bases supported.
 */

#include "logtab.h"

/* }}} */
#define LOG_V_2(R)  s_logv_2[(R)]

#else

#include <math.h>
#define LOG_V_2(R)  (log(2.0)/log(R))

#endif

/* Default precision for newly created mp_int's      */
static unsigned int s_mp_defprec = MP_DEFPREC;

/* {{{ Digit arithmetic macros */

/*
  When adding and multiplying digits, the results can be larger than
  can be contained in an mp_digit.  Thus, an mp_word is used.  These
  macros mask off the upper and lower digits of the mp_word (the
  mp_word may be more than 2 mp_digits wide, but we only concern
  ourselves with the low-order 2 mp_digits)

  If your mp_word DOES have more than 2 mp_digits, you need to
  uncomment the first line, and comment out the second.
 */

/* #define  CARRYOUT(W)  (((W)>>DIGIT_BIT)&MP_DIGIT_MAX) */
#define  CARRYOUT(W)  ((W)>>DIGIT_BIT)
#define  ACCUM(W)     ((W)&MP_DIGIT_MAX)

/* }}} */

/* {{{ Comparison constants */

#define  MP_LT       -1
#define  MP_EQ        0
#define  MP_GT        1

/* }}} */

/* {{{ Constant strings */

/* Constant strings returned by mp_strerror() */
static const char *const mp_err_string[] = {
  "unknown result code",     /* say what?            */
  "boolean true",            /* MP_OKAY, MP_YES      */
  "boolean false",           /* MP_NO                */
  "out of memory",           /* MP_MEM               */
  "argument out of range",   /* MP_RANGE             */
  "invalid input parameter", /* MP_BADARG            */
  "result is undefined"      /* MP_UNDEF             */
};

/* Value to digit maps for radix conversion   */

/* s_dmap_1 - standard digits and letters */
static const char *s_dmap_1 =
  "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";

#if 0
/* s_dmap_2 - base64 ordering for digits  */
static const char *s_dmap_2 =
  "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
#endif

/* }}} */

/* {{{ Static function declarations */

/*
   If MP_MACRO is false, these will be defined as actual functions;
   otherwise, suitable macro definitions will be used.  This works
   around the fact that ANSI C89 doesn't support an 'inline' keyword
   (although I hear C9x will ... about bloody time).  At present, the
   macro definitions are identical to the function bodies, but they'll
   expand in place, instead of generating a function call.

   I chose these particular functions to be made into macros because
   some profiling showed they are called a lot on a typical workload,
   and yet they are primarily housekeeping.
 */
#if MP_MACRO == 0
 void     s_mp_setz(mp_digit *dp, mp_size count); /* zero digits           */
 void     s_mp_copy(mp_digit *sp, mp_digit *dp, mp_size count); /* copy    */
 void    *s_mp_alloc(size_t nb, size_t ni);       /* general allocator     */
 void     s_mp_free(void *ptr);                   /* general free function */
#else

 /* Even if these are defined as macros, we need to respect the settings
    of the MP_MEMSET and MP_MEMCPY configuration options...
  */
 #if MP_MEMSET == 0
  #define  s_mp_setz(dp, count) \
       {int ix;for(ix=0;ix<(count);ix++)(dp)[ix]=0;}
 #else
  #define  s_mp_setz(dp, count) memset(dp, 0, (count) * sizeof(mp_digit))
 #endif /* MP_MEMSET */

 #if MP_MEMCPY == 0
  #define  s_mp_copy(sp, dp, count) \
       {int ix;for(ix=0;ix<(count);ix++)(dp)[ix]=(sp)[ix];}
 #else
  #define  s_mp_copy(sp, dp, count) memcpy(dp, sp, (count) * sizeof(mp_digit))
 #endif /* MP_MEMCPY */

 #define  s_mp_alloc(nb, ni)  calloc(nb, ni)
 #define  s_mp_free(ptr) {if(ptr) free(ptr);}
#endif /* MP_MACRO */

mp_err   s_mp_grow(mp_int *mp, mp_size min);   /* increase allocated size */
mp_err   s_mp_pad(mp_int *mp, mp_size min);    /* left pad with zeroes    */

void     s_mp_clamp(mp_int *mp);               /* clip leading zeroes     */

void     s_mp_exch(mp_int *a, mp_int *b);      /* swap a and b in place   */

mp_err   s_mp_lshd(mp_int *mp, mp_size p);     /* left-shift by p digits  */
void     s_mp_rshd(mp_int *mp, mp_size p);     /* right-shift by p digits */
void     s_mp_div_2d(mp_int *mp, mp_digit d);  /* divide by 2^d in place  */
void     s_mp_mod_2d(mp_int *mp, mp_digit d);  /* modulo 2^d in place     */
mp_err   s_mp_mul_2d(mp_int *mp, mp_digit d);  /* multiply by 2^d in place*/
void     s_mp_div_2(mp_int *mp);               /* divide by 2 in place    */
mp_err   s_mp_mul_2(mp_int *mp);               /* multiply by 2 in place  */
mp_digit s_mp_norm(mp_int *a, mp_int *b);      /* normalize for division  */
mp_err   s_mp_add_d(mp_int *mp, mp_digit d);   /* unsigned digit addition */
mp_err   s_mp_sub_d(mp_int *mp, mp_digit d);   /* unsigned digit subtract */
mp_err   s_mp_mul_d(mp_int *mp, mp_digit d);   /* unsigned digit multiply */
mp_err   s_mp_div_d(mp_int *mp, mp_digit d, mp_digit *r);
		                               /* unsigned digit divide   */
mp_err   s_mp_reduce(mp_int *x, mp_int *m, mp_int *mu);
                                               /* Barrett reduction       */
mp_err   s_mp_add(mp_int *a, mp_int *b);       /* magnitude addition      */
mp_err   s_mp_sub(mp_int *a, mp_int *b);       /* magnitude subtract      */
mp_err   s_mp_mul(mp_int *a, mp_int *b);       /* magnitude multiply      */
#if 0
void     s_mp_kmul(mp_digit *a, mp_digit *b, mp_digit *out, mp_size len);
                                               /* multiply buffers in place */
#endif
#if MP_SQUARE
mp_err   s_mp_sqr(mp_int *a);                  /* magnitude square        */
#else
#define  s_mp_sqr(a) s_mp_mul(a, a)
#endif
mp_err   s_mp_div(mp_int *a, mp_int *b);       /* magnitude divide        */
mp_err   s_mp_2expt(mp_int *a, mp_digit k);    /* a = 2^k                 */
int      s_mp_cmp(mp_int *a, mp_int *b);       /* magnitude comparison    */
int      s_mp_cmp_d(mp_int *a, mp_digit d);    /* magnitude digit compare */
int      s_mp_ispow2(mp_int *v);               /* is v a power of 2?      */
int      s_mp_ispow2d(mp_digit d);             /* is d a power of 2?      */

int      s_mp_tovalue(char ch, int r);          /* convert ch to value    */
char     s_mp_todigit(int val, int r, int low); /* convert val to digit   */
int      s_mp_outlen(int bits, int r);          /* output length in bytes */

/* }}} */

/* {{{ Default precision manipulation */

unsigned int mp_get_prec(void)
{
  return s_mp_defprec;

} /* end mp_get_prec() */

void         mp_set_prec(unsigned int prec)
{
  if(prec == 0)
    s_mp_defprec = MP_DEFPREC;
  else
    s_mp_defprec = prec;

} /* end mp_set_prec() */

/* }}} */

/*------------------------------------------------------------------------*/
/* {{{ mp_init(mp) */

/*
  mp_init(mp)

  Initialize a new zero-valued mp_int.  Returns MP_OKAY if successful,
  MP_MEM if memory could not be allocated for the structure.
 */

mp_err mp_init(mp_int *mp)
{
  return mp_init_size(mp, s_mp_defprec);

} /* end mp_init() */

/* }}} */

/* {{{ mp_init_array(mp[], count) */

mp_err mp_init_array(mp_int mp[], int count)
{
  mp_err  res;
  int     pos;

  ARGCHK(mp !=NULL && count > 0, MP_BADARG);

  for(pos = 0; pos < count; ++pos) {
    if((res = mp_init(&mp[pos])) != MP_OKAY)
      goto CLEANUP;
  }

  return MP_OKAY;

 CLEANUP:
  while(--pos >= 0)
    mp_clear(&mp[pos]);

  return res;

} /* end mp_init_array() */

/* }}} */

/* {{{ mp_init_size(mp, prec) */

/*
  mp_init_size(mp, prec)

  Initialize a new zero-valued mp_int with at least the given
  precision; returns MP_OKAY if successful, or MP_MEM if memory could
  not be allocated for the structure.
 */

mp_err mp_init_size(mp_int *mp, mp_size prec)
{
  ARGCHK(mp != NULL && prec > 0, MP_BADARG);

  if((DIGITS(mp) = s_mp_alloc(prec, sizeof(mp_digit))) == NULL)
    return MP_MEM;

  SIGN(mp) = MP_ZPOS;
  USED(mp) = 1;
  ALLOC(mp) = prec;

  return MP_OKAY;

} /* end mp_init_size() */

/* }}} */

/* {{{ mp_init_copy(mp, from) */

/*
  mp_init_copy(mp, from)

  Initialize mp as an exact copy of from.  Returns MP_OKAY if
  successful, MP_MEM if memory could not be allocated for the new
  structure.
 */

mp_err mp_init_copy(mp_int *mp, mp_int *from)
{
  ARGCHK(mp != NULL && from != NULL, MP_BADARG);

  if(mp == from)
    return MP_OKAY;

  if((DIGITS(mp) = s_mp_alloc(USED(from), sizeof(mp_digit))) == NULL)
    return MP_MEM;

  s_mp_copy(DIGITS(from), DIGITS(mp), USED(from));
  USED(mp) = USED(from);
  ALLOC(mp) = USED(from);
  SIGN(mp) = SIGN(from);

  return MP_OKAY;

} /* end mp_init_copy() */

/* }}} */

/* {{{ mp_copy(from, to) */

/*
  mp_copy(from, to)

  Copies the mp_int 'from' to the mp_int 'to'.  It is presumed that
  'to' has already been initialized (if not, use mp_init_copy()
  instead). If 'from' and 'to' are identical, nothing happens.
 */

mp_err mp_copy(mp_int *from, mp_int *to)
{
  ARGCHK(from != NULL && to != NULL, MP_BADARG);

  if(from == to)
    return MP_OKAY;

  { /* copy */
    mp_digit   *tmp;

    /*
      If the allocated buffer in 'to' already has enough space to hold
      all the used digits of 'from', we'll re-use it to avoid hitting
      the memory allocater more than necessary; otherwise, we'd have
      to grow anyway, so we just allocate a hunk and make the copy as
      usual
     */
    if(ALLOC(to) >= USED(from)) {
      s_mp_setz(DIGITS(to) + USED(from), ALLOC(to) - USED(from));
      s_mp_copy(DIGITS(from), DIGITS(to), USED(from));

    } else {
      if((tmp = s_mp_alloc(USED(from), sizeof(mp_digit))) == NULL)
	return MP_MEM;

      s_mp_copy(DIGITS(from), tmp, USED(from));

      if(DIGITS(to) != NULL) {
#if MP_CRYPTO
	s_mp_setz(DIGITS(to), ALLOC(to));
#endif
	s_mp_free(DIGITS(to));
      }

      DIGITS(to) = tmp;
      ALLOC(to) = USED(from);
    }

    /* Copy the precision and sign from the original */
    USED(to) = USED(from);
    SIGN(to) = SIGN(from);
  } /* end copy */

  return MP_OKAY;

} /* end mp_copy() */

/* }}} */

/* {{{ mp_exch(mp1, mp2) */

/*
  mp_exch(mp1, mp2)

  Exchange mp1 and mp2 without allocating any intermediate memory
  (well, unless you count the stack space needed for this call and the
  locals it creates...).  This cannot fail.
 */

void mp_exch(mp_int *mp1, mp_int *mp2)
{
#if MP_ARGCHK == 2
  assert(mp1 != NULL && mp2 != NULL);
#else
  if(mp1 == NULL || mp2 == NULL)
    return;
#endif

  s_mp_exch(mp1, mp2);

} /* end mp_exch() */

/* }}} */

/* {{{ mp_clear(mp) */

/*
  mp_clear(mp)

  Release the storage used by an mp_int, and void its fields so that
  if someone calls mp_clear() again for the same int later, we won't
  get tollchocked.
 */

void   mp_clear(mp_int *mp)
{
  if(mp == NULL)
    return;

  if(DIGITS(mp) != NULL) {
#if MP_CRYPTO
    s_mp_setz(DIGITS(mp), ALLOC(mp));
#endif
    s_mp_free(DIGITS(mp));
    DIGITS(mp) = NULL;
  }

  USED(mp) = 0;
  ALLOC(mp) = 0;

} /* end mp_clear() */

/* }}} */

/* {{{ mp_clear_array(mp[], count) */

void   mp_clear_array(mp_int mp[], int count)
{
  ARGCHK(mp != NULL && count > 0, MP_BADARG);

  while(--count >= 0)
    mp_clear(&mp[count]);

} /* end mp_clear_array() */

/* }}} */

/* {{{ mp_zero(mp) */

/*
  mp_zero(mp)

  Set mp to zero.  Does not change the allocated size of the structure,
  and therefore cannot fail (except on a bad argument, which we ignore)
 */
void   mp_zero(mp_int *mp)
{
  if(mp == NULL)
    return;

  s_mp_setz(DIGITS(mp), ALLOC(mp));
  USED(mp) = 1;
  SIGN(mp) = MP_ZPOS;

} /* end mp_zero() */

/* }}} */

/* {{{ mp_set(mp, d) */

void   mp_set(mp_int *mp, mp_digit d)
{
  if(mp == NULL)
    return;

  mp_zero(mp);
  DIGIT(mp, 0) = d;

} /* end mp_set() */

/* }}} */

/* {{{ mp_set_int(mp, z) */

mp_err mp_set_int(mp_int *mp, long z)
{
  int            ix;
  unsigned long  v = abs(z);
  mp_err         res;

  ARGCHK(mp != NULL, MP_BADARG);

  mp_zero(mp);
  if(z == 0)
    return MP_OKAY;  /* shortcut for zero */

  for(ix = sizeof(long) - 1; ix >= 0; ix--) {

    if((res = s_mp_mul_2d(mp, CHAR_BIT)) != MP_OKAY)
      return res;

    res = s_mp_add_d(mp,
		     (mp_digit)((v >> (ix * CHAR_BIT)) & UCHAR_MAX));
    if(res != MP_OKAY)
      return res;

  }

  if(z < 0)
    SIGN(mp) = MP_NEG;

  return MP_OKAY;

} /* end mp_set_int() */

/* }}} */

/*------------------------------------------------------------------------*/
/* {{{ Digit arithmetic */

/* {{{ mp_add_d(a, d, b) */

/*
  mp_add_d(a, d, b)

  Compute the sum b = a + d, for a single digit d.  Respects the sign of
  its primary addend (single digits are unsigned anyway).
 */

mp_err mp_add_d(mp_int *a, mp_digit d, mp_int *b)
{
  mp_err   res = MP_OKAY;

  ARGCHK(a != NULL && b != NULL, MP_BADARG);

  if((res = mp_copy(a, b)) != MP_OKAY)
    return res;

  if(SIGN(b) == MP_ZPOS) {
    res = s_mp_add_d(b, d);
  } else if(s_mp_cmp_d(b, d) >= 0) {
    res = s_mp_sub_d(b, d);
  } else {
    SIGN(b) = MP_ZPOS;

    DIGIT(b, 0) = d - DIGIT(b, 0);
  }

  return res;

} /* end mp_add_d() */

/* }}} */

/* {{{ mp_sub_d(a, d, b) */

/*
  mp_sub_d(a, d, b)

  Compute the difference b = a - d, for a single digit d.  Respects the
  sign of its subtrahend (single digits are unsigned anyway).
 */

mp_err mp_sub_d(mp_int *a, mp_digit d, mp_int *b)
{
  mp_err   res;

  ARGCHK(a != NULL && b != NULL, MP_BADARG);

  if((res = mp_copy(a, b)) != MP_OKAY)
    return res;

  if(SIGN(b) == MP_NEG) {
    if((res = s_mp_add_d(b, d)) != MP_OKAY)
      return res;

  } else if(s_mp_cmp_d(b, d) >= 0) {
    if((res = s_mp_sub_d(b, d)) != MP_OKAY)
      return res;

  } else {
    mp_neg(b, b);

    DIGIT(b, 0) = d - DIGIT(b, 0);
    SIGN(b) = MP_NEG;
  }

  if(s_mp_cmp_d(b, 0) == 0)
    SIGN(b) = MP_ZPOS;

  return MP_OKAY;

} /* end mp_sub_d() */

/* }}} */

/* {{{ mp_mul_d(a, d, b) */

/*
  mp_mul_d(a, d, b)

  Compute the product b = a * d, for a single digit d.  Respects the sign
  of its multiplicand (single digits are unsigned anyway)
 */

mp_err mp_mul_d(mp_int *a, mp_digit d, mp_int *b)
{
  mp_err  res;

  ARGCHK(a != NULL && b != NULL, MP_BADARG);

  if(d == 0) {
    mp_zero(b);
    return MP_OKAY;
  }

  if((res = mp_copy(a, b)) != MP_OKAY)
    return res;

  res = s_mp_mul_d(b, d);

  return res;

} /* end mp_mul_d() */

/* }}} */

/* {{{ mp_mul_2(a, c) */

mp_err mp_mul_2(mp_int *a, mp_int *c)
{
  mp_err  res;

  ARGCHK(a != NULL && c != NULL, MP_BADARG);

  if((res = mp_copy(a, c)) != MP_OKAY)
    return res;

  return s_mp_mul_2(c);

} /* end mp_mul_2() */

/* }}} */

/* {{{ mp_div_d(a, d, q, r) */

/*
  mp_div_d(a, d, q, r)

  Compute the quotient q = a / d and remainder r = a mod d, for a
  single digit d.  Respects the sign of its divisor (single digits are
  unsigned anyway).
 */

mp_err mp_div_d(mp_int *a, mp_digit d, mp_int *q, mp_digit *r)
{
  mp_err   res;
  mp_digit rem;
  int      pow;

  ARGCHK(a != NULL, MP_BADARG);

  if(d == 0)
    return MP_RANGE;

  /* Shortcut for powers of two ... */
  if((pow = s_mp_ispow2d(d)) >= 0) {
    mp_digit  mask;

    mask = (1 << pow) - 1;
    rem = DIGIT(a, 0) & mask;

    if(q) {
      mp_copy(a, q);
      s_mp_div_2d(q, pow);
    }

    if(r)
      *r = rem;

    return MP_OKAY;
  }

  /*
    If the quotient is actually going to be returned, we'll try to
    avoid hitting the memory allocator by copying the dividend into it
    and doing the division there.  This can't be any _worse_ than
    always copying, and will sometimes be better (since it won't make
    another copy)

    If it's not going to be returned, we need to allocate a temporary
    to hold the quotient, which will just be discarded.
   */
  if(q) {
    if((res = mp_copy(a, q)) != MP_OKAY)
      return res;

    res = s_mp_div_d(q, d, &rem);
    if(s_mp_cmp_d(q, 0) == MP_EQ)
      SIGN(q) = MP_ZPOS;

  } else {
    mp_int  qp;

    if((res = mp_init_copy(&qp, a)) != MP_OKAY)
      return res;

    res = s_mp_div_d(&qp, d, &rem);
    if(s_mp_cmp_d(&qp, 0) == 0)
      SIGN(&qp) = MP_ZPOS;

    mp_clear(&qp);
  }

  if(r)
    *r = rem;

  return res;

} /* end mp_div_d() */

/* }}} */

/* {{{ mp_div_2(a, c) */

/*
  mp_div_2(a, c)

  Compute c = a / 2, disregarding the remainder.
 */

mp_err mp_div_2(mp_int *a, mp_int *c)
{
  mp_err  res;

  ARGCHK(a != NULL && c != NULL, MP_BADARG);

  if((res = mp_copy(a, c)) != MP_OKAY)
    return res;

  s_mp_div_2(c);

  return MP_OKAY;

} /* end mp_div_2() */

/* }}} */

/* {{{ mp_expt_d(a, d, b) */

mp_err mp_expt_d(mp_int *a, mp_digit d, mp_int *c)
{
  mp_int   s, x;
  mp_err   res;

  ARGCHK(a != NULL && c != NULL, MP_BADARG);

  if((res = mp_init(&s)) != MP_OKAY)
    return res;
  if((res = mp_init_copy(&x, a)) != MP_OKAY)
    goto X;

  DIGIT(&s, 0) = 1;

  while(d != 0) {
    if(d & 1) {
      if((res = s_mp_mul(&s, &x)) != MP_OKAY)
	goto CLEANUP;
    }

    d >>= 1;

    if((res = s_mp_sqr(&x)) != MP_OKAY)
      goto CLEANUP;
  }

  s_mp_exch(&s, c);

CLEANUP:
  mp_clear(&x);
X:
  mp_clear(&s);

  return res;

} /* end mp_expt_d() */

/* }}} */

/* }}} */

/*------------------------------------------------------------------------*/
/* {{{ Full arithmetic */

/* {{{ mp_abs(a, b) */

/*
  mp_abs(a, b)

  Compute b = |a|.  'a' and 'b' may be identical.
 */

mp_err mp_abs(mp_int *a, mp_int *b)
{
  mp_err   res;

  ARGCHK(a != NULL && b != NULL, MP_BADARG);

  if((res = mp_copy(a, b)) != MP_OKAY)
    return res;

  SIGN(b) = MP_ZPOS;

  return MP_OKAY;

} /* end mp_abs() */

/* }}} */

/* {{{ mp_neg(a, b) */

/*
  mp_neg(a, b)

  Compute b = -a.  'a' and 'b' may be identical.
 */

mp_err mp_neg(mp_int *a, mp_int *b)
{
  mp_err   res;

  ARGCHK(a != NULL && b != NULL, MP_BADARG);

  if((res = mp_copy(a, b)) != MP_OKAY)
    return res;

  if(s_mp_cmp_d(b, 0) == MP_EQ)
    SIGN(b) = MP_ZPOS;
  else
    SIGN(b) = (SIGN(b) == MP_NEG) ? MP_ZPOS : MP_NEG;

  return MP_OKAY;

} /* end mp_neg() */

/* }}} */

/* {{{ mp_add(a, b, c) */

/*
  mp_add(a, b, c)

