bn_asm.c

/*
 * Copyright 1995-2023 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 <openssl/crypto.h>
#include "internal/cryptlib.h"
#include "bn_local.h"

#if defined(BN_LLONG) || defined(BN_UMULT_HIGH)

BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num,
                          BN_ULONG w)
{
    BN_ULONG c1 = 0;

    assert(num >= 0);
    if (num <= 0)
        return c1;

# ifndef OPENSSL_SMALL_FOOTPRINT
    while (num & ~3) {
        mul_add(rp[0], ap[0], w, c1);
        mul_add(rp[1], ap[1], w, c1);
        mul_add(rp[2], ap[2], w, c1);
        mul_add(rp[3], ap[3], w, c1);
        ap += 4;
        rp += 4;
        num -= 4;
    }
# endif
    while (num) {
        mul_add(rp[0], ap[0], w, c1);
        ap++;
        rp++;
        num--;
    }

    return c1;
}

BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w)
{
    BN_ULONG c1 = 0;

    assert(num >= 0);
    if (num <= 0)
        return c1;

# ifndef OPENSSL_SMALL_FOOTPRINT
    while (num & ~3) {
        mul(rp[0], ap[0], w, c1);
        mul(rp[1], ap[1], w, c1);
        mul(rp[2], ap[2], w, c1);
        mul(rp[3], ap[3], w, c1);
        ap += 4;
        rp += 4;
        num -= 4;
    }
# endif
    while (num) {
        mul(rp[0], ap[0], w, c1);
        ap++;
        rp++;
        num--;
    }
    return c1;
}

void bn_sqr_words(BN_ULONG *r, const BN_ULONG *a, int n)
{
    assert(n >= 0);
    if (n <= 0)
        return;

# ifndef OPENSSL_SMALL_FOOTPRINT
    while (n & ~3) {
        sqr(r[0], r[1], a[0]);
        sqr(r[2], r[3], a[1]);
        sqr(r[4], r[5], a[2]);
        sqr(r[6], r[7], a[3]);
        a += 4;
        r += 8;
        n -= 4;
    }
# endif
    while (n) {
        sqr(r[0], r[1], a[0]);
        a++;
        r += 2;
        n--;
    }
}

#else                           /* !(defined(BN_LLONG) ||
                                 * defined(BN_UMULT_HIGH)) */

BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num,
                          BN_ULONG w)
{
    BN_ULONG c = 0;
    BN_ULONG bl, bh;

    assert(num >= 0);
    if (num <= 0)
        return (BN_ULONG)0;

    bl = LBITS(w);
    bh = HBITS(w);

# ifndef OPENSSL_SMALL_FOOTPRINT
    while (num & ~3) {
        mul_add(rp[0], ap[0], bl, bh, c);
        mul_add(rp[1], ap[1], bl, bh, c);
        mul_add(rp[2], ap[2], bl, bh, c);
        mul_add(rp[3], ap[3], bl, bh, c);
        ap += 4;
        rp += 4;
        num -= 4;
    }
# endif
    while (num) {
        mul_add(rp[0], ap[0], bl, bh, c);
        ap++;
        rp++;
        num--;
    }
    return c;
}

BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w)
{
    BN_ULONG carry = 0;
    BN_ULONG bl, bh;

    assert(num >= 0);
    if (num <= 0)
        return (BN_ULONG)0;

    bl = LBITS(w);
    bh = HBITS(w);

# ifndef OPENSSL_SMALL_FOOTPRINT
    while (num & ~3) {
        mul(rp[0], ap[0], bl, bh, carry);
        mul(rp[1], ap[1], bl, bh, carry);
        mul(rp[2], ap[2], bl, bh, carry);
        mul(rp[3], ap[3], bl, bh, carry);
        ap += 4;
        rp += 4;
        num -= 4;
    }
# endif
    while (num) {
        mul(rp[0], ap[0], bl, bh, carry);
        ap++;
        rp++;
        num--;
    }
    return carry;
}

void bn_sqr_words(BN_ULONG *r, const BN_ULONG *a, int n)
{
    assert(n >= 0);
    if (n <= 0)
        return;

# ifndef OPENSSL_SMALL_FOOTPRINT
    while (n & ~3) {
        sqr64(r[0], r[1], a[0]);
        sqr64(r[2], r[3], a[1]);
        sqr64(r[4], r[5], a[2]);
        sqr64(r[6], r[7], a[3]);
        a += 4;
        r += 8;
        n -= 4;
    }
# endif
    while (n) {
        sqr64(r[0], r[1], a[0]);
        a++;
        r += 2;
        n--;
    }
}

#endif                          /* !(defined(BN_LLONG) ||
                                 * defined(BN_UMULT_HIGH)) */

