text: /* 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 <openssl/bn.h>
  
  #include <limits.h>
  #include <openssl/err.h>
  
  #include "internal.h"
  
  
  #define asm __asm__
  
  #if !defined(OPENSSL_NO_ASM)
  # if defined(__GNUC__) && __GNUC__>=2
  #  if defined(OPENSSL_X86)
     /*
      * 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 div_asm
  #  define div_asm(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(OPENSSL_X86_64)
     /*
      * Same story here, but it's 128-bit by 64-bit division. Wow!
      *					<appro@fy.chalmers.se>
      */
  #  undef div_asm
  #  define div_asm(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. */
  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 */
    if ((num->top > 0 && num->d[num->top - 1] == 0) ||
        (divisor->top > 0 && divisor->d[divisor->top - 1] == 0)) {
      OPENSSL_PUT_ERROR(BN, BN_div, BN_R_NOT_INITIALIZED);
      return 0;
    }
  
    if ((num->flags & BN_FLG_CONSTTIME) != 0 ||
        (divisor->flags & BN_FLG_CONSTTIME) != 0) {
      no_branch = 1;
    }
  
    if (BN_is_zero(divisor)) {
      OPENSSL_PUT_ERROR(BN, 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) {
        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 */
      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(div_asm)
        q = (BN_ULONG)(((((BN_ULLONG)n0) << BN_BITS2) | n1) / d0);
  #else
        q = div_asm(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;
  
  #if defined(div_asm)
        q = div_asm(n0, n1, d0);
  #else
        q = bn_div_words(n0, n1, d0);
  #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 */
      }
  
      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;
      if (!BN_rshift(rm, snum, norm_shift)) {
        goto err;
      }
      if (!BN_is_zero(rm)) {
        rm->neg = neg;
      }
    }
    if (no_branch) {
      bn_correct_top(res);
    }
    BN_CTX_end(ctx);
    return 1;
  
  err:
    BN_CTX_end(ctx);
    return 0;
  }
  
  int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx) {
    if (!(BN_mod(r, m, d, ctx))) {
      return 0;
    }
    if (!r->neg) {
      return 1;
    }
  
    /* now -|d| < r < 0, so we have to set r := r + |d|. */
    return (d->neg ? BN_sub : BN_add)(r, r, d);
  }
  
  int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
                 BN_CTX *ctx) {
    if (!BN_add(r, a, b)) {
      return 0;
    }
    return BN_nnmod(r, r, m, ctx);
  }
  
  int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
                       const BIGNUM *m) {
    if (!BN_uadd(r, a, b)) {
      return 0;
    }
    if (BN_ucmp(r, m) >= 0) {
      return BN_usub(r, r, m);
    }
    return 1;
  }
  
  int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
                 BN_CTX *ctx) {
    if (!BN_sub(r, a, b)) {
      return 0;
    }
    return BN_nnmod(r, r, m, ctx);
  }
  
  /* BN_mod_sub variant that may be used if both  a  and  b  are non-negative
   * and less than  m */
  int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
                       const BIGNUM *m) {
    if (!BN_sub(r, a, b)) {
      return 0;
    }
    if (r->neg) {
      return BN_add(r, r, m);
    }
    return 1;
  }
  
  int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
                 BN_CTX *ctx) {
    BIGNUM *t;
    int ret = 0;
  
    BN_CTX_start(ctx);
    t = BN_CTX_get(ctx);
    if (t == NULL) {
      goto err;
    }
  
    if (a == b) {
      if (!BN_sqr(t, a, ctx)) {
        goto err;
      }
    } else {
      if (!BN_mul(t, a, b, ctx)) {
        goto err;
      }
    }
  
    if (!BN_nnmod(r, t, m, ctx)) {
      goto err;
    }
  
    ret = 1;
  
  err:
    BN_CTX_end(ctx);
    return ret;
  }
  
  int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx) {
    if (!BN_sqr(r, a, ctx)) {
      return 0;
    }
  