  Compute c = a + b.  All parameters may be identical.
 */

mp_err mp_add(mp_int *a, mp_int *b, mp_int *c)
{
  mp_err  res;
  int     cmp;

  ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);

  if(SIGN(a) == SIGN(b)) { /* same sign:  add values, keep sign */

    /* Commutativity of addition lets us do this in either order,
       so we avoid having to use a temporary even if the result
       is supposed to replace the output
     */
    if(c == b) {
      if((res = s_mp_add(c, a)) != MP_OKAY)
	return res;
    } else {
      if(c != a && (res = mp_copy(a, c)) != MP_OKAY)
	return res;

      if((res = s_mp_add(c, b)) != MP_OKAY)
	return res;
    }

  } else if((cmp = s_mp_cmp(a, b)) > 0) {  /* different sign: a > b   */

    /* If the output is going to be clobbered, we will use a temporary
       variable; otherwise, we'll do it without touching the memory
       allocator at all, if possible
     */
    if(c == b) {
      mp_int  tmp;

      if((res = mp_init_copy(&tmp, a)) != MP_OKAY)
	return res;
      if((res = s_mp_sub(&tmp, b)) != MP_OKAY) {
	mp_clear(&tmp);
	return res;
      }

      s_mp_exch(&tmp, c);
      mp_clear(&tmp);

    } else {

      if(c != a && (res = mp_copy(a, c)) != MP_OKAY)
	return res;
      if((res = s_mp_sub(c, b)) != MP_OKAY)
	return res;

    }

  } else if(cmp == 0) {             /* different sign, a == b   */

    mp_zero(c);
    return MP_OKAY;

  } else {                          /* different sign: a < b    */

    /* See above... */
    if(c == a) {
      mp_int  tmp;

      if((res = mp_init_copy(&tmp, b)) != MP_OKAY)
	return res;
      if((res = s_mp_sub(&tmp, a)) != MP_OKAY) {
	mp_clear(&tmp);
	return res;
      }

      s_mp_exch(&tmp, c);
      mp_clear(&tmp);

    } else {

      if(c != b && (res = mp_copy(b, c)) != MP_OKAY)
	return res;
      if((res = s_mp_sub(c, a)) != MP_OKAY)
	return res;

    }
  }

  if(USED(c) == 1 && DIGIT(c, 0) == 0)
    SIGN(c) = MP_ZPOS;

  return MP_OKAY;

} /* end mp_add() */

/* }}} */

/* {{{ mp_sub(a, b, c) */

/*
  mp_sub(a, b, c)

  Compute c = a - b.  All parameters may be identical.
 */

mp_err mp_sub(mp_int *a, mp_int *b, mp_int *c)
{
  mp_err  res;
  int     cmp;

  ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);

  if(SIGN(a) != SIGN(b)) {
    if(c == a) {
      if((res = s_mp_add(c, b)) != MP_OKAY)
	return res;
    } else {
      if(c != b && ((res = mp_copy(b, c)) != MP_OKAY))
	return res;
      if((res = s_mp_add(c, a)) != MP_OKAY)
	return res;
      SIGN(c) = SIGN(a);
    }

  } else if((cmp = s_mp_cmp(a, b)) > 0) { /* Same sign, a > b */
    if(c == b) {
      mp_int  tmp;

      if((res = mp_init_copy(&tmp, a)) != MP_OKAY)
	return res;
      if((res = s_mp_sub(&tmp, b)) != MP_OKAY) {
	mp_clear(&tmp);
	return res;
      }
      s_mp_exch(&tmp, c);
      mp_clear(&tmp);

    } else {
      if(c != a && ((res = mp_copy(a, c)) != MP_OKAY))
	return res;

      if((res = s_mp_sub(c, b)) != MP_OKAY)
	return res;
    }

  } else if(cmp == 0) {  /* Same sign, equal magnitude */
    mp_zero(c);
    return MP_OKAY;

  } else {               /* Same sign, b > a */
    if(c == a) {
      mp_int  tmp;

      if((res = mp_init_copy(&tmp, b)) != MP_OKAY)
	return res;

      if((res = s_mp_sub(&tmp, a)) != MP_OKAY) {
	mp_clear(&tmp);
	return res;
      }
      s_mp_exch(&tmp, c);
      mp_clear(&tmp);

    } else {
      if(c != b && ((res = mp_copy(b, c)) != MP_OKAY))
	return res;

      if((res = s_mp_sub(c, a)) != MP_OKAY)
	return res;
    }

    SIGN(c) = !SIGN(b);
  }

  if(USED(c) == 1 && DIGIT(c, 0) == 0)
    SIGN(c) = MP_ZPOS;

  return MP_OKAY;

} /* end mp_sub() */

/* }}} */

/* {{{ mp_mul(a, b, c) */

/*
  mp_mul(a, b, c)

  Compute c = a * b.  All parameters may be identical.
 */

mp_err mp_mul(mp_int *a, mp_int *b, mp_int *c)
{
  mp_err   res;
  mp_sign  sgn;

  ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);

  sgn = (SIGN(a) == SIGN(b)) ? MP_ZPOS : MP_NEG;

  if(c == b) {
    if((res = s_mp_mul(c, a)) != MP_OKAY)
      return res;

  } else {
    if((res = mp_copy(a, c)) != MP_OKAY)
      return res;

    if((res = s_mp_mul(c, b)) != MP_OKAY)
      return res;
  }

  if(sgn == MP_ZPOS || s_mp_cmp_d(c, 0) == MP_EQ)
    SIGN(c) = MP_ZPOS;
  else
    SIGN(c) = sgn;

  return MP_OKAY;

} /* end mp_mul() */

/* }}} */

/* {{{ mp_mul_2d(a, d, c) */

/*
  mp_mul_2d(a, d, c)

  Compute c = a * 2^d.  a may be the same as c.
 */

mp_err mp_mul_2d(mp_int *a, mp_digit d, mp_int *c)
{
  mp_err   res;

  ARGCHK(a != NULL && c != NULL, MP_BADARG);

  if((res = mp_copy(a, c)) != MP_OKAY)
    return res;

  if(d == 0)
    return MP_OKAY;

  return s_mp_mul_2d(c, d);

} /* end mp_mul() */

/* }}} */

/* {{{ mp_sqr(a, b) */

#if MP_SQUARE
mp_err mp_sqr(mp_int *a, mp_int *b)
{
  mp_err   res;

  ARGCHK(a != NULL && b != NULL, MP_BADARG);

  if((res = mp_copy(a, b)) != MP_OKAY)
    return res;

  if((res = s_mp_sqr(b)) != MP_OKAY)
    return res;

  SIGN(b) = MP_ZPOS;

  return MP_OKAY;

} /* end mp_sqr() */
#endif

/* }}} */

/* {{{ mp_div(a, b, q, r) */

/*
  mp_div(a, b, q, r)

  Compute q = a / b and r = a mod b.  Input parameters may be re-used
  as output parameters.  If q or r is NULL, that portion of the
  computation will be discarded (although it will still be computed)

  Pay no attention to the hacker behind the curtain.
 */

mp_err mp_div(mp_int *a, mp_int *b, mp_int *q, mp_int *r)
{
  mp_err   res;
  mp_int   qtmp, rtmp;
  int      cmp;

  ARGCHK(a != NULL && b != NULL, MP_BADARG);

  if(mp_cmp_z(b) == MP_EQ)
    return MP_RANGE;

  /* If a <= b, we can compute the solution without division, and
     avoid any memory allocation
   */
  if((cmp = s_mp_cmp(a, b)) < 0) {
    if(r) {
      if((res = mp_copy(a, r)) != MP_OKAY)
	return res;
    }

    if(q)
      mp_zero(q);

    return MP_OKAY;

  } else if(cmp == 0) {

    /* Set quotient to 1, with appropriate sign */
    if(q) {
      int qneg = (SIGN(a) != SIGN(b));

      mp_set(q, 1);
      if(qneg)
	SIGN(q) = MP_NEG;
    }

    if(r)
      mp_zero(r);

    return MP_OKAY;
  }

  /* If we get here, it means we actually have to do some division */

  /* Set up some temporaries... */
  if((res = mp_init_copy(&qtmp, a)) != MP_OKAY)
    return res;
  if((res = mp_init_copy(&rtmp, b)) != MP_OKAY)
    goto CLEANUP;

  if((res = s_mp_div(&qtmp, &rtmp)) != MP_OKAY)
    goto CLEANUP;

  /* Compute the signs for the output  */
  SIGN(&rtmp) = SIGN(a); /* Sr = Sa              */
  if(SIGN(a) == SIGN(b))
    SIGN(&qtmp) = MP_ZPOS;  /* Sq = MP_ZPOS if Sa = Sb */
  else
    SIGN(&qtmp) = MP_NEG;   /* Sq = MP_NEG if Sa != Sb */

  if(s_mp_cmp_d(&qtmp, 0) == MP_EQ)
    SIGN(&qtmp) = MP_ZPOS;
  if(s_mp_cmp_d(&rtmp, 0) == MP_EQ)
    SIGN(&rtmp) = MP_ZPOS;

  /* Copy output, if it is needed      */
  if(q)
    s_mp_exch(&qtmp, q);

  if(r)
    s_mp_exch(&rtmp, r);

CLEANUP:
  mp_clear(&rtmp);
  mp_clear(&qtmp);

  return res;

} /* end mp_div() */

/* }}} */

/* {{{ mp_div_2d(a, d, q, r) */

mp_err mp_div_2d(mp_int *a, mp_digit d, mp_int *q, mp_int *r)
{
  mp_err  res;

  ARGCHK(a != NULL, MP_BADARG);

  if(q) {
    if((res = mp_copy(a, q)) != MP_OKAY)
      return res;

    s_mp_div_2d(q, d);
  }

  if(r) {
    if((res = mp_copy(a, r)) != MP_OKAY)
      return res;

    s_mp_mod_2d(r, d);
  }

  return MP_OKAY;

} /* end mp_div_2d() */

/* }}} */

/* {{{ mp_expt(a, b, c) */

/*
  mp_expt(a, b, c)

  Compute c = a ** b, that is, raise a to the b power.  Uses a
  standard iterative square-and-multiply technique.
 */

mp_err mp_expt(mp_int *a, mp_int *b, mp_int *c)
{
  mp_int   s, x;
  mp_err   res;
  mp_digit d;
  unsigned int bit, dig;

  ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);

  if(mp_cmp_z(b) < 0)
    return MP_RANGE;

  if((res = mp_init(&s)) != MP_OKAY)
    return res;

  mp_set(&s, 1);

  if((res = mp_init_copy(&x, a)) != MP_OKAY)
    goto X;

  /* Loop over low-order digits in ascending order */
  for(dig = 0; dig < (USED(b) - 1); dig++) {
    d = DIGIT(b, dig);

    /* Loop over bits of each non-maximal digit */
    for(bit = 0; bit < DIGIT_BIT; bit++) {
      if(d & 1) {
	if((res = s_mp_mul(&s, &x)) != MP_OKAY)
	  goto CLEANUP;
      }

      d >>= 1;

      if((res = s_mp_sqr(&x)) != MP_OKAY)
	goto CLEANUP;
    }
  }

  /* Consider now the last digit... */
  d = DIGIT(b, dig);

  while(d) {
    if(d & 1) {
      if((res = s_mp_mul(&s, &x)) != MP_OKAY)
	goto CLEANUP;
    }

    d >>= 1;

    if((res = s_mp_sqr(&x)) != MP_OKAY)
      goto CLEANUP;
  }

  if(mp_iseven(b))
    SIGN(&s) = SIGN(a);

  res = mp_copy(&s, c);

CLEANUP:
  mp_clear(&x);
X:
  mp_clear(&s);

  return res;

} /* end mp_expt() */

/* }}} */

/* {{{ mp_2expt(a, k) */

/* Compute a = 2^k */

mp_err mp_2expt(mp_int *a, mp_digit k)
{
  ARGCHK(a != NULL, MP_BADARG);

  return s_mp_2expt(a, k);

} /* end mp_2expt() */

/* }}} */

/* {{{ mp_mod(a, m, c) */

/*
  mp_mod(a, m, c)

  Compute c = a (mod m).  Result will always be 0 <= c < m.
 */

mp_err mp_mod(mp_int *a, mp_int *m, mp_int *c)
{
  mp_err  res;
  int     mag;

  ARGCHK(a != NULL && m != NULL && c != NULL, MP_BADARG);

  if(SIGN(m) == MP_NEG)
    return MP_RANGE;

  /*
     If |a| > m, we need to divide to get the remainder and take the
     absolute value.

     If |a| < m, we don't need to do any division, just copy and adjust
     the sign (if a is negative).

     If |a| == m, we can simply set the result to zero.

     This order is intended to minimize the average path length of the
     comparison chain on common workloads -- the most frequent cases are
     that |a| != m, so we do those first.
   */
  if((mag = s_mp_cmp(a, m)) > 0) {
    if((res = mp_div(a, m, NULL, c)) != MP_OKAY)
      return res;

    if(SIGN(c) == MP_NEG) {
      if((res = mp_add(c, m, c)) != MP_OKAY)
	return res;
    }

  } else if(mag < 0) {
    if((res = mp_copy(a, c)) != MP_OKAY)
      return res;

    if(mp_cmp_z(a) < 0) {
      if((res = mp_add(c, m, c)) != MP_OKAY)
	return res;

    }

  } else {
    mp_zero(c);

  }

  return MP_OKAY;

} /* end mp_mod() */

/* }}} */

/* {{{ mp_mod_d(a, d, c) */

/*
  mp_mod_d(a, d, c)

  Compute c = a (mod d).  Result will always be 0 <= c < d
 */
mp_err mp_mod_d(mp_int *a, mp_digit d, mp_digit *c)
{
  mp_err   res;
  mp_digit rem;

  ARGCHK(a != NULL && c != NULL, MP_BADARG);

  if(s_mp_cmp_d(a, d) > 0) {
    if((res = mp_div_d(a, d, NULL, &rem)) != MP_OKAY)
      return res;

  } else {
    if(SIGN(a) == MP_NEG)
      rem = d - DIGIT(a, 0);
    else
      rem = DIGIT(a, 0);
  }

  if(c)
    *c = rem;

  return MP_OKAY;

} /* end mp_mod_d() */

/* }}} */

/* {{{ mp_sqrt(a, b) */

/*
  mp_sqrt(a, b)

  Compute the integer square root of a, and store the result in b.
  Uses an integer-arithmetic version of Newton's iterative linear
  approximation technique to determine this value; the result has the
  following two properties:

     b^2 <= a
     (b+1)^2 >= a

  It is a range error to pass a negative value.
 */
mp_err mp_sqrt(mp_int *a, mp_int *b)
{
  mp_int   x, t;
  mp_err   res;

  ARGCHK(a != NULL && b != NULL, MP_BADARG);

  /* Cannot take square root of a negative value */
  if(SIGN(a) == MP_NEG)
    return MP_RANGE;

  /* Special cases for zero and one, trivial     */
  if(mp_cmp_d(a, 0) == MP_EQ || mp_cmp_d(a, 1) == MP_EQ)
    return mp_copy(a, b);

  /* Initialize the temporaries we'll use below  */
  if((res = mp_init_size(&t, USED(a))) != MP_OKAY)
    return res;

  /* Compute an initial guess for the iteration as a itself */
  if((res = mp_init_copy(&x, a)) != MP_OKAY)
    goto X;

s_mp_rshd(&x, (USED(&x)/2)+1);
mp_add_d(&x, 1, &x);

  for(;;) {
    /* t = (x * x) - a */
    mp_copy(&x, &t);      /* can't fail, t is big enough for original x */
    if((res = mp_sqr(&t, &t)) != MP_OKAY ||
       (res = mp_sub(&t, a, &t)) != MP_OKAY)
      goto CLEANUP;

    /* t = t / 2x       */
    s_mp_mul_2(&x);
    if((res = mp_div(&t, &x, &t, NULL)) != MP_OKAY)
      goto CLEANUP;
    s_mp_div_2(&x);

    /* Terminate the loop, if the quotient is zero */
    if(mp_cmp_z(&t) == MP_EQ)
      break;

    /* x = x - t       */
    if((res = mp_sub(&x, &t, &x)) != MP_OKAY)
      goto CLEANUP;

  }

  /* Copy result to output parameter */
  mp_sub_d(&x, 1, &x);
  s_mp_exch(&x, b);

 CLEANUP:
  mp_clear(&x);
 X:
  mp_clear(&t);

  return res;

} /* end mp_sqrt() */

/* }}} */

/* }}} */

/*------------------------------------------------------------------------*/
/* {{{ Modular arithmetic */

#if MP_MODARITH
/* {{{ mp_addmod(a, b, m, c) */

/*
  mp_addmod(a, b, m, c)

  Compute c = (a + b) mod m
 */

mp_err mp_addmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c)
{
  mp_err  res;

  ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG);

  if((res = mp_add(a, b, c)) != MP_OKAY)
    return res;
  if((res = mp_mod(c, m, c)) != MP_OKAY)
    return res;

  return MP_OKAY;

}

/* }}} */

/* {{{ mp_submod(a, b, m, c) */

/*
  mp_submod(a, b, m, c)

  Compute c = (a - b) mod m
 */

mp_err mp_submod(mp_int *a, mp_int *b, mp_int *m, mp_int *c)
{
  mp_err  res;

  ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG);

  if((res = mp_sub(a, b, c)) != MP_OKAY)
    return res;
  if((res = mp_mod(c, m, c)) != MP_OKAY)
    return res;

  return MP_OKAY;

}

/* }}} */

/* {{{ mp_mulmod(a, b, m, c) */

/*
  mp_mulmod(a, b, m, c)

  Compute c = (a * b) mod m
 */

mp_err mp_mulmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c)
{
  mp_err  res;

  ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG);

  if((res = mp_mul(a, b, c)) != MP_OKAY)
    return res;
  if((res = mp_mod(c, m, c)) != MP_OKAY)
    return res;

  return MP_OKAY;

}

/* }}} */

/* {{{ mp_sqrmod(a, m, c) */

#if MP_SQUARE
mp_err mp_sqrmod(mp_int *a, mp_int *m, mp_int *c)
{
  mp_err  res;

  ARGCHK(a != NULL && m != NULL && c != NULL, MP_BADARG);

  if((res = mp_sqr(a, c)) != MP_OKAY)
    return res;
  if((res = mp_mod(c, m, c)) != MP_OKAY)
    return res;

  return MP_OKAY;

} /* end mp_sqrmod() */
#endif

/* }}} */

/* {{{ mp_exptmod(a, b, m, c) */

/*
  mp_exptmod(a, b, m, c)

  Compute c = (a ** b) mod m.  Uses a standard square-and-multiply
  method with modular reductions at each step. (This is basically the
  same code as mp_expt(), except for the addition of the reductions)

  The modular reductions are done using Barrett's algorithm (see
  s_mp_reduce() below for details)
 */

mp_err mp_exptmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c)
{
  mp_int   s, x, mu;
  mp_err   res;
  mp_digit d, *db = DIGITS(b);
  mp_size  ub = USED(b);
  unsigned int bit, dig;

  ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);

  if(mp_cmp_z(b) < 0 || mp_cmp_z(m) <= 0)
    return MP_RANGE;

  if((res = mp_init(&s)) != MP_OKAY)
    return res;
  if((res = mp_init_copy(&x, a)) != MP_OKAY)
    goto X;
  if((res = mp_mod(&x, m, &x)) != MP_OKAY ||
     (res = mp_init(&mu)) != MP_OKAY)
    goto MU;

  mp_set(&s, 1);

  /* mu = b^2k / m */
  s_mp_add_d(&mu, 1);
  s_mp_lshd(&mu, 2 * USED(m));
  if((res = mp_div(&mu, m, &mu, NULL)) != MP_OKAY)
    goto CLEANUP;

  /* Loop over digits of b in ascending order, except highest order */
  for(dig = 0; dig < (ub - 1); dig++) {
    d = *db++;

    /* Loop over the bits of the lower-order digits */
    for(bit = 0; bit < DIGIT_BIT; bit++) {
      if(d & 1) {
	if((res = s_mp_mul(&s, &x)) != MP_OKAY)
	  goto CLEANUP;
	if((res = s_mp_reduce(&s, m, &mu)) != MP_OKAY)
	  goto CLEANUP;
      }

      d >>= 1;

      if((res = s_mp_sqr(&x)) != MP_OKAY)
	goto CLEANUP;
      if((res = s_mp_reduce(&x, m, &mu)) != MP_OKAY)
	goto CLEANUP;
    }
  }

  /* Now do the last digit... */
  d = *db;

  while(d) {
    if(d & 1) {
      if((res = s_mp_mul(&s, &x)) != MP_OKAY)
	goto CLEANUP;
      if((res = s_mp_reduce(&s, m, &mu)) != MP_OKAY)
	goto CLEANUP;
    }

    d >>= 1;

    if((res = s_mp_sqr(&x)) != MP_OKAY)
      goto CLEANUP;
    if((res = s_mp_reduce(&x, m, &mu)) != MP_OKAY)
      goto CLEANUP;
  }

  s_mp_exch(&s, c);

 CLEANUP:
  mp_clear(&mu);
 MU:
  mp_clear(&x);
 X:
  mp_clear(&s);

  return res;

} /* end mp_exptmod() */

/* }}} */

/* {{{ mp_exptmod_d(a, d, m, c) */

mp_err mp_exptmod_d(mp_int *a, mp_digit d, mp_int *m, mp_int *c)
{
  mp_int   s, x;
  mp_err   res;

  ARGCHK(a != NULL && c != NULL, MP_BADARG);

  if((res = mp_init(&s)) != MP_OKAY)
    return res;
  if((res = mp_init_copy(&x, a)) != MP_OKAY)
    goto X;

  mp_set(&s, 1);

  while(d != 0) {
    if(d & 1) {
      if((res = s_mp_mul(&s, &x)) != MP_OKAY ||
	 (res = mp_mod(&s, m, &s)) != MP_OKAY)
	goto CLEANUP;
    }

    d /= 2;

    if((res = s_mp_sqr(&x)) != MP_OKAY ||
       (res = mp_mod(&x, m, &x)) != MP_OKAY)
      goto CLEANUP;
  }

  s_mp_exch(&s, c);

CLEANUP:
  mp_clear(&x);
X:
  mp_clear(&s);

  return res;

} /* end mp_exptmod_d() */

/* }}} */
#endif /* if MP_MODARITH */

/* }}} */

/*------------------------------------------------------------------------*/
/* {{{ Comparison functions */

/* {{{ mp_cmp_z(a) */

/*
  mp_cmp_z(a)

