/*

 * Copyright 1995-2019 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 <openssl/bn.h>

#include "internal/cryptlib.h"

#include "bn_local.h"

/* The old slow way */

#if 0

int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,

           BN_CTX *ctx)

{

    int i, nm, nd;

    int ret = 0;

    BIGNUM *D;

    bn_check_top(m);

    bn_check_top(d);

    if (BN_is_zero(d)) {

        BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO);

        return 0;

    }

    if (BN_ucmp(m, d) < 0) {

        if (rem != NULL) {

            if (BN_copy(rem, m) == NULL)

                return 0;

        }

        if (dv != NULL)

            BN_zero(dv);

        return 1;

    }

    BN_CTX_start(ctx);

    D = BN_CTX_get(ctx);

    if (dv == NULL)

        dv = BN_CTX_get(ctx);

    if (rem == NULL)

        rem = BN_CTX_get(ctx);

    if (D == NULL || dv == NULL || rem == NULL)

        goto end;

    nd = BN_num_bits(d);

    nm = BN_num_bits(m);

    if (BN_copy(D, d) == NULL)

        goto end;

    if (BN_copy(rem, m) == NULL)

        goto end;

    /*

     * The next 2 are needed so we can do a dv->d[0]|=1 later since

     * BN_lshift1 will only work once there is a value :-)

     */

    BN_zero(dv);

    if (bn_wexpand(dv, 1) == NULL)

        goto end;

    dv->top = 1;

    if (!BN_lshift(D, D, nm - nd))

        goto end;

    for (i = nm - nd; i >= 0; i--) {

        if (!BN_lshift1(dv, dv))

            goto end;

        if (BN_ucmp(rem, D) >= 0) {

            dv->d[0] |= 1;

            if (!BN_usub(rem, rem, D))

                goto end;

        }

/* CAN IMPROVE (and have now :=) */

        if (!BN_rshift1(D, D))

            goto end;

    }

    rem->neg = BN_is_zero(rem) ? 0 : m->neg;

    dv->neg = m->neg ^ d->neg;

    ret = 1;

 end:

    BN_CTX_end(ctx);

    return ret;

}

#else

# if defined(BN_DIV3W)

BN_ULONG bn_div_3_words(const BN_ULONG *m, BN_ULONG d1, BN_ULONG d0);

# elif 0

/*

 * This is #if-ed away, because it's a reference for assembly implementations,

 * where it can and should be made constant-time. But if you want to test it,

 * just replace 0 with 1.

 */

#  if BN_BITS2 == 64 && defined(__SIZEOF_INT128__) && __SIZEOF_INT128__==16

#   undef BN_ULLONG

#   define BN_ULLONG __uint128_t

#   define BN_LLONG

#  endif

#  ifdef BN_LLONG

#   define BN_DIV3W

/*

 * Interface is somewhat quirky, |m| is pointer to most significant limb,

 * and less significant limb is referred at |m[-1]|. This means that caller

 * is responsible for ensuring that |m[-1]| is valid. Second condition that

 * has to be met is that |d0|'s most significant bit has to be set. Or in

 * other words divisor has to be "bit-aligned to the left." bn_div_fixed_top

 * does all this. The subroutine considers four limbs, two of which are

 * "overlapping," hence the name...

 */

static BN_ULONG bn_div_3_words(const BN_ULONG *m, BN_ULONG d1, BN_ULONG d0)

{

    BN_ULLONG R = ((BN_ULLONG)m[0] << BN_BITS2) | m[-1];

    BN_ULLONG D = ((BN_ULLONG)d0 << BN_BITS2) | d1;

    BN_ULONG Q = 0, mask;

    int i;

    for (i = 0; i < BN_BITS2; i++) {

        Q <<= 1;

        if (R >= D) {

            Q |= 1;

            R -= D;

        }

        D >>= 1;

    }

    mask = 0 - (Q >> (BN_BITS2 - 1));   /* does it overflow? */

    Q <<= 1;

    Q |= (R >= D);

    return (Q | mask) & BN_MASK2;

}

#  endif

# endif

static int bn_left_align(BIGNUM *num)

{

    BN_ULONG *d = num->d, n, m, rmask;

    int top = num->top;

    int rshift = BN_num_bits_word(d[top - 1]), lshift, i;

    lshift = BN_BITS2 - rshift;

    rshift %= BN_BITS2;            /* say no to undefined behaviour */

    rmask = (BN_ULONG)0 - rshift;  /* rmask = 0 - (rshift != 0) */

    rmask |= rmask >> 8;

    for (i = 0, m = 0; i < top; i++) {

        n = d[i];

        d[i] = ((n << lshift) | m) & BN_MASK2;

        m = (n >> rshift) & rmask;

    }

    return lshift;

}

# if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \

    && !defined(PEDANTIC) && !defined(BN_DIV3W)

#  if defined(__GNUC__) && __GNUC__>=2

#   if defined(__i386) || defined (__i386__)

   /*-

    * There were two reasons for implementing this template:

    * - GNU C generates a call to a function (__udivdi3 to be exact)

    *   in reply to ((((BN_ULLONG)n0)<

    *   understand why...);

    * - divl doesn't only calculate quotient, but also leaves

    *   remainder in %edx which we can definitely use here:-)

    */

#    undef bn_div_words

#    define bn_div_words(n0,n1,d0)                \

        ({  asm volatile (                      \

                "divl   %4"                     \

                : "=a"(q), "=d"(rem)            \

                : "a"(n1), "d"(n0), "r"(d0)     \

                : "cc");                        \

            q;                                  \

        })

#    define REMAINDER_IS_ALREADY_CALCULATED

#   elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)

   /*

    * Same story here, but it's 128-bit by 64-bit division. Wow!