    /* r->neg == 0,  thus we don't need BN_nnmod */
    return BN_mod(r, r, m, ctx);
  }
  
  int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
                    BN_CTX *ctx) {
    BIGNUM *abs_m = NULL;
    int ret;
  
    if (!BN_nnmod(r, a, m, ctx)) {
      return 0;
    }
  
    if (m->neg) {
      abs_m = BN_dup(m);
      if (abs_m == NULL) {
        return 0;
      }
      abs_m->neg = 0;
    }
  
    ret = BN_mod_lshift_quick(r, r, n, (abs_m ? abs_m : m));
  
    BN_free(abs_m);
    return ret;
  }
  
  int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m) {
    if (r != a) {
      if (BN_copy(r, a) == NULL) {
        return 0;
      }
    }
  
    while (n > 0) {
      int max_shift;
  
      /* 0 < r < m */
      max_shift = BN_num_bits(m) - BN_num_bits(r);
      /* max_shift >= 0 */
  
      if (max_shift < 0) {
        OPENSSL_PUT_ERROR(BN, BN_mod_lshift_quick, BN_R_INPUT_NOT_REDUCED);
        return 0;
      }
  
      if (max_shift > n) {
        max_shift = n;
      }
  
      if (max_shift) {
        if (!BN_lshift(r, r, max_shift)) {
          return 0;
        }
        n -= max_shift;
      } else {
        if (!BN_lshift1(r, r)) {
          return 0;
        }
        --n;
      }
  
      /* BN_num_bits(r) <= BN_num_bits(m) */
      if (BN_cmp(r, m) >= 0) {
        if (!BN_sub(r, r, m)) {
          return 0;
        }
      }
    }
  
    return 1;
  }
  
  int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx) {
    if (!BN_lshift1(r, a)) {
      return 0;
    }
  
    return BN_nnmod(r, r, m, ctx);
  }
  
  int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m) {
    if (!BN_lshift1(r, a)) {
      return 0;
    }
    if (BN_cmp(r, m) >= 0) {
      return BN_sub(r, r, m);
    }
  
    return 1;
  }
  
  BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w) {
    BN_ULONG ret = 0;
    int i, j;
  
    w &= BN_MASK2;
  
    if (!w) {
      /* actually this an error (division by zero) */
      return (BN_ULONG) - 1;
    }
  
    if (a->top == 0) {
      return 0;
    }
  
    /* normalize input (so bn_div_words doesn't complain) */
    j = BN_BITS2 - BN_num_bits_word(w);
    w <<= j;
    if (!BN_lshift(a, a, j)) {
      return (BN_ULONG) - 1;
    }
  
    for (i = a->top - 1; i >= 0; i--) {
      BN_ULONG l, d;
  
      l = a->d[i];
      d = bn_div_words(ret, l, w);
      ret = (l - ((d * w) & BN_MASK2)) & BN_MASK2;
      a->d[i] = d;
    }
  
    if ((a->top > 0) && (a->d[a->top - 1] == 0)) {
      a->top--;
    }
  
    ret >>= j;
    return ret;
  }
  
  BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w) {
  #ifndef BN_LLONG
    BN_ULONG ret = 0;
  #else
    BN_ULLONG ret = 0;
  #endif
    int i;
  
    if (w == 0) {
      return (BN_ULONG) -1;
    }
  
    w &= BN_MASK2;
    for (i = a->top - 1; i >= 0; i--) {
  #ifndef BN_LLONG
      ret = ((ret << BN_BITS4) | ((a->d[i] >> BN_BITS4) & BN_MASK2l)) % w;
      ret = ((ret << BN_BITS4) | (a->d[i] & BN_MASK2l)) % w;
  #else
      ret = (BN_ULLONG)(((ret << (BN_ULLONG)BN_BITS2) | a->d[i]) % (BN_ULLONG)w);
  #endif
    }
    return (BN_ULONG)ret;
  }
  