/* crypto/bn/bn_div.c */

/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)

 * All rights reserved.

 *

 * This package is an SSL implementation written

 * by Eric Young (eay@cryptsoft.com).

 * The implementation was written so as to conform with Netscapes SSL.

 *

 * This library is free for commercial and non-commercial use as long as

 * the following conditions are aheared to.  The following conditions

 * apply to all code found in this distribution, be it the RC4, RSA,

 * lhash, DES, etc., code; not just the SSL code.  The SSL documentation

 * included with this distribution is covered by the same copyright terms

 * except that the holder is Tim Hudson (tjh@cryptsoft.com).

 *

 * Copyright remains Eric Young's, and as such any Copyright notices in

 * the code are not to be removed.

 * If this package is used in a product, Eric Young should be given attribution

 * as the author of the parts of the library used.

 * This can be in the form of a textual message at program startup or

 * in documentation (online or textual) provided with the package.

 *

 * Redistribution and use in source and binary forms, with or without

 * modification, are permitted provided that the following conditions

 * are met:

 * 1. Redistributions of source code must retain the copyright

 *    notice, this list of conditions and the following disclaimer.

 * 2. Redistributions in binary form must reproduce the above copyright

 *    notice, this list of conditions and the following disclaimer in the

 *    documentation and/or other materials provided with the distribution.

 * 3. All advertising materials mentioning features or use of this software

 *    must display the following acknowledgement:

 *    "This product includes cryptographic software written by

 *     Eric Young (eay@cryptsoft.com)"

 *    The word 'cryptographic' can be left out if the rouines from the library

 *    being used are not cryptographic related :-).

 * 4. If you include any Windows specific code (or a derivative thereof) from

 *    the apps directory (application code) you must include an acknowledgement:

 *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"

 *

 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND

 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE

 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE

 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE

 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL

 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS

 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)

 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT

 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY

 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF

 * SUCH DAMAGE.

 *

 * The licence and distribution terms for any publically available version or

 * derivative of this code cannot be changed.  i.e. this code cannot simply be

 * copied and put under another distribution licence

 * [including the GNU Public Licence.]

 */

#include <stdio.h>

#include <openssl/bn.h>

#include "cryptlib.h"

#include "bn_lcl.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(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)<<BN_BITS2)|n1)/d0 (I fail to

    *   understand why...);

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

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

    *

    *                                   <appro@fy.chalmers.se>

    */

#    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!

    *                                   <appro@fy.chalmers.se>

    */

#    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 norm_shift, i, loop;

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

    BN_ULONG *resp, *wnump;

    BN_ULONG d0, d1;

    int num_n, div_n;

    int no_branch = 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 ((num->top > 0 && num->d[num->top - 1] == 0) ||

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

        BNerr(BN_F_BN_DIV, BN_R_NOT_INITIALIZED);

        return 0;

    }

    bn_check_top(num);

    bn_check_top(divisor);

    if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0)

        || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0)) {

        no_branch = 1;

    }

    bn_check_top(dv);

    bn_check_top(rm);

    /*- bn_check_top(num); *//*

     * 'num' has been checked already

     */

    /*- bn_check_top(divisor); *//*

     * 'divisor' has been checked already

     */

    if (BN_is_zero(divisor)) {

        BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO);

        return (0);

    }

    if (!no_branch && BN_ucmp(num, divisor) < 0) {

        if (rm != NULL) {

            if (BN_copy(rm, num) == NULL)

                return (0);

        }

        if (dv != NULL)

            BN_zero(dv);

        return (1);

    }

    BN_CTX_start(ctx);

    tmp = BN_CTX_get(ctx);

    snum = BN_CTX_get(ctx);

    sdiv = BN_CTX_get(ctx);

    if (dv == NULL)

        res = BN_CTX_get(ctx);

    else

        res = dv;

    if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL)

        goto err;

    /* First we normalise the numbers */

    norm_shift = BN_BITS2 - ((BN_num_bits(divisor)) % BN_BITS2);

    if (!(BN_lshift(sdiv, divisor, norm_shift)))

        goto err;

    sdiv->neg = 0;

    norm_shift += BN_BITS2;

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

        goto err;

    snum->neg = 0;

    if (no_branch) {

        /*

         * Since we don't know whether snum is larger than sdiv, we pad snum

         * with enough zeroes without changing its value.

