--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/libtommath/bn_mp_toom_mul.c	Thu Jan 11 03:14:55 2007 +0000
@@ -0,0 +1,284 @@
+#include <tommath.h>
+#ifdef BN_MP_TOOM_MUL_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, [email protected], http://math.libtomcrypt.com
+ */
+
+/* multiplication using the Toom-Cook 3-way algorithm 
+ *
+ * Much more complicated than Karatsuba but has a lower 
+ * asymptotic running time of O(N**1.464).  This algorithm is 
+ * only particularly useful on VERY large inputs 
+ * (we're talking 1000s of digits here...).
+*/
+int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
+{
+    mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
+    int res, B;
+        
+    /* init temps */
+    if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, 
+                             &a0, &a1, &a2, &b0, &b1, 
+                             &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) {
+       return res;
+    }
+    
+    /* B */
+    B = MIN(a->used, b->used) / 3;
+    
+    /* a = a2 * B**2 + a1 * B + a0 */
+    if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
+       goto ERR;
+    }
+
+    if ((res = mp_copy(a, &a1)) != MP_OKAY) {
+       goto ERR;
+    }
+    mp_rshd(&a1, B);
+    mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
+
+    if ((res = mp_copy(a, &a2)) != MP_OKAY) {
+       goto ERR;
+    }
+    mp_rshd(&a2, B*2);
+    
+    /* b = b2 * B**2 + b1 * B + b0 */
+    if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) {
+       goto ERR;
+    }
+
+    if ((res = mp_copy(b, &b1)) != MP_OKAY) {
+       goto ERR;
+    }
+    mp_rshd(&b1, B);
+    mp_mod_2d(&b1, DIGIT_BIT * B, &b1);
+
+    if ((res = mp_copy(b, &b2)) != MP_OKAY) {
+       goto ERR;
+    }
+    mp_rshd(&b2, B*2);
+    
+    /* w0 = a0*b0 */
+    if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) {
+       goto ERR;
+    }
+    
+    /* w4 = a2 * b2 */
+    if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) {
+       goto ERR;
+    }
+    
+    /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
+    if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
+       goto ERR;
+    }
+    if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
+       goto ERR;
+    }
+    if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
+       goto ERR;
+    }
+    if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
+       goto ERR;
+    }
+    
+    if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) {
+       goto ERR;
+    }
+    if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
+       goto ERR;
+    }
+    if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
+       goto ERR;
+    }
+    if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) {
+       goto ERR;
+    }
+    
+    if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) {
+       goto ERR;
+    }
+    
+    /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
+    if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
+       goto ERR;
+    }
+    if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
+       goto ERR;
+    }
+    if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
+       goto ERR;
+    }
+    if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
+       goto ERR;
+    }
+    
+    if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) {
+       goto ERR;
+    }
+    if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
+       goto ERR;
+    }
+    if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
+       goto ERR;
+    }
+    if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
+       goto ERR;
+    }
+    
+    if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) {
+       goto ERR;
+    }
+    
+
+    /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
+    if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
+       goto ERR;
+    }
+    if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
+       goto ERR;
+    }
+    if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) {
+       goto ERR;
+    }
+    if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
+       goto ERR;
+    }
+    if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) {
+       goto ERR;
+    }
+    
+    /* now solve the matrix 
+    
+       0  0  0  0  1
+       1  2  4  8  16
+       1  1  1  1  1
+       16 8  4  2  1
+       1  0  0  0  0
+       
+       using 12 subtractions, 4 shifts, 
+              2 small divisions and 1 small multiplication 
+     */
+     
+     /* r1 - r4 */
+     if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
+        goto ERR;
+     }
+     /* r3 - r0 */
+     if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
+        goto ERR;
+     }
+     /* r1/2 */
+     if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
+        goto ERR;
+     }
+     /* r3/2 */
+     if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
+        goto ERR;
+     }
+     /* r2 - r0 - r4 */
+     if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
+        goto ERR;
+     }
+     if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
+        goto ERR;
+     }
+     /* r1 - r2 */
+     if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
+        goto ERR;
+     }
+     /* r3 - r2 */
+     if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
+        goto ERR;
+     }
+     /* r1 - 8r0 */
+     if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
+        goto ERR;
+     }
+     if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
+        goto ERR;
+     }
+     /* r3 - 8r4 */
+     if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
+        goto ERR;
+     }
+     if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
+        goto ERR;
+     }
+     /* 3r2 - r1 - r3 */
+     if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
+        goto ERR;
+     }
+     if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
+        goto ERR;
+     }
+     if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
+        goto ERR;
+     }
+     /* r1 - r2 */
+     if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
+        goto ERR;
+     }
+     /* r3 - r2 */
+     if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
+        goto ERR;
+     }
+     /* r1/3 */
+     if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
+        goto ERR;
+     }
+     /* r3/3 */
+     if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
+        goto ERR;
+     }
+     
+     /* at this point shift W[n] by B*n */
+     if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
+        goto ERR;
+     }
+     if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
+        goto ERR;
+     }
+     if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
+        goto ERR;
+     }
+     if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
+        goto ERR;
+     }     
+     
+     if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) {
+        goto ERR;
+     }
+     if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
+        goto ERR;
+     }
+     if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
+        goto ERR;
+     }
+     if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) {
+        goto ERR;
+     }     
+     
+ERR:
+     mp_clear_multi(&w0, &w1, &w2, &w3, &w4, 
+                    &a0, &a1, &a2, &b0, &b1, 
+                    &b2, &tmp1, &tmp2, NULL);
+     return res;
+}     
+     
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_toom_mul.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */