/* crypto/bn/bn_mul.c */

 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)

  * All rights reserved.

  *

  * This package is an SSL implementation written

  * by Eric Young (eay@cryptsoft.com).

  * The implementation was written so as to conform with Netscapes SSL.

  * 

  * This library is free for commercial and non-commercial use as long as

  * the following conditions are aheared to.  The following conditions

  * apply to all code found in this distribution, be it the RC4, RSA,

  * lhash, DES, etc., code; not just the SSL code.  The SSL documentation

  * included with this distribution is covered by the same copyright terms

  * except that the holder is Tim Hudson (tjh@cryptsoft.com).

  * 

  * Copyright remains Eric Young's, and as such any Copyright notices in

  * the code are not to be removed.

  * If this package is used in a product, Eric Young should be given attribution

  * as the author of the parts of the library used.

  * This can be in the form of a textual message at program startup or

  * in documentation (online or textual) provided with the package.

  * 

  * Redistribution and use in source and binary forms, with or without

  * modification, are permitted provided that the following conditions

  * are met:

  * 1. Redistributions of source code must retain the copyright

  *    notice, this list of conditions and the following disclaimer.

  * 2. Redistributions in binary form must reproduce the above copyright

  *    notice, this list of conditions and the following disclaimer in the

  *    documentation and/or other materials provided with the distribution.

  * 3. All advertising materials mentioning features or use of this software

  *    must display the following acknowledgement:

  *    "This product includes cryptographic software written by

  *     Eric Young (eay@cryptsoft.com)"

  *    The word 'cryptographic' can be left out if the rouines from the library

  *    being used are not cryptographic related :-).

  * 4. If you include any Windows specific code (or a derivative thereof) from 

  *    the apps directory (application code) you must include an acknowledgement:

  *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"

  * 

  * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND

  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE

  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE

  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE

  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL

  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS

  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)

  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT

  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY

  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF

  * SUCH DAMAGE.

  * 

  * The licence and distribution terms for any publically available version or

  * derivative of this code cannot be changed.  i.e. this code cannot simply be

  * copied and put under another distribution licence

  * [including the GNU Public Licence.]

  */

 #ifndef BN_DEBUG

 # undef NDEBUG /* avoid conflicting definitions */

 # define NDEBUG

 #endif

 #include <stdio.h>

 #include <assert.h>

 #include "cryptlib.h"

 #include "bn_lcl.h"

 #if defined(OPENSSL_NO_ASM) || !defined(OPENSSL_BN_ASM_PART_WORDS)

 /* Here follows specialised variants of bn_add_words() and

    bn_sub_words().  They have the property performing operations on

    arrays of different sizes.  The sizes of those arrays is expressed through

    cl, which is the common length ( basicall, min(len(a),len(b)) ), and dl,

    which is the delta between the two lengths, calculated as len(a)-len(b).

    All lengths are the number of BN_ULONGs...  For the operations that require

    a result array as parameter, it must have the length cl+abs(dl).

    These functions should probably end up in bn_asm.c as soon as there are

    assembler counterparts for the systems that use assembler files.  */

 EXPORT_C BN_ULONG bn_sub_part_words(BN_ULONG *r,

 	const BN_ULONG *a, const BN_ULONG *b,

 	int cl, int dl)

 	{

 	BN_ULONG c, t;

 	assert(cl >= 0);

 	c = bn_sub_words(r, a, b, cl);

 	if (dl == 0)

 		return c;

 	r += cl;

 	a += cl;

 	b += cl;

 	if (dl < 0)

 		{

 #ifdef BN_COUNT

 		fprintf(stderr, "  bn_sub_part_words %d + %d (dl < 0, c = %d)\n", cl, dl, c);

 #endif

 		for (;;)

