Tcl Source Code

*/config.cache
*/config.log
*/config.status
*/tclConfig.sh
*/tclsh*
*/tcltest*
*/versions.vc

html
libtommath/bn.ilg
libtommath/bn.ind
libtommath/pretty.build
libtommath/tommath.src
libtommath/*.pdf
libtommath/*.pl
................................................................................
libtommath/*.out
libtommath/*.tex
unix/autoMkindex.tcl
unix/dltest.marker
unix/tcl.pc
unix/tclIndex
unix/pkgs/*
win/Debug_VC*
win/Release_VC*
win/pkgs/*
win/tcl.hpj

*/config.cache
*/config.log
*/config.status
*/tclConfig.sh
*/tclsh*
*/tcltest*
*/versions.vc
*/version.vc
html
libtommath/bn.ilg
libtommath/bn.ind
libtommath/pretty.build
libtommath/tommath.src
libtommath/*.pdf
libtommath/*.pl
................................................................................
libtommath/*.out
libtommath/*.tex
unix/autoMkindex.tcl
unix/dltest.marker
unix/tcl.pc
unix/tclIndex
unix/pkgs/*
win/Debug*
win/Release*
win/pkgs/*
win/tcl.hpj
win/nmhlp-out.txt

#endif

/*
 * misc
 */

#define	NOTREACHED	0
#define	xxx		1

#define	DUPMAX	_POSIX2_RE_DUP_MAX
#define	DUPINF	(DUPMAX+1)

#define	REMAGIC	0xfed7		/* magic number for main struct */

/*

#endif

/*
 * misc
 */

#define	NOTREACHED	0


#define	DUPMAX	_POSIX2_RE_DUP_MAX
#define	DUPINF	(DUPMAX+1)

#define	REMAGIC	0xfed7		/* magic number for main struct */

/*

	return 0;
    }

    /*
     * We must delete this command, even though both traces and delete procs
     * may try to avoid this (renaming the command etc). Also traces and
     * delete procs may try to delete the command themsevles. This flag
     * declares that a delete is in progress and that recursive deletes should
     * be ignored.
     */

    cmdPtr->flags |= CMD_IS_DELETED;

    /*
................................................................................
			return TCL_OK;
		    }
		    string++;
		}
	    }
	    goto unChanged;
	} else if (l == LONG_MIN) {
	    TclBNInitBignumFromLong(&big, l);
	    goto tooLarge;
	}
	Tcl_SetObjResult(interp, Tcl_NewLongObj(-l));
	return TCL_OK;
    }

    if (type == TCL_NUMBER_DOUBLE) {
................................................................................
    if (type == TCL_NUMBER_WIDE) {
	Tcl_WideInt w = *((const Tcl_WideInt *) ptr);

	if (w >= (Tcl_WideInt)0) {
	    goto unChanged;
	}
	if (w == LLONG_MIN) {
	    TclBNInitBignumFromWideInt(&big, w);
	    goto tooLarge;
	}
	Tcl_SetObjResult(interp, Tcl_NewWideIntObj(-w));
	return TCL_OK;
    }
#endif

................................................................................
	return TCL_ERROR;
    }

    if (!(iPtr->flags & RAND_SEED_INITIALIZED)) {
	iPtr->flags |= RAND_SEED_INITIALIZED;

	/*
	 * Take into consideration the thread this interp is running in order
	 * to insure different seeds in different threads (bug #416643)

	 */

	iPtr->randSeed = TclpGetClicks() + (PTR2INT(Tcl_GetCurrentThread())<<12);

	/*
	 * Make sure 1 <= randSeed <= (2^31) - 2. See below.
	 */
................................................................................
    corPtr->callerEEPtr = iPtr->execEnvPtr;
    RESTORE_CONTEXT(corPtr->running);
    iPtr->execEnvPtr = corPtr->eePtr;

    TclNRAddCallback(interp, NRCoroutineExitCallback, corPtr,
	    NULL, NULL, NULL);

    /* insure that the command is looked up in the correct namespace */
    iPtr->lookupNsPtr = lookupNsPtr;
    Tcl_NREvalObj(interp, Tcl_NewListObj(objc-2, objv+2), 0);
    iPtr->numLevels--;

    SAVE_CONTEXT(corPtr->running);
    RESTORE_CONTEXT(corPtr->caller);
    iPtr->execEnvPtr = corPtr->callerEEPtr;

	return 0;
    }

    /*
     * We must delete this command, even though both traces and delete procs
     * may try to avoid this (renaming the command etc). Also traces and
     * delete procs may try to delete the command themselves. This flag
     * declares that a delete is in progress and that recursive deletes should
     * be ignored.
     */

    cmdPtr->flags |= CMD_IS_DELETED;

    /*
................................................................................
			return TCL_OK;
		    }
		    string++;
		}
	    }
	    goto unChanged;
	} else if (l == LONG_MIN) {
	    TclInitBignumFromLong(&big, l);
	    goto tooLarge;
	}
	Tcl_SetObjResult(interp, Tcl_NewLongObj(-l));
	return TCL_OK;
    }

    if (type == TCL_NUMBER_DOUBLE) {
................................................................................
    if (type == TCL_NUMBER_WIDE) {
	Tcl_WideInt w = *((const Tcl_WideInt *) ptr);

	if (w >= (Tcl_WideInt)0) {
	    goto unChanged;
	}
	if (w == LLONG_MIN) {
	    TclInitBignumFromWideInt(&big, w);
	    goto tooLarge;
	}
	Tcl_SetObjResult(interp, Tcl_NewWideIntObj(-w));
	return TCL_OK;
    }
#endif

................................................................................
	return TCL_ERROR;
    }

    if (!(iPtr->flags & RAND_SEED_INITIALIZED)) {
	iPtr->flags |= RAND_SEED_INITIALIZED;

	/*

	 * To ensure different seeds in different threads (bug #416643), 
	 * take into consideration the thread this interp is running in.
	 */

	iPtr->randSeed = TclpGetClicks() + (PTR2INT(Tcl_GetCurrentThread())<<12);

	/*
	 * Make sure 1 <= randSeed <= (2^31) - 2. See below.
	 */
................................................................................
    corPtr->callerEEPtr = iPtr->execEnvPtr;
    RESTORE_CONTEXT(corPtr->running);
    iPtr->execEnvPtr = corPtr->eePtr;

    TclNRAddCallback(interp, NRCoroutineExitCallback, corPtr,
	    NULL, NULL, NULL);

    /* ensure that the command is looked up in the correct namespace */
    iPtr->lookupNsPtr = lookupNsPtr;
    Tcl_NREvalObj(interp, Tcl_NewListObj(objc-2, objv+2), 0);
    iPtr->numLevels--;

    SAVE_CONTEXT(corPtr->running);
    RESTORE_CONTEXT(corPtr->caller);
    iPtr->execEnvPtr = corPtr->callerEEPtr;

		    | (((Tcl_WideUInt) buffer[1]) << 48)
		    | (((Tcl_WideUInt) buffer[0]) << 56);
	}
	if (flags & BINARY_UNSIGNED) {
	    Tcl_Obj *bigObj = NULL;
	    mp_int big;

	    TclBNInitBignumFromWideUInt(&big, uwvalue);
	    bigObj = Tcl_NewBignumObj(&big);
	    return bigObj;
	}
	return Tcl_NewWideIntObj((Tcl_WideInt) uwvalue);

	/*
	 * Do not cache double values; they are already too large to use as

		    | (((Tcl_WideUInt) buffer[1]) << 48)
		    | (((Tcl_WideUInt) buffer[0]) << 56);
	}
	if (flags & BINARY_UNSIGNED) {
	    Tcl_Obj *bigObj = NULL;
	    mp_int big;

	    TclInitBignumFromWideUInt(&big, uwvalue);
	    bigObj = Tcl_NewBignumObj(&big);
	    return bigObj;
	}
	return Tcl_NewWideIntObj((Tcl_WideInt) uwvalue);

	/*
	 * Do not cache double values; they are already too large to use as

	}

	if (appendObjPtr) {
	    if (Tcl_IsShared(valuePtr)) {
		valuePtr = Tcl_DuplicateObj(valuePtr);
	    }


	    Tcl_AppendObjToObj(valuePtr, appendObjPtr);

	}

	Tcl_DictObjPut(NULL, dictPtr, objv[2], valuePtr);
    }

    /*
     * Even if nothing changed, we still overwrite so that variable

	}

	if (appendObjPtr) {
	    if (Tcl_IsShared(valuePtr)) {
		valuePtr = Tcl_DuplicateObj(valuePtr);
	    }

	    Tcl_IncrRefCount(appendObjPtr);
	    Tcl_AppendObjToObj(valuePtr, appendObjPtr);
	    Tcl_DecrRefCount(appendObjPtr);
	}

	Tcl_DictObjPut(NULL, dictPtr, objv[2], valuePtr);
    }

    /*
     * Even if nothing changed, we still overwrite so that variable

    /*
     * Create a few initial encodings. Note that the UTF-8 to UTF-8
     * translation is not a no-op, because it will turn a stream of improperly
     * formed UTF-8 into a properly formed stream.
     */

    type.encodingName	= "identity";
    type.toUtfProc	= BinaryProc;
    type.fromUtfProc	= BinaryProc;
    type.freeProc	= NULL;
    type.nullSize	= 1;
    type.clientData	= NULL;
    tclIdentityEncoding = Tcl_CreateEncoding(&type);

................................................................................
    if (encodingPtr->refCount-- <= 1) {
	if (encodingPtr->freeProc != NULL) {
	    encodingPtr->freeProc(encodingPtr->clientData);
	}
	if (encodingPtr->hPtr != NULL) {
	    Tcl_DeleteHashEntry(encodingPtr->hPtr);
	}

	ckfree(encodingPtr->name);

	ckfree(encodingPtr);
    }
}
 
/*
 *-------------------------------------------------------------------------
 *
................................................................................
 */

Tcl_Encoding
Tcl_CreateEncoding(
    const Tcl_EncodingType *typePtr)
				/* The encoding type. */
{
    Tcl_HashEntry *hPtr;
    int isNew;
    Encoding *encodingPtr;
    char *name;

    Tcl_MutexLock(&encodingMutex);
    hPtr = Tcl_CreateHashEntry(&encodingTable, typePtr->encodingName, &isNew);
    if (isNew == 0) {
	/*
	 * Remove old encoding from hash table, but don't delete it until last
	 * reference goes away.
	 */

	encodingPtr = Tcl_GetHashValue(hPtr);
	encodingPtr->hPtr = NULL;
    }

    name = ckalloc(strlen(typePtr->encodingName) + 1);

    encodingPtr = ckalloc(sizeof(Encoding));
    encodingPtr->name		= strcpy(name, typePtr->encodingName);
    encodingPtr->toUtfProc	= typePtr->toUtfProc;
    encodingPtr->fromUtfProc	= typePtr->fromUtfProc;
    encodingPtr->freeProc	= typePtr->freeProc;
    encodingPtr->nullSize	= typePtr->nullSize;
    encodingPtr->clientData	= typePtr->clientData;
    if (typePtr->nullSize == 1) {
	encodingPtr->lengthProc = (LengthProc *) strlen;
    } else {
	encodingPtr->lengthProc = (LengthProc *) unilen;
    }
    encodingPtr->refCount	= 1;





















    encodingPtr->hPtr		= hPtr;
    Tcl_SetHashValue(hPtr, encodingPtr);

    Tcl_MutexUnlock(&encodingMutex);

    return (Tcl_Encoding) encodingPtr;
}
 
/*
 *-------------------------------------------------------------------------
 *
 * Tcl_ExternalToUtfDString --

    /*
     * Create a few initial encodings. Note that the UTF-8 to UTF-8
     * translation is not a no-op, because it will turn a stream of improperly
     * formed UTF-8 into a properly formed stream.
     */

    type.encodingName	= NULL;
    type.toUtfProc	= BinaryProc;
    type.fromUtfProc	= BinaryProc;
    type.freeProc	= NULL;
    type.nullSize	= 1;
    type.clientData	= NULL;
    tclIdentityEncoding = Tcl_CreateEncoding(&type);

................................................................................
    if (encodingPtr->refCount-- <= 1) {
	if (encodingPtr->freeProc != NULL) {
	    encodingPtr->freeProc(encodingPtr->clientData);
	}
	if (encodingPtr->hPtr != NULL) {
	    Tcl_DeleteHashEntry(encodingPtr->hPtr);
	}
	if (encodingPtr->name) {
	    ckfree(encodingPtr->name);
	}
	ckfree(encodingPtr);
    }
}
 
/*
 *-------------------------------------------------------------------------
 *
................................................................................
 */

Tcl_Encoding
Tcl_CreateEncoding(
    const Tcl_EncodingType *typePtr)
				/* The encoding type. */
{



















    Encoding *encodingPtr = ckalloc(sizeof(Encoding));
    encodingPtr->name		= NULL;
    encodingPtr->toUtfProc	= typePtr->toUtfProc;
    encodingPtr->fromUtfProc	= typePtr->fromUtfProc;
    encodingPtr->freeProc	= typePtr->freeProc;
    encodingPtr->nullSize	= typePtr->nullSize;
    encodingPtr->clientData	= typePtr->clientData;
    if (typePtr->nullSize == 1) {
	encodingPtr->lengthProc = (LengthProc *) strlen;
    } else {
	encodingPtr->lengthProc = (LengthProc *) unilen;
    }
    encodingPtr->refCount	= 1;
    encodingPtr->hPtr		= NULL;

  if (typePtr->encodingName) {
    Tcl_HashEntry *hPtr;
    int isNew;
    char *name;

    Tcl_MutexLock(&encodingMutex);
    hPtr = Tcl_CreateHashEntry(&encodingTable, typePtr->encodingName, &isNew);
    if (isNew == 0) {
	/*
	 * Remove old encoding from hash table, but don't delete it until last
	 * reference goes away.
	 */

	Encoding *replaceMe = Tcl_GetHashValue(hPtr);
	replaceMe->hPtr = NULL;
    }

    name = ckalloc(strlen(typePtr->encodingName) + 1);
    encodingPtr->name		= strcpy(name, typePtr->encodingName);
    encodingPtr->hPtr		= hPtr;
    Tcl_SetHashValue(hPtr, encodingPtr);

    Tcl_MutexUnlock(&encodingMutex);
  }
    return (Tcl_Encoding) encodingPtr;
}
 
/*
 *-------------------------------------------------------------------------
 *
 * Tcl_ExternalToUtfDString --

	    if (p2 == NULL) {
		/*
		 * This condition seem to happen occasionally under some
		 * versions of Solaris, or when encoding accidents swallow the
		 * '='; ignore the entry.
		 */


		continue;
	    }
	    p2++;
	    p2[-1] = '\0';
	    obj1 = Tcl_NewStringObj(p1, -1);
	    obj2 = Tcl_NewStringObj(p2, -1);
	    Tcl_DStringFree(&envString);

	    if (p2 == NULL) {
		/*
		 * This condition seem to happen occasionally under some
		 * versions of Solaris, or when encoding accidents swallow the
		 * '='; ignore the entry.
		 */

		Tcl_DStringFree(&envString);
		continue;
	    }
	    p2++;
	    p2[-1] = '\0';
	    obj1 = Tcl_NewStringObj(p1, -1);
	    obj2 = Tcl_NewStringObj(p2, -1);
	    Tcl_DStringFree(&envString);

	    /* TODO: internals intrusion */
	    if ((w1 > ((Tcl_WideInt) 0)) ^ (big2.sign == MP_ZPOS)) {
		/*
		 * Arguments are opposite sign; remainder is sum.
		 */

		TclBNInitBignumFromWideInt(&big1, w1);
		mp_add(&big2, &big1, &big2);
		mp_clear(&big1);
		BIG_RESULT(&big2);
	    }

	    /*
	     * Arguments are same sign; remainder is first operand.
................................................................................
	case TCL_NUMBER_DOUBLE:
	    DOUBLE_RESULT(-(*((const double *) ptr)));
	case TCL_NUMBER_LONG:
	    w = (Tcl_WideInt) (*((const long *) ptr));
	    if (w != LLONG_MIN) {
		WIDE_RESULT(-w);
	    }
	    TclBNInitBignumFromLong(&big, *(const long *) ptr);
	    break;
#ifndef TCL_WIDE_INT_IS_LONG
	case TCL_NUMBER_WIDE:
	    w = *((const Tcl_WideInt *) ptr);
	    if (w != LLONG_MIN) {
		WIDE_RESULT(-w);
	    }
	    TclBNInitBignumFromWideInt(&big, w);
	    break;
#endif
	default:
	    Tcl_TakeBignumFromObj(NULL, valuePtr, &big);
	}
	mp_neg(&big, &big);
	BIG_RESULT(&big);

	    /* TODO: internals intrusion */
	    if ((w1 > ((Tcl_WideInt) 0)) ^ (big2.sign == MP_ZPOS)) {
		/*
		 * Arguments are opposite sign; remainder is sum.
		 */

		TclInitBignumFromWideInt(&big1, w1);
		mp_add(&big2, &big1, &big2);
		mp_clear(&big1);
		BIG_RESULT(&big2);
	    }

	    /*
	     * Arguments are same sign; remainder is first operand.
................................................................................
	case TCL_NUMBER_DOUBLE:
	    DOUBLE_RESULT(-(*((const double *) ptr)));
	case TCL_NUMBER_LONG:
	    w = (Tcl_WideInt) (*((const long *) ptr));
	    if (w != LLONG_MIN) {
		WIDE_RESULT(-w);
	    }
	    TclInitBignumFromLong(&big, *(const long *) ptr);
	    break;
#ifndef TCL_WIDE_INT_IS_LONG
	case TCL_NUMBER_WIDE:
	    w = *((const Tcl_WideInt *) ptr);
	    if (w != LLONG_MIN) {
		WIDE_RESULT(-w);
	    }
	    TclInitBignumFromWideInt(&big, w);
	    break;
#endif
	default:
	    Tcl_TakeBignumFromObj(NULL, valuePtr, &big);
	}
	mp_neg(&big, &big);
	BIG_RESULT(&big);

		&driveNameLen, &driveName) == TCL_PATH_ABSOLUTE) {
	    pathPrefix = driveName;
	    tail += driveNameLen;
	}
    }

    /*
     * To process a [glob] invokation, this function may be called multiple
     * times. Each time, the previously discovered filenames are in the
     * interpreter result. We stash that away here so the result is free for
     * error messsages.
     */

    savedResultObj = Tcl_GetObjResult(interp);
    Tcl_IncrRefCount(savedResultObj);

		&driveNameLen, &driveName) == TCL_PATH_ABSOLUTE) {
	    pathPrefix = driveName;
	    tail += driveNameLen;
	}
    }

    /*
     * To process a [glob] invocation, this function may be called multiple
     * times. Each time, the previously discovered filenames are in the
     * interpreter result. We stash that away here so the result is free for
     * error messsages.
     */

    savedResultObj = Tcl_GetObjResult(interp);
    Tcl_IncrRefCount(savedResultObj);

 * Prototypes for the array hash key methods.
 */

static Tcl_HashEntry *	AllocArrayEntry(Tcl_HashTable *tablePtr, void *keyPtr);
static int		CompareArrayKeys(void *keyPtr, Tcl_HashEntry *hPtr);
static TCL_HASH_TYPE	HashArrayKey(Tcl_HashTable *tablePtr, void *keyPtr);

/*
 * Prototypes for the one word hash key methods. Not actually declared because
 * this is a critical path that is implemented in the core hash table access
 * function.
 */

#if 0
static Tcl_HashEntry *	AllocOneWordEntry(Tcl_HashTable *tablePtr,
			    void *keyPtr);
static int		CompareOneWordKeys(void *keyPtr, Tcl_HashEntry *hPtr);
static unsigned int	HashOneWordKey(Tcl_HashTable *tablePtr, void *keyPtr);
#endif

/*
 * Prototypes for the string hash key methods.
 */

static Tcl_HashEntry *	AllocStringEntry(Tcl_HashTable *tablePtr,
			    void *keyPtr);
static int		CompareStringKeys(void *keyPtr, Tcl_HashEntry *hPtr);

 * Prototypes for the array hash key methods.
 */

static Tcl_HashEntry *	AllocArrayEntry(Tcl_HashTable *tablePtr, void *keyPtr);
static int		CompareArrayKeys(void *keyPtr, Tcl_HashEntry *hPtr);
static TCL_HASH_TYPE	HashArrayKey(Tcl_HashTable *tablePtr, void *keyPtr);














/*
 * Prototypes for the string hash key methods.
 */

static Tcl_HashEntry *	AllocStringEntry(Tcl_HashTable *tablePtr,
			    void *keyPtr);
static int		CompareStringKeys(void *keyPtr, Tcl_HashEntry *hPtr);

    /*
     * This operation should occur at the top of a channel stack.
     */

    chanPtr = statePtr->topChanPtr;

    if (CheckChannelErrors(statePtr, TCL_WRITABLE) != 0) {
	return -1;
    }

    result = FlushChannel(NULL, chanPtr, 0);
    if (result != 0) {
	return TCL_ERROR;
    }

    /*
     * This operation should occur at the top of a channel stack.
     */

    chanPtr = statePtr->topChanPtr;

    if (CheckChannelErrors(statePtr, TCL_WRITABLE) != 0) {
	return TCL_ERROR;
    }

    result = FlushChannel(NULL, chanPtr, 0);
    if (result != 0) {
	return TCL_ERROR;
    }

 * TclNRLmapCmd and their compilations.
 */

#define TCL_EACH_KEEP_NONE  0	/* Discard iteration result like [foreach] */
#define TCL_EACH_COLLECT    1	/* Collect iteration result like [lmap] */

/*
 * Macros providing a faster path to integers: Tcl_GetLongFromObj everywhere,
 * Tcl_GetIntFromObj and TclGetIntForIndex on platforms where longs are ints.
 *
 * WARNING: these macros eval their args more than once.
 */

#define TclGetLongFromObj(interp, objPtr, longPtr) \
    (((objPtr)->typePtr == &tclIntType)	\
	    ? ((*(longPtr) = (objPtr)->internalRep.longValue), TCL_OK) \
................................................................................
	    : Tcl_GetIntFromObj((interp), (objPtr), (intPtr)))
#define TclGetIntForIndexM(interp, objPtr, endValue, idxPtr) \
    (((objPtr)->typePtr == &tclIntType)	\
	    ? ((*(idxPtr) = (objPtr)->internalRep.longValue), TCL_OK) \
	    : TclGetIntForIndex((interp), (objPtr), (endValue), (idxPtr)))
#else
#define TclGetIntFromObj(interp, objPtr, intPtr) \




    Tcl_GetIntFromObj((interp), (objPtr), (intPtr))
#define TclGetIntForIndexM(interp, objPtr, ignore, idxPtr)	\
    TclGetIntForIndex(interp, objPtr, ignore, idxPtr)





#endif

/*
 * Macro used to save a function call for common uses of
 * Tcl_GetWideIntFromObj(). The ANSI C "prototype" is:
 *
 * MODULE_SCOPE int TclGetWideIntFromObj(Tcl_Interp *interp, Tcl_Obj *objPtr,
................................................................................
MODULE_SCOPE int	TclInfoGlobalsCmd(ClientData dummy, Tcl_Interp *interp,
			    int objc, Tcl_Obj *const objv[]);
MODULE_SCOPE int	TclInfoLocalsCmd(ClientData dummy, Tcl_Interp *interp,
			    int objc, Tcl_Obj *const objv[]);
MODULE_SCOPE int	TclInfoVarsCmd(ClientData dummy, Tcl_Interp *interp,
			    int objc, Tcl_Obj *const objv[]);
MODULE_SCOPE void	TclInitAlloc(void);



MODULE_SCOPE void	TclInitDbCkalloc(void);
MODULE_SCOPE void	TclInitDoubleConversion(void);
MODULE_SCOPE void	TclInitEmbeddedConfigurationInformation(
			    Tcl_Interp *interp);
MODULE_SCOPE void	TclInitEncodingSubsystem(void);
MODULE_SCOPE void	TclInitIOSubsystem(void);
MODULE_SCOPE void	TclInitLimitSupport(Tcl_Interp *interp);

 * TclNRLmapCmd and their compilations.
 */

#define TCL_EACH_KEEP_NONE  0	/* Discard iteration result like [foreach] */
#define TCL_EACH_COLLECT    1	/* Collect iteration result like [lmap] */

/*
 * Macros providing a faster path to integers: Tcl_GetLongFromObj,
 * Tcl_GetIntFromObj and TclGetIntForIndex.
 *
 * WARNING: these macros eval their args more than once.
 */

#define TclGetLongFromObj(interp, objPtr, longPtr) \
    (((objPtr)->typePtr == &tclIntType)	\
	    ? ((*(longPtr) = (objPtr)->internalRep.longValue), TCL_OK) \
................................................................................
	    : Tcl_GetIntFromObj((interp), (objPtr), (intPtr)))
#define TclGetIntForIndexM(interp, objPtr, endValue, idxPtr) \
    (((objPtr)->typePtr == &tclIntType)	\
	    ? ((*(idxPtr) = (objPtr)->internalRep.longValue), TCL_OK) \
	    : TclGetIntForIndex((interp), (objPtr), (endValue), (idxPtr)))
#else
#define TclGetIntFromObj(interp, objPtr, intPtr) \
    (((objPtr)->typePtr == &tclIntType \
	    && (objPtr)->internalRep.longValue >= -(Tcl_WideInt)(UINT_MAX) \
	    && (objPtr)->internalRep.longValue <= (Tcl_WideInt)(UINT_MAX))	\
	    ? ((*(intPtr) = (objPtr)->internalRep.longValue), TCL_OK) \
	    : Tcl_GetIntFromObj((interp), (objPtr), (intPtr)))
#define TclGetIntForIndexM(interp, objPtr, endValue, idxPtr) \

    (((objPtr)->typePtr == &tclIntType \
	    && (objPtr)->internalRep.longValue >= INT_MIN \
	    && (objPtr)->internalRep.longValue <= INT_MAX)	\
	    ? ((*(idxPtr) = (objPtr)->internalRep.longValue), TCL_OK) \
	    : TclGetIntForIndex((interp), (objPtr), (endValue), (idxPtr)))
#endif

/*
 * Macro used to save a function call for common uses of
 * Tcl_GetWideIntFromObj(). The ANSI C "prototype" is:
 *
 * MODULE_SCOPE int TclGetWideIntFromObj(Tcl_Interp *interp, Tcl_Obj *objPtr,
................................................................................
MODULE_SCOPE int	TclInfoGlobalsCmd(ClientData dummy, Tcl_Interp *interp,
			    int objc, Tcl_Obj *const objv[]);
MODULE_SCOPE int	TclInfoLocalsCmd(ClientData dummy, Tcl_Interp *interp,
			    int objc, Tcl_Obj *const objv[]);
MODULE_SCOPE int	TclInfoVarsCmd(ClientData dummy, Tcl_Interp *interp,
			    int objc, Tcl_Obj *const objv[]);
MODULE_SCOPE void	TclInitAlloc(void);
MODULE_SCOPE void	TclInitBignumFromLong(mp_int *, long);
MODULE_SCOPE void	TclInitBignumFromWideInt(mp_int *, Tcl_WideInt);
MODULE_SCOPE void	TclInitBignumFromWideUInt(mp_int *, Tcl_WideUInt);
MODULE_SCOPE void	TclInitDbCkalloc(void);
MODULE_SCOPE void	TclInitDoubleConversion(void);
MODULE_SCOPE void	TclInitEmbeddedConfigurationInformation(
			    Tcl_Interp *interp);
MODULE_SCOPE void	TclInitEncodingSubsystem(void);
MODULE_SCOPE void	TclInitIOSubsystem(void);
MODULE_SCOPE void	TclInitLimitSupport(Tcl_Interp *interp);

    }

    /*
     * The namespace is only deleted if it hasn't already been deleted. [Bug
     * 2950259]
     */

    if (((Namespace *) oPtr->namespacePtr)->earlyDeleteProc != NULL) {
	Tcl_DeleteNamespace(oPtr->namespacePtr);
    }
    if (oPtr->classPtr) {
	DelRef(oPtr->classPtr);
    }
    DelRef(fPtr->classCls->thisPtr);
    DelRef(fPtr->objectCls->thisPtr);
................................................................................
	FOREACH(instancePtr, clsPtr->instances) {
	    int j;
	    if (instancePtr->selfCls == clsPtr) {
		instancePtr->flags |= CLASS_GONE;
	    }
	    for(j=0 ; j<instancePtr->mixins.num ; j++) {
		Class *mixin = instancePtr->mixins.list[j];

		if (mixin == clsPtr) {





		    instancePtr->mixins.list[j] = NULL;




		}
	    }
	    if (instancePtr != NULL && !IsRoot(instancePtr)) {
		AddRef(instancePtr);
	    }
	}
    }
................................................................................
				 * being deleted. */
{
    Object *oPtr = clientData;
    FOREACH_HASH_DECLS;
    Class *clsPtr = oPtr->classPtr, *mixinPtr;
    Method *mPtr;
    Tcl_Obj *filterObj, *variableObj;
    int i;

    /*
     * Instruct everyone to no longer use any allocated fields of the object.
     * Also delete the commands that refer to the object at this point (if
     * they still exist) because otherwise their references to the object
     * point into freed memory, allowing crashes.
     */

    if (oPtr->command) {









	Tcl_DeleteCommandFromToken(oPtr->fPtr->interp, oPtr->command);
    }
    if (oPtr->myCommand) {
	Tcl_DeleteCommandFromToken(oPtr->fPtr->interp, oPtr->myCommand);
    }

    /*
................................................................................

	ClearMixins(clsPtr);

	ClearSuperclasses(clsPtr);

	if (clsPtr->subclasses.list) {
	    ckfree(clsPtr->subclasses.list);

	    clsPtr->subclasses.num = 0;
	}
	if (clsPtr->instances.list) {
	    ckfree(clsPtr->instances.list);

	    clsPtr->instances.num = 0;
	}
	if (clsPtr->mixinSubs.list) {
	    ckfree(clsPtr->mixinSubs.list);

	    clsPtr->mixinSubs.num = 0;
	}

	FOREACH_HASH_VALUE(mPtr, &clsPtr->classMethods) {
	    TclOODelMethodRef(mPtr);
	}
	Tcl_DeleteHashTable(&clsPtr->classMethods);
................................................................................
	DelRef(clsPtr);
    }

    /*
     * Delete the object structure itself.
     */





    DelRef(oPtr);


}
 
/*
 * ----------------------------------------------------------------------
 *
 * TclOORemoveFromInstances --
 *
................................................................................
}
 
/*
 * ----------------------------------------------------------------------
 *
 * PublicObjectCmd, PrivateObjectCmd, TclOOInvokeObject --
 *
 *	Main entry point for object invokations. The Public* and Private*
 *	wrapper functions (implementations of both object instance commands
 *	and [my]) are just thin wrappers round the main TclOOObjectCmdCore
 *	function. Note that the core is function is NRE-aware.
 *
 * ----------------------------------------------------------------------
 */

................................................................................
}
 
/*
 * ----------------------------------------------------------------------
 *
 * TclOOObjectCmdCore, FinalizeObjectCall --
 *
 *	Main function for object invokations. Does call chain creation,
 *	management and invokation. The function FinalizeObjectCall exists to
 *	clean up after the non-recursive processing of TclOOObjectCmdCore.
 *
 * ----------------------------------------------------------------------
 */

int
TclOOObjectCmdCore(
    Object *oPtr,		/* The object being invoked. */
    Tcl_Interp *interp,		/* The interpreter containing the object. */
    int objc,			/* How many arguments are being passed in. */
    Tcl_Obj *const *objv,	/* The array of arguments. */
    int flags,			/* Whether this is an invokation through the
				 * public or the private command interface. */
    Class *startCls)		/* Where to start in the call chain, or NULL
				 * if we are to start at the front with
				 * filters and the object's methods (which is
				 * the normal case). */
{
    CallContext *contextPtr;
................................................................................
    }

    /*
     * Advance to the next method implementation in the chain in the method
     * call context while we process the body. However, need to adjust the
     * argument-skip control because we're guaranteed to have a single prefix
     * arg (i.e., 'next') and not the variable amount that can happen because
     * method invokations (i.e., '$obj meth' and 'my meth'), constructors
     * (i.e., '$cls new' and '$cls create obj') and destructors (no args at
     * all) come through the same code.
     */

    contextPtr->index++;
    contextPtr->skip = skip;

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

    /*
     * Advance to the next method implementation in the chain in the method
     * call context while we process the body. However, need to adjust the
     * argument-skip control because we're guaranteed to have a single prefix
     * arg (i.e., 'next') and not the variable amount that can happen because
     * method invokations (i.e., '$obj meth' and 'my meth'), constructors
     * (i.e., '$cls new' and '$cls create obj') and destructors (no args at
     * all) come through the same code.
     */

    TclNRAddCallback(interp, FinalizeNext, contextPtr,
	    INT2PTR(contextPtr->index), INT2PTR(contextPtr->skip), NULL);
    contextPtr->index++;

    }

    /*
     * The namespace is only deleted if it hasn't already been deleted. [Bug
     * 2950259]
     */

    if (oPtr->namespacePtr && ((Namespace *) oPtr->namespacePtr)->earlyDeleteProc != NULL) {
	Tcl_DeleteNamespace(oPtr->namespacePtr);
    }
    if (oPtr->classPtr) {
	DelRef(oPtr->classPtr);
    }
    DelRef(fPtr->classCls->thisPtr);
    DelRef(fPtr->objectCls->thisPtr);
................................................................................
	FOREACH(instancePtr, clsPtr->instances) {
	    int j;
	    if (instancePtr->selfCls == clsPtr) {
		instancePtr->flags |= CLASS_GONE;
	    }
	    for(j=0 ; j<instancePtr->mixins.num ; j++) {
		Class *mixin = instancePtr->mixins.list[j];
		Class *nextMixin = NULL;
		if (mixin == clsPtr) {
		    if (j < instancePtr->mixins.num - 1) {
			nextMixin = instancePtr->mixins.list[j+1];
		    }
		    if (j == 0) {
			instancePtr->mixins.num = 0;
			instancePtr->mixins.list = NULL;
		    } else {
			instancePtr->mixins.list[j-1] = nextMixin;
		    }
		    instancePtr->mixins.num -= 1;
		}
	    }
	    if (instancePtr != NULL && !IsRoot(instancePtr)) {
		AddRef(instancePtr);
	    }
	}
    }
................................................................................
				 * being deleted. */
{
    Object *oPtr = clientData;
    FOREACH_HASH_DECLS;
    Class *clsPtr = oPtr->classPtr, *mixinPtr;
    Method *mPtr;
    Tcl_Obj *filterObj, *variableObj;
    int deleteAlreadyInProgress = 0, i;

    /*
     * Instruct everyone to no longer use any allocated fields of the object.
     * Also delete the commands that refer to the object at this point (if
     * they still exist) because otherwise their references to the object
     * point into freed memory, allowing crashes.
     */

    if (oPtr->command) {
	if ((((Command *)oPtr->command)->flags && CMD_IS_DELETED)) {
	    /*
	     * Namespace deletion must have been triggered by a trace on command
	     * deletion , meaning that ObjectRenamedTrace() is eventually going
	     * to be called .
	     */
	    deleteAlreadyInProgress = 1;
	}

	Tcl_DeleteCommandFromToken(oPtr->fPtr->interp, oPtr->command);
    }
    if (oPtr->myCommand) {
	Tcl_DeleteCommandFromToken(oPtr->fPtr->interp, oPtr->myCommand);
    }

    /*
................................................................................

