bn_mul.c   [plain text]

/*
 * Copyright (c) 2000-2001 Apple Computer, Inc. All Rights Reserved.
 * 
 * The contents of this file constitute Original Code as defined in and are
 * subject to the Apple Public Source License Version 1.2 (the 'License').
 * You may not use this file except in compliance with the License. Please obtain
 * a copy of the License at http://www.apple.com/publicsource and read it before
 * using this file.
 * 
 * This Original Code and all software distributed under the License are
 * distributed on an 'AS IS' basis, WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESS
 * OR IMPLIED, AND APPLE HEREBY DISCLAIMS ALL SUCH WARRANTIES, INCLUDING WITHOUT
 * LIMITATION, ANY WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR
 * PURPOSE, QUIET ENJOYMENT OR NON-INFRINGEMENT. Please see the License for the
 * specific language governing rights and limitations under the License.
 */


/* 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.]
 */

#include <stdio.h>
#include "cryptlib.h"
#include "bn_lcl.h"

#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]
 */
void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
	     BN_ULONG *t)
	{
	int n=n2/2,c1,c2;
	unsigned int neg,zero;
	BN_ULONG ln,lo,*p;

# ifdef BN_COUNT
	printf(" 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
	if (n2 == 8)
		{
		bn_mul_comba8(r,a,b);
		return; 
		}
# endif /* BN_MUL_COMBA */
	if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
		{
		/* This should not happen */
		bn_mul_normal(r,a,n2,b,n2);
		return;
		}
	/* r=(a[0]-a[1])*(b[1]-b[0]) */
	c1=bn_cmp_words(a,&(a[n]),n);
	c2=bn_cmp_words(&(b[n]),b,n);
	zero=neg=0;
	switch (c1*3+c2)
		{
	case -4:
		bn_sub_words(t,      &(a[n]),a,      n); /* - */
		bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
		break;
	case -3:
		zero=1;
		break;
	case -2:
		bn_sub_words(t,      &(a[n]),a,      n); /* - */
		bn_sub_words(&(t[n]),&(b[n]),b,      n); /* + */
		neg=1;
		break;
	case -1:
	case 0:
	case 1:
		zero=1;
		break;
	case 2:
		bn_sub_words(t,      a,      &(a[n]),n); /* + */
		bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
		neg=1;
		break;
	case 3:
		zero=1;
		break;
	case 4:
		bn_sub_words(t,      a,      &(a[n]),n);
		bn_sub_words(&(t[n]),&(b[n]),b,      n);
		break;
		}

# ifdef BN_MUL_COMBA
	if (n == 4)
		{
		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)
		{
		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,p);
		else
			memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
		bn_mul_recursive(r,a,b,n,p);
		bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,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 */
void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int tn,
	     int n, BN_ULONG *t)
	{
	int i,j,n2=n*2;
	unsigned int c1,c2,neg,zero;
	BN_ULONG ln,lo,*p;

# ifdef BN_COUNT
	printf(" bn_mul_part_recursive %d * %d\n",tn+n,tn+n);
# endif
	if (n < 8)
		{
		i=tn+n;
		bn_mul_normal(r,a,i,b,i);
		return;
		}

	/* r=(a[0]-a[1])*(b[1]-b[0]) */
	c1=bn_cmp_words(a,&(a[n]),n);
	c2=bn_cmp_words(&(b[n]),b,n);
	zero=neg=0;
	switch (c1*3+c2)
		{
	case -4:
		bn_sub_words(t,      &(a[n]),a,      n); /* - */
		bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
		break;
	case -3:
		zero=1;
		/* break; */
	case -2:
		bn_sub_words(t,      &(a[n]),a,      n); /* - */
		bn_sub_words(&(t[n]),&(b[n]),b,      n); /* + */
		neg=1;
		break;
	case -1:
	case 0:
	case 1:
		zero=1;
		/* break; */
	case 2:
		bn_sub_words(t,      a,      &(a[n]),n); /* + */
		bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
		neg=1;
		break;
	case 3:
		zero=1;
		/* break; */
	case 4:
		bn_sub_words(t,      a,      &(a[n]),n);
		bn_sub_words(&(t[n]),&(b[n]),b,      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]),tn,&(b[n]),tn);
		memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
		}
	else
		{
		p= &(t[n2*2]);
		bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
		bn_mul_recursive(r,a,b,n,p);
		i=n/2;
		/* If there is only a bottom half to the number,
		 * just do it */
		j=tn-i;
		if (j == 0)
			{
			bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),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]),
					j,i,p);
				memset(&(r[n2+tn*2]),0,
					sizeof(BN_ULONG)*(n2-tn*2));
				}
		else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
			{
			memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
			if (tn < BN_MUL_RECURSIVE_SIZE_NORMAL)
				{
				bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
				}
			else
				{
				for (;;)
					{
					i/=2;
					if (i < tn)
						{
						bn_mul_part_recursive(&(r[n2]),
							&(a[n]),&(b[n]),
							tn-i,i,p);
						break;
						}
					else if (i == tn)
						{
						bn_mul_recursive(&(r[n2]),
							&(a[n]),&(b[n]),
							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 < 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
 */
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
	printf(" bn_mul_low_recursive %d * %d\n",n2,n2);
# endif

	bn_mul_recursive(r,a,b,n,&(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
 */
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
	printf(" 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,&(t[n2]));
		bn_mul_recursive(r,&(a[n]),&(b[n]),n,&(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 */

int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
	{
	int top,al,bl;
	BIGNUM *rr;
	int ret = 0;
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
	int i;
#endif
#ifdef BN_RECURSION
	BIGNUM *t;
	int j,k;
#endif

#ifdef BN_COUNT
	printf("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;
	r->neg=a->neg^b->neg;

	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;

#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 && !BN_get_flags(b,BN_FLG_STATIC_DATA))
			{
			bn_wexpand(b,al);
			b->d[bl]=0;
			bl++;
			i--;
			}
		else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
			{
			bn_wexpand(a,bl);
			a->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 */
				{
				bn_wexpand(t,k*2);
				bn_wexpand(rr,k*2);
				bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
				}
			else
				{
				bn_wexpand(a,k);
				bn_wexpand(b,k);
				bn_wexpand(t,k*4);
				bn_wexpand(rr,k*4);
				for (i=a->top; i<k; i++)
					a->d[i]=0;
				for (i=b->top; i<k; i++)
					b->d[i]=0;
				bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
				}
			rr->top=top;
			goto end;
			}
		}
#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_fix_top(rr);
	if (r != rr) BN_copy(r,rr);
	ret=1;
err:
	BN_CTX_end(ctx);
	return(ret);
	}

void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
	{
	BN_ULONG *rr;

#ifdef BN_COUNT
	printf(" 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]);
	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;
		}
	}

void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
	{
#ifdef BN_COUNT
	printf(" 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;
		}
	}