 			{

 			t = b[0];

 			r[0] = (0-t-c)&BN_MASK2;

 			if (t != 0) c=1;

 			if (++dl >= 0) break;

 			t = b[1];

 			r[1] = (0-t-c)&BN_MASK2;

 			if (t != 0) c=1;

 			if (++dl >= 0) break;

 			t = b[2];

 			r[2] = (0-t-c)&BN_MASK2;

 			if (t != 0) c=1;

 			if (++dl >= 0) break;

 			t = b[3];

 			r[3] = (0-t-c)&BN_MASK2;

 			if (t != 0) c=1;

 			if (++dl >= 0) break;

 			b += 4;

 			r += 4;

 			}

 		}

 	else

 		{

 		int save_dl = dl;

 #ifdef BN_COUNT

 		fprintf(stderr, "  bn_sub_part_words %d + %d (dl > 0, c = %d)\n", cl, dl, c);

 #endif

 		while(c)

 			{

 			t = a[0];

 			r[0] = (t-c)&BN_MASK2;

 			if (t != 0) c=0;

 			if (--dl <= 0) break;

 			t = a[1];

 			r[1] = (t-c)&BN_MASK2;

 			if (t != 0) c=0;

 			if (--dl <= 0) break;

 			t = a[2];

 			r[2] = (t-c)&BN_MASK2;

 			if (t != 0) c=0;

 			if (--dl <= 0) break;

 			t = a[3];

 			r[3] = (t-c)&BN_MASK2;

 			if (t != 0) c=0;

 			if (--dl <= 0) break;

 			save_dl = dl;

 			a += 4;

 			r += 4;

 			}

 		if (dl > 0)

 			{

 #ifdef BN_COUNT

 			fprintf(stderr, "  bn_sub_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);

 #endif

 			if (save_dl > dl)

 				{

 				switch (save_dl - dl)

 					{

 				case 1:

 					r[1] = a[1];

 					if (--dl <= 0) break;

 				case 2:

 					r[2] = a[2];

 					if (--dl <= 0) break;

 				case 3:

 					r[3] = a[3];

 					if (--dl <= 0) break;

 					}

 				a += 4;

 				r += 4;

 				}

 			}

 		if (dl > 0)

 			{

 #ifdef BN_COUNT

 			fprintf(stderr, "  bn_sub_part_words %d + %d (dl > 0, copy)\n", cl, dl);

 #endif

 			for(;;)

 				{

 				r[0] = a[0];

 				if (--dl <= 0) break;

 				r[1] = a[1];

 				if (--dl <= 0) break;

 				r[2] = a[2];

 				if (--dl <= 0) break;

 				r[3] = a[3];

 				if (--dl <= 0) break;

 				a += 4;

 				r += 4;

 				}

 			}

 		}

 	return c;

 	}

 #endif

 EXPORT_C BN_ULONG bn_add_part_words(BN_ULONG *r,

 	const BN_ULONG *a, const BN_ULONG *b,

 	int cl, int dl)

 	{

 	BN_ULONG c, l, t;

 	assert(cl >= 0);

 	c = bn_add_words(r, a, b, cl);

 	if (dl == 0)

 		return c;

 	r += cl;

 	a += cl;

 	b += cl;

 	if (dl < 0)

 		{

 		int save_dl = dl;

 #ifdef BN_COUNT

 		fprintf(stderr, "  bn_add_part_words %d + %d (dl < 0, c = %d)\n", cl, dl, c);

 #endif

 		while (c)

 			{

 			l=(c+b[0])&BN_MASK2;

 			c=(l < c);

 			r[0]=l;

 			if (++dl >= 0) break;

 			l=(c+b[1])&BN_MASK2;

 			c=(l < c);

 			r[1]=l;

 			if (++dl >= 0) break;

 			l=(c+b[2])&BN_MASK2;

 			c=(l < c);

 			r[2]=l;

 			if (++dl >= 0) break;

 			l=(c+b[3])&BN_MASK2;

 			c=(l < c);

 			r[3]=l;

 			if (++dl >= 0) break;

 			save_dl = dl;

 			b+=4;

 			r+=4;

 			}

 		if (dl < 0)

 			{

 #ifdef BN_COUNT

 			fprintf(stderr, "  bn_add_part_words %d + %d (dl < 0, c == 0)\n", cl, dl);

 #endif

 			if (save_dl < dl)

 				{

 				switch (dl - save_dl)

 					{

 				case 1:

 					r[1] = b[1];

 					if (++dl >= 0) break;

 				case 2:

 					r[2] = b[2];

 					if (++dl >= 0) break;

 				case 3:

 					r[3] = b[3];

 					if (++dl >= 0) break;

 					}

 				b += 4;

 				r += 4;

 				}

 			}

 		if (dl < 0)

 			{

 #ifdef BN_COUNT

 			fprintf(stderr, "  bn_add_part_words %d + %d (dl < 0, copy)\n", cl, dl);

 #endif

 			for(;;)

 				{

 				r[0] = b[0];

 				if (++dl >= 0) break;

 				r[1] = b[1];

 				if (++dl >= 0) break;

 				r[2] = b[2];

 				if (++dl >= 0) break;

 				r[3] = b[3];

 				if (++dl >= 0) break;

 				b += 4;

 				r += 4;

 				}

 			}

 		}

 	else

 		{

 		int save_dl = dl;

 #ifdef BN_COUNT

 		fprintf(stderr, "  bn_add_part_words %d + %d (dl > 0)\n", cl, dl);

 #endif

 		while (c)

 			{

 			t=(a[0]+c)&BN_MASK2;

 			c=(t < c);

 			r[0]=t;

 			if (--dl <= 0) break;

 			t=(a[1]+c)&BN_MASK2;

 			c=(t < c);

 			r[1]=t;

 			if (--dl <= 0) break;

 			t=(a[2]+c)&BN_MASK2;

 			c=(t < c);

 			r[2]=t;

 			if (--dl <= 0) break;

 			t=(a[3]+c)&BN_MASK2;

 			c=(t < c);

 			r[3]=t;

 			if (--dl <= 0) break;

 			save_dl = dl;

 			a+=4;

 			r+=4;

 			}

 #ifdef BN_COUNT

 		fprintf(stderr, "  bn_add_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);

 #endif

 		if (dl > 0)

 			{

 			if (save_dl > dl)

 				{

 				switch (save_dl - dl)

 					{

 				case 1:

 					r[1] = a[1];

 					if (--dl <= 0) break;

 				case 2:

 					r[2] = a[2];

 					if (--dl <= 0) break;

 				case 3:

 					r[3] = a[3];

 					if (--dl <= 0) break;

 					}

 				a += 4;

 				r += 4;

 				}

 			}

 		if (dl > 0)

 			{

 #ifdef BN_COUNT

 			fprintf(stderr, "  bn_add_part_words %d + %d (dl > 0, copy)\n", cl, dl);

 #endif

 			for(;;)

 				{

 				r[0] = a[0];

 				if (--dl <= 0) break;

 				r[1] = a[1];

 				if (--dl <= 0) break;

 				r[2] = a[2];

 				if (--dl <= 0) break;

 				r[3] = a[3];

 				if (--dl <= 0) break;

 				a += 4;

 				r += 4;

 				}

 			}

 		}

 	return c;

 	}

 #ifdef BN_RECURSION

 /* Karatsuba recursive multiplication algorithm

  * (cf. Knuth, The Art of Computer Programming, Vol. 2) */

 /* r is 2*n2 words in size,

  * a and b are both n2 words in size.

  * n2 must be a power of 2.

  * We multiply and return the result.

