/src/openssl/crypto/bn/bn_mul.c

Source (jump to first uncovered line)
/*
 * Copyright 1995-2018 The OpenSSL Project Authors. All Rights Reserved.
 *
 * Licensed under the Apache License 2.0 (the "License").  You may not use
 * this file except in compliance with the License.  You can obtain a copy
 * in the file LICENSE in the source distribution or at
 * https://www.openssl.org/source/license.html
 */

#include <assert.h>
#include "internal/cryptlib.h"
#include "bn_local.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 ( basically, 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) {
        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;
        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) {
            if (save_dl > dl) {
                switch (save_dl - dl) {
                case 1:
                    r[1] = a[1];
                    if (--dl <= 0)
                        break;
                    /* fall through */
                case 2:
                    r[2] = a[2];
                    if (--dl <= 0)
                        break;
                    /* fall through */
                case 3:
                    r[3] = a[3];
                    if (--dl <= 0)
                        break;
                }
                a += 4;
                r += 4;
            }
        }
        if (dl > 0) {
            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

#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_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, sizeof(*t) * 8);

        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, sizeof(*t) * 16);

        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, sizeof(*t) * n2);
        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;

    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:
    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:
    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:
    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(*r) * (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(*r) * (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(*r) * (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(*r) * 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;

    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);
    }
}
#endif                          /* BN_RECURSION */

int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
{
    int ret = bn_mul_fixed_top(r, a, b, ctx);

    bn_correct_top(r);
    bn_check_top(r);

    return ret;
}

int bn_mul_fixed_top(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

    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;

#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;
        }
    }
#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
    rr->neg = a->neg ^ b->neg;
    rr->flags |= BN_FLG_FIXED_TOP;
    if (r != rr && BN_copy(r, rr) == NULL)
        goto err;

    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;

    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)
{
    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;
    }
}

