/*

 * Copyright 1995-2018 The OpenSSL Project Authors. All Rights Reserved.

 *

 * Licensed under the OpenSSL license (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 thru */

                case 2:

                    r[2] = a[2];

                    if (--dl <= 0)

                        break;

                    /* fall thru */

                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;

    }

}