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authorjan.nijtmans <nijtmans@users.sourceforge.net>2017-09-18 08:31:55 (GMT)
committerjan.nijtmans <nijtmans@users.sourceforge.net>2017-09-18 08:31:55 (GMT)
commita187f65cfd5964971d7ed52f09e18fdbb4bf51cc (patch)
tree6b7bbde03122d1571d4543d10eccfe88610bd680 /libtommath/bn_mp_karatsuba_mul.c
parent0faaca01de4e9fa2039c7fdd34f60b138f665249 (diff)
parent30f7e69b182d1267056ee2628a860891f6555aa3 (diff)
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Merge libtommath upstream changes (astyle formatting only). No functional changes. All Tcl-specific modifications are kept.
Diffstat (limited to 'libtommath/bn_mp_karatsuba_mul.c')
-rw-r--r--libtommath/bn_mp_karatsuba_mul.c263
1 files changed, 135 insertions, 128 deletions
diff --git a/libtommath/bn_mp_karatsuba_mul.c b/libtommath/bn_mp_karatsuba_mul.c
index 1e6a42b..1a84211 100644
--- a/libtommath/bn_mp_karatsuba_mul.c
+++ b/libtommath/bn_mp_karatsuba_mul.c
@@ -15,150 +15,157 @@
* Tom St Denis, tstdenis82@gmail.com, http://libtom.org
*/
-/* c = |a| * |b| using Karatsuba Multiplication using
+/* c = |a| * |b| using Karatsuba Multiplication using
* three half size multiplications
*
- * Let B represent the radix [e.g. 2**DIGIT_BIT] and
- * let n represent half of the number of digits in
+ * Let B represent the radix [e.g. 2**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 =>
+ * 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
+ * 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
+ * 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.
*/
-int mp_karatsuba_mul (const mp_int * a, const mp_int * b, mp_int * c)
+int 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, err;
-
- /* default the return code to an error */
- err = MP_MEM;
-
- /* min # of digits */
- B = 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 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);
+ mp_int x0, x1, y0, y1, t1, x0y0, x1y1;
+ int B, err;
+
+ /* default the return code to an error */
+ err = MP_MEM;
+
+ /* min # of digits */
+ B = 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 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);
ERR:
- return err;
+ return err;
}
#endif