	ClearMixins(clsPtr);

	ClearSuperclasses(clsPtr);

	if (clsPtr->subclasses.list) {
	    ckfree(clsPtr->subclasses.list);
	    clsPtr->subclasses.list = NULL;
	    clsPtr->subclasses.num = 0;
	}
	if (clsPtr->instances.list) {
	    ckfree(clsPtr->instances.list);
	    clsPtr->instances.list = NULL;
	    clsPtr->instances.num = 0;
	}
	if (clsPtr->mixinSubs.list) {
	    ckfree(clsPtr->mixinSubs.list);
	    clsPtr->mixinSubs.list = NULL;
	    clsPtr->mixinSubs.num = 0;
	}

	FOREACH_HASH_VALUE(mPtr, &clsPtr->classMethods) {
	    TclOODelMethodRef(mPtr);
	}
	Tcl_DeleteHashTable(&clsPtr->classMethods);
................................................................................
	DelRef(clsPtr);
    }

    /*
     * Delete the object structure itself.
     */

    if (deleteAlreadyInProgress) {
	oPtr->classPtr = NULL;
	oPtr->namespacePtr = NULL;
    } else {
	DelRef(oPtr);
    }

}
 
/*
 * ----------------------------------------------------------------------
 *
 * TclOORemoveFromInstances --
 *
................................................................................
}
 
/*
 * ----------------------------------------------------------------------
 *
 * PublicObjectCmd, PrivateObjectCmd, TclOOInvokeObject --
 *
 *	Main entry point for object invocations. The Public* and Private*
 *	wrapper functions (implementations of both object instance commands
 *	and [my]) are just thin wrappers round the main TclOOObjectCmdCore
 *	function. Note that the core is function is NRE-aware.
 *
 * ----------------------------------------------------------------------
 */

................................................................................
}
 
/*
 * ----------------------------------------------------------------------
 *
 * TclOOObjectCmdCore, FinalizeObjectCall --
 *
 *	Main function for object invocations. Does call chain creation,
 *	management and invocation. The function FinalizeObjectCall exists to
 *	clean up after the non-recursive processing of TclOOObjectCmdCore.
 *
 * ----------------------------------------------------------------------
 */

int
TclOOObjectCmdCore(
    Object *oPtr,		/* The object being invoked. */
    Tcl_Interp *interp,		/* The interpreter containing the object. */
    int objc,			/* How many arguments are being passed in. */
    Tcl_Obj *const *objv,	/* The array of arguments. */
    int flags,			/* Whether this is an invocation through the
				 * public or the private command interface. */
    Class *startCls)		/* Where to start in the call chain, or NULL
				 * if we are to start at the front with
				 * filters and the object's methods (which is
				 * the normal case). */
{
    CallContext *contextPtr;
................................................................................
    }

    /*
     * Advance to the next method implementation in the chain in the method
     * call context while we process the body. However, need to adjust the
     * argument-skip control because we're guaranteed to have a single prefix
     * arg (i.e., 'next') and not the variable amount that can happen because
     * method invocations (i.e., '$obj meth' and 'my meth'), constructors
     * (i.e., '$cls new' and '$cls create obj') and destructors (no args at
     * all) come through the same code.
     */

    contextPtr->index++;
    contextPtr->skip = skip;

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

    /*
     * Advance to the next method implementation in the chain in the method
     * call context while we process the body. However, need to adjust the
     * argument-skip control because we're guaranteed to have a single prefix
     * arg (i.e., 'next') and not the variable amount that can happen because
     * method invocations (i.e., '$obj meth' and 'my meth'), constructors
     * (i.e., '$cls new' and '$cls create obj') and destructors (no args at
     * all) come through the same code.
     */

    TclNRAddCallback(interp, FinalizeNext, contextPtr,
	    INT2PTR(contextPtr->index), INT2PTR(contextPtr->skip), NULL);
    contextPtr->index++;

 * Function declarations for things defined in this file.
 */

static void		AddClassFiltersToCallContext(Object *const oPtr,
			    Class *clsPtr, struct ChainBuilder *const cbPtr,
			    Tcl_HashTable *const doneFilters, int flags);
static void		AddClassMethodNames(Class *clsPtr, const int flags,
			    Tcl_HashTable *const namesPtr);

static inline void	AddMethodToCallChain(Method *const mPtr,
			    struct ChainBuilder *const cbPtr,
			    Tcl_HashTable *const doneFilters,
			    Class *const filterDecl, int flags);
static inline void	AddSimpleChainToCallContext(Object *const oPtr,
			    Tcl_Obj *const methodNameObj,
			    struct ChainBuilder *const cbPtr,
................................................................................
 
/*
 * ----------------------------------------------------------------------
 *
 * TclOOInvokeContext --
 *
 *	Invokes a single step along a method call-chain context. Note that the
 *	invokation of a step along the chain can cause further steps along the
 *	chain to be invoked. Note that this function is written to be as light
 *	in stack usage as possible.
 *
 * ----------------------------------------------------------------------
 */

int
................................................................................
    int flags,			/* Whether we just want the public method
				 * names. */
    const char ***stringsPtr)	/* Where to write a pointer to the array of
				 * strings to. */
{
    Tcl_HashTable names;	/* Tcl_Obj* method name to "wanted in list"
				 * mapping. */




    FOREACH_HASH_DECLS;
    int i;
    Class *mixinPtr;
    Tcl_Obj *namePtr;
    Method *mPtr;
    int isWantedIn;
    void *isWanted;

    Tcl_InitObjHashTable(&names);


    /*
     * Name the bits used in the names table values.
     */
#define IN_LIST 1
#define NO_IMPLEMENTATION 2

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

    /*
     * Process (normal) method names from the class hierarchy and the mixin
     * hierarchy.
     */

    AddClassMethodNames(oPtr->selfCls, flags, &names);
    FOREACH(mixinPtr, oPtr->mixins) {
	AddClassMethodNames(mixinPtr, flags|TRAVERSED_MIXIN, &names);

    }



    /*
     * See how many (visible) method names there are. If none, we do not (and
     * should not) try to sort the list of them.
     */

    i = 0;
................................................................................
    int flags,			/* Whether we just want the public method
				 * names. */
    const char ***stringsPtr)	/* Where to write a pointer to the array of
				 * strings to. */
{
    Tcl_HashTable names;	/* Tcl_Obj* method name to "wanted in list"
				 * mapping. */




    FOREACH_HASH_DECLS;
    int i;
    Tcl_Obj *namePtr;
    void *isWanted;

    Tcl_InitObjHashTable(&names);


    /*
     * Process method names from the class hierarchy and the mixin hierarchy.
     */

    AddClassMethodNames(clsPtr, flags, &names);


    /*
     * See how many (visible) method names there are. If none, we do not (and
     * should not) try to sort the list of them.
     */

    i = 0;
................................................................................
 */

static void
AddClassMethodNames(
    Class *clsPtr,		/* Class to get method names from. */
    const int flags,		/* Whether we are interested in just the
				 * public method names. */
    Tcl_HashTable *const namesPtr)
				/* Reference to the hash table to put the
				 * information in. The hash table maps the
				 * Tcl_Obj * method name to an integral value
				 * describing whether the method is wanted.
				 * This ensures that public/private override
				 * semantics are handled correctly.*/





{









    /*
     * Scope all declarations so that the compiler can stand a good chance of
     * making the recursive step highly efficient. We also hand-implement the
     * tail-recursive case using a while loop; C compilers typically cannot do
     * tail-recursion optimization usefully.
     */

    if (clsPtr->mixins.num != 0) {
	Class *mixinPtr;
	int i;

	/* TODO: Beware of infinite loops! */
	FOREACH(mixinPtr, clsPtr->mixins) {
	    AddClassMethodNames(mixinPtr, flags|TRAVERSED_MIXIN, namesPtr);
	}
    }

    while (1) {
	FOREACH_HASH_DECLS;
	Tcl_Obj *namePtr;
	Method *mPtr;


	FOREACH_HASH(namePtr, mPtr, &clsPtr->classMethods) {








	    int isNew;










	    hPtr = Tcl_CreateHashEntry(namesPtr, (char *) namePtr, &isNew);
	    if (isNew) {
		int isWanted = (!(flags & PUBLIC_METHOD)
			|| (mPtr->flags & PUBLIC_METHOD)) ? IN_LIST : 0;

		isWanted |= (mPtr->typePtr == NULL ? NO_IMPLEMENTATION : 0);
		Tcl_SetHashValue(hPtr, INT2PTR(isWanted));
................................................................................
	clsPtr = clsPtr->superclasses.list[0];
    }
    if (clsPtr->superclasses.num != 0) {
	Class *superPtr;
	int i;

	FOREACH(superPtr, clsPtr->superclasses) {
	    AddClassMethodNames(superPtr, flags, namesPtr);

	}
    }
}
 
/*
 * ----------------------------------------------------------------------
 *
................................................................................
    for (i=cbPtr->filterLength ; i<callPtr->numChain ; i++) {
	if (callPtr->chain[i].mPtr == mPtr &&
		callPtr->chain[i].isFilter == (doneFilters != NULL)) {
	    /*
	     * Call chain semantics states that methods come as *late* in the
	     * call chain as possible. This is done by copying down the
	     * following methods. Note that this does not change the number of
	     * method invokations in the call chain; it just rearranges them.
	     */

	    Class *declCls = callPtr->chain[i].filterDeclarer;

	    for (; i+1<callPtr->numChain ; i++) {
		callPtr->chain[i] = callPtr->chain[i+1];
	    }
................................................................................
 
/*
 * ----------------------------------------------------------------------
 *
 * TclOOGetCallContext --
 *
 *	Responsible for constructing the call context, an ordered list of all
 *	method implementations to be called as part of a method invokation.
 *	This method is central to the whole operation of the OO system.
 *
 * ----------------------------------------------------------------------
 */

CallContext *
TclOOGetCallContext(
................................................................................
    Tcl_IncrRefCount(methodLiteral);
    objectLiteral = Tcl_NewStringObj("object", -1);
    Tcl_IncrRefCount(objectLiteral);

    /*
     * Do the actual construction of the descriptions. They consist of a list
     * of triples that describe the details of how a method is understood. For
     * each triple, the first word is the type of invokation ("method" is
     * normal, "unknown" is special because it adds the method name as an
     * extra argument when handled by some method types, and "filter" is
     * special because it's a filter method). The second word is the name of
     * the method in question (which differs for "unknown" and "filter" types)
     * and the third word is the full name of the class that declares the
     * method (or "object" if it is declared on the instance).
     */

 * Function declarations for things defined in this file.
 */

static void		AddClassFiltersToCallContext(Object *const oPtr,
			    Class *clsPtr, struct ChainBuilder *const cbPtr,
			    Tcl_HashTable *const doneFilters, int flags);
static void		AddClassMethodNames(Class *clsPtr, const int flags,
			    Tcl_HashTable *const namesPtr,
			    Tcl_HashTable *const examinedClassesPtr);
static inline void	AddMethodToCallChain(Method *const mPtr,
			    struct ChainBuilder *const cbPtr,
			    Tcl_HashTable *const doneFilters,
			    Class *const filterDecl, int flags);
static inline void	AddSimpleChainToCallContext(Object *const oPtr,
			    Tcl_Obj *const methodNameObj,
			    struct ChainBuilder *const cbPtr,
................................................................................
 
/*
 * ----------------------------------------------------------------------
 *
 * TclOOInvokeContext --
 *
 *	Invokes a single step along a method call-chain context. Note that the
 *	invocation of a step along the chain can cause further steps along the
 *	chain to be invoked. Note that this function is written to be as light
 *	in stack usage as possible.
 *
 * ----------------------------------------------------------------------
 */

int
................................................................................
    int flags,			/* Whether we just want the public method
				 * names. */
    const char ***stringsPtr)	/* Where to write a pointer to the array of
				 * strings to. */
{
    Tcl_HashTable names;	/* Tcl_Obj* method name to "wanted in list"
				 * mapping. */
    Tcl_HashTable examinedClasses;
				/* Used to track what classes have been looked
				 * at. Is set-like in nature and keyed by
				 * pointer to class. */
    FOREACH_HASH_DECLS;
    int i;
    Class *mixinPtr;
    Tcl_Obj *namePtr;
    Method *mPtr;
    int isWantedIn;
    void *isWanted;

    Tcl_InitObjHashTable(&names);
    Tcl_InitHashTable(&examinedClasses, TCL_ONE_WORD_KEYS);

    /*
     * Name the bits used in the names table values.
     */
#define IN_LIST 1
#define NO_IMPLEMENTATION 2

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

    /*
     * Process (normal) method names from the class hierarchy and the mixin
     * hierarchy.
     */

    AddClassMethodNames(oPtr->selfCls, flags, &names, &examinedClasses);
    FOREACH(mixinPtr, oPtr->mixins) {
	AddClassMethodNames(mixinPtr, flags|TRAVERSED_MIXIN, &names,
		&examinedClasses);
    }

    Tcl_DeleteHashTable(&examinedClasses);

    /*
     * See how many (visible) method names there are. If none, we do not (and
     * should not) try to sort the list of them.
     */

    i = 0;
................................................................................
    int flags,			/* Whether we just want the public method
				 * names. */
    const char ***stringsPtr)	/* Where to write a pointer to the array of
				 * strings to. */
{
    Tcl_HashTable names;	/* Tcl_Obj* method name to "wanted in list"
				 * mapping. */
    Tcl_HashTable examinedClasses;
				/* Used to track what classes have been looked
				 * at. Is set-like in nature and keyed by
				 * pointer to class. */
    FOREACH_HASH_DECLS;
    int i;
    Tcl_Obj *namePtr;
    void *isWanted;

    Tcl_InitObjHashTable(&names);
    Tcl_InitHashTable(&examinedClasses, TCL_ONE_WORD_KEYS);

    /*
     * Process method names from the class hierarchy and the mixin hierarchy.
     */

    AddClassMethodNames(clsPtr, flags, &names, &examinedClasses);
    Tcl_DeleteHashTable(&examinedClasses);

    /*
     * See how many (visible) method names there are. If none, we do not (and
     * should not) try to sort the list of them.
     */

    i = 0;
................................................................................
 */

static void
AddClassMethodNames(
    Class *clsPtr,		/* Class to get method names from. */
    const int flags,		/* Whether we are interested in just the
				 * public method names. */
    Tcl_HashTable *const namesPtr,
				/* Reference to the hash table to put the
				 * information in. The hash table maps the
				 * Tcl_Obj * method name to an integral value
				 * describing whether the method is wanted.
				 * This ensures that public/private override
				 * semantics are handled correctly. */
    Tcl_HashTable *const examinedClassesPtr)
				/* Hash table that tracks what classes have
				 * already been looked at. The keys are the
				 * pointers to the classes, and the values are
				 * immaterial. */
{
    /*
     * If we've already started looking at this class, stop working on it now
     * to prevent repeated work.
     */

    if (Tcl_FindHashEntry(examinedClassesPtr, (char *) clsPtr)) {
	return;
    }

    /*
     * Scope all declarations so that the compiler can stand a good chance of
     * making the recursive step highly efficient. We also hand-implement the
     * tail-recursive case using a while loop; C compilers typically cannot do
     * tail-recursion optimization usefully.
     */











    while (1) {
	FOREACH_HASH_DECLS;
	Tcl_Obj *namePtr;
	Method *mPtr;
	int isNew;


	(void) Tcl_CreateHashEntry(examinedClassesPtr, (char *) clsPtr,
		&isNew);
	if (!isNew) {
	    break;
	}

	if (clsPtr->mixins.num != 0) {
	    Class *mixinPtr;
	    int i;

	    FOREACH(mixinPtr, clsPtr->mixins) {
		if (mixinPtr != clsPtr) {
		    AddClassMethodNames(mixinPtr, flags|TRAVERSED_MIXIN,
			    namesPtr, examinedClassesPtr);
		}
	    }
	}

	FOREACH_HASH(namePtr, mPtr, &clsPtr->classMethods) {
	    hPtr = Tcl_CreateHashEntry(namesPtr, (char *) namePtr, &isNew);
	    if (isNew) {
		int isWanted = (!(flags & PUBLIC_METHOD)
			|| (mPtr->flags & PUBLIC_METHOD)) ? IN_LIST : 0;

		isWanted |= (mPtr->typePtr == NULL ? NO_IMPLEMENTATION : 0);
		Tcl_SetHashValue(hPtr, INT2PTR(isWanted));
................................................................................
	clsPtr = clsPtr->superclasses.list[0];
    }
    if (clsPtr->superclasses.num != 0) {
	Class *superPtr;
	int i;

	FOREACH(superPtr, clsPtr->superclasses) {
	    AddClassMethodNames(superPtr, flags, namesPtr,
		    examinedClassesPtr);
	}
    }
}
 
/*
 * ----------------------------------------------------------------------
 *
................................................................................
    for (i=cbPtr->filterLength ; i<callPtr->numChain ; i++) {
	if (callPtr->chain[i].mPtr == mPtr &&
		callPtr->chain[i].isFilter == (doneFilters != NULL)) {
	    /*
	     * Call chain semantics states that methods come as *late* in the
	     * call chain as possible. This is done by copying down the
	     * following methods. Note that this does not change the number of
	     * method invocations in the call chain; it just rearranges them.
	     */

	    Class *declCls = callPtr->chain[i].filterDeclarer;

	    for (; i+1<callPtr->numChain ; i++) {
		callPtr->chain[i] = callPtr->chain[i+1];
	    }
................................................................................
 
/*
 * ----------------------------------------------------------------------
 *
 * TclOOGetCallContext --
 *
 *	Responsible for constructing the call context, an ordered list of all
 *	method implementations to be called as part of a method invocation.
 *	This method is central to the whole operation of the OO system.
 *
 * ----------------------------------------------------------------------
 */

CallContext *
TclOOGetCallContext(
................................................................................
    Tcl_IncrRefCount(methodLiteral);
    objectLiteral = Tcl_NewStringObj("object", -1);
    Tcl_IncrRefCount(objectLiteral);

    /*
     * Do the actual construction of the descriptions. They consist of a list
     * of triples that describe the details of how a method is understood. For
     * each triple, the first word is the type of invocation ("method" is
     * normal, "unknown" is special because it adds the method name as an
     * extra argument when handled by some method types, and "filter" is
     * special because it's a filter method). The second word is the name of
     * the method in question (which differs for "unknown" and "filter" types)
     * and the third word is the full name of the class that declares the
     * method (or "object" if it is declared on the instance).
     */

 * Now, the definition of what an object actually is.
 */

typedef struct Object {
    struct Foundation *fPtr;	/* The basis for the object system. Putting
				 * this here allows the avoidance of quite a
				 * lot of hash lookups on the critical path
				 * for object invokation and creation. */
    Tcl_Namespace *namespacePtr;/* This object's tame namespace. */
    Tcl_Command command;	/* Reference to this object's public
				 * command. */
    Tcl_Command myCommand;	/* Reference to this object's internal
				 * command. */
    struct Class *selfCls;	/* This object's class. */
    Tcl_HashTable *methodsPtr;	/* Object-local Tcl_Obj (method name) to
				 * Method* mapping. */
    LIST_STATIC(struct Class *) mixins;
				/* Classes mixed into this object. */
    LIST_STATIC(Tcl_Obj *) filters;
				/* List of filter names. */
    struct Class *classPtr;	/* All classes have this non-NULL; it points
				 * to the class structure. Everything else has
				 * this NULL. */
    int refCount;		/* Number of strong references to this object.
				 * Note that there may be many more weak
				 * references; this mechanism is there to
				 * avoid Tcl_Preserve. */
    int flags;
    int creationEpoch;		/* Unique value to make comparisons of objects
				 * easier. */
    int epoch;			/* Per-object epoch, incremented when the way
				 * an object should resolve call chains is
				 * changed. */
................................................................................
				 * destructor. */
    Tcl_Obj *clonedName;	/* Shared object containing the name of a
				 * "<cloned>" pseudo-constructor. */
    Tcl_Obj *defineName;	/* Fully qualified name of oo::define. */
} Foundation;

/*
 * A call context structure is built when a method is called. They contain the
 * chain of method implementations that are to be invoked by a particular
 * call, and the process of calling walks the chain, with the [next] command
 * proceeding to the next entry in the chain.
 */

#define CALL_CHAIN_STATIC_SIZE 4

struct MInvoke {
    Method *mPtr;		/* Reference to the method implementation
				 * record. */
    int isFilter;		/* Whether this is a filter invokation. */
    Class *filterDeclarer;	/* What class decided to add the filter; if
				 * NULL, it was added by the object. */
};

typedef struct CallChain {
    int objectCreationEpoch;	/* The object's creation epoch. Note that the
				 * object reference is not stored in the call

 * Now, the definition of what an object actually is.
 */

typedef struct Object {
    struct Foundation *fPtr;	/* The basis for the object system. Putting
				 * this here allows the avoidance of quite a
				 * lot of hash lookups on the critical path
				 * for object invocation and creation. */
    Tcl_Namespace *namespacePtr;/* This object's namespace. */
    Tcl_Command command;	/* Reference to this object's public
				 * command. */
    Tcl_Command myCommand;	/* Reference to this object's internal
				 * command. */
    struct Class *selfCls;	/* This object's class. */
    Tcl_HashTable *methodsPtr;	/* Object-local Tcl_Obj (method name) to
				 * Method* mapping. */
    LIST_STATIC(struct Class *) mixins;
				/* Classes mixed into this object. */
    LIST_STATIC(Tcl_Obj *) filters;
				/* List of filter names. */
    struct Class *classPtr;	/* This is non-NULL for all classes, and NULL
				 *  for everything else. It points to the class
				 *  structure. */
    int refCount;		/* Number of strong references to this object.
				 * Note that there may be many more weak
				 * references; this mechanism exists to
				 * avoid Tcl_Preserve. */
    int flags;
    int creationEpoch;		/* Unique value to make comparisons of objects
				 * easier. */
    int epoch;			/* Per-object epoch, incremented when the way
				 * an object should resolve call chains is
				 * changed. */
................................................................................
				 * destructor. */
    Tcl_Obj *clonedName;	/* Shared object containing the name of a
				 * "<cloned>" pseudo-constructor. */
    Tcl_Obj *defineName;	/* Fully qualified name of oo::define. */
} Foundation;

/*
 * A call context structure is built when a method is called. It contains the
 * chain of method implementations that are to be invoked by a particular
 * call, and the process of calling walks the chain, with the [next] command
 * proceeding to the next entry in the chain.
 */

#define CALL_CHAIN_STATIC_SIZE 4

struct MInvoke {
    Method *mPtr;		/* Reference to the method implementation
				 * record. */
    int isFilter;		/* Whether this is a filter invocation. */
    Class *filterDeclarer;	/* What class decided to add the filter; if
				 * NULL, it was added by the object. */
};

typedef struct CallChain {
    int objectCreationEpoch;	/* The object's creation epoch. Note that the
				 * object reference is not stored in the call

    /*
     * Must strip the internal representation in order to ensure that any
     * bound references to instance variables are removed. [Bug 3609693]
     */

    bodyObj = Tcl_DuplicateObj(pmPtr->procPtr->bodyPtr);

    TclFreeIntRep(bodyObj);

    /*
     * Create the actual copy of the method record, manufacturing a new proc
     * record.
     */

    /*
     * Must strip the internal representation in order to ensure that any
     * bound references to instance variables are removed. [Bug 3609693]
     */

    bodyObj = Tcl_DuplicateObj(pmPtr->procPtr->bodyPtr);
    Tcl_GetString(bodyObj);
    TclFreeIntRep(bodyObj);

    /*
     * Create the actual copy of the method record, manufacturing a new proc
     * record.
     */

	TclSetLongObj(objPtr, (long) wideValue);
    } else {
#ifndef TCL_WIDE_INT_IS_LONG
	TclSetWideIntObj(objPtr, wideValue);
#else
	mp_int big;

	TclBNInitBignumFromWideInt(&big, wideValue);
	Tcl_SetBignumObj(objPtr, &big);
#endif
    }
}
 
/*
 *----------------------------------------------------------------------
................................................................................
		if (objPtr->bytes == NULL) {
		    TclInitStringRep(objPtr, &tclEmptyString, 0);
		}
	    }
	    return TCL_OK;
	}
	if (objPtr->typePtr == &tclIntType) {
	    TclBNInitBignumFromLong(bignumValue, objPtr->internalRep.longValue);
	    return TCL_OK;
	}
#ifndef TCL_WIDE_INT_IS_LONG
	if (objPtr->typePtr == &tclWideIntType) {
	    TclBNInitBignumFromWideInt(bignumValue,
		    objPtr->internalRep.wideValue);
	    return TCL_OK;
	}
#endif
	if (objPtr->typePtr == &tclDoubleType) {
	    if (interp != NULL) {
                Tcl_SetObjResult(interp, Tcl_ObjPrintf(

	TclSetLongObj(objPtr, (long) wideValue);
    } else {
#ifndef TCL_WIDE_INT_IS_LONG
	TclSetWideIntObj(objPtr, wideValue);
#else
	mp_int big;

	TclInitBignumFromWideInt(&big, wideValue);
	Tcl_SetBignumObj(objPtr, &big);
#endif
    }
}
 
/*
 *----------------------------------------------------------------------
................................................................................
		if (objPtr->bytes == NULL) {
		    TclInitStringRep(objPtr, &tclEmptyString, 0);
		}
	    }
	    return TCL_OK;
	}
	if (objPtr->typePtr == &tclIntType) {
	    TclInitBignumFromLong(bignumValue, objPtr->internalRep.longValue);
	    return TCL_OK;
	}
#ifndef TCL_WIDE_INT_IS_LONG
	if (objPtr->typePtr == &tclWideIntType) {
	    TclInitBignumFromWideInt(bignumValue,
		    objPtr->internalRep.wideValue);
	    return TCL_OK;
	}
#endif
	if (objPtr->typePtr == &tclDoubleType) {
	    if (interp != NULL) {
                Tcl_SetObjResult(interp, Tcl_ObjPrintf(

    Tcl_Obj *globObjPtr;	/* Glob pattern rep of RE or NULL if none. */
    regmatch_t *matches;	/* Array of indices into the Tcl_UniChar
				 * representation of the last string matched
				 * with this regexp to indicate the location
				 * of subexpressions. */
    rm_detail_t details;	/* Detailed information on match (currently
				 * used only for REG_EXPECT). */
    unsigned int refCount;	/* Count of number of references to this
				 * compiled regexp. */
} TclRegexp;

#endif /* _TCLREGEXP */
 
/*
 * Local Variables:
 * mode: c
 * c-basic-offset: 4
 * fill-column: 78
 * End:
 */

    Tcl_Obj *globObjPtr;	/* Glob pattern rep of RE or NULL if none. */
    regmatch_t *matches;	/* Array of indices into the Tcl_UniChar
				 * representation of the last string matched
				 * with this regexp to indicate the location
				 * of subexpressions. */
    rm_detail_t details;	/* Detailed information on match (currently
				 * used only for REG_EXPECT). */
    size_t refCount;		/* Count of number of references to this
				 * compiled regexp. */
} TclRegexp;

#endif /* _TCLREGEXP */
 
/*
 * Local Variables:
 * mode: c
 * c-basic-offset: 4
 * fill-column: 78
 * End:
 */

			if ((octalSignificandWide != 0)
				&& (((size_t)shift >=
					CHAR_BIT*sizeof(Tcl_WideUInt))
				|| (octalSignificandWide >
					(~(Tcl_WideUInt)0 >> shift)))) {
			    octalSignificandOverflow = 1;
			    TclBNInitBignumFromWideUInt(&octalSignificandBig,
				    octalSignificandWide);
			}
		    }
		    if (!octalSignificandOverflow) {
			octalSignificandWide =
				(octalSignificandWide << shift) + (c - '0');
		    } else {
................................................................................
		     * large shifts first.
		     */

		    if (significandWide != 0 &&
			    ((size_t)shift >= CHAR_BIT*sizeof(Tcl_WideUInt) ||
			    significandWide > (~(Tcl_WideUInt)0 >> shift))) {
			significandOverflow = 1;
			TclBNInitBignumFromWideUInt(&significandBig,
				significandWide);
		    }
		}
		if (!significandOverflow) {
		    significandWide = (significandWide << shift) + d;
		} else {
		    mp_mul_2d(&significandBig, shift, &significandBig);
................................................................................
		     * large shifts first.
		     */

		    if (significandWide != 0 &&
			    ((size_t)shift >= CHAR_BIT*sizeof(Tcl_WideUInt) ||
			    significandWide > (~(Tcl_WideUInt)0 >> shift))) {
			significandOverflow = 1;
			TclBNInitBignumFromWideUInt(&significandBig,
				significandWide);
		    }
		}
		if (!significandOverflow) {
		    significandWide = (significandWide << shift) + 1;
		} else {
		    mp_mul_2d(&significandBig, shift, &significandBig);
................................................................................
		    acceptState, bytes);
	case BINARY:
	    shift = numTrailZeros;
	    if (!significandOverflow && significandWide != 0 &&
		    ((size_t)shift >= CHAR_BIT*sizeof(Tcl_WideUInt) ||
		    significandWide > (MOST_BITS + signum) >> shift)) {
		significandOverflow = 1;
		TclBNInitBignumFromWideUInt(&significandBig, significandWide);
	    }
	    if (shift) {
		if (!significandOverflow) {
		    significandWide <<= shift;
		} else {
		    mp_mul_2d(&significandBig, shift, &significandBig);
		}
................................................................................
	     */

	    shift = 4 * numTrailZeros;
	    if (!significandOverflow && significandWide !=0 &&
		    ((size_t)shift >= CHAR_BIT*sizeof(Tcl_WideUInt) ||
		    significandWide > (MOST_BITS + signum) >> shift)) {
		significandOverflow = 1;
		TclBNInitBignumFromWideUInt(&significandBig, significandWide);
	    }
	    if (shift) {
		if (!significandOverflow) {
		    significandWide <<= shift;
		} else {
		    mp_mul_2d(&significandBig, shift, &significandBig);
		}
................................................................................
	     */

	    shift = 3 * numTrailZeros;
	    if (!octalSignificandOverflow && octalSignificandWide != 0 &&
		    ((size_t)shift >= CHAR_BIT*sizeof(Tcl_WideUInt) ||
		    octalSignificandWide > (MOST_BITS + signum) >> shift)) {
		octalSignificandOverflow = 1;
		TclBNInitBignumFromWideUInt(&octalSignificandBig,
			octalSignificandWide);
	    }
	    if (shift) {
		if (!octalSignificandOverflow) {
		    octalSignificandWide <<= shift;
		} else {
		    mp_mul_2d(&octalSignificandBig, shift,
................................................................................
			} else {
			    objPtr->internalRep.wideValue =
				    (Tcl_WideInt) octalSignificandWide;
			}
			break;
		    }
#endif
		    TclBNInitBignumFromWideUInt(&octalSignificandBig,
			    octalSignificandWide);
		    octalSignificandOverflow = 1;
		} else {
		    objPtr->typePtr = &tclIntType;
		    if (signum) {
			objPtr->internalRep.longValue =
				- (long) octalSignificandWide;
................................................................................

	case ZERO:
	case DECIMAL:
	    significandOverflow = AccumulateDecimalDigit(0, numTrailZeros-1,
		    &significandWide, &significandBig, significandOverflow);
	    if (!significandOverflow && (significandWide > MOST_BITS+signum)){
		significandOverflow = 1;
		TclBNInitBignumFromWideUInt(&significandBig, significandWide);
	    }
	returnInteger:
	    if (!significandOverflow) {
		if (significandWide >
			(Tcl_WideUInt)(((~(unsigned long)0) >> 1) + signum)) {
#ifndef TCL_WIDE_INT_IS_LONG
		    if (significandWide <= MOST_BITS+signum) {
................................................................................
			} else {
			    objPtr->internalRep.wideValue =
				    (Tcl_WideInt) significandWide;
			}
			break;
		    }
#endif
		    TclBNInitBignumFromWideUInt(&significandBig,
			    significandWide);
		    significandOverflow = 1;
		} else {
		    objPtr->typePtr = &tclIntType;
		    if (signum) {
			objPtr->internalRep.longValue =
				- (long) significandWide;
................................................................................
	} else if (numZeros >= maxpow10_wide
		|| w > ((~(Tcl_WideUInt)0)-digit)/pow10_wide[numZeros+1]) {
	    /*
	     * Wide multiplication will overflow.  Expand the number to a
	     * bignum and fall through into the bignum case.
	     */

	    TclBNInitBignumFromWideUInt(bignumRepPtr, w);
	} else {
	    /*
	     * Wide multiplication.
	     */

	    *wideRepPtr = w * pow10_wide[numZeros+1] + digit;
	    return 0;
................................................................................
    }

    /*
     * All the easy cases have failed. Promote ths significand to bignum and
     * call MakeHighPrecisionDouble to do it the hard way.
     */

    TclBNInitBignumFromWideUInt(&significandBig, significand);
    retval = MakeHighPrecisionDouble(0, &significandBig, numSigDigs,
	    exponent);
    mp_clear(&significandBig);

    /*
     * Come here to return the computed value.
     */
................................................................................
    int r1;

    /*
     * b = bw * 2**b2 * 5**b5
     * mminus = 5**m5
     */

    TclBNInitBignumFromWideUInt(&b, bw);
    mp_init_set_int(&mminus, 1);
    MulPow5(&b, b5, &b);
    mp_mul_2d(&b, b2, &b);

    /*
     * Adjust if the logarithm was guessed wrong.
     */
................................................................................
    int i;			/* Index in the output buffer. */
    mp_int temp;

    /*
     * b = bw * 2**b2 * 5**b5
     */

    TclBNInitBignumFromWideUInt(&b, bw);
    MulPow5(&b, b5, &b);
    mp_mul_2d(&b, b2, &b);

    /*
     * Adjust if the logarithm was guessed wrong.
     */

................................................................................
    int r1;

    /*
     * b = bw * 2**b2 * 5**b5
     * S = 2**s2 * 5*s5
     */

    TclBNInitBignumFromWideUInt(&b, bw);
    mp_mul_2d(&b, b2, &b);
    mp_init_set_int(&S, 1);
    MulPow5(&S, s5, &S); mp_mul_2d(&S, s2, &S);

    /*
     * Handle the case where we guess the position of the decimal point wrong.
     */
................................................................................