#if defined(BN_LLONG) && defined(BN_DIV2W)

BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d)
{
    return ((BN_ULONG)(((((BN_ULLONG) h) << BN_BITS2) | l) / (BN_ULLONG) d));
}

#else

/* Divide h,l by d and return the result. */
/* I need to test this some more :-( */
BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d)
{
    BN_ULONG dh, dl, q, ret = 0, th, tl, t;
    int i, count = 2;

    if (d == 0)
        return BN_MASK2;

    i = BN_num_bits_word(d);
    assert((i == BN_BITS2) || (h <= (BN_ULONG)1 << i));

    i = BN_BITS2 - i;
    if (h >= d)
        h -= d;

    if (i) {
        d <<= i;
        h = (h << i) | (l >> (BN_BITS2 - i));
        l <<= i;
    }
    dh = (d & BN_MASK2h) >> BN_BITS4;
    dl = (d & BN_MASK2l);
    for (;;) {
        if ((h >> BN_BITS4) == dh)
            q = BN_MASK2l;
        else
            q = h / dh;

        th = q * dh;
        tl = dl * q;
        for (;;) {
            t = h - th;
            if ((t & BN_MASK2h) ||
                ((tl) <= ((t << BN_BITS4) | ((l & BN_MASK2h) >> BN_BITS4))))
                break;
            q--;
            th -= dh;
            tl -= dl;
        }
        t = (tl >> BN_BITS4);
        tl = (tl << BN_BITS4) & BN_MASK2h;
        th += t;

        if (l < tl)
            th++;
        l -= tl;
        if (h < th) {
            h += d;
            q--;
        }
        h -= th;

        if (--count == 0)
            break;

        ret = q << BN_BITS4;
        h = ((h << BN_BITS4) | (l >> BN_BITS4)) & BN_MASK2;
        l = (l & BN_MASK2l) << BN_BITS4;
    }
    ret |= q;
    return ret;
}
#endif                          /* !defined(BN_LLONG) && defined(BN_DIV2W) */

#ifdef BN_LLONG
BN_ULONG bn_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
                      int n)
{
    BN_ULLONG ll = 0;

    assert(n >= 0);
    if (n <= 0)
        return (BN_ULONG)0;

# ifndef OPENSSL_SMALL_FOOTPRINT
    while (n & ~3) {
        ll += (BN_ULLONG) a[0] + b[0];
        r[0] = (BN_ULONG)ll & BN_MASK2;
        ll >>= BN_BITS2;
        ll += (BN_ULLONG) a[1] + b[1];
        r[1] = (BN_ULONG)ll & BN_MASK2;
        ll >>= BN_BITS2;
        ll += (BN_ULLONG) a[2] + b[2];
        r[2] = (BN_ULONG)ll & BN_MASK2;
        ll >>= BN_BITS2;
        ll += (BN_ULLONG) a[3] + b[3];
        r[3] = (BN_ULONG)ll & BN_MASK2;
        ll >>= BN_BITS2;
        a += 4;
        b += 4;
        r += 4;
        n -= 4;
    }
# endif
    while (n) {
        ll += (BN_ULLONG) a[0] + b[0];
        r[0] = (BN_ULONG)ll & BN_MASK2;
        ll >>= BN_BITS2;
        a++;
        b++;
        r++;
        n--;
    }
    return (BN_ULONG)ll;
}
#else                           /* !BN_LLONG */
BN_ULONG bn_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
                      int n)
{
    BN_ULONG c, l, t;

    assert(n >= 0);
    if (n <= 0)
        return (BN_ULONG)0;

    c = 0;
# ifndef OPENSSL_SMALL_FOOTPRINT
    while (n & ~3) {
        t = a[0];
        t = (t + c) & BN_MASK2;
        c = (t < c);
        l = (t + b[0]) & BN_MASK2;
        c += (l < t);
        r[0] = l;
        t = a[1];
        t = (t + c) & BN_MASK2;
        c = (t < c);
        l = (t + b[1]) & BN_MASK2;
        c += (l < t);
        r[1] = l;
        t = a[2];
        t = (t + c) & BN_MASK2;
        c = (t < c);
        l = (t + b[2]) & BN_MASK2;
        c += (l < t);
        r[2] = l;
        t = a[3];
        t = (t + c) & BN_MASK2;
        c = (t < c);
        l = (t + b[3]) & BN_MASK2;
        c += (l < t);
        r[3] = l;
        a += 4;
        b += 4;
        r += 4;
        n -= 4;
    }
# endif
    while (n) {
        t = a[0];
        t = (t + c) & BN_MASK2;
        c = (t < c);
        l = (t + b[0]) & BN_MASK2;
        c += (l < t);
        r[0] = l;
        a++;
        b++;
        r++;
        n--;
    }
    return (BN_ULONG)c;
}
#endif                          /* !BN_LLONG */