  Compare a <=> 0.  Returns <0 if a<0, 0 if a=0, >0 if a>0.
 */

int    mp_cmp_z(mp_int *a)
{
  if(SIGN(a) == MP_NEG)
    return MP_LT;
  else if(USED(a) == 1 && DIGIT(a, 0) == 0)
    return MP_EQ;
  else
    return MP_GT;

} /* end mp_cmp_z() */

/* }}} */

/* {{{ mp_cmp_d(a, d) */

/*
  mp_cmp_d(a, d)

  Compare a <=> d.  Returns <0 if a<d, 0 if a=d, >0 if a>d
 */

int    mp_cmp_d(mp_int *a, mp_digit d)
{
  ARGCHK(a != NULL, MP_EQ);

  if(SIGN(a) == MP_NEG)
    return MP_LT;

  return s_mp_cmp_d(a, d);

} /* end mp_cmp_d() */

/* }}} */

/* {{{ mp_cmp(a, b) */

int    mp_cmp(mp_int *a, mp_int *b)
{
  ARGCHK(a != NULL && b != NULL, MP_EQ);

  if(SIGN(a) == SIGN(b)) {
    int  mag;

    if((mag = s_mp_cmp(a, b)) == MP_EQ)
      return MP_EQ;

    if(SIGN(a) == MP_ZPOS)
      return mag;
    else
      return -mag;

  } else if(SIGN(a) == MP_ZPOS) {
    return MP_GT;
  } else {
    return MP_LT;
  }

} /* end mp_cmp() */

/* }}} */

/* {{{ mp_cmp_mag(a, b) */

/*
  mp_cmp_mag(a, b)

  Compares |a| <=> |b|, and returns an appropriate comparison result
 */

int    mp_cmp_mag(mp_int *a, mp_int *b)
{
  ARGCHK(a != NULL && b != NULL, MP_EQ);

  return s_mp_cmp(a, b);

} /* end mp_cmp_mag() */

/* }}} */

/* {{{ mp_cmp_int(a, z) */

/*
  This just converts z to an mp_int, and uses the existing comparison
  routines.  This is sort of inefficient, but it's not clear to me how
  frequently this wil get used anyway.  For small positive constants,
  you can always use mp_cmp_d(), and for zero, there is mp_cmp_z().
 */
int    mp_cmp_int(mp_int *a, long z)
{
  mp_int  tmp;
  int     out;

  ARGCHK(a != NULL, MP_EQ);

  mp_init(&tmp); mp_set_int(&tmp, z);
  out = mp_cmp(a, &tmp);
  mp_clear(&tmp);

  return out;

} /* end mp_cmp_int() */

/* }}} */

/* {{{ mp_isodd(a) */

/*
  mp_isodd(a)

  Returns a true (non-zero) value if a is odd, false (zero) otherwise.
 */
int    mp_isodd(mp_int *a)
{
  ARGCHK(a != NULL, 0);

  return (DIGIT(a, 0) & 1);

} /* end mp_isodd() */

/* }}} */

/* {{{ mp_iseven(a) */

int    mp_iseven(mp_int *a)
{
  return !mp_isodd(a);

} /* end mp_iseven() */

/* }}} */

/* }}} */

/*------------------------------------------------------------------------*/
/* {{{ Number theoretic functions */

#if MP_NUMTH
/* {{{ mp_gcd(a, b, c) */

/*
  Like the old mp_gcd() function, except computes the GCD using the
  binary algorithm due to Josef Stein in 1961 (via Knuth).
 */
mp_err mp_gcd(mp_int *a, mp_int *b, mp_int *c)
{
  mp_err   res;
  mp_int   u, v, t;
  mp_size  k = 0;

  ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);

  if(mp_cmp_z(a) == MP_EQ && mp_cmp_z(b) == MP_EQ)
      return MP_RANGE;
  if(mp_cmp_z(a) == MP_EQ) {
    return mp_copy(b, c);
  } else if(mp_cmp_z(b) == MP_EQ) {
    return mp_copy(a, c);
  }

  if((res = mp_init(&t)) != MP_OKAY)
    return res;
  if((res = mp_init_copy(&u, a)) != MP_OKAY)
    goto U;
  if((res = mp_init_copy(&v, b)) != MP_OKAY)
    goto V;

  SIGN(&u) = MP_ZPOS;
  SIGN(&v) = MP_ZPOS;

  /* Divide out common factors of 2 until at least 1 of a, b is even */
  while(mp_iseven(&u) && mp_iseven(&v)) {
    s_mp_div_2(&u);
    s_mp_div_2(&v);
    ++k;
  }

  /* Initialize t */
  if(mp_isodd(&u)) {
    if((res = mp_copy(&v, &t)) != MP_OKAY)
      goto CLEANUP;

    /* t = -v */
    if(SIGN(&v) == MP_ZPOS)
      SIGN(&t) = MP_NEG;
    else
      SIGN(&t) = MP_ZPOS;

  } else {
    if((res = mp_copy(&u, &t)) != MP_OKAY)
      goto CLEANUP;

  }

  for(;;) {
    while(mp_iseven(&t)) {
      s_mp_div_2(&t);
    }

    if(mp_cmp_z(&t) == MP_GT) {
      if((res = mp_copy(&t, &u)) != MP_OKAY)
	goto CLEANUP;

    } else {
      if((res = mp_copy(&t, &v)) != MP_OKAY)
	goto CLEANUP;

      /* v = -t */
      if(SIGN(&t) == MP_ZPOS)
	SIGN(&v) = MP_NEG;
      else
	SIGN(&v) = MP_ZPOS;
    }

    if((res = mp_sub(&u, &v, &t)) != MP_OKAY)
      goto CLEANUP;

    if(s_mp_cmp_d(&t, 0) == MP_EQ)
      break;
  }

  s_mp_2expt(&v, k);       /* v = 2^k   */
  res = mp_mul(&u, &v, c); /* c = u * v */

 CLEANUP:
  mp_clear(&v);
 V:
  mp_clear(&u);
 U:
  mp_clear(&t);

  return res;

} /* end mp_bgcd() */

/* }}} */

/* {{{ mp_lcm(a, b, c) */

/* We compute the least common multiple using the rule:

   ab = [a, b](a, b)

   ... by computing the product, and dividing out the gcd.
 */

mp_err mp_lcm(mp_int *a, mp_int *b, mp_int *c)
{
  mp_int  gcd, prod;
  mp_err  res;

  ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);

  /* Set up temporaries */
  if((res = mp_init(&gcd)) != MP_OKAY)
    return res;
  if((res = mp_init(&prod)) != MP_OKAY)
    goto GCD;

  if((res = mp_mul(a, b, &prod)) != MP_OKAY)
    goto CLEANUP;
  if((res = mp_gcd(a, b, &gcd)) != MP_OKAY)
    goto CLEANUP;

  res = mp_div(&prod, &gcd, c, NULL);

 CLEANUP:
  mp_clear(&prod);
 GCD:
  mp_clear(&gcd);

  return res;

} /* end mp_lcm() */

/* }}} */

/* {{{ mp_xgcd(a, b, g, x, y) */

/*
  mp_xgcd(a, b, g, x, y)

  Compute g = (a, b) and values x and y satisfying Bezout's identity
  (that is, ax + by = g).  This uses the extended binary GCD algorithm
  based on the Stein algorithm used for mp_gcd()
 */

mp_err mp_xgcd(mp_int *a, mp_int *b, mp_int *g, mp_int *x, mp_int *y)
{
  mp_int   gx, xc, yc, u, v, A, B, C, D;
  mp_int  *clean[9];
  mp_err   res;
  int      last = -1;

  if(mp_cmp_z(b) == 0)
    return MP_RANGE;

  /* Initialize all these variables we need */
  if((res = mp_init(&u)) != MP_OKAY) goto CLEANUP;
  clean[++last] = &u;
  if((res = mp_init(&v)) != MP_OKAY) goto CLEANUP;
  clean[++last] = &v;
  if((res = mp_init(&gx)) != MP_OKAY) goto CLEANUP;
  clean[++last] = &gx;
  if((res = mp_init(&A)) != MP_OKAY) goto CLEANUP;
  clean[++last] = &A;
  if((res = mp_init(&B)) != MP_OKAY) goto CLEANUP;
  clean[++last] = &B;
  if((res = mp_init(&C)) != MP_OKAY) goto CLEANUP;
  clean[++last] = &C;
  if((res = mp_init(&D)) != MP_OKAY) goto CLEANUP;
  clean[++last] = &D;
  if((res = mp_init_copy(&xc, a)) != MP_OKAY) goto CLEANUP;
  clean[++last] = &xc;
  mp_abs(&xc, &xc);
  if((res = mp_init_copy(&yc, b)) != MP_OKAY) goto CLEANUP;
  clean[++last] = &yc;
  mp_abs(&yc, &yc);

  mp_set(&gx, 1);

  /* Divide by two until at least one of them is even */
  while(mp_iseven(&xc) && mp_iseven(&yc)) {
    s_mp_div_2(&xc);
    s_mp_div_2(&yc);
    if((res = s_mp_mul_2(&gx)) != MP_OKAY)
      goto CLEANUP;
  }

  mp_copy(&xc, &u);
  mp_copy(&yc, &v);
  mp_set(&A, 1); mp_set(&D, 1);

  /* Loop through binary GCD algorithm */
  for(;;) {
    while(mp_iseven(&u)) {
      s_mp_div_2(&u);

      if(mp_iseven(&A) && mp_iseven(&B)) {
	s_mp_div_2(&A); s_mp_div_2(&B);
      } else {
	if((res = mp_add(&A, &yc, &A)) != MP_OKAY) goto CLEANUP;
	s_mp_div_2(&A);
	if((res = mp_sub(&B, &xc, &B)) != MP_OKAY) goto CLEANUP;
	s_mp_div_2(&B);
      }
    }

    while(mp_iseven(&v)) {
      s_mp_div_2(&v);

      if(mp_iseven(&C) && mp_iseven(&D)) {
	s_mp_div_2(&C); s_mp_div_2(&D);
      } else {
	if((res = mp_add(&C, &yc, &C)) != MP_OKAY) goto CLEANUP;
	s_mp_div_2(&C);
	if((res = mp_sub(&D, &xc, &D)) != MP_OKAY) goto CLEANUP;
	s_mp_div_2(&D);
      }
    }

    if(mp_cmp(&u, &v) >= 0) {
      if((res = mp_sub(&u, &v, &u)) != MP_OKAY) goto CLEANUP;
      if((res = mp_sub(&A, &C, &A)) != MP_OKAY) goto CLEANUP;
      if((res = mp_sub(&B, &D, &B)) != MP_OKAY) goto CLEANUP;

    } else {
      if((res = mp_sub(&v, &u, &v)) != MP_OKAY) goto CLEANUP;
      if((res = mp_sub(&C, &A, &C)) != MP_OKAY) goto CLEANUP;
      if((res = mp_sub(&D, &B, &D)) != MP_OKAY) goto CLEANUP;

    }

    /* If we're done, copy results to output */
    if(mp_cmp_z(&u) == 0) {
      if(x)
	if((res = mp_copy(&C, x)) != MP_OKAY) goto CLEANUP;

      if(y)
	if((res = mp_copy(&D, y)) != MP_OKAY) goto CLEANUP;

      if(g)
	if((res = mp_mul(&gx, &v, g)) != MP_OKAY) goto CLEANUP;

      break;
    }
  }

 CLEANUP:
  while(last >= 0)
    mp_clear(clean[last--]);

  return res;

} /* end mp_xgcd() */

/* }}} */

/* {{{ mp_invmod(a, m, c) */

/*
  mp_invmod(a, m, c)

  Compute c = a^-1 (mod m), if there is an inverse for a (mod m).
  This is equivalent to the question of whether (a, m) = 1.  If not,
  MP_UNDEF is returned, and there is no inverse.
 */

mp_err mp_invmod(mp_int *a, mp_int *m, mp_int *c)
{
  mp_int  g, x;
  mp_err  res;

  ARGCHK(a && m && c, MP_BADARG);

  if(mp_cmp_z(a) == 0 || mp_cmp_z(m) == 0)
    return MP_RANGE;

  if((res = mp_init(&g)) != MP_OKAY)
    return res;
  if((res = mp_init(&x)) != MP_OKAY)
    goto X;

  if((res = mp_xgcd(a, m, &g, &x, NULL)) != MP_OKAY)
    goto CLEANUP;

  if(mp_cmp_d(&g, 1) != MP_EQ) {
    res = MP_UNDEF;
    goto CLEANUP;
  }

  res = mp_mod(&x, m, c);
  SIGN(c) = SIGN(a);

CLEANUP:
  mp_clear(&x);
X:
  mp_clear(&g);

  return res;

} /* end mp_invmod() */

/* }}} */
#endif /* if MP_NUMTH */

/* }}} */

/*------------------------------------------------------------------------*/
/* {{{ mp_print(mp, ofp) */

#if MP_IOFUNC
/*
  mp_print(mp, ofp)

  Print a textual representation of the given mp_int on the output
  stream 'ofp'.  Output is generated using the internal radix.
 */

void   mp_print(mp_int *mp, FILE *ofp)
{
  int   ix;

  if(mp == NULL || ofp == NULL)
    return;

  fputc((SIGN(mp) == MP_NEG) ? '-' : '+', ofp);

  for(ix = USED(mp) - 1; ix >= 0; ix--) {
    fprintf(ofp, DIGIT_FMT, DIGIT(mp, ix));
  }

} /* end mp_print() */

#endif /* if MP_IOFUNC */

/* }}} */

/*------------------------------------------------------------------------*/
/* {{{ More I/O Functions */

/* {{{ mp_read_signed_bin(mp, str, len) */

/*
   mp_read_signed_bin(mp, str, len)

   Read in a raw value (base 256) into the given mp_int
 */

mp_err  mp_read_signed_bin(mp_int *mp, unsigned char *str, int len)
{
  mp_err         res;

  ARGCHK(mp != NULL && str != NULL && len > 0, MP_BADARG);

  if((res = mp_read_unsigned_bin(mp, str + 1, len - 1)) == MP_OKAY) {
    /* Get sign from first byte */
    if(str[0])
      SIGN(mp) = MP_NEG;
    else
      SIGN(mp) = MP_ZPOS;
  }

  return res;

} /* end mp_read_signed_bin() */

/* }}} */

/* {{{ mp_signed_bin_size(mp) */

int    mp_signed_bin_size(mp_int *mp)
{
  ARGCHK(mp != NULL, 0);

  return mp_unsigned_bin_size(mp) + 1;

} /* end mp_signed_bin_size() */

/* }}} */

/* {{{ mp_to_signed_bin(mp, str) */

mp_err mp_to_signed_bin(mp_int *mp, unsigned char *str)
{
  ARGCHK(mp != NULL && str != NULL, MP_BADARG);

  /* Caller responsible for allocating enough memory (use mp_raw_size(mp)) */
  str[0] = (char)SIGN(mp);

  return mp_to_unsigned_bin(mp, str + 1);

} /* end mp_to_signed_bin() */

/* }}} */

/* {{{ mp_read_unsigned_bin(mp, str, len) */

/*
  mp_read_unsigned_bin(mp, str, len)

  Read in an unsigned value (base 256) into the given mp_int
 */

mp_err  mp_read_unsigned_bin(mp_int *mp, unsigned char *str, int len)
{
  int     ix;
  mp_err  res;

  ARGCHK(mp != NULL && str != NULL && len > 0, MP_BADARG);

  mp_zero(mp);

  for(ix = 0; ix < len; ix++) {
    if((res = s_mp_mul_2d(mp, CHAR_BIT)) != MP_OKAY)
      return res;

    if((res = mp_add_d(mp, str[ix], mp)) != MP_OKAY)
      return res;
  }

  return MP_OKAY;

} /* end mp_read_unsigned_bin() */

/* }}} */

/* {{{ mp_unsigned_bin_size(mp) */

int     mp_unsigned_bin_size(mp_int *mp)
{
  mp_digit   topdig;
  int        count;

  ARGCHK(mp != NULL, 0);

  /* Special case for the value zero */
  if(USED(mp) == 1 && DIGIT(mp, 0) == 0)
    return 1;

  count = (USED(mp) - 1) * sizeof(mp_digit);
  topdig = DIGIT(mp, USED(mp) - 1);

  while(topdig != 0) {
    ++count;
    topdig >>= CHAR_BIT;
  }

  return count;

} /* end mp_unsigned_bin_size() */

/* }}} */

/* {{{ mp_to_unsigned_bin(mp, str) */

mp_err mp_to_unsigned_bin(mp_int *mp, unsigned char *str)
{
  mp_digit      *dp, *end, d;
  unsigned char *spos;

  ARGCHK(mp != NULL && str != NULL, MP_BADARG);

  dp = DIGITS(mp);
  end = dp + USED(mp) - 1;
  spos = str;

  /* Special case for zero, quick test */
  if(dp == end && *dp == 0) {
    *str = '\0';
    return MP_OKAY;
  }

  /* Generate digits in reverse order */
  while(dp < end) {
    unsigned int ix;

    d = *dp;
    for(ix = 0; ix < sizeof(mp_digit); ++ix) {
      *spos = d & UCHAR_MAX;
      d >>= CHAR_BIT;
      ++spos;
    }

    ++dp;
  }

  /* Now handle last digit specially, high order zeroes are not written */
  d = *end;
  while(d != 0) {
    *spos = d & UCHAR_MAX;
    d >>= CHAR_BIT;
    ++spos;
  }

  /* Reverse everything to get digits in the correct order */
  while(--spos > str) {
    unsigned char t = *str;
    *str = *spos;
    *spos = t;

    ++str;
  }

  return MP_OKAY;

} /* end mp_to_unsigned_bin() */

/* }}} */

/* {{{ mp_count_bits(mp) */

int    mp_count_bits(mp_int *mp)
{
  int      len;
  mp_digit d;

  ARGCHK(mp != NULL, MP_BADARG);

  len = DIGIT_BIT * (USED(mp) - 1);
  d = DIGIT(mp, USED(mp) - 1);

  while(d != 0) {
    ++len;
    d >>= 1;
  }

  return len;

} /* end mp_count_bits() */

/* }}} */

/* {{{ mp_read_radix(mp, str, radix) */

/*
  mp_read_radix(mp, str, radix)

  Read an integer from the given string, and set mp to the resulting
  value.  The input is presumed to be in base 10.  Leading non-digit
  characters are ignored, and the function reads until a non-digit
  character or the end of the string.
 */

mp_err  mp_read_radix(mp_int *mp, unsigned char *str, int radix)
{
  int     ix = 0, val = 0;
  mp_err  res;
  mp_sign sig = MP_ZPOS;

  ARGCHK(mp != NULL && str != NULL && radix >= 2 && radix <= MAX_RADIX,
	 MP_BADARG);

  mp_zero(mp);

  /* Skip leading non-digit characters until a digit or '-' or '+' */
  while(str[ix] &&
	(s_mp_tovalue(str[ix], radix) < 0) &&
	str[ix] != '-' &&
	str[ix] != '+') {
    ++ix;
  }

  if(str[ix] == '-') {
    sig = MP_NEG;
    ++ix;
  } else if(str[ix] == '+') {
    sig = MP_ZPOS; /* this is the default anyway... */
    ++ix;
  }

  while((val = s_mp_tovalue(str[ix], radix)) >= 0) {
    if((res = s_mp_mul_d(mp, radix)) != MP_OKAY)
      return res;
    if((res = s_mp_add_d(mp, val)) != MP_OKAY)
      return res;
    ++ix;
  }

  if(s_mp_cmp_d(mp, 0) == MP_EQ)
    SIGN(mp) = MP_ZPOS;
  else
    SIGN(mp) = sig;

  return MP_OKAY;

} /* end mp_read_radix() */

/* }}} */

/* {{{ mp_radix_size(mp, radix) */

int    mp_radix_size(mp_int *mp, int radix)
{
  int  len;
  ARGCHK(mp != NULL, 0);

  len = s_mp_outlen(mp_count_bits(mp), radix) + 1; /* for NUL terminator */

  if(mp_cmp_z(mp) < 0)
    ++len; /* for sign */

  return len;

} /* end mp_radix_size() */

/* }}} */

/* {{{ mp_value_radix_size(num, qty, radix) */

/* num = number of digits
   qty = number of bits per digit
   radix = target base

   Return the number of digits in the specified radix that would be
   needed to express 'num' digits of 'qty' bits each.
 */
int    mp_value_radix_size(int num, int qty, int radix)
{
  ARGCHK(num >= 0 && qty > 0 && radix >= 2 && radix <= MAX_RADIX, 0);

  return s_mp_outlen(num * qty, radix);

} /* end mp_value_radix_size() */

/* }}} */

/* {{{ mp_toradix(mp, str, radix) */

mp_err mp_toradix(mp_int *mp, char *str, int radix)
{
  int  ix, pos = 0;

  ARGCHK(mp != NULL && str != NULL, MP_BADARG);
  ARGCHK(radix > 1 && radix <= MAX_RADIX, MP_RANGE);

  if(mp_cmp_z(mp) == MP_EQ) {
    str[0] = '0';
    str[1] = '\0';
  } else {
    mp_err   res;
    mp_int   tmp;
    mp_sign  sgn;
    mp_digit rem, rdx = (mp_digit)radix;
    char     ch;

    if((res = mp_init_copy(&tmp, mp)) != MP_OKAY)
      return res;

    /* Save sign for later, and take absolute value */
    sgn = SIGN(&tmp); SIGN(&tmp) = MP_ZPOS;

    /* Generate output digits in reverse order      */
    while(mp_cmp_z(&tmp) != 0) {
      if((res = s_mp_div_d(&tmp, rdx, &rem)) != MP_OKAY) {
	mp_clear(&tmp);
	return res;
      }

      /* Generate digits, use capital letters */
      ch = s_mp_todigit(rem, radix, 0);

      str[pos++] = ch;
    }

    /* Add - sign if original value was negative */
    if(sgn == MP_NEG)
      str[pos++] = '-';

    /* Add trailing NUL to end the string        */
    str[pos--] = '\0';

    /* Reverse the digits and sign indicator     */
    ix = 0;
    while(ix < pos) {
      char _tmp = str[ix];

      str[ix] = str[pos];
      str[pos] = _tmp;
      ++ix;
      --pos;
    }

    mp_clear(&tmp);
  }

  return MP_OKAY;

} /* end mp_toradix() */

/* }}} */

/* {{{ mp_char2value(ch, r) */

int    mp_char2value(char ch, int r)
{
  return s_mp_tovalue(ch, r);

} /* end mp_tovalue() */

/* }}} */

/* }}} */

/* {{{ mp_strerror(ec) */

/*
  mp_strerror(ec)

  Return a string describing the meaning of error code 'ec'.  The
  string returned is allocated in static memory, so the caller should
  not attempt to modify or free the memory associated with this
  string.
 */
const char  *mp_strerror(mp_err ec)
{
  int   aec = (ec < 0) ? -ec : ec;

  /* Code values are negative, so the senses of these comparisons
     are accurate */
  if(ec < MP_LAST_CODE || ec > MP_OKAY) {
    return mp_err_string[0];  /* unknown error code */
  } else {
    return mp_err_string[aec + 1];
  }

} /* end mp_strerror() */

/* }}} */

/*========================================================================*/
/*------------------------------------------------------------------------*/
/* Static function definitions (internal use only)                        */

/* {{{ Memory management */

/* {{{ s_mp_grow(mp, min) */

/* Make sure there are at least 'min' digits allocated to mp              */
mp_err   s_mp_grow(mp_int *mp, mp_size min)
{
  if(min > ALLOC(mp)) {
    mp_digit   *tmp;

    /* Set min to next nearest default precision block size */
    min = ((min + (s_mp_defprec - 1)) / s_mp_defprec) * s_mp_defprec;

    if((tmp = s_mp_alloc(min, sizeof(mp_digit))) == NULL)
      return MP_MEM;

    s_mp_copy(DIGITS(mp), tmp, USED(mp));

#if MP_CRYPTO
    s_mp_setz(DIGITS(mp), ALLOC(mp));
#endif
    s_mp_free(DIGITS(mp));
    DIGITS(mp) = tmp;
    ALLOC(mp) = min;
  }

  return MP_OKAY;

} /* end s_mp_grow() */

/* }}} */

/* {{{ s_mp_pad(mp, min) */

/* Make sure the used size of mp is at least 'min', growing if needed     */
mp_err   s_mp_pad(mp_int *mp, mp_size min)
{
  if(min > USED(mp)) {
    mp_err  res;

    /* Make sure there is room to increase precision  */
    if(min > ALLOC(mp) && (res = s_mp_grow(mp, min)) != MP_OKAY)
      return res;

    /* Increase precision; should already be 0-filled */
    USED(mp) = min;
  }

  return MP_OKAY;

} /* end s_mp_pad() */

/* }}} */

/* {{{ s_mp_setz(dp, count) */

#if MP_MACRO == 0
/* Set 'count' digits pointed to by dp to be zeroes                       */
void s_mp_setz(mp_digit *dp, mp_size count)
{
#if MP_MEMSET == 0
  int  ix;

  for(ix = 0; ix < count; ix++)
    dp[ix] = 0;
#else
  memset(dp, 0, count * sizeof(mp_digit));
#endif

} /* end s_mp_setz() */
#endif

/* }}} */

/* {{{ s_mp_copy(sp, dp, count) */

#if MP_MACRO == 0
/* Copy 'count' digits from sp to dp                                      */
void s_mp_copy(mp_digit *sp, mp_digit *dp, mp_size count)
{
#if MP_MEMCPY == 0
  int  ix;

  for(ix = 0; ix < count; ix++)
    dp[ix] = sp[ix];
#else
  memcpy(dp, sp, count * sizeof(mp_digit));
#endif

} /* end s_mp_copy() */
#endif

/* }}} */

/* {{{ s_mp_alloc(nb, ni) */

#if MP_MACRO == 0
/* Allocate ni records of nb bytes each, and return a pointer to that     */
void    *s_mp_alloc(size_t nb, size_t ni)
{
  return calloc(nb, ni);

} /* end s_mp_alloc() */
#endif

/* }}} */

/* {{{ s_mp_free(ptr) */

#if MP_MACRO == 0
/* Free the memory pointed to by ptr                                      */
void     s_mp_free(void *ptr)
{
  if(ptr)
    free(ptr);

} /* end s_mp_free() */
#endif

/* }}} */

/* {{{ s_mp_clamp(mp) */

/* Remove leading zeroes from the given value                             */
void     s_mp_clamp(mp_int *mp)
{
  mp_size   du = USED(mp);
  mp_digit *zp = DIGITS(mp) + du - 1;

  while(du > 1 && !*zp--)
    --du;

  USED(mp) = du;

} /* end s_mp_clamp() */


/* }}} */

/* {{{ s_mp_exch(a, b) */

/* Exchange the data for a and b; (b, a) = (a, b)                         */
void     s_mp_exch(mp_int *a, mp_int *b)
{
  mp_int   tmp;

  tmp = *a;
  *a = *b;
  *b = tmp;

} /* end s_mp_exch() */

/* }}} */

/* }}} */

/* {{{ Arithmetic helpers */

/* {{{ s_mp_lshd(mp, p) */

/*
   Shift mp leftward by p digits, growing if needed, and zero-filling
   the in-shifted digits at the right end.  This is a convenient
   alternative to multiplication by powers of the radix
 */

mp_err   s_mp_lshd(mp_int *mp, mp_size p)
{
  mp_err   res;
  mp_size  pos;
  mp_digit *dp;
  int ix;

  if(p == 0)
    return MP_OKAY;

  if((res = s_mp_pad(mp, USED(mp) + p)) != MP_OKAY)
    return res;

  pos = USED(mp) - 1;
  dp = DIGITS(mp);

  /* Shift all the significant figures over as needed */
  for(ix = pos - p; ix >= 0; ix--)
    dp[ix + p] = dp[ix];

  /* Fill the bottom digits with zeroes */
  for(ix = 0; (unsigned)ix < p; ix++)
    dp[ix] = 0;

  return MP_OKAY;

} /* end s_mp_lshd() */

/* }}} */

/* {{{ s_mp_rshd(mp, p) */

/*
   Shift mp rightward by p digits.  Maintains the invariant that
   digits above the precision are all zero.  Digits shifted off the
   end are lost.  Cannot fail.
 */

void     s_mp_rshd(mp_int *mp, mp_size p)
{
  mp_size  ix;
  mp_digit *dp;

  if(p == 0)
    return;

  /* Shortcut when all digits are to be shifted off */
  if(p >= USED(mp)) {
    s_mp_setz(DIGITS(mp), ALLOC(mp));
    USED(mp) = 1;
    SIGN(mp) = MP_ZPOS;
    return;
  }

  /* Shift all the significant figures over as needed */
  dp = DIGITS(mp);
  for(ix = p; ix < USED(mp); ix++)
    dp[ix - p] = dp[ix];

  /* Fill the top digits with zeroes */
  ix -= p;
  while(ix < USED(mp))
    dp[ix++] = 0;

  /* Strip off any leading zeroes    */
  s_mp_clamp(mp);

} /* end s_mp_rshd() */

/* }}} */

/* {{{ s_mp_div_2(mp) */

/* Divide by two -- take advantage of radix properties to do it fast      */
void     s_mp_div_2(mp_int *mp)
{
  s_mp_div_2d(mp, 1);

} /* end s_mp_div_2() */

/* }}} */

/* {{{ s_mp_mul_2(mp) */

mp_err s_mp_mul_2(mp_int *mp)
{
  unsigned int ix;
  mp_digit kin = 0, kout, *dp = DIGITS(mp);
  mp_err   res;

  /* Shift digits leftward by 1 bit */
  for(ix = 0; ix < USED(mp); ix++) {
    kout = (dp[ix] >> (DIGIT_BIT - 1)) & 1;
    dp[ix] = (dp[ix] << 1) | kin;

    kin = kout;
  }

  /* Deal with rollover from last digit */
  if(kin) {
    if(ix >= ALLOC(mp)) {
      if((res = s_mp_grow(mp, ALLOC(mp) + 1)) != MP_OKAY)
	return res;
      dp = DIGITS(mp);
    }

    dp[ix] = kin;
    USED(mp) += 1;
  }

  return MP_OKAY;

} /* end s_mp_mul_2() */

/* }}} */

/* {{{ s_mp_mod_2d(mp, d) */

/*
  Remainder the integer by 2^d, where d is a number of bits.  This
  amounts to a bitwise AND of the value, and does not require the full
  division code
 */
void     s_mp_mod_2d(mp_int *mp, mp_digit d)
{
  unsigned int  ndig = (d / DIGIT_BIT), nbit = (d % DIGIT_BIT);
  unsigned int  ix;
  mp_digit      dmask, *dp = DIGITS(mp);

  if(ndig >= USED(mp))
    return;

  /* Flush all the bits above 2^d in its digit */
  dmask = (1 << nbit) - 1;
  dp[ndig] &= dmask;

  /* Flush all digits above the one with 2^d in it */
  for(ix = ndig + 1; ix < USED(mp); ix++)
    dp[ix] = 0;

  s_mp_clamp(mp);

} /* end s_mp_mod_2d() */

/* }}} */

/* {{{ s_mp_mul_2d(mp, d) */

/*
  Multiply by the integer 2^d, where d is a number of bits.  This
  amounts to a bitwise shift of the value, and does not require the
  full multiplication code.
 */
mp_err    s_mp_mul_2d(mp_int *mp, mp_digit d)
{
  mp_err   res;
  mp_digit save, next, mask, *dp;
  mp_size  used;
  unsigned int ix;

  if((res = s_mp_lshd(mp, d / DIGIT_BIT)) != MP_OKAY)
    return res;

  dp = DIGITS(mp); used = USED(mp);
  d %= DIGIT_BIT;

  mask = (1 << d) - 1;

  /* If the shift requires another digit, make sure we've got one to
     work with */
  if((dp[used - 1] >> (DIGIT_BIT - d)) & mask) {
    if((res = s_mp_grow(mp, used + 1)) != MP_OKAY)
      return res;
    dp = DIGITS(mp);
  }

  /* Do the shifting... */
  save = 0;
  for(ix = 0; ix < used; ix++) {
    next = (dp[ix] >> (DIGIT_BIT - d)) & mask;
    dp[ix] = (dp[ix] << d) | save;
    save = next;
  }

  /* If, at this point, we have a nonzero carryout into the next
     digit, we'll increase the size by one digit, and store it...
   */
  if(save) {
    dp[used] = save;
    USED(mp) += 1;
  }

  s_mp_clamp(mp);
  return MP_OKAY;

} /* end s_mp_mul_2d() */

/* }}} */

/* {{{ s_mp_div_2d(mp, d) */

/*
  Divide the integer by 2^d, where d is a number of bits.  This
  amounts to a bitwise shift of the value, and does not require the
  full division code (used in Barrett reduction, see below)
 */
void     s_mp_div_2d(mp_int *mp, mp_digit d)
{
  int       ix;
  mp_digit  save, next, mask, *dp = DIGITS(mp);

  s_mp_rshd(mp, d / DIGIT_BIT);
  d %= DIGIT_BIT;

  mask = (1 << d) - 1;

  save = 0;
  for(ix = USED(mp) - 1; ix >= 0; ix--) {
    next = dp[ix] & mask;
    dp[ix] = (dp[ix] >> d) | (save << (DIGIT_BIT - d));
    save = next;
  }

  s_mp_clamp(mp);

} /* end s_mp_div_2d() */

/* }}} */

/* {{{ s_mp_norm(a, b) */

/*
  s_mp_norm(a, b)

  Normalize a and b for division, where b is the divisor.  In order
  that we might make good guesses for quotient digits, we want the
  leading digit of b to be at least half the radix, which we
  accomplish by multiplying a and b by a constant.  This constant is
  returned (so that it can be divided back out of the remainder at the
  end of the division process).

  We multiply by the smallest power of 2 that gives us a leading digit
  at least half the radix.  By choosing a power of 2, we simplify the
  multiplication and division steps to simple shifts.
 */
mp_digit s_mp_norm(mp_int *a, mp_int *b)
{
  mp_digit  t, d = 0;

  t = DIGIT(b, USED(b) - 1);
  while(t < (RADIX / 2)) {
    t <<= 1;
    ++d;
  }

  if(d != 0) {
    s_mp_mul_2d(a, d);
    s_mp_mul_2d(b, d);
  }

  return d;

} /* end s_mp_norm() */

/* }}} */

/* }}} */

/* {{{ Primitive digit arithmetic */

/* {{{ s_mp_add_d(mp, d) */

/* Add d to |mp| in place                                                 */
mp_err   s_mp_add_d(mp_int *mp, mp_digit d)    /* unsigned digit addition */
{
  mp_word   w, k = 0;
  mp_size   ix = 1, used = USED(mp);
  mp_digit *dp = DIGITS(mp);

  w = dp[0] + d;
  dp[0] = ACCUM(w);
  k = CARRYOUT(w);

  while(ix < used && k) {
    w = dp[ix] + k;
    dp[ix] = ACCUM(w);
    k = CARRYOUT(w);
    ++ix;
  }

  if(k != 0) {
    mp_err  res;

    if((res = s_mp_pad(mp, USED(mp) + 1)) != MP_OKAY)
      return res;

    DIGIT(mp, ix) = k;
  }

  return MP_OKAY;

} /* end s_mp_add_d() */

/* }}} */

/* {{{ s_mp_sub_d(mp, d) */

/* Subtract d from |mp| in place, assumes |mp| > d                        */
mp_err   s_mp_sub_d(mp_int *mp, mp_digit d)    /* unsigned digit subtract */
{
  mp_word   w, b = 0;
  mp_size   ix = 1, used = USED(mp);
  mp_digit *dp = DIGITS(mp);

  /* Compute initial subtraction    */
  w = (RADIX + dp[0]) - d;
  b = CARRYOUT(w) ? 0 : 1;
  dp[0] = ACCUM(w);

  /* Propagate borrows leftward     */
  while(b && ix < used) {
    w = (RADIX + dp[ix]) - b;
    b = CARRYOUT(w) ? 0 : 1;
    dp[ix] = ACCUM(w);
    ++ix;
  }

  /* Remove leading zeroes          */
  s_mp_clamp(mp);

  /* If we have a borrow out, it's a violation of the input invariant */
  if(b)
    return MP_RANGE;
  else
    return MP_OKAY;

} /* end s_mp_sub_d() */

/* }}} */

/* {{{ s_mp_mul_d(a, d) */

/* Compute a = a * d, single digit multiplication                         */
mp_err   s_mp_mul_d(mp_int *a, mp_digit d)
{
  mp_word w, k = 0;
  mp_size ix, max;
  mp_err  res;
  mp_digit *dp = DIGITS(a);

  /*
    Single-digit multiplication will increase the precision of the
    output by at most one digit.  However, we can detect when this
    will happen -- if the high-order digit of a, times d, gives a
    two-digit result, then the precision of the result will increase;
    otherwise it won't.  We use this fact to avoid calling s_mp_pad()
    unless absolutely necessary.
   */
  max = USED(a);
  w = dp[max - 1] * d;
  if(CARRYOUT(w) != 0) {
    if((res = s_mp_pad(a, max + 1)) != MP_OKAY)
      return res;
    dp = DIGITS(a);
  }

  for(ix = 0; ix < max; ix++) {
    w = (dp[ix] * d) + k;
    dp[ix] = ACCUM(w);
    k = CARRYOUT(w);
  }

  /* If there is a precision increase, take care of it here; the above
     test guarantees we have enough storage to do this safely.
   */
  if(k) {
    dp[max] = k;
    USED(a) = max + 1;
  }

  s_mp_clamp(a);

  return MP_OKAY;

} /* end s_mp_mul_d() */

/* }}} */

/* {{{ s_mp_div_d(mp, d, r) */

/*
  s_mp_div_d(mp, d, r)

  Compute the quotient mp = mp / d and remainder r = mp mod d, for a
  single digit d.  If r is null, the remainder will be discarded.
 */

mp_err   s_mp_div_d(mp_int *mp, mp_digit d, mp_digit *r)
{
  mp_word   w = 0, t;
  mp_int    quot;
  mp_err    res;
  mp_digit *dp = DIGITS(mp), *qp;
  int       ix;

  if(d == 0)
    return MP_RANGE;

  /* Make room for the quotient */
  if((res = mp_init_size(&quot, USED(mp))) != MP_OKAY)
    return res;

  USED(&quot) = USED(mp); /* so clamping will work below */
  qp = DIGITS(&quot);

  /* Divide without subtraction */
  for(ix = USED(mp) - 1; ix >= 0; ix--) {
    w = (w << DIGIT_BIT) | dp[ix];

    if(w >= d) {
      t = w / d;
      w = w % d;
    } else {
      t = 0;
    }

    qp[ix] = t;
  }

  /* Deliver the remainder, if desired */
  if(r)
    *r = w;

  s_mp_clamp(&quot);
  mp_exch(&quot, mp);
  mp_clear(&quot);

  return MP_OKAY;

} /* end s_mp_div_d() */

/* }}} */

/* }}} */

/* {{{ Primitive full arithmetic */

/* {{{ s_mp_add(a, b) */

/* Compute a = |a| + |b|                                                  */
mp_err   s_mp_add(mp_int *a, mp_int *b)        /* magnitude addition      */
{
  mp_word   w = 0;
  mp_digit *pa, *pb;
  mp_size   ix, used = USED(b);
  mp_err    res;

  /* Make sure a has enough precision for the output value */
  if((used > USED(a)) && (res = s_mp_pad(a, used)) != MP_OKAY)
    return res;

  /*
    Add up all digits up to the precision of b.  If b had initially
    the same precision as a, or greater, we took care of it by the
    padding step above, so there is no problem.  If b had initially
    less precision, we'll have to make sure the carry out is duly
    propagated upward among the higher-order digits of the sum.
   */
  pa = DIGITS(a);
  pb = DIGITS(b);
  for(ix = 0; ix < used; ++ix) {
    w += *pa + *pb++;
    *pa++ = ACCUM(w);
    w = CARRYOUT(w);
  }

  /* If we run out of 'b' digits before we're actually done, make
     sure the carries get propagated upward...
   */
  used = USED(a);
  while(w && ix < used) {
    w += *pa;
    *pa++ = ACCUM(w);
    w = CARRYOUT(w);
    ++ix;
  }

  /* If there's an overall carry out, increase precision and include
     it.  We could have done this initially, but why touch the memory
     allocator unless we're sure we have to?
   */
  if(w) {
    if((res = s_mp_pad(a, used + 1)) != MP_OKAY)
      return res;

    DIGIT(a, ix) = w;  /* pa may not be valid after s_mp_pad() call */
  }

  return MP_OKAY;

} /* end s_mp_add() */

/* }}} */

/* {{{ s_mp_sub(a, b) */

/* Compute a = |a| - |b|, assumes |a| >= |b|                              */
mp_err   s_mp_sub(mp_int *a, mp_int *b)        /* magnitude subtract      */
{
  mp_word   w = 0;
  mp_digit *pa, *pb;
  mp_size   ix, used = USED(b);

  /*
    Subtract and propagate borrow.  Up to the precision of b, this
    accounts for the digits of b; after that, we just make sure the
    carries get to the right place.  This saves having to pad b out to
    the precision of a just to make the loops work right...
   */
  pa = DIGITS(a);
  pb = DIGITS(b);

  for(ix = 0; ix < used; ++ix) {
    w = (RADIX + *pa) - w - *pb++;
    *pa++ = ACCUM(w);
    w = CARRYOUT(w) ? 0 : 1;
  }

  used = USED(a);
  while(ix < used) {
    w = RADIX + *pa - w;
    *pa++ = ACCUM(w);
    w = CARRYOUT(w) ? 0 : 1;
    ++ix;
  }

  /* Clobber any leading zeroes we created    */
  s_mp_clamp(a);

  /*
     If there was a borrow out, then |b| > |a| in violation
     of our input invariant.  We've already done the work,
     but we'll at least complain about it...
   */
  if(w)
    return MP_RANGE;
  else
    return MP_OKAY;

} /* end s_mp_sub() */

/* }}} */

mp_err   s_mp_reduce(mp_int *x, mp_int *m, mp_int *mu)
{
  mp_int   q;
  mp_err   res;
  mp_size  um = USED(m);

  if((res = mp_init_copy(&q, x)) != MP_OKAY)
    return res;

  s_mp_rshd(&q, um - 1);       /* q1 = x / b^(k-1)  */
  s_mp_mul(&q, mu);            /* q2 = q1 * mu      */
  s_mp_rshd(&q, um + 1);       /* q3 = q2 / b^(k+1) */

  /* x = x mod b^(k+1), quick (no division) */
  s_mp_mod_2d(x, (mp_digit)(DIGIT_BIT * (um + 1)));

  /* q = q * m mod b^(k+1), quick (no division), uses the short multiplier */
#ifndef SHRT_MUL
  s_mp_mul(&q, m);
  s_mp_mod_2d(&q, (mp_digit)(DIGIT_BIT * (um + 1)));
#else
  s_mp_mul_dig(&q, m, um + 1);
#endif

  /* x = x - q */
  if((res = mp_sub(x, &q, x)) != MP_OKAY)
    goto CLEANUP;

  /* If x < 0, add b^(k+1) to it */
  if(mp_cmp_z(x) < 0) {
    mp_set(&q, 1);
    if((res = s_mp_lshd(&q, um + 1)) != MP_OKAY)
      goto CLEANUP;
    if((res = mp_add(x, &q, x)) != MP_OKAY)
      goto CLEANUP;
  }

  /* Back off if it's too big */
  while(mp_cmp(x, m) >= 0) {
    if((res = s_mp_sub(x, m)) != MP_OKAY)
      break;
  }

 CLEANUP:
  mp_clear(&q);

  return res;

} /* end s_mp_reduce() */



/* {{{ s_mp_mul(a, b) */

/* Compute a = |a| * |b|                                                  */
mp_err   s_mp_mul(mp_int *a, mp_int *b)
{
  mp_word   w, k = 0;
  mp_int    tmp;
  mp_err    res;
  mp_size   ix, jx, ua = USED(a), ub = USED(b);
  mp_digit *pa, *pb, *pt, *pbt;

  if((res = mp_init_size(&tmp, ua + ub)) != MP_OKAY)
    return res;

  /* This has the effect of left-padding with zeroes... */
  USED(&tmp) = ua + ub;

  /* We're going to need the base value each iteration */
  pbt = DIGITS(&tmp);

  /* Outer loop:  Digits of b */

  pb = DIGITS(b);
  for(ix = 0; ix < ub; ++ix, ++pb) {
    if(*pb == 0)
      continue;

    /* Inner product:  Digits of a */
    pa = DIGITS(a);
    for(jx = 0; jx < ua; ++jx, ++pa) {
      pt = pbt + ix + jx;
      w = *pb * *pa + k + *pt;
      *pt = ACCUM(w);
      k = CARRYOUT(w);
    }

    pbt[ix + jx] = k;
    k = 0;
  }

  s_mp_clamp(&tmp);
  s_mp_exch(&tmp, a);

  mp_clear(&tmp);

  return MP_OKAY;

