--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/bn_fast_mp_montgomery_reduce.c	Mon May 31 18:25:22 2004 +0000
@@ -0,0 +1,167 @@
+/* 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, [email protected], http://math.libtomcrypt.org
+ */
+#include <tommath.h>
+
+/* computes xR**-1 == x (mod N) via Montgomery Reduction
+ *
+ * This is an optimized implementation of mp_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;
+}