BN_ULONG bn_sub_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
                      int n)
{
    BN_ULONG t1, t2;
    int c = 0;

    assert(n >= 0);
    if (n <= 0)
        return (BN_ULONG)0;

#ifndef OPENSSL_SMALL_FOOTPRINT
    while (n & ~3) {
        t1 = a[0];
        t2 = (t1 - c) & BN_MASK2;
        c  = (t2 > t1);
        t1 = b[0];
        t1 = (t2 - t1) & BN_MASK2;
        r[0] = t1;
        c += (t1 > t2);
        t1 = a[1];
        t2 = (t1 - c) & BN_MASK2;
        c  = (t2 > t1);
        t1 = b[1];
        t1 = (t2 - t1) & BN_MASK2;
        r[1] = t1;
        c += (t1 > t2);
        t1 = a[2];
        t2 = (t1 - c) & BN_MASK2;
        c  = (t2 > t1);
        t1 = b[2];
        t1 = (t2 - t1) & BN_MASK2;
        r[2] = t1;
        c += (t1 > t2);
        t1 = a[3];
        t2 = (t1 - c) & BN_MASK2;
        c  = (t2 > t1);
        t1 = b[3];
        t1 = (t2 - t1) & BN_MASK2;
        r[3] = t1;
        c += (t1 > t2);
        a += 4;
        b += 4;
        r += 4;
        n -= 4;
    }
#endif
    while (n) {
        t1 = a[0];
        t2 = (t1 - c) & BN_MASK2;
        c  = (t2 > t1);
        t1 = b[0];
        t1 = (t2 - t1) & BN_MASK2;
        r[0] = t1;
        c += (t1 > t2);
        a++;
        b++;
        r++;
        n--;
    }
    return c;
}

#if defined(BN_MUL_COMBA) && !defined(OPENSSL_SMALL_FOOTPRINT)

/* mul_add_c(a,b,c0,c1,c2)  -- c+=a*b for three word number c=(c2,c1,c0) */
/* mul_add_c2(a,b,c0,c1,c2) -- c+=2*a*b for three word number c=(c2,c1,c0) */
/* sqr_add_c(a,i,c0,c1,c2)  -- c+=a[i]^2 for three word number c=(c2,c1,c0) */
/*
 * sqr_add_c2(a,i,c0,c1,c2) -- c+=2*a[i]*a[j] for three word number
 * c=(c2,c1,c0)
 */

# ifdef BN_LLONG
/*
 * Keep in mind that additions to multiplication result can not
 * overflow, because its high half cannot be all-ones.
 */
#  define mul_add_c(a,b,c0,c1,c2)       do {    \
        BN_ULONG hi;                            \
        BN_ULLONG t = (BN_ULLONG)(a)*(b);       \
        t += c0;                /* no carry */  \
        c0 = (BN_ULONG)Lw(t);                   \
        hi = (BN_ULONG)Hw(t);                   \
        c1 = (c1+hi)&BN_MASK2; c2 += (c1<hi);   \
        } while(0)

#  define mul_add_c2(a,b,c0,c1,c2)      do {    \
        BN_ULONG hi;                            \
        BN_ULLONG t = (BN_ULLONG)(a)*(b);       \
        BN_ULLONG tt = t+c0;    /* no carry */  \
        c0 = (BN_ULONG)Lw(tt);                  \
        hi = (BN_ULONG)Hw(tt);                  \
        c1 = (c1+hi)&BN_MASK2; c2 += (c1<hi);   \
        t += c0;                /* no carry */  \
        c0 = (BN_ULONG)Lw(t);                   \
        hi = (BN_ULONG)Hw(t);                   \
        c1 = (c1+hi)&BN_MASK2; c2 += (c1<hi);   \
        } while(0)

#  define sqr_add_c(a,i,c0,c1,c2)       do {    \
        BN_ULONG hi;                            \
        BN_ULLONG t = (BN_ULLONG)a[i]*a[i];     \
        t += c0;                /* no carry */  \
        c0 = (BN_ULONG)Lw(t);                   \
        hi = (BN_ULONG)Hw(t);                   \
        c1 = (c1+hi)&BN_MASK2; c2 += (c1<hi);   \
        } while(0)