    /*
     * b = bw * 2**b2 * 5**b5
     * S = 2**s2 * 5*s5
     */

    mp_init_multi(&temp, &dig, NULL);
    TclBNInitBignumFromWideUInt(&b, bw);
    mp_mul_2d(&b, b2, &b);
    mp_init_set_int(&S, 1);
    MulPow5(&S, s5, &S); mp_mul_2d(&S, s2, &S);

    /*
     * Handle the case where we guess the position of the decimal point wrong.
     */
................................................................................
    if (expt <= 0) {
	mp_init(b);
	mp_zero(b);
    } else {
	Tcl_WideInt w = (Tcl_WideInt) ldexp(fract, mantBits);
	int shift = expt - mantBits;

	TclBNInitBignumFromWideInt(b, w);
	if (shift < 0) {
	    mp_div_2d(b, -shift, b, NULL);
	} else if (shift > 0) {
	    mp_mul_2d(b, shift, b);
	}
    }
    return TCL_OK;

			if ((octalSignificandWide != 0)
				&& (((size_t)shift >=
					CHAR_BIT*sizeof(Tcl_WideUInt))
				|| (octalSignificandWide >
					(~(Tcl_WideUInt)0 >> shift)))) {
			    octalSignificandOverflow = 1;
			    TclInitBignumFromWideUInt(&octalSignificandBig,
				    octalSignificandWide);
			}
		    }
		    if (!octalSignificandOverflow) {
			octalSignificandWide =
				(octalSignificandWide << shift) + (c - '0');
		    } else {
................................................................................
		     * large shifts first.
		     */

		    if (significandWide != 0 &&
			    ((size_t)shift >= CHAR_BIT*sizeof(Tcl_WideUInt) ||
			    significandWide > (~(Tcl_WideUInt)0 >> shift))) {
			significandOverflow = 1;
			TclInitBignumFromWideUInt(&significandBig,
				significandWide);
		    }
		}
		if (!significandOverflow) {
		    significandWide = (significandWide << shift) + d;
		} else {
		    mp_mul_2d(&significandBig, shift, &significandBig);
................................................................................
		     * large shifts first.
		     */

		    if (significandWide != 0 &&
			    ((size_t)shift >= CHAR_BIT*sizeof(Tcl_WideUInt) ||
			    significandWide > (~(Tcl_WideUInt)0 >> shift))) {
			significandOverflow = 1;
			TclInitBignumFromWideUInt(&significandBig,
				significandWide);
		    }
		}
		if (!significandOverflow) {
		    significandWide = (significandWide << shift) + 1;
		} else {
		    mp_mul_2d(&significandBig, shift, &significandBig);
................................................................................
		    acceptState, bytes);
	case BINARY:
	    shift = numTrailZeros;
	    if (!significandOverflow && significandWide != 0 &&
		    ((size_t)shift >= CHAR_BIT*sizeof(Tcl_WideUInt) ||
		    significandWide > (MOST_BITS + signum) >> shift)) {
		significandOverflow = 1;
		TclInitBignumFromWideUInt(&significandBig, significandWide);
	    }
	    if (shift) {
		if (!significandOverflow) {
		    significandWide <<= shift;
		} else {
		    mp_mul_2d(&significandBig, shift, &significandBig);
		}
................................................................................
	     */

	    shift = 4 * numTrailZeros;
	    if (!significandOverflow && significandWide !=0 &&
		    ((size_t)shift >= CHAR_BIT*sizeof(Tcl_WideUInt) ||
		    significandWide > (MOST_BITS + signum) >> shift)) {
		significandOverflow = 1;
		TclInitBignumFromWideUInt(&significandBig, significandWide);
	    }
	    if (shift) {
		if (!significandOverflow) {
		    significandWide <<= shift;
		} else {
		    mp_mul_2d(&significandBig, shift, &significandBig);
		}
................................................................................
	     */

	    shift = 3 * numTrailZeros;
	    if (!octalSignificandOverflow && octalSignificandWide != 0 &&
		    ((size_t)shift >= CHAR_BIT*sizeof(Tcl_WideUInt) ||
		    octalSignificandWide > (MOST_BITS + signum) >> shift)) {
		octalSignificandOverflow = 1;
		TclInitBignumFromWideUInt(&octalSignificandBig,
			octalSignificandWide);
	    }
	    if (shift) {
		if (!octalSignificandOverflow) {
		    octalSignificandWide <<= shift;
		} else {
		    mp_mul_2d(&octalSignificandBig, shift,
................................................................................
			} else {
			    objPtr->internalRep.wideValue =
				    (Tcl_WideInt) octalSignificandWide;
			}
			break;
		    }
#endif
		    TclInitBignumFromWideUInt(&octalSignificandBig,
			    octalSignificandWide);
		    octalSignificandOverflow = 1;
		} else {
		    objPtr->typePtr = &tclIntType;
		    if (signum) {
			objPtr->internalRep.longValue =
				- (long) octalSignificandWide;
................................................................................

	case ZERO:
	case DECIMAL:
	    significandOverflow = AccumulateDecimalDigit(0, numTrailZeros-1,
		    &significandWide, &significandBig, significandOverflow);
	    if (!significandOverflow && (significandWide > MOST_BITS+signum)){
		significandOverflow = 1;
		TclInitBignumFromWideUInt(&significandBig, significandWide);
	    }
	returnInteger:
	    if (!significandOverflow) {
		if (significandWide >
			(Tcl_WideUInt)(((~(unsigned long)0) >> 1) + signum)) {
#ifndef TCL_WIDE_INT_IS_LONG
		    if (significandWide <= MOST_BITS+signum) {
................................................................................
			} else {
			    objPtr->internalRep.wideValue =
				    (Tcl_WideInt) significandWide;
			}
			break;
		    }
#endif
		    TclInitBignumFromWideUInt(&significandBig,
			    significandWide);
		    significandOverflow = 1;
		} else {
		    objPtr->typePtr = &tclIntType;
		    if (signum) {
			objPtr->internalRep.longValue =
				- (long) significandWide;
................................................................................
	} else if (numZeros >= maxpow10_wide
		|| w > ((~(Tcl_WideUInt)0)-digit)/pow10_wide[numZeros+1]) {
	    /*
	     * Wide multiplication will overflow.  Expand the number to a
	     * bignum and fall through into the bignum case.
	     */

	    TclInitBignumFromWideUInt(bignumRepPtr, w);
	} else {
	    /*
	     * Wide multiplication.
	     */

	    *wideRepPtr = w * pow10_wide[numZeros+1] + digit;
	    return 0;
................................................................................
    }

    /*
     * All the easy cases have failed. Promote ths significand to bignum and
     * call MakeHighPrecisionDouble to do it the hard way.
     */

    TclInitBignumFromWideUInt(&significandBig, significand);
    retval = MakeHighPrecisionDouble(0, &significandBig, numSigDigs,
	    exponent);
    mp_clear(&significandBig);

    /*
     * Come here to return the computed value.
     */
................................................................................
    int r1;

    /*
     * b = bw * 2**b2 * 5**b5
     * mminus = 5**m5
     */

    TclInitBignumFromWideUInt(&b, bw);
    mp_init_set_int(&mminus, 1);
    MulPow5(&b, b5, &b);
    mp_mul_2d(&b, b2, &b);

    /*
     * Adjust if the logarithm was guessed wrong.
     */
................................................................................
    int i;			/* Index in the output buffer. */
    mp_int temp;

    /*
     * b = bw * 2**b2 * 5**b5
     */

    TclInitBignumFromWideUInt(&b, bw);
    MulPow5(&b, b5, &b);
    mp_mul_2d(&b, b2, &b);

    /*
     * Adjust if the logarithm was guessed wrong.
     */

................................................................................
    int r1;

    /*
     * b = bw * 2**b2 * 5**b5
     * S = 2**s2 * 5*s5
     */

    TclInitBignumFromWideUInt(&b, bw);
    mp_mul_2d(&b, b2, &b);
    mp_init_set_int(&S, 1);
    MulPow5(&S, s5, &S); mp_mul_2d(&S, s2, &S);

    /*
     * Handle the case where we guess the position of the decimal point wrong.
     */
................................................................................

    /*
     * b = bw * 2**b2 * 5**b5
     * S = 2**s2 * 5*s5
     */

    mp_init_multi(&temp, &dig, NULL);
    TclInitBignumFromWideUInt(&b, bw);
    mp_mul_2d(&b, b2, &b);
    mp_init_set_int(&S, 1);
    MulPow5(&S, s5, &S); mp_mul_2d(&S, s2, &S);

    /*
     * Handle the case where we guess the position of the decimal point wrong.
     */
................................................................................
    if (expt <= 0) {
	mp_init(b);
	mp_zero(b);
    } else {
	Tcl_WideInt w = (Tcl_WideInt) ldexp(fract, mantBits);
	int shift = expt - mantBits;

	TclInitBignumFromWideInt(b, w);
	if (shift < 0) {
	    mp_div_2d(b, -shift, b, NULL);
	} else if (shift > 0) {
	    mp_mul_2d(b, shift, b);
	}
    }
    return TCL_OK;

	    dst = Tcl_GetUnicode(objResultPtr) + start;
	} else {
	    Tcl_UniChar ch = 0;

	    /* Ugly interface! No scheme to init array size. */
	    objResultPtr = Tcl_NewUnicodeObj(&ch, 0);	/* PANIC? */
	    if (0 == Tcl_AttemptSetObjLength(objResultPtr, length)) {

		if (interp) {
		    Tcl_SetObjResult(interp, Tcl_ObjPrintf(
		    	"concatenation failed: unable to alloc %"
			TCL_LL_MODIFIER "d bytes",
			(Tcl_WideUInt)STRING_SIZE(length)));
		    Tcl_SetErrorCode(interp, "TCL", "MEMORY", NULL);
		}
................................................................................
	    dst = Tcl_GetString(objResultPtr) + start;

	    /* assert ( length > start ) */
	    TclFreeIntRep(objResultPtr);
	} else {
	    objResultPtr = Tcl_NewObj();	/* PANIC? */
	    if (0 == Tcl_AttemptSetObjLength(objResultPtr, length)) {

		if (interp) {
		    Tcl_SetObjResult(interp, Tcl_ObjPrintf(
		    	"concatenation failed: unable to alloc %u bytes",
			length));
		    Tcl_SetErrorCode(interp, "TCL", "MEMORY", NULL);
		}
		return TCL_ERROR;
................................................................................
		return (try - bh);
	    }
	    try++;
	}
	return -1;
    }









    lh = Tcl_GetCharLength(haystack);
    if (haystack->bytes && (lh == haystack->length)) {
	/* haystack is all single-byte chars */





	if (needle->bytes && (ln == needle->length)) {
	    /* needle is also all single-byte chars */
	    char *found = strstr(haystack->bytes + start, needle->bytes);

	    if (found) {
		return (found - haystack->bytes);
	    } else {
		return -1;
	    }
	} else {
	    /*
	     * Cannot find substring with a multi-byte char inside
	     * a string with no multi-byte chars.
	     */
	    return -1;
	}
    } else {




	Tcl_UniChar *try, *end, *uh;
	Tcl_UniChar *un = Tcl_GetUnicodeFromObj(needle, &ln);

	uh = Tcl_GetUnicodeFromObj(haystack, &lh);
	end = uh + lh;

	try = uh + start;
	while (try + ln <= end) {
	    if ((*try == *un)
		    && (0 == memcmp(try+1, un+1, (ln-1)*sizeof(Tcl_UniChar)))) {
		return (try - uh);
	    }
	    try++;
	}
	return -1;
    }
}
 
/*
 *---------------------------------------------------------------------------

	    dst = Tcl_GetUnicode(objResultPtr) + start;
	} else {
	    Tcl_UniChar ch = 0;

	    /* Ugly interface! No scheme to init array size. */
	    objResultPtr = Tcl_NewUnicodeObj(&ch, 0);	/* PANIC? */
	    if (0 == Tcl_AttemptSetObjLength(objResultPtr, length)) {
		Tcl_DecrRefCount(objResultPtr);
		if (interp) {
		    Tcl_SetObjResult(interp, Tcl_ObjPrintf(
		    	"concatenation failed: unable to alloc %"
			TCL_LL_MODIFIER "d bytes",
			(Tcl_WideUInt)STRING_SIZE(length)));
		    Tcl_SetErrorCode(interp, "TCL", "MEMORY", NULL);
		}
................................................................................
	    dst = Tcl_GetString(objResultPtr) + start;

	    /* assert ( length > start ) */
	    TclFreeIntRep(objResultPtr);
	} else {
	    objResultPtr = Tcl_NewObj();	/* PANIC? */
	    if (0 == Tcl_AttemptSetObjLength(objResultPtr, length)) {
		Tcl_DecrRefCount(objResultPtr);
		if (interp) {
		    Tcl_SetObjResult(interp, Tcl_ObjPrintf(
		    	"concatenation failed: unable to alloc %u bytes",
			length));
		    Tcl_SetErrorCode(interp, "TCL", "MEMORY", NULL);
		}
		return TCL_ERROR;
................................................................................
		return (try - bh);
	    }
	    try++;
	}
	return -1;
    }

    /*
     * Check if we have two strings of single-byte characters. If we have, we
     * can use strstr() to do the search. Note that we can sometimes have
     * multibyte characters when the string could be minimally represented
     * using single byte characters; we can't assume that a mismatch here
     * means no match.
     */

    lh = Tcl_GetCharLength(haystack);
    if (haystack->bytes && (lh == haystack->length) && needle->bytes

		&& (ln == needle->length)) {
	/*
	 * Both haystack and needle are all single-byte chars.
	 */



	char *found = strstr(haystack->bytes + start, needle->bytes);

	if (found) {
	    return (found - haystack->bytes);
	} else {







	    return -1;
	}
    } else {
	/*
	 * Do the search on the unicode representation for simplicity.
	 */

	Tcl_UniChar *try, *end, *uh;
	Tcl_UniChar *un = Tcl_GetUnicodeFromObj(needle, &ln);

	uh = Tcl_GetUnicodeFromObj(haystack, &lh);
	end = uh + lh;

	for (try = uh + start; try + ln <= end; try++) {

	    if ((*try == *un) && (0 ==
		    memcmp(try + 1, un + 1, (ln-1) * sizeof(Tcl_UniChar)))) {
		return (try - uh);
	    }

	}
	return -1;
    }
}
 
/*
 *---------------------------------------------------------------------------

#   define TclSetStartupScriptFileName 0
#   define TclGetStartupScriptFileName 0
#   define TclpInetNtoa 0
#   define TclWinGetServByName 0
#   define TclWinGetSockOpt 0
#   define TclWinSetSockOpt 0
#   define TclWinNToHS 0



#else
#define TclSetStartupScriptPath setStartupScriptPath
static void TclSetStartupScriptPath(Tcl_Obj *path)
{
    Tcl_SetStartupScript(path, NULL);
}
#define TclGetStartupScriptPath getStartupScriptPath
................................................................................
#if defined(_WIN32) || defined(__CYGWIN__)
#undef TclWinNToHS
#define TclWinNToHS winNToHS
static unsigned short TclWinNToHS(unsigned short ns) {
	return ntohs(ns);
}
#endif



#endif /* TCL_NO_DEPRECATED */

#ifdef _WIN32
#   define TclUnixWaitForFile 0
#   define TclUnixCopyFile 0
#   define TclUnixOpenTemporaryFile 0
#   define TclpReaddir 0
................................................................................
    TclBN_mp_cnt_lsb, /* 63 */
    TclBNInitBignumFromLong, /* 64 */
    TclBNInitBignumFromWideInt, /* 65 */
    TclBNInitBignumFromWideUInt, /* 66 */
    TclBN_mp_expt_d_ex, /* 67 */
    TclBN_mp_set_long_long, /* 68 */
    TclBN_mp_get_long_long, /* 69 */


};

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

#   define TclSetStartupScriptFileName 0
#   define TclGetStartupScriptFileName 0
#   define TclpInetNtoa 0
#   define TclWinGetServByName 0
#   define TclWinGetSockOpt 0
#   define TclWinSetSockOpt 0
#   define TclWinNToHS 0
#   define TclBNInitBignumFromWideUInt 0
#   define TclBNInitBignumFromWideInt 0
#   define TclBNInitBignumFromLong 0
#else
#define TclSetStartupScriptPath setStartupScriptPath
static void TclSetStartupScriptPath(Tcl_Obj *path)
{
    Tcl_SetStartupScript(path, NULL);
}
#define TclGetStartupScriptPath getStartupScriptPath
................................................................................
#if defined(_WIN32) || defined(__CYGWIN__)
#undef TclWinNToHS
#define TclWinNToHS winNToHS
static unsigned short TclWinNToHS(unsigned short ns) {
	return ntohs(ns);
}
#endif
#   define TclBNInitBignumFromWideUInt TclInitBignumFromWideUInt
#   define TclBNInitBignumFromWideInt TclInitBignumFromWideInt
#   define TclBNInitBignumFromLong TclInitBignumFromLong
#endif /* TCL_NO_DEPRECATED */

#ifdef _WIN32
#   define TclUnixWaitForFile 0
#   define TclUnixCopyFile 0
#   define TclUnixOpenTemporaryFile 0
#   define TclpReaddir 0
................................................................................
    TclBN_mp_cnt_lsb, /* 63 */
    TclBNInitBignumFromLong, /* 64 */
    TclBNInitBignumFromWideInt, /* 65 */
    TclBNInitBignumFromWideUInt, /* 66 */
    TclBN_mp_expt_d_ex, /* 67 */
    TclBN_mp_set_long_long, /* 68 */
    TclBN_mp_get_long_long, /* 69 */
    TclBN_mp_set_long, /* 70 */
    TclBN_mp_get_long, /* 71 */
};

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

static void		PrintParse(Tcl_Interp *interp, Tcl_Parse *parsePtr);
static void		SpecialFree(char *blockPtr);
static int		StaticInitProc(Tcl_Interp *interp);
static int		TestasyncCmd(ClientData dummy,
			    Tcl_Interp *interp, int argc, const char **argv);
static int		TestbytestringObjCmd(ClientData clientData,
			    Tcl_Interp *interp, int objc,



			    Tcl_Obj *const objv[]);
static int		TestcmdinfoCmd(ClientData dummy,
			    Tcl_Interp *interp, int argc, const char **argv);
static int		TestcmdtokenCmd(ClientData dummy,
			    Tcl_Interp *interp, int argc, const char **argv);
static int		TestcmdtraceCmd(ClientData dummy,
			    Tcl_Interp *interp, int argc, const char **argv);
................................................................................
     * Create additional commands and math functions for testing Tcl.
     */

    Tcl_CreateObjCommand(interp, "gettimes", GetTimesObjCmd, NULL, NULL);
    Tcl_CreateCommand(interp, "noop", NoopCmd, NULL, NULL);
    Tcl_CreateObjCommand(interp, "noop", NoopObjCmd, NULL, NULL);
    Tcl_CreateObjCommand(interp, "testbytestring", TestbytestringObjCmd, NULL, NULL);

    Tcl_CreateObjCommand(interp, "testwrongnumargs", TestWrongNumArgsObjCmd,
	    NULL, NULL);
    Tcl_CreateObjCommand(interp, "testfilesystem", TestFilesystemObjCmd,
	    NULL, NULL);
    Tcl_CreateObjCommand(interp, "testsimplefilesystem", TestSimpleFilesystemObjCmd,
	    NULL, NULL);
    Tcl_CreateObjCommand(interp, "testgetindexfromobjstruct",
................................................................................
	Tcl_CreateEncoding(&type);
	break;
    }
    case ENC_DELETE:
	if (objc != 3) {
	    return TCL_ERROR;
	}
	encoding = Tcl_GetEncoding(NULL, Tcl_GetString(objv[2]));


	Tcl_FreeEncoding(encoding);
	Tcl_FreeEncoding(encoding);

	break;
    }
    return TCL_OK;
}

static int
EncodingToUtfProc(
................................................................................
    ClientData unused,		/* Not used. */
    Tcl_Interp *interp,		/* Current interpreter. */
    int objc,			/* Number of arguments. */
    Tcl_Obj *const objv[])	/* The argument objects. */
{
    return TCL_OK;
}


































 
/*
 *----------------------------------------------------------------------
 *
 * TestbytestringObjCmd --
 *
 *	This object-based procedure constructs a string which can

static void		PrintParse(Tcl_Interp *interp, Tcl_Parse *parsePtr);
static void		SpecialFree(char *blockPtr);
static int		StaticInitProc(Tcl_Interp *interp);
static int		TestasyncCmd(ClientData dummy,
			    Tcl_Interp *interp, int argc, const char **argv);
static int		TestbytestringObjCmd(ClientData clientData,
			    Tcl_Interp *interp, int objc,
			    Tcl_Obj *const objv[]);
static int		TeststringbytesObjCmd(ClientData clientData,
			    Tcl_Interp *interp, int objc,
			    Tcl_Obj *const objv[]);
static int		TestcmdinfoCmd(ClientData dummy,
			    Tcl_Interp *interp, int argc, const char **argv);
static int		TestcmdtokenCmd(ClientData dummy,
			    Tcl_Interp *interp, int argc, const char **argv);
static int		TestcmdtraceCmd(ClientData dummy,
			    Tcl_Interp *interp, int argc, const char **argv);
................................................................................
     * Create additional commands and math functions for testing Tcl.
     */

    Tcl_CreateObjCommand(interp, "gettimes", GetTimesObjCmd, NULL, NULL);
    Tcl_CreateCommand(interp, "noop", NoopCmd, NULL, NULL);
    Tcl_CreateObjCommand(interp, "noop", NoopObjCmd, NULL, NULL);
    Tcl_CreateObjCommand(interp, "testbytestring", TestbytestringObjCmd, NULL, NULL);
    Tcl_CreateObjCommand(interp, "teststringbytes", TeststringbytesObjCmd, NULL, NULL);
    Tcl_CreateObjCommand(interp, "testwrongnumargs", TestWrongNumArgsObjCmd,
	    NULL, NULL);
    Tcl_CreateObjCommand(interp, "testfilesystem", TestFilesystemObjCmd,
	    NULL, NULL);
    Tcl_CreateObjCommand(interp, "testsimplefilesystem", TestSimpleFilesystemObjCmd,
	    NULL, NULL);
    Tcl_CreateObjCommand(interp, "testgetindexfromobjstruct",
................................................................................
	Tcl_CreateEncoding(&type);
	break;
    }
    case ENC_DELETE:
	if (objc != 3) {
	    return TCL_ERROR;
	}
	if (TCL_OK != Tcl_GetEncodingFromObj(interp, objv[2], &encoding)) {
	    return TCL_ERROR;
	}
	Tcl_FreeEncoding(encoding);	/* Free returned reference */
	Tcl_FreeEncoding(encoding);	/* Free to match CREATE */
	TclFreeIntRep(objv[2]);		/* Free the cached ref */
	break;
    }
    return TCL_OK;
}

static int
EncodingToUtfProc(
................................................................................
    ClientData unused,		/* Not used. */
    Tcl_Interp *interp,		/* Current interpreter. */
    int objc,			/* Number of arguments. */
    Tcl_Obj *const objv[])	/* The argument objects. */
{
    return TCL_OK;
}
 
/*
 *----------------------------------------------------------------------
 *
 * TeststringbytesObjCmd --
 *	Returns bytearray value of the bytes in argument string rep
 *
 * Results:
 *	Returns the TCL_OK result code.
 *
 * Side effects:
 *	None.
 *
 *----------------------------------------------------------------------
 */

static int
TeststringbytesObjCmd(
    ClientData unused,		/* Not used. */
    Tcl_Interp *interp,		/* Current interpreter. */
    int objc,			/* Number of arguments. */
    Tcl_Obj *const objv[])	/* The argument objects. */
{
    int n;
    const unsigned char *p;

    if (objc != 2) {
	Tcl_WrongNumArgs(interp, 1, objv, "value");
	return TCL_ERROR;
    }
    p = (const unsigned char *)Tcl_GetStringFromObj(objv[1], &n);
    Tcl_SetObjResult(interp, Tcl_NewByteArrayObj(p, n));
    return TCL_OK;
}
 
/*
 *----------------------------------------------------------------------
 *
 * TestbytestringObjCmd --
 *
 *	This object-based procedure constructs a string which can

    int TclBN_epoch(void)
}
declare 1 {
    int TclBN_revision(void)
}

declare 2 {
    int TclBN_mp_add(mp_int *a, mp_int *b, mp_int *c)
}
declare 3 {
    int TclBN_mp_add_d(mp_int *a, mp_digit b, mp_int *c)
}
declare 4 {
    int TclBN_mp_and(mp_int *a, mp_int *b, mp_int *c)
}
declare 5 {
    void TclBN_mp_clamp(mp_int *a)
}
declare 6 {
    void TclBN_mp_clear(mp_int *a)
}
................................................................................
declare 11 {
    int TclBN_mp_copy(const mp_int *a, mp_int *b)
}
declare 12 {
    int TclBN_mp_count_bits(const mp_int *a)
}
declare 13 {
    int TclBN_mp_div(mp_int *a, mp_int *b, mp_int *q, mp_int *r)
}
declare 14 {
    int TclBN_mp_div_d(mp_int *a, mp_digit b, mp_int *q, mp_digit *r)
}
declare 15 {
    int TclBN_mp_div_2(const mp_int *a, mp_int *q)
}
declare 16 {
    int TclBN_mp_div_2d(const mp_int *a, int b, mp_int *q, mp_int *r)
}
declare 17 {
    int TclBN_mp_div_3(mp_int *a, mp_int *q, mp_digit *r)
}
declare 18 {
    void TclBN_mp_exch(mp_int *a, mp_int *b)
}
declare 19 {
    int TclBN_mp_expt_d(mp_int *a, mp_digit b, mp_int *c)
}
declare 20 {
    int TclBN_mp_grow(mp_int *a, int size)
}
declare 21 {
    int TclBN_mp_init(mp_int *a)
}
................................................................................
declare 25 {
    int TclBN_mp_init_size(mp_int *a, int size)
}
declare 26 {
    int TclBN_mp_lshd(mp_int *a, int shift)
}
declare 27 {
    int TclBN_mp_mod(mp_int *a, mp_int *b, mp_int *r)
}
declare 28 {
    int TclBN_mp_mod_2d(const mp_int *a, int b, mp_int *r)
}
declare 29 {
    int TclBN_mp_mul(mp_int *a, mp_int *b, mp_int *p)
}
declare 30 {
    int TclBN_mp_mul_d(mp_int *a, mp_digit b, mp_int *p)
}
declare 31 {
    int TclBN_mp_mul_2(const mp_int *a, mp_int *p)
}
declare 32 {
    int TclBN_mp_mul_2d(const mp_int *a, int d, mp_int *p)
}
declare 33 {
    int TclBN_mp_neg(const mp_int *a, mp_int *b)
}
declare 34 {
    int TclBN_mp_or(mp_int *a, mp_int *b, mp_int *c)
}
declare 35 {
    int TclBN_mp_radix_size(const mp_int *a, int radix, int *size)
}
declare 36 {
    int TclBN_mp_read_radix(mp_int *a, const char *str, int radix)
}
................................................................................
declare 38 {
    int TclBN_mp_shrink(mp_int *a)
}
declare 39 {
    void TclBN_mp_set(mp_int *a, mp_digit b)
}
declare 40 {
    int TclBN_mp_sqr(mp_int *a, mp_int *b)
}
declare 41 {
    int TclBN_mp_sqrt(mp_int *a, mp_int *b)
}
declare 42 {
    int TclBN_mp_sub(mp_int *a, mp_int *b, mp_int *c)
}
declare 43 {
    int TclBN_mp_sub_d(mp_int *a, mp_digit b, mp_int *c)
}
declare 44 {
    int TclBN_mp_to_unsigned_bin(mp_int *a, unsigned char *b)
}
declare 45 {
    int TclBN_mp_to_unsigned_bin_n(mp_int *a, unsigned char *b,
	    unsigned long *outlen)
}
declare 46 {
    int TclBN_mp_toradix_n(mp_int *a, char *str, int radix, int maxlen)
}
declare 47 {
    int TclBN_mp_unsigned_bin_size(mp_int *a)
}
declare 48 {
    int TclBN_mp_xor(mp_int *a, mp_int *b, mp_int *c)
}
declare 49 {
    void TclBN_mp_zero(mp_int *a)
}

# internal routines to libtommath - should not be called but must be
# exported to accommodate the "tommath" extension

declare 50 {
    void TclBN_reverse(unsigned char *s, int len)
}
declare 51 {
    int TclBN_fast_s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs)
}
declare 52 {
    int TclBN_fast_s_mp_sqr(mp_int *a, mp_int *b)
}
declare 53 {
    int TclBN_mp_karatsuba_mul(mp_int *a, mp_int *b, mp_int *c)
}
declare 54 {
    int TclBN_mp_karatsuba_sqr(mp_int *a, mp_int *b)
}
declare 55 {
    int TclBN_mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
}
declare 56 {
    int TclBN_mp_toom_sqr(mp_int *a, mp_int *b)
}
declare 57 {
    int TclBN_s_mp_add(mp_int *a, mp_int *b, mp_int *c)
}
declare 58 {
    int TclBN_s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs)
}
declare 59 {
    int TclBN_s_mp_sqr(mp_int *a, mp_int *b)
}
declare 60 {
    int TclBN_s_mp_sub(mp_int *a, mp_int *b, mp_int *c)
}
declare 61 {
    int TclBN_mp_init_set_int(mp_int *a, unsigned long i)
}
declare 62 {
    int TclBN_mp_set_int(mp_int *a, unsigned long i)
}
declare 63 {
    int TclBN_mp_cnt_lsb(const mp_int *a)
}

# Formerly internal API to allow initialisation of bignums without knowing the
# typedefs of how a bignum works internally.
declare 64 {
    void TclBNInitBignumFromLong(mp_int *bignum, long initVal)
}
declare 65 {
    void TclBNInitBignumFromWideInt(mp_int *bignum, Tcl_WideInt initVal)
}
declare 66 {
    void TclBNInitBignumFromWideUInt(mp_int *bignum, Tcl_WideUInt initVal)
}

# Added in libtommath 1.0
declare 67 {
    int TclBN_mp_expt_d_ex(mp_int *a, mp_digit b, mp_int *c, int fast)
}
# Added in libtommath 1.0.1
declare 68 {
    int TclBN_mp_set_long_long(mp_int *a, Tcl_WideUInt i)
}
declare 69 {
    Tcl_WideUInt TclBN_mp_get_long_long(const mp_int *a)
}







# Local Variables:
# mode: tcl
# End:

    int TclBN_epoch(void)
}
declare 1 {
    int TclBN_revision(void)
}

declare 2 {
    int TclBN_mp_add(const mp_int *a, const mp_int *b, mp_int *c)
}
declare 3 {
    int TclBN_mp_add_d(const mp_int *a, mp_digit b, mp_int *c)
}
declare 4 {
    int TclBN_mp_and(const mp_int *a, const mp_int *b, mp_int *c)
}
declare 5 {
    void TclBN_mp_clamp(mp_int *a)
}
declare 6 {
    void TclBN_mp_clear(mp_int *a)
}
................................................................................
declare 11 {
    int TclBN_mp_copy(const mp_int *a, mp_int *b)
}
declare 12 {
    int TclBN_mp_count_bits(const mp_int *a)
}
declare 13 {
    int TclBN_mp_div(const mp_int *a, const mp_int *b, mp_int *q, mp_int *r)
}
declare 14 {
    int TclBN_mp_div_d(const mp_int *a, mp_digit b, mp_int *q, mp_digit *r)
}
declare 15 {
    int TclBN_mp_div_2(const mp_int *a, mp_int *q)
}
declare 16 {
    int TclBN_mp_div_2d(const mp_int *a, int b, mp_int *q, mp_int *r)
}
declare 17 {
    int TclBN_mp_div_3(const mp_int *a, mp_int *q, mp_digit *r)
}
declare 18 {
    void TclBN_mp_exch(mp_int *a, mp_int *b)
}
declare 19 {
    int TclBN_mp_expt_d(const mp_int *a, mp_digit b, mp_int *c)
}
declare 20 {
    int TclBN_mp_grow(mp_int *a, int size)
}
declare 21 {
    int TclBN_mp_init(mp_int *a)
}
................................................................................
declare 25 {
    int TclBN_mp_init_size(mp_int *a, int size)
}
declare 26 {
    int TclBN_mp_lshd(mp_int *a, int shift)
}
declare 27 {
    int TclBN_mp_mod(const mp_int *a, const mp_int *b, mp_int *r)
}
declare 28 {
    int TclBN_mp_mod_2d(const mp_int *a, int b, mp_int *r)
}
declare 29 {
    int TclBN_mp_mul(const mp_int *a, const mp_int *b, mp_int *p)
}
declare 30 {
    int TclBN_mp_mul_d(const mp_int *a, mp_digit b, mp_int *p)
}
declare 31 {
    int TclBN_mp_mul_2(const mp_int *a, mp_int *p)
}
declare 32 {
    int TclBN_mp_mul_2d(const mp_int *a, int d, mp_int *p)
}
declare 33 {
    int TclBN_mp_neg(const mp_int *a, mp_int *b)
}
declare 34 {
    int TclBN_mp_or(const mp_int *a, const mp_int *b, mp_int *c)
}
declare 35 {
    int TclBN_mp_radix_size(const mp_int *a, int radix, int *size)
}
declare 36 {
    int TclBN_mp_read_radix(mp_int *a, const char *str, int radix)
}
................................................................................
declare 38 {
    int TclBN_mp_shrink(mp_int *a)
}
declare 39 {
    void TclBN_mp_set(mp_int *a, mp_digit b)
}
declare 40 {
    int TclBN_mp_sqr(const mp_int *a, mp_int *b)
}
declare 41 {
    int TclBN_mp_sqrt(const mp_int *a, mp_int *b)
}
declare 42 {
    int TclBN_mp_sub(const mp_int *a, const mp_int *b, mp_int *c)
}
declare 43 {
    int TclBN_mp_sub_d(const mp_int *a, mp_digit b, mp_int *c)
}
declare 44 {
    int TclBN_mp_to_unsigned_bin(const mp_int *a, unsigned char *b)
}
declare 45 {
    int TclBN_mp_to_unsigned_bin_n(const mp_int *a, unsigned char *b,
	    unsigned long *outlen)
}
declare 46 {
    int TclBN_mp_toradix_n(const mp_int *a, char *str, int radix, int maxlen)
}
declare 47 {
    int TclBN_mp_unsigned_bin_size(const mp_int *a)
}
declare 48 {
    int TclBN_mp_xor(const mp_int *a, const mp_int *b, mp_int *c)
}
declare 49 {
    void TclBN_mp_zero(mp_int *a)
}

# internal routines to libtommath - should not be called but must be
# exported to accommodate the "tommath" extension

declare 50 {
    void TclBN_reverse(unsigned char *s, int len)
}
declare 51 {
    int TclBN_fast_s_mp_mul_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs)
}
declare 52 {
    int TclBN_fast_s_mp_sqr(const mp_int *a, mp_int *b)
}
declare 53 {
    int TclBN_mp_karatsuba_mul(const mp_int *a, const mp_int *b, mp_int *c)
}
declare 54 {
    int TclBN_mp_karatsuba_sqr(const mp_int *a, mp_int *b)
}
declare 55 {
    int TclBN_mp_toom_mul(const mp_int *a, const mp_int *b, mp_int *c)
}
declare 56 {
    int TclBN_mp_toom_sqr(const mp_int *a, mp_int *b)
}
declare 57 {
    int TclBN_s_mp_add(const mp_int *a, const mp_int *b, mp_int *c)
}
declare 58 {
    int TclBN_s_mp_mul_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs)
}
declare 59 {
    int TclBN_s_mp_sqr(const mp_int *a, mp_int *b)
}
declare 60 {
    int TclBN_s_mp_sub(const mp_int *a, const mp_int *b, mp_int *c)
}
declare 61 {
    int TclBN_mp_init_set_int(mp_int *a, unsigned long i)
}
declare 62 {
    int TclBN_mp_set_int(mp_int *a, unsigned long i)
}
declare 63 {
    int TclBN_mp_cnt_lsb(const mp_int *a)
}

