text: #include <tommath.h>
  #ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
  /* LibTomMath, multiple-precision integer library -- Tom St Denis
   *
   * LibTomMath is a library that provides multiple-precision
   * integer arithmetic as well as number theoretic functionality.
   *
   * The library was designed directly after the MPI library by
   * Michael Fromberger but has been written from scratch with
   * additional optimizations in place.
   *
   * The library is free for all purposes without any express
   * guarantee it works.
   *
   * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
   */
  
  /* computes xR**-1 == x (mod N) via Montgomery Reduction
   *
   * This is an optimized implementation of montgomery_reduce
   * which uses the comba method to quickly calculate the columns of the
   * reduction.
   *
   * Based on Algorithm 14.32 on pp.601 of HAC.
  */
  int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
  {
    int     ix, res, olduse;
    mp_word W[MP_WARRAY];
  
    /* get old used count */
    olduse = x->used;
  
    /* grow a as required */
    if (x->alloc < n->used + 1) {
      if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
        return res;
      }
    }
  
    /* first we have to get the digits of the input into
     * an array of double precision words W[...]
     */
    {
      register mp_word *_W;
      register mp_digit *tmpx;
  
      /* alias for the W[] array */
      _W   = W;
  
      /* alias for the digits of  x*/
      tmpx = x->dp;
  
      /* copy the digits of a into W[0..a->used-1] */
      for (ix = 0; ix < x->used; ix++) {
        *_W++ = *tmpx++;
      }
  
      /* zero the high words of W[a->used..m->used*2] */
      for (; ix < n->used * 2 + 1; ix++) {
        *_W++ = 0;
      }
    }
  
    /* now we proceed to zero successive digits
     * from the least significant upwards
     */
    for (ix = 0; ix < n->used; ix++) {
      /* mu = ai * m' mod b
       *
       * We avoid a double precision multiplication (which isn't required)
       * by casting the value down to a mp_digit.  Note this requires
       * that W[ix-1] have  the carry cleared (see after the inner loop)
       */
      register mp_digit mu;
      mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
  
      /* a = a + mu * m * b**i
       *
       * This is computed in place and on the fly.  The multiplication
       * by b**i is handled by offseting which columns the results
       * are added to.
       *
       * Note the comba method normally doesn't handle carries in the
       * inner loop In this case we fix the carry from the previous
       * column since the Montgomery reduction requires digits of the
       * result (so far) [see above] to work.  This is
       * handled by fixing up one carry after the inner loop.  The
       * carry fixups are done in order so after these loops the
       * first m->used words of W[] have the carries fixed
       */
      {
        register int iy;
        register mp_digit *tmpn;
        register mp_word *_W;
  
        /* alias for the digits of the modulus */
        tmpn = n->dp;
  
        /* Alias for the columns set by an offset of ix */
        _W = W + ix;
  
        /* inner loop */
        for (iy = 0; iy < n->used; iy++) {
            *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
        }
      }
  
      /* now fix carry for next digit, W[ix+1] */
      W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
    }
  
    /* now we have to propagate the carries and
     * shift the words downward [all those least
     * significant digits we zeroed].
     */
    {
      register mp_digit *tmpx;
      register mp_word *_W, *_W1;
  
      /* nox fix rest of carries */
  
      /* alias for current word */
      _W1 = W + ix;
  
      /* alias for next word, where the carry goes */
      _W = W + ++ix;
  
      for (; ix <= n->used * 2 + 1; ix++) {
        *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
      }
  
      /* copy out, A = A/b**n
       *
       * The result is A/b**n but instead of converting from an
       * array of mp_word to mp_digit than calling mp_rshd
       * we just copy them in the right order
       */
  
      /* alias for destination word */
      tmpx = x->dp;
  
      /* alias for shifted double precision result */
      _W = W + n->used;
  
      for (ix = 0; ix < n->used + 1; ix++) {
        *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
      }
  
      /* zero oldused digits, if the input a was larger than
       * m->used+1 we'll have to clear the digits
       */
      for (; ix < olduse; ix++) {
        *tmpx++ = 0;
      }
    }
  
    /* set the max used and clamp */
    x->used = n->used + 1;
    mp_clamp (x);
  
    /* if A >= m then A = A - m */
    if (mp_cmp_mag (x, n) != MP_LT) {
      return s_mp_sub (x, n, x);
    }
    return MP_OKAY;
  }
  #endif
  
  /* $Source$ */
  /* $Revision$ */
  /* $Date$ */
  