#  define sqr_add_c2(a,i,j,c0,c1,c2) \
        mul_add_c2((a)[i],(a)[j],c0,c1,c2)

# elif defined(BN_UMULT_LOHI)
/*
 * Keep in mind that additions to hi can not overflow, because
 * the high word of a multiplication result cannot be all-ones.
 */
#  define mul_add_c(a,b,c0,c1,c2)       do {    \
        BN_ULONG ta = (a), tb = (b);            \
        BN_ULONG lo, hi;                        \
        BN_UMULT_LOHI(lo,hi,ta,tb);             \
        c0 += lo; hi += (c0<lo);                \
        c1 += hi; c2 += (c1<hi);                \
        } while(0)

#  define mul_add_c2(a,b,c0,c1,c2)      do {    \
        BN_ULONG ta = (a), tb = (b);            \
        BN_ULONG lo, hi, tt;                    \
        BN_UMULT_LOHI(lo,hi,ta,tb);             \
        c0 += lo; tt = hi + (c0<lo);            \
        c1 += tt; c2 += (c1<tt);                \
        c0 += lo; hi += (c0<lo);                \
        c1 += hi; c2 += (c1<hi);                \
        } while(0)

#  define sqr_add_c(a,i,c0,c1,c2)       do {    \
        BN_ULONG ta = (a)[i];                   \
        BN_ULONG lo, hi;                        \
        BN_UMULT_LOHI(lo,hi,ta,ta);             \
        c0 += lo; hi += (c0<lo);                \
        c1 += hi; c2 += (c1<hi);                \
        } while(0)

#  define sqr_add_c2(a,i,j,c0,c1,c2)    \
        mul_add_c2((a)[i],(a)[j],c0,c1,c2)

# elif defined(BN_UMULT_HIGH)
/*
 * Keep in mind that additions to hi can not overflow, because
 * the high word of a multiplication result cannot be all-ones.
 */
#  define mul_add_c(a,b,c0,c1,c2)       do {    \
        BN_ULONG ta = (a), tb = (b);            \
        BN_ULONG lo = ta * tb;                  \
        BN_ULONG hi = BN_UMULT_HIGH(ta,tb);     \
        c0 += lo; hi += (c0<lo);                \
        c1 += hi; c2 += (c1<hi);                \
        } while(0)

#  define mul_add_c2(a,b,c0,c1,c2)      do {    \
        BN_ULONG ta = (a), tb = (b), tt;        \
        BN_ULONG lo = ta * tb;                  \
        BN_ULONG hi = BN_UMULT_HIGH(ta,tb);     \
        c0 += lo; tt = hi + (c0<lo);            \
        c1 += tt; c2 += (c1<tt);                \
        c0 += lo; hi += (c0<lo);                \
        c1 += hi; c2 += (c1<hi);                \
        } while(0)

#  define sqr_add_c(a,i,c0,c1,c2)       do {    \
        BN_ULONG ta = (a)[i];                   \
        BN_ULONG lo = ta * ta;                  \
        BN_ULONG hi = BN_UMULT_HIGH(ta,ta);     \
        c0 += lo; hi += (c0<lo);                \
        c1 += hi; c2 += (c1<hi);                \
        } while(0)

#  define sqr_add_c2(a,i,j,c0,c1,c2)      \
        mul_add_c2((a)[i],(a)[j],c0,c1,c2)

# else                          /* !BN_LLONG */
/*
 * Keep in mind that additions to hi can not overflow, because
 * the high word of a multiplication result cannot be all-ones.
 */
#  define mul_add_c(a,b,c0,c1,c2)       do {    \
        BN_ULONG lo = LBITS(a), hi = HBITS(a);  \
        BN_ULONG bl = LBITS(b), bh = HBITS(b);  \
        mul64(lo,hi,bl,bh);                     \
        c0 = (c0+lo)&BN_MASK2; hi += (c0<lo);   \
        c1 = (c1+hi)&BN_MASK2; c2 += (c1<hi);   \
        } while(0)

#  define mul_add_c2(a,b,c0,c1,c2)      do {    \
        BN_ULONG tt;                            \
        BN_ULONG lo = LBITS(a), hi = HBITS(a);  \
        BN_ULONG bl = LBITS(b), bh = HBITS(b);  \
        mul64(lo,hi,bl,bh);                     \
        tt = hi;                                \
        c0 = (c0+lo)&BN_MASK2; tt += (c0<lo);   \
        c1 = (c1+tt)&BN_MASK2; c2 += (c1<tt);   \
        c0 = (c0+lo)&BN_MASK2; hi += (c0<lo);   \
        c1 = (c1+hi)&BN_MASK2; c2 += (c1<hi);   \
        } while(0)