# Formerly internal API to allow initialisation of bignums without knowing the
# typedefs of how a bignum works internally.
declare 64 {deprecated {Use mp_init() + mp_set_long_long()}} {
    void TclBNInitBignumFromLong(mp_int *bignum, long initVal)
}
declare 65 {deprecated {Use mp_init() + mp_set_long_long()}} {
    void TclBNInitBignumFromWideInt(mp_int *bignum, Tcl_WideInt initVal)
}
declare 66 {deprecated {Use mp_init() + mp_set_long_long()}} {
    void TclBNInitBignumFromWideUInt(mp_int *bignum, Tcl_WideUInt initVal)
}

# Added in libtommath 1.0
declare 67 {
    int TclBN_mp_expt_d_ex(const mp_int *a, mp_digit b, mp_int *c, int fast)
}
# Added in libtommath 1.0.1
declare 68 {
    int TclBN_mp_set_long_long(mp_int *a, Tcl_WideUInt i)
}
declare 69 {
    Tcl_WideUInt TclBN_mp_get_long_long(const mp_int *a)
}
declare 70 {
    int TclBN_mp_set_long(mp_int *a, unsigned long i)
}
declare 71 {
    unsigned long TclBN_mp_get_long(const mp_int *a)
}

# Local Variables:
# mode: tcl
# End:

#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
#ifndef MP_WORD_DECLARED
   typedef uint16_t             mp_word;
#define MP_WORD_DECLARED
#endif
#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
#ifndef MP_WORD_DECLARED
   typedef uint32_t             mp_word;
#define MP_WORD_DECLARED
#endif
#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 MP_DIGIT_DECLARED
   typedef uint64_t mp_digit;
#define MP_DIGIT_DECLARED
#endif
#if defined(_WIN32)
#ifndef MP_WORD_DECLARED
   typedef unsigned __int128    mp_word;
#define MP_WORD_DECLARED
#endif
#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 */
#ifndef MP_WORD_DECLARED
   typedef uint128_t            mp_word;
#define MP_WORD_DECLARED
#endif
#endif

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

   /* this is to make porting into LibTomCrypt easier :-) */
#ifndef MP_DIGIT_DECLARED
   typedef uint32_t             mp_digit;
#define MP_DIGIT_DECLARED
#endif
#ifndef MP_WORD_DECLARED
   typedef uint64_t             mp_word;
#define MP_WORD_DECLARED
#endif

#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

/* use arc4random on platforms that support it */
#if defined(__FreeBSD__) || defined(__OpenBSD__) || defined(__NetBSD__) || defined(__DragonFly__)
    #define MP_GEN_RANDOM()    arc4random()
    #define MP_GEN_RANDOM_MAX  0xffffffff
#endif

/* use rand() as fall-back if there's no better rand function */
#ifndef MP_GEN_RANDOM
    #define MP_GEN_RANDOM()    rand()
    #define MP_GEN_RANDOM_MAX  RAND_MAX
#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 LTM_PRIME_2MSB_ON  0x0008 /* force 2nd MSB to 1 */

typedef int           mp_err;

/* you'll have to tune these... */
#if defined(BUILD_tcl) || !defined(_WIN32)
MODULE_SCOPE int KARATSUBA_MUL_CUTOFF,
           KARATSUBA_SQR_CUTOFF,
           TOOM_MUL_CUTOFF,
           TOOM_SQR_CUTOFF;
#endif

/* define this to use lower memory usage routines (exptmods mostly) */
/* #define MP_LOW_MEM */

/* default precision */
#ifndef MP_PREC
   #ifndef MP_LOW_MEM
      #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 {
    int used, alloc, sign;
    mp_digit *dp;
};

/* callback for mp_prime_random, should fill dst with random bytes and return how many read [upto len] */
typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat);


#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 */
/*
................................................................................
/* 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, Tcl_WideUInt b);
*/

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

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

/* get a platform dependent unsigned long long value */
/*
Tcl_WideUInt mp_get_long_long(const 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_set_int (mp_int * a, unsigned long b);
*/

/* copy, b = a */
/*
int mp_copy(const 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);
................................................................................
/*
int mp_rand(mp_int *a, int digits);
*/

/* ---> binary operations <--- */
/* c = a XOR b  */
/*
int mp_xor(mp_int *a, mp_int *b, mp_int *c);
*/

/* c = a OR b */
/*
int mp_or(mp_int *a, mp_int *b, mp_int *c);
*/

/* c = a AND b */
/*
int mp_and(mp_int *a, mp_int *b, mp_int *c);
*/

/* ---> Basic arithmetic <--- */

/* b = -a */
/*
int mp_neg(const mp_int *a, mp_int *b);
*/

/* b = |a| */
/*
int mp_abs(mp_int *a, mp_int *b);
*/

/* compare a to b */
/*
int mp_cmp(const mp_int *a, const mp_int *b);
*/

................................................................................
/* compare |a| to |b| */
/*
int mp_cmp_mag(const mp_int *a, const mp_int *b);
*/

/* c = a + b */
/*
int mp_add(mp_int *a, mp_int *b, mp_int *c);
*/

/* c = a - b */
/*
int mp_sub(mp_int *a, mp_int *b, mp_int *c);
*/

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

/* b = a*a  */
/*
int mp_sqr(mp_int *a, mp_int *b);
*/

/* a/b => cb + d == a */
/*
int mp_div(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
*/

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

/* ---> single digit functions <--- */

/* compare against a single digit */
/*
int mp_cmp_d(const mp_int *a, mp_digit b);
*/

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

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

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

/* a/b => cb + d == a */
/*
int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d);
*/

/* a/3 => 3c + d == a */
/*
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 <--- */

/* d = a + b (mod c) */
/*
int mp_addmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
*/

/* d = a - b (mod c) */
/*
int mp_submod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
*/

/* d = a * b (mod c) */
/*
int mp_mulmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
*/

/* c = a * a (mod b) */
/*
int mp_sqrmod(mp_int *a, mp_int *b, mp_int *c);
*/

/* c = 1/a (mod b) */
/*
int mp_invmod(mp_int *a, mp_int *b, mp_int *c);
*/

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

/* produces value such that U1*a + U2*b = U3 */
/*
int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3);
*/

/* c = [a, b] or (a*b)/(a, b) */
/*
int mp_lcm(mp_int *a, mp_int *b, mp_int *c);
*/

/* 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)  */
/*
int mp_jacobi(mp_int *a, mp_int *n, int *c);
*/

/* used to setup the Barrett reduction for a given modulus b */
/*
int mp_reduce_setup(mp_int *a, mp_int *b);
*/

/* Barrett Reduction, computes a (mod b) with a precomputed value c
 *
 * Assumes that 0 < a <= b*b, note if 0 > a > -(b*b) then you can merely
 * compute the reduction as -1 * mp_reduce(mp_abs(a)) [pseudo code].
 */
/*
int mp_reduce(mp_int *a, mp_int *b, mp_int *c);
*/

/* setups the montgomery reduction */
/*
int mp_montgomery_setup(mp_int *a, mp_digit *mp);
*/

/* computes a = B**n mod b without division or multiplication useful for
 * normalizing numbers in a Montgomery system.
 */
/*
int mp_montgomery_calc_normalization(mp_int *a, mp_int *b);
*/

/* computes x/R == x (mod N) via Montgomery Reduction */
/*
int mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
*/

/* returns 1 if a is a valid DR modulus */
/*
int mp_dr_is_modulus(mp_int *a);
*/

/* sets the value of "d" required for mp_dr_reduce */
/*
void mp_dr_setup(mp_int *a, mp_digit *d);
*/

/* reduces a modulo b using the Diminished Radix method */
/*
int mp_dr_reduce(mp_int *a, mp_int *b, mp_digit mp);
*/

/* returns true if a can be reduced with mp_reduce_2k */
/*
int mp_reduce_is_2k(mp_int *a);
*/

/* determines k value for 2k reduction */
/*
int mp_reduce_2k_setup(mp_int *a, mp_digit *d);
*/

/* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
/*
int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d);
*/

/* returns true if a can be reduced with mp_reduce_2k_l */
/*
int mp_reduce_is_2k_l(mp_int *a);
*/

/* determines k value for 2k reduction */
/*
int mp_reduce_2k_setup_l(mp_int *a, mp_int *d);
*/

/* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
/*
int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d);
*/

/* d = a**b (mod c) */
/*
int mp_exptmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
*/

/* ---> Primes <--- */

/* number of primes */
#ifdef MP_8BIT
#  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);
*/

/* performs one Fermat test of "a" using base "b".
 * Sets result to 0 if composite or 1 if probable prime
 */
/*
int mp_prime_fermat(mp_int *a, mp_int *b, int *result);
*/

/* performs one Miller-Rabin test of "a" using base "b".
 * Sets result to 0 if composite or 1 if probable prime
 */
/*
int mp_prime_miller_rabin(mp_int *a, mp_int *b, int *result);
*/

/* This gives [for a given bit size] the number of trials required
 * such that Miller-Rabin gives a prob of failure lower than 2^-96
 */
/*
int mp_prime_rabin_miller_trials(int size);
................................................................................
 * t prime bases.  Also performs an initial sieve of trial
 * division.  Determines if "a" is prime with probability
 * of error no more than (1/4)**t.
 *
 * Sets result to 1 if probably prime, 0 otherwise
 */
/*
int mp_prime_is_prime(mp_int *a, int t, int *result);
*/

/* finds the next prime after the number "a" using "t" trials
 * of Miller-Rabin.
 *
 * bbs_style = 1 means the prime must be congruent to 3 mod 4
 */
................................................................................

/* ---> radix conversion <--- */
/*
int mp_count_bits(const mp_int *a);
*/

/*
int mp_unsigned_bin_size(mp_int *a);
*/
/*
int mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c);
*/
/*
int mp_to_unsigned_bin(mp_int *a, unsigned char *b);
*/
/*
int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen);
*/

/*
int mp_signed_bin_size(mp_int *a);
*/
/*
int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c);
*/
/*
int mp_to_signed_bin(mp_int *a,  unsigned char *b);
*/
/*
int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen);
*/

/*
int mp_read_radix(mp_int *a, const char *str, int radix);
*/
/*
int mp_toradix(mp_int *a, char *str, int radix);
*/
/*
int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen);
*/
/*
int mp_radix_size(const 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_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


/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

#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
#ifndef MP_WORD_DECLARED
typedef uint16_t             mp_word;
#define MP_WORD_DECLARED
#endif
#   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
#ifndef MP_WORD_DECLARED
typedef uint32_t             mp_word;
#define MP_WORD_DECLARED
#endif
#   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 MP_DIGIT_DECLARED
typedef uint64_t mp_digit;
#define MP_DIGIT_DECLARED
#endif
#   if defined(_WIN32)
#ifndef MP_WORD_DECLARED
typedef unsigned __int128    mp_word;
#define MP_WORD_DECLARED
#endif
#   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 */
#ifndef MP_WORD_DECLARED
typedef uint128_t            mp_word;
#define MP_WORD_DECLARED
#endif
#   endif

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

/* this is to make porting into LibTomCrypt easier :-) */
#ifndef MP_DIGIT_DECLARED
typedef uint32_t             mp_digit;
#define MP_DIGIT_DECLARED
#endif
#ifndef MP_WORD_DECLARED
typedef uint64_t             mp_word;
#define MP_WORD_DECLARED
#endif

#   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

/* use arc4random on platforms that support it */
#if defined(__FreeBSD__) || defined(__OpenBSD__) || defined(__NetBSD__) || defined(__DragonFly__)
#   define MP_GEN_RANDOM()    arc4random()
#   define MP_GEN_RANDOM_MAX  0xffffffff
#endif

/* use rand() as fall-back if there's no better rand function */
#ifndef MP_GEN_RANDOM
#   define MP_GEN_RANDOM()    rand()
#   define MP_GEN_RANDOM_MAX  RAND_MAX
#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 LTM_PRIME_2MSB_ON  0x0008 /* force 2nd MSB to 1 */

typedef int           mp_err;

/* you'll have to tune these... */
#if defined(BUILD_tcl) || !defined(_WIN32)
MODULE_SCOPE int KARATSUBA_MUL_CUTOFF,
       KARATSUBA_SQR_CUTOFF,
       TOOM_MUL_CUTOFF,
       TOOM_SQR_CUTOFF;
#endif

/* define this to use lower memory usage routines (exptmods mostly) */
/* #define MP_LOW_MEM */

/* default precision */
#ifndef MP_PREC
#   ifndef MP_LOW_MEM
#      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 {
   int used, alloc, sign;
   mp_digit *dp;
};

/* callback for mp_prime_random, should fill dst with random bytes and return how many read [upto len] */
typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat);


#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 */
/*
................................................................................
/* 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(const mp_int *a);
*/

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

/* get a platform dependent unsigned long long value */
/*
unsigned long long mp_get_long_long(const 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_set_int(mp_int *a, unsigned long b);
*/

/* copy, b = a */
/*
int mp_copy(const 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, const mp_int *op);
*/

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

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

/* ---> binary operations <--- */
/* c = a XOR b  */
/*
int mp_xor(const mp_int *a, const mp_int *b, mp_int *c);
*/

/* c = a OR b */
/*
int mp_or(const mp_int *a, const mp_int *b, mp_int *c);
*/

/* c = a AND b */
/*
int mp_and(const mp_int *a, const mp_int *b, mp_int *c);
*/

/* ---> Basic arithmetic <--- */

/* b = -a */
/*
int mp_neg(const mp_int *a, mp_int *b);
*/

/* b = |a| */
/*
int mp_abs(const mp_int *a, mp_int *b);
*/

/* compare a to b */
/*
int mp_cmp(const mp_int *a, const mp_int *b);
*/

................................................................................
/* compare |a| to |b| */
/*
int mp_cmp_mag(const mp_int *a, const mp_int *b);
*/

/* c = a + b */
/*
int mp_add(const mp_int *a, const mp_int *b, mp_int *c);
*/

/* c = a - b */
/*
int mp_sub(const mp_int *a, const mp_int *b, mp_int *c);
*/

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

/* b = a*a  */
/*
int mp_sqr(const mp_int *a, mp_int *b);
*/

/* a/b => cb + d == a */
/*
int mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d);
*/

/* c = a mod b, 0 <= c < b  */
/*
int mp_mod(const mp_int *a, const mp_int *b, mp_int *c);
*/

/* ---> single digit functions <--- */

/* compare against a single digit */
/*
int mp_cmp_d(const mp_int *a, mp_digit b);
*/

/* c = a + b */
/*
int mp_add_d(const mp_int *a, mp_digit b, mp_int *c);
*/

/* c = a - b */
/*
int mp_sub_d(const mp_int *a, mp_digit b, mp_int *c);
*/

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

/* a/b => cb + d == a */
/*
int mp_div_d(const mp_int *a, mp_digit b, mp_int *c, mp_digit *d);
*/

/* a/3 => 3c + d == a */
/*
int mp_div_3(const mp_int *a, mp_int *c, mp_digit *d);
*/

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

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

/* ---> number theory <--- */

/* d = a + b (mod c) */
/*
int mp_addmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d);
*/

/* d = a - b (mod c) */
/*
int mp_submod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d);
*/

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

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

/* c = 1/a (mod b) */
/*
int mp_invmod(const mp_int *a, const mp_int *b, mp_int *c);
*/

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

/* produces value such that U1*a + U2*b = U3 */
/*
int mp_exteuclid(const mp_int *a, const mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3);
*/

/* c = [a, b] or (a*b)/(a, b) */
/*
int mp_lcm(const mp_int *a, const mp_int *b, mp_int *c);
*/

/* 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(const mp_int *a, mp_digit b, mp_int *c);
*/
/*
int mp_n_root_ex(const mp_int *a, mp_digit b, mp_int *c, int fast);
*/

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

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

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

/* computes the jacobi c = (a | n) (or Legendre if b is prime)  */
/*
int mp_jacobi(const mp_int *a, const mp_int *n, int *c);
*/

/* used to setup the Barrett reduction for a given modulus b */
/*
int mp_reduce_setup(mp_int *a, const mp_int *b);
*/

/* Barrett Reduction, computes a (mod b) with a precomputed value c
 *
 * Assumes that 0 < a <= b*b, note if 0 > a > -(b*b) then you can merely
 * compute the reduction as -1 * mp_reduce(mp_abs(a)) [pseudo code].
 */
/*
int mp_reduce(mp_int *a, const mp_int *b, const mp_int *c);
*/

/* setups the montgomery reduction */
/*
int mp_montgomery_setup(const mp_int *a, mp_digit *mp);
*/

/* computes a = B**n mod b without division or multiplication useful for
 * normalizing numbers in a Montgomery system.
 */
/*
int mp_montgomery_calc_normalization(mp_int *a, const mp_int *b);
*/

/* computes x/R == x (mod N) via Montgomery Reduction */
/*
int mp_montgomery_reduce(mp_int *a, const mp_int *m, mp_digit mp);
*/

/* returns 1 if a is a valid DR modulus */
/*
int mp_dr_is_modulus(const mp_int *a);
*/

/* sets the value of "d" required for mp_dr_reduce */
/*
void mp_dr_setup(const mp_int *a, mp_digit *d);
*/

/* reduces a modulo b using the Diminished Radix method */
/*
int mp_dr_reduce(mp_int *a, const mp_int *b, mp_digit mp);
*/

/* returns true if a can be reduced with mp_reduce_2k */
/*
int mp_reduce_is_2k(const mp_int *a);
*/

/* determines k value for 2k reduction */
/*
int mp_reduce_2k_setup(const mp_int *a, mp_digit *d);
*/

/* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
/*
int mp_reduce_2k(mp_int *a, const mp_int *n, mp_digit d);
*/

/* returns true if a can be reduced with mp_reduce_2k_l */
/*
int mp_reduce_is_2k_l(const mp_int *a);
*/

/* determines k value for 2k reduction */
/*
int mp_reduce_2k_setup_l(const mp_int *a, mp_int *d);
*/

/* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
/*
int mp_reduce_2k_l(mp_int *a, const mp_int *n, const mp_int *d);
*/

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

/* ---> Primes <--- */

/* number of primes */
#ifdef MP_8BIT
#  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(const mp_int *a, int *result);
*/

/* performs one Fermat test of "a" using base "b".
 * Sets result to 0 if composite or 1 if probable prime
 */
/*
int mp_prime_fermat(const mp_int *a, const mp_int *b, int *result);
*/

/* performs one Miller-Rabin test of "a" using base "b".
 * Sets result to 0 if composite or 1 if probable prime
 */
/*
int mp_prime_miller_rabin(const mp_int *a, const mp_int *b, int *result);
*/

/* This gives [for a given bit size] the number of trials required
 * such that Miller-Rabin gives a prob of failure lower than 2^-96
 */
/*
int mp_prime_rabin_miller_trials(int size);
................................................................................
 * t prime bases.  Also performs an initial sieve of trial
 * division.  Determines if "a" is prime with probability
 * of error no more than (1/4)**t.
 *
 * Sets result to 1 if probably prime, 0 otherwise
 */
/*
int mp_prime_is_prime(const mp_int *a, int t, int *result);
*/

/* finds the next prime after the number "a" using "t" trials
 * of Miller-Rabin.
 *
 * bbs_style = 1 means the prime must be congruent to 3 mod 4
 */
................................................................................

/* ---> radix conversion <--- */
/*
int mp_count_bits(const mp_int *a);
*/

/*
int mp_unsigned_bin_size(const mp_int *a);
*/
/*
int mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c);
*/
/*
int mp_to_unsigned_bin(const mp_int *a, unsigned char *b);
*/
/*
int mp_to_unsigned_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen);
*/

/*
int mp_signed_bin_size(const mp_int *a);
*/
/*
int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c);
*/
/*
int mp_to_signed_bin(const mp_int *a,  unsigned char *b);
*/
/*
int mp_to_signed_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen);
*/

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

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


/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

#define mp_div_2d TclBN_mp_div_2d
#define mp_div_3 TclBN_mp_div_3
#define mp_div_d TclBN_mp_div_d
#define mp_exch TclBN_mp_exch
#define mp_expt_d TclBN_mp_expt_d
#define mp_expt_d_ex TclBN_mp_expt_d_ex
#define mp_get_int TclBN_mp_get_int

#define mp_get_long_long TclBN_mp_get_long_long
#define mp_grow TclBN_mp_grow
#define mp_init TclBN_mp_init
#define mp_init_copy TclBN_mp_init_copy
#define mp_init_multi TclBN_mp_init_multi
#define mp_init_set TclBN_mp_init_set
#define mp_init_set_int TclBN_mp_init_set_int
................................................................................
#define mp_or TclBN_mp_or
#define mp_radix_size TclBN_mp_radix_size
#define mp_read_radix TclBN_mp_read_radix
#define mp_rshd TclBN_mp_rshd
#define mp_s_rmap TclBNMpSRmap
#define mp_set TclBN_mp_set
#define mp_set_int TclBN_mp_set_int

#define mp_set_long_long TclBN_mp_set_long_long
#define mp_shrink TclBN_mp_shrink
#define mp_sqr TclBN_mp_sqr
#define mp_sqrt TclBN_mp_sqrt
#define mp_sub TclBN_mp_sub
#define mp_sub_d TclBN_mp_sub_d
#define mp_to_unsigned_bin TclBN_mp_to_unsigned_bin
................................................................................
 */

/* 0 */
EXTERN int		TclBN_epoch(void);
/* 1 */
EXTERN int		TclBN_revision(void);
/* 2 */
EXTERN int		TclBN_mp_add(mp_int *a, mp_int *b, mp_int *c);

/* 3 */
EXTERN int		TclBN_mp_add_d(mp_int *a, mp_digit b, mp_int *c);

/* 4 */
EXTERN int		TclBN_mp_and(mp_int *a, mp_int *b, mp_int *c);

/* 5 */
EXTERN void		TclBN_mp_clamp(mp_int *a);
/* 6 */
EXTERN void		TclBN_mp_clear(mp_int *a);
/* 7 */
EXTERN void		TclBN_mp_clear_multi(mp_int *a, ...);
/* 8 */
................................................................................
/* 10 */
EXTERN int		TclBN_mp_cmp_mag(const mp_int *a, const mp_int *b);
/* 11 */
EXTERN int		TclBN_mp_copy(const mp_int *a, mp_int *b);
/* 12 */
EXTERN int		TclBN_mp_count_bits(const mp_int *a);
/* 13 */
EXTERN int		TclBN_mp_div(mp_int *a, mp_int *b, mp_int *q,
				mp_int *r);
/* 14 */
EXTERN int		TclBN_mp_div_d(mp_int *a, mp_digit b, mp_int *q,
				mp_digit *r);
/* 15 */
EXTERN int		TclBN_mp_div_2(const mp_int *a, mp_int *q);
/* 16 */
EXTERN int		TclBN_mp_div_2d(const mp_int *a, int b, mp_int *q,
				mp_int *r);
/* 17 */
EXTERN int		TclBN_mp_div_3(mp_int *a, mp_int *q, mp_digit *r);

/* 18 */
EXTERN void		TclBN_mp_exch(mp_int *a, mp_int *b);
/* 19 */
EXTERN int		TclBN_mp_expt_d(mp_int *a, mp_digit b, mp_int *c);

/* 20 */
EXTERN int		TclBN_mp_grow(mp_int *a, int size);
/* 21 */
EXTERN int		TclBN_mp_init(mp_int *a);
/* 22 */
EXTERN int		TclBN_mp_init_copy(mp_int *a, const mp_int *b);
/* 23 */
................................................................................
/* 24 */
EXTERN int		TclBN_mp_init_set(mp_int *a, mp_digit b);
/* 25 */
EXTERN int		TclBN_mp_init_size(mp_int *a, int size);
/* 26 */
EXTERN int		TclBN_mp_lshd(mp_int *a, int shift);
/* 27 */
EXTERN int		TclBN_mp_mod(mp_int *a, mp_int *b, mp_int *r);

/* 28 */
EXTERN int		TclBN_mp_mod_2d(const mp_int *a, int b, mp_int *r);
/* 29 */
EXTERN int		TclBN_mp_mul(mp_int *a, mp_int *b, mp_int *p);

/* 30 */
EXTERN int		TclBN_mp_mul_d(mp_int *a, mp_digit b, mp_int *p);

/* 31 */
EXTERN int		TclBN_mp_mul_2(const mp_int *a, mp_int *p);
/* 32 */
EXTERN int		TclBN_mp_mul_2d(const mp_int *a, int d, mp_int *p);
/* 33 */
EXTERN int		TclBN_mp_neg(const mp_int *a, mp_int *b);
/* 34 */
EXTERN int		TclBN_mp_or(mp_int *a, mp_int *b, mp_int *c);

/* 35 */
EXTERN int		TclBN_mp_radix_size(const mp_int *a, int radix,
				int *size);
/* 36 */
EXTERN int		TclBN_mp_read_radix(mp_int *a, const char *str,
				int radix);
/* 37 */
EXTERN void		TclBN_mp_rshd(mp_int *a, int shift);
/* 38 */
EXTERN int		TclBN_mp_shrink(mp_int *a);
/* 39 */
EXTERN void		TclBN_mp_set(mp_int *a, mp_digit b);
/* 40 */
EXTERN int		TclBN_mp_sqr(mp_int *a, mp_int *b);
/* 41 */
EXTERN int		TclBN_mp_sqrt(mp_int *a, mp_int *b);
/* 42 */
EXTERN int		TclBN_mp_sub(mp_int *a, mp_int *b, mp_int *c);

/* 43 */
EXTERN int		TclBN_mp_sub_d(mp_int *a, mp_digit b, mp_int *c);

/* 44 */
EXTERN int		TclBN_mp_to_unsigned_bin(mp_int *a, unsigned char *b);

/* 45 */
EXTERN int		TclBN_mp_to_unsigned_bin_n(mp_int *a,
				unsigned char *b, unsigned long *outlen);
/* 46 */
EXTERN int		TclBN_mp_toradix_n(mp_int *a, char *str, int radix,
				int maxlen);
/* 47 */
EXTERN int		TclBN_mp_unsigned_bin_size(mp_int *a);
/* 48 */
EXTERN int		TclBN_mp_xor(mp_int *a, mp_int *b, mp_int *c);

/* 49 */
EXTERN void		TclBN_mp_zero(mp_int *a);
/* 50 */
EXTERN void		TclBN_reverse(unsigned char *s, int len);
/* 51 */
EXTERN int		TclBN_fast_s_mp_mul_digs(mp_int *a, mp_int *b,
				mp_int *c, int digs);
/* 52 */
EXTERN int		TclBN_fast_s_mp_sqr(mp_int *a, mp_int *b);
/* 53 */
EXTERN int		TclBN_mp_karatsuba_mul(mp_int *a, mp_int *b,
				mp_int *c);
/* 54 */
EXTERN int		TclBN_mp_karatsuba_sqr(mp_int *a, mp_int *b);
/* 55 */
EXTERN int		TclBN_mp_toom_mul(mp_int *a, mp_int *b, mp_int *c);

/* 56 */
EXTERN int		TclBN_mp_toom_sqr(mp_int *a, mp_int *b);
/* 57 */
EXTERN int		TclBN_s_mp_add(mp_int *a, mp_int *b, mp_int *c);

/* 58 */
EXTERN int		TclBN_s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c,
				int digs);
/* 59 */
EXTERN int		TclBN_s_mp_sqr(mp_int *a, mp_int *b);
/* 60 */
EXTERN int		TclBN_s_mp_sub(mp_int *a, mp_int *b, mp_int *c);

/* 61 */
EXTERN int		TclBN_mp_init_set_int(mp_int *a, unsigned long i);
/* 62 */
EXTERN int		TclBN_mp_set_int(mp_int *a, unsigned long i);
/* 63 */
EXTERN int		TclBN_mp_cnt_lsb(const mp_int *a);
/* 64 */

EXTERN void		TclBNInitBignumFromLong(mp_int *bignum, long initVal);
/* 65 */

EXTERN void		TclBNInitBignumFromWideInt(mp_int *bignum,
				Tcl_WideInt initVal);
/* 66 */

EXTERN void		TclBNInitBignumFromWideUInt(mp_int *bignum,
				Tcl_WideUInt initVal);
/* 67 */
EXTERN int		TclBN_mp_expt_d_ex(mp_int *a, mp_digit b, mp_int *c,
				int fast);
/* 68 */
EXTERN int		TclBN_mp_set_long_long(mp_int *a, Tcl_WideUInt i);
/* 69 */
EXTERN Tcl_WideUInt	TclBN_mp_get_long_long(const mp_int *a);





typedef struct TclTomMathStubs {
    int magic;
    void *hooks;

    int (*tclBN_epoch) (void); /* 0 */
    int (*tclBN_revision) (void); /* 1 */
    int (*tclBN_mp_add) (mp_int *a, mp_int *b, mp_int *c); /* 2 */
    int (*tclBN_mp_add_d) (mp_int *a, mp_digit b, mp_int *c); /* 3 */
    int (*tclBN_mp_and) (mp_int *a, mp_int *b, mp_int *c); /* 4 */
    void (*tclBN_mp_clamp) (mp_int *a); /* 5 */
    void (*tclBN_mp_clear) (mp_int *a); /* 6 */
    void (*tclBN_mp_clear_multi) (mp_int *a, ...); /* 7 */
    int (*tclBN_mp_cmp) (const mp_int *a, const mp_int *b); /* 8 */
    int (*tclBN_mp_cmp_d) (const mp_int *a, mp_digit b); /* 9 */
    int (*tclBN_mp_cmp_mag) (const mp_int *a, const mp_int *b); /* 10 */
    int (*tclBN_mp_copy) (const mp_int *a, mp_int *b); /* 11 */
    int (*tclBN_mp_count_bits) (const mp_int *a); /* 12 */
    int (*tclBN_mp_div) (mp_int *a, mp_int *b, mp_int *q, mp_int *r); /* 13 */
    int (*tclBN_mp_div_d) (mp_int *a, mp_digit b, mp_int *q, mp_digit *r); /* 14 */
    int (*tclBN_mp_div_2) (const mp_int *a, mp_int *q); /* 15 */
    int (*tclBN_mp_div_2d) (const mp_int *a, int b, mp_int *q, mp_int *r); /* 16 */
    int (*tclBN_mp_div_3) (mp_int *a, mp_int *q, mp_digit *r); /* 17 */
    void (*tclBN_mp_exch) (mp_int *a, mp_int *b); /* 18 */
    int (*tclBN_mp_expt_d) (mp_int *a, mp_digit b, mp_int *c); /* 19 */
    int (*tclBN_mp_grow) (mp_int *a, int size); /* 20 */
    int (*tclBN_mp_init) (mp_int *a); /* 21 */
    int (*tclBN_mp_init_copy) (mp_int *a, const mp_int *b); /* 22 */
    int (*tclBN_mp_init_multi) (mp_int *a, ...); /* 23 */
    int (*tclBN_mp_init_set) (mp_int *a, mp_digit b); /* 24 */
    int (*tclBN_mp_init_size) (mp_int *a, int size); /* 25 */
    int (*tclBN_mp_lshd) (mp_int *a, int shift); /* 26 */
    int (*tclBN_mp_mod) (mp_int *a, mp_int *b, mp_int *r); /* 27 */
    int (*tclBN_mp_mod_2d) (const mp_int *a, int b, mp_int *r); /* 28 */
    int (*tclBN_mp_mul) (mp_int *a, mp_int *b, mp_int *p); /* 29 */
    int (*tclBN_mp_mul_d) (mp_int *a, mp_digit b, mp_int *p); /* 30 */
    int (*tclBN_mp_mul_2) (const mp_int *a, mp_int *p); /* 31 */
    int (*tclBN_mp_mul_2d) (const mp_int *a, int d, mp_int *p); /* 32 */
    int (*tclBN_mp_neg) (const mp_int *a, mp_int *b); /* 33 */
    int (*tclBN_mp_or) (mp_int *a, mp_int *b, mp_int *c); /* 34 */
    int (*tclBN_mp_radix_size) (const mp_int *a, int radix, int *size); /* 35 */
    int (*tclBN_mp_read_radix) (mp_int *a, const char *str, int radix); /* 36 */
    void (*tclBN_mp_rshd) (mp_int *a, int shift); /* 37 */
    int (*tclBN_mp_shrink) (mp_int *a); /* 38 */
    void (*tclBN_mp_set) (mp_int *a, mp_digit b); /* 39 */
    int (*tclBN_mp_sqr) (mp_int *a, mp_int *b); /* 40 */
    int (*tclBN_mp_sqrt) (mp_int *a, mp_int *b); /* 41 */
    int (*tclBN_mp_sub) (mp_int *a, mp_int *b, mp_int *c); /* 42 */
    int (*tclBN_mp_sub_d) (mp_int *a, mp_digit b, mp_int *c); /* 43 */
    int (*tclBN_mp_to_unsigned_bin) (mp_int *a, unsigned char *b); /* 44 */
    int (*tclBN_mp_to_unsigned_bin_n) (mp_int *a, unsigned char *b, unsigned long *outlen); /* 45 */
    int (*tclBN_mp_toradix_n) (mp_int *a, char *str, int radix, int maxlen); /* 46 */
    int (*tclBN_mp_unsigned_bin_size) (mp_int *a); /* 47 */
    int (*tclBN_mp_xor) (mp_int *a, mp_int *b, mp_int *c); /* 48 */
    void (*tclBN_mp_zero) (mp_int *a); /* 49 */
    void (*tclBN_reverse) (unsigned char *s, int len); /* 50 */
    int (*tclBN_fast_s_mp_mul_digs) (mp_int *a, mp_int *b, mp_int *c, int digs); /* 51 */
    int (*tclBN_fast_s_mp_sqr) (mp_int *a, mp_int *b); /* 52 */
    int (*tclBN_mp_karatsuba_mul) (mp_int *a, mp_int *b, mp_int *c); /* 53 */
    int (*tclBN_mp_karatsuba_sqr) (mp_int *a, mp_int *b); /* 54 */
    int (*tclBN_mp_toom_mul) (mp_int *a, mp_int *b, mp_int *c); /* 55 */
    int (*tclBN_mp_toom_sqr) (mp_int *a, mp_int *b); /* 56 */
    int (*tclBN_s_mp_add) (mp_int *a, mp_int *b, mp_int *c); /* 57 */
    int (*tclBN_s_mp_mul_digs) (mp_int *a, mp_int *b, mp_int *c, int digs); /* 58 */
    int (*tclBN_s_mp_sqr) (mp_int *a, mp_int *b); /* 59 */
    int (*tclBN_s_mp_sub) (mp_int *a, mp_int *b, mp_int *c); /* 60 */
    int (*tclBN_mp_init_set_int) (mp_int *a, unsigned long i); /* 61 */
    int (*tclBN_mp_set_int) (mp_int *a, unsigned long i); /* 62 */
    int (*tclBN_mp_cnt_lsb) (const mp_int *a); /* 63 */
    void (*tclBNInitBignumFromLong) (mp_int *bignum, long initVal); /* 64 */
    void (*tclBNInitBignumFromWideInt) (mp_int *bignum, Tcl_WideInt initVal); /* 65 */
    void (*tclBNInitBignumFromWideUInt) (mp_int *bignum, Tcl_WideUInt initVal); /* 66 */
    int (*tclBN_mp_expt_d_ex) (mp_int *a, mp_digit b, mp_int *c, int fast); /* 67 */
    int (*tclBN_mp_set_long_long) (mp_int *a, Tcl_WideUInt i); /* 68 */
    Tcl_WideUInt (*tclBN_mp_get_long_long) (const mp_int *a); /* 69 */