    */

#    undef bn_div_words

#    define bn_div_words(n0,n1,d0)                \

        ({  asm volatile (                      \

                "divq   %4"                     \

                : "=a"(q), "=d"(rem)            \

                : "a"(n1), "d"(n0), "r"(d0)     \

                : "cc");                        \

            q;                                  \

        })

#    define REMAINDER_IS_ALREADY_CALCULATED

#   endif                       /* __<cpu> */

#  endif                        /* __GNUC__ */

# endif                         /* OPENSSL_NO_ASM */

/*-

 * BN_div computes  dv := num / divisor, rounding towards

 * zero, and sets up rm  such that  dv*divisor + rm = num  holds.

 * Thus:

 *     dv->neg == num->neg ^ divisor->neg  (unless the result is zero)

 *     rm->neg == num->neg                 (unless the remainder is zero)

 * If 'dv' or 'rm' is NULL, the respective value is not returned.

 */

int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,

           BN_CTX *ctx)

{

    int ret;

    if (BN_is_zero(divisor)) {

        BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO);

        return 0;

    }

    /*

     * Invalid zero-padding would have particularly bad consequences so don't

     * just rely on bn_check_top() here (bn_check_top() works only for

     * BN_DEBUG builds)

     */

    if (divisor->d[divisor->top - 1] == 0) {

        BNerr(BN_F_BN_DIV, BN_R_NOT_INITIALIZED);

        return 0;

    }

    ret = bn_div_fixed_top(dv, rm, num, divisor, ctx);

    if (ret) {

        if (dv != NULL)

            bn_correct_top(dv);

        if (rm != NULL)

            bn_correct_top(rm);

    }

    return ret;

}

/*

 * It's argued that *length* of *significant* part of divisor is public.

 * Even if it's private modulus that is. Again, *length* is assumed

 * public, but not *value*. Former is likely to be pre-defined by

 * algorithm with bit granularity, though below subroutine is invariant

 * of limb length. Thanks to this assumption we can require that |divisor|

 * may not be zero-padded, yet claim this subroutine "constant-time"(*).

 * This is because zero-padded dividend, |num|, is tolerated, so that

 * caller can pass dividend of public length(*), but with smaller amount

 * of significant limbs. This naturally means that quotient, |dv|, would

 * contain correspongly less significant limbs as well, and will be zero-

 * padded accordingly. Returned remainder, |rm|, will have same bit length

 * as divisor, also zero-padded if needed. These actually leave sign bits

 * in ambiguous state. In sense that we try to avoid negative zeros, while

 * zero-padded zeros would retain sign.

 *

 * (*) "Constant-time-ness" has two pre-conditions:

 *

 *     - availability of constant-time bn_div_3_words;

 *     - dividend is at least as "wide" as divisor, limb-wise, zero-padded

 *       if so required, which shouldn't be a privacy problem, because

 *       divisor's length is considered public;

 */

int bn_div_fixed_top(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num,

                     const BIGNUM *divisor, BN_CTX *ctx)

{

    int norm_shift, i, j, loop;

    BIGNUM *tmp, *snum, *sdiv, *res;

    BN_ULONG *resp, *wnum, *wnumtop;

    BN_ULONG d0, d1;

    int num_n, div_n;

    assert(divisor->top > 0 && divisor->d[divisor->top - 1] != 0);

    bn_check_top(num);

    bn_check_top(divisor);

    bn_check_top(dv);

    bn_check_top(rm);

    BN_CTX_start(ctx);

    res = (dv == NULL) ? BN_CTX_get(ctx) : dv;

    tmp = BN_CTX_get(ctx);

    snum = BN_CTX_get(ctx);

    sdiv = BN_CTX_get(ctx);

    if (sdiv == NULL)

        goto err;

    /* First we normalise the numbers */

    if (!BN_copy(sdiv, divisor))

        goto err;

    norm_shift = bn_left_align(sdiv);

    sdiv->neg = 0;

    /*

     * Note that bn_lshift_fixed_top's output is always one limb longer

     * than input, even when norm_shift is zero. This means that amount of

     * inner loop iterations is invariant of dividend value, and that one

     * doesn't need to compare dividend and divisor if they were originally

     * of the same bit length.