Coverage Report

Created: 2024-11-21 07:03

Line	Count	Source (jump to first uncovered line)
1		/*
2		* Copyright 1995-2018 The OpenSSL Project Authors. All Rights Reserved.
3		*
4		* Licensed under the Apache License 2.0 (the "License"). You may not use
5		* this file except in compliance with the License. You can obtain a copy
6		* in the file LICENSE in the source distribution or at
7		* https://www.openssl.org/source/license.html
8		*/
9
10		#include <assert.h>
11		#include "internal/cryptlib.h"
12		#include "bn_local.h"
13
14		#if defined(OPENSSL_NO_ASM) \|\| !defined(OPENSSL_BN_ASM_PART_WORDS)
15		/*
16		* Here follows specialised variants of bn_add_words() and bn_sub_words().
17		* They have the property performing operations on arrays of different sizes.
18		* The sizes of those arrays is expressed through cl, which is the common
19		* length ( basically, min(len(a),len(b)) ), and dl, which is the delta
20		* between the two lengths, calculated as len(a)-len(b). All lengths are the
21		* number of BN_ULONGs... For the operations that require a result array as
22		* parameter, it must have the length cl+abs(dl). These functions should
23		* probably end up in bn_asm.c as soon as there are assembler counterparts
24		* for the systems that use assembler files.
25		*/
26
27		BN_ULONG bn_sub_part_words(BN_ULONG *r,
28		const BN_ULONG a, const BN_ULONG b,
29		int cl, int dl)
30	34.8M	{
31	34.8M	BN_ULONG c, t;
32
33	34.8M	assert(cl >= 0);
34	34.8M	c = bn_sub_words(r, a, b, cl);
35
36	34.8M	if (dl == 0)
37	32.8M	return c;
38
39	1.97M	r += cl;
40	1.97M	a += cl;
41	1.97M	b += cl;
42
43	1.97M	if (dl < 0) {
44	938	for (;;) {
45	938	t = b[0];
46	938	r[0] = (0 - t - c) & BN_MASK2;
47	938	if (t != 0)
48	0	c = 1;
49	938	if (++dl >= 0)
50	14	break;
51
52	924	t = b[1];
53	924	r[1] = (0 - t - c) & BN_MASK2;
54	924	if (t != 0)
55	0	c = 1;
56	924	if (++dl >= 0)
57	28	break;
58
59	896	t = b[2];
60	896	r[2] = (0 - t - c) & BN_MASK2;
61	896	if (t != 0)
62	0	c = 1;
63	896	if (++dl >= 0)
64	53	break;
65
66	843	t = b[3];
67	843	r[3] = (0 - t - c) & BN_MASK2;
68	843	if (t != 0)
69	0	c = 1;
70	843	if (++dl >= 0)
71	49	break;
72
73	794	b += 4;
74	794	r += 4;
75	794	}
76	1.97M	} else {
77	1.97M	int save_dl = dl;
78	2.03M	while (c) {
79	119k	t = a[0];
80	119k	r[0] = (t - c) & BN_MASK2;
81	119k	if (t != 0)
82	119k	c = 0;
83	119k	if (--dl <= 0)
84	17.4k	break;
85
86	101k	t = a[1];
87	101k	r[1] = (t - c) & BN_MASK2;
88	101k	if (t != 0)
89	101k	c = 0;
90	101k	if (--dl <= 0)
91	3.85k	break;
92
93	97.7k	t = a[2];
94	97.7k	r[2] = (t - c) & BN_MASK2;
95	97.7k	if (t != 0)
96	97.7k	c = 0;
97	97.7k	if (--dl <= 0)
98	1.49k	break;
99
100	96.2k	t = a[3];
101	96.2k	r[3] = (t - c) & BN_MASK2;
102	96.2k	if (t != 0)
103	96.2k	c = 0;
104	96.2k	if (--dl <= 0)
105	37.1k	break;
106
107	59.1k	save_dl = dl;
108	59.1k	a += 4;
109	59.1k	r += 4;
110	59.1k	}
111	1.97M	if (dl > 0) {
112	1.91M	if (save_dl > dl) {
113	0	switch (save_dl - dl) {
114	0	case 1:
115	0	r[1] = a[1];
116	0	if (--dl <= 0)
117	0	break;
118		/* fall through */
119	0	case 2:
120	0	r[2] = a[2];
121	0	if (--dl <= 0)
122	0	break;
123		/* fall through */
124	0	case 3:
