text: #include <tommath.h>
  #ifdef BN_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://libtom.org
   */
  
  /* computes xR**-1 == x (mod N) via Montgomery Reduction */
  int
  mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
  {
    int     ix, res, digs;
    mp_digit mu;
  
    /* can the fast reduction [comba] method be used?
     *
     * Note that unlike in mul you're safely allowed *less*
     * than the available columns [255 per default] since carries
     * are fixed up in the inner loop.
     */
    digs = n->used * 2 + 1;
    if ((digs < MP_WARRAY) &&
        n->used <
        (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
      return fast_mp_montgomery_reduce (x, n, rho);
    }
  
    /* grow the input as required */
    if (x->alloc < digs) {
      if ((res = mp_grow (x, digs)) != MP_OKAY) {
        return res;
      }
    }
    x->used = digs;
  
    for (ix = 0; ix < n->used; ix++) {
      /* mu = ai * rho mod b
       *
       * The value of rho must be precalculated via
       * montgomery_setup() such that
       * it equals -1/n0 mod b this allows the
       * following inner loop to reduce the
       * input one digit at a time
       */
      mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK);
  
      /* a = a + mu * m * b**i */
      {
        register int iy;
        register mp_digit *tmpn, *tmpx, u;
        register mp_word r;
  
        /* alias for digits of the modulus */
        tmpn = n->dp;
  
        /* alias for the digits of x [the input] */
        tmpx = x->dp + ix;
  
        /* set the carry to zero */
        u = 0;
  
        /* Multiply and add in place */
        for (iy = 0; iy < n->used; iy++) {
          /* compute product and sum */
          r       = ((mp_word)mu) * ((mp_word)*tmpn++) +
                    ((mp_word) u) + ((mp_word) * tmpx);
  
          /* get carry */
          u       = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
  
          /* fix digit */
          *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
        }
        /* At this point the ix'th digit of x should be zero */
  
  
        /* propagate carries upwards as required*/
        while (u) {
          *tmpx   += u;
          u        = *tmpx >> DIGIT_BIT;
          *tmpx++ &= MP_MASK;
        }
      }
    }
  
    /* at this point the n.used'th least
     * significant digits of x are all zero
     * which means we can shift x to the
     * right by n.used digits and the
     * residue is unchanged.
     */
  
    /* x = x/b**n.used */
    mp_clamp(x);
    mp_rshd (x, n->used);
  
    /* if x >= n then x = x - n */
    if (mp_cmp_mag (x, n) != MP_LT) {
      return s_mp_sub (x, n, x);
    }
  
    return MP_OKAY;
  }
  #endif
  
  /* $Source: /cvs/libtom/libtommath/bn_mp_montgomery_reduce.c,v $ */
  /* $Revision: 1.4 $ */
  /* $Date: 2006/12/28 01:25:13 $ */
  