#  define sqr_add_c(a,i,c0,c1,c2)       do {    \
        BN_ULONG lo, hi;                        \
        sqr64(lo,hi,(a)[i]);                    \
        c0 = (c0+lo)&BN_MASK2; hi += (c0<lo);   \
        c1 = (c1+hi)&BN_MASK2; c2 += (c1<hi);   \
        } while(0)

#  define sqr_add_c2(a,i,j,c0,c1,c2) \
        mul_add_c2((a)[i],(a)[j],c0,c1,c2)
# endif                         /* !BN_LLONG */

void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
{
    BN_ULONG c1, c2, c3;

    c1 = 0;
    c2 = 0;
    c3 = 0;
    mul_add_c(a[0], b[0], c1, c2, c3);
    r[0] = c1;
    c1 = 0;
    mul_add_c(a[0], b[1], c2, c3, c1);
    mul_add_c(a[1], b[0], c2, c3, c1);
    r[1] = c2;
    c2 = 0;
    mul_add_c(a[2], b[0], c3, c1, c2);
    mul_add_c(a[1], b[1], c3, c1, c2);
    mul_add_c(a[0], b[2], c3, c1, c2);
    r[2] = c3;
    c3 = 0;
    mul_add_c(a[0], b[3], c1, c2, c3);
    mul_add_c(a[1], b[2], c1, c2, c3);
    mul_add_c(a[2], b[1], c1, c2, c3);
    mul_add_c(a[3], b[0], c1, c2, c3);
    r[3] = c1;
    c1 = 0;
    mul_add_c(a[4], b[0], c2, c3, c1);
    mul_add_c(a[3], b[1], c2, c3, c1);
    mul_add_c(a[2], b[2], c2, c3, c1);
    mul_add_c(a[1], b[3], c2, c3, c1);
    mul_add_c(a[0], b[4], c2, c3, c1);
    r[4] = c2;
    c2 = 0;
    mul_add_c(a[0], b[5], c3, c1, c2);
    mul_add_c(a[1], b[4], c3, c1, c2);
    mul_add_c(a[2], b[3], c3, c1, c2);
    mul_add_c(a[3], b[2], c3, c1, c2);
    mul_add_c(a[4], b[1], c3, c1, c2);
    mul_add_c(a[5], b[0], c3, c1, c2);
    r[5] = c3;
    c3 = 0;
    mul_add_c(a[6], b[0], c1, c2, c3);
    mul_add_c(a[5], b[1], c1, c2, c3);
    mul_add_c(a[4], b[2], c1, c2, c3);
    mul_add_c(a[3], b[3], c1, c2, c3);
    mul_add_c(a[2], b[4], c1, c2, c3);
    mul_add_c(a[1], b[5], c1, c2, c3);
    mul_add_c(a[0], b[6], c1, c2, c3);
    r[6] = c1;
    c1 = 0;
    mul_add_c(a[0], b[7], c2, c3, c1);
    mul_add_c(a[1], b[6], c2, c3, c1);
    mul_add_c(a[2], b[5], c2, c3, c1);
    mul_add_c(a[3], b[4], c2, c3, c1);
    mul_add_c(a[4], b[3], c2, c3, c1);
    mul_add_c(a[5], b[2], c2, c3, c1);
    mul_add_c(a[6], b[1], c2, c3, c1);
    mul_add_c(a[7], b[0], c2, c3, c1);
    r[7] = c2;
    c2 = 0;
    mul_add_c(a[7], b[1], c3, c1, c2);
    mul_add_c(a[6], b[2], c3, c1, c2);
    mul_add_c(a[5], b[3], c3, c1, c2);
    mul_add_c(a[4], b[4], c3, c1, c2);
    mul_add_c(a[3], b[5], c3, c1, c2);
    mul_add_c(a[2], b[6], c3, c1, c2);
    mul_add_c(a[1], b[7], c3, c1, c2);
    r[8] = c3;
    c3 = 0;
    mul_add_c(a[2], b[7], c1, c2, c3);
    mul_add_c(a[3], b[6], c1, c2, c3);
    mul_add_c(a[4], b[5], c1, c2, c3);
    mul_add_c(a[5], b[4], c1, c2, c3);
    mul_add_c(a[6], b[3], c1, c2, c3);
    mul_add_c(a[7], b[2], c1, c2, c3);
    r[9] = c1;
    c1 = 0;
    mul_add_c(a[7], b[3], c2, c3, c1);
    mul_add_c(a[6], b[4], c2, c3, c1);
    mul_add_c(a[5], b[5], c2, c3, c1);
    mul_add_c(a[4], b[6], c2, c3, c1);
    mul_add_c(a[3], b[7], c2, c3, c1);
    r[10] = c2;
    c2 = 0;
    mul_add_c(a[4], b[7], c3, c1, c2);
    mul_add_c(a[5], b[6], c3, c1, c2);
    mul_add_c(a[6], b[5], c3, c1, c2);
    mul_add_c(a[7], b[4], c3, c1, c2);
    r[11] = c3;
    c3 = 0;
    mul_add_c(a[7], b[5], c1, c2, c3);
    mul_add_c(a[6], b[6], c1, c2, c3);
    mul_add_c(a[5], b[7], c1, c2, c3);
    r[12] = c1;
    c1 = 0;
    mul_add_c(a[6], b[7], c2, c3, c1);
    mul_add_c(a[7], b[6], c2, c3, c1);
    r[13] = c2;
    c2 = 0;
    mul_add_c(a[7], b[7], c3, c1, c2);
    r[14] = c3;
    r[15] = c1;
}