125	0	r[3] = a[3];
126	0	if (--dl <= 0)
127	0	break;
128	0	}
129	0	a += 4;
130	0	r += 4;
131	0	}
132	1.91M	}
133	1.97M	if (dl > 0) {
134	6.98M	for (;;) {
135	6.98M	r[0] = a[0];
136	6.98M	if (--dl <= 0)
137	536k	break;
138	6.44M	r[1] = a[1];
139	6.44M	if (--dl <= 0)
140	165k	break;
141	6.28M	r[2] = a[2];
142	6.28M	if (--dl <= 0)
143	438k	break;
144	5.84M	r[3] = a[3];
145	5.84M	if (--dl <= 0)
146	776k	break;
147
148	5.06M	a += 4;
149	5.06M	r += 4;
150	5.06M	}
151	1.91M	}
152	1.97M	}
153	1.97M	return c;
154	1.97M	}
155		#endif
156
157		#ifdef BN_RECURSION
158		/*
159		* Karatsuba recursive multiplication algorithm (cf. Knuth, The Art of
160		* Computer Programming, Vol. 2)
161		*/
162
163		/*-
164		* r is 2*n2 words in size,
165		* a and b are both n2 words in size.
166		* n2 must be a power of 2.
167		* We multiply and return the result.
168		* t must be 2*n2 words in size
169		* We calculate
170		* a[0]*b[0]
171		* a[0]b[0]+a[1]b[1]+(a[0]-a[1])*(b[1]-b[0])
172		* a[1]*b[1]
173		*/
174		/* dnX may not be positive, but n2/2+dnX has to be */
175		void bn_mul_recursive(BN_ULONG r, BN_ULONG a, BN_ULONG *b, int n2,
176		int dna, int dnb, BN_ULONG *t)
177	16.8M	{
178	16.8M	int n = n2 / 2, c1, c2;
179	16.8M	int tna = n + dna, tnb = n + dnb;
180	16.8M	unsigned int neg, zero;
181	16.8M	BN_ULONG ln, lo, *p;
182
183	16.8M	# ifdef BN_MUL_COMBA
184		# if 0
185		if (n2 == 4) {
186		bn_mul_comba4(r, a, b);
187		return;
188		}
189		# endif
190		/*
191		* Only call bn_mul_comba 8 if n2 == 8 and the two arrays are complete
192		* [steve]
193		*/
194	16.8M	if (n2 == 8 && dna == 0 && dnb == 0) {
195	121k	bn_mul_comba8(r, a, b);
196	121k	return;
197	121k	}
198	16.7M	# endif /* BN_MUL_COMBA */
199		/* Else do normal multiply */
200	16.7M	if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL) {
201	21.1k	bn_mul_normal(r, a, n2 + dna, b, n2 + dnb);
202	21.1k	if ((dna + dnb) < 0)
203	21.1k	memset(&r[2 * n2 + dna + dnb], 0,
204	21.1k	sizeof(BN_ULONG) * -(dna + dnb));
205	21.1k	return;
206	21.1k	}
207		/* r=(a[0]-a[1])(b[1]-b[0]) /
208	16.7M	c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
209	16.7M	c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n);
210	16.7M	zero = neg = 0;
211	16.7M	switch (c1 * 3 + c2) {
212	3.95M	case -4:
213	3.95M	bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
214	3.95M	bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
215	3.95M	break;
216	72.9k	case -3:
217	72.9k	zero = 1;
218	72.9k	break;
219	2.99M	case -2:
220	2.99M	bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
221	2.99M	bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */
222	2.99M	neg = 1;
223	2.99M	break;
224	19.4k	case -1:
225	84.9k	case 0:
226	102k	case 1:
227	102k	zero = 1;
228	102k	break;
229	5.75M	case 2:
230	5.75M	bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */
231	5.75M	bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
232	5.75M	neg = 1;
233	5.75M	break;
234	107k	case 3:
235	107k	zero = 1;
236	107k	break;
237	3.74M	case 4:
238	3.74M	bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
239	3.74M	bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
240	3.74M	break;
