--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/libtommath/bn_s_mp_karatsuba_mul.c	Thu Oct 15 19:55:15 2020 +0800
@@ -0,0 +1,174 @@
+#include "tommath_private.h"
+#ifdef BN_S_MP_KARATSUBA_MUL_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis */
+/* SPDX-License-Identifier: Unlicense */
+
+/* c = |a| * |b| using Karatsuba Multiplication using
+ * three half size multiplications
+ *
+ * Let B represent the radix [e.g. 2**MP_DIGIT_BIT] and
+ * let n represent half of the number of digits in
+ * the min(a,b)
+ *
+ * a = a1 * B**n + a0
+ * b = b1 * B**n + b0
+ *
+ * Then, a * b =>
+   a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0
+ *
+ * Note that a1b1 and a0b0 are used twice and only need to be
+ * computed once.  So in total three half size (half # of
+ * digit) multiplications are performed, a0b0, a1b1 and
+ * (a1+b1)(a0+b0)
+ *
+ * Note that a multiplication of half the digits requires
+ * 1/4th the number of single precision multiplications so in
+ * total after one call 25% of the single precision multiplications
+ * are saved.  Note also that the call to mp_mul can end up back
+ * in this function if the a0, a1, b0, or b1 are above the threshold.
+ * This is known as divide-and-conquer and leads to the famous
+ * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than
+ * the standard O(N**2) that the baseline/comba methods use.
+ * Generally though the overhead of this method doesn't pay off
+ * until a certain size (N ~ 80) is reached.
+ */
+mp_err s_mp_karatsuba_mul(const mp_int *a, const mp_int *b, mp_int *c)
+{
+   mp_int  x0, x1, y0, y1, t1, x0y0, x1y1;
+   int     B;
+   mp_err  err = MP_MEM; /* default the return code to an error */
+
+   /* min # of digits */
+   B = MP_MIN(a->used, b->used);
+
+   /* now divide in two */
+   B = B >> 1;
+
+   /* init copy all the temps */
+   if (mp_init_size(&x0, B) != MP_OKAY) {
+      goto LBL_ERR;
+   }
+   if (mp_init_size(&x1, a->used - B) != MP_OKAY) {
+      goto X0;
+   }
+   if (mp_init_size(&y0, B) != MP_OKAY) {
+      goto X1;
+   }
+   if (mp_init_size(&y1, b->used - B) != MP_OKAY) {
+      goto Y0;
+   }
+
+   /* init temps */
+   if (mp_init_size(&t1, B * 2) != MP_OKAY) {
+      goto Y1;
+   }
+   if (mp_init_size(&x0y0, B * 2) != MP_OKAY) {
+      goto T1;
+   }
+   if (mp_init_size(&x1y1, B * 2) != MP_OKAY) {
+      goto X0Y0;
+   }
+
+   /* now shift the digits */
+   x0.used = y0.used = B;
+   x1.used = a->used - B;
+   y1.used = b->used - B;
+
+   {
+      int x;
+      mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
+
+      /* we copy the digits directly instead of using higher level functions
+       * since we also need to shift the digits
+       */
+      tmpa = a->dp;
+      tmpb = b->dp;
+
+      tmpx = x0.dp;
+      tmpy = y0.dp;
+      for (x = 0; x < B; x++) {
+         *tmpx++ = *tmpa++;
+         *tmpy++ = *tmpb++;
+      }
+
+      tmpx = x1.dp;
+      for (x = B; x < a->used; x++) {
+         *tmpx++ = *tmpa++;
+      }
+
+      tmpy = y1.dp;
+      for (x = B; x < b->used; x++) {
+         *tmpy++ = *tmpb++;
+      }
+   }
+
+   /* only need to clamp the lower words since by definition the
+    * upper words x1/y1 must have a known number of digits
+    */
+   mp_clamp(&x0);
+   mp_clamp(&y0);
+
+   /* now calc the products x0y0 and x1y1 */
+   /* after this x0 is no longer required, free temp [x0==t2]! */
+   if (mp_mul(&x0, &y0, &x0y0) != MP_OKAY) {
+      goto X1Y1;          /* x0y0 = x0*y0 */
+   }
+   if (mp_mul(&x1, &y1, &x1y1) != MP_OKAY) {
+      goto X1Y1;          /* x1y1 = x1*y1 */
+   }
+
+   /* now calc x1+x0 and y1+y0 */
+   if (s_mp_add(&x1, &x0, &t1) != MP_OKAY) {
+      goto X1Y1;          /* t1 = x1 - x0 */
+   }
+   if (s_mp_add(&y1, &y0, &x0) != MP_OKAY) {
+      goto X1Y1;          /* t2 = y1 - y0 */
+   }
+   if (mp_mul(&t1, &x0, &t1) != MP_OKAY) {
+      goto X1Y1;          /* t1 = (x1 + x0) * (y1 + y0) */
+   }
+
+   /* add x0y0 */
+   if (mp_add(&x0y0, &x1y1, &x0) != MP_OKAY) {
+      goto X1Y1;          /* t2 = x0y0 + x1y1 */
+   }
+   if (s_mp_sub(&t1, &x0, &t1) != MP_OKAY) {
+      goto X1Y1;          /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */
+   }
+
+   /* shift by B */
+   if (mp_lshd(&t1, B) != MP_OKAY) {
+      goto X1Y1;          /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
+   }
+   if (mp_lshd(&x1y1, B * 2) != MP_OKAY) {
+      goto X1Y1;          /* x1y1 = x1y1 << 2*B */
+   }
+
+   if (mp_add(&x0y0, &t1, &t1) != MP_OKAY) {
+      goto X1Y1;          /* t1 = x0y0 + t1 */
+   }
+   if (mp_add(&t1, &x1y1, c) != MP_OKAY) {
+      goto X1Y1;          /* t1 = x0y0 + t1 + x1y1 */
+   }
+
+   /* Algorithm succeeded set the return code to MP_OKAY */
+   err = MP_OKAY;
+
+X1Y1:
+   mp_clear(&x1y1);
+X0Y0:
+   mp_clear(&x0y0);
+T1:
+   mp_clear(&t1);
+Y1:
+   mp_clear(&y1);
+Y0:
+   mp_clear(&y0);
+X1:
+   mp_clear(&x1);
+X0:
+   mp_clear(&x0);
+LBL_ERR:
+   return err;
+}
+#endif