  * t must be 2*n2 words in size

  * We calculate

  * a[0]*b[0]

  * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])

  * a[1]*b[1]

  */

 EXPORT_C void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,

 	int dna, int dnb, BN_ULONG *t)

 	{

 	int n=n2/2,c1,c2;

 	int tna=n+dna, tnb=n+dnb;

 	unsigned int neg,zero;

 	BN_ULONG ln,lo,*p;

 # ifdef BN_COUNT

 	fprintf(stderr," bn_mul_recursive %d * %d\n",n2,n2);

 # endif

 # ifdef BN_MUL_COMBA

 #  if 0

 	if (n2 == 4)

 		{

 		bn_mul_comba4(r,a,b);

 		return;

 		}

 #  endif

 	/* Only call bn_mul_comba 8 if n2 == 8 and the

 	 * two arrays are complete [steve]

 	 */

 	if (n2 == 8 && dna == 0 && dnb == 0)

 		{

 		bn_mul_comba8(r,a,b);

 		return; 

 		}

 # endif /* BN_MUL_COMBA */

 	/* Else do normal multiply */

 	if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)

 		{

 		bn_mul_normal(r,a,n2+dna,b,n2+dnb);

 		if ((dna + dnb) < 0)

 			memset(&r[2*n2 + dna + dnb], 0,

 				sizeof(BN_ULONG) * -(dna + dnb));

 		return;

 		}

 	/* r=(a[0]-a[1])*(b[1]-b[0]) */

 	c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);

 	c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);

 	zero=neg=0;

 	switch (c1*3+c2)

 		{

 	case -4:

 		bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */

 		bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */

 		break;

 	case -3:

 		zero=1;

 		break;

 	case -2:

 		bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */

 		bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n); /* + */

 		neg=1;

 		break;

 	case -1:

 	case 0:

 	case 1:

 		zero=1;

 		break;

 	case 2:

 		bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna); /* + */

 		bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */

 		neg=1;

 		break;

 	case 3:

 		zero=1;

 		break;

 	case 4:

 		bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna);

 		bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n);

 		break;

 		}

 # ifdef BN_MUL_COMBA

 	if (n == 4 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba4 could take

 					       extra args to do this well */

 		{

 		if (!zero)

 			bn_mul_comba4(&(t[n2]),t,&(t[n]));

 		else

 			memset(&(t[n2]),0,8*sizeof(BN_ULONG));

 		bn_mul_comba4(r,a,b);

 		bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n]));

 		}

 	else if (n == 8 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba8 could

 						    take extra args to do this

 						    well */

 		{

 		if (!zero)

 			bn_mul_comba8(&(t[n2]),t,&(t[n]));

 		else

 			memset(&(t[n2]),0,16*sizeof(BN_ULONG));

 		bn_mul_comba8(r,a,b);

 		bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n]));

 		}

 	else

 # endif /* BN_MUL_COMBA */

 		{

 		p= &(t[n2*2]);

 		if (!zero)

 			bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);

 		else

 			memset(&(t[n2]),0,n2*sizeof(BN_ULONG));

 		bn_mul_recursive(r,a,b,n,0,0,p);

 		bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,dna,dnb,p);

 		}

 	/* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign

 	 * r[10] holds (a[0]*b[0])

 	 * r[32] holds (b[1]*b[1])

 	 */

 	c1=(int)(bn_add_words(t,r,&(r[n2]),n2));

 	if (neg) /* if t[32] is negative */

 		{

 		c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));

 		}

 	else

 		{

 		/* Might have a carry */

 		c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));

 		}

 	/* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])

 	 * r[10] holds (a[0]*b[0])

 	 * r[32] holds (b[1]*b[1])

 	 * c1 holds the carry bits

 	 */

 	c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));

 	if (c1)

 		{

 		p= &(r[n+n2]);

 		lo= *p;

 		ln=(lo+c1)&BN_MASK2;

 		*p=ln;

 		/* The overflow will stop before we over write

 		 * words we should not overwrite */

 		if (ln < (BN_ULONG)c1)

 			{

 			do	{

 				p++;

 				lo= *p;

 				ln=(lo+1)&BN_MASK2;

 				*p=ln;

 				} while (ln == 0);

 			}

 		}

 	}

 /* n+tn is the word length

  * t needs to be n*4 is size, as does r */

 EXPORT_C void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n,

 	     int tna, int tnb, BN_ULONG *t)

 	{

 	int i,j,n2=n*2;

 	int c1,c2,neg,zero;

 	BN_ULONG ln,lo,*p;