241	16.7M	}
242
243	16.7M	# ifdef BN_MUL_COMBA
244	16.7M	if (n == 4 && dna == 0 && dnb == 0) { /* XXX: bn_mul_comba4 could take
245		* extra args to do this well */
246	0	if (!zero)
247	0	bn_mul_comba4(&(t[n2]), t, &(t[n]));
248	0	else
249	0	memset(&t[n2], 0, sizeof(t) 8);
250
251	0	bn_mul_comba4(r, a, b);
252	0	bn_mul_comba4(&(r[n2]), &(a[n]), &(b[n]));
253	16.7M	} else if (n == 8 && dna == 0 && dnb == 0) { /* XXX: bn_mul_comba8 could
254		* take extra args to do
255		* this well */
256	13.7M	if (!zero)
257	13.5M	bn_mul_comba8(&(t[n2]), t, &(t[n]));
258	220k	else
259	220k	memset(&t[n2], 0, sizeof(t) 16);
260
261	13.7M	bn_mul_comba8(r, a, b);
262	13.7M	bn_mul_comba8(&(r[n2]), &(a[n]), &(b[n]));
263	13.7M	} else
264	2.98M	# endif /* BN_MUL_COMBA */
265	2.98M	{
266	2.98M	p = &(t[n2 * 2]);
267	2.98M	if (!zero)
268	2.92M	bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
269	62.8k	else
270	62.8k	memset(&t[n2], 0, sizeof(t) n2);
271	2.98M	bn_mul_recursive(r, a, b, n, 0, 0, p);
272	2.98M	bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), n, dna, dnb, p);
273	2.98M	}
274
275		/*-
276		* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
277		* r[10] holds (a[0]*b[0])
278		* r[32] holds (b[1]*b[1])
279		*/
280
281	16.7M	c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
282
283	16.7M	if (neg) { /* if t[32] is negative */
284	8.75M	c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
285	8.75M	} else {
286		/* Might have a carry */
287	7.99M	c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
288	7.99M	}
289
290		/*-
291		* t[32] holds (a[0]-a[1])(b[1]-b[0])+(a[0]b[0])+(a[1]*b[1])
292		* r[10] holds (a[0]*b[0])
293		* r[32] holds (b[1]*b[1])
294		* c1 holds the carry bits
295		*/
296	16.7M	c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
297	16.7M	if (c1) {
298	6.85M	p = &(r[n + n2]);
299	6.85M	lo = *p;
300	6.85M	ln = (lo + c1) & BN_MASK2;
301	6.85M	*p = ln;
302
303		/*
304		* The overflow will stop before we over write words we should not
305		* overwrite
306		*/
307	6.85M	if (ln < (BN_ULONG)c1) {
308	4	do {
309	4	p++;
310	4	lo = *p;
311	4	ln = (lo + 1) & BN_MASK2;
312	4	*p = ln;
313	4	} while (ln == 0);
314	2	}
315	6.85M	}
316	16.7M	}
317
318		/*
319		* n+tn is the word length t needs to be n*4 is size, as does r
320		*/
321		/* tnX may not be negative but less than n */
322		void bn_mul_part_recursive(BN_ULONG r, BN_ULONG a, BN_ULONG *b, int n,
323		int tna, int tnb, BN_ULONG *t)
324	967k	{
325	967k	int i, j, n2 = n * 2;
326	967k	int c1, c2, neg;
327	967k	BN_ULONG ln, lo, *p;
328
329	967k	if (n < 8) {
330	0	bn_mul_normal(r, a, n + tna, b, n + tnb);
331	0	return;
332	0	}
333
334		/* r=(a[0]-a[1])(b[1]-b[0]) /
335	967k	c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
336	967k	c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n);
337	967k	neg = 0;
338	967k	switch (c1 * 3 + c2) {
339	3	case -4:
340	3	bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
341	3	bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
342	3	break;
343	0	case -3:
344	22	case -2:
345	22	bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
