kc3-lang/libtommath/s_mp_montgomery_reduce_fast.c

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• Hash : 7a68f128
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  Date : 2019-10-19T16:24:39
  

  Execute move.sh - Rename files from bn_* to match the function names. * git blame <renamed-file> is not affected * git log --follow <renamed-file> can be used to show log across renames

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• s_mp_montgomery_reduce_fast.c

• #include "tommath_private.h"
  #ifdef S_MP_MONTGOMERY_REDUCE_FAST_C
  /* LibTomMath, multiple-precision integer library -- Tom St Denis */
  /* SPDX-License-Identifier: Unlicense */
  
  /* 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.
  */
  mp_err s_mp_montgomery_reduce_fast(mp_int *x, const mp_int *n, mp_digit rho)
  {
     int     ix, olduse;
     mp_err  err;
     mp_word W[MP_WARRAY];
  
     if (x->used > MP_WARRAY) {
        return MP_VAL;
     }
  
     /* get old used count */
     olduse = x->used;
  
     /* grow a as required */
     if (x->alloc < (n->used + 1)) {
        if ((err = mp_grow(x, n->used + 1)) != MP_OKAY) {
           return err;
        }
     }
  
     /* first we have to get the digits of the input into
      * an array of double precision words W[...]
      */
     {
        mp_word *_W;
        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] */
        if (ix < ((n->used * 2) + 1)) {
           MP_ZERO_BUFFER(_W, sizeof(mp_word) * (size_t)(((n->used * 2) + 1) - ix));
        }
     }
  
     /* 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)
         */
        mp_digit mu;
        mu = ((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
         */
        {
           int iy;
           mp_digit *tmpn;
           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)MP_DIGIT_BIT;
     }
  
     /* now we have to propagate the carries and
      * shift the words downward [all those least
      * significant digits we zeroed].
      */
     {
        mp_digit *tmpx;
        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)MP_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++ = *_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
         */
        MP_ZERO_DIGITS(tmpx, olduse - ix);
     }
  
     /* 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
  

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