--- /dev/null
+/* -*-c-*-
+ *
+ * $Id: mpx-kmul.c,v 1.1 1999/12/10 23:23:51 mdw Exp $
+ *
+ * Karatsuba's multiplication algorithm
+ *
+ * (c) 1999 Straylight/Edgeware
+ */
+
+/*----- Licensing notice --------------------------------------------------*
+ *
+ * This file is part of Catacomb.
+ *
+ * Catacomb is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU Library General Public License as
+ * published by the Free Software Foundation; either version 2 of the
+ * License, or (at your option) any later version.
+ *
+ * Catacomb is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU Library General Public License for more details.
+ *
+ * You should have received a copy of the GNU Library General Public
+ * License along with Catacomb; if not, write to the Free
+ * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ */
+
+/*----- Revision history --------------------------------------------------*
+ *
+ * $Log: mpx-kmul.c,v $
+ * Revision 1.1 1999/12/10 23:23:51 mdw
+ * Karatsuba-Ofman multiplication algorithm.
+ *
+ */
+
+/*----- Header files ------------------------------------------------------*/
+
+#include <stdio.h>
+
+#include "mpx.h"
+
+/*----- Tweakables --------------------------------------------------------*/
+
+/* --- @KARATSUBA_CUTOFF@ --- *
+ *
+ * If either of the arguments to @mpx_kmul@ contains this number of words or
+ * fewer, the job is dumped out to @mpx_umul@ instead. Reduce the size when
+ * testing, to ensure better coverage.
+ */
+
+#ifdef TEST_RIG
+# undef KARATSUBA_CUTOFF
+# define KARATSUBA_CUTOFF 2
+#endif
+
+/*----- Addition macros ---------------------------------------------------*/
+
+#define UADD(dv, av, avl) do { \
+ mpw *_dv = (dv); \
+ const mpw *_av = (av), *_avl = (avl); \
+ mpw _c = 0; \
+ \
+ while (_av < _avl) { \
+ mpw _a, _b; \
+ mpd _x; \
+ _a = *_av++; \
+ _b = *_dv; \
+ _x = (mpd)_a + (mpd)_b + _c; \
+ *_dv++ = MPW(_x); \
+ _c = _x >> MPW_BITS; \
+ } \
+ while (_c) { \
+ mpd _x = (mpd)*_dv + (mpd)_c; \
+ *_dv++ = MPW(_x); \
+ _c = _x >> MPW_BITS; \
+ } \
+} while (0)
+
+#define UADD2(dv, dvl, av, avl, bv, bvl) do { \
+ mpw *_dv = (dv), *_dvl = (dvl); \
+ const mpw *_av = (av), *_avl = (avl); \
+ const mpw *_bv = (bv), *_bvl = (bvl); \
+ mpw _c = 0; \
+ \
+ while (_av < _avl || _bv < _bvl) { \
+ mpw _a, _b; \
+ mpd _x; \
+ _a = (_av < _avl) ? *_av++ : 0; \
+ _b = (_bv < _bvl) ? *_bv++ : 0; \
+ _x = (mpd)_a + (mpd)_b + _c; \
+ *_dv++ = MPW(_x); \
+ _c = _x >> MPW_BITS; \
+ } \
+ *_dv++ = _c; \
+ while (_dv < _dvl) \
+ *_dv++ = 0; \
+} while (0)
+
+#define USUB(dv, av, avl) do { \
+ mpw *_dv = (dv); \
+ const mpw *_av = (av), *_avl = (avl); \
+ mpw _c = 0; \
+ \
+ while (_av < _avl) { \
+ mpw _a, _b; \
+ mpd _x; \
+ _a = *_av++; \
+ _b = *_dv; \
+ _x = (mpd)_b - (mpd)_a - _c; \
+ *_dv++ = MPW(_x); \
+ if (_x >> MPW_BITS) \
+ _c = 1; \
+ else \
+ _c = 0; \
+ } \
+ while (_c) { \
+ mpd _x = (mpd)*_dv - (mpd)_c; \
+ *_dv++ = MPW(_x); \
+ if (_x >> MPW_BITS) \
+ _c = 1; \
+ else \
+ _c = 0; \
+ } \
+} while (0)
+
+/*----- Main code ---------------------------------------------------------*/
+
+/* --- @mpx_kmul@ --- *
+ *
+ * Arguments: @mpw *dv, *dvl@ = pointer to destination buffer
+ * @const mpw *av, *avl@ = pointer to first argument
+ * @const mpw *bv, *bvl@ = pointer to second argument
+ * @mpw *sv, *svl@ = pointer to scratch workspace
+ *
+ * Returns: ---
+ *
+ * Use: Multiplies two multiprecision integers using Karatsuba's
+ * algorithm. This is rather faster than traditional long
+ * multiplication (e.g., @mpx_umul@) on large numbers, although
+ * more expensive on small ones.