     */

    if (!(bn_lshift_fixed_top(snum, num, norm_shift)))

        goto err;

    div_n = sdiv->top;

    num_n = snum->top;

    if (num_n <= div_n) {

        /* caller didn't pad dividend -> no constant-time guarantee... */

        if (bn_wexpand(snum, div_n + 1) == NULL)

            goto err;

        memset(&(snum->d[num_n]), 0, (div_n - num_n + 1) * sizeof(BN_ULONG));

        snum->top = num_n = div_n + 1;

    }

    loop = num_n - div_n;

    /*

     * Lets setup a 'window' into snum This is the part that corresponds to

     * the current 'area' being divided

     */

    wnum = &(snum->d[loop]);

    wnumtop = &(snum->d[num_n - 1]);

    /* Get the top 2 words of sdiv */

    d0 = sdiv->d[div_n - 1];

    d1 = (div_n == 1) ? 0 : sdiv->d[div_n - 2];

    /* Setup quotient */

    if (!bn_wexpand(res, loop))

        goto err;

    res->neg = (num->neg ^ divisor->neg);

    res->top = loop;

    res->flags |= BN_FLG_FIXED_TOP;

    resp = &(res->d[loop]);

    /* space for temp */

    if (!bn_wexpand(tmp, (div_n + 1)))

        goto err;

    for (i = 0; i < loop; i++, wnumtop--) {

        BN_ULONG q, l0;

        /*

         * the first part of the loop uses the top two words of snum and sdiv

         * to calculate a BN_ULONG q such that | wnum - sdiv * q | < sdiv

         */

# if defined(BN_DIV3W)

        q = bn_div_3_words(wnumtop, d1, d0);

# else

        BN_ULONG n0, n1, rem = 0;

        n0 = wnumtop[0];

        n1 = wnumtop[-1];

        if (n0 == d0)

            q = BN_MASK2;

        else {                  /* n0 < d0 */

            BN_ULONG n2 = (wnumtop == wnum) ? 0 : wnumtop[-2];

#  ifdef BN_LLONG

            BN_ULLONG t2;

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

            q = (BN_ULONG)(((((BN_ULLONG) n0) << BN_BITS2) | n1) / d0);

#   else

            q = bn_div_words(n0, n1, d0);

#   endif

#   ifndef REMAINDER_IS_ALREADY_CALCULATED

            /*

             * rem doesn't have to be BN_ULLONG. The least we

             * know it's less that d0, isn't it?

             */

            rem = (n1 - q * d0) & BN_MASK2;

#   endif

            t2 = (BN_ULLONG) d1 *q;

            for (;;) {

                if (t2 <= ((((BN_ULLONG) rem) << BN_BITS2) | n2))

                    break;

                q--;

                rem += d0;

                if (rem < d0)

                    break;      /* don't let rem overflow */

                t2 -= d1;

            }

#  else                         /* !BN_LLONG */

            BN_ULONG t2l, t2h;

            q = bn_div_words(n0, n1, d0);

#   ifndef REMAINDER_IS_ALREADY_CALCULATED

            rem = (n1 - q * d0) & BN_MASK2;

#   endif

#   if defined(BN_UMULT_LOHI)

            BN_UMULT_LOHI(t2l, t2h, d1, q);

#   elif defined(BN_UMULT_HIGH)

            t2l = d1 * q;

            t2h = BN_UMULT_HIGH(d1, q);

#   else

            {

                BN_ULONG ql, qh;

                t2l = LBITS(d1);

                t2h = HBITS(d1);

                ql = LBITS(q);

                qh = HBITS(q);

                mul64(t2l, t2h, ql, qh); /* t2=(BN_ULLONG)d1*q; */

            }

#   endif

            for (;;) {

                if ((t2h < rem) || ((t2h == rem) && (t2l <= n2)))

                    break;

                q--;

                rem += d0;

                if (rem < d0)

                    break;      /* don't let rem overflow */

                if (t2l < d1)

                    t2h--;

                t2l -= d1;

            }

#  endif                        /* !BN_LLONG */

        }

# endif                         /* !BN_DIV3W */

        l0 = bn_mul_words(tmp->d, sdiv->d, div_n, q);

        tmp->d[div_n] = l0;

        wnum--;

        /*

         * ignore top values of the bignums just sub the two BN_ULONG arrays

         * with bn_sub_words

         */

        l0 = bn_sub_words(wnum, wnum, tmp->d, div_n + 1);

        q -= l0;

        /*

         * Note: As we have considered only the leading two BN_ULONGs in

         * the calculation of q, sdiv * q might be greater than wnum (but

         * then (q-1) * sdiv is less or equal than wnum)

         */

        for (l0 = 0 - l0, j = 0; j < div_n; j++)

            tmp->d[j] = sdiv->d[j] & l0;

        l0 = bn_add_words(wnum, wnum, tmp->d, div_n);

        (*wnumtop) += l0;

        assert((*wnumtop) == 0);

        /* store part of the result */

        *--resp = q;

    }

    /* snum holds remainder, it's as wide as divisor */

    snum->neg = num->neg;

    snum->top = div_n;

    snum->flags |= BN_FLG_FIXED_TOP;

    if (rm != NULL)

        bn_rshift_fixed_top(rm, snum, norm_shift);

    BN_CTX_end(ctx);

    return 1;

 err:

    bn_check_top(rm);

    BN_CTX_end(ctx);

    return 0;

}

#endif