void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
{
    BN_ULONG c1, c2, c3;

    c1 = 0;
    c2 = 0;
    c3 = 0;
    mul_add_c(a[0], b[0], c1, c2, c3);
    r[0] = c1;
    c1 = 0;
    mul_add_c(a[0], b[1], c2, c3, c1);
    mul_add_c(a[1], b[0], c2, c3, c1);
    r[1] = c2;
    c2 = 0;
    mul_add_c(a[2], b[0], c3, c1, c2);
    mul_add_c(a[1], b[1], c3, c1, c2);
    mul_add_c(a[0], b[2], c3, c1, c2);
    r[2] = c3;
    c3 = 0;
    mul_add_c(a[0], b[3], c1, c2, c3);
    mul_add_c(a[1], b[2], c1, c2, c3);
    mul_add_c(a[2], b[1], c1, c2, c3);
    mul_add_c(a[3], b[0], c1, c2, c3);
    r[3] = c1;
    c1 = 0;
    mul_add_c(a[3], b[1], c2, c3, c1);
    mul_add_c(a[2], b[2], c2, c3, c1);
    mul_add_c(a[1], b[3], c2, c3, c1);
    r[4] = c2;
    c2 = 0;
    mul_add_c(a[2], b[3], c3, c1, c2);
    mul_add_c(a[3], b[2], c3, c1, c2);
    r[5] = c3;
    c3 = 0;
    mul_add_c(a[3], b[3], c1, c2, c3);
    r[6] = c1;
    r[7] = c2;
}

void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a)
{
    BN_ULONG c1, c2, c3;

    c1 = 0;
    c2 = 0;
    c3 = 0;
    sqr_add_c(a, 0, c1, c2, c3);
    r[0] = c1;
    c1 = 0;
    sqr_add_c2(a, 1, 0, c2, c3, c1);
    r[1] = c2;
    c2 = 0;
    sqr_add_c(a, 1, c3, c1, c2);
    sqr_add_c2(a, 2, 0, c3, c1, c2);
    r[2] = c3;
    c3 = 0;
    sqr_add_c2(a, 3, 0, c1, c2, c3);
    sqr_add_c2(a, 2, 1, c1, c2, c3);
    r[3] = c1;
    c1 = 0;
    sqr_add_c(a, 2, c2, c3, c1);
    sqr_add_c2(a, 3, 1, c2, c3, c1);
    sqr_add_c2(a, 4, 0, c2, c3, c1);
    r[4] = c2;
    c2 = 0;
    sqr_add_c2(a, 5, 0, c3, c1, c2);
    sqr_add_c2(a, 4, 1, c3, c1, c2);
    sqr_add_c2(a, 3, 2, c3, c1, c2);
    r[5] = c3;
    c3 = 0;
    sqr_add_c(a, 3, c1, c2, c3);
    sqr_add_c2(a, 4, 2, c1, c2, c3);
    sqr_add_c2(a, 5, 1, c1, c2, c3);
    sqr_add_c2(a, 6, 0, c1, c2, c3);
    r[6] = c1;
    c1 = 0;
    sqr_add_c2(a, 7, 0, c2, c3, c1);
    sqr_add_c2(a, 6, 1, c2, c3, c1);
    sqr_add_c2(a, 5, 2, c2, c3, c1);
    sqr_add_c2(a, 4, 3, c2, c3, c1);
    r[7] = c2;
    c2 = 0;
    sqr_add_c(a, 4, c3, c1, c2);
    sqr_add_c2(a, 5, 3, c3, c1, c2);
    sqr_add_c2(a, 6, 2, c3, c1, c2);
    sqr_add_c2(a, 7, 1, c3, c1, c2);
    r[8] = c3;
    c3 = 0;
    sqr_add_c2(a, 7, 2, c1, c2, c3);
    sqr_add_c2(a, 6, 3, c1, c2, c3);
    sqr_add_c2(a, 5, 4, c1, c2, c3);
    r[9] = c1;
    c1 = 0;
    sqr_add_c(a, 5, c2, c3, c1);
    sqr_add_c2(a, 6, 4, c2, c3, c1);
    sqr_add_c2(a, 7, 3, c2, c3, c1);
    r[10] = c2;
    c2 = 0;
    sqr_add_c2(a, 7, 4, c3, c1, c2);
    sqr_add_c2(a, 6, 5, c3, c1, c2);
    r[11] = c3;
    c3 = 0;
    sqr_add_c(a, 6, c1, c2, c3);
    sqr_add_c2(a, 7, 5, c1, c2, c3);
    r[12] = c1;
    c1 = 0;
    sqr_add_c2(a, 7, 6, c2, c3, c1);
    r[13] = c2;
    c2 = 0;
    sqr_add_c(a, 7, c3, c1, c2);
    r[14] = c3;
    r[15] = c1;
}

