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bn_div.c

/* 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>
    */
#  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(SIXTY_FOUR_BIT_LONG)
   /*
    * Same story here, but it's 128-bit by 64-bit division. Wow!
    *                         <appro@fy.chalmers.se>
    */
#  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[_no_branch] 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_no_branch(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num,
        const BIGNUM *divisor, BN_CTX *ctx);
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;

      /* 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)
            {
            BNerr(BN_F_BN_DIV,BN_R_NOT_INITIALIZED);
            return 0;
            }

      bn_check_top(num);

      if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0))
            {
            return BN_div_no_branch(dv, rm, num, divisor, ctx);
            }

      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))
            {
            BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
            return(0);
            }

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

      /* space for temp */
      if (!bn_wexpand(tmp,(div_n+1))) goto err;

      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,ql,qh;

                  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
                  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);
            }
      BN_CTX_end(ctx);
      return(1);
err:
      bn_check_top(rm);
      BN_CTX_end(ctx);
      return(0);
      }


/* BN_div_no_branch is a special version of BN_div. It does not contain
 * branches that may leak sensitive information.
 */
static int BN_div_no_branch(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;

      bn_check_top(dv);
      bn_check_top(rm);
      /* bn_check_top(num); */ /* 'num' has been checked in BN_div() */
      bn_check_top(divisor);

      if (BN_is_zero(divisor))
            {
            BNerr(BN_F_BN_DIV_NO_BRANCH,BN_R_DIV_BY_ZERO);
            return(0);
            }

      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) 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;

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

      /* space for temp */
      if (!bn_wexpand(tmp,(div_n+1))) goto err;

      /* 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,ql,qh;

                  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
                  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);
            }
      bn_correct_top(res);
      BN_CTX_end(ctx);
      return(1);
err:
      bn_check_top(rm);
      BN_CTX_end(ctx);
      return(0);
      }

#endif

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