Change the compiler's big integer library to use libTomMath

This now replaces Bill's crappy big int implementation

src/libtommath/mp_montgomery_reduce.c

@@ -0,0 +1,89 @@
+#include "tommath_private.h"
+#ifdef MP_MONTGOMERY_REDUCE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis */
+/* SPDX-License-Identifier: Unlicense */
+
+/* computes xR**-1 == x (mod N) via Montgomery Reduction */
+mp_err mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho)
+{
+   mp_err err;
+   int ix, digs;
+
+   /* 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) &&
+       (x->used <= MP_WARRAY) &&
+       (n->used < MP_MAX_COMBA)) {
+      return s_mp_montgomery_reduce_comba(x, n, rho);
+   }
+
+   /* grow the input as required */
+   if ((err = mp_grow(x, digs)) != MP_OKAY) {
+      return err;
+   }
+   x->used = digs;
+
+   for (ix = 0; ix < n->used; ix++) {
+      int iy;
+      mp_digit u, mu;
+
+      /* 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 */
+
+      /* Multiply and add in place */
+      u = 0;
+      for (iy = 0; iy < n->used; iy++) {
+         /* compute product and sum */
+         mp_word r = ((mp_word)mu * (mp_word)n->dp[iy]) +
+                     (mp_word)u + (mp_word)x->dp[ix + iy];
+
+         /* get carry */
+         u       = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT);
+
+         /* fix digit */
+         x->dp[ix + iy] = (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 != 0u) {
+         x->dp[ix + iy]   += u;
+         u        = x->dp[ix + iy] >> MP_DIGIT_BIT;
+         x->dp[ix + iy] &= MP_MASK;
+         ++iy;
+      }
+   }
+
+   /* 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