} TclTomMathStubs;

extern const TclTomMathStubs *tclTomMathStubsPtr;

#ifdef __cplusplus
}
#endif
................................................................................
	(tclTomMathStubsPtr->tclBNInitBignumFromWideUInt) /* 66 */
#define TclBN_mp_expt_d_ex \
	(tclTomMathStubsPtr->tclBN_mp_expt_d_ex) /* 67 */
#define TclBN_mp_set_long_long \
	(tclTomMathStubsPtr->tclBN_mp_set_long_long) /* 68 */
#define TclBN_mp_get_long_long \
	(tclTomMathStubsPtr->tclBN_mp_get_long_long) /* 69 */





#endif /* defined(USE_TCL_STUBS) */

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

#undef TCL_STORAGE_CLASS
#define TCL_STORAGE_CLASS DLLIMPORT

#endif /* _TCLINTDECLS */

#define mp_div_2d TclBN_mp_div_2d
#define mp_div_3 TclBN_mp_div_3
#define mp_div_d TclBN_mp_div_d
#define mp_exch TclBN_mp_exch
#define mp_expt_d TclBN_mp_expt_d
#define mp_expt_d_ex TclBN_mp_expt_d_ex
#define mp_get_int TclBN_mp_get_int
#define mp_get_long TclBN_mp_get_long
#define mp_get_long_long TclBN_mp_get_long_long
#define mp_grow TclBN_mp_grow
#define mp_init TclBN_mp_init
#define mp_init_copy TclBN_mp_init_copy
#define mp_init_multi TclBN_mp_init_multi
#define mp_init_set TclBN_mp_init_set
#define mp_init_set_int TclBN_mp_init_set_int
................................................................................
#define mp_or TclBN_mp_or
#define mp_radix_size TclBN_mp_radix_size
#define mp_read_radix TclBN_mp_read_radix
#define mp_rshd TclBN_mp_rshd
#define mp_s_rmap TclBNMpSRmap
#define mp_set TclBN_mp_set
#define mp_set_int TclBN_mp_set_int
#define mp_set_long TclBN_mp_set_long
#define mp_set_long_long TclBN_mp_set_long_long
#define mp_shrink TclBN_mp_shrink
#define mp_sqr TclBN_mp_sqr
#define mp_sqrt TclBN_mp_sqrt
#define mp_sub TclBN_mp_sub
#define mp_sub_d TclBN_mp_sub_d
#define mp_to_unsigned_bin TclBN_mp_to_unsigned_bin
................................................................................
 */

/* 0 */
EXTERN int		TclBN_epoch(void);
/* 1 */
EXTERN int		TclBN_revision(void);
/* 2 */
EXTERN int		TclBN_mp_add(const mp_int *a, const mp_int *b,
				mp_int *c);
/* 3 */
EXTERN int		TclBN_mp_add_d(const mp_int *a, mp_digit b,
				mp_int *c);
/* 4 */
EXTERN int		TclBN_mp_and(const mp_int *a, const mp_int *b,
				mp_int *c);
/* 5 */
EXTERN void		TclBN_mp_clamp(mp_int *a);
/* 6 */
EXTERN void		TclBN_mp_clear(mp_int *a);
/* 7 */
EXTERN void		TclBN_mp_clear_multi(mp_int *a, ...);
/* 8 */
................................................................................
/* 10 */
EXTERN int		TclBN_mp_cmp_mag(const mp_int *a, const mp_int *b);
/* 11 */
EXTERN int		TclBN_mp_copy(const mp_int *a, mp_int *b);
/* 12 */
EXTERN int		TclBN_mp_count_bits(const mp_int *a);
/* 13 */
EXTERN int		TclBN_mp_div(const mp_int *a, const mp_int *b,
				mp_int *q, mp_int *r);
/* 14 */
EXTERN int		TclBN_mp_div_d(const mp_int *a, mp_digit b,
				mp_int *q, mp_digit *r);
/* 15 */
EXTERN int		TclBN_mp_div_2(const mp_int *a, mp_int *q);
/* 16 */
EXTERN int		TclBN_mp_div_2d(const mp_int *a, int b, mp_int *q,
				mp_int *r);
/* 17 */
EXTERN int		TclBN_mp_div_3(const mp_int *a, mp_int *q,
				mp_digit *r);
/* 18 */
EXTERN void		TclBN_mp_exch(mp_int *a, mp_int *b);
/* 19 */
EXTERN int		TclBN_mp_expt_d(const mp_int *a, mp_digit b,
				mp_int *c);
/* 20 */
EXTERN int		TclBN_mp_grow(mp_int *a, int size);
/* 21 */
EXTERN int		TclBN_mp_init(mp_int *a);
/* 22 */
EXTERN int		TclBN_mp_init_copy(mp_int *a, const mp_int *b);
/* 23 */
................................................................................
/* 24 */
EXTERN int		TclBN_mp_init_set(mp_int *a, mp_digit b);
/* 25 */
EXTERN int		TclBN_mp_init_size(mp_int *a, int size);
/* 26 */
EXTERN int		TclBN_mp_lshd(mp_int *a, int shift);
/* 27 */
EXTERN int		TclBN_mp_mod(const mp_int *a, const mp_int *b,
				mp_int *r);
/* 28 */
EXTERN int		TclBN_mp_mod_2d(const mp_int *a, int b, mp_int *r);
/* 29 */
EXTERN int		TclBN_mp_mul(const mp_int *a, const mp_int *b,
				mp_int *p);
/* 30 */
EXTERN int		TclBN_mp_mul_d(const mp_int *a, mp_digit b,
				mp_int *p);
/* 31 */
EXTERN int		TclBN_mp_mul_2(const mp_int *a, mp_int *p);
/* 32 */
EXTERN int		TclBN_mp_mul_2d(const mp_int *a, int d, mp_int *p);
/* 33 */
EXTERN int		TclBN_mp_neg(const mp_int *a, mp_int *b);
/* 34 */
EXTERN int		TclBN_mp_or(const mp_int *a, const mp_int *b,
				mp_int *c);
/* 35 */
EXTERN int		TclBN_mp_radix_size(const mp_int *a, int radix,
				int *size);
/* 36 */
EXTERN int		TclBN_mp_read_radix(mp_int *a, const char *str,
				int radix);
/* 37 */
EXTERN void		TclBN_mp_rshd(mp_int *a, int shift);
/* 38 */
EXTERN int		TclBN_mp_shrink(mp_int *a);
/* 39 */
EXTERN void		TclBN_mp_set(mp_int *a, mp_digit b);
/* 40 */
EXTERN int		TclBN_mp_sqr(const mp_int *a, mp_int *b);
/* 41 */
EXTERN int		TclBN_mp_sqrt(const mp_int *a, mp_int *b);
/* 42 */
EXTERN int		TclBN_mp_sub(const mp_int *a, const mp_int *b,
				mp_int *c);
/* 43 */
EXTERN int		TclBN_mp_sub_d(const mp_int *a, mp_digit b,
				mp_int *c);
/* 44 */
EXTERN int		TclBN_mp_to_unsigned_bin(const mp_int *a,
				unsigned char *b);
/* 45 */
EXTERN int		TclBN_mp_to_unsigned_bin_n(const mp_int *a,
				unsigned char *b, unsigned long *outlen);
/* 46 */
EXTERN int		TclBN_mp_toradix_n(const mp_int *a, char *str,
				int radix, int maxlen);
/* 47 */
EXTERN int		TclBN_mp_unsigned_bin_size(const mp_int *a);
/* 48 */
EXTERN int		TclBN_mp_xor(const mp_int *a, const mp_int *b,
				mp_int *c);
/* 49 */
EXTERN void		TclBN_mp_zero(mp_int *a);
/* 50 */
EXTERN void		TclBN_reverse(unsigned char *s, int len);
/* 51 */
EXTERN int		TclBN_fast_s_mp_mul_digs(const mp_int *a,
				const mp_int *b, mp_int *c, int digs);
/* 52 */
EXTERN int		TclBN_fast_s_mp_sqr(const mp_int *a, mp_int *b);
/* 53 */
EXTERN int		TclBN_mp_karatsuba_mul(const mp_int *a,
				const mp_int *b, mp_int *c);
/* 54 */
EXTERN int		TclBN_mp_karatsuba_sqr(const mp_int *a, mp_int *b);
/* 55 */
EXTERN int		TclBN_mp_toom_mul(const mp_int *a, const mp_int *b,
				mp_int *c);
/* 56 */
EXTERN int		TclBN_mp_toom_sqr(const mp_int *a, mp_int *b);
/* 57 */
EXTERN int		TclBN_s_mp_add(const mp_int *a, const mp_int *b,
				mp_int *c);
/* 58 */
EXTERN int		TclBN_s_mp_mul_digs(const mp_int *a, const mp_int *b,
				mp_int *c, int digs);
/* 59 */
EXTERN int		TclBN_s_mp_sqr(const mp_int *a, mp_int *b);
/* 60 */
EXTERN int		TclBN_s_mp_sub(const mp_int *a, const mp_int *b,
				mp_int *c);
/* 61 */
EXTERN int		TclBN_mp_init_set_int(mp_int *a, unsigned long i);
/* 62 */
EXTERN int		TclBN_mp_set_int(mp_int *a, unsigned long i);
/* 63 */
EXTERN int		TclBN_mp_cnt_lsb(const mp_int *a);
/* 64 */
TCL_DEPRECATED("Use mp_init() + mp_set_long_long()")
void			TclBNInitBignumFromLong(mp_int *bignum, long initVal);
/* 65 */
TCL_DEPRECATED("Use mp_init() + mp_set_long_long()")
void			TclBNInitBignumFromWideInt(mp_int *bignum,
				Tcl_WideInt initVal);
/* 66 */
TCL_DEPRECATED("Use mp_init() + mp_set_long_long()")
void			TclBNInitBignumFromWideUInt(mp_int *bignum,
				Tcl_WideUInt initVal);
/* 67 */
EXTERN int		TclBN_mp_expt_d_ex(const mp_int *a, mp_digit b,
				mp_int *c, int fast);
/* 68 */
EXTERN int		TclBN_mp_set_long_long(mp_int *a, Tcl_WideUInt i);
/* 69 */
EXTERN Tcl_WideUInt	TclBN_mp_get_long_long(const mp_int *a);
/* 70 */
EXTERN int		TclBN_mp_set_long(mp_int *a, unsigned long i);
/* 71 */
EXTERN unsigned long	TclBN_mp_get_long(const mp_int *a);

typedef struct TclTomMathStubs {
    int magic;
    void *hooks;

    int (*tclBN_epoch) (void); /* 0 */
    int (*tclBN_revision) (void); /* 1 */
    int (*tclBN_mp_add) (const mp_int *a, const mp_int *b, mp_int *c); /* 2 */
    int (*tclBN_mp_add_d) (const mp_int *a, mp_digit b, mp_int *c); /* 3 */
    int (*tclBN_mp_and) (const mp_int *a, const mp_int *b, mp_int *c); /* 4 */
    void (*tclBN_mp_clamp) (mp_int *a); /* 5 */
    void (*tclBN_mp_clear) (mp_int *a); /* 6 */
    void (*tclBN_mp_clear_multi) (mp_int *a, ...); /* 7 */
    int (*tclBN_mp_cmp) (const mp_int *a, const mp_int *b); /* 8 */
    int (*tclBN_mp_cmp_d) (const mp_int *a, mp_digit b); /* 9 */
    int (*tclBN_mp_cmp_mag) (const mp_int *a, const mp_int *b); /* 10 */
    int (*tclBN_mp_copy) (const mp_int *a, mp_int *b); /* 11 */
    int (*tclBN_mp_count_bits) (const mp_int *a); /* 12 */
    int (*tclBN_mp_div) (const mp_int *a, const mp_int *b, mp_int *q, mp_int *r); /* 13 */
    int (*tclBN_mp_div_d) (const mp_int *a, mp_digit b, mp_int *q, mp_digit *r); /* 14 */
    int (*tclBN_mp_div_2) (const mp_int *a, mp_int *q); /* 15 */
    int (*tclBN_mp_div_2d) (const mp_int *a, int b, mp_int *q, mp_int *r); /* 16 */
    int (*tclBN_mp_div_3) (const mp_int *a, mp_int *q, mp_digit *r); /* 17 */
    void (*tclBN_mp_exch) (mp_int *a, mp_int *b); /* 18 */
    int (*tclBN_mp_expt_d) (const mp_int *a, mp_digit b, mp_int *c); /* 19 */
    int (*tclBN_mp_grow) (mp_int *a, int size); /* 20 */
    int (*tclBN_mp_init) (mp_int *a); /* 21 */
    int (*tclBN_mp_init_copy) (mp_int *a, const mp_int *b); /* 22 */
    int (*tclBN_mp_init_multi) (mp_int *a, ...); /* 23 */
    int (*tclBN_mp_init_set) (mp_int *a, mp_digit b); /* 24 */
    int (*tclBN_mp_init_size) (mp_int *a, int size); /* 25 */
    int (*tclBN_mp_lshd) (mp_int *a, int shift); /* 26 */
    int (*tclBN_mp_mod) (const mp_int *a, const mp_int *b, mp_int *r); /* 27 */
    int (*tclBN_mp_mod_2d) (const mp_int *a, int b, mp_int *r); /* 28 */
    int (*tclBN_mp_mul) (const mp_int *a, const mp_int *b, mp_int *p); /* 29 */
    int (*tclBN_mp_mul_d) (const mp_int *a, mp_digit b, mp_int *p); /* 30 */
    int (*tclBN_mp_mul_2) (const mp_int *a, mp_int *p); /* 31 */
    int (*tclBN_mp_mul_2d) (const mp_int *a, int d, mp_int *p); /* 32 */
    int (*tclBN_mp_neg) (const mp_int *a, mp_int *b); /* 33 */
    int (*tclBN_mp_or) (const mp_int *a, const mp_int *b, mp_int *c); /* 34 */
    int (*tclBN_mp_radix_size) (const mp_int *a, int radix, int *size); /* 35 */
    int (*tclBN_mp_read_radix) (mp_int *a, const char *str, int radix); /* 36 */
    void (*tclBN_mp_rshd) (mp_int *a, int shift); /* 37 */
    int (*tclBN_mp_shrink) (mp_int *a); /* 38 */
    void (*tclBN_mp_set) (mp_int *a, mp_digit b); /* 39 */
    int (*tclBN_mp_sqr) (const mp_int *a, mp_int *b); /* 40 */
    int (*tclBN_mp_sqrt) (const mp_int *a, mp_int *b); /* 41 */
    int (*tclBN_mp_sub) (const mp_int *a, const mp_int *b, mp_int *c); /* 42 */
    int (*tclBN_mp_sub_d) (const mp_int *a, mp_digit b, mp_int *c); /* 43 */
    int (*tclBN_mp_to_unsigned_bin) (const mp_int *a, unsigned char *b); /* 44 */
    int (*tclBN_mp_to_unsigned_bin_n) (const mp_int *a, unsigned char *b, unsigned long *outlen); /* 45 */
    int (*tclBN_mp_toradix_n) (const mp_int *a, char *str, int radix, int maxlen); /* 46 */
    int (*tclBN_mp_unsigned_bin_size) (const mp_int *a); /* 47 */
    int (*tclBN_mp_xor) (const mp_int *a, const mp_int *b, mp_int *c); /* 48 */
    void (*tclBN_mp_zero) (mp_int *a); /* 49 */
    void (*tclBN_reverse) (unsigned char *s, int len); /* 50 */
    int (*tclBN_fast_s_mp_mul_digs) (const mp_int *a, const mp_int *b, mp_int *c, int digs); /* 51 */
    int (*tclBN_fast_s_mp_sqr) (const mp_int *a, mp_int *b); /* 52 */
    int (*tclBN_mp_karatsuba_mul) (const mp_int *a, const mp_int *b, mp_int *c); /* 53 */
    int (*tclBN_mp_karatsuba_sqr) (const mp_int *a, mp_int *b); /* 54 */
    int (*tclBN_mp_toom_mul) (const mp_int *a, const mp_int *b, mp_int *c); /* 55 */
    int (*tclBN_mp_toom_sqr) (const mp_int *a, mp_int *b); /* 56 */
    int (*tclBN_s_mp_add) (const mp_int *a, const mp_int *b, mp_int *c); /* 57 */
    int (*tclBN_s_mp_mul_digs) (const mp_int *a, const mp_int *b, mp_int *c, int digs); /* 58 */
    int (*tclBN_s_mp_sqr) (const mp_int *a, mp_int *b); /* 59 */
    int (*tclBN_s_mp_sub) (const mp_int *a, const mp_int *b, mp_int *c); /* 60 */
    int (*tclBN_mp_init_set_int) (mp_int *a, unsigned long i); /* 61 */
    int (*tclBN_mp_set_int) (mp_int *a, unsigned long i); /* 62 */
    int (*tclBN_mp_cnt_lsb) (const mp_int *a); /* 63 */
    TCL_DEPRECATED_API("Use mp_init() + mp_set_long_long()") void (*tclBNInitBignumFromLong) (mp_int *bignum, long initVal); /* 64 */
    TCL_DEPRECATED_API("Use mp_init() + mp_set_long_long()") void (*tclBNInitBignumFromWideInt) (mp_int *bignum, Tcl_WideInt initVal); /* 65 */
    TCL_DEPRECATED_API("Use mp_init() + mp_set_long_long()") void (*tclBNInitBignumFromWideUInt) (mp_int *bignum, Tcl_WideUInt initVal); /* 66 */
    int (*tclBN_mp_expt_d_ex) (const mp_int *a, mp_digit b, mp_int *c, int fast); /* 67 */
    int (*tclBN_mp_set_long_long) (mp_int *a, Tcl_WideUInt i); /* 68 */
    Tcl_WideUInt (*tclBN_mp_get_long_long) (const mp_int *a); /* 69 */
    int (*tclBN_mp_set_long) (mp_int *a, unsigned long i); /* 70 */
    unsigned long (*tclBN_mp_get_long) (const mp_int *a); /* 71 */
} TclTomMathStubs;

extern const TclTomMathStubs *tclTomMathStubsPtr;

#ifdef __cplusplus
}
#endif
................................................................................
	(tclTomMathStubsPtr->tclBNInitBignumFromWideUInt) /* 66 */
#define TclBN_mp_expt_d_ex \
	(tclTomMathStubsPtr->tclBN_mp_expt_d_ex) /* 67 */
#define TclBN_mp_set_long_long \
	(tclTomMathStubsPtr->tclBN_mp_set_long_long) /* 68 */
#define TclBN_mp_get_long_long \
	(tclTomMathStubsPtr->tclBN_mp_get_long_long) /* 69 */
#define TclBN_mp_set_long \
	(tclTomMathStubsPtr->tclBN_mp_set_long) /* 70 */
#define TclBN_mp_get_long \
	(tclTomMathStubsPtr->tclBN_mp_get_long) /* 71 */

#endif /* defined(USE_TCL_STUBS) */

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

#undef TCL_STORAGE_CLASS
#define TCL_STORAGE_CLASS DLLIMPORT

#endif /* _TCLINTDECLS */

 */

int
TclBN_revision(void)
{
    return TCLTOMMATH_REVISION;
}
#if 0
 
/*
 *----------------------------------------------------------------------
 *
 * TclBNAlloc --
 *
 *	Allocate memory for libtommath.
 *
 * Results:
 *	Returns a pointer to the allocated block.
 *
 * This procedure is a wrapper around Tcl_Alloc, needed because of a
 * mismatched type signature between Tcl_Alloc and malloc.
 *
 *----------------------------------------------------------------------
 */

extern void *
TclBNAlloc(
    size_t x)
{
    return (void *) ckalloc((unsigned int) x);
}
 
/*
 *----------------------------------------------------------------------
 *
 * TclBNRealloc --
 *
 *	Change the size of an allocated block of memory in libtommath
 *
 * Results:
 *	Returns a pointer to the allocated block.
 *
 * This procedure is a wrapper around Tcl_Realloc, needed because of a
 * mismatched type signature between Tcl_Realloc and realloc.
 *
 *----------------------------------------------------------------------
 */

void *
TclBNRealloc(
    void *p,
    size_t s)
{
    return (void *) ckrealloc((char *) p, (unsigned int) s);
}
 
/*
 *----------------------------------------------------------------------
 *
 * TclBNFree --
 *
 *	Free allocated memory in libtommath.
 *
 * Results:
 *	None.
 *
 * Side effects:
 *	Memory is freed.
 *
 * This function is simply a wrapper around Tcl_Free, needed in libtommath
 * because of a type mismatch between free and Tcl_Free.
 *
 *----------------------------------------------------------------------
 */

extern void
TclBNFree(
    void *p)
{
    ckree((char *) p);
}
#endif
 
/*
 *----------------------------------------------------------------------
 *
 * TclBNInitBignumFromLong --
 *
 *	Allocate and initialize a 'bignum' from a native 'long'.
 *
 * Results:
 *	None.
 *
 * Side effects:
 *	The 'bignum' is constructed.
 *
 *----------------------------------------------------------------------
 */

extern void
TclBNInitBignumFromLong(
    mp_int *a,
    long initVal)
{
    int status;
    unsigned long v;
    mp_digit *p;

    /*
     * Allocate enough memory to hold the largest possible long
     */

    status = mp_init_size(a,
	    (CHAR_BIT * sizeof(long) + DIGIT_BIT - 1) / DIGIT_BIT);
    if (status != MP_OKAY) {
	Tcl_Panic("initialization failure in TclBNInitBignumFromLong");
    }

    /*
     * Convert arg to sign and magnitude.
     */

    if (initVal < 0) {
	a->sign = MP_NEG;
	v = -initVal;



    } else {
	a->sign = MP_ZPOS;
	v = initVal;

    }

    /*
     * Store the magnitude in the bignum.
     */

    p = a->dp;
    while (v) {
	*p++ = (mp_digit) (v & MP_MASK);
	v >>= MP_DIGIT_BIT;
    }
    a->used = p - a->dp;
}
 
/*
 *----------------------------------------------------------------------
 *
 * TclBNInitBignumFromWideInt --
 *
................................................................................
 *
 * Side effects:
 *	The 'bignum' is constructed.
 *
 *----------------------------------------------------------------------
 */

extern void
TclBNInitBignumFromWideInt(
    mp_int *a,			/* Bignum to initialize */
    Tcl_WideInt v)		/* Initial value */
{



    if (v < (Tcl_WideInt)0) {
	TclBNInitBignumFromWideUInt(a, (Tcl_WideUInt)(-v));
	mp_neg(a, a);
    } else {
	TclBNInitBignumFromWideUInt(a, (Tcl_WideUInt)v);
    }
}
 
/*
 *----------------------------------------------------------------------
 *
 * TclBNInitBignumFromWideUInt --
................................................................................
 *
 * Side effects:
 *	The 'bignum' is constructed.
 *
 *----------------------------------------------------------------------
 */

extern void
TclBNInitBignumFromWideUInt(
    mp_int *a,			/* Bignum to initialize */
    Tcl_WideUInt v)		/* Initial value */
{
    int status;
    mp_digit *p;

    /*
     * Allocate enough memory to hold the largest possible Tcl_WideUInt.
     */

    status = mp_init_size(a,
	    (CHAR_BIT * sizeof(Tcl_WideUInt) + DIGIT_BIT - 1) / DIGIT_BIT);
    if (status != MP_OKAY) {
	Tcl_Panic("initialization failure in TclBNInitBignumFromWideUInt");
    }

    a->sign = MP_ZPOS;

    /*
     * Store the magnitude in the bignum.
     */

    p = a->dp;
    while (v) {
	*p++ = (mp_digit) (v & MP_MASK);
	v >>= MP_DIGIT_BIT;
    }
    a->used = p - a->dp;

}
 
/*
 * Local Variables:
 * mode: c
 * c-basic-offset: 4
 * fill-column: 78
 * End:
 */

 */

int
TclBN_revision(void)
{
    return TCLTOMMATH_REVISION;
}

 
/*
 *----------------------------------------------------------------------
 *










































































 * TclInitBignumFromLong --
 *
 *	Allocate and initialize a 'bignum' from a native 'long'.
 *
 * Results:
 *	None.
 *
 * Side effects:
 *	The 'bignum' is constructed.
 *
 *----------------------------------------------------------------------
 */

void
TclInitBignumFromLong(
    mp_int *a,



    long v)

{





    if (mp_init_size(a, (CHAR_BIT * sizeof(long) + DIGIT_BIT - 1) / DIGIT_BIT) != MP_OKAY) {

	Tcl_Panic("initialization failure in TclInitBignumFromLong");
    }








    if (v < (long)0) {
	mp_set_long_long(a, (Tcl_WideUInt)(-(Tcl_WideInt)v));
	mp_neg(a, a);
    } else {


	mp_set_long_long(a, (Tcl_WideUInt)v);
    }











}
 
/*
 *----------------------------------------------------------------------
 *
 * TclBNInitBignumFromWideInt --
 *
................................................................................
 *
 * Side effects:
 *	The 'bignum' is constructed.
 *
 *----------------------------------------------------------------------
 */

void
TclInitBignumFromWideInt(
    mp_int *a,			/* Bignum to initialize */
    Tcl_WideInt v)		/* Initial value */
{
	if (mp_init_size(a, (CHAR_BIT * sizeof(Tcl_WideUInt) + DIGIT_BIT - 1) / DIGIT_BIT) != MP_OKAY) {
		Tcl_Panic("initialization failure in TclInitBignumFromWideInt");
	}
    if (v < (Tcl_WideInt)0) {
	mp_set_long_long(a, (Tcl_WideUInt)(-v));
	mp_neg(a, a);
    } else {
	mp_set_long_long(a, (Tcl_WideUInt)v);
    }
}
 
/*
 *----------------------------------------------------------------------
 *
 * TclBNInitBignumFromWideUInt --
................................................................................
 *
 * Side effects:
 *	The 'bignum' is constructed.
 *
 *----------------------------------------------------------------------
 */

void
TclInitBignumFromWideUInt(
    mp_int *a,			/* Bignum to initialize */
    Tcl_WideUInt v)		/* Initial value */
{








	if (mp_init_size(a, (CHAR_BIT * sizeof(Tcl_WideUInt) + DIGIT_BIT - 1) / DIGIT_BIT) != MP_OKAY) {

	    Tcl_Panic("initialization failure in TclInitBignumFromWideUInt");
	}













	mp_set_long_long(a, v);
}
 
/*
 * Local Variables:
 * mode: c
 * c-basic-offset: 4
 * fill-column: 78
 * End:
 */

#
# Arguments:
# name -			Name of a command.

if {$tcl_platform(platform) eq "windows"} {
# Windows version.
#
# Note that info executable doesn't work under Windows, so we have to
# look for files with .exe, .com, or .bat extensions.  Also, the path
# may be in the Path or PATH environment variables, and path
# components are separated with semicolons, not colons as under Unix.
#
proc auto_execok name {
    global auto_execs env tcl_platform

#
# Arguments:
# name -			Name of a command.

if {$tcl_platform(platform) eq "windows"} {
# Windows version.
#
# Note that file executable doesn't work under Windows, so we have to
# look for files with .exe, .com, or .bat extensions.  Also, the path
# may be in the Path or PATH environment variables, and path
# components are separated with semicolons, not colons as under Unix.
#
proc auto_execok name {
    global auto_execs env tcl_platform

#       Primarily used internally by the safe:: code.
#
#	WARNING: This code will go away in a future release
#	of Tcl.  It is NOT supported and you should not rely
#	on it.  If your code does rely on this package you
#	may directly incorporate this code into your application.

package require Tcl 8.2
# When this version number changes, update the pkgIndex.tcl file
# and the install directory in the Makefiles.
package provide opt 0.4.6

namespace eval ::tcl {

    # Exported APIs
    namespace export OptKeyRegister OptKeyDelete OptKeyError OptKeyParse \
             OptProc OptProcArgGiven OptParse \
	     Lempty Lget \

#       Primarily used internally by the safe:: code.
#
#	WARNING: This code will go away in a future release
#	of Tcl.  It is NOT supported and you should not rely
#	on it.  If your code does rely on this package you
#	may directly incorporate this code into your application.

package require Tcl 8.5-
# When this version number changes, update the pkgIndex.tcl file
# and the install directory in the Makefiles.
package provide opt 0.4.7

namespace eval ::tcl {

    # Exported APIs
    namespace export OptKeyRegister OptKeyDelete OptKeyError OptKeyParse \
             OptProc OptProcArgGiven OptParse \
	     Lempty Lget \

# by a "package unknown" script.  It invokes the
# "package ifneeded" command to set up package-related
# information so that packages will be loaded automatically
# in response to "package require" commands.  When this
# script is sourced, the variable $dir must contain the
# full path name of this file's directory.

if {![package vsatisfies [package provide Tcl] 8.2]} {return}
package ifneeded opt 0.4.6 [list source [file join $dir optparse.tcl]]

# by a "package unknown" script.  It invokes the
# "package ifneeded" command to set up package-related
# information so that packages will be loaded automatically
# in response to "package require" commands.  When this
# script is sourced, the variable $dir must contain the
# full path name of this file's directory.

if {![package vsatisfies [package provide Tcl] 8.5-]} {return}
package ifneeded opt 0.4.7 [list source [file join $dir optparse.tcl]]

# by a "package unknown" script.  It invokes the
# "package ifneeded" command to set up package-related
# information so that packages will be loaded automatically
# in response to "package require" commands.  When this
# script is sourced, the variable $dir must contain the
# full path name of this file's directory.

if {![package vsatisfies [package provide Tcl] 8.5]} {return}
package ifneeded tcltest 2.4.0 [list source [file join $dir tcltest.tcl]]

# by a "package unknown" script.  It invokes the
# "package ifneeded" command to set up package-related
# information so that packages will be loaded automatically
# in response to "package require" commands.  When this
# script is sourced, the variable $dir must contain the
# full path name of this file's directory.

if {![package vsatisfies [package provide Tcl] 8.5-]} {return}
package ifneeded tcltest 2.4.1 [list source [file join $dir tcltest.tcl]]

package require Tcl 8.5-		;# -verbose line uses [info frame]
namespace eval tcltest {

    # When the version number changes, be sure to update the pkgIndex.tcl file,
    # and the install directory in the Makefiles.  When the minor version
    # changes (new feature) be sure to update the man page as well.
    variable Version 2.4.0

    # Compatibility support for dumb variables defined in tcltest 1
    # Do not use these.  Call [package provide Tcl] and [info patchlevel]
    # yourself.  You don't need tcltest to wrap it for you.
    variable version [package provide Tcl]
    variable patchLevel [info patchlevel]

package require Tcl 8.5-		;# -verbose line uses [info frame]
namespace eval tcltest {

    # When the version number changes, be sure to update the pkgIndex.tcl file,
    # and the install directory in the Makefiles.  When the minor version
    # changes (new feature) be sure to update the man page as well.
    variable Version 2.4.1

    # Compatibility support for dumb variables defined in tcltest 1
    # Do not use these.  Call [package provide Tcl] and [info patchlevel]
    # yourself.  You don't need tcltest to wrap it for you.
    variable version [package provide Tcl]
    variable patchLevel [info patchlevel]

# created by tools/tclZIC.tcl - do not edit
if {![info exists TZData(Africa/Khartoum)]} {
    LoadTimeZoneFile Africa/Khartoum
}
set TZData(:Africa/Juba) $TZData(:Africa/Khartoum)

# created by tools/tclZIC.tcl - do not edit



set TZData(:Africa/Juba) {
    {-9223372036854775808 7588 0 LMT}
    {-1230775588 7200 0 CAT}
    {10360800 10800 1 CAST}
    {24786000 7200 0 CAT}
    {41810400 10800 1 CAST}
    {56322000 7200 0 CAT}
    {73432800 10800 1 CAST}
    {87944400 7200 0 CAT}
    {104882400 10800 1 CAST}
    {119480400 7200 0 CAT}
    {136332000 10800 1 CAST}
    {151016400 7200 0 CAT}
    {167781600 10800 1 CAST}
    {182552400 7200 0 CAT}
    {199231200 10800 1 CAST}
    {214174800 7200 0 CAT}
    {230680800 10800 1 CAST}
    {245710800 7200 0 CAT}
    {262735200 10800 1 CAST}
    {277246800 7200 0 CAT}
    {294184800 10800 1 CAST}
    {308782800 7200 0 CAT}
    {325634400 10800 1 CAST}
    {340405200 7200 0 CAT}
    {357084000 10800 1 CAST}
    {371941200 7200 0 CAT}
    {388533600 10800 1 CAST}
    {403477200 7200 0 CAT}
    {419983200 10800 1 CAST}
    {435013200 7200 0 CAT}
    {452037600 10800 1 CAST}
    {466635600 7200 0 CAT}
    {483487200 10800 1 CAST}
    {498171600 7200 0 CAT}
    {947930400 10800 0 EAT}
}

    {419983200 10800 1 CAST}
    {435013200 7200 0 CAT}
    {452037600 10800 1 CAST}
    {466635600 7200 0 CAT}
    {483487200 10800 1 CAST}
    {498171600 7200 0 CAT}
    {947930400 10800 0 EAT}

}

    {419983200 10800 1 CAST}
    {435013200 7200 0 CAT}
    {452037600 10800 1 CAST}
    {466635600 7200 0 CAT}
    {483487200 10800 1 CAST}
    {498171600 7200 0 CAT}
    {947930400 10800 0 EAT}
    {1509483600 7200 0 CAT}
}

set TZData(:Africa/Windhoek) {
    {-9223372036854775808 4104 0 LMT}
    {-2458170504 5400 0 +0130}
    {-2109288600 7200 0 SAST}
    {-860976000 10800 1 SAST}
    {-845254800 7200 0 SAST}
    {637970400 7200 0 CAT}
    {765324000 3600 0 WAT}

    {778640400 7200 1 WAST}
    {796780800 3600 0 WAT}
    {810090000 7200 1 WAST}
    {828835200 3600 0 WAT}
    {841539600 7200 1 WAST}
    {860284800 3600 0 WAT}
    {873594000 7200 1 WAST}
................................................................................
    {1396742400 3600 0 WAT}
    {1410051600 7200 1 WAST}
    {1428192000 3600 0 WAT}
    {1441501200 7200 1 WAST}
    {1459641600 3600 0 WAT}
    {1472950800 7200 1 WAST}
    {1491091200 3600 0 WAT}
    {1504400400 7200 1 WAST}
    {1522540800 3600 0 WAT}
    {1535850000 7200 1 WAST}
    {1554595200 3600 0 WAT}
    {1567299600 7200 1 WAST}
    {1586044800 3600 0 WAT}
    {1599354000 7200 1 WAST}
    {1617494400 3600 0 WAT}
    {1630803600 7200 1 WAST}
    {1648944000 3600 0 WAT}
    {1662253200 7200 1 WAST}
    {1680393600 3600 0 WAT}
    {1693702800 7200 1 WAST}
    {1712448000 3600 0 WAT}
    {1725152400 7200 1 WAST}
    {1743897600 3600 0 WAT}
    {1757206800 7200 1 WAST}
    {1775347200 3600 0 WAT}
    {1788656400 7200 1 WAST}
    {1806796800 3600 0 WAT}
    {1820106000 7200 1 WAST}
    {1838246400 3600 0 WAT}
    {1851555600 7200 1 WAST}
    {1869696000 3600 0 WAT}
    {1883005200 7200 1 WAST}
    {1901750400 3600 0 WAT}
    {1914454800 7200 1 WAST}
    {1933200000 3600 0 WAT}
    {1946509200 7200 1 WAST}
    {1964649600 3600 0 WAT}
    {1977958800 7200 1 WAST}
    {1996099200 3600 0 WAT}
    {2009408400 7200 1 WAST}
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    {2072307600 7200 1 WAST}
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    {2167261200 7200 1 WAST}
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    {2248905600 3600 0 WAT}
    {2261610000 7200 1 WAST}
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    {2356563600 7200 1 WAST}
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    {2406153600 3600 0 WAT}
    {2419462800 7200 1 WAST}
    {2438208000 3600 0 WAT}
    {2450912400 7200 1 WAST}
    {2469657600 3600 0 WAT}
    {2482966800 7200 1 WAST}
    {2501107200 3600 0 WAT}
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    {2532556800 3600 0 WAT}
    {2545866000 7200 1 WAST}
    {2564006400 3600 0 WAT}
    {2577315600 7200 1 WAST}
    {2596060800 3600 0 WAT}
    {2608765200 7200 1 WAST}
    {2627510400 3600 0 WAT}
    {2640819600 7200 1 WAST}
    {2658960000 3600 0 WAT}
    {2672269200 7200 1 WAST}
    {2690409600 3600 0 WAT}
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    {2721859200 3600 0 WAT}
    {2735168400 7200 1 WAST}
    {2753308800 3600 0 WAT}
    {2766618000 7200 1 WAST}
    {2785363200 3600 0 WAT}
    {2798067600 7200 1 WAST}
    {2816812800 3600 0 WAT}
    {2830122000 7200 1 WAST}
    {2848262400 3600 0 WAT}
    {2861571600 7200 1 WAST}
    {2879712000 3600 0 WAT}
    {2893021200 7200 1 WAST}
    {2911161600 3600 0 WAT}
    {2924470800 7200 1 WAST}
    {2942611200 3600 0 WAT}
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    {2974665600 3600 0 WAT}
    {2987974800 7200 1 WAST}
    {3006115200 3600 0 WAT}
    {3019424400 7200 1 WAST}
    {3037564800 3600 0 WAT}
    {3050874000 7200 1 WAST}
    {3069014400 3600 0 WAT}
    {3082323600 7200 1 WAST}
    {3100464000 3600 0 WAT}
    {3113773200 7200 1 WAST}
    {3132518400 3600 0 WAT}
    {3145222800 7200 1 WAST}
    {3163968000 3600 0 WAT}
    {3177277200 7200 1 WAST}
    {3195417600 3600 0 WAT}
    {3208726800 7200 1 WAST}
    {3226867200 3600 0 WAT}
    {3240176400 7200 1 WAST}
    {3258316800 3600 0 WAT}
    {3271626000 7200 1 WAST}
    {3289766400 3600 0 WAT}
    {3303075600 7200 1 WAST}
    {3321820800 3600 0 WAT}
    {3334525200 7200 1 WAST}
    {3353270400 3600 0 WAT}
    {3366579600 7200 1 WAST}
    {3384720000 3600 0 WAT}
    {3398029200 7200 1 WAST}
    {3416169600 3600 0 WAT}
    {3429478800 7200 1 WAST}
    {3447619200 3600 0 WAT}
    {3460928400 7200 1 WAST}
    {3479673600 3600 0 WAT}
    {3492378000 7200 1 WAST}
    {3511123200 3600 0 WAT}
    {3524432400 7200 1 WAST}
    {3542572800 3600 0 WAT}
    {3555882000 7200 1 WAST}
    {3574022400 3600 0 WAT}
    {3587331600 7200 1 WAST}
    {3605472000 3600 0 WAT}
    {3618781200 7200 1 WAST}
    {3636921600 3600 0 WAT}
    {3650230800 7200 1 WAST}
    {3668976000 3600 0 WAT}
    {3681680400 7200 1 WAST}
    {3700425600 3600 0 WAT}
    {3713734800 7200 1 WAST}
    {3731875200 3600 0 WAT}
    {3745184400 7200 1 WAST}
    {3763324800 3600 0 WAT}
    {3776634000 7200 1 WAST}
    {3794774400 3600 0 WAT}
    {3808083600 7200 1 WAST}
    {3826224000 3600 0 WAT}
    {3839533200 7200 1 WAST}
    {3858278400 3600 0 WAT}
    {3871587600 7200 1 WAST}
    {3889728000 3600 0 WAT}
    {3903037200 7200 1 WAST}
    {3921177600 3600 0 WAT}
    {3934486800 7200 1 WAST}
    {3952627200 3600 0 WAT}
    {3965936400 7200 1 WAST}
    {3984076800 3600 0 WAT}
    {3997386000 7200 1 WAST}
    {4016131200 3600 0 WAT}
    {4028835600 7200 1 WAST}
    {4047580800 3600 0 WAT}
    {4060890000 7200 1 WAST}
    {4079030400 3600 0 WAT}
    {4092339600 7200 1 WAST}
}

set TZData(:Africa/Windhoek) {
    {-9223372036854775808 4104 0 LMT}
    {-2458170504 5400 0 +0130}
    {-2109288600 7200 0 SAST}
    {-860976000 10800 1 SAST}
    {-845254800 7200 0 SAST}
    {637970400 7200 0 CAT}
    {764200800 3600 0 WAT}
    {764204400 3600 0 WAT}
    {778640400 7200 1 WAST}
    {796780800 3600 0 WAT}
    {810090000 7200 1 WAST}
    {828835200 3600 0 WAT}
    {841539600 7200 1 WAST}
    {860284800 3600 0 WAT}
    {873594000 7200 1 WAST}
................................................................................
    {1396742400 3600 0 WAT}
    {1410051600 7200 1 WAST}
    {1428192000 3600 0 WAT}
    {1441501200 7200 1 WAST}
    {1459641600 3600 0 WAT}
    {1472950800 7200 1 WAST}
    {1491091200 3600 0 WAT}
    {1504400400 7200 0 CAT}




































































































































































}

# created by tools/tclZIC.tcl - do not edit

set TZData(:America/Adak) {
    {-9223372036854775808 44001 0 LMT}
    {-3225356001 -42398 0 LMT}
    {-2188944802 -39600 0 NST}
    {-883573200 -39600 0 NST}
    {-880196400 -36000 1 NWT}
    {-769395600 -36000 1 NPT}
    {-765374400 -39600 0 NST}
    {-757342800 -39600 0 NST}
    {-86878800 -39600 0 BST}

# created by tools/tclZIC.tcl - do not edit

set TZData(:America/Adak) {
    {-9223372036854775808 44002 0 LMT}
    {-3225223727 -42398 0 LMT}
    {-2188944802 -39600 0 NST}
    {-883573200 -39600 0 NST}
    {-880196400 -36000 1 NWT}
    {-769395600 -36000 1 NPT}
    {-765374400 -39600 0 NST}
    {-757342800 -39600 0 NST}
    {-86878800 -39600 0 BST}

# created by tools/tclZIC.tcl - do not edit

set TZData(:America/Anchorage) {
    {-9223372036854775808 50424 0 LMT}
    {-3225362424 -35976 0 LMT}
    {-2188951224 -36000 0 AST}
    {-883576800 -36000 0 AST}
    {-880200000 -32400 1 AWT}
    {-769395600 -32400 1 APT}
    {-765378000 -36000 0 AST}
    {-86882400 -36000 0 AHST}
    {-31500000 -36000 0 AHST}

# created by tools/tclZIC.tcl - do not edit

set TZData(:America/Anchorage) {
    {-9223372036854775808 50424 0 LMT}
    {-3225223727 -35976 0 LMT}
    {-2188951224 -36000 0 AST}
    {-883576800 -36000 0 AST}
    {-880200000 -32400 1 AWT}
    {-769395600 -32400 1 APT}
    {-765378000 -36000 0 AST}
    {-86882400 -36000 0 AHST}
    {-31500000 -36000 0 AHST}

    {-883594800 -18000 0 EST}
    {-880218000 -14400 1 EWT}
    {-769395600 -14400 1 EPT}
    {-765396000 -18000 0 EST}
    {-757364400 -18000 0 EST}
    {-684349200 -14400 1 EDT}
    {-671047200 -18000 0 EST}
    {-80499600 -14400 1 EDT}
    {-68666400 -18000 0 EST}
    {94712400 -18000 0 EST}
    {104914800 -14400 1 EDT}
    {120636000 -18000 0 EST}
    {126687600 -14400 1 EDT}
    {152085600 -18000 0 EST}
    {157784400 -18000 0 EST}
    {167814000 -14400 0 EDT}

    {-883594800 -18000 0 EST}
    {-880218000 -14400 1 EWT}
    {-769395600 -14400 1 EPT}
    {-765396000 -18000 0 EST}
    {-757364400 -18000 0 EST}
    {-684349200 -14400 1 EDT}
    {-671047200 -18000 0 EST}


    {94712400 -18000 0 EST}
    {104914800 -14400 1 EDT}
    {120636000 -18000 0 EST}
    {126687600 -14400 1 EDT}
    {152085600 -18000 0 EST}
    {157784400 -18000 0 EST}
    {167814000 -14400 0 EDT}

    {1352008800 -18000 0 EST}
    {1362898800 -14400 1 EDT}
    {1383458400 -18000 0 EST}
    {1394348400 -14400 1 EDT}
    {1414908000 -18000 0 EST}
    {1425798000 -14400 1 EDT}
    {1446361200 -14400 0 AST}




































































































































































}

    {1352008800 -18000 0 EST}
    {1362898800 -14400 1 EDT}
    {1383458400 -18000 0 EST}
    {1394348400 -14400 1 EDT}
    {1414908000 -18000 0 EST}
    {1425798000 -14400 1 EDT}
    {1446361200 -14400 0 AST}
    {1520751600 -14400 0 EDT}
    {1541311200 -18000 0 EST}
    {1552201200 -14400 1 EDT}
    {1572760800 -18000 0 EST}
    {1583650800 -14400 1 EDT}
    {1604210400 -18000 0 EST}
    {1615705200 -14400 1 EDT}
    {1636264800 -18000 0 EST}
    {1647154800 -14400 1 EDT}
    {1667714400 -18000 0 EST}
    {1678604400 -14400 1 EDT}
    {1699164000 -18000 0 EST}
    {1710054000 -14400 1 EDT}
    {1730613600 -18000 0 EST}
    {1741503600 -14400 1 EDT}
    {1762063200 -18000 0 EST}
    {1772953200 -14400 1 EDT}
    {1793512800 -18000 0 EST}
    {1805007600 -14400 1 EDT}
    {1825567200 -18000 0 EST}
    {1836457200 -14400 1 EDT}
    {1857016800 -18000 0 EST}
    {1867906800 -14400 1 EDT}
    {1888466400 -18000 0 EST}
    {1899356400 -14400 1 EDT}
    {1919916000 -18000 0 EST}
    {1930806000 -14400 1 EDT}
    {1951365600 -18000 0 EST}
    {1962860400 -14400 1 EDT}
    {1983420000 -18000 0 EST}
    {1994310000 -14400 1 EDT}
    {2014869600 -18000 0 EST}
    {2025759600 -14400 1 EDT}
    {2046319200 -18000 0 EST}
    {2057209200 -14400 1 EDT}
    {2077768800 -18000 0 EST}
    {2088658800 -14400 1 EDT}
    {2109218400 -18000 0 EST}
    {2120108400 -14400 1 EDT}
    {2140668000 -18000 0 EST}
    {2152162800 -14400 1 EDT}
    {2172722400 -18000 0 EST}
    {2183612400 -14400 1 EDT}
    {2204172000 -18000 0 EST}
    {2215062000 -14400 1 EDT}
    {2235621600 -18000 0 EST}
    {2246511600 -14400 1 EDT}
    {2267071200 -18000 0 EST}
    {2277961200 -14400 1 EDT}
    {2298520800 -18000 0 EST}
    {2309410800 -14400 1 EDT}
    {2329970400 -18000 0 EST}
    {2341465200 -14400 1 EDT}
    {2362024800 -18000 0 EST}
    {2372914800 -14400 1 EDT}
    {2393474400 -18000 0 EST}
    {2404364400 -14400 1 EDT}
    {2424924000 -18000 0 EST}
    {2435814000 -14400 1 EDT}
    {2456373600 -18000 0 EST}
    {2467263600 -14400 1 EDT}
    {2487823200 -18000 0 EST}
    {2499318000 -14400 1 EDT}
    {2519877600 -18000 0 EST}
    {2530767600 -14400 1 EDT}
    {2551327200 -18000 0 EST}
    {2562217200 -14400 1 EDT}
    {2582776800 -18000 0 EST}
    {2593666800 -14400 1 EDT}
    {2614226400 -18000 0 EST}
    {2625116400 -14400 1 EDT}
    {2645676000 -18000 0 EST}
    {2656566000 -14400 1 EDT}
    {2677125600 -18000 0 EST}
    {2688620400 -14400 1 EDT}
    {2709180000 -18000 0 EST}
    {2720070000 -14400 1 EDT}
    {2740629600 -18000 0 EST}
    {2751519600 -14400 1 EDT}
    {2772079200 -18000 0 EST}
    {2782969200 -14400 1 EDT}
    {2803528800 -18000 0 EST}
    {2814418800 -14400 1 EDT}
    {2834978400 -18000 0 EST}
    {2846473200 -14400 1 EDT}
    {2867032800 -18000 0 EST}
    {2877922800 -14400 1 EDT}
    {2898482400 -18000 0 EST}
    {2909372400 -14400 1 EDT}
    {2929932000 -18000 0 EST}
    {2940822000 -14400 1 EDT}
    {2961381600 -18000 0 EST}
    {2972271600 -14400 1 EDT}
    {2992831200 -18000 0 EST}
    {3003721200 -14400 1 EDT}
    {3024280800 -18000 0 EST}
    {3035775600 -14400 1 EDT}
    {3056335200 -18000 0 EST}
    {3067225200 -14400 1 EDT}
    {3087784800 -18000 0 EST}
    {3098674800 -14400 1 EDT}
    {3119234400 -18000 0 EST}
    {3130124400 -14400 1 EDT}
    {3150684000 -18000 0 EST}
    {3161574000 -14400 1 EDT}
    {3182133600 -18000 0 EST}
    {3193023600 -14400 1 EDT}
    {3213583200 -18000 0 EST}
    {3225078000 -14400 1 EDT}
    {3245637600 -18000 0 EST}
    {3256527600 -14400 1 EDT}
    {3277087200 -18000 0 EST}
    {3287977200 -14400 1 EDT}
    {3308536800 -18000 0 EST}
    {3319426800 -14400 1 EDT}
    {3339986400 -18000 0 EST}
    {3350876400 -14400 1 EDT}
    {3371436000 -18000 0 EST}
    {3382930800 -14400 1 EDT}
    {3403490400 -18000 0 EST}
    {3414380400 -14400 1 EDT}
    {3434940000 -18000 0 EST}
    {3445830000 -14400 1 EDT}
    {3466389600 -18000 0 EST}
    {3477279600 -14400 1 EDT}
    {3497839200 -18000 0 EST}
    {3508729200 -14400 1 EDT}
    {3529288800 -18000 0 EST}
    {3540178800 -14400 1 EDT}
    {3560738400 -18000 0 EST}
    {3572233200 -14400 1 EDT}
    {3592792800 -18000 0 EST}
    {3603682800 -14400 1 EDT}
    {3624242400 -18000 0 EST}
    {3635132400 -14400 1 EDT}
    {3655692000 -18000 0 EST}
    {3666582000 -14400 1 EDT}
    {3687141600 -18000 0 EST}
    {3698031600 -14400 1 EDT}
    {3718591200 -18000 0 EST}
    {3730086000 -14400 1 EDT}
    {3750645600 -18000 0 EST}
    {3761535600 -14400 1 EDT}
    {3782095200 -18000 0 EST}
    {3792985200 -14400 1 EDT}
    {3813544800 -18000 0 EST}
    {3824434800 -14400 1 EDT}
    {3844994400 -18000 0 EST}
    {3855884400 -14400 1 EDT}
    {3876444000 -18000 0 EST}
    {3887334000 -14400 1 EDT}
    {3907893600 -18000 0 EST}
    {3919388400 -14400 1 EDT}
    {3939948000 -18000 0 EST}
    {3950838000 -14400 1 EDT}
    {3971397600 -18000 0 EST}
    {3982287600 -14400 1 EDT}
    {4002847200 -18000 0 EST}
    {4013737200 -14400 1 EDT}
    {4034296800 -18000 0 EST}
    {4045186800 -14400 1 EDT}
    {4065746400 -18000 0 EST}
    {4076636400 -14400 1 EDT}
    {4097196000 -18000 0 EST}
}

# created by tools/tclZIC.tcl - do not edit

set TZData(:America/Juneau) {
    {-9223372036854775808 54139 0 LMT}
    {-3225366139 -32261 0 LMT}
    {-2188954939 -28800 0 PST}
    {-883584000 -28800 0 PST}
    {-880207200 -25200 1 PWT}
    {-769395600 -25200 1 PPT}
    {-765385200 -28800 0 PST}
    {-757353600 -28800 0 PST}
    {-31507200 -28800 0 PST}

# created by tools/tclZIC.tcl - do not edit

set TZData(:America/Juneau) {
    {-9223372036854775808 54139 0 LMT}
    {-3225223727 -32261 0 LMT}
    {-2188954939 -28800 0 PST}
    {-883584000 -28800 0 PST}
    {-880207200 -25200 1 PWT}
    {-769395600 -25200 1 PPT}
    {-765385200 -28800 0 PST}
    {-757353600 -28800 0 PST}
    {-31507200 -28800 0 PST}

# created by tools/tclZIC.tcl - do not edit

set TZData(:America/Metlakatla) {
    {-9223372036854775808 54822 0 LMT}
    {-3225366822 -31578 0 LMT}
    {-2188955622 -28800 0 PST}
    {-883584000 -28800 0 PST}
    {-880207200 -25200 1 PWT}
    {-769395600 -25200 1 PPT}
    {-765385200 -28800 0 PST}
    {-757353600 -28800 0 PST}
    {-31507200 -28800 0 PST}

# created by tools/tclZIC.tcl - do not edit

set TZData(:America/Metlakatla) {
    {-9223372036854775808 54822 0 LMT}
    {-3225223727 -31578 0 LMT}
    {-2188955622 -28800 0 PST}
    {-883584000 -28800 0 PST}
    {-880207200 -25200 1 PWT}
    {-769395600 -25200 1 PPT}
    {-765385200 -28800 0 PST}
    {-757353600 -28800 0 PST}
    {-31507200 -28800 0 PST}

# created by tools/tclZIC.tcl - do not edit

set TZData(:America/Nome) {
    {-9223372036854775808 46701 0 LMT}
    {-3225358701 -39698 0 LMT}
    {-2188947502 -39600 0 NST}
    {-883573200 -39600 0 NST}
    {-880196400 -36000 1 NWT}
    {-769395600 -36000 1 NPT}
    {-765374400 -39600 0 NST}
    {-757342800 -39600 0 NST}
    {-86878800 -39600 0 BST}

# created by tools/tclZIC.tcl - do not edit

set TZData(:America/Nome) {
    {-9223372036854775808 46702 0 LMT}
    {-3225223727 -39698 0 LMT}
    {-2188947502 -39600 0 NST}
    {-883573200 -39600 0 NST}
    {-880196400 -36000 1 NWT}
    {-769395600 -36000 1 NPT}
    {-765374400 -39600 0 NST}
    {-757342800 -39600 0 NST}
    {-86878800 -39600 0 BST}

# created by tools/tclZIC.tcl - do not edit

set TZData(:America/Sitka) {
    {-9223372036854775808 53927 0 LMT}
    {-3225365927 -32473 0 LMT}
    {-2188954727 -28800 0 PST}
    {-883584000 -28800 0 PST}
    {-880207200 -25200 1 PWT}
    {-769395600 -25200 1 PPT}
    {-765385200 -28800 0 PST}
    {-757353600 -28800 0 PST}
    {-31507200 -28800 0 PST}

# created by tools/tclZIC.tcl - do not edit

set TZData(:America/Sitka) {
    {-9223372036854775808 53927 0 LMT}
    {-3225223727 -32473 0 LMT}
    {-2188954727 -28800 0 PST}
    {-883584000 -28800 0 PST}
    {-880207200 -25200 1 PWT}
    {-769395600 -25200 1 PPT}
    {-765385200 -28800 0 PST}
    {-757353600 -28800 0 PST}
    {-31507200 -28800 0 PST}

# created by tools/tclZIC.tcl - do not edit

set TZData(:America/Yakutat) {
    {-9223372036854775808 52865 0 LMT}
    {-3225364865 -33535 0 LMT}
    {-2188953665 -32400 0 YST}
    {-883580400 -32400 0 YST}
    {-880203600 -28800 1 YWT}
    {-769395600 -28800 1 YPT}
    {-765381600 -32400 0 YST}
    {-757350000 -32400 0 YST}
    {-31503600 -32400 0 YST}

# created by tools/tclZIC.tcl - do not edit

set TZData(:America/Yakutat) {
    {-9223372036854775808 52865 0 LMT}
    {-3225223727 -33535 0 LMT}
    {-2188953665 -32400 0 YST}
    {-883580400 -32400 0 YST}
    {-880203600 -28800 1 YWT}
    {-769395600 -28800 1 YPT}
    {-765381600 -32400 0 YST}
    {-757350000 -32400 0 YST}
    {-31503600 -32400 0 YST}

    {1382835600 7200 0 EET}
    {1396141200 10800 1 EEST}
    {1414285200 7200 0 EET}
    {1427590800 10800 1 EEST}
    {1445734800 7200 0 EET}
    {1459040400 10800 1 EEST}
    {1473285600 10800 0 +03}





































































































































































}

    {1382835600 7200 0 EET}
    {1396141200 10800 1 EEST}
    {1414285200 7200 0 EET}
    {1427590800 10800 1 EEST}
    {1445734800 7200 0 EET}
    {1459040400 10800 1 EEST}
    {1473285600 10800 0 +03}
    {1509238800 7200 0 EET}
    {1521939600 10800 1 EEST}
    {1540688400 7200 0 EET}
    {1553994000 10800 1 EEST}
    {1572138000 7200 0 EET}
    {1585443600 10800 1 EEST}
    {1603587600 7200 0 EET}
    {1616893200 10800 1 EEST}
    {1635642000 7200 0 EET}
    {1648342800 10800 1 EEST}
    {1667091600 7200 0 EET}
    {1679792400 10800 1 EEST}
    {1698541200 7200 0 EET}
    {1711846800 10800 1 EEST}
    {1729990800 7200 0 EET}
    {1743296400 10800 1 EEST}
    {1761440400 7200 0 EET}
    {1774746000 10800 1 EEST}
    {1792890000 7200 0 EET}
    {1806195600 10800 1 EEST}
    {1824944400 7200 0 EET}
    {1837645200 10800 1 EEST}
    {1856394000 7200 0 EET}
    {1869094800 10800 1 EEST}
    {1887843600 7200 0 EET}
    {1901149200 10800 1 EEST}
    {1919293200 7200 0 EET}
    {1932598800 10800 1 EEST}
    {1950742800 7200 0 EET}
    {1964048400 10800 1 EEST}
    {1982797200 7200 0 EET}
    {1995498000 10800 1 EEST}
    {2014246800 7200 0 EET}
    {2026947600 10800 1 EEST}
    {2045696400 7200 0 EET}
    {2058397200 10800 1 EEST}
    {2077146000 7200 0 EET}
    {2090451600 10800 1 EEST}
    {2108595600 7200 0 EET}
    {2121901200 10800 1 EEST}
    {2140045200 7200 0 EET}
    {2153350800 10800 1 EEST}
    {2172099600 7200 0 EET}
    {2184800400 10800 1 EEST}
    {2203549200 7200 0 EET}
    {2216250000 10800 1 EEST}
    {2234998800 7200 0 EET}
    {2248304400 10800 1 EEST}
    {2266448400 7200 0 EET}
    {2279754000 10800 1 EEST}
    {2297898000 7200 0 EET}
    {2311203600 10800 1 EEST}
    {2329347600 7200 0 EET}
    {2342653200 10800 1 EEST}
    {2361402000 7200 0 EET}
    {2374102800 10800 1 EEST}
    {2392851600 7200 0 EET}
    {2405552400 10800 1 EEST}
    {2424301200 7200 0 EET}
    {2437606800 10800 1 EEST}
    {2455750800 7200 0 EET}
    {2469056400 10800 1 EEST}
    {2487200400 7200 0 EET}
    {2500506000 10800 1 EEST}
    {2519254800 7200 0 EET}
    {2531955600 10800 1 EEST}
    {2550704400 7200 0 EET}
    {2563405200 10800 1 EEST}
    {2582154000 7200 0 EET}
    {2595459600 10800 1 EEST}
    {2613603600 7200 0 EET}
    {2626909200 10800 1 EEST}
    {2645053200 7200 0 EET}
    {2658358800 10800 1 EEST}
    {2676502800 7200 0 EET}
    {2689808400 10800 1 EEST}
    {2708557200 7200 0 EET}
    {2721258000 10800 1 EEST}
    {2740006800 7200 0 EET}
    {2752707600 10800 1 EEST}
    {2771456400 7200 0 EET}
    {2784762000 10800 1 EEST}
    {2802906000 7200 0 EET}
    {2816211600 10800 1 EEST}
    {2834355600 7200 0 EET}
    {2847661200 10800 1 EEST}
    {2866410000 7200 0 EET}
    {2879110800 10800 1 EEST}
    {2897859600 7200 0 EET}
    {2910560400 10800 1 EEST}
    {2929309200 7200 0 EET}
    {2942010000 10800 1 EEST}
    {2960758800 7200 0 EET}
    {2974064400 10800 1 EEST}
    {2992208400 7200 0 EET}
    {3005514000 10800 1 EEST}
    {3023658000 7200 0 EET}
    {3036963600 10800 1 EEST}
    {3055712400 7200 0 EET}
    {3068413200 10800 1 EEST}
    {3087162000 7200 0 EET}
    {3099862800 10800 1 EEST}
    {3118611600 7200 0 EET}
    {3131917200 10800 1 EEST}
    {3150061200 7200 0 EET}
    {3163366800 10800 1 EEST}
    {3181510800 7200 0 EET}
    {3194816400 10800 1 EEST}
    {3212960400 7200 0 EET}
    {3226266000 10800 1 EEST}
    {3245014800 7200 0 EET}
    {3257715600 10800 1 EEST}
    {3276464400 7200 0 EET}
    {3289165200 10800 1 EEST}
    {3307914000 7200 0 EET}
    {3321219600 10800 1 EEST}
    {3339363600 7200 0 EET}
    {3352669200 10800 1 EEST}
    {3370813200 7200 0 EET}
    {3384118800 10800 1 EEST}
    {3402867600 7200 0 EET}
    {3415568400 10800 1 EEST}
    {3434317200 7200 0 EET}
    {3447018000 10800 1 EEST}
    {3465766800 7200 0 EET}
    {3479072400 10800 1 EEST}
    {3497216400 7200 0 EET}
    {3510522000 10800 1 EEST}
    {3528666000 7200 0 EET}
    {3541971600 10800 1 EEST}
    {3560115600 7200 0 EET}
    {3573421200 10800 1 EEST}
    {3592170000 7200 0 EET}
    {3604870800 10800 1 EEST}
    {3623619600 7200 0 EET}
    {3636320400 10800 1 EEST}
    {3655069200 7200 0 EET}
    {3668374800 10800 1 EEST}
    {3686518800 7200 0 EET}
    {3699824400 10800 1 EEST}
    {3717968400 7200 0 EET}
    {3731274000 10800 1 EEST}
    {3750022800 7200 0 EET}
    {3762723600 10800 1 EEST}
    {3781472400 7200 0 EET}
    {3794173200 10800 1 EEST}
    {3812922000 7200 0 EET}
    {3825622800 10800 1 EEST}
    {3844371600 7200 0 EET}
    {3857677200 10800 1 EEST}
    {3875821200 7200 0 EET}
    {3889126800 10800 1 EEST}
    {3907270800 7200 0 EET}
    {3920576400 10800 1 EEST}
    {3939325200 7200 0 EET}
    {3952026000 10800 1 EEST}
    {3970774800 7200 0 EET}
    {3983475600 10800 1 EEST}
    {4002224400 7200 0 EET}
    {4015530000 10800 1 EEST}
    {4033674000 7200 0 EET}
    {4046979600 10800 1 EEST}
    {4065123600 7200 0 EET}
    {4078429200 10800 1 EEST}
    {4096573200 7200 0 EET}
}

# created by tools/tclZIC.tcl - do not edit

set TZData(:Asia/Kolkata) {
    {-9223372036854775808 21208 0 LMT}
    {-2840162008 21200 0 HMT}
    {-891582800 23400 0 +0630}


    {-872058600 19800 0 IST}
    {-862637400 23400 1 +0630}
    {-764145000 19800 0 IST}
}

# created by tools/tclZIC.tcl - do not edit

set TZData(:Asia/Kolkata) {
    {-9223372036854775808 21208 0 LMT}
    {-3645237208 21200 0 HMT}
    {-3155694800 19270 0 MMT}
    {-2019705670 19800 0 IST}
    {-891581400 23400 1 +0630}
    {-872058600 19800 0 IST}
    {-862637400 23400 1 +0630}
    {-764145000 19800 0 IST}
}

# created by tools/tclZIC.tcl - do not edit

set TZData(:Asia/Yangon) {
    {-9223372036854775808 23080 0 LMT}
    {-2840163880 23080 0 RMT}
    {-1577946280 23400 0 +0630}
    {-873268200 32400 0 +09}
    {-778410000 23400 0 +0630}
}

# created by tools/tclZIC.tcl - do not edit

set TZData(:Asia/Yangon) {
    {-9223372036854775808 23087 0 LMT}
    {-2840163887 23087 0 RMT}
    {-1577946287 23400 0 +0630}
    {-873268200 32400 0 +09}
    {-778410000 23400 0 +0630}
}

    {1193522400 14400 0 +04}
    {1206828000 18000 1 +05}
    {1224972000 14400 0 +04}
    {1238277600 18000 1 +05}
    {1256421600 14400 0 +04}
    {1269727200 18000 1 +05}
    {1288476000 14400 0 +04}

    {1301176800 18000 1 +05}
    {1319925600 14400 0 +04}
}

    {1193522400 14400 0 +04}
    {1206828000 18000 1 +05}
    {1224972000 14400 0 +04}
    {1238277600 18000 1 +05}
    {1256421600 14400 0 +04}
    {1269727200 18000 1 +05}
    {1288476000 14400 0 +04}
    {1293825600 14400 0 +04}
    {1301176800 18000 1 +05}
    {1319925600 14400 0 +04}
}

    {-1049061600 0 0 IST}
    {-1032127200 3600 1 IST}
    {-1017612000 0 0 IST}
    {-1001282400 3600 1 IST}
    {-986162400 0 0 IST}
    {-969228000 3600 1 IST}
    {-950479200 0 0 IST}
    {-942015600 3600 1 IST}
    {-733359600 0 0 GMT}
    {-719445600 3600 1 IST}
    {-699490800 0 0 GMT}
    {-684972000 3600 0 IST}
    {-668037600 0 0 IST}
    {-654732000 3600 1 IST}
    {-636588000 0 0 IST}
    {-622072800 3600 1 IST}
    {-605743200 0 0 IST}
    {-590623200 3600 1 IST}

    {-1049061600 0 0 IST}
    {-1032127200 3600 1 IST}
    {-1017612000 0 0 IST}
    {-1001282400 3600 1 IST}
    {-986162400 0 0 IST}
    {-969228000 3600 1 IST}
    {-950479200 0 0 IST}
    {-942012000 3600 1 IST}
    {-733356000 0 0 GMT}
    {-719445600 3600 1 IST}
    {-699487200 0 0 GMT}
    {-684972000 3600 0 IST}
    {-668037600 0 0 IST}
    {-654732000 3600 1 IST}
    {-636588000 0 0 IST}
    {-622072800 3600 1 IST}
    {-605743200 0 0 IST}
    {-590623200 3600 1 IST}

# created by tools/tclZIC.tcl - do not edit

set TZData(:Pacific/Apia) {
    {-9223372036854775808 45184 0 LMT}
    {-2855737984 -41216 0 LMT}
    {-1861878784 -41400 0 -1130}
    {-631110600 -39600 0 -10}
    {1285498800 -36000 1 -10}
    {1301752800 -39600 0 -10}
    {1316872800 -36000 1 -10}
    {1325239200 50400 0 +14}
    {1333202400 46800 0 +14}

# created by tools/tclZIC.tcl - do not edit

set TZData(:Pacific/Apia) {
    {-9223372036854775808 45184 0 LMT}
    {-2445424384 -41216 0 LMT}
    {-1861878784 -41400 0 -1130}
    {-631110600 -39600 0 -10}
    {1285498800 -36000 1 -10}
    {1301752800 -39600 0 -10}
    {1316872800 -36000 1 -10}
    {1325239200 50400 0 +14}
    {1333202400 46800 0 +14}