} /* end s_mp_mul() */

/* }}} */

/* {{{ s_mp_kmul(a, b, out, len) */

#if 0
void   s_mp_kmul(mp_digit *a, mp_digit *b, mp_digit *out, mp_size len)
{
  mp_word   w, k = 0;
  mp_size   ix, jx;
  mp_digit *pa, *pt;

  for(ix = 0; ix < len; ++ix, ++b) {
    if(*b == 0)
      continue;

    pa = a;
    for(jx = 0; jx < len; ++jx, ++pa) {
      pt = out + ix + jx;
      w = *b * *pa + k + *pt;
      *pt = ACCUM(w);
      k = CARRYOUT(w);
    }

    out[ix + jx] = k;
    k = 0;
  }

} /* end s_mp_kmul() */
#endif

/* }}} */

/* {{{ s_mp_sqr(a) */

/*
  Computes the square of a, in place.  This can be done more
  efficiently than a general multiplication, because many of the
  computation steps are redundant when squaring.  The inner product
  step is a bit more complicated, but we save a fair number of
  iterations of the multiplication loop.
 */
#if MP_SQUARE
mp_err   s_mp_sqr(mp_int *a)
{
  mp_word  w, k = 0;
  mp_int   tmp;
  mp_err   res;
  mp_size  ix, jx, kx, used = USED(a);
  mp_digit *pa1, *pa2, *pt, *pbt;

  if((res = mp_init_size(&tmp, 2 * used)) != MP_OKAY)
    return res;

  /* Left-pad with zeroes */
  USED(&tmp) = 2 * used;

  /* We need the base value each time through the loop */
  pbt = DIGITS(&tmp);

  pa1 = DIGITS(a);
  for(ix = 0; ix < used; ++ix, ++pa1) {
    if(*pa1 == 0)
      continue;

    w = DIGIT(&tmp, ix + ix) + (*pa1 * *pa1);

    pbt[ix + ix] = ACCUM(w);
    k = CARRYOUT(w);

    /*
      The inner product is computed as:

         (C, S) = t[i,j] + 2 a[i] a[j] + C

      This can overflow what can be represented in an mp_word, and
      since C arithmetic does not provide any way to check for
      overflow, we have to check explicitly for overflow conditions
      before they happen.
     */
    for(jx = ix + 1, pa2 = DIGITS(a) + jx; jx < used; ++jx, ++pa2) {
      mp_word  u = 0, v;

      /* Store this in a temporary to avoid indirections later */
      pt = pbt + ix + jx;

      /* Compute the multiplicative step */
      w = *pa1 * *pa2;

      /* If w is more than half MP_WORD_MAX, the doubling will
	 overflow, and we need to record a carry out into the next
	 word */
      u = (w >> (MP_WORD_BIT - 1)) & 1;

      /* Double what we've got, overflow will be ignored as defined
	 for C arithmetic (we've already noted if it is to occur)
       */
      w *= 2;

      /* Compute the additive step */
      v = *pt + k;

      /* If we do not already have an overflow carry, check to see
	 if the addition will cause one, and set the carry out if so
       */
      u |= ((MP_WORD_MAX - v) < w);

      /* Add in the rest, again ignoring overflow */
      w += v;

      /* Set the i,j digit of the output */
      *pt = ACCUM(w);

      /* Save carry information for the next iteration of the loop.
	 This is why k must be an mp_word, instead of an mp_digit */
      k = CARRYOUT(w) | (u << DIGIT_BIT);

    } /* for(jx ...) */

    /* Set the last digit in the cycle and reset the carry */
    k = DIGIT(&tmp, ix + jx) + k;
    pbt[ix + jx] = ACCUM(k);
    k = CARRYOUT(k);

    /* If we are carrying out, propagate the carry to the next digit
       in the output.  This may cascade, so we have to be somewhat
       circumspect -- but we will have enough precision in the output
       that we won't overflow
     */
    kx = 1;
    while(k) {
      k = pbt[ix + jx + kx] + 1;
      pbt[ix + jx + kx] = ACCUM(k);
      k = CARRYOUT(k);
      ++kx;
    }
  } /* for(ix ...) */

  s_mp_clamp(&tmp);
  s_mp_exch(&tmp, a);

  mp_clear(&tmp);

  return MP_OKAY;

} /* end s_mp_sqr() */
#endif

/* }}} */

/* {{{ s_mp_div(a, b) */

/*
  s_mp_div(a, b)

  Compute a = a / b and b = a mod b.  Assumes b > a.
 */

mp_err   s_mp_div(mp_int *a, mp_int *b)
{
  mp_int   quot, rem, t;
  mp_word  q;
  mp_err   res;
  mp_digit d;
  int      ix;

  if(mp_cmp_z(b) == 0)
    return MP_RANGE;

  /* Shortcut if b is power of two */
  if((ix = s_mp_ispow2(b)) >= 0) {
    mp_copy(a, b);  /* need this for remainder */
    s_mp_div_2d(a, (mp_digit)ix);
    s_mp_mod_2d(b, (mp_digit)ix);

    return MP_OKAY;
  }

  /* Allocate space to store the quotient */
  if((res = mp_init_size(&quot, USED(a))) != MP_OKAY)
    return res;

  /* A working temporary for division     */
  if((res = mp_init_size(&t, USED(a))) != MP_OKAY)
    goto T;

  /* Allocate space for the remainder     */
  if((res = mp_init_size(&rem, USED(a))) != MP_OKAY)
    goto REM;

  /* Normalize to optimize guessing       */
  d = s_mp_norm(a, b);

  /* Perform the division itself...woo!   */
  ix = USED(a) - 1;

  while(ix >= 0) {
    /* Find a partial substring of a which is at least b */
    while(s_mp_cmp(&rem, b) < 0 && ix >= 0) {
      if((res = s_mp_lshd(&rem, 1)) != MP_OKAY)
	goto CLEANUP;

      if((res = s_mp_lshd(&quot, 1)) != MP_OKAY)
	goto CLEANUP;

      DIGIT(&rem, 0) = DIGIT(a, ix);
      s_mp_clamp(&rem);
      --ix;
    }

    /* If we didn't find one, we're finished dividing    */
    if(s_mp_cmp(&rem, b) < 0)
      break;

    /* Compute a guess for the next quotient digit       */
    q = DIGIT(&rem, USED(&rem) - 1);
    if(q <= DIGIT(b, USED(b) - 1) && USED(&rem) > 1)
      q = (q << DIGIT_BIT) | DIGIT(&rem, USED(&rem) - 2);

    q /= DIGIT(b, USED(b) - 1);

    /* The guess can be as much as RADIX + 1 */
    if(q >= RADIX)
      q = RADIX - 1;

    /* See what that multiplies out to                   */
    mp_copy(b, &t);
    if((res = s_mp_mul_d(&t, q)) != MP_OKAY)
      goto CLEANUP;

    /*
       If it's too big, back it off.  We should not have to do this
       more than once, or, in rare cases, twice.  Knuth describes a
       method by which this could be reduced to a maximum of once, but
       I didn't implement that here.
     */
    while(s_mp_cmp(&t, &rem) > 0) {
      --q;
      s_mp_sub(&t, b);
    }

    /* At this point, q should be the right next digit   */
    if((res = s_mp_sub(&rem, &t)) != MP_OKAY)
      goto CLEANUP;

    /*
      Include the digit in the quotient.  We allocated enough memory
      for any quotient we could ever possibly get, so we should not
      have to check for failures here
     */
    DIGIT(&quot, 0) = q;
  }

  /* Denormalize remainder                */
  if(d != 0)
    s_mp_div_2d(&rem, d);

  s_mp_clamp(&quot);
  s_mp_clamp(&rem);

  /* Copy quotient back to output         */
  s_mp_exch(&quot, a);

  /* Copy remainder back to output        */
  s_mp_exch(&rem, b);

CLEANUP:
  mp_clear(&rem);
REM:
  mp_clear(&t);
T:
  mp_clear(&quot);

  return res;

} /* end s_mp_div() */

/* }}} */

/* {{{ s_mp_2expt(a, k) */

mp_err   s_mp_2expt(mp_int *a, mp_digit k)
{
  mp_err    res;
  mp_size   dig, bit;

  dig = k / DIGIT_BIT;
  bit = k % DIGIT_BIT;

  mp_zero(a);
  if((res = s_mp_pad(a, dig + 1)) != MP_OKAY)
    return res;

  DIGIT(a, dig) |= (1 << bit);

  return MP_OKAY;

} /* end s_mp_2expt() */

/* }}} */


/* }}} */

/* }}} */

/* {{{ Primitive comparisons */

/* {{{ s_mp_cmp(a, b) */

/* Compare |a| <=> |b|, return 0 if equal, <0 if a<b, >0 if a>b           */
int      s_mp_cmp(mp_int *a, mp_int *b)
{
  mp_size   ua = USED(a), ub = USED(b);

  if(ua > ub)
    return MP_GT;
  else if(ua < ub)
    return MP_LT;
  else {
    int      ix = ua - 1;
    mp_digit *ap = DIGITS(a) + ix, *bp = DIGITS(b) + ix;

    while(ix >= 0) {
      if(*ap > *bp)
	return MP_GT;
      else if(*ap < *bp)
	return MP_LT;

      --ap; --bp; --ix;
    }

    return MP_EQ;
  }

} /* end s_mp_cmp() */

/* }}} */

/* {{{ s_mp_cmp_d(a, d) */

/* Compare |a| <=> d, return 0 if equal, <0 if a<d, >0 if a>d             */
int      s_mp_cmp_d(mp_int *a, mp_digit d)
{
  mp_size  ua = USED(a);
  mp_digit *ap = DIGITS(a);

  if(ua > 1)
    return MP_GT;

  if(*ap < d)
    return MP_LT;
  else if(*ap > d)
    return MP_GT;
  else
    return MP_EQ;

} /* end s_mp_cmp_d() */

/* }}} */

/* {{{ s_mp_ispow2(v) */

/*
  Returns -1 if the value is not a power of two; otherwise, it returns
  k such that v = 2^k, i.e. lg(v).
 */
int      s_mp_ispow2(mp_int *v)
{
  mp_digit d, *dp;
  mp_size  uv = USED(v);
  int      extra = 0, ix;

  d = DIGIT(v, uv - 1); /* most significant digit of v */

  while(d && ((d & 1) == 0)) {
    d >>= 1;
    ++extra;
  }

  if(d == 1) {
    ix = uv - 2;
    dp = DIGITS(v) + ix;

    while(ix >= 0) {
      if(*dp)
	return -1; /* not a power of two */

      --dp; --ix;
    }

    return ((uv - 1) * DIGIT_BIT) + extra;
  }

  return -1;

} /* end s_mp_ispow2() */

/* }}} */

/* {{{ s_mp_ispow2d(d) */

int      s_mp_ispow2d(mp_digit d)
{
  int   pow = 0;

  while((d & 1) == 0) {
    ++pow; d >>= 1;
  }

  if(d == 1)
    return pow;

  return -1;

} /* end s_mp_ispow2d() */

/* }}} */

/* }}} */

/* {{{ Primitive I/O helpers */

/* {{{ s_mp_tovalue(ch, r) */

/*
  Convert the given character to its digit value, in the given radix.
  If the given character is not understood in the given radix, -1 is
  returned.  Otherwise the digit's numeric value is returned.

  The results will be odd if you use a radix < 2 or > 62, you are
  expected to know what you're up to.
 */
int      s_mp_tovalue(char ch, int r)
{
  int    val, xch;

  if(r > 36)
    xch = ch;
  else
    xch = toupper(ch);

  if(isdigit(xch))
    val = xch - '0';
  else if(isupper(xch))
    val = xch - 'A' + 10;
  else if(islower(xch))
    val = xch - 'a' + 36;
  else if(xch == '+')
    val = 62;
  else if(xch == '/')
    val = 63;
  else
    return -1;

  if(val < 0 || val >= r)
    return -1;

  return val;

} /* end s_mp_tovalue() */

/* }}} */

/* {{{ s_mp_todigit(val, r, low) */

/*
  Convert val to a radix-r digit, if possible.  If val is out of range
  for r, returns zero.  Otherwise, returns an ASCII character denoting
  the value in the given radix.

  The results may be odd if you use a radix < 2 or > 64, you are
  expected to know what you're doing.
 */

char     s_mp_todigit(int val, int r, int low)
{
  char   ch;

  if(val < 0 || val >= r)
    return 0;

  ch = s_dmap_1[val];

  if(r <= 36 && low)
    ch = tolower(ch);

  return ch;

} /* end s_mp_todigit() */

/* }}} */

/* {{{ s_mp_outlen(bits, radix) */

/*
   Return an estimate for how long a string is needed to hold a radix
   r representation of a number with 'bits' significant bits.

   Does not include space for a sign or a NUL terminator.
 */
int      s_mp_outlen(int bits, int r)
{
  return (int)((double)bits * LOG_V_2(r));

} /* end s_mp_outlen() */

/* }}} */

/* }}} */

/*------------------------------------------------------------------------*/
/* HERE THERE BE DRAGONS                                                  */
/* crc==4242132123, version==2, Sat Feb 02 06:43:52 2002 */

/* $Source$ */
/* $Revision$ */
/* $Date$ */
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/*
    mpi.h

    by Michael J. Fromberger <[email protected]>
    Copyright (C) 1998 Michael J. Fromberger, All Rights Reserved

    Arbitrary precision integer arithmetic library

    $Id$
 */

#ifndef _H_MPI_
#define _H_MPI_

#include "mpi-config.h"

#define  MP_LT       -1
#define  MP_EQ        0
#define  MP_GT        1

#if MP_DEBUG
#undef MP_IOFUNC
#define MP_IOFUNC 1
#endif

#if MP_IOFUNC
#include <stdio.h>
#include <ctype.h>
#endif

#include <limits.h>

#define  MP_NEG  1
#define  MP_ZPOS 0

/* Included for compatibility... */
#define  NEG     MP_NEG
#define  ZPOS    MP_ZPOS

#define  MP_OKAY          0 /* no error, all is well */
#define  MP_YES           0 /* yes (boolean result)  */
#define  MP_NO           -1 /* no (boolean result)   */
#define  MP_MEM          -2 /* out of memory         */
#define  MP_RANGE        -3 /* argument out of range */
#define  MP_BADARG       -4 /* invalid parameter     */
#define  MP_UNDEF        -5 /* answer is undefined   */
#define  MP_LAST_CODE    MP_UNDEF

#include "mpi-types.h"

/* Included for compatibility... */
#define DIGIT_BIT         MP_DIGIT_BIT
#define DIGIT_MAX         MP_DIGIT_MAX

/* Macros for accessing the mp_int internals           */
#define  SIGN(MP)     ((MP)->sign)
#define  USED(MP)     ((MP)->used)
#define  ALLOC(MP)    ((MP)->alloc)
#define  DIGITS(MP)   ((MP)->dp)
#define  DIGIT(MP,N)  (MP)->dp[(N)]

#if MP_ARGCHK == 1
#define  ARGCHK(X,Y)  {if(!(X)){return (Y);}}
#elif MP_ARGCHK == 2
#include <assert.h>
#define  ARGCHK(X,Y)  assert(X)
#else
#define  ARGCHK(X,Y)  /*  */
#endif

/* This defines the maximum I/O base (minimum is 2)   */
#define MAX_RADIX         64

typedef struct {
  mp_sign       sign;    /* sign of this quantity      */
  mp_size       alloc;   /* how many digits allocated  */
  mp_size       used;    /* how many digits used       */
  mp_digit     *dp;      /* the digits themselves      */
} mp_int;

/*------------------------------------------------------------------------*/
/* Default precision                                                      */

unsigned int mp_get_prec(void);
void         mp_set_prec(unsigned int prec);

/*------------------------------------------------------------------------*/
/* Memory management                                                      */

mp_err mp_init(mp_int *mp);
mp_err mp_init_array(mp_int mp[], int count);
mp_err mp_init_size(mp_int *mp, mp_size prec);
mp_err mp_init_copy(mp_int *mp, mp_int *from);
mp_err mp_copy(mp_int *from, mp_int *to);
void   mp_exch(mp_int *mp1, mp_int *mp2);
void   mp_clear(mp_int *mp);
void   mp_clear_array(mp_int mp[], int count);
void   mp_zero(mp_int *mp);
void   mp_set(mp_int *mp, mp_digit d);
mp_err mp_set_int(mp_int *mp, long z);
mp_err mp_shrink(mp_int *a);


/*------------------------------------------------------------------------*/
/* Single digit arithmetic                                                */

mp_err mp_add_d(mp_int *a, mp_digit d, mp_int *b);
mp_err mp_sub_d(mp_int *a, mp_digit d, mp_int *b);
mp_err mp_mul_d(mp_int *a, mp_digit d, mp_int *b);
mp_err mp_mul_2(mp_int *a, mp_int *c);
mp_err mp_div_d(mp_int *a, mp_digit d, mp_int *q, mp_digit *r);
mp_err mp_div_2(mp_int *a, mp_int *c);
mp_err mp_expt_d(mp_int *a, mp_digit d, mp_int *c);

/*------------------------------------------------------------------------*/
/* Sign manipulations                                                     */

mp_err mp_abs(mp_int *a, mp_int *b);
mp_err mp_neg(mp_int *a, mp_int *b);

/*------------------------------------------------------------------------*/
/* Full arithmetic                                                        */

mp_err mp_add(mp_int *a, mp_int *b, mp_int *c);
mp_err mp_sub(mp_int *a, mp_int *b, mp_int *c);
mp_err mp_mul(mp_int *a, mp_int *b, mp_int *c);
mp_err mp_mul_2d(mp_int *a, mp_digit d, mp_int *c);
#if MP_SQUARE
mp_err mp_sqr(mp_int *a, mp_int *b);
#else
#define mp_sqr(a, b) mp_mul(a, a, b)
#endif
mp_err mp_div(mp_int *a, mp_int *b, mp_int *q, mp_int *r);
mp_err mp_div_2d(mp_int *a, mp_digit d, mp_int *q, mp_int *r);
mp_err mp_expt(mp_int *a, mp_int *b, mp_int *c);
mp_err mp_2expt(mp_int *a, mp_digit k);
mp_err mp_sqrt(mp_int *a, mp_int *b);

/*------------------------------------------------------------------------*/
/* Modular arithmetic                                                     */

#if MP_MODARITH
mp_err mp_mod(mp_int *a, mp_int *m, mp_int *c);
mp_err mp_mod_d(mp_int *a, mp_digit d, mp_digit *c);
mp_err mp_addmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c);
mp_err mp_submod(mp_int *a, mp_int *b, mp_int *m, mp_int *c);
mp_err mp_mulmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c);
#if MP_SQUARE
mp_err mp_sqrmod(mp_int *a, mp_int *m, mp_int *c);
#else
#define mp_sqrmod(a, m, c) mp_mulmod(a, a, m, c)
#endif
mp_err mp_exptmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c);
mp_err mp_exptmod_d(mp_int *a, mp_digit d, mp_int *m, mp_int *c);
#endif /* MP_MODARITH */

/*------------------------------------------------------------------------*/
/* Comparisons                                                            */

int    mp_cmp_z(mp_int *a);
int    mp_cmp_d(mp_int *a, mp_digit d);
int    mp_cmp(mp_int *a, mp_int *b);
int    mp_cmp_mag(mp_int *a, mp_int *b);
int    mp_cmp_int(mp_int *a, long z);
int    mp_isodd(mp_int *a);
int    mp_iseven(mp_int *a);

/*------------------------------------------------------------------------*/
/* Number theoretic                                                       */

#if MP_NUMTH
mp_err mp_gcd(mp_int *a, mp_int *b, mp_int *c);
mp_err mp_lcm(mp_int *a, mp_int *b, mp_int *c);
mp_err mp_xgcd(mp_int *a, mp_int *b, mp_int *g, mp_int *x, mp_int *y);
mp_err mp_invmod(mp_int *a, mp_int *m, mp_int *c);
#endif /* end MP_NUMTH */

/*------------------------------------------------------------------------*/
/* Input and output                                                       */

#if MP_IOFUNC
void   mp_print(mp_int *mp, FILE *ofp);
#endif /* end MP_IOFUNC */

/*------------------------------------------------------------------------*/
/* Base conversion                                                        */

#define BITS     1
#define BYTES    CHAR_BIT

mp_err mp_read_signed_bin(mp_int *mp, unsigned char *str, int len);
int    mp_signed_bin_size(mp_int *mp);
mp_err mp_to_signed_bin(mp_int *mp, unsigned char *str);

mp_err mp_read_unsigned_bin(mp_int *mp, unsigned char *str, int len);
int    mp_unsigned_bin_size(mp_int *mp);
mp_err mp_to_unsigned_bin(mp_int *mp, unsigned char *str);

int    mp_count_bits(mp_int *mp);

#if MP_COMPAT_MACROS
#define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
#define mp_raw_size(mp)           mp_signed_bin_size(mp)
#define mp_toraw(mp, str)         mp_to_signed_bin((mp), (str))
#define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
#define mp_mag_size(mp)           mp_unsigned_bin_size(mp)
#define mp_tomag(mp, str)         mp_to_unsigned_bin((mp), (str))
#endif

mp_err mp_read_radix(mp_int *mp, unsigned char *str, int radix);
int    mp_radix_size(mp_int *mp, int radix);
int    mp_value_radix_size(int num, int qty, int radix);
mp_err mp_toradix(mp_int *mp, char *str, int radix);

int    mp_char2value(char ch, int r);

#define mp_tobinary(M, S)  mp_toradix((M), (S), 2)
#define mp_tooctal(M, S)   mp_toradix((M), (S), 8)
#define mp_todecimal(M, S) mp_toradix((M), (S), 10)
#define mp_tohex(M, S)     mp_toradix((M), (S), 16)

/*------------------------------------------------------------------------*/
/* Error strings                                                          */

const  char  *mp_strerror(mp_err ec);

#endif /* end _H_MPI_ */

/* $Source$ */
/* $Revision$ */
/* $Date$ */
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Deleted libtommath/mtest/mtest.c.