+ *
+ * The destination must be twice as large as the larger
+ * argument. The scratch space must be twice as large as the
+ * larger argument, plus the magic number @KARATSUBA_SLOP@.
+ * (Actually, a number of words proportional to the depth of
+ * recursion, but since recusion is strongly bounded by memory,
+ * I can replace it with a constant as long as it's `big
+ * enough'.)
+ */
+
+void mpx_kmul(mpw *dv, mpw *dvl,
+ const mpw *av, const mpw *avl,
+ const mpw *bv, const mpw *bvl,
+ mpw *sv, mpw *svl)
+{
+ const mpw *avm, *bvm;
+ size_t m;
+
+ /* --- Dispose of easy cases to @mpx_umul@ --- *
+ *
+ * Karatsuba is only a win on large numbers, because of all the
+ * recursiveness and bookkeeping. The recursive calls make a quick check
+ * to see whether to bottom out to @mpx_umul@ which should help quite a
+ * lot, but sometimes the only way to know is to make sure...
+ */
+
+ MPX_SHRINK(av, avl);
+ MPX_SHRINK(bv, bvl);
+
+ if (avl - av <= KARATSUBA_CUTOFF || bvl - bv <= KARATSUBA_CUTOFF) {
+ mpx_umul(dv, dvl, av, avl, bv, bvl);
+ return;
+ }
+
+ /* --- How the algorithm works --- *
+ *
+ * Let %$A = xb + y$% and %$B = ub + v$%. Then, simply by expanding, %$AB
+ * = x u b^2 + b(x v + y u) + y v$%. That's not helped any, because I've
+ * got four multiplications, each four times easier than the one I started
+ * with. However, note that I can rewrite the coefficient of %$b$% as
+ * %$xv + yu = (x + y)(u + v) - xu - yv$%. The terms %$xu$% and %$yv$%
+ * I've already calculated, and that leaves only one more multiplication to
+ * do. So now I have three multiplications, each four times easier, and
+ * that's a win.
+ */
+
+ /* --- First things --- *
+ *
+ * Sort out where to break the factors in half. I'll choose the midpoint
+ * of the largest one, since this minimizes the amount of work I have to do
+ * most effectively.
+ */
+
+ if (avl - av > bvl - bv) {
+ m = (avl - av + 1) >> 1;
+ avm = av + m;
+ if (bvl - bv > m)
+ bvm = bv + m;
+ else
+ bvm = bvl;
+ } else {
+ m = (bvl - bv + 1) >> 1;
+ bvm = bv + m;
+ if (avl - av > m)
+ avm = av + m;
+ else
+ avm = avl;
+ }
+
+ /* --- Sort out the middle term --- *
+ *
+ * I'm going to keep track of the carry by hand rather than pass it down to
+ * the next level, because it means multiplication by one or zero, which I
+ * can do easily myself.
+ */
+
+ {
+ unsigned f = 0;
+ enum {
+ carry_a = 1,
+ carry_b = 2
+ };
+
+ mpw *bsv = sv + m, *ssv = bsv + m;
+ mpw *rdv = dv + m, *rdvl = rdv + 2 * m;
+
+ UADD2(sv, bsv + 1, av, avm, avm, avl);
+ if (*bsv)
+ f |= carry_a;
+ UADD2(bsv, ssv + 1, bv, bvm, bvm, bvl);
+ if (*ssv)
+ f |= carry_b;
+ MPX_ZERO(dv, rdv);
+ if (m > KARATSUBA_CUTOFF)
+ mpx_kmul(rdv, rdvl, sv, bsv, bsv, ssv, ssv, svl);
+ else
+ mpx_umul(rdv, rdvl, sv, bsv, bsv, ssv);
+ MPX_ZERO(rdvl, dvl);
+ rdv += m; rdvl += m;
+ if (f & carry_b)
+ UADD(rdv, sv, bsv);
+ if (f & carry_a)
+ UADD(rdv, bsv, ssv);
+ if (!(~f & (carry_a | carry_b)))