 # ifdef BN_COUNT

 	fprintf(stderr," bn_mul_part_recursive (%d+%d) * (%d+%d)\n",

 		tna, n, tnb, n);

 # endif

 	if (n < 8)

 		{

 		bn_mul_normal(r,a,n+tna,b,n+tnb);

 		return;

 		}

 	/* r=(a[0]-a[1])*(b[1]-b[0]) */

 	c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);

 	c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);

 	zero=neg=0;

 	switch (c1*3+c2)

 		{

 	case -4:

 		bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */

 		bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */

 		break;

 	case -3:

 		zero=1;

 		/* break; */

 	case -2:

 		bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */

 		bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n); /* + */

 		neg=1;

 		break;

 	case -1:

 	case 0:

 	case 1:

 		zero=1;

 		/* break; */

 	case 2:

 		bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna); /* + */

 		bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */

 		neg=1;

 		break;

 	case 3:

 		zero=1;

 		/* break; */

 	case 4:

 		bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna);

 		bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n);

 		break;

 		}

 		/* The zero case isn't yet implemented here. The speedup

 		   would probably be negligible. */

 # if 0

 	if (n == 4)

 		{

 		bn_mul_comba4(&(t[n2]),t,&(t[n]));

 		bn_mul_comba4(r,a,b);

 		bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);

 		memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));

 		}

 	else

 # endif

 	if (n == 8)

 		{

 		bn_mul_comba8(&(t[n2]),t,&(t[n]));

 		bn_mul_comba8(r,a,b);

 		bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);

 		memset(&(r[n2+tna+tnb]),0,sizeof(BN_ULONG)*(n2-tna-tnb));

 		}

 	else

 		{

 		p= &(t[n2*2]);

 		bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);

 		bn_mul_recursive(r,a,b,n,0,0,p);

 		i=n/2;

 		/* If there is only a bottom half to the number,

 		 * just do it */

 		if (tna > tnb)

 			j = tna - i;

 		else

 			j = tnb - i;

 		if (j == 0)

 			{

 			bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),

 				i,tna-i,tnb-i,p);

 			memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));

 			}

 		else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */

 				{

 				bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),

 					i,tna-i,tnb-i,p);

 				memset(&(r[n2+tna+tnb]),0,

 					sizeof(BN_ULONG)*(n2-tna-tnb));

 				}

 		else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */

 			{

 			memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);

 			if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL

 				&& tnb < BN_MUL_RECURSIVE_SIZE_NORMAL)

 				{

 				bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);

 				}

 			else

 				{

 				for (;;)

 					{

 					i/=2;

 					if (i <= tna && tna == tnb)

 						{

 						bn_mul_recursive(&(r[n2]),

 							&(a[n]),&(b[n]),

 							i,tna-i,tnb-i,p);

 						break;

 						}

 					else if (i < tna || i < tnb)

 						{

 						bn_mul_part_recursive(&(r[n2]),

 							&(a[n]),&(b[n]),

 							i,tna-i,tnb-i,p);

 						break;

 						}

 					}

 				}

 			}

 		}

 	/* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign

 	 * r[10] holds (a[0]*b[0])

 	 * r[32] holds (b[1]*b[1])

 	 */

 	c1=(int)(bn_add_words(t,r,&(r[n2]),n2));

 	if (neg) /* if t[32] is negative */

 		{

 		c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));

 		}

 	else

 		{

 		/* Might have a carry */

 		c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));

 		}

 	/* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])

 	 * r[10] holds (a[0]*b[0])

 	 * r[32] holds (b[1]*b[1])

 	 * c1 holds the carry bits

 	 */

 	c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));

 	if (c1)

 		{

 		p= &(r[n+n2]);

 		lo= *p;

 		ln=(lo+c1)&BN_MASK2;

 		*p=ln;

 		/* The overflow will stop before we over write

 		 * words we should not overwrite */

 		if (ln < (BN_ULONG)c1)

 			{

 			do	{

 				p++;

 				lo= *p;

 				ln=(lo+1)&BN_MASK2;

 				*p=ln;

 				} while (ln == 0);

 			}

 		}

 	}

 /* a and b must be the same size, which is n2.

