libcrypto/bn/bn_mul.c

/* $OpenBSD: bn_mul.c,v 1.17 2014/07/10 13:58:22 jsing Exp $ */
/* 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 <assert.h>
#include <stdio.h>
#include <string.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.  */

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

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]
 */
/* dnX may not be positive, but n2/2+dnX has to be */
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 * %d%+d\n",n2,dna,n2,dnb);
# 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 */
/* tnX may not be negative but less than n */
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;
	BN_ULONG ln, lo, *p;

# ifdef BN_COUNT
	fprintf(stderr, " bn_mul_part_recursive (%d%+d) * (%d%+d)\n",
	    n, tna, n, tnb);
# 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);
	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:
		/* 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:
		/* 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:
		/* 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;
					/* these simplified conditions work
					 * exclusively because difference
					 * between tna and tnb is 1 or 0 */
					if (i < tna || i < tnb) {
						bn_mul_part_recursive(&(r[n2]),
						    &(a[n]), &(b[n]), i,
						    tna - i, tnb - i, p);
						break;
					} else if (i == tna || i == tnb) {
						bn_mul_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
 */
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
 */
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 */

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) {
			/* 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);
			}
			j = 1 << (j - 1);
			assert(j <= al || j <= bl);
			k = j + j;
			t = BN_CTX_get(ctx);
			if (t == NULL)
				goto err;
			if (al > j || bl > j) {
				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,
				    j, al - j, bl - j, t->d);
			}
			else	/* al <= j || bl <= j */
			{
				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,
				    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);
}

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;
	}
}

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;
	}
}