346	22	bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */
347	22	neg = 1;
348	22	break;
349	728	case -1:
350	12.2k	case 0:
351	12.2k	case 1:
352	966k	case 2:
353	966k	bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */
354	966k	bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
355	966k	neg = 1;
356	966k	break;
357	48	case 3:
358	97	case 4:
359	97	bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
360	97	bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
361	97	break;
362	967k	}
363		/*
364		* The zero case isn't yet implemented here. The speedup would probably
365		* be negligible.
366		*/
367		# if 0
368		if (n == 4) {
369		bn_mul_comba4(&(t[n2]), t, &(t[n]));
370		bn_mul_comba4(r, a, b);
371		bn_mul_normal(&(r[n2]), &(a[n]), tn, &(b[n]), tn);
372		memset(&r[n2 + tn * 2], 0, sizeof(r) (n2 - tn * 2));
373		} else
374		# endif
375	967k	if (n == 8) {
376	118k	bn_mul_comba8(&(t[n2]), t, &(t[n]));
377	118k	bn_mul_comba8(r, a, b);
378	118k	bn_mul_normal(&(r[n2]), &(a[n]), tna, &(b[n]), tnb);
379	118k	memset(&r[n2 + tna + tnb], 0, sizeof(r) (n2 - tna - tnb));
380	848k	} else {
381	848k	p = &(t[n2 * 2]);
382	848k	bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
383	848k	bn_mul_recursive(r, a, b, n, 0, 0, p);
384	848k	i = n / 2;
385		/*
386		* If there is only a bottom half to the number, just do it
387		*/
388	848k	if (tna > tnb)
389	135k	j = tna - i;
390	713k	else
391	713k	j = tnb - i;
392	848k	if (j == 0) {
393	96.8k	bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]),
394	96.8k	i, tna - i, tnb - i, p);
395	96.8k	memset(&r[n2 + i * 2], 0, sizeof(r) (n2 - i * 2));
396	751k	} else if (j > 0) { /* eg, n == 16, i == 8 and tn == 11 */
397	402k	bn_mul_part_recursive(&(r[n2]), &(a[n]), &(b[n]),
398	402k	i, tna - i, tnb - i, p);
399	402k	memset(&(r[n2 + tna + tnb]), 0,
400	402k	sizeof(BN_ULONG) * (n2 - tna - tnb));
401	402k	} else { /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
402
403	348k	memset(&r[n2], 0, sizeof(r) n2);
404	348k	if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL
405	348k	&& tnb < BN_MUL_RECURSIVE_SIZE_NORMAL) {
406	348k	bn_mul_normal(&(r[n2]), &(a[n]), tna, &(b[n]), tnb);
407	348k	} else {
408	579	for (;;) {
409	579	i /= 2;
410		/*
411		* these simplified conditions work exclusively because
412		* difference between tna and tnb is 1 or 0
413		*/
414	579	if (i < tna \|\| i < tnb) {
415	290	bn_mul_part_recursive(&(r[n2]),
416	290	&(a[n]), &(b[n]),
417	290	i, tna - i, tnb - i, p);
418	290	break;
419	290	} else if (i == tna \|\| i == tnb) {
420	0	bn_mul_recursive(&(r[n2]),
421	0	&(a[n]), &(b[n]),
422	0	i, tna - i, tnb - i, p);
423	0	break;
424	0	}
425	579	}
426	290	}
427	348k	}
428	848k	}
429
430		/*-
431		* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
432		* r[10] holds (a[0]*b[0])
433		* r[32] holds (b[1]*b[1])
434		*/
435
436	967k	c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
437
438	967k	if (neg) { /* if t[32] is negative */
439	966k	c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
440	966k	} else {
441		/* Might have a carry */
442	100	c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
443	100	}
444
445		/*-