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/* makes a bignum test harness with NUM tests per operation
 *
 * the output is made in the following format [one parameter per line]

operation
operand1
operand2
[... operandN]
result1
result2
[... resultN]

So for example "a * b mod n" would be

mulmod
a
b
n
a*b mod n

e.g. if a=3, b=4 n=11 then

mulmod
3
4
11
1

 */

#ifdef MP_8BIT
#define THE_MASK 127
#else
#define THE_MASK 32767
#endif

#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include "mpi.c"

#ifdef LTM_MTEST_REAL_RAND
#define getRandChar() fgetc(rng)
FILE *rng;
#else
#define getRandChar() (rand()&0xFF)
#endif

void rand_num(mp_int *a)
{
   int size;
   unsigned char buf[2048];
   size_t sz;

   size = 1 + ((getRandChar()<<8) + getRandChar()) % 101;
   buf[0] = (getRandChar()&1)?1:0;
#ifdef LTM_MTEST_REAL_RAND
   sz = fread(buf+1, 1, size, rng);
#else
   sz = 1;
   while (sz < (unsigned)size) {
       buf[sz] = getRandChar();
       ++sz;
   }
#endif
   if (sz != (unsigned)size) {
       fprintf(stderr, "\nWarning: fread failed\n\n");
   }
   while (buf[1] == 0) buf[1] = getRandChar();
   mp_read_raw(a, buf, 1+size);
}

void rand_num2(mp_int *a)
{
   int size;
   unsigned char buf[2048];
   size_t sz;

   size = 10 + ((getRandChar()<<8) + getRandChar()) % 101;
   buf[0] = (getRandChar()&1)?1:0;
#ifdef LTM_MTEST_REAL_RAND
   sz = fread(buf+1, 1, size, rng);
#else
   sz = 1;
   while (sz < (unsigned)size) {
       buf[sz] = getRandChar();
       ++sz;
   }
#endif
   if (sz != (unsigned)size) {
       fprintf(stderr, "\nWarning: fread failed\n\n");
   }
   while (buf[1] == 0) buf[1] = getRandChar();
   mp_read_raw(a, buf, 1+size);
}

#define mp_to64(a, b) mp_toradix(a, b, 64)

int main(int argc, char *argv[])
{
   int n, tmp;
   long long max;
   mp_int a, b, c, d, e;
#ifdef MTEST_NO_FULLSPEED
   clock_t t1;
#endif
   char buf[4096];

   mp_init(&a);
   mp_init(&b);
   mp_init(&c);
   mp_init(&d);
   mp_init(&e);

   if (argc > 1) {
       max = strtol(argv[1], NULL, 0);
       if (max < 0) {
           if (max > -64) {
               max = (1 << -(max)) + 1;
           } else {
               max = 1;
           }
       } else if (max == 0) {
           max = 1;
       }
   }
   else {
       max = 0;
   }


   /* initial (2^n - 1)^2 testing, makes sure the comba multiplier works [it has the new carry code] */
/*
   mp_set(&a, 1);
   for (n = 1; n < 8192; n++) {
       mp_mul(&a, &a, &c);
       printf("mul\n");
       mp_to64(&a, buf);
       printf("%s\n%s\n", buf, buf);
       mp_to64(&c, buf);
       printf("%s\n", buf);

       mp_add_d(&a, 1, &a);
       mp_mul_2(&a, &a);
       mp_sub_d(&a, 1, &a);
   }
*/

#ifdef LTM_MTEST_REAL_RAND
   rng = fopen("/dev/urandom", "rb");
   if (rng == NULL) {
      rng = fopen("/dev/random", "rb");
      if (rng == NULL) {
         fprintf(stderr, "\nWarning:  stdin used as random source\n\n");
         rng = stdin;
      }
   }
#else
   srand(23);
#endif

#ifdef MTEST_NO_FULLSPEED
   t1 = clock();
#endif
   for (;;) {
#ifdef MTEST_NO_FULLSPEED
      if (clock() - t1 > CLOCKS_PER_SEC) {
         sleep(2);
         t1 = clock();
      }
#endif
       n = getRandChar() % 15;

       if (max != 0) {
           --max;
           if (max == 0)
             n = 255;
       }

   if (n == 0) {
       /* add tests */
       rand_num(&a);
       rand_num(&b);
       mp_add(&a, &b, &c);
       printf("add\n");
       mp_to64(&a, buf);
       printf("%s\n", buf);
       mp_to64(&b, buf);
       printf("%s\n", buf);
       mp_to64(&c, buf);
       printf("%s\n", buf);
   } else if (n == 1) {
      /* sub tests */
       rand_num(&a);
       rand_num(&b);
       mp_sub(&a, &b, &c);
       printf("sub\n");
       mp_to64(&a, buf);
       printf("%s\n", buf);
       mp_to64(&b, buf);
       printf("%s\n", buf);
       mp_to64(&c, buf);
       printf("%s\n", buf);
   } else if (n == 2) {
       /* mul tests */
       rand_num(&a);
       rand_num(&b);
       mp_mul(&a, &b, &c);
       printf("mul\n");
       mp_to64(&a, buf);
       printf("%s\n", buf);
       mp_to64(&b, buf);
       printf("%s\n", buf);
       mp_to64(&c, buf);
       printf("%s\n", buf);
   } else if (n == 3) {
      /* div tests */
       rand_num(&a);
       rand_num(&b);
       mp_div(&a, &b, &c, &d);
       printf("div\n");
       mp_to64(&a, buf);
       printf("%s\n", buf);
       mp_to64(&b, buf);
       printf("%s\n", buf);
       mp_to64(&c, buf);
       printf("%s\n", buf);
       mp_to64(&d, buf);
       printf("%s\n", buf);
   } else if (n == 4) {
      /* sqr tests */
       rand_num(&a);
       mp_sqr(&a, &b);
       printf("sqr\n");
       mp_to64(&a, buf);
       printf("%s\n", buf);
       mp_to64(&b, buf);
       printf("%s\n", buf);
   } else if (n == 5) {
      /* mul_2d test */
      rand_num(&a);
      mp_copy(&a, &b);
      n = getRandChar() & 63;
      mp_mul_2d(&b, n, &b);
      mp_to64(&a, buf);
      printf("mul2d\n");
      printf("%s\n", buf);
      printf("%d\n", n);
      mp_to64(&b, buf);
      printf("%s\n", buf);
   } else if (n == 6) {
      /* div_2d test */
      rand_num(&a);
      mp_copy(&a, &b);
      n = getRandChar() & 63;
      mp_div_2d(&b, n, &b, NULL);
      mp_to64(&a, buf);
      printf("div2d\n");
      printf("%s\n", buf);
      printf("%d\n", n);
      mp_to64(&b, buf);
      printf("%s\n", buf);
   } else if (n == 7) {
      /* gcd test */
      rand_num(&a);
      rand_num(&b);
      a.sign = MP_ZPOS;
      b.sign = MP_ZPOS;
      mp_gcd(&a, &b, &c);
      printf("gcd\n");
      mp_to64(&a, buf);
      printf("%s\n", buf);
      mp_to64(&b, buf);
      printf("%s\n", buf);
      mp_to64(&c, buf);
      printf("%s\n", buf);
   } else if (n == 8) {
      /* lcm test */
      rand_num(&a);
      rand_num(&b);
      a.sign = MP_ZPOS;
      b.sign = MP_ZPOS;
      mp_lcm(&a, &b, &c);
      printf("lcm\n");
      mp_to64(&a, buf);
      printf("%s\n", buf);
      mp_to64(&b, buf);
      printf("%s\n", buf);
      mp_to64(&c, buf);
      printf("%s\n", buf);
   } else if (n == 9) {
      /* exptmod test */
      rand_num2(&a);
      rand_num2(&b);
      rand_num2(&c);
//      if (c.dp[0]&1) mp_add_d(&c, 1, &c);
      a.sign = b.sign = c.sign = 0;
      mp_exptmod(&a, &b, &c, &d);
      printf("expt\n");
      mp_to64(&a, buf);
      printf("%s\n", buf);
      mp_to64(&b, buf);
      printf("%s\n", buf);
      mp_to64(&c, buf);
      printf("%s\n", buf);
      mp_to64(&d, buf);
      printf("%s\n", buf);
   } else if (n == 10) {
      /* invmod test */
      rand_num2(&a);
      rand_num2(&b);
      b.sign = MP_ZPOS;
      a.sign = MP_ZPOS;
      mp_gcd(&a, &b, &c);
      if (mp_cmp_d(&c, 1) != 0) continue;
      if (mp_cmp_d(&b, 1) == 0) continue;
      mp_invmod(&a, &b, &c);
      printf("invmod\n");
      mp_to64(&a, buf);
      printf("%s\n", buf);
      mp_to64(&b, buf);
      printf("%s\n", buf);
      mp_to64(&c, buf);
      printf("%s\n", buf);
   } else if (n == 11) {
      rand_num(&a);
      mp_mul_2(&a, &a);
      mp_div_2(&a, &b);
      printf("div2\n");
      mp_to64(&a, buf);
      printf("%s\n", buf);
      mp_to64(&b, buf);
      printf("%s\n", buf);
   } else if (n == 12) {
      rand_num2(&a);
      mp_mul_2(&a, &b);
      printf("mul2\n");
      mp_to64(&a, buf);
      printf("%s\n", buf);
      mp_to64(&b, buf);
      printf("%s\n", buf);
   } else if (n == 13) {
      rand_num2(&a);
      tmp = abs(rand()) & THE_MASK;
      mp_add_d(&a, tmp, &b);
      printf("add_d\n");
      mp_to64(&a, buf);
      printf("%s\n%d\n", buf, tmp);
      mp_to64(&b, buf);
      printf("%s\n", buf);
   } else if (n == 14) {
      rand_num2(&a);
      tmp = abs(rand()) & THE_MASK;
      mp_sub_d(&a, tmp, &b);
      printf("sub_d\n");
      mp_to64(&a, buf);
      printf("%s\n%d\n", buf, tmp);
      mp_to64(&b, buf);
      printf("%s\n", buf);
   } else if (n == 255) {
      printf("exit\n");
      break;
   }

   }
#ifdef LTM_MTEST_REAL_RAND
   fclose(rng);
#endif
   return 0;
}

/* $Source$ */
/* $Revision$ */
/* $Date$ */
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Deleted libtommath/pics/design_process.sxd.

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# makes the images... yeah

default:  pses

design_process.ps: design_process.tif
	tiff2ps -s -e design_process.tif > design_process.ps

sliding_window.ps: sliding_window.tif
	tiff2ps -s -e sliding_window.tif > sliding_window.ps
	
expt_state.ps: expt_state.tif
	tiff2ps -s -e expt_state.tif > expt_state.ps

primality.ps: primality.tif
	tiff2ps -s -e primality.tif > primality.ps

design_process.pdf: design_process.ps
	epstopdf design_process.ps

sliding_window.pdf: sliding_window.ps
	epstopdf sliding_window.ps
	
expt_state.pdf: expt_state.ps
	epstopdf expt_state.ps

primality.pdf: primality.ps
	epstopdf primality.ps


pses: sliding_window.ps expt_state.ps primality.ps design_process.ps
pdfes: sliding_window.pdf expt_state.pdf primality.pdf design_process.pdf

clean:
	rm -rf *.ps *.pdf .xvpics
   
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\documentclass[landscape,11pt]{article}
\usepackage{amsmath, amssymb}
\usepackage{hyperref}
\begin{document}
\hspace*{-3in}
\begin{tabular}{llllll}
$c = a + b$  & {\tt mp\_add(\&a, \&b, \&c)} & $b = 2a$  & {\tt mp\_mul\_2(\&a, \&b)} & \\
$c = a - b$  & {\tt mp\_sub(\&a, \&b, \&c)} & $b = a/2$ & {\tt mp\_div\_2(\&a, \&b)} & \\
$c = ab $   & {\tt mp\_mul(\&a, \&b, \&c)}  & $c = 2^ba$  & {\tt mp\_mul\_2d(\&a, b, \&c)}  \\
$b = a^2 $  & {\tt mp\_sqr(\&a, \&b)}       & $c = a/2^b, d = a \mod 2^b$ & {\tt mp\_div\_2d(\&a, b, \&c, \&d)} \\
$c = \lfloor a/b \rfloor, d = a \mod b$ & {\tt mp\_div(\&a, \&b, \&c, \&d)} & $c = a \mod 2^b $  & {\tt mp\_mod\_2d(\&a, b, \&c)}  \\
 && \\
$a = b $  & {\tt mp\_set\_int(\&a, b)}  & $c = a \vee b$  & {\tt mp\_or(\&a, \&b, \&c)}  \\
$b = a $  & {\tt mp\_copy(\&a, \&b)} & $c = a \wedge b$  & {\tt mp\_and(\&a, \&b, \&c)}  \\
 && $c = a \oplus b$  & {\tt mp\_xor(\&a, \&b, \&c)}  \\
 & \\
$b = -a $  & {\tt mp\_neg(\&a, \&b)}  & $d = a + b \mod c$  & {\tt mp\_addmod(\&a, \&b, \&c, \&d)}  \\
$b = |a| $  & {\tt mp\_abs(\&a, \&b)} & $d = a - b \mod c$  & {\tt mp\_submod(\&a, \&b, \&c, \&d)}  \\
 && $d = ab \mod c$  & {\tt mp\_mulmod(\&a, \&b, \&c, \&d)}  \\
Compare $a$ and $b$ & {\tt mp\_cmp(\&a, \&b)} & $c = a^2 \mod b$  & {\tt mp\_sqrmod(\&a, \&b, \&c)}  \\
Is Zero? & {\tt mp\_iszero(\&a)} & $c = a^{-1} \mod b$  & {\tt mp\_invmod(\&a, \&b, \&c)} \\
Is Even? & {\tt mp\_iseven(\&a)} & $d = a^b \mod c$ & {\tt mp\_exptmod(\&a, \&b, \&c, \&d)} \\
Is Odd ? & {\tt mp\_isodd(\&a)} \\
&\\
$\vert \vert a \vert \vert$ & {\tt mp\_unsigned\_bin\_size(\&a)} & $res$ = 1 if $a$ prime to $t$ rounds? & {\tt mp\_prime\_is\_prime(\&a, t, \&res)} \\
$buf \leftarrow a$          & {\tt mp\_to\_unsigned\_bin(\&a, buf)} & Next prime after $a$ to $t$ rounds. & {\tt mp\_prime\_next\_prime(\&a, t, bbs\_style)} \\
$a \leftarrow buf[0..len-1]$          & {\tt mp\_read\_unsigned\_bin(\&a, buf, len)} \\
&\\
$b = \sqrt{a}$ & {\tt mp\_sqrt(\&a, \&b)}  & $c = \mbox{gcd}(a, b)$ & {\tt mp\_gcd(\&a, \&b, \&c)} \\
$c = a^{1/b}$ & {\tt mp\_n\_root(\&a, b, \&c)} & $c = \mbox{lcm}(a, b)$ & {\tt mp\_lcm(\&a, \&b, \&c)} \\
&\\
Greater Than & MP\_GT & Equal To & MP\_EQ \\
Less Than & MP\_LT & Bits per digit & DIGIT\_BIT \\
\end{tabular}
\end{document}
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/* Start: bn_error.c */
#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, [email protected], 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

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

/* End: bn_error.c */

/* Start: bn_fast_mp_invmod.c */
#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, [email protected], 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;
  }

  /* x == modulus, y == value to invert */
  if ((res = mp_copy (b, &x)) != MP_OKAY) {
    goto LBL_ERR;
  }

  /* we need y = |a| */
  if ((res = mp_mod (a, b, &y)) != MP_OKAY) {
    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;
  }
  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) {
      goto LBL_ERR;
    }
  }

  /* 6.  if u >= v then */
  if (mp_cmp (&u, &v) != MP_LT) {
    /* u = u - v, B = B - D */
    if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
      goto LBL_ERR;
    }

    if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
      goto LBL_ERR;
    }
  } else {
    /* v - v - u, D = D - B */
    if ((res = mp_sub (&v, &u, &v)) != 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;
    goto LBL_ERR;
  }

  /* b is now the inverse */
  neg = a->sign;
  while (D.sign == MP_NEG) {
    if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }
  mp_exch (&D, c);
  c->sign = neg;
  res = MP_OKAY;

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

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

/* End: bn_fast_mp_invmod.c */

/* Start: bn_fast_mp_montgomery_reduce.c */
#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, [email protected], 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.
 *
 * Based on Algorithm 14.32 on pp.601 of HAC.
*/
int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
{
  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.
     *
     * Note the comba method normally doesn't handle carries in the
     * inner loop In this case we fix the carry from the previous
     * 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;

      /* inner loop */
      for (iy = 0; iy < n->used; iy++) {
          *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
      }
    }

    /* now fix carry for next digit, W[ix+1] */
    W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
  }

  /* 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
     * we just copy them in the right order
     */

    /* 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++) {
      *tmpx++ = 0;
    }
  }

  /* set the max used and clamp */
  x->used = n->used + 1;
  mp_clamp (x);

  /* 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

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

/* End: bn_fast_mp_montgomery_reduce.c */

/* Start: bn_fast_s_mp_mul_digs.c */
#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, [email protected], 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
 * of making the nested loops that compute the columns very
 * simple and schedulable on super-scalar processors.
 *
 * This has been modified to produce a variable number of
 * digits of output so if say only a half-product is required
 * you don't have to compute the upper half (a feature
 * required for fast Barrett reduction).
 *
 * 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;
    }
  }

  /* number of output digits to produce */
  pa = MIN(digs, a->used + b->used);

  /* clear the carry */
  _W = 0;
  for (ix = 0; ix < pa; ix++) {
      int      tx, ty;
      int      iy;
      mp_digit *tmpx, *tmpy;

      /* get offsets into the two bignums */
      ty = MIN(b->used-1, ix);
      tx = ix - ty;

      /* setup temp aliases */
      tmpx = a->dp + tx;
      tmpy = b->dp + ty;

      /* this is the number of times the loop will iterrate, essentially
         while (tx++ < a->used && ty-- >= 0) { ... }
       */
      iy = MIN(a->used-tx, ty+1);

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

      }

      /* 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

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

/* End: bn_fast_s_mp_mul_digs.c */

/* Start: bn_fast_s_mp_mul_high_digs.c */
#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, [email protected], 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
 * only the higher digits were needed.  This essentially halves the work.
 *
 * Based on Algorithm 14.12 on pp.595 of HAC.
 */
int fast_s_mp_mul_high_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 */
  pa = a->used + b->used;
  if (c->alloc < pa) {
    if ((res = mp_grow (c, pa)) != MP_OKAY) {
      return res;
    }
  }

  /* number of output digits to produce */
  pa = a->used + b->used;
  _W = 0;
  for (ix = digs; ix < pa; ix++) {
      int      tx, ty, iy;
      mp_digit *tmpx, *tmpy;

      /* get offsets into the two bignums */
      ty = MIN(b->used-1, ix);
      tx = ix - ty;

      /* setup temp aliases */
      tmpx = a->dp + tx;
      tmpy = b->dp + ty;

      /* this is the number of times the loop will iterrate, essentially its
         while (tx++ < a->used && ty-- >= 0) { ... }
       */
      iy = MIN(a->used-tx, ty+1);

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

      /* 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 + digs;
    for (ix = digs; ix < pa; 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

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

/* End: bn_fast_s_mp_mul_high_digs.c */

/* Start: bn_fast_s_mp_sqr.c */
#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, [email protected], 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
 * you add in the inner loop

After that loop you do the squares and add them in.
*/

int fast_s_mp_sqr (mp_int * a, mp_int * b)
{
  int       olduse, res, pa, ix, iz;
  mp_digit   W[MP_WARRAY], *tmpx;
  mp_word   W1;

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

  /* number of output digits to produce */
  W1 = 0;
  for (ix = 0; ix < pa; ix++) {
      int      tx, ty, iy;
      mp_word  _W;
      mp_digit *tmpy;

      /* clear counter */
      _W = 0;

      /* get offsets into the two bignums */
      ty = MIN(a->used-1, ix);
      tx = ix - ty;

      /* setup temp aliases */
      tmpx = a->dp + tx;
      tmpy = a->dp + ty;

      /* this is the number of times the loop will iterrate, essentially
         while (tx++ < a->used && ty-- >= 0) { ... }
       */
      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 */
      _W = _W + _W + W1;

      /* even columns have the square term in them */
      if ((ix&1) == 0) {
         _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]);
      }

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

      /* make next carry */
      W1 = _W >> ((mp_word)DIGIT_BIT);
  }

  /* setup dest */
  olduse  = b->used;
  b->used = a->used+a->used;

  {
    mp_digit *tmpb;
    tmpb = b->dp;
    for (ix = 0; ix < pa; ix++) {
      *tmpb++ = W[ix] & MP_MASK;
    }

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

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

/* End: bn_fast_s_mp_sqr.c */

/* Start: bn_mp_2expt.c */
#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, [email protected], http://math.libtomcrypt.com
 */

/* computes a = 2**b
 *
 * Simple algorithm which zeroes the int, grows it then just sets one bit
 * as required.
 */
int
mp_2expt (mp_int * a, int b)
{
  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

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

/* End: bn_mp_2expt.c */

/* Start: bn_mp_abs.c */
#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, [email protected], http://math.libtomcrypt.com
 */

/* b = |a|
 *
 * Simple function copies the input and fixes the sign to positive
 */
int
mp_abs (mp_int * a, mp_int * b)
{
  int     res;

  /* copy a to b */
  if (a != b) {
     if ((res = mp_copy (a, b)) != MP_OKAY) {
       return res;
     }
  }

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

  return MP_OKAY;
}
#endif

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

/* End: bn_mp_abs.c */

/* Start: bn_mp_add.c */
#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, [email protected], 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;

  /* get sign of both inputs */
  sa = a->sign;
  sb = b->sign;

  /* handle two cases, not four */
  if (sa == sb) {
    /* both positive or both negative */
    /* add their magnitudes, copy the sign */
    c->sign = sa;
    res = s_mp_add (a, b, c);
  } else {
    /* one positive, the other negative */
    /* subtract the one with the greater magnitude from */
    /* the one of the lesser magnitude.  The result gets */
    /* the sign of the one with the greater magnitude. */
    if (mp_cmp_mag (a, b) == MP_LT) {
      c->sign = sb;
      res = s_mp_sub (b, a, c);
    } else {
      c->sign = sa;
      res = s_mp_sub (a, b, c);
    }
  }
  return res;
}

#endif

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

/* End: bn_mp_add.c */

/* Start: bn_mp_add_d.c */
#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, [email protected], 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 sign  */
     a->sign = c->sign = MP_NEG;

     /* clamp */
     mp_clamp(c);

     return res;
  }

  /* old number of used digits in c */
  oldused = c->used;

  /* sign always positive */
  c->sign = MP_ZPOS;

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

  /* destination alias */
  tmpc    = c->dp;

