bn_mul.c

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/* crypto/bn/bn_mul.c */
/* Copyright (C) 1995-1998 Eric Young ([e-mail])
 * All rights reserved.
 *
 * This package is an SSL implementation written
 * by Eric Young ([e-mail]).
 * 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 ([e-mail]).
 * 
 * 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 ([e-mail])"
 *    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 ([e-mail])"
 * 
 * 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);