void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a)
{
    BN_ULONG c1, c2, c3;

    c1 = 0;
    c2 = 0;
    c3 = 0;
    sqr_add_c(a, 0, c1, c2, c3);
    r[0] = c1;
    c1 = 0;
    sqr_add_c2(a, 1, 0, c2, c3, c1);
    r[1] = c2;
    c2 = 0;
    sqr_add_c(a, 1, c3, c1, c2);
    sqr_add_c2(a, 2, 0, c3, c1, c2);
    r[2] = c3;
    c3 = 0;
    sqr_add_c2(a, 3, 0, c1, c2, c3);
    sqr_add_c2(a, 2, 1, c1, c2, c3);
    r[3] = c1;
    c1 = 0;
    sqr_add_c(a, 2, c2, c3, c1);
    sqr_add_c2(a, 3, 1, c2, c3, c1);
    r[4] = c2;
    c2 = 0;
    sqr_add_c2(a, 3, 2, c3, c1, c2);
    r[5] = c3;
    c3 = 0;
    sqr_add_c(a, 3, c1, c2, c3);
    r[6] = c1;
    r[7] = c2;
}

# ifdef OPENSSL_NO_ASM
#  ifdef OPENSSL_BN_ASM_MONT
#   include <alloca.h>
/*
 * This is essentially reference implementation, which may or may not
 * result in performance improvement. E.g. on IA-32 this routine was
 * observed to give 40% faster rsa1024 private key operations and 10%
 * faster rsa4096 ones, while on AMD64 it improves rsa1024 sign only
 * by 10% and *worsens* rsa4096 sign by 15%. Once again, it's a
 * reference implementation, one to be used as starting point for
 * platform-specific assembler. Mentioned numbers apply to compiler
 * generated code compiled with and without -DOPENSSL_BN_ASM_MONT and
 * can vary not only from platform to platform, but even for compiler
 * versions. Assembler vs. assembler improvement coefficients can
 * [and are known to] differ and are to be documented elsewhere.
 */
int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
                const BN_ULONG *np, const BN_ULONG *n0p, int num)
{
    BN_ULONG c0, c1, ml, *tp, n0;
#   ifdef mul64
    BN_ULONG mh;
#   endif
    volatile BN_ULONG *vp;
    int i = 0, j;

#   if 0                        /* template for platform-specific
                                 * implementation */
    if (ap == bp)
        return bn_sqr_mont(rp, ap, np, n0p, num);
#   endif
    vp = tp = alloca((num + 2) * sizeof(BN_ULONG));

    n0 = *n0p;

    c0 = 0;
    ml = bp[0];
#   ifdef mul64
    mh = HBITS(ml);
    ml = LBITS(ml);
    for (j = 0; j < num; ++j)
        mul(tp[j], ap[j], ml, mh, c0);
#   else
    for (j = 0; j < num; ++j)
        mul(tp[j], ap[j], ml, c0);
#   endif

    tp[num] = c0;
    tp[num + 1] = 0;
    goto enter;

    for (i = 0; i < num; i++) {
        c0 = 0;
        ml = bp[i];
#   ifdef mul64
        mh = HBITS(ml);
        ml = LBITS(ml);
        for (j = 0; j < num; ++j)
            mul_add(tp[j], ap[j], ml, mh, c0);
#   else
        for (j = 0; j < num; ++j)
            mul_add(tp[j], ap[j], ml, c0);
#   endif
        c1 = (tp[num] + c0) & BN_MASK2;
        tp[num] = c1;
        tp[num + 1] = (c1 < c0 ? 1 : 0);
 enter:
        c1 = tp[0];
        ml = (c1 * n0) & BN_MASK2;
        c0 = 0;
#   ifdef mul64
        mh = HBITS(ml);
        ml = LBITS(ml);
        mul_add(c1, np[0], ml, mh, c0);
#   else
        mul_add(c1, ml, np[0], c0);
#   endif
        for (j = 1; j < num; j++) {
            c1 = tp[j];
#   ifdef mul64
            mul_add(c1, np[j], ml, mh, c0);
#   else
            mul_add(c1, ml, np[j], c0);
#   endif
            tp[j - 1] = c1 & BN_MASK2;
        }
        c1 = (tp[num] + c0) & BN_MASK2;
        tp[num - 1] = c1;
        tp[num] = tp[num + 1] + (c1 < c0 ? 1 : 0);
    }

    if (tp[num] != 0 || tp[num - 1] >= np[num - 1]) {
        c0 = bn_sub_words(rp, tp, np, num);
        if (tp[num] != 0 || c0 == 0) {
            for (i = 0; i < num + 2; i++)
                vp[i] = 0;
            return 1;
        }
    }
    for (i = 0; i < num; i++)
        rp[i] = tp[i], vp[i] = 0;
    vp[num] = 0;
    vp[num + 1] = 0;
    return 1;
}
#  else
/*
 * Return value of 0 indicates that multiplication/convolution was not
 * performed to signal the caller to fall down to alternative/original
 * code-path.
 */
int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
                const BN_ULONG *np, const BN_ULONG *n0, int num)
{
    return 0;
}
#  endif                        /* OPENSSL_BN_ASM_MONT */
# endif

#else                           /* !BN_MUL_COMBA */

/* hmm... is it faster just to do a multiply? */
void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a)
{
    BN_ULONG t[8];
    bn_sqr_normal(r, a, 4, t);
}

void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a)
{
    BN_ULONG t[16];
    bn_sqr_normal(r, a, 8, t);
}

void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
{
    r[4] = bn_mul_words(&(r[0]), a, 4, b[0]);
    r[5] = bn_mul_add_words(&(r[1]), a, 4, b[1]);
    r[6] = bn_mul_add_words(&(r[2]), a, 4, b[2]);
    r[7] = bn_mul_add_words(&(r[3]), a, 4, b[3]);
}

void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
{
    r[8] = bn_mul_words(&(r[0]), a, 8, b[0]);
    r[9] = bn_mul_add_words(&(r[1]), a, 8, b[1]);
    r[10] = bn_mul_add_words(&(r[2]), a, 8, b[2]);
    r[11] = bn_mul_add_words(&(r[3]), a, 8, b[3]);
    r[12] = bn_mul_add_words(&(r[4]), a, 8, b[4]);
    r[13] = bn_mul_add_words(&(r[5]), a, 8, b[5]);
    r[14] = bn_mul_add_words(&(r[6]), a, 8, b[6]);
    r[15] = bn_mul_add_words(&(r[7]), a, 8, b[7]);
}

# ifdef OPENSSL_NO_ASM
#  ifdef OPENSSL_BN_ASM_MONT
#   include <alloca.h>
int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
                const BN_ULONG *np, const BN_ULONG *n0p, int num)
{
    BN_ULONG c0, c1, *tp, n0 = *n0p;
    volatile BN_ULONG *vp;
    int i = 0, j;

    vp = tp = alloca((num + 2) * sizeof(BN_ULONG));

    for (i = 0; i <= num; i++)
        tp[i] = 0;

    for (i = 0; i < num; i++) {
        c0 = bn_mul_add_words(tp, ap, num, bp[i]);
        c1 = (tp[num] + c0) & BN_MASK2;
        tp[num] = c1;
        tp[num + 1] = (c1 < c0 ? 1 : 0);

        c0 = bn_mul_add_words(tp, np, num, tp[0] * n0);
        c1 = (tp[num] + c0) & BN_MASK2;
        tp[num] = c1;
        tp[num + 1] += (c1 < c0 ? 1 : 0);
        for (j = 0; j <= num; j++)
            tp[j] = tp[j + 1];
    }

    if (tp[num] != 0 || tp[num - 1] >= np[num - 1]) {
        c0 = bn_sub_words(rp, tp, np, num);
        if (tp[num] != 0 || c0 == 0) {
            for (i = 0; i < num + 2; i++)
                vp[i] = 0;
            return 1;
        }
    }
    for (i = 0; i < num; i++)
        rp[i] = tp[i], vp[i] = 0;
    vp[num] = 0;
    vp[num + 1] = 0;
    return 1;
}
#  else
int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
                const BN_ULONG *np, const BN_ULONG *n0, int num)
{
    return 0;
}
#  endif                        /* OPENSSL_BN_ASM_MONT */
# endif

#endif                          /* !BN_MUL_COMBA */