  /* if a is positive */
  if (a->sign == MP_ZPOS) {
     /* add digit, after this we're propagating
      * the carry.
      */
     *tmpc   = *tmpa++ + b;
     mu      = *tmpc >> DIGIT_BIT;
     *tmpc++ &= MP_MASK;

     /* now handle rest of the digits */
     for (ix = 1; ix < a->used; ix++) {
        *tmpc   = *tmpa++ + mu;
        mu      = *tmpc >> DIGIT_BIT;
        *tmpc++ &= MP_MASK;
     }
     /* set final carry */
     ix++;
     *tmpc++  = mu;

     /* setup size */
     c->used = a->used + 1;
  } else {
     /* a was negative and |a| < b */
     c->used  = 1;

     /* the result is a single digit */
     if (a->used == 1) {
        *tmpc++  =  b - a->dp[0];
     } else {
        *tmpc++  =  b;
     }

     /* setup count so the clearing of oldused
      * can fall through correctly
      */
     ix       = 1;
  }

  /* now zero to oldused */
  while (ix++ < oldused) {
     *tmpc++ = 0;
  }
  mp_clamp(c);

  return MP_OKAY;
}

#endif

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

/* End: bn_mp_add_d.c */

/* Start: bn_mp_addmod.c */
#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, [email protected], 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;
  mp_int  t;

  if ((res = mp_init (&t)) != MP_OKAY) {
    return res;
  }

  if ((res = mp_add (a, b, &t)) != MP_OKAY) {
    mp_clear (&t);
    return res;
  }
  res = mp_mod (&t, c, d);
  mp_clear (&t);
  return res;
}
#endif

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

/* End: bn_mp_addmod.c */

/* Start: bn_mp_and.c */
#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, [email protected], 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_int  t, *x;

  if (a->used > b->used) {
    if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
      return res;
    }
    px = b->used;
    x = b;
  } else {
    if ((res = mp_init_copy (&t, b)) != MP_OKAY) {
      return res;
    }
    px = a->used;
    x = a;
  }

  for (ix = 0; ix < px; ix++) {
    t.dp[ix] &= x->dp[ix];
  }

  /* zero digits above the last from the smallest mp_int */
  for (; ix < t.used; ix++) {
    t.dp[ix] = 0;
  }

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

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

/* End: bn_mp_and.c */

/* Start: bn_mp_clamp.c */
#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, [email protected], 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
 * are no more leading digits
 */
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

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

/* End: bn_mp_clamp.c */

/* Start: bn_mp_clear.c */
#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, [email protected], http://math.libtomcrypt.com
 */

/* clear one (frees)  */
void
mp_clear (mp_int * a)
{
  int i;

  /* only do anything if a hasn't been freed previously */
  if (a->dp != NULL) {
    /* first zero the digits */
    for (i = 0; i < a->used; i++) {
        a->dp[i] = 0;
    }

    /* free ram */
    XFREE(a->dp);

    /* reset members to make debugging easier */
    a->dp    = NULL;
    a->alloc = a->used = 0;
    a->sign  = MP_ZPOS;
  }
}
#endif

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

/* End: bn_mp_clear.c */

/* Start: bn_mp_clear_multi.c */
#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, [email protected], http://math.libtomcrypt.com
 */
#include <stdarg.h>

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

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

/* End: bn_mp_clear_multi.c */

/* Start: bn_mp_cmp.c */
#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, [email protected], http://math.libtomcrypt.com
 */

/* compare two ints (signed)*/
int
mp_cmp (mp_int * a, mp_int * b)
{
  /* compare based on sign */
  if (a->sign != b->sign) {
     if (a->sign == MP_NEG) {
        return MP_LT;
     } else {
        return MP_GT;
     }
  }

  /* compare digits */
  if (a->sign == MP_NEG) {
     /* if negative compare opposite direction */
     return mp_cmp_mag(b, a);
  } else {
     return mp_cmp_mag(a, b);
  }
}
#endif

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

/* End: bn_mp_cmp.c */

/* Start: bn_mp_cmp_d.c */
#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, [email protected], http://math.libtomcrypt.com
 */

/* compare a digit */
int mp_cmp_d(mp_int * a, mp_digit b)
{
  /* compare based on sign */
  if (a->sign == MP_NEG) {
    return MP_LT;
  }

  /* compare based on magnitude */
  if (a->used > 1) {
    return MP_GT;
  }

  /* compare the only digit of a to b */
  if (a->dp[0] > b) {
    return MP_GT;
  } else if (a->dp[0] < b) {
    return MP_LT;
  } else {
    return MP_EQ;
  }
}
#endif

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

/* End: bn_mp_cmp_d.c */

/* Start: bn_mp_cmp_mag.c */
#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, [email protected], http://math.libtomcrypt.com
 */

/* compare maginitude of two ints (unsigned) */
int mp_cmp_mag (mp_int * a, mp_int * b)
{
  int     n;
  mp_digit *tmpa, *tmpb;

  /* compare based on # of non-zero digits */
  if (a->used > b->used) {
    return MP_GT;
  }

  if (a->used < b->used) {
    return MP_LT;
  }

  /* alias for a */
  tmpa = a->dp + (a->used - 1);

  /* alias for b */
  tmpb = b->dp + (a->used - 1);

  /* compare based on digits  */
  for (n = 0; n < a->used; ++n, --tmpa, --tmpb) {
    if (*tmpa > *tmpb) {
      return MP_GT;
    }

    if (*tmpa < *tmpb) {
      return MP_LT;
    }
  }
  return MP_EQ;
}
#endif

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

/* End: bn_mp_cmp_mag.c */

/* Start: bn_mp_cnt_lsb.c */
#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, [email protected], 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(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;
         x  += lnz[qq];
         q >>= 4;
      } while (qq == 0);
   }
   return x;
}

#endif

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

/* End: bn_mp_cnt_lsb.c */

/* Start: bn_mp_copy.c */
#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, [email protected], http://math.libtomcrypt.com
 */

/* copy, b = a */
int
mp_copy (mp_int * a, mp_int * b)
{
  int     res, n;

  /* if dst == src do nothing */
  if (a == b) {
    return MP_OKAY;
  }

  /* grow dest */
  if (b->alloc < a->used) {
     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 */
    tmpb = b->dp;

    /* copy all the digits */
    for (n = 0; n < a->used; n++) {
      *tmpb++ = *tmpa++;
    }

    /* clear high digits */
    for (; n < b->used; n++) {
      *tmpb++ = 0;
    }
  }

  /* copy used count and sign */
  b->used = a->used;
  b->sign = a->sign;
  return MP_OKAY;
}
#endif

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

/* End: bn_mp_copy.c */

/* Start: bn_mp_count_bits.c */
#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, [email protected], http://math.libtomcrypt.com
 */

/* returns the number of bits in an int */
int
mp_count_bits (mp_int * a)
{
  int     r;
  mp_digit q;

  /* shortcut */
  if (a->used == 0) {
    return 0;
  }

  /* get number of digits and add that */
  r = (a->used - 1) * DIGIT_BIT;

  /* take the last digit and count the bits in it */
  q = a->dp[a->used - 1];
  while (q > ((mp_digit) 0)) {
    ++r;
    q >>= ((mp_digit) 1);
  }
  return r;
}
#endif

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

/* End: bn_mp_count_bits.c */

/* Start: bn_mp_div.c */
#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, [email protected], 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);
    } else {
      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) {
        if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
            ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
           goto LBL_ERR;
        }
     }
     if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
         ((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);
    } else {
      res = MP_OKAY;
    }
    if (c != NULL) {
      mp_zero (c);
    }
    return res;
  }

  if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) {
    return res;
  }
  q.used = a->used + 2;

  if ((res = mp_init (&t1)) != MP_OKAY) {
    goto LBL_Q;
  }

  if ((res = mp_init (&t2)) != MP_OKAY) {
    goto LBL_T1;
  }

  if ((res = mp_init_copy (&x, a)) != MP_OKAY) {
    goto LBL_T2;
  }

  if ((res = mp_init_copy (&y, b)) != MP_OKAY) {
    goto LBL_X;
  }

  /* fix the sign */
  neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
  x.sign = y.sign = MP_ZPOS;

  /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
  norm = mp_count_bits(&y) % DIGIT_BIT;
  if (norm < (int)(DIGIT_BIT-1)) {
     norm = (DIGIT_BIT-1) - norm;
     if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) {
       goto LBL_Y;
     }
     if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) {
       goto LBL_Y;
     }
  } else {
     norm = 0;
  }

  /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
  n = x.used - 1;
  t = y.used - 1;

  /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
  if ((res = mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */
    goto LBL_Y;
  }

  while (mp_cmp (&x, &y) != MP_LT) {
    ++(q.dp[n - t]);
    if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) {
      goto LBL_Y;
    }
  }

  /* reset y by shifting it back down */
  mp_rshd (&y, n - t);

  /* 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_T2:mp_clear (&t2);
LBL_T1:mp_clear (&t1);
LBL_Q:mp_clear (&q);
  return res;
}

#endif

#endif

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

/* End: bn_mp_div.c */

/* Start: bn_mp_div_2.c */
#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, [email protected], http://math.libtomcrypt.com
 */

/* b = a/2 */
int mp_div_2(mp_int * a, mp_int * b)
{
  int     x, res, oldused;

  /* copy */
  if (b->alloc < a->used) {
    if ((res = mp_grow (b, a->used)) != MP_OKAY) {
      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;

    /* carry */
    r = 0;
    for (x = b->used - 1; x >= 0; x--) {
      /* get the carry for the next iteration */
      rr = *tmpa & 1;

      /* shift the current digit, add in carry and store */
      *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));

      /* forward carry to next iteration */
      r = rr;
    }

    /* zero excess digits */
    tmpb = b->dp + b->used;
    for (x = b->used; x < oldused; x++) {
      *tmpb++ = 0;
    }
  }
  b->sign = a->sign;
  mp_clamp (b);
  return MP_OKAY;
}
#endif

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

/* End: bn_mp_div_2.c */

/* Start: bn_mp_div_2d.c */
#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, [email protected], http://math.libtomcrypt.com
 */

/* shift right by a certain bit count (store quotient in c, optional remainder in d) */
int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
{
  mp_digit D, r, rr;
  int     x, res;
  mp_int  t;


  /* if the shift count is <= 0 then we do no work */
  if (b <= 0) {
    res = mp_copy (a, c);
    if (d != NULL) {
      mp_zero (d);
    }
    return res;
  }

  if ((res = mp_init (&t)) != MP_OKAY) {
    return res;
  }

  /* get the remainder */
  if (d != NULL) {
    if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) {
      mp_clear (&t);
      return res;
    }
  }

  /* copy */
  if ((res = mp_copy (a, c)) != MP_OKAY) {
    mp_clear (&t);
    return res;
  }

  /* shift by as many digits in the bit count */
  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;

    /* alias */
    tmpc = c->dp + (c->used - 1);

    /* carry */
    r = 0;
    for (x = c->used - 1; x >= 0; x--) {
      /* get the lower  bits of this word in a temp */
      rr = *tmpc & mask;

      /* shift the current word and mix in the carry bits from the previous word */
      *tmpc = (*tmpc >> D) | (r << shift);
      --tmpc;

      /* set the carry to the carry bits of the current word found above */
      r = rr;
    }
  }
  mp_clamp (c);
  if (d != NULL) {
    mp_exch (&t, d);
  }
  mp_clear (&t);
  return MP_OKAY;
}
#endif

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

/* End: bn_mp_div_2d.c */

/* Start: bn_mp_div_3.c */
#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, [email protected], 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_word  w, t;
  mp_digit b;
  int      res, ix;

  /* b = 2**DIGIT_BIT / 3 */
  b = (((mp_word)1) << ((mp_word)DIGIT_BIT)) / ((mp_word)3);

  if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
     return res;
  }

  q.used = a->used;
  q.sign = a->sign;
  w = 0;
  for (ix = a->used - 1; ix >= 0; ix--) {
     w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);

     if (w >= 3) {
        /* multiply w by [1/3] */
        t = (w * ((mp_word)b)) >> ((mp_word)DIGIT_BIT);

        /* now subtract 3 * [w/3] from w, to get the remainder */
        w -= t+t+t;

        /* fixup the remainder as required since
         * the optimization is not exact.
         */
        while (w >= 3) {
           t += 1;
           w -= 3;
        }
      } else {
        t = 0;
      }
      q.dp[ix] = (mp_digit)t;
  }

  /* [optional] store the remainder */
  if (d != NULL) {
     *d = (mp_digit)w;
  }

  /* [optional] store the quotient */
  if (c != NULL) {
     mp_clamp(&q);
     mp_exch(&q, c);
  }
  mp_clear(&q);

  return res;
}

#endif

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

/* End: bn_mp_div_3.c */

/* Start: bn_mp_div_d.c */
#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, [email protected], http://math.libtomcrypt.com
 */

static int s_is_power_of_two(mp_digit b, int *p)
{
   int x;

   /* fast return if no power of two */
   if ((b==0) || (b & (b-1))) {
      return 0;
   }

   for (x = 0; x < DIGIT_BIT; x++) {
      if (b == (((mp_digit)1)<<x)) {
         *p = x;
         return 1;
      }
   }
   return 0;
}

/* single digit division (based on routine from MPI) */
int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
{
  mp_int  q;
  mp_word w;
  mp_digit t;
  int     res, ix;

  /* 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;
  }

  /* power of two ? */
  if (s_is_power_of_two(b, &ix) == 1) {
     if (d != NULL) {
        *d = a->dp[0] & ((((mp_digit)1)<<ix) - 1);
     }
     if (c != NULL) {
        return mp_div_2d(a, ix, c, NULL);
     }
     return MP_OKAY;
  }

#ifdef BN_MP_DIV_3_C
  /* three? */
  if (b == 3) {
     return mp_div_3(a, c, d);
  }
#endif

  /* no easy answer [c'est la vie].  Just division */
  if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
     return res;
  }

  q.used = a->used;
  q.sign = a->sign;
  w = 0;
  for (ix = a->used - 1; ix >= 0; ix--) {
     w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);

     if (w >= b) {
        t = (mp_digit)(w / b);
        w -= ((mp_word)t) * ((mp_word)b);
      } else {
        t = 0;
      }
      q.dp[ix] = (mp_digit)t;
  }

  if (d != NULL) {
     *d = (mp_digit)w;
  }

  if (c != NULL) {
     mp_clamp(&q);
     mp_exch(&q, c);
  }
  mp_clear(&q);

  return res;
}

#endif

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

/* End: bn_mp_div_d.c */

/* Start: bn_mp_dr_is_modulus.c */
#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, [email protected], http://math.libtomcrypt.com
 */

/* determines if a number is a valid DR modulus */
int mp_dr_is_modulus(mp_int *a)
{
   int ix;

   /* must be at least two digits */
   if (a->used < 2) {
      return 0;
   }

   /* must be of the form b**k - a [a <= b] so all
    * but the first digit must be equal to -1 (mod b).
    */
   for (ix = 1; ix < a->used; ix++) {
       if (a->dp[ix] != MP_MASK) {
          return 0;
       }
   }
   return 1;
}

#endif

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

/* End: bn_mp_dr_is_modulus.c */

/* Start: bn_mp_dr_reduce.c */
#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, [email protected], 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"
 *                 Chae Hoon Lim, Pil Joong Lee,
 *          POSTECH Information Research Laboratories
 *
 * The modulus must be of a special format [see manual]
 *
 * Has been modified to use algorithm 7.10 from the LTM book instead
 *
 * Input x must be in the range 0 <= x <= (n-1)**2
 */
int
mp_dr_reduce (mp_int * x, mp_int * n, mp_digit k)
{
  int      err, i, m;
  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.
 */
top:
  /* aliases for digits */
  /* alias for lower half of x */
  tmpx1 = x->dp;

  /* alias for upper half of x, or x/B**m */
  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;

  /* zero words above m */
  for (i = m + 1; i < x->used; i++) {
      *tmpx1++ = 0;
  }

  /* 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

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

/* End: bn_mp_dr_reduce.c */

/* Start: bn_mp_dr_setup.c */
#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, [email protected], 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

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

/* End: bn_mp_dr_setup.c */

/* Start: bn_mp_exch.c */
#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, [email protected], 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

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

/* End: bn_mp_exch.c */

/* Start: bn_mp_expt_d.c */
#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, [email protected], 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

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

/* End: bn_mp_expt_d.c */

/* Start: bn_mp_exptmod.c */
#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, [email protected], 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)
 */
int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
{
  int dr;

  /* modulus P must be positive */
  if (P->sign == MP_NEG) {
     return MP_VAL;
  }

  /* if exponent X is negative we have to recurse */
  if (X->sign == MP_NEG) {
#ifdef BN_MP_INVMOD_C
     mp_int tmpG, tmpX;
     int err;

     /* first compute 1/G mod P */
     if ((err = mp_init(&tmpG)) != MP_OKAY) {
        return err;
     }
     if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) {
        mp_clear(&tmpG);
        return err;
     }

     /* now get |X| */
     if ((err = mp_init(&tmpX)) != MP_OKAY) {
        mp_clear(&tmpG);
        return err;
     }
     if ((err = mp_abs(X, &tmpX)) != MP_OKAY) {
        mp_clear_multi(&tmpG, &tmpX, NULL);
        return err;
     }

     /* and now compute (1/G)**|X| instead of G**X [X < 0] */
     err = mp_exptmod(&tmpG, &tmpX, P, Y);
     mp_clear_multi(&tmpG, &tmpX, NULL);
     return err;
#else
     /* no invmod */
     return MP_VAL;
#endif
  }

/* modified diminished radix reduction */
#if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) && defined(BN_S_MP_EXPTMOD_C)
  if (mp_reduce_is_2k_l(P) == MP_YES) {
     return s_mp_exptmod(G, X, P, Y, 1);
  }
#endif

#ifdef BN_MP_DR_IS_MODULUS_C
  /* is it a DR modulus? */
  dr = mp_dr_is_modulus(P);
#else
  /* default to no */
  dr = 0;
#endif

#ifdef BN_MP_REDUCE_IS_2K_C
  /* if not, is it a unrestricted DR modulus? */
  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
    /* no exptmod for evens */
    return MP_VAL;
#endif
#ifdef BN_MP_EXPTMOD_FAST_C
  }
#endif
}

#endif

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

/* End: bn_mp_exptmod.c */

/* Start: bn_mp_exptmod_fast.c */
#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, [email protected], 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.
 *
 * Uses Montgomery or Diminished Radix reduction [whichever appropriate]
 */

#ifdef MP_LOW_MEM
   #define TAB_SIZE 32
#else
   #define TAB_SIZE 256
#endif

int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
{
  mp_int  M[TAB_SIZE], res;
  mp_digit buf, mp;
  int     err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;

  /* use a pointer to the reduction algorithm.  This allows us to use
   * one of many reduction algorithms without modding the guts of
   * the code with if statements everywhere.
   */
  int     (*redux)(mp_int*,mp_int*,mp_digit);

  /* find window size */
  x = mp_count_bits (X);
  if (x <= 7) {
    winsize = 2;
  } else if (x <= 36) {
    winsize = 3;
  } else if (x <= 140) {
    winsize = 4;
  } else if (x <= 450) {
    winsize = 5;
  } else if (x <= 1303) {
    winsize = 6;
  } else if (x <= 3529) {
    winsize = 7;
  } else {
    winsize = 8;
  }

#ifdef MP_LOW_MEM
  if (winsize > 5) {
     winsize = 5;
  }
#endif

  /* init M array */
  /* init first cell */
  if ((err = mp_init(&M[1])) != MP_OKAY) {
     return err;
  }

  /* now init the second half of the array */
  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
    if ((err = mp_init(&M[x])) != MP_OKAY) {
      for (y = 1<<(winsize-1); y < x; y++) {
        mp_clear (&M[y]);
      }
      mp_clear(&M[1]);
      return err;
    }
  }

  /* determine and setup reduction code */
  if (redmode == 0) {
#ifdef BN_MP_MONTGOMERY_SETUP_C
     /* now setup montgomery  */
     if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
        goto LBL_M;
     }
#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;
#else
        err = MP_VAL;
        goto LBL_M;
#endif
     }
  } else if (redmode == 1) {
#if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C)
     /* setup DR reduction for moduli of the form B**k - b */
     mp_dr_setup(P, &mp);
     redux = mp_dr_reduce;
#else
     err = MP_VAL;
     goto LBL_M;
#endif
  } else {
#if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C)
     /* setup DR reduction for moduli of the form 2**k - b */
     if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
        goto LBL_M;
     }
     redux = mp_reduce_2k;
#else
     err = MP_VAL;
     goto LBL_M;
#endif
  }

  /* setup result */
  if ((err = mp_init (&res)) != MP_OKAY) {
    goto LBL_M;
  }

  /* create M table
   *

   *
   * The first half of the table is not computed though accept for M[0] and M[1]
   */

  if (redmode == 0) {
#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
     /* now we need R mod m */
     if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
       goto LBL_RES;
     }
#else
     err = MP_VAL;
     goto LBL_RES;
#endif

     /* now set M[1] to G * R mod m */
     if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
       goto LBL_RES;
     }
  } else {
     mp_set(&res, 1);
     if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
        goto LBL_RES;
     }
  }

  /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
  if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
    goto LBL_RES;
  }

  for (x = 0; x < (winsize - 1); x++) {
    if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
      goto LBL_RES;
    }
    if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
      goto LBL_RES;
    }
  }

  /* create upper table */
  for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
    if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
      goto LBL_RES;
    }
    if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
      goto LBL_RES;
    }
  }

  /* set initial mode and bit cnt */
  mode   = 0;
  bitcnt = 1;
  buf    = 0;
  digidx = X->used - 1;
  bitcpy = 0;
  bitbuf = 0;

  for (;;) {
    /* grab next digit as required */
    if (--bitcnt == 0) {
      /* if digidx == -1 we are out of digits so break */
      if (digidx == -1) {
        break;
      }
      /* read next digit and reset bitcnt */
      buf    = X->dp[digidx--];
      bitcnt = (int)DIGIT_BIT;
    }

    /* grab the next msb from the exponent */
    y     = (mp_digit)(buf >> (DIGIT_BIT - 1)) & 1;
    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;
    }

    /* else we add it to the window */
    bitbuf |= (y << (winsize - ++bitcpy));
    mode    = 2;

    if (bitcpy == winsize) {
      /* ok window is filled so square as required and multiply  */
      /* square first */
      for (x = 0; x < winsize; x++) {
        if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
          goto LBL_RES;
        }
        if ((err = redux (&res, P, mp)) != MP_OKAY) {
          goto LBL_RES;
        }
      }