  * r needs to be n2 words and t needs to be n2*2

  */

 EXPORT_C void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,

 	     BN_ULONG *t)

 	{

 	int n=n2/2;

 # ifdef BN_COUNT

 	fprintf(stderr," bn_mul_low_recursive %d * %d\n",n2,n2);

 # endif

 	bn_mul_recursive(r,a,b,n,0,0,&(t[0]));

 	if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL)

 		{

 		bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2]));

 		bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);

 		bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2]));

 		bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);

 		}

 	else

 		{

 		bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n);

 		bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n);

 		bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);

 		bn_add_words(&(r[n]),&(r[n]),&(t[n]),n);

 		}

 	}

 /* a and b must be the same size, which is n2.

  * r needs to be n2 words and t needs to be n2*2

  * l is the low words of the output.

  * t needs to be n2*3

  */

 EXPORT_C void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,

 	     BN_ULONG *t)

 	{

 	int i,n;

 	int c1,c2;

 	int neg,oneg,zero;

 	BN_ULONG ll,lc,*lp,*mp;

 # ifdef BN_COUNT

 	fprintf(stderr," bn_mul_high %d * %d\n",n2,n2);

 # endif

 	n=n2/2;

 	/* Calculate (al-ah)*(bh-bl) */

 	neg=zero=0;

 	c1=bn_cmp_words(&(a[0]),&(a[n]),n);

 	c2=bn_cmp_words(&(b[n]),&(b[0]),n);

 	switch (c1*3+c2)

 		{

 	case -4:

 		bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);

 		bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);

 		break;

 	case -3:

 		zero=1;

 		break;

 	case -2:

 		bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);

 		bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);

 		neg=1;

 		break;

 	case -1:

 	case 0:

 	case 1:

 		zero=1;

 		break;

 	case 2:

 		bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);

 		bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);

 		neg=1;

 		break;

 	case 3:

 		zero=1;

 		break;

 	case 4:

 		bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);

 		bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);

 		break;

 		}

 	oneg=neg;

 	/* t[10] = (a[0]-a[1])*(b[1]-b[0]) */

 	/* r[10] = (a[1]*b[1]) */

 # ifdef BN_MUL_COMBA

 	if (n == 8)

 		{

 		bn_mul_comba8(&(t[0]),&(r[0]),&(r[n]));

 		bn_mul_comba8(r,&(a[n]),&(b[n]));

 		}

 	else

 # endif

 		{

 		bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,0,0,&(t[n2]));

 		bn_mul_recursive(r,&(a[n]),&(b[n]),n,0,0,&(t[n2]));

 		}

 	/* s0 == low(al*bl)

 	 * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)

 	 * We know s0 and s1 so the only unknown is high(al*bl)

 	 * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))

 	 * high(al*bl) == s1 - (r[0]+l[0]+t[0])

 	 */

 	if (l != NULL)

 		{

 		lp= &(t[n2+n]);

 		c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n));

 		}

 	else

 		{

 		c1=0;

 		lp= &(r[0]);

 		}

 	if (neg)

 		neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n));

 	else

 		{

 		bn_add_words(&(t[n2]),lp,&(t[0]),n);

 		neg=0;

 		}

 	if (l != NULL)

 		{

 		bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n);

 		}

 	else

 		{

 		lp= &(t[n2+n]);

 		mp= &(t[n2]);

 		for (i=0; i<n; i++)

 			lp[i]=((~mp[i])+1)&BN_MASK2;

 		}

 	/* s[0] = low(al*bl)

 	 * t[3] = high(al*bl)

 	 * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign

 	 * r[10] = (a[1]*b[1])

 	 */

 	/* R[10] = al*bl

 	 * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])

 	 * R[32] = ah*bh

 	 */

 	/* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)

 	 * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)

 	 * R[3]=r[1]+(carry/borrow)

