bn_mul.c

#include "bn.h"

#ifndef WITH_LIBCRYPTO
//FIXME Not checked on threadsafety yet; after checking please remove this line
/* 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 license 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 license
 * [including the GNU Public License.]
 */

#include <stdio.h>
#include <string.h>
#include "bn_lcl.h"
#include "openssl_mods.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 c1, c2, i, j, n2 = n * 2;
	unsigned int neg;
	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);
	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:
	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:
	case 2:
		bn_sub_words(t,      a,      &(a[n]), n); /* + */
		bn_sub_words(&(t[n]), b,      &(b[n]), n); /* - */
		neg = 1;
		break;
	case 3:
	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 < (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
 */
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 = 0, oneg;
	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) */
	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:
		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:
		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:
		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);
	}

	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;

	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 && !BN_get_flags(b, BN_FLG_STATIC_DATA))
		{
			if(bn_wexpand(b, al) == NULL) { goto err; }
			b->d[bl] = 0;
			bl++;
			i--;
		}
		else if(i == -1 && !BN_get_flags(a, BN_FLG_STATIC_DATA))
		{
			if(bn_wexpand(a, bl) == NULL) { goto err; }
			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 */
			{
				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(a, k) == NULL) { goto err; }
				if(bn_wexpand(b, k) == NULL) { goto err; }
				if(bn_wexpand(t, k * 4) == NULL) { goto err; }
				if(bn_wexpand(rr, k * 4) == NULL) { goto err; }
				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;
	}
}
#endif