446		* t[32] holds (a[0]-a[1])(b[1]-b[0])+(a[0]b[0])+(a[1]*b[1])
447		* r[10] holds (a[0]*b[0])
448		* r[32] holds (b[1]*b[1])
449		* c1 holds the carry bits
450		*/
451	967k	c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
452	967k	if (c1) {
453	0	p = &(r[n + n2]);
454	0	lo = *p;
455	0	ln = (lo + c1) & BN_MASK2;
456	0	*p = ln;
457
458		/*
459		* The overflow will stop before we over write words we should not
460		* overwrite
461		*/
462	0	if (ln < (BN_ULONG)c1) {
463	0	do {
464	0	p++;
465	0	lo = *p;
466	0	ln = (lo + 1) & BN_MASK2;
467	0	*p = ln;
468	0	} while (ln == 0);
469	0	}
470	0	}
471	967k	}
472
473		/*-
474		* a and b must be the same size, which is n2.
475		* r needs to be n2 words and t needs to be n2*2
476		*/
477		void bn_mul_low_recursive(BN_ULONG r, BN_ULONG a, BN_ULONG *b, int n2,
478		BN_ULONG *t)
479	0	{
480	0	int n = n2 / 2;
481
482	0	bn_mul_recursive(r, a, b, n, 0, 0, &(t[0]));
483	0	if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL) {
484	0	bn_mul_low_recursive(&(t[0]), &(a[0]), &(b[n]), n, &(t[n2]));
485	0	bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
486	0	bn_mul_low_recursive(&(t[0]), &(a[n]), &(b[0]), n, &(t[n2]));
487	0	bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
488	0	} else {
489	0	bn_mul_low_normal(&(t[0]), &(a[0]), &(b[n]), n);
490	0	bn_mul_low_normal(&(t[n]), &(a[n]), &(b[0]), n);
491	0	bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
492	0	bn_add_words(&(r[n]), &(r[n]), &(t[n]), n);
493	0	}
494	0	}
495		#endif /* BN_RECURSION */
496
497		int BN_mul(BIGNUM r, const BIGNUM a, const BIGNUM b, BN_CTX ctx)
498	2.21M	{
499	2.21M	int ret = bn_mul_fixed_top(r, a, b, ctx);
500
501	2.21M	bn_correct_top(r);
502	2.21M	bn_check_top(r);
503
504	2.21M	return ret;
505	2.21M	}
506
507		int bn_mul_fixed_top(BIGNUM r, const BIGNUM a, const BIGNUM b, BN_CTX ctx)
508	10.2M	{
509	10.2M	int ret = 0;
510	10.2M	int top, al, bl;
511	10.2M	BIGNUM *rr;
512	10.2M	#if defined(BN_MUL_COMBA) \|\| defined(BN_RECURSION)
513	10.2M	int i;
514	10.2M	#endif
515	10.2M	#ifdef BN_RECURSION
516	10.2M	BIGNUM *t = NULL;
517	10.2M	int j = 0, k;
518	10.2M	#endif
519
520	10.2M	bn_check_top(a);
521	10.2M	bn_check_top(b);
522	10.2M	bn_check_top(r);
523
524	10.2M	al = a->top;
525	10.2M	bl = b->top;
526
527	10.2M	if ((al == 0) \|\| (bl == 0)) {
528	83.1k	BN_zero(r);
529	83.1k	return 1;
530	83.1k	}
531	10.2M	top = al + bl;
532
533	10.2M	BN_CTX_start(ctx);
534	10.2M	if ((r == a) \|\| (r == b)) {
535	525k	if ((rr = BN_CTX_get(ctx)) == NULL)
536	0	goto err;
537	525k	} else
538	9.68M	rr = r;
539
540	10.2M	#if defined(BN_MUL_COMBA) \|\| defined(BN_RECURSION)
541	10.2M	i = al - bl;
542	10.2M	#endif
543	10.2M	#ifdef BN_MUL_COMBA
544	10.2M	if (i == 0) {
545		# if 0
546		if (al == 4) {
547		if (bn_wexpand(rr, 8) == NULL)
548		goto err;
549		rr->top = 8;
550		bn_mul_comba4(rr->d, a->d, b->d);
551		goto end;
552		}
553		# endif
554	9.66M	if (al == 8) {
555	232k	if (bn_wexpand(rr, 16) == NULL)
556	0	goto err;
557	232k	rr->top = 16;
558	232k	bn_mul_comba8(rr->d, a->d, b->d);
559	232k	goto end;
560	232k	}
561	9.66M	}
562	9.97M	#endif /* BN_MUL_COMBA */
563	9.97M	#ifdef BN_RECURSION