 	 */

 	if (l != NULL)

 		{

 		lp= &(t[n2]);

 		c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n));

 		}

 	else

 		{

 		lp= &(t[n2+n]);

 		c1=0;

 		}

 	c1+=(int)(bn_add_words(&(t[n2]),lp,  &(r[0]),n));

 	if (oneg)

 		c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n));

 	else

 		c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n));

 	c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n));

 	c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n));

 	if (oneg)

 		c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n));

 	else

 		c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n));

 	if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */

 		{

 		i=0;

 		if (c1 > 0)

 			{

 			lc=c1;

 			do	{

 				ll=(r[i]+lc)&BN_MASK2;

 				r[i++]=ll;

 				lc=(lc > ll);

 				} while (lc);

 			}

 		else

 			{

 			lc= -c1;

 			do	{

 				ll=r[i];

 				r[i++]=(ll-lc)&BN_MASK2;

 				lc=(lc > ll);

 				} while (lc);

 			}

 		}

 	if (c2 != 0) /* Add starting at r[1] */

 		{

 		i=n;

 		if (c2 > 0)

 			{

 			lc=c2;

 			do	{

 				ll=(r[i]+lc)&BN_MASK2;

 				r[i++]=ll;

 				lc=(lc > ll);

 				} while (lc);

 			}

 		else

 			{

 			lc= -c2;

 			do	{

 				ll=r[i];

 				r[i++]=(ll-lc)&BN_MASK2;

 				lc=(lc > ll);

 				} while (lc);

 			}

 		}

 	}

 #endif /* BN_RECURSION */

 EXPORT_C int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)

 	{

 	int ret=0;

 	int top,al,bl;

 	BIGNUM *rr;

 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)

 	int i;

 #endif

 #ifdef BN_RECURSION

 	BIGNUM *t=NULL;

 	int j=0,k;

 #endif

 #ifdef BN_COUNT

 	fprintf(stderr,"BN_mul %d * %d\n",a->top,b->top);

 #endif

 	bn_check_top(a);

 	bn_check_top(b);

 	bn_check_top(r);

 	al=a->top;

 	bl=b->top;

 	if ((al == 0) || (bl == 0))

 		{

 		BN_zero(r);

 		return(1);

 		}

 	top=al+bl;

 	BN_CTX_start(ctx);

 	if ((r == a) || (r == b))

 		{

 		if ((rr = BN_CTX_get(ctx)) == NULL) goto err;

 		}

 	else

 		rr = r;

 	rr->neg=a->neg^b->neg;

 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)

 	i = al-bl;

 #endif

 #ifdef BN_MUL_COMBA

 	if (i == 0)

 		{

 # if 0

 		if (al == 4)

 			{

 			if (bn_wexpand(rr,8) == NULL) goto err;

 			rr->top=8;

 			bn_mul_comba4(rr->d,a->d,b->d);

 			goto end;

 			}

 # endif

 		if (al == 8)

 			{

 			if (bn_wexpand(rr,16) == NULL) goto err;

 			rr->top=16;

 			bn_mul_comba8(rr->d,a->d,b->d);

 			goto end;

 			}

 		}

 #endif /* BN_MUL_COMBA */

 #ifdef BN_RECURSION

 	if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL))

 		{

 		if (i >= -1 && i <= 1)

 			{

 			int sav_j =0;

 			/* Find out the power of two lower or equal

 			   to the longest of the two numbers */

 			if (i >= 0)

 				{

 				j = BN_num_bits_word((BN_ULONG)al);

 				}

 			if (i == -1)

 				{

 				j = BN_num_bits_word((BN_ULONG)bl);

 				}

 			sav_j = j;

 			j = 1<<(j-1);

 			assert(j <= al || j <= bl);

 			k = j+j;

 			t = BN_CTX_get(ctx);

 			if (al > j || bl > j)

 				{

 				bn_wexpand(t,k*4);

 				bn_wexpand(rr,k*4);

 				bn_mul_part_recursive(rr->d,a->d,b->d,

 					j,al-j,bl-j,t->d);

