/* $OpenBSD: bn_div.c,v 1.25 2017/01/29 17:49:22 beck Exp $ */

/* 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/opensslconf.h>

#include <openssl/bn.h>

#include <openssl/err.h>

#include "bn_lcl.h"

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

    && !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), "g"(d0) \

    : "cc");      \

      q;          \

  })

#  define REMAINDER_IS_ALREADY_CALCULATED

#  elif defined(__x86_64) && defined(_LP64)

   /*

    * 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), "g"(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.

 */

static int

BN_div_internal(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,

    BN_CTX *ctx, int ct)

{

  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

   * in the case of 'num', so don't just rely on bn_check_top() for this one

   * (bn_check_top() works only for BN_DEBUG builds) */

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

    BNerror(BN_R_NOT_INITIALIZED);

    return 0;

  }

  bn_check_top(num);

  if (ct)

    no_branch = 1;

  bn_check_top(dv);

  bn_check_top(rm);

  /* bn_check_top(num); */ /* 'num' has been checked already */

  bn_check_top(divisor);

  if (BN_is_zero(divisor)) {

    BNerror(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 (tmp == NULL || snum == NULL || sdiv == NULL || res == 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 */

  wnum.flags = snum->flags | BN_FLG_STATIC_DATA;

  /* 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_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) |

            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);

#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);

}

int

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

    BN_CTX *ctx)

{

  int ct = ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) ||

      (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0));

  return BN_div_internal(dv, rm, num, divisor, ctx, ct);

}

int

BN_div_nonct(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,

    BN_CTX *ctx)

{

  return BN_div_internal(dv, rm, num, divisor, ctx, 0);

}

int

BN_div_ct(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,

    BN_CTX *ctx)

{

  return BN_div_internal(dv, rm, num, divisor, ctx, 1);

}