      /* then multiply */
      if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
        goto LBL_RES;
      }
      if ((err = redux (&res, P, mp)) != MP_OKAY) {
        goto LBL_RES;
      }

      /* empty window and reset */
      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;
      }

      /* get next bit of the window */
      bitbuf <<= 1;
      if ((bitbuf & (1 << winsize)) != 0) {
        /* then multiply */
        if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
          goto LBL_RES;
        }
        if ((err = redux (&res, P, mp)) != MP_OKAY) {
          goto LBL_RES;
        }
      }
    }
  }

  if (redmode == 0) {
     /* fixup result if Montgomery reduction is used
      * recall that any value in a Montgomery system is
      * actually multiplied by R mod n.  So we have
      * to reduce one more time to cancel out the factor
      * of R.
      */
     if ((err = redux(&res, P, mp)) != MP_OKAY) {
       goto LBL_RES;
     }
  }

  /* swap res with Y */
  mp_exch (&res, Y);
  err = MP_OKAY;
LBL_RES:mp_clear (&res);
LBL_M:
  mp_clear(&M[1]);
  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
    mp_clear (&M[x]);
  }
  return err;
}
#endif


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

/* End: bn_mp_exptmod_fast.c */

/* Start: bn_mp_exteuclid.c */
#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, [email protected], 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_init_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL)) != MP_OKAY) {
      return err;
   }

   /* initialize, (u1,u2,u3) = (1,0,a) */
   mp_set(&u1, 1);
   if ((err = mp_copy(a, &u3)) != MP_OKAY)                                        { goto _ERR; }

   /* initialize, (v1,v2,v3) = (0,1,b) */
   mp_set(&v2, 1);
   if ((err = mp_copy(b, &v3)) != MP_OKAY)                                        { goto _ERR; }

   /* loop while v3 != 0 */
   while (mp_iszero(&v3) == MP_NO) {
       /* q = u3/v3 */
       if ((err = mp_div(&u3, &v3, &q, NULL)) != MP_OKAY)                         { goto _ERR; }

       /* (t1,t2,t3) = (u1,u2,u3) - (v1,v2,v3)q */
       if ((err = mp_mul(&v1, &q, &tmp)) != MP_OKAY)                              { goto _ERR; }
       if ((err = mp_sub(&u1, &tmp, &t1)) != MP_OKAY)                             { goto _ERR; }
       if ((err = mp_mul(&v2, &q, &tmp)) != MP_OKAY)                              { goto _ERR; }
       if ((err = mp_sub(&u2, &tmp, &t2)) != MP_OKAY)                             { goto _ERR; }
       if ((err = mp_mul(&v3, &q, &tmp)) != MP_OKAY)                              { goto _ERR; }
       if ((err = mp_sub(&u3, &tmp, &t3)) != MP_OKAY)                             { goto _ERR; }

       /* (u1,u2,u3) = (v1,v2,v3) */
       if ((err = mp_copy(&v1, &u1)) != MP_OKAY)                                  { goto _ERR; }
       if ((err = mp_copy(&v2, &u2)) != MP_OKAY)                                  { goto _ERR; }
       if ((err = mp_copy(&v3, &u3)) != MP_OKAY)                                  { goto _ERR; }

       /* (v1,v2,v3) = (t1,t2,t3) */
       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

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

/* End: bn_mp_exteuclid.c */

/* Start: bn_mp_fread.c */
#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, [email protected], 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;

   /* clear a */
   mp_zero(a);

   /* if first digit is - then set negative */
   ch = fgetc(stream);
   if (ch == '-') {
      neg = MP_NEG;
      ch = fgetc(stream);
   } else {
      neg = MP_ZPOS;
   }

   for (;;) {
      /* find y in the radix map */
      for (y = 0; y < radix; y++) {
          if (mp_s_rmap[y] == ch) {
             break;
          }
      }
      if (y == radix) {
         break;
      }

      /* shift up and add */
      if ((err = mp_mul_d(a, radix, a)) != MP_OKAY) {
         return err;
      }
      if ((err = mp_add_d(a, y, a)) != MP_OKAY) {
         return err;
      }

      ch = fgetc(stream);
   }
   if (mp_cmp_d(a, 0) != MP_EQ) {
      a->sign = neg;
   }

   return MP_OKAY;
}

#endif

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

/* End: bn_mp_fread.c */

/* Start: bn_mp_fwrite.c */
#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, [email protected], http://math.libtomcrypt.com
 */

int mp_fwrite(mp_int *a, int radix, FILE *stream)
{
   char *buf;
   int err, len, x;

   if ((err = mp_radix_size(a, radix, &len)) != MP_OKAY) {
      return err;
   }

   buf = OPT_CAST(char) XMALLOC (len);
   if (buf == NULL) {
      return MP_MEM;
   }

   if ((err = mp_toradix(a, buf, radix)) != MP_OKAY) {
      XFREE (buf);
      return err;
   }

   for (x = 0; x < len; x++) {
       if (fputc(buf[x], stream) == EOF) {
          XFREE (buf);
          return MP_VAL;
       }
   }

   XFREE (buf);
   return MP_OKAY;
}

#endif

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

/* End: bn_mp_fwrite.c */

/* Start: bn_mp_gcd.c */
#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, [email protected], 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;

  /* either zero than gcd is the largest */
  if (mp_iszero (a) == MP_YES) {
    return mp_abs (b, c);
  }
  if (mp_iszero (b) == MP_YES) {
    return mp_abs (a, c);
  }

  /* get copies of a and b we can modify */
  if ((res = mp_init_copy (&u, a)) != MP_OKAY) {
    return res;
  }

  if ((res = mp_init_copy (&v, b)) != MP_OKAY) {
    goto LBL_U;
  }

  /* must be positive for the remainder of the algorithm */
  u.sign = v.sign = MP_ZPOS;

  /* B1.  Find the common power of two for u and v */
  u_lsb = mp_cnt_lsb(&u);
  v_lsb = mp_cnt_lsb(&v);
  k     = MIN(u_lsb, v_lsb);

  if (k > 0) {
     /* divide the power of two out */
     if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) {
        goto LBL_V;
     }

     if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) {
        goto LBL_V;
     }
  }

  /* divide any remaining factors of two out */
  if (u_lsb != k) {
     if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) {
        goto LBL_V;
     }
  }

  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 */
     if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) {
        goto LBL_V;
     }

     /* Divide out all factors of two */
     if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) {
        goto LBL_V;
     }
  }

  /* multiply by 2**k which we divided out at the beginning */
  if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) {
     goto LBL_V;
  }
  c->sign = MP_ZPOS;
  res = MP_OKAY;
LBL_V:mp_clear (&u);
LBL_U:mp_clear (&v);
  return res;
}
#endif

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

/* End: bn_mp_gcd.c */

/* Start: bn_mp_get_int.c */
#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, [email protected], 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

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

/* End: bn_mp_get_int.c */

/* Start: bn_mp_grow.c */
#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, [email protected], http://math.libtomcrypt.com
 */

/* grow as required */
int mp_grow (mp_int * a, int size)
{
  int     i;
  mp_digit *tmp;

  /* if the alloc size is smaller alloc more ram */
  if (a->alloc < size) {
    /* ensure there are always at least MP_PREC digits extra on top */
    size += (MP_PREC * 2) - (size % MP_PREC);

    /* reallocate the array a->dp
     *
     * We store the return in a temporary variable
     * in case the operation failed we don't want
     * to overwrite the dp member of a.
     */
    tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * size);
    if (tmp == NULL) {
      /* reallocation failed but "a" is still valid [can be freed] */
      return MP_MEM;
    }

    /* reallocation succeeded so set a->dp */
    a->dp = tmp;

    /* zero excess digits */
    i        = a->alloc;
    a->alloc = size;
    for (; i < a->alloc; i++) {
      a->dp[i] = 0;
    }
  }
  return MP_OKAY;
}
#endif

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

/* End: bn_mp_grow.c */

/* Start: bn_mp_init.c */
#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, [email protected], http://math.libtomcrypt.com
 */

/* init a new mp_int */
int mp_init (mp_int * a)
{
  int i;

  /* allocate memory required and clear it */
  a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC);
  if (a->dp == NULL) {
    return MP_MEM;
  }

  /* set the digits to zero */
  for (i = 0; i < MP_PREC; i++) {
      a->dp[i] = 0;
  }

  /* set the used to zero, allocated digits to the default precision
   * and sign to positive */
  a->used  = 0;
  a->alloc = MP_PREC;
  a->sign  = MP_ZPOS;

  return MP_OKAY;
}
#endif

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

/* End: bn_mp_init.c */

/* Start: bn_mp_init_copy.c */
#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, [email protected], 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

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

/* End: bn_mp_init_copy.c */

/* Start: bn_mp_init_multi.c */
#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, [email protected], 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 */
    mp_int* cur_arg = mp;
    va_list args;

    va_start(args, mp);        /* init args to next argument from caller */
    while (cur_arg != NULL) {
        if (mp_init(cur_arg) != MP_OKAY) {
            /* Oops - error! Back-track and mp_clear what we already
               succeeded in init-ing, then return error.
            */
            va_list clean_args;

            /* 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;
        }
        n++;
        cur_arg = va_arg(args, mp_int*);
    }
    va_end(args);
    return res;                /* Assumed ok, if error flagged above. */
}

#endif

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

/* End: bn_mp_init_multi.c */

/* Start: bn_mp_init_set.c */
#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, [email protected], 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

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

/* End: bn_mp_init_set.c */

/* Start: bn_mp_init_set_int.c */
#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, [email protected], 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

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

/* End: bn_mp_init_set_int.c */

/* Start: bn_mp_init_size.c */
#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, [email protected], http://math.libtomcrypt.com
 */

/* init an mp_init for a given size */
int mp_init_size (mp_int * a, int size)
{
  int x;

  /* pad size so there are always extra digits */
  size += (MP_PREC * 2) - (size % MP_PREC);	

  /* alloc mem */
  a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size);
  if (a->dp == NULL) {
    return MP_MEM;
  }

  /* set the members */
  a->used  = 0;
  a->alloc = size;
  a->sign  = MP_ZPOS;

  /* zero the digits */
  for (x = 0; x < size; x++) {
      a->dp[x] = 0;
  }

  return MP_OKAY;
}
#endif

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

/* End: bn_mp_init_size.c */

/* Start: bn_mp_invmod.c */
#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, [email protected], 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

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

/* End: bn_mp_invmod.c */

/* Start: bn_mp_invmod_slow.c */
#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, [email protected], 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;
  }

  /* x = a, y = b */
  if ((res = mp_mod(a, b, &x)) != MP_OKAY) {
      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;
  }
  if ((res = mp_copy (&y, &v)) != MP_OKAY) {
    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;
      }
    }
    /* A = A/2, B = B/2 */
    if ((res = mp_div_2 (&A, &A)) != 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;
      }
    }
    /* C = C/2, D = D/2 */
    if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
      goto LBL_ERR;
    }
    if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* 6.  if u >= v then */
  if (mp_cmp (&u, &v) != MP_LT) {
    /* u = u - v, A = A - C, B = B - D */
    if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
      goto LBL_ERR;
    }

    if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
      goto LBL_ERR;
    }

    if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
      goto LBL_ERR;
    }
  } else {
    /* v - v - u, C = C - A, D = D - B */
    if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
      goto LBL_ERR;
    }

    if ((res = mp_sub (&C, &A, &C)) != 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;
    goto LBL_ERR;
  }

  /* if its too low */
  while (mp_cmp_d(&C, 0) == MP_LT) {
      if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
         goto LBL_ERR;
      }
  }

  /* too big */
  while (mp_cmp_mag(&C, b) != MP_LT) {
      if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
         goto LBL_ERR;
      }
  }

  /* 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

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

/* End: bn_mp_invmod_slow.c */

/* Start: bn_mp_is_square.c */
#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, [email protected], 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,
 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
 1, 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,
 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1
};

static const char rem_105[105] = {
 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1,
 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1,
 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,
 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1,
 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1
};

/* Store non-zero to ret if arg is square, and zero if not */
int mp_is_square(mp_int *arg,int *ret)
{
  int           res;
  mp_digit      c;
  mp_int        t;
  unsigned long r;

  /* Default to Non-square :) */
  *ret = MP_NO;

  if (arg->sign == MP_NEG) {
    return MP_VAL;
  }

  /* digits used?  (TSD) */
  if (arg->used == 0) {
     return MP_OKAY;
  }

  /* First check mod 128 (suppose that DIGIT_BIT is at least 7) */
  if (rem_128[127 & DIGIT(arg,0)] == 1) {
     return MP_OKAY;
  }

  /* Next check mod 105 (3*5*7) */
  if ((res = mp_mod_d(arg,105,&c)) != MP_OKAY) {
     return res;
  }
  if (rem_105[c] == 1) {
     return MP_OKAY;
  }


  if ((res = mp_init_set_int(&t,11L*13L*17L*19L*23L*29L*31L)) != MP_OKAY) {
     return res;
  }
  if ((res = mp_mod(arg,&t,&t)) != MP_OKAY) {
     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

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

/* End: bn_mp_is_square.c */

/* Start: bn_mp_jacobi.c */
#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, [email protected], 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;
  }

  /* default */
  s = 0;

  /* step 3.  write a = a1 * 2**k  */
  if ((res = mp_init_copy (&a1, a)) != MP_OKAY) {
    return res;
  }

  if ((res = mp_init (&p1)) != MP_OKAY) {
    goto LBL_A1;
  }

  /* divide out larger power of two */
  k = mp_cnt_lsb(&a1);
  if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) {
     goto LBL_P1;
  }

  /* 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

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

/* End: bn_mp_jacobi.c */

/* Start: bn_mp_karatsuba_mul.c */
#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, [email protected], 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
 * the min(a,b)
 *
 * a = a1 * B**n + a0
 * b = b1 * B**n + b0
 *
 * Then, a * b =>
   a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0
 *
 * Note that a1b1 and a0b0 are used twice and only need to be
 * computed once.  So in total three half size (half # of
 * digit) multiplications are performed, a0b0, a1b1 and
 * (a1+b1)(a0+b0)
 *
 * Note that a multiplication of half the digits requires
 * 1/4th the number of single precision multiplications so in
 * total after one call 25% of the single precision multiplications
 * are saved.  Note also that the call to mp_mul can end up back
 * in this function if the a0, a1, b0, or b1 are above the threshold.
 * This is known as divide-and-conquer and leads to the famous
 * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than
 * the standard O(N**2) that the baseline/comba methods use.
 * Generally though the overhead of this method doesn't pay off
 * until a certain size (N ~ 80) is reached.
 */
int mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int  x0, x1, y0, y1, t1, x0y0, x1y1;
  int     B, err;

  /* default the return code to an error */
  err = MP_MEM;

  /* min # of digits */
  B = MIN (a->used, b->used);

  /* now divide in two */
  B = B >> 1;

  /* init copy all the temps */
  if (mp_init_size (&x0, B) != MP_OKAY)
    goto ERR;
  if (mp_init_size (&x1, a->used - B) != MP_OKAY)
    goto X0;
  if (mp_init_size (&y0, B) != MP_OKAY)
    goto X1;
  if (mp_init_size (&y1, b->used - B) != MP_OKAY)
    goto Y0;

  /* init temps */
  if (mp_init_size (&t1, B * 2) != MP_OKAY)
    goto Y1;
  if (mp_init_size (&x0y0, B * 2) != MP_OKAY)
    goto T1;
  if (mp_init_size (&x1y1, B * 2) != MP_OKAY)
    goto X0Y0;

  /* 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;

    tmpx = x0.dp;
    tmpy = y0.dp;
    for (x = 0; x < B; x++) {
      *tmpx++ = *tmpa++;
      *tmpy++ = *tmpb++;
    }

    tmpx = x1.dp;
    for (x = B; x < a->used; x++) {
      *tmpx++ = *tmpa++;
    }

    tmpy = y1.dp;
    for (x = B; x < b->used; x++) {
      *tmpy++ = *tmpb++;
    }
  }

  /* only need to clamp the lower words since by definition the
   * upper words x1/y1 must have a known number of digits
   */
  mp_clamp (&x0);
  mp_clamp (&y0);

  /* now calc the products x0y0 and x1y1 */
  /* after this x0 is no longer required, free temp [x0==t2]! */
  if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY)
    goto X1Y1;          /* x0y0 = x0*y0 */
  if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY)
    goto X1Y1;          /* x1y1 = x1*y1 */

  /* now calc x1+x0 and y1+y0 */
  if (s_mp_add (&x1, &x0, &t1) != MP_OKAY)
    goto X1Y1;          /* t1 = x1 - x0 */
  if (s_mp_add (&y1, &y0, &x0) != MP_OKAY)
    goto X1Y1;          /* t2 = y1 - y0 */
  if (mp_mul (&t1, &x0, &t1) != MP_OKAY)
    goto X1Y1;          /* t1 = (x1 + x0) * (y1 + y0) */

  /* add x0y0 */
  if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY)
    goto X1Y1;          /* t2 = x0y0 + x1y1 */
  if (s_mp_sub (&t1, &x0, &t1) != MP_OKAY)
    goto X1Y1;          /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */

  /* shift by B */
  if (mp_lshd (&t1, B) != MP_OKAY)
    goto X1Y1;          /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
  if (mp_lshd (&x1y1, B * 2) != MP_OKAY)
    goto X1Y1;          /* x1y1 = x1y1 << 2*B */

  if (mp_add (&x0y0, &t1, &t1) != MP_OKAY)
    goto X1Y1;          /* t1 = x0y0 + t1 */
  if (mp_add (&t1, &x1y1, c) != MP_OKAY)
    goto X1Y1;          /* t1 = x0y0 + t1 + x1y1 */

  /* Algorithm succeeded set the return code to MP_OKAY */
  err = MP_OKAY;

X1Y1:mp_clear (&x1y1);
X0Y0:mp_clear (&x0y0);
T1:mp_clear (&t1);
Y1:mp_clear (&y1);
Y0:mp_clear (&y0);
X1:mp_clear (&x1);
X0:mp_clear (&x0);
ERR:
  return err;
}
#endif

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

/* End: bn_mp_karatsuba_mul.c */

/* Start: bn_mp_karatsuba_sqr.c */
#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, [email protected], 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
 * tuned to perform recursive squarings.
 */
int mp_karatsuba_sqr (mp_int * a, mp_int * b)
{
  mp_int  x0, x1, t1, t2, x0x0, x1x1;
  int     B, err;

  err = MP_MEM;

  /* min # of digits */
  B = a->used;

  /* now divide in two */
  B = B >> 1;

  /* init copy all the temps */
  if (mp_init_size (&x0, B) != MP_OKAY)
    goto ERR;
  if (mp_init_size (&x1, a->used - B) != MP_OKAY)
    goto X0;

  /* init temps */
  if (mp_init_size (&t1, a->used * 2) != MP_OKAY)
    goto X1;
  if (mp_init_size (&t2, a->used * 2) != MP_OKAY)
    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++;
    }

    dst = x1.dp;
    for (x = B; x < a->used; x++) {
      *dst++ = *src++;
    }
  }

  x0.used = B;
  x1.used = a->used - B;

  mp_clamp (&x0);

  /* now calc the products x0*x0 and x1*x1 */
  if (mp_sqr (&x0, &x0x0) != MP_OKAY)
    goto X1X1;           /* x0x0 = x0*x0 */
  if (mp_sqr (&x1, &x1x1) != MP_OKAY)
    goto X1X1;           /* x1x1 = x1*x1 */

  /* now calc (x1+x0)**2 */
  if (s_mp_add (&x1, &x0, &t1) != MP_OKAY)
    goto X1X1;           /* t1 = x1 - x0 */
  if (mp_sqr (&t1, &t1) != MP_OKAY)
    goto X1X1;           /* t1 = (x1 - x0) * (x1 - x0) */

  /* add x0y0 */
  if (s_mp_add (&x0x0, &x1x1, &t2) != MP_OKAY)
    goto X1X1;           /* t2 = x0x0 + x1x1 */
  if (s_mp_sub (&t1, &t2, &t1) != MP_OKAY)
    goto X1X1;           /* t1 = (x1+x0)**2 - (x0x0 + x1x1) */

  /* shift by B */
  if (mp_lshd (&t1, B) != MP_OKAY)
    goto X1X1;           /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<<B */
  if (mp_lshd (&x1x1, B * 2) != MP_OKAY)
    goto X1X1;           /* x1x1 = x1x1 << 2*B */

  if (mp_add (&x0x0, &t1, &t1) != MP_OKAY)
    goto X1X1;           /* t1 = x0x0 + t1 */
  if (mp_add (&t1, &x1x1, b) != MP_OKAY)
    goto X1X1;           /* t1 = x0x0 + t1 + x1x1 */

  err = MP_OKAY;

X1X1:mp_clear (&x1x1);
X0X0:mp_clear (&x0x0);
T2:mp_clear (&t2);
T1:mp_clear (&t1);
X1:mp_clear (&x1);
X0:mp_clear (&x0);
ERR:
  return err;
}
#endif

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

/* End: bn_mp_karatsuba_sqr.c */

/* Start: bn_mp_lcm.c */
#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, [email protected], 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;


  if ((res = mp_init_multi (&t1, &t2, NULL)) != MP_OKAY) {
    return res;
  }

  /* t1 = get the GCD of the two inputs */
  if ((res = mp_gcd (a, b, &t1)) != MP_OKAY) {
    goto LBL_T;
  }

  /* divide the smallest by the GCD */
  if (mp_cmp_mag(a, b) == MP_LT) {
     /* store quotient in t2 such that t2 * b is the LCM */
     if ((res = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) {
        goto LBL_T;
     }
     res = mp_mul(b, &t2, c);
  } else {
     /* store quotient in t2 such that t2 * a is the LCM */
     if ((res = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) {
        goto LBL_T;
     }
     res = mp_mul(a, &t2, c);
  }

  /* fix the sign to positive */
  c->sign = MP_ZPOS;

LBL_T:
  mp_clear_multi (&t1, &t2, NULL);
  return res;
}
#endif

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

/* End: bn_mp_lcm.c */

/* Start: bn_mp_lshd.c */
#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, [email protected], 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--;
    }

    /* zero the lower digits */
    top = a->dp;
    for (x = 0; x < b; x++) {
      *top++ = 0;
    }
  }
  return MP_OKAY;
}
#endif

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

/* End: bn_mp_lshd.c */

/* Start: bn_mp_mod.c */
#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, [email protected], 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) {
    return res;
  }

  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;
}