564	9.97M	if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL)) {
565	6.78M	if (i >= -1 && i <= 1) {
566		/*
567		* Find out the power of two lower or equal to the longest of the
568		* two numbers
569		*/
570	6.76M	if (i >= 0) {
571	6.66M	j = BN_num_bits_word((BN_ULONG)al);
572	6.66M	}
573	6.76M	if (i == -1) {
574	97.6k	j = BN_num_bits_word((BN_ULONG)bl);
575	97.6k	}
576	6.76M	j = 1 << (j - 1);
577	6.76M	assert(j <= al \|\| j <= bl);
578	6.76M	k = j + j;
579	6.76M	t = BN_CTX_get(ctx);
580	6.76M	if (t == NULL)
581	0	goto err;
582	6.76M	if (al > j \|\| bl > j) {
583	563k	if (bn_wexpand(t, k * 4) == NULL)
584	0	goto err;
585	563k	if (bn_wexpand(rr, k * 4) == NULL)
586	0	goto err;
587	563k	bn_mul_part_recursive(rr->d, a->d, b->d,
588	563k	j, al - j, bl - j, t->d);
589	6.19M	} else { /* al <= j \|\| bl <= j */
590
591	6.19M	if (bn_wexpand(t, k * 2) == NULL)
592	0	goto err;
593	6.19M	if (bn_wexpand(rr, k * 2) == NULL)
594	0	goto err;
595	6.19M	bn_mul_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d);
596	6.19M	}
597	6.76M	rr->top = top;
598	6.76M	goto end;
599	6.76M	}
600	6.78M	}
601	3.21M	#endif /* BN_RECURSION */
602	3.21M	if (bn_wexpand(rr, top) == NULL)
603	0	goto err;
604	3.21M	rr->top = top;
605	3.21M	bn_mul_normal(rr->d, a->d, al, b->d, bl);
606
607	3.21M	#if defined(BN_MUL_COMBA) \|\| defined(BN_RECURSION)
608	10.2M	end:
609	10.2M	#endif
610	10.2M	rr->neg = a->neg ^ b->neg;
611	10.2M	rr->flags \|= BN_FLG_FIXED_TOP;
612	10.2M	if (r != rr && BN_copy(r, rr) == NULL)
613	0	goto err;
614
615	10.2M	ret = 1;
616	10.2M	err:
617	10.2M	bn_check_top(r);
618	10.2M	BN_CTX_end(ctx);
619	10.2M	return ret;
620	10.2M	}
621
622		void bn_mul_normal(BN_ULONG r, BN_ULONG a, int na, BN_ULONG *b, int nb)
623	3.70M	{
624	3.70M	BN_ULONG *rr;
625
626	3.70M	if (na < nb) {
627	385k	int itmp;
628	385k	BN_ULONG *ltmp;
629
630	385k	itmp = na;
631	385k	na = nb;
632	385k	nb = itmp;
633	385k	ltmp = a;
634	385k	a = b;
635	385k	b = ltmp;
636
637	385k	}
638	3.70M	rr = &(r[na]);
639	3.70M	if (nb <= 0) {
640	84.4k	(void)bn_mul_words(r, a, na, 0);
641	84.4k	return;
642	84.4k	} else
643	3.61M	rr[0] = bn_mul_words(r, a, na, b[0]);
644
645	5.62M	for (;;) {
646	5.62M	if (--nb <= 0)
647	862k	return;
648	4.75M	rr[1] = bn_mul_add_words(&(r[1]), a, na, b[1]);
649	4.75M	if (--nb <= 0)
650	665k	return;
651	4.09M	rr[2] = bn_mul_add_words(&(r[2]), a, na, b[2]);
652	4.09M	if (--nb <= 0)
653	1.24M	return;
654	2.84M	rr[3] = bn_mul_add_words(&(r[3]), a, na, b[3]);
655	2.84M	if (--nb <= 0)
656	841k	return;
657	2.00M	rr[4] = bn_mul_add_words(&(r[4]), a, na, b[4]);
658	2.00M	rr += 4;
659	2.00M	r += 4;
660	2.00M	b += 4;
661	2.00M	}
662	3.61M	}
663
664		void bn_mul_low_normal(BN_ULONG r, BN_ULONG a, BN_ULONG *b, int n)
665	0	{
666	0	bn_mul_words(r, a, n, b[0]);
667
668	0	for (;;) {
669	0	if (--n <= 0)
670	0	return;
671	0	bn_mul_add_words(&(r[1]), a, n, b[1]);
672	0	if (--n <= 0)
673	0	return;
674	0	bn_mul_add_words(&(r[2]), a, n, b[2]);
675	0	if (--n <= 0)
676	0	return;
677	0	bn_mul_add_words(&(r[3]), a, n, b[3]);
678	0	if (--n <= 0)
679	0	return;
680	0	bn_mul_add_words(&(r[4]), a, n, b[4]);
681	0	r += 4;
682	0	b += 4;
683	0	}
684	0	}