 				}

 			else	/* al <= j || bl <= j */

 				{

 				bn_wexpand(t,k*2);

 				bn_wexpand(rr,k*2);

 				bn_mul_recursive(rr->d,a->d,b->d,

 					j,al-j,bl-j,t->d);

 				}

 			rr->top=top;

 			goto end;

 			}

 #if 0

 		if (i == 1 && !BN_get_flags(b,BN_FLG_STATIC_DATA))

 			{

 			BIGNUM *tmp_bn = (BIGNUM *)b;

 			if (bn_wexpand(tmp_bn,al) == NULL) goto err;

 			tmp_bn->d[bl]=0;

 			bl++;

 			i--;

 			}

 		else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))

 			{

 			BIGNUM *tmp_bn = (BIGNUM *)a;

 			if (bn_wexpand(tmp_bn,bl) == NULL) goto err;

 			tmp_bn->d[al]=0;

 			al++;

 			i++;

 			}

 		if (i == 0)

 			{

 			/* symmetric and > 4 */

 			/* 16 or larger */

 			j=BN_num_bits_word((BN_ULONG)al);

 			j=1<<(j-1);

 			k=j+j;

 			t = BN_CTX_get(ctx);

 			if (al == j) /* exact multiple */

 				{

 				if (bn_wexpand(t,k*2) == NULL) goto err;

 				if (bn_wexpand(rr,k*2) == NULL) goto err;

 				bn_mul_recursive(rr->d,a->d,b->d,al,t->d);

 				}

 			else

 				{

 				if (bn_wexpand(t,k*4) == NULL) goto err;

 				if (bn_wexpand(rr,k*4) == NULL) goto err;

 				bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);

 				}

 			rr->top=top;

 			goto end;

 			}

 #endif

 		}

 #endif /* BN_RECURSION */

 	if (bn_wexpand(rr,top) == NULL) goto err;

 	rr->top=top;

 	bn_mul_normal(rr->d,a->d,al,b->d,bl);

 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)

 end:

 #endif

 	bn_correct_top(rr);

 	if (r != rr) BN_copy(r,rr);

 	ret=1;

 err:

 	bn_check_top(r);

 	BN_CTX_end(ctx);

 	return(ret);

 	}

 EXPORT_C void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)

 	{

 	BN_ULONG *rr;

 #ifdef BN_COUNT

 	fprintf(stderr," bn_mul_normal %d * %d\n",na,nb);

 #endif

 	if (na < nb)

 		{

 		int itmp;

 		BN_ULONG *ltmp;

 		itmp=na; na=nb; nb=itmp;

 		ltmp=a;   a=b;   b=ltmp;

 		}

 	rr= &(r[na]);

 	if (nb <= 0)

 		{

 		(void)bn_mul_words(r,a,na,0);

 		return;

 		}

 	else

 		rr[0]=bn_mul_words(r,a,na,b[0]);

 	for (;;)

 		{

 		if (--nb <= 0) return;

 		rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);

 		if (--nb <= 0) return;

 		rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);

 		if (--nb <= 0) return;

 		rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);

 		if (--nb <= 0) return;

 		rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);

 		rr+=4;

 		r+=4;

 		b+=4;

 		}

 	}

 EXPORT_C void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)

 	{

 #ifdef BN_COUNT

 	fprintf(stderr," bn_mul_low_normal %d * %d\n",n,n);

 #endif

 	bn_mul_words(r,a,n,b[0]);

 	for (;;)

 		{

 		if (--n <= 0) return;

 		bn_mul_add_words(&(r[1]),a,n,b[1]);

 		if (--n <= 0) return;

 		bn_mul_add_words(&(r[2]),a,n,b[2]);

 		if (--n <= 0) return;

 		bn_mul_add_words(&(r[3]),a,n,b[3]);

 		if (--n <= 0) return;

 		bn_mul_add_words(&(r[4]),a,n,b[4]);

 		r+=4;

 		b+=4;

 		}

 	}