    {1414850400 46800 1 +13}
    {1421503200 43200 0 +12}
    {1446300000 46800 1 +13}
    {1452952800 43200 0 +12}
    {1478354400 46800 1 +13}
    {1484402400 43200 0 +12}
    {1509804000 46800 1 +13}
    {1516456800 43200 0 +12}
    {1541253600 46800 1 +13}
    {1547906400 43200 0 +12}
    {1572703200 46800 1 +13}
    {1579356000 43200 0 +12}
    {1604152800 46800 1 +13}
    {1610805600 43200 0 +12}
    {1636207200 46800 1 +13}
    {1642255200 43200 0 +12}
    {1667656800 46800 1 +13}
    {1673704800 43200 0 +12}
    {1699106400 46800 1 +13}
    {1705759200 43200 0 +12}
    {1730556000 46800 1 +13}
    {1737208800 43200 0 +12}
    {1762005600 46800 1 +13}
    {1768658400 43200 0 +12}
    {1793455200 46800 1 +13}
    {1800108000 43200 0 +12}
    {1825509600 46800 1 +13}
    {1831557600 43200 0 +12}
    {1856959200 46800 1 +13}
    {1863612000 43200 0 +12}
    {1888408800 46800 1 +13}
    {1895061600 43200 0 +12}
    {1919858400 46800 1 +13}
    {1926511200 43200 0 +12}
    {1951308000 46800 1 +13}
    {1957960800 43200 0 +12}
    {1983362400 46800 1 +13}
    {1989410400 43200 0 +12}
    {2014812000 46800 1 +13}
    {2020860000 43200 0 +12}
    {2046261600 46800 1 +13}
    {2052914400 43200 0 +12}
    {2077711200 46800 1 +13}
    {2084364000 43200 0 +12}
    {2109160800 46800 1 +13}
    {2115813600 43200 0 +12}
    {2140610400 46800 1 +13}
    {2147263200 43200 0 +12}
    {2172664800 46800 1 +13}
................................................................................
    {2298463200 46800 1 +13}
    {2305116000 43200 0 +12}
    {2329912800 46800 1 +13}
    {2336565600 43200 0 +12}
    {2361967200 46800 1 +13}
    {2368015200 43200 0 +12}
    {2393416800 46800 1 +13}
    {2400069600 43200 0 +12}
    {2424866400 46800 1 +13}
    {2431519200 43200 0 +12}
    {2456316000 46800 1 +13}
    {2462968800 43200 0 +12}
    {2487765600 46800 1 +13}
    {2494418400 43200 0 +12}
    {2519820000 46800 1 +13}
    {2525868000 43200 0 +12}
    {2551269600 46800 1 +13}
    {2557317600 43200 0 +12}
    {2582719200 46800 1 +13}
    {2589372000 43200 0 +12}
    {2614168800 46800 1 +13}
    {2620821600 43200 0 +12}
    {2645618400 46800 1 +13}
    {2652271200 43200 0 +12}
    {2677068000 46800 1 +13}
    {2683720800 43200 0 +12}
    {2709122400 46800 1 +13}
    {2715170400 43200 0 +12}
    {2740572000 46800 1 +13}
    {2747224800 43200 0 +12}
    {2772021600 46800 1 +13}
    {2778674400 43200 0 +12}
    {2803471200 46800 1 +13}
    {2810124000 43200 0 +12}
    {2834920800 46800 1 +13}
    {2841573600 43200 0 +12}
    {2866975200 46800 1 +13}
    {2873023200 43200 0 +12}
    {2898424800 46800 1 +13}
    {2904472800 43200 0 +12}
    {2929874400 46800 1 +13}
    {2936527200 43200 0 +12}
    {2961324000 46800 1 +13}
    {2967976800 43200 0 +12}
    {2992773600 46800 1 +13}
    {2999426400 43200 0 +12}
    {3024223200 46800 1 +13}
    {3030876000 43200 0 +12}
    {3056277600 46800 1 +13}
................................................................................
    {3182076000 46800 1 +13}
    {3188728800 43200 0 +12}
    {3213525600 46800 1 +13}
    {3220178400 43200 0 +12}
    {3245580000 46800 1 +13}
    {3251628000 43200 0 +12}
    {3277029600 46800 1 +13}
    {3283682400 43200 0 +12}
    {3308479200 46800 1 +13}
    {3315132000 43200 0 +12}
    {3339928800 46800 1 +13}
    {3346581600 43200 0 +12}
    {3371378400 46800 1 +13}
    {3378031200 43200 0 +12}
    {3403432800 46800 1 +13}
    {3409480800 43200 0 +12}
    {3434882400 46800 1 +13}
    {3440930400 43200 0 +12}
    {3466332000 46800 1 +13}
    {3472984800 43200 0 +12}
    {3497781600 46800 1 +13}
    {3504434400 43200 0 +12}
    {3529231200 46800 1 +13}
    {3535884000 43200 0 +12}
    {3560680800 46800 1 +13}
    {3567333600 43200 0 +12}
    {3592735200 46800 1 +13}
    {3598783200 43200 0 +12}
    {3624184800 46800 1 +13}
    {3630837600 43200 0 +12}
    {3655634400 46800 1 +13}
    {3662287200 43200 0 +12}
    {3687084000 46800 1 +13}
    {3693736800 43200 0 +12}
    {3718533600 46800 1 +13}
    {3725186400 43200 0 +12}
    {3750588000 46800 1 +13}
    {3756636000 43200 0 +12}
    {3782037600 46800 1 +13}
    {3788085600 43200 0 +12}
    {3813487200 46800 1 +13}
    {3820140000 43200 0 +12}
    {3844936800 46800 1 +13}
    {3851589600 43200 0 +12}
    {3876386400 46800 1 +13}
    {3883039200 43200 0 +12}
    {3907836000 46800 1 +13}
    {3914488800 43200 0 +12}
    {3939890400 46800 1 +13}

    {1414850400 46800 1 +13}
    {1421503200 43200 0 +12}
    {1446300000 46800 1 +13}
    {1452952800 43200 0 +12}
    {1478354400 46800 1 +13}
    {1484402400 43200 0 +12}
    {1509804000 46800 1 +13}
    {1515852000 43200 0 +12}
    {1541253600 46800 1 +13}
    {1547906400 43200 0 +12}
    {1572703200 46800 1 +13}
    {1579356000 43200 0 +12}
    {1604152800 46800 1 +13}
    {1610805600 43200 0 +12}
    {1636207200 46800 1 +13}
    {1642255200 43200 0 +12}
    {1667656800 46800 1 +13}
    {1673704800 43200 0 +12}
    {1699106400 46800 1 +13}
    {1705154400 43200 0 +12}
    {1730556000 46800 1 +13}
    {1737208800 43200 0 +12}
    {1762005600 46800 1 +13}
    {1768658400 43200 0 +12}
    {1793455200 46800 1 +13}
    {1800108000 43200 0 +12}
    {1825509600 46800 1 +13}
    {1831557600 43200 0 +12}
    {1856959200 46800 1 +13}
    {1863007200 43200 0 +12}
    {1888408800 46800 1 +13}
    {1895061600 43200 0 +12}
    {1919858400 46800 1 +13}
    {1926511200 43200 0 +12}
    {1951308000 46800 1 +13}
    {1957960800 43200 0 +12}
    {1983362400 46800 1 +13}
    {1989410400 43200 0 +12}
    {2014812000 46800 1 +13}
    {2020860000 43200 0 +12}
    {2046261600 46800 1 +13}
    {2052309600 43200 0 +12}
    {2077711200 46800 1 +13}
    {2084364000 43200 0 +12}
    {2109160800 46800 1 +13}
    {2115813600 43200 0 +12}
    {2140610400 46800 1 +13}
    {2147263200 43200 0 +12}
    {2172664800 46800 1 +13}
................................................................................
    {2298463200 46800 1 +13}
    {2305116000 43200 0 +12}
    {2329912800 46800 1 +13}
    {2336565600 43200 0 +12}
    {2361967200 46800 1 +13}
    {2368015200 43200 0 +12}
    {2393416800 46800 1 +13}
    {2399464800 43200 0 +12}
    {2424866400 46800 1 +13}
    {2431519200 43200 0 +12}
    {2456316000 46800 1 +13}
    {2462968800 43200 0 +12}
    {2487765600 46800 1 +13}
    {2494418400 43200 0 +12}
    {2519820000 46800 1 +13}
    {2525868000 43200 0 +12}
    {2551269600 46800 1 +13}
    {2557317600 43200 0 +12}
    {2582719200 46800 1 +13}
    {2588767200 43200 0 +12}
    {2614168800 46800 1 +13}
    {2620821600 43200 0 +12}
    {2645618400 46800 1 +13}
    {2652271200 43200 0 +12}
    {2677068000 46800 1 +13}
    {2683720800 43200 0 +12}
    {2709122400 46800 1 +13}
    {2715170400 43200 0 +12}
    {2740572000 46800 1 +13}
    {2746620000 43200 0 +12}
    {2772021600 46800 1 +13}
    {2778674400 43200 0 +12}
    {2803471200 46800 1 +13}
    {2810124000 43200 0 +12}
    {2834920800 46800 1 +13}
    {2841573600 43200 0 +12}
    {2866975200 46800 1 +13}
    {2873023200 43200 0 +12}
    {2898424800 46800 1 +13}
    {2904472800 43200 0 +12}
    {2929874400 46800 1 +13}
    {2935922400 43200 0 +12}
    {2961324000 46800 1 +13}
    {2967976800 43200 0 +12}
    {2992773600 46800 1 +13}
    {2999426400 43200 0 +12}
    {3024223200 46800 1 +13}
    {3030876000 43200 0 +12}
    {3056277600 46800 1 +13}
................................................................................
    {3182076000 46800 1 +13}
    {3188728800 43200 0 +12}
    {3213525600 46800 1 +13}
    {3220178400 43200 0 +12}
    {3245580000 46800 1 +13}
    {3251628000 43200 0 +12}
    {3277029600 46800 1 +13}
    {3283077600 43200 0 +12}
    {3308479200 46800 1 +13}
    {3315132000 43200 0 +12}
    {3339928800 46800 1 +13}
    {3346581600 43200 0 +12}
    {3371378400 46800 1 +13}
    {3378031200 43200 0 +12}
    {3403432800 46800 1 +13}
    {3409480800 43200 0 +12}
    {3434882400 46800 1 +13}
    {3440930400 43200 0 +12}
    {3466332000 46800 1 +13}
    {3472380000 43200 0 +12}
    {3497781600 46800 1 +13}
    {3504434400 43200 0 +12}
    {3529231200 46800 1 +13}
    {3535884000 43200 0 +12}
    {3560680800 46800 1 +13}
    {3567333600 43200 0 +12}
    {3592735200 46800 1 +13}
    {3598783200 43200 0 +12}
    {3624184800 46800 1 +13}
    {3630232800 43200 0 +12}
    {3655634400 46800 1 +13}
    {3662287200 43200 0 +12}
    {3687084000 46800 1 +13}
    {3693736800 43200 0 +12}
    {3718533600 46800 1 +13}
    {3725186400 43200 0 +12}
    {3750588000 46800 1 +13}
    {3756636000 43200 0 +12}
    {3782037600 46800 1 +13}
    {3788085600 43200 0 +12}
    {3813487200 46800 1 +13}
    {3819535200 43200 0 +12}
    {3844936800 46800 1 +13}
    {3851589600 43200 0 +12}
    {3876386400 46800 1 +13}
    {3883039200 43200 0 +12}
    {3907836000 46800 1 +13}
    {3914488800 43200 0 +12}
    {3939890400 46800 1 +13}

# created by tools/tclZIC.tcl - do not edit

set TZData(:Pacific/Pago_Pago) {
    {-9223372036854775808 45432 0 LMT}
    {-2855738232 -40968 0 LMT}
    {-1861879032 -39600 0 SST}
}

# created by tools/tclZIC.tcl - do not edit

set TZData(:Pacific/Pago_Pago) {
    {-9223372036854775808 45432 0 LMT}
    {-2445424632 -40968 0 LMT}
    {-1861879032 -39600 0 SST}
}

    {953384400 46800 0 +13}
    {973342800 50400 1 +14}
    {980596800 46800 0 +13}
    {1004792400 50400 1 +14}
    {1012046400 46800 0 +13}
    {1478350800 50400 1 +14}
    {1484398800 46800 0 +13}
    {1509800400 50400 1 +14}
    {1516453200 46800 0 +13}
    {1541250000 50400 1 +14}
    {1547902800 46800 0 +13}
    {1572699600 50400 1 +14}
    {1579352400 46800 0 +13}
    {1604149200 50400 1 +14}
    {1610802000 46800 0 +13}
    {1636203600 50400 1 +14}
    {1642251600 46800 0 +13}
    {1667653200 50400 1 +14}
    {1673701200 46800 0 +13}
    {1699102800 50400 1 +14}
    {1705755600 46800 0 +13}
    {1730552400 50400 1 +14}
    {1737205200 46800 0 +13}
    {1762002000 50400 1 +14}
    {1768654800 46800 0 +13}
    {1793451600 50400 1 +14}
    {1800104400 46800 0 +13}
    {1825506000 50400 1 +14}
    {1831554000 46800 0 +13}
    {1856955600 50400 1 +14}
    {1863608400 46800 0 +13}
    {1888405200 50400 1 +14}
    {1895058000 46800 0 +13}
    {1919854800 50400 1 +14}
    {1926507600 46800 0 +13}
    {1951304400 50400 1 +14}
    {1957957200 46800 0 +13}
    {1983358800 50400 1 +14}
    {1989406800 46800 0 +13}
    {2014808400 50400 1 +14}
    {2020856400 46800 0 +13}
    {2046258000 50400 1 +14}
    {2052910800 46800 0 +13}
    {2077707600 50400 1 +14}
    {2084360400 46800 0 +13}
    {2109157200 50400 1 +14}
    {2115810000 46800 0 +13}
    {2140606800 50400 1 +14}
    {2147259600 46800 0 +13}
    {2172661200 50400 1 +14}
    {2178709200 46800 0 +13}
    {2204110800 50400 1 +14}
    {2210158800 46800 0 +13}
    {2235560400 50400 1 +14}
    {2242213200 46800 0 +13}
    {2267010000 50400 1 +14}
    {2273662800 46800 0 +13}
    {2298459600 50400 1 +14}
    {2305112400 46800 0 +13}
    {2329909200 50400 1 +14}
    {2336562000 46800 0 +13}
    {2361963600 50400 1 +14}
    {2368011600 46800 0 +13}
    {2393413200 50400 1 +14}
    {2400066000 46800 0 +13}
    {2424862800 50400 1 +14}
    {2431515600 46800 0 +13}
    {2456312400 50400 1 +14}
    {2462965200 46800 0 +13}
    {2487762000 50400 1 +14}
    {2494414800 46800 0 +13}
    {2519816400 50400 1 +14}
    {2525864400 46800 0 +13}
    {2551266000 50400 1 +14}
    {2557314000 46800 0 +13}
    {2582715600 50400 1 +14}
    {2589368400 46800 0 +13}
    {2614165200 50400 1 +14}
    {2620818000 46800 0 +13}
    {2645614800 50400 1 +14}
    {2652267600 46800 0 +13}
    {2677064400 50400 1 +14}
    {2683717200 46800 0 +13}
    {2709118800 50400 1 +14}
    {2715166800 46800 0 +13}
    {2740568400 50400 1 +14}
    {2747221200 46800 0 +13}
    {2772018000 50400 1 +14}
    {2778670800 46800 0 +13}
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}

# Artistic Style, see http://astyle.sourceforge.net/
# full documentation, see: http://astyle.sourceforge.net/astyle.html
#
# usage:
#       astyle --options=astylerc *.[ch]

## Bracket Style Options
style=kr

## Tab Options
indent=spaces=3

## Bracket Modify Options

## Indentation Options
min-conditional-indent=0

## Padding Options
pad-header
unpad-paren
align-pointer=name

## Formatting Options
break-after-logical
max-code-length=120
convert-tabs
mode=c

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

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

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

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

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

#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

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

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

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

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

#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

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

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

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

  /* 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) == MP_YES) {
    /* 4.1 u = u/2 */
    if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
      goto LBL_ERR;
    }
    /* 4.2 if B is odd then */
    if (mp_isodd (&B) == MP_YES) {
      if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
        goto LBL_ERR;
      }
    }
    /* B = B/2 */
    if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

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

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

  /* if v != 1 then there is no inverse */
  if (mp_cmp_d (&v, 1) != MP_EQ) {
    res = MP_VAL;
    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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

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

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

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

   /* 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) == MP_YES) {
      /* 4.1 u = u/2 */
      if ((res = mp_div_2(&u, &u)) != MP_OKAY) {
         goto LBL_ERR;
      }
      /* 4.2 if B is odd then */
      if (mp_isodd(&B) == MP_YES) {
         if ((res = mp_sub(&B, &x, &B)) != MP_OKAY) {
            goto LBL_ERR;
         }
      }
      /* B = B/2 */
      if ((res = mp_div_2(&B, &B)) != MP_OKAY) {
         goto LBL_ERR;
      }
   }

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

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

   /* if v != 1 then there is no inverse */
   if (mp_cmp_d(&v, 1) != MP_EQ) {
      res = MP_VAL;
      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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * 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[...]
   */
  {
    mp_word *_W;
    mp_digit *tmpx;

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

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

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

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

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

    /* a = a + mu * m * b**i
     *
     * This is computed in place and on the fly.  The multiplication
     * by b**i is handled by offseting which columns the results
     * are added to.
     *
     * 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
     */
    {
      int iy;
      mp_digit *tmpn;
      mp_word *_W;

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

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

      /* 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].
   */
  {
    mp_digit *tmpx;
    mp_word *_W, *_W1;

    /* nox fix rest of carries */

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

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

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

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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * 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, const 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[...]
    */
   {
      mp_word *_W;
      mp_digit *tmpx;

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

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

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

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

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

      /* a = a + mu * m * b**i
       *
       * This is computed in place and on the fly.  The multiplication
       * by b**i is handled by offseting which columns the results
       * are added to.
       *
       * 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
       */
      {
         int iy;
         mp_digit *tmpn;
         mp_word *_W;

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

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

         /* 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].
    */
   {
      mp_digit *tmpx;
      mp_word *_W, *_W1;

      /* nox fix rest of carries */

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

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

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

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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* Fast (comba) multiplier
 *
 * This is the fast column-array [comba] multiplier.  It is 
 * designed to compute the columns of the product first 
 * then handle the carries afterwards.  This has the effect 
 * 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];
  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;

  {
    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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

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

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

   /* 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;

   {
      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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * 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;

  {
    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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * 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(const mp_int *a, const 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;

   {
      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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

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

................................................................................
      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++) {
................................................................................
      }

      /* 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* the jist of squaring...
 * you do like mult except the offset of the tmpx [one that
 * starts closer to zero] can't equal the offset of tmpy.
 * So basically you set up iy like before then you min it with
 * (ty-tx) so that it never happens.  You double all those
 * you add in the inner loop

After that loop you do the squares and add them in.
*/

int fast_s_mp_sqr(const 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;

................................................................................
      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++) {
................................................................................
      }

      /* 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* high level addition (handles signs) */
int mp_add(const mp_int *a, const 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

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

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

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

     /* temporarily fix sign of a */
     a->sign = MP_ZPOS;

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

     /* fix sign  */
     a->sign = c->sign = MP_NEG;

     /* clamp */
     mp_clamp(c);

     return res;
  }

  /* old number of used digits in c */
  oldused = c->used;

  /* 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;
  }

  /* sign always positive */
  c->sign = MP_ZPOS;

  /* now zero to oldused */
  while (ix++ < oldused) {
     *tmpc++ = 0;
  }
  mp_clamp(c);

  return MP_OKAY;
}

#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* single digit addition */

int mp_add_d(const 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))) {
      mp_int a_ = *a;
      /* temporarily fix sign of a */
      a_.sign = MP_ZPOS;

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

      /* fix sign  */
      c->sign = MP_NEG;

      /* clamp */
      mp_clamp(c);

      return res;
   }

   /* old number of used digits in c */
   oldused = c->used;

   /* 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;
   }

   /* sign always positive */
   c->sign = MP_ZPOS;

   /* now zero to oldused */
   while (ix++ < oldused) {
      *tmpc++ = 0;
   }
   mp_clamp(c);

   return MP_OKAY;
}

#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* d = a + b (mod c) */
int
mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
  int     res;
  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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* d = a + b (mod c) */
int mp_addmod(const mp_int *a, const mp_int *b, const 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* AND two ints together */
int mp_and(const mp_int *a, const mp_int *b, mp_int *c)

{
   int     res, ix, px;
   mp_int  t;
   const mp_int *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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* trim unused digits 
 *
 * This is used to ensure that leading zero digits are
 * trimed and the leading "used" digit will be non-zero
 * Typically very fast.  Also fixes the sign if there
 * 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* trim unused digits
 *
 * This is used to ensure that leading zero digits are
 * trimed and the leading "used" digit will be non-zero
 * Typically very fast.  Also fixes the sign if there
 * 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */
#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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */
#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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* compare two ints (signed)*/
int
mp_cmp (const mp_int * a, const 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* compare two ints (signed)*/

int mp_cmp(const mp_int *a, const 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* compare a digit */
int mp_cmp_d(const mp_int * a, mp_digit b)
{
  /* compare based on sign */
  if (a->sign == MP_NEG) {
    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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* compare a digit */
int mp_cmp_d(const mp_int *a, mp_digit b)
{
   /* compare based on sign */
   if (a->sign == MP_NEG) {
      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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* compare maginitude of two ints (unsigned) */
int mp_cmp_mag (const mp_int * a, const mp_int * b)
{
  int     n;
  mp_digit *tmpa, *tmpb;

  /* 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* compare maginitude of two ints (unsigned) */
int mp_cmp_mag(const mp_int *a, const mp_int *b)
{
   int     n;
   mp_digit *tmpa, *tmpb;

   /* 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

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

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

 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

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

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

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* copy, b = a */
int
mp_copy (const 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 */
  {
    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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* copy, b = a */

int mp_copy(const 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 */
   {
      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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* returns the number of bits in an int */
int
mp_count_bits (const 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* returns the number of bits in an int */

int mp_count_bits(const 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * Tom St Denis, [email protected], http://libtom.org
 */

#ifdef BN_MP_DIV_SMALL

/* slower bit-bang division... also smaller */
int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
   mp_int ta, tb, tq, q;
   int    res, n, n2;

  /* is divisor zero ? */
  if (mp_iszero (b) == MP_YES) {
    return MP_VAL;
  }

  /* if a < b then q=0, r = a */
  if (mp_cmp_mag (a, b) == MP_LT) {
    if (d != NULL) {
      res = mp_copy (a, d);
    } 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

................................................................................
 * the case where digits are removed from 'x' in
 * the inner loop.  It also doesn't consider the
 * case that y has fewer than three digits, etc..
 *
 * The overall algorithm is as described as
 * 14.20 from HAC but fixed to treat these cases.
*/
int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
  mp_int  q, x, y, t1, t2;
  int     res, n, t, i, norm, neg;

  /* is divisor zero ? */
  if (mp_iszero (b) == MP_YES) {
    return MP_VAL;
  }

  /* if a < b then q=0, r = a */
  if (mp_cmp_mag (a, b) == MP_LT) {
    if (d != NULL) {
      res = mp_copy (a, d);
    } 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) {
    if ((res = mp_div_2d (&x, norm, &x, NULL)) != MP_OKAY) {
      goto LBL_Y;
    }
    mp_exch (&x, d);
  }

  res = MP_OKAY;


LBL_Y:mp_clear (&y);

LBL_X:mp_clear (&x);
LBL_T2:mp_clear (&t2);

LBL_T1:mp_clear (&t1);


LBL_Q:mp_clear (&q);
  return res;
}

#endif

#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * Tom St Denis, [email protected], http://libtom.org
 */

#ifdef BN_MP_DIV_SMALL

/* slower bit-bang division... also smaller */
int mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d)
{
   mp_int ta, tb, tq, q;
   int    res, n, n2;

   /* is divisor zero ? */
   if (mp_iszero(b) == MP_YES) {
      return MP_VAL;
   }

   /* if a < b then q=0, r = a */
   if (mp_cmp_mag(a, b) == MP_LT) {
      if (d != NULL) {
         res = mp_copy(a, d);
      } 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

................................................................................
 * 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(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d)
{
   mp_int  q, x, y, t1, t2;
   int     res, n, t, i, norm, neg;

   /* is divisor zero ? */
   if (mp_iszero(b) == MP_YES) {
      return MP_VAL;
   }

   /* if a < b then q=0, r = a */
   if (mp_cmp_mag(a, b) == MP_LT) {
      if (d != NULL) {
         res = mp_copy(a, d);
      } 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) {
      if ((res = mp_div_2d(&x, norm, &x, NULL)) != MP_OKAY) {
         goto LBL_Y;
      }
      mp_exch(&x, d);
   }

   res = MP_OKAY;

LBL_Y:
   mp_clear(&y);
LBL_X:
   mp_clear(&x);
LBL_T2:
   mp_clear(&t2);
LBL_T1:
   mp_clear(&t1);
LBL_Q:
   mp_clear(&q);
   return res;
}

#endif

#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* b = a/2 */
int mp_div_2(const 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;
  {
    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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* b = a/2 */
int mp_div_2(const 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;
   {
      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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* shift right by a certain bit count (store quotient in c, optional remainder in d) */
int mp_div_2d (const mp_int * a, int b, mp_int * c, mp_int * d)
{
  mp_digit D, r, rr;
  int     x, res;

  /* if 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;
  }

  /* copy */
  if ((res = mp_copy (a, c)) != MP_OKAY) {
    return res;
  }
  /* 'a' should not be used after here - it might be the same as d */

  /* get the remainder */
  if (d != NULL) {
    if ((res = mp_mod_2d (a, b, d)) != MP_OKAY) {
      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) {
    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);
  return MP_OKAY;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* shift right by a certain bit count (store quotient in c, optional remainder in d) */
int mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d)
{
   mp_digit D, r, rr;
   int     x, res;

   /* if 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;
   }

   /* copy */
   if ((res = mp_copy(a, c)) != MP_OKAY) {
      return res;
   }
   /* 'a' should not be used after here - it might be the same as d */

   /* get the remainder */
   if (d != NULL) {
      if ((res = mp_mod_2d(a, b, d)) != MP_OKAY) {
         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) {
      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);
   return MP_OKAY;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* divide by three (based on routine from MPI and the GMP manual) */
int
mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
{
  mp_int   q;
  mp_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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* divide by three (based on routine from MPI and the GMP manual) */

int mp_div_3(const 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

static int s_is_power_of_two(mp_digit b, int *p)
{
   int x;

   /* quick out - if (b & (b-1)) isn't zero, b isn't a power of two */
   if ((b == 0) || ((b & (b-1)) != 0)) {
       return 0;
   }
   for (x = 1; x < DIGIT_BIT; x++) {
      if (b == (((mp_digit)1)<<x)) {
         *p = x;
         return 1;
      }
   }
   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) == MP_YES)) {
     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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */


















/* single digit division (based on routine from MPI) */

int mp_div_d(const 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) == MP_YES)) {
      if (d != NULL) {
         *d = 0;
      }
      if (c != NULL) {
         return mp_copy(a, c);
      }
      return MP_OKAY;
   }

   /* power of two ? */

   if (((b & (b-1)) == 0)) {
      for (ix = 1; ix < DIGIT_BIT; ix++) {
         if (b == (((mp_digit)1)<<ix)) {
            break;
         }
      }
      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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* determines if a number is a valid DR modulus */
int mp_dr_is_modulus(const 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * 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) {
    if ((err = s_mp_sub(x, n, x)) != MP_OKAY) {
      return err;
    }
    goto top;
  }
  return MP_OKAY;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * 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, const 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) {
      if ((err = s_mp_sub(x, n, x)) != MP_OKAY) {
         return err;
      }
      goto top;
   }
   return MP_OKAY;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* determines the setup value */
void mp_dr_setup(mp_int *a, mp_digit *d)
{
   /* the casts are required if DIGIT_BIT is one less than
    * the number of bits in a mp_digit [e.g. DIGIT_BIT==31]
    */
   *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) - 
        ((mp_word)a->dp[0]));
}

#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* determines the setup value */
void mp_dr_setup(const 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* swap the elements of two integers, for cases where you can't simply swap the 
 * mp_int pointers around
 */
void
mp_exch (mp_int * a, mp_int * b)
{
  mp_int  t;

  t  = *a;
  *a = *b;
  *b = t;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* swap the elements of two integers, for cases where you can't simply swap the
 * mp_int pointers around
 */
void mp_exch(mp_int *a, mp_int *b)

{
   mp_int  t;

   t  = *a;
   *a = *b;
   *b = t;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * Tom St Denis, [email protected], 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * Tom St Denis, [email protected], 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, const 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* wrapper function for mp_expt_d_ex() */
int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
{
  return mp_expt_d_ex(a, b, c, 0);
}

#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* wrapper function for mp_expt_d_ex() */
int mp_expt_d(const mp_int *a, mp_digit b, mp_int *c)
{
   return mp_expt_d_ex(a, b, c, 0);
}

#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* calculate c = a**b  using a square-multiply algorithm */
int mp_expt_d_ex (mp_int * a, mp_digit b, mp_int * c, int fast)
{
  int     res;
  unsigned int x;

  mp_int  g;

  if ((res = mp_init_copy (&g, a)) != MP_OKAY) {
    return res;
  }

  /* set initial result */
  mp_set (c, 1);

  if (fast != 0) {
    while (b > 0) {
      /* if the bit is set multiply */
      if ((b & 1) != 0) {
        if ((res = mp_mul (c, &g, c)) != MP_OKAY) {
          mp_clear (&g);
          return res;
        }
      }

      /* square */
      if (b > 1) {
        if ((res = mp_sqr (&g, &g)) != MP_OKAY) {
          mp_clear (&g);
          return res;
        }
      }

      /* shift to next bit */
      b >>= 1;
    }
  }
  else {
    for (x = 0; x < DIGIT_BIT; x++) {
      /* square */
      if ((res = mp_sqr (c, c)) != MP_OKAY) {
        mp_clear (&g);
        return res;
      }

      /* if the bit is set multiply */
      if ((b & (mp_digit) (((mp_digit)1) << (DIGIT_BIT - 1))) != 0) {
        if ((res = mp_mul (c, &g, c)) != MP_OKAY) {
           mp_clear (&g);
           return res;
        }
      }

      /* shift to next bit */
      b <<= 1;
    }
  } /* if ... else */

  mp_clear (&g);
  return MP_OKAY;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* calculate c = a**b  using a square-multiply algorithm */
int mp_expt_d_ex(const mp_int *a, mp_digit b, mp_int *c, int fast)
{
   int     res;
   unsigned int x;

   mp_int  g;

   if ((res = mp_init_copy(&g, a)) != MP_OKAY) {
      return res;
   }

   /* set initial result */
   mp_set(c, 1);

   if (fast != 0) {
      while (b > 0) {
         /* if the bit is set multiply */
         if ((b & 1) != 0) {
            if ((res = mp_mul(c, &g, c)) != MP_OKAY) {
               mp_clear(&g);
               return res;
            }
         }

         /* square */
         if (b > 1) {
            if ((res = mp_sqr(&g, &g)) != MP_OKAY) {
               mp_clear(&g);
               return res;
            }
         }

         /* shift to next bit */
         b >>= 1;
      }

   } else {
      for (x = 0; x < DIGIT_BIT; x++) {
         /* square */
         if ((res = mp_sqr(c, c)) != MP_OKAY) {
            mp_clear(&g);
            return res;
         }

         /* if the bit is set multiply */
         if ((b & (mp_digit)(((mp_digit)1) << (DIGIT_BIT - 1))) != 0) {
            if ((res = mp_mul(c, &g, c)) != MP_OKAY) {
               mp_clear(&g);
               return res;
            }
         }

         /* shift to next bit */
         b <<= 1;
      }
   } /* if ... else */

   mp_clear(&g);
   return MP_OKAY;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

/* 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) == MP_YES) || (dr !=  0)) {
    return mp_exptmod_fast (G, X, P, Y, dr);
  } else {
#endif
#ifdef BN_S_MP_EXPTMOD_C
    /* otherwise use the generic Barrett reduction technique */
    return s_mp_exptmod (G, X, P, Y, 0);
#else
    /* no exptmod for evens */
    return MP_VAL;
#endif
#ifdef BN_MP_EXPTMOD_FAST_C
  }
#endif
}

#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

/* 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(const mp_int *G, const mp_int *X, const 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) == MP_YES) || (dr !=  0)) {
      return mp_exptmod_fast(G, X, P, Y, dr);
   } else {
#endif
#ifdef BN_S_MP_EXPTMOD_C
      /* otherwise use the generic Barrett reduction technique */
      return s_mp_exptmod(G, X, P, Y, 0);
#else
      /* no exptmod for evens */
      return MP_VAL;
#endif
#ifdef BN_MP_EXPTMOD_FAST_C
   }
#endif
}

#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * 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_size(&M[1], P->alloc)) != 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_size(&M[x], P->alloc)) != 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_size (&res, P->alloc)) != 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;
     }

     /* now set M[1] to G * R mod m */
     if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
       goto LBL_RES;
     }
#else
     err = MP_VAL;
     goto LBL_RES;
#endif
  } 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


/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * 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(const mp_int *G, const mp_int *X, const 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 *,const 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_size(&M[1], P->alloc)) != 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_size(&M[x], P->alloc)) != 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_size(&res, P->alloc)) != 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;
      }

      /* now set M[1] to G * R mod m */
      if ((err = mp_mulmod(G, &res, P, &M[1])) != MP_OKAY) {
         goto LBL_RES;
      }
#else
      err = MP_VAL;
      goto LBL_RES;
#endif
   } 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


/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* Extended euclidean algorithm of (a, b) produces
   a*u1 + b*u2 = u3
 */
int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
{
   mp_int u1,u2,u3,v1,v2,v3,t1,t2,t3,q,tmp;
   int err;

   if ((err = mp_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 LBL_ERR; }



   /* initialize, (v1,v2,v3) = (0,1,b) */
   mp_set(&v2, 1);
   if ((err = mp_copy(b, &v3)) != MP_OKAY)                                        { goto LBL_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 LBL_ERR; }



       /* (t1,t2,t3) = (u1,u2,u3) - (v1,v2,v3)q */
       if ((err = mp_mul(&v1, &q, &tmp)) != MP_OKAY)                              { goto LBL_ERR; }


       if ((err = mp_sub(&u1, &tmp, &t1)) != MP_OKAY)                             { goto LBL_ERR; }


       if ((err = mp_mul(&v2, &q, &tmp)) != MP_OKAY)                              { goto LBL_ERR; }


       if ((err = mp_sub(&u2, &tmp, &t2)) != MP_OKAY)                             { goto LBL_ERR; }


       if ((err = mp_mul(&v3, &q, &tmp)) != MP_OKAY)                              { goto LBL_ERR; }


       if ((err = mp_sub(&u3, &tmp, &t3)) != MP_OKAY)                             { goto LBL_ERR; }



       /* (u1,u2,u3) = (v1,v2,v3) */
       if ((err = mp_copy(&v1, &u1)) != MP_OKAY)                                  { goto LBL_ERR; }


       if ((err = mp_copy(&v2, &u2)) != MP_OKAY)                                  { goto LBL_ERR; }


       if ((err = mp_copy(&v3, &u3)) != MP_OKAY)                                  { goto LBL_ERR; }