         */

        if (snum->top <= sdiv->top + 1) {

            if (bn_wexpand(snum, sdiv->top + 2) == NULL)

                goto err;

            for (i = snum->top; i < sdiv->top + 2; i++)

                snum->d[i] = 0;

            snum->top = sdiv->top + 2;

        } else {

            if (bn_wexpand(snum, snum->top + 1) == NULL)

                goto err;

            snum->d[snum->top] = 0;

            snum->top++;

        }

    }

    div_n = sdiv->top;

    num_n = snum->top;

    loop = num_n - div_n;

    /*

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

     * the current 'area' being divided

     */

    wnum.neg = 0;

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

    wnum.top = div_n;

    /*

     * only needed when BN_ucmp messes up the values between top and max

     */

    wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */

    /* Get the top 2 words of sdiv */

    /* div_n=sdiv->top; */

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

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

    /* pointer to the 'top' of snum */

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

    /* Setup to 'res' */

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

    if (!bn_wexpand(res, (loop + 1)))

        goto err;

    res->top = loop - no_branch;

    resp = &(res->d[loop - 1]);

    /* space for temp */

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

        goto err;

    if (!no_branch) {

        if (BN_ucmp(&wnum, sdiv) >= 0) {

            /*

             * If BN_DEBUG_RAND is defined BN_ucmp changes (via bn_pollute)

             * the const bignum arguments => clean the values between top and

             * max again

             */

            bn_clear_top2max(&wnum);

            bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);

            *resp = 1;

        } else

            res->top--;

    }

    /*

     * if res->top == 0 then clear the neg value otherwise decrease the resp

     * pointer

     */

    if (res->top == 0)

        res->neg = 0;

    else

        resp--;

    for (i = 0; i < loop - 1; i++, wnump--, resp--) {

        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) && !defined(OPENSSL_NO_ASM)

        BN_ULONG bn_div_3_words(BN_ULONG *, BN_ULONG, BN_ULONG);

        q = bn_div_3_words(wnump, d1, d0);

# else

        BN_ULONG n0, n1, rem = 0;

        n0 = wnump[0];

        n1 = wnump[-1];

        if (n0 == d0)

            q = BN_MASK2;

        else {                  /* n0 < d0 */

#  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);

#    ifdef BN_DEBUG_LEVITTE

            fprintf(stderr, "DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\

X) -> 0x%08X\n", n0, n1, d0, q);

#    endif

#   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) | wnump[-2]))

                    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);

#   ifdef BN_DEBUG_LEVITTE

            fprintf(stderr, "DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\

X) -> 0x%08X\n", n0, n1, d0, q);

#   endif

#   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 <= wnump[-2])))

                    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.d--;

        /*

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

         * with bn_sub_words

         */

        if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n + 1)) {

            /*

             * 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)

             */

            q--;

            if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))

                /*

                 * we can't have an overflow here (assuming that q != 0, but

                 * if q == 0 then tmp is zero anyway)

                 */

                (*wnump)++;

        }

        /* store part of the result */

        *resp = q;

    }

    bn_correct_top(snum);

    if (rm != NULL) {

        /*

         * Keep a copy of the neg flag in num because if rm==num BN_rshift()

         * will overwrite it.

         */

        int neg = num->neg;

        BN_rshift(rm, snum, norm_shift);

        if (!BN_is_zero(rm))

            rm->neg = neg;

        bn_check_top(rm);

    }

    if (no_branch)

        bn_correct_top(res);

    BN_CTX_end(ctx);

    return (1);

 err:

    bn_check_top(rm);

    BN_CTX_end(ctx);

    return (0);

}

#endif