/*

 * 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);