       /* (v1,v2,v3) = (t1,t2,t3) */
       if ((err = mp_copy(&t1, &v1)) != MP_OKAY)                                  { goto LBL_ERR; }


       if ((err = mp_copy(&t2, &v2)) != MP_OKAY)                                  { goto LBL_ERR; }


       if ((err = mp_copy(&t3, &v3)) != MP_OKAY)                                  { goto LBL_ERR; }


   }

   /* make sure U3 >= 0 */
   if (u3.sign == MP_NEG) {
       if ((err = mp_neg(&u1, &u1)) != MP_OKAY)                                   { goto LBL_ERR; }


       if ((err = mp_neg(&u2, &u2)) != MP_OKAY)                                   { goto LBL_ERR; }


       if ((err = mp_neg(&u3, &u3)) != MP_OKAY)                                   { goto LBL_ERR; }

   }


   /* copy result out */
   if (U1 != NULL) { mp_exch(U1, &u1); }


   if (U2 != NULL) { mp_exch(U2, &u2); }


   if (U3 != NULL) { mp_exch(U3, &u3); }



   err = MP_OKAY;
LBL_ERR:
   mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
   return err;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* Extended euclidean algorithm of (a, b) produces
   a*u1 + b*u2 = u3
 */
int mp_exteuclid(const mp_int *a, const 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 LBL_ERR;
   }

   /* initialize, (v1,v2,v3) = (0,1,b) */
   mp_set(&v2, 1);
   if ((err = mp_copy(b, &v3)) != MP_OKAY)                                        {
      goto LBL_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 LBL_ERR;
      }

      /* (t1,t2,t3) = (u1,u2,u3) - (v1,v2,v3)q */
      if ((err = mp_mul(&v1, &q, &tmp)) != MP_OKAY)                              {
         goto LBL_ERR;
      }
      if ((err = mp_sub(&u1, &tmp, &t1)) != MP_OKAY)                             {
         goto LBL_ERR;
      }
      if ((err = mp_mul(&v2, &q, &tmp)) != MP_OKAY)                              {
         goto LBL_ERR;
      }
      if ((err = mp_sub(&u2, &tmp, &t2)) != MP_OKAY)                             {
         goto LBL_ERR;
      }
      if ((err = mp_mul(&v3, &q, &tmp)) != MP_OKAY)                              {
         goto LBL_ERR;
      }
      if ((err = mp_sub(&u3, &tmp, &t3)) != MP_OKAY)                             {
         goto LBL_ERR;
      }

      /* (u1,u2,u3) = (v1,v2,v3) */
      if ((err = mp_copy(&v1, &u1)) != MP_OKAY)                                  {
         goto LBL_ERR;
      }
      if ((err = mp_copy(&v2, &u2)) != MP_OKAY)                                  {
         goto LBL_ERR;
      }
      if ((err = mp_copy(&v3, &u3)) != MP_OKAY)                                  {
         goto LBL_ERR;
      }

      /* (v1,v2,v3) = (t1,t2,t3) */
      if ((err = mp_copy(&t1, &v1)) != MP_OKAY)                                  {
         goto LBL_ERR;
      }
      if ((err = mp_copy(&t2, &v2)) != MP_OKAY)                                  {
         goto LBL_ERR;
      }
      if ((err = mp_copy(&t3, &v3)) != MP_OKAY)                                  {
         goto LBL_ERR;
      }
   }

   /* make sure U3 >= 0 */
   if (u3.sign == MP_NEG) {
      if ((err = mp_neg(&u1, &u1)) != MP_OKAY)                                   {
         goto LBL_ERR;
      }
      if ((err = mp_neg(&u2, &u2)) != MP_OKAY)                                   {
         goto LBL_ERR;
      }
      if ((err = mp_neg(&u3, &u3)) != MP_OKAY)                                   {
         goto LBL_ERR;
      }
   }

   /* copy result out */
   if (U1 != NULL) {
      mp_exch(U1, &u1);
   }
   if (U2 != NULL) {
      mp_exch(U2, &u2);
   }
   if (U3 != NULL) {
      mp_exch(U3, &u3);
   }

   err = MP_OKAY;
LBL_ERR:
   mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
   return err;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 */

#ifndef LTM_NO_FILE
/* 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

#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 */

#ifndef LTM_NO_FILE
/* 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

#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

#ifndef LTM_NO_FILE
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

#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

#ifndef LTM_NO_FILE
int mp_fwrite(const 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

#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* Greatest Common Divisor using the binary method */
int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int  u, v;
  int     k, u_lsb, v_lsb, res;

  /* 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) == MP_NO) {
     /* make sure v is the largest */
     if (mp_cmp_mag(&u, &v) == MP_GT) {
        /* swap u and v to make sure v is >= u */
        mp_exch(&u, &v);
     }
     
     /* subtract smallest from largest */
     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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* Greatest Common Divisor using the binary method */
int mp_gcd(const mp_int *a, const 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) == MP_NO) {
      /* make sure v is the largest */
      if (mp_cmp_mag(&u, &v) == MP_GT) {
         /* swap u and v to make sure v is >= u */
         mp_exch(&u, &v);
      }

      /* subtract smallest from largest */
      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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* get the lower 32-bits of an mp_int */
unsigned long mp_get_int(const mp_int * a)
{
  int i;
  mp_min_u32 res;

  if (a->used == 0) {
     return 0;
  }

  /* get number of digits of the lsb we have to read */
  i = MIN(a->used,(int)(((sizeof(unsigned long) * CHAR_BIT) + DIGIT_BIT - 1) / DIGIT_BIT)) - 1;

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

  while (--i >= 0) {
    res = (res << DIGIT_BIT) | DIGIT(a,i);
  }

  /* force result to 32-bits always so it is consistent on non 32-bit platforms */
  return res & 0xFFFFFFFFUL;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* get the lower 32-bits of an mp_int */
unsigned long mp_get_int(const mp_int *a)
{
   int i;
   mp_min_u32 res;

   if (a->used == 0) {
      return 0;
   }

   /* get number of digits of the lsb we have to read */
   i = MIN(a->used, (int)(((sizeof(unsigned long) * CHAR_BIT) + DIGIT_BIT - 1) / DIGIT_BIT)) - 1;

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

   while (--i >= 0) {
      res = (res << DIGIT_BIT) | DIGIT(a, i);
   }

   /* force result to 32-bits always so it is consistent on non 32-bit platforms */
   return res & 0xFFFFFFFFUL;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * 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(const 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

 * 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(const 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

 * 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 */
Tcl_WideUInt mp_get_long_long (const mp_int * a)
{
  int i;
  Tcl_WideUInt res;

  if (a->used == 0) {
     return 0;
  }

  /* get number of digits of the lsb we have to read */
  i = MIN(a->used,(int)(((sizeof(Tcl_WideUInt) * 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

 * 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 */
Tcl_WideUInt mp_get_long_long(const mp_int *a)
{
   int i;
   Tcl_WideUInt res;

   if (a->used == 0) {
      return 0;
   }

   /* get number of digits of the lsb we have to read */
   i = MIN(a->used, (int)(((sizeof(Tcl_WideUInt) * 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

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* creates "a" then copies b into it */
int mp_init_copy (mp_int * a, const mp_int * b)
{
  int     res;

  if ((res = mp_init_size (a, b->used)) != MP_OKAY) {
    return res;
  }

  if((res = mp_copy (b, a)) != MP_OKAY) {
    mp_clear(a);
  }

  return res;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* creates "a" then copies b into it */
int mp_init_copy(mp_int *a, const mp_int *b)
{
   int     res;

   if ((res = mp_init_size(a, b->used)) != MP_OKAY) {
      return res;
   }

   if ((res = mp_copy(b, a)) != MP_OKAY) {
      mp_clear(a);
   }

   return res;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */
#include <stdarg.h>

int mp_init_multi(mp_int *mp, ...) 
{
    mp_err res = MP_OKAY;      /* Assume ok until proven otherwise */
    int n = 0;                 /* Number of ok inits */
    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;
            
            /* now start cleaning up */            
            cur_arg = mp;
            va_start(clean_args, mp);
            while (n-- != 0) {
                mp_clear(cur_arg);
                cur_arg = va_arg(clean_args, mp_int*);
            }
            va_end(clean_args);
            res = MP_MEM;
            break;
        }
        n++;
        cur_arg = va_arg(args, mp_int*);
    }
    va_end(args);
    return res;                /* Assumed ok, if error flagged above. */
}

#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */
#include <stdarg.h>

int mp_init_multi(mp_int *mp, ...)
{
   mp_err res = MP_OKAY;      /* Assume ok until proven otherwise */
   int n = 0;                 /* Number of ok inits */
   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;

         /* now start cleaning up */
         cur_arg = mp;
         va_start(clean_args, mp);
         while (n-- != 0) {
            mp_clear(cur_arg);
            cur_arg = va_arg(clean_args, mp_int *);
         }
         va_end(clean_args);
         res = MP_MEM;
         break;
      }
      n++;
      cur_arg = va_arg(args, mp_int *);
   }
   va_end(args);
   return res;                /* Assumed ok, if error flagged above. */
}

#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* initialize and set a digit */
int mp_init_set (mp_int * a, mp_digit b)
{
  int err;
  if ((err = mp_init(a)) != MP_OKAY) {
     return err;
  }
  mp_set(a, b);
  return err;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* initialize and set a digit */
int mp_init_set(mp_int *a, mp_digit b)
{
   int err;
   if ((err = mp_init(a)) != MP_OKAY) {
      return err;
   }
   mp_set(a, b);
   return err;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* initialize and set a digit */
int mp_init_set_int (mp_int * a, unsigned long b)
{
  int err;
  if ((err = mp_init(a)) != MP_OKAY) {
     return err;
  }
  return mp_set_int(a, b);
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* initialize and set a digit */
int mp_init_set_int(mp_int *a, unsigned long b)
{
   int err;
   if ((err = mp_init(a)) != MP_OKAY) {
      return err;
   }
   return mp_set_int(a, b);
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* hac 14.61, pp608 */
int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
{
  /* b cannot be negative */
  if ((b->sign == MP_NEG) || (mp_iszero(b) == MP_YES)) {
    return MP_VAL;
  }

#ifdef BN_FAST_MP_INVMOD_C
  /* if the modulus is odd we can use a faster routine instead */
  if ((mp_isodd(b) == MP_YES) && (mp_cmp_d(b, 1) != MP_EQ)) {
    return fast_mp_invmod (a, b, c);
  }
#endif

#ifdef BN_MP_INVMOD_SLOW_C
  return mp_invmod_slow(a, b, c);
#else
  return MP_VAL;
#endif
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* hac 14.61, pp608 */
int mp_invmod(const mp_int *a, const mp_int *b, mp_int *c)
{
   /* b cannot be negative */
   if ((b->sign == MP_NEG) || (mp_iszero(b) == MP_YES)) {
      return MP_VAL;
   }

#ifdef BN_FAST_MP_INVMOD_C
   /* if the modulus is odd we can use a faster routine instead */
   if ((mp_isodd(b) == MP_YES) && (mp_cmp_d(b, 1) != MP_EQ)) {
      return fast_mp_invmod(a, b, c);
   }
#endif

#ifdef BN_MP_INVMOD_SLOW_C
   return mp_invmod_slow(a, b, c);
#else
   return MP_VAL;
#endif
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* hac 14.61, pp608 */
int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int  x, y, u, v, A, B, C, D;
  int     res;

  /* b cannot be negative */
  if ((b->sign == MP_NEG) || (mp_iszero(b) == MP_YES)) {
    return MP_VAL;
  }

  /* init temps */
  if ((res = mp_init_multi(&x, &y, &u, &v, 
                           &A, &B, &C, &D, NULL)) != MP_OKAY) {
     return res;
  }

  /* 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) == MP_YES) && (mp_iseven (&y) == MP_YES)) {
    res = MP_VAL;
    goto LBL_ERR;
  }

  /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
  if ((res = mp_copy (&x, &u)) != MP_OKAY) {
    goto LBL_ERR;
  }
  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) == MP_YES) {
    /* 4.1 u = u/2 */
    if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
      goto LBL_ERR;
    }
    /* 4.2 if A or B is odd then */
    if ((mp_isodd (&A) == MP_YES) || (mp_isodd (&B) == MP_YES)) {
      /* A = (A+y)/2, B = (B-x)/2 */
      if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
         goto LBL_ERR;
      }
      if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
         goto LBL_ERR;
      }
    }
    /* 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) == MP_YES) {
    /* 5.1 v = v/2 */
    if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
      goto LBL_ERR;
    }
    /* 5.2 if C or D is odd then */
    if ((mp_isodd (&C) == MP_YES) || (mp_isodd (&D) == MP_YES)) {
      /* C = (C+y)/2, D = (D-x)/2 */
      if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
         goto LBL_ERR;
      }
      if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
         goto LBL_ERR;
      }
    }
    /* 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) == MP_NO)
    goto top;

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

  /* if v != 1 then there is no inverse */
  if (mp_cmp_d (&v, 1) != MP_EQ) {
    res = MP_VAL;
    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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* hac 14.61, pp608 */
int mp_invmod_slow(const mp_int *a, const mp_int *b, mp_int *c)
{
   mp_int  x, y, u, v, A, B, C, D;
   int     res;

   /* b cannot be negative */
   if ((b->sign == MP_NEG) || (mp_iszero(b) == MP_YES)) {
      return MP_VAL;
   }

   /* init temps */
   if ((res = mp_init_multi(&x, &y, &u, &v,
                            &A, &B, &C, &D, NULL)) != MP_OKAY) {
      return res;
   }

   /* 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) == MP_YES) && (mp_iseven(&y) == MP_YES)) {
      res = MP_VAL;
      goto LBL_ERR;
   }

   /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
   if ((res = mp_copy(&x, &u)) != MP_OKAY) {
      goto LBL_ERR;
   }
   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) == MP_YES) {
      /* 4.1 u = u/2 */
      if ((res = mp_div_2(&u, &u)) != MP_OKAY) {
         goto LBL_ERR;
      }
      /* 4.2 if A or B is odd then */
      if ((mp_isodd(&A) == MP_YES) || (mp_isodd(&B) == MP_YES)) {
         /* A = (A+y)/2, B = (B-x)/2 */
         if ((res = mp_add(&A, &y, &A)) != MP_OKAY) {
            goto LBL_ERR;
         }
         if ((res = mp_sub(&B, &x, &B)) != MP_OKAY) {
            goto LBL_ERR;
         }
      }
      /* 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) == MP_YES) {
      /* 5.1 v = v/2 */
      if ((res = mp_div_2(&v, &v)) != MP_OKAY) {
         goto LBL_ERR;
      }
      /* 5.2 if C or D is odd then */
      if ((mp_isodd(&C) == MP_YES) || (mp_isodd(&D) == MP_YES)) {
         /* C = (C+y)/2, D = (D-x)/2 */
         if ((res = mp_add(&C, &y, &C)) != MP_OKAY) {
            goto LBL_ERR;
         }
         if ((res = mp_sub(&D, &x, &D)) != MP_OKAY) {
            goto LBL_ERR;
         }
      }
      /* 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) == MP_NO)
      goto top;

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

   /* if v != 1 then there is no inverse */
   if (mp_cmp_d(&v, 1) != MP_EQ) {
      res = MP_VAL;
      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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* Check if remainders are possible squares - fast exclude non-squares */
static const char rem_128[128] = {
 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
 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) != 0L)       goto ERR;
  if (((1L<<(r%13)) & 0x9E4L) != 0L)       goto ERR;
  if (((1L<<(r%17)) & 0x5CE8L) != 0L)      goto ERR;
  if (((1L<<(r%19)) & 0x4F50CL) != 0L)     goto ERR;
  if (((1L<<(r%23)) & 0x7ACCA0L) != 0L)    goto ERR;
  if (((1L<<(r%29)) & 0xC2EDD0CL) != 0L)   goto ERR;
  if (((1L<<(r%31)) & 0x6DE2B848L) != 0L)  goto ERR;

  /* Final check - is sqr(sqrt(arg)) == arg ? */
  if ((res = mp_sqrt(arg,&t)) != MP_OKAY) {
     goto ERR;
  }
  if ((res = mp_sqr(&t,&t)) != MP_OKAY) {
     goto ERR;
  }

  *ret = (mp_cmp_mag(&t,arg) == MP_EQ) ? MP_YES : MP_NO;

ERR:mp_clear(&t);
  return res;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* Check if remainders are possible squares - fast exclude non-squares */
static const char rem_128[128] = {
   0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
   0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
   1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
   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(const 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) != 0L)       goto ERR;
   if (((1L<<(r%13)) & 0x9E4L) != 0L)       goto ERR;
   if (((1L<<(r%17)) & 0x5CE8L) != 0L)      goto ERR;
   if (((1L<<(r%19)) & 0x4F50CL) != 0L)     goto ERR;
   if (((1L<<(r%23)) & 0x7ACCA0L) != 0L)    goto ERR;
   if (((1L<<(r%29)) & 0xC2EDD0CL) != 0L)   goto ERR;
   if (((1L<<(r%31)) & 0x6DE2B848L) != 0L)  goto ERR;

   /* Final check - is sqr(sqrt(arg)) == arg ? */
   if ((res = mp_sqrt(arg, &t)) != MP_OKAY) {
      goto ERR;
   }
   if ((res = mp_sqr(&t, &t)) != MP_OKAY) {
      goto ERR;
   }

   *ret = (mp_cmp_mag(&t, arg) == MP_EQ) ? MP_YES : MP_NO;
ERR:
   mp_clear(&t);
   return res;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 */

/* computes the jacobi c = (a | n) (or Legendre if n is prime)
 * HAC pp. 73 Algorithm 2.149
 * HAC is wrong here, as the special case of (0 | 1) is not
 * handled correctly.
 */
int mp_jacobi (mp_int * a, mp_int * n, int *c)
{
  mp_int  a1, p1;
  int     k, s, r, res;
  mp_digit residue;

  /* if a < 0 return MP_VAL */
  if (mp_isneg(a) == MP_YES) {
     return MP_VAL;
  }

  /* if n <= 0 return MP_VAL */
  if (mp_cmp_d(n, 0) != MP_GT) {
     return MP_VAL;
  }

  /* step 1. handle case of a == 0 */
  if (mp_iszero (a) == MP_YES) {
     /* special case of a == 0 and n == 1 */
     if (mp_cmp_d (n, 1) == MP_EQ) {
       *c = 1;
     } else {
       *c = 0;
     }
     return MP_OKAY;
  }

  /* step 2.  if a == 1, return 1 */
  if (mp_cmp_d (a, 1) == MP_EQ) {
    *c = 1;
    return MP_OKAY;
  }

  /* 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 = n->dp[0] & 7;

    if ((residue == 1) || (residue == 7)) {
      s = 1;
    } else if ((residue == 3) || (residue == 5)) {
      s = -1;
    }
  }

  /* step 5.  if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
  if ( ((n->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) {
    s = -s;
  }

  /* if a1 == 1 we're done */
  if (mp_cmp_d (&a1, 1) == MP_EQ) {
    *c = s;
  } else {
    /* n1 = n mod a1 */
    if ((res = mp_mod (n, &a1, &p1)) != MP_OKAY) {
      goto LBL_P1;
    }
    if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) {
      goto LBL_P1;
    }
    *c = s * r;
  }

  /* done */
  res = MP_OKAY;
LBL_P1:mp_clear (&p1);

LBL_A1:mp_clear (&a1);

  return res;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 */

/* computes the jacobi c = (a | n) (or Legendre if n is prime)
 * HAC pp. 73 Algorithm 2.149
 * HAC is wrong here, as the special case of (0 | 1) is not
 * handled correctly.
 */
int mp_jacobi(const mp_int *a, const mp_int *n, int *c)
{
   mp_int  a1, p1;
   int     k, s, r, res;
   mp_digit residue;

   /* if a < 0 return MP_VAL */
   if (mp_isneg(a) == MP_YES) {
      return MP_VAL;
   }

   /* if n <= 0 return MP_VAL */
   if (mp_cmp_d(n, 0) != MP_GT) {
      return MP_VAL;
   }

   /* step 1. handle case of a == 0 */
   if (mp_iszero(a) == MP_YES) {
      /* special case of a == 0 and n == 1 */
      if (mp_cmp_d(n, 1) == MP_EQ) {
         *c = 1;
      } else {
         *c = 0;
      }
      return MP_OKAY;
   }

   /* step 2.  if a == 1, return 1 */
   if (mp_cmp_d(a, 1) == MP_EQ) {
      *c = 1;
      return MP_OKAY;
   }

   /* 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 = n->dp[0] & 7;

      if ((residue == 1) || (residue == 7)) {
         s = 1;
      } else if ((residue == 3) || (residue == 5)) {
         s = -1;
      }
   }

   /* step 5.  if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
   if (((n->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) {
      s = -s;
   }

   /* if a1 == 1 we're done */
   if (mp_cmp_d(&a1, 1) == MP_EQ) {
      *c = s;
   } else {
      /* n1 = n mod a1 */
      if ((res = mp_mod(n, &a1, &p1)) != MP_OKAY) {
         goto LBL_P1;
      }
      if ((res = mp_jacobi(&p1, &a1, &r)) != MP_OKAY) {
         goto LBL_P1;
      }
      *c = s * r;
   }

   /* done */
   res = MP_OKAY;
LBL_P1:
   mp_clear(&p1);
LBL_A1:
   mp_clear(&a1);
   return res;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* c = |a| * |b| using Karatsuba Multiplication using 
 * three half size multiplications
 *
 * Let B represent the radix [e.g. 2**DIGIT_BIT] and 
 * let n represent half of the number of digits in 
 * 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;

  {
    int x;
    mp_digit *tmpa, *tmpb, *tmpx, *tmpy;

    /* we copy the digits directly instead of using higher level functions
     * since we also need to shift the digits
     */
    tmpa = a->dp;
    tmpb = b->dp;

    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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* c = |a| * |b| using Karatsuba Multiplication using
 * three half size multiplications
 *
 * Let B represent the radix [e.g. 2**DIGIT_BIT] and
 * let n represent half of the number of digits in
 * 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(const mp_int *a, const 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;

   {
      int x;
      mp_digit *tmpa, *tmpb, *tmpx, *tmpy;

      /* we copy the digits directly instead of using higher level functions
       * since we also need to shift the digits
       */
      tmpa = a->dp;
      tmpb = b->dp;

      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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* Karatsuba squaring, computes b = a*a using three 
 * half size squarings
 *
 * See comments of karatsuba_mul for details.  It 
 * is essentially the same algorithm but merely 
 * 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;

  {
    int x;
    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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* Karatsuba squaring, computes b = a*a using three
 * half size squarings
 *
 * See comments of karatsuba_mul for details.  It
 * is essentially the same algorithm but merely
 * tuned to perform recursive squarings.
 */
int mp_karatsuba_sqr(const 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;

   {
      int x;
      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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* computes least common multiple as |a*b|/(a, b) */
int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
{
  int     res;
  mp_int  t1, t2;


  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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* computes least common multiple as |a*b|/(a, b) */
int mp_lcm(const mp_int *a, const 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

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* shift left a certain amount of digits */
int mp_lshd (mp_int * a, int b)
{
  int     x, res;

  /* if its less than zero return */
  if (b <= 0) {
    return MP_OKAY;
  }

  /* grow to fit the new digits */
  if (a->alloc < (a->used + b)) {
     if ((res = mp_grow (a, a->used + b)) != MP_OKAY) {
       return res;
     }
  }

  {
    mp_digit *top, *bottom;

    /* increment the used by the shift amount then copy upwards */
    a->used += b;

    /* top */
    top = a->dp + a->used - 1;

    /* base */
    bottom = (a->dp + a->used - 1) - b;

    /* much like mp_rshd this is implemented using a sliding window
     * except the window goes the otherway around.  Copying from
     * the bottom to the top.  see bn_mp_rshd.c for more info.
     */
    for (x = a->used - 1; x >= b; x--) {
      *top-- = *bottom--;
    }

    /* zero the lower digits */
    top = a->dp;
    for (x = 0; x < b; x++) {
      *top++ = 0;
    }
  }
  return MP_OKAY;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* shift left a certain amount of digits */
int mp_lshd(mp_int *a, int b)
{
   int     x, res;

   /* if its less than zero return */
   if (b <= 0) {
      return MP_OKAY;
   }

   /* grow to fit the new digits */
   if (a->alloc < (a->used + b)) {
      if ((res = mp_grow(a, a->used + b)) != MP_OKAY) {
         return res;
      }
   }

   {
      mp_digit *top, *bottom;

      /* increment the used by the shift amount then copy upwards */
      a->used += b;

      /* top */
      top = a->dp + a->used - 1;

      /* base */
      bottom = (a->dp + a->used - 1) - b;

      /* much like mp_rshd this is implemented using a sliding window
       * except the window goes the otherway around.  Copying from
       * the bottom to the top.  see bn_mp_rshd.c for more info.
       */
      for (x = a->used - 1; x >= b; x--) {
         *top-- = *bottom--;
      }

      /* zero the lower digits */
      top = a->dp;
      for (x = 0; x < b; x++) {
         *top++ = 0;
      }
   }
   return MP_OKAY;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* c = a mod b, 0 <= c < b if b > 0, b < c <= 0 if b < 0 */
int
mp_mod (mp_int * a, mp_int * b, mp_int * c)
{
  mp_int  t;
  int     res;

  if ((res = mp_init_size (&t, b->used)) != MP_OKAY) {
    return res;
  }

  if ((res = mp_div (a, b, NULL, &t)) != MP_OKAY) {
    mp_clear (&t);
    return res;
  }

  if ((mp_iszero(&t) != MP_NO) || (t.sign == b->sign)) {
    res = MP_OKAY;
    mp_exch (&t, c);
  } else {
    res = mp_add (b, &t, c);
  }

  mp_clear (&t);
  return res;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* c = a mod b, 0 <= c < b if b > 0, b < c <= 0 if b < 0 */
int mp_mod(const mp_int *a, const mp_int *b, mp_int *c)

{
   mp_int  t;
   int     res;

   if ((res = mp_init_size(&t, b->used)) != MP_OKAY) {
      return res;
   }

   if ((res = mp_div(a, b, NULL, &t)) != MP_OKAY) {
      mp_clear(&t);
      return res;
   }

   if ((mp_iszero(&t) != MP_NO) || (t.sign == b->sign)) {
      res = MP_OKAY;
      mp_exch(&t, c);
   } else {
      res = mp_add(b, &t, c);
   }

   mp_clear(&t);
   return res;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* calc a value mod 2**b */
int
mp_mod_2d (const mp_int * a, int b, mp_int * c)
{
  int     x, res;

  /* if b is <= 0 then zero the int */
  if (b <= 0) {
    mp_zero (c);
    return MP_OKAY;
  }

  /* if the modulus is larger than the value than return */
  if (b >= (int) (a->used * DIGIT_BIT)) {
    res = mp_copy (a, c);
    return res;
  }

  /* copy */
  if ((res = mp_copy (a, c)) != MP_OKAY) {
    return res;
  }

  /* zero digits above the last digit of the modulus */
  for (x = (b / DIGIT_BIT) + (((b % DIGIT_BIT) == 0) ? 0 : 1); x < c->used; x++) {
    c->dp[x] = 0;
  }
  /* clear the digit that is not completely outside/inside the modulus */
  c->dp[b / DIGIT_BIT] &=
    (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1));
  mp_clamp (c);
  return MP_OKAY;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* calc a value mod 2**b */

int mp_mod_2d(const mp_int *a, int b, mp_int *c)
{
   int     x, res;

   /* if b is <= 0 then zero the int */
   if (b <= 0) {
      mp_zero(c);
      return MP_OKAY;
   }

   /* if the modulus is larger than the value than return */
   if (b >= (int)(a->used * DIGIT_BIT)) {
      res = mp_copy(a, c);
      return res;
   }

   /* copy */
   if ((res = mp_copy(a, c)) != MP_OKAY) {
      return res;
   }

   /* zero digits above the last digit of the modulus */
   for (x = (b / DIGIT_BIT) + (((b % DIGIT_BIT) == 0) ? 0 : 1); x < c->used; x++) {
      c->dp[x] = 0;
   }
   /* clear the digit that is not completely outside/inside the modulus */
   c->dp[b / DIGIT_BIT] &=
      (mp_digit)((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1));
   mp_clamp(c);
   return MP_OKAY;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

int
mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
{
  return mp_div_d(a, b, NULL, c);
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
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 *
 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */


int mp_mod_d(const mp_int *a, mp_digit b, mp_digit *c)
{
   return mp_div_d(a, b, NULL, c);
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
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/*
 * shifts with subtractions when the result is greater than b.
 *
 * The method is slightly modified to shift B unconditionally upto just under
 * the leading bit of b.  This saves alot of multiple precision shifting.
 */
int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
{
  int     x, bits, res;

  /* how many bits of last digit does b use */
  bits = mp_count_bits (b) % DIGIT_BIT;

  if (b->used > 1) {
     if ((res = mp_2expt (a, ((b->used - 1) * DIGIT_BIT) + bits - 1)) != MP_OKAY) {
        return res;
     }
  } else {
     mp_set(a, 1);
     bits = 1;
  }


  /* now compute C = A * B mod b */
  for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
    if ((res = mp_mul_2 (a, a)) != MP_OKAY) {
      return res;
    }
    if (mp_cmp_mag (a, b) != MP_LT) {
      if ((res = s_mp_sub (a, b, a)) != MP_OKAY) {
        return res;
      }
    }
  }

  return MP_OKAY;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

/*
 * shifts with subtractions when the result is greater than b.
 *
 * The method is slightly modified to shift B unconditionally upto just under
 * the leading bit of b.  This saves alot of multiple precision shifting.
 */
int mp_montgomery_calc_normalization(mp_int *a, const mp_int *b)
{
   int     x, bits, res;

   /* how many bits of last digit does b use */
   bits = mp_count_bits(b) % DIGIT_BIT;

   if (b->used > 1) {
      if ((res = mp_2expt(a, ((b->used - 1) * DIGIT_BIT) + bits - 1)) != MP_OKAY) {
         return res;
      }
   } else {
      mp_set(a, 1);
      bits = 1;
   }


   /* now compute C = A * B mod b */
   for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
      if ((res = mp_mul_2(a, a)) != MP_OKAY) {
         return res;
      }
      if (mp_cmp_mag(a, b) != MP_LT) {
         if ((res = s_mp_sub(a, b, a)) != MP_OKAY) {
            return res;
         }
      }
   }

   return MP_OKAY;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* computes xR**-1 == x (mod N) via Montgomery Reduction */
int
mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
{
  int     ix, res, digs;
  mp_digit mu;

  /* can the fast reduction [comba] method be used?
   *
   * Note that unlike in mul you're safely allowed *less*
   * than the available columns [255 per default] since carries
   * are fixed up in the inner loop.
   */
  digs = (n->used * 2) + 1;
  if ((digs < MP_WARRAY) &&
      (n->used <
      (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) {
    return fast_mp_montgomery_reduce (x, n, rho);
  }

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

  for (ix = 0; ix < n->used; ix++) {
    /* mu = ai * rho mod b
     *
     * The value of rho must be precalculated via
     * montgomery_setup() such that
     * it equals -1/n0 mod b this allows the
     * following inner loop to reduce the
     * input one digit at a time
     */
    mu = (mp_digit) (((mp_word)x->dp[ix] * (mp_word)rho) & MP_MASK);

    /* a = a + mu * m * b**i */
    {
      int iy;
      mp_digit *tmpn, *tmpx, u;
      mp_word r;

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

      /* alias for the digits of x [the input] */
      tmpx = x->dp + ix;

      /* set the carry to zero */
      u = 0;

      /* Multiply and add in place */
      for (iy = 0; iy < n->used; iy++) {
        /* compute product and sum */
        r       = ((mp_word)mu * (mp_word)*tmpn++) +
                   (mp_word) u + (mp_word) *tmpx;

        /* get carry */
        u       = (mp_digit)(r >> ((mp_word) DIGIT_BIT));

        /* fix digit */
        *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
      }
      /* At this point the ix'th digit of x should be zero */


      /* propagate carries upwards as required*/
      while (u != 0) {
        *tmpx   += u;
        u        = *tmpx >> DIGIT_BIT;
        *tmpx++ &= MP_MASK;
      }
    }
  }

  /* at this point the n.used'th least
   * significant digits of x are all zero
   * which means we can shift x to the
   * right by n.used digits and the
   * residue is unchanged.
   */

  /* x = x/b**n.used */
  mp_clamp(x);
  mp_rshd (x, n->used);

  /* if x >= n then x = x - n */
  if (mp_cmp_mag (x, n) != MP_LT) {
    return s_mp_sub (x, n, x);
  }

  return MP_OKAY;
}
#endif

/* ref:         $Format:%D$ */
/* git commit:  $Format:%H$ */
/* commit time: $Format:%ai$ */

 * The library is free for all purposes without any express
 * guarantee it works.
 *
 * Tom St Denis, [email protected], http://libtom.org
 */

/* computes xR**-1 == x (mod N) via Montgomery Reduction */
int mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho)

{
   int     ix, res, digs;
   mp_digit mu;

   /* can the fast reduction [comba] method be used?
    *
    * Note that unlike in mul you're safely allowed *less*
    * than the available columns [255 per default] since carries
    * are fixed up in the inner loop.
    */
   digs = (n->used * 2) + 1;
   if ((digs < MP_WARRAY) &&
       (n->used <
        (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) {
      return fast_mp_montgomery_reduce(x, n, rho);
   }

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

   for (ix = 0; ix < n->used; ix++) {
      /* mu = ai * rho mod b
       *
       * The value of rho must be precalculated via
       * montgomery_setup() such that
       * it equals -1/n0 mod b this allows the
       * following inner loop to reduce the
       * input one digit at a time
       */
      mu = (mp_digit)(((mp_word)x->dp[ix] * (mp_word)rho) & MP_MASK);

      /* a = a + mu * m * b**i */
      {
         int iy;
         mp_digit *tmpn, *tmpx, u;
         mp_word r;

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

         /* alias for the digits of x [the input] */
         tmpx = x->dp + ix;

         /* set the carry to zero */
         u = 0;

         /* Multiply and add in place */
         for (iy = 0; iy < n->used; iy++) {
            /* compute product and sum */
            r       = ((mp_word)mu * (mp_word)*tmpn++) +
                      (mp_word) u + (mp_word) *tmpx;

            /* get carry */
            u       = (mp_digit)(r >> ((mp_word) DIGIT_BIT));

            /* fix digit */
            *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
         }
         /* At this point the ix'th digit of x should be zero */


         /* propagate carries upwards as required*/
         while (u != 0) {
            *tmpx   += u;
            u        = *tmpx >> DIGIT_BIT;
            *tmpx++ &= MP_MASK;
         }
      }
   }

   /* at this point the n.used'th least
    * significant digits of x are all zero
    * which means we can shift x to the
    * right by n.used digits and the
    * residue is unchanged.
    */

   /* x = x/b**n.used */
   mp_clamp(x);
   mp_rshd(x, n->used);

   /* if x >= n then x = x - n */
   if (mp_cmp_mag(x, n) != MP_LT) {
      return s_mp_sub(x, n, x);
   }

   return MP_OKAY;
}
#endif

/* ref:         $Format:%D$ */
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/* commit time: $Format:%ai$ */