+ MPX_UADDN(rdv + m, rdvl, 1);
+ }
+
+ /* --- Sort out the other two terms --- */
+
+ {
+ mpw *ssv = sv + 2 * m;
+ mpw *tdv = dv + m;
+ mpw *rdv = tdv + m;
+
+ if (m > KARATSUBA_CUTOFF)
+ mpx_kmul(sv, ssv, avm, avl, bvm, bvl, ssv, svl);
+ else
+ mpx_umul(sv, ssv, avm, avl, bvm, bvl);
+ UADD(rdv, sv, ssv);
+ USUB(tdv, sv, ssv);
+
+ if (m > KARATSUBA_CUTOFF)
+ mpx_kmul(sv, ssv, av, avm, bv, bvm, ssv, svl);
+ else
+ mpx_umul(sv, ssv, av, avm, bv, bvm);
+ USUB(tdv, sv, ssv);
+ UADD(dv, sv, ssv);
+ }
+}
+
+/*----- Test rig ----------------------------------------------------------*/
+
+#ifdef TEST_RIG
+
+#include <mLib/alloc.h>
+#include <mLib/testrig.h>
+
+#include "mpscan.h"
+
+#define ALLOC(v, vl, sz) do { \
+ size_t _sz = (sz); \
+ mpw *_vv = xmalloc(MPWS(_sz)); \
+ mpw *_vvl = _vv + _sz; \
+ (v) = _vv; \
+ (vl) = _vvl; \
+} while (0)
+
+#define LOAD(v, vl, d) do { \
+ const dstr *_d = (d); \
+ mpw *_v, *_vl; \
+ ALLOC(_v, _vl, MPW_RQ(_d->len)); \
+ mpx_loadb(_v, _vl, _d->buf, _d->len); \
+ (v) = _v; \
+ (vl) = _vl; \
+} while (0)
+
+#define MAX(x, y) ((x) > (y) ? (x) : (y))
+
+static void dumpmp(const char *msg, const mpw *v, const mpw *vl)
+{
+ fputs(msg, stderr);
+ MPX_SHRINK(v, vl);
+ while (v < vl)
+ fprintf(stderr, " %08lx", (unsigned long)*--vl);
+ fputc('\n', stderr);
+}
+
+static int umul(dstr *v)
+{
+ mpw *a, *al;
+ mpw *b, *bl;
+ mpw *c, *cl;
+ mpw *d, *dl;
+ mpw *s, *sl;
+ size_t m;
+ int ok = 1;
+
+ LOAD(a, al, &v[0]);
+ LOAD(b, bl, &v[1]);
+ LOAD(c, cl, &v[2]);
+ m = MAX(al - a, bl - b) + 1;
+ ALLOC(d, dl, 2 * m);
+ ALLOC(s, sl, 2 * m + 32);
+
+ mpx_kmul(d, dl, a, al, b, bl, s, sl);
+ if (MPX_UCMP(d, dl, !=, c, cl)) {
+ fprintf(stderr, "\n*** umul failed\n");
+ dumpmp(" a", a, al);
+ dumpmp(" b", b, bl);
+ dumpmp("expected", c, cl);
+ dumpmp(" result", d, dl);
+ ok = 0;
+ }
+
+ free(a); free(b); free(c); free(d); free(s);
+ return (ok);
+}
+
+static test_chunk defs[] = {
+ { "umul", umul, { &type_hex, &type_hex, &type_hex, 0 } },
+ { 0, 0, { 0 } }
+};
+
+int main(int argc, char *argv[])
+{
+ test_run(argc, argv, defs, SRCDIR"/tests/mpx");
+ return (0);
+}
+
+#endif
+
+/*----- That's all, folks -------------------------------------------------*/
# Test vectors for low-level MP functions
#
-# $Id: mpx,v 1.2 1999/11/14 13:53:12 mdw Exp $
+# $Id: mpx,v 1.3 1999/12/10 23:26:40 mdw Exp $
# --- Load-store tests ---
#
08d95fc1d6dd6b9423c7bb033598df0c
6c03f5958677efd383509141bf257375
03bbd76f19ba19e3f255c24063f6384d4ac913d9e582392589a525195bcc547c;
+
+ # --- Karatsuba regression ---
+ #
+ # This bug was caused by kmul (a) choosing the split point too low on
+ # odd-sized inputs and (b) not allocating enough workspace.
+
+ 21a9269d7b8b63cf18faa933b3c868ba1e8cb3f00b57e197709abf96eeb9bf12e8fe22b3
+ 0144c992b68e3ca712678215d5bc968702ccfea17717737ba501a38d26fa5091ba
+ 2ab495f91afd7c36f85ece6fd58577f995de88d62a98a07c6d9e3500ae67b0f100bc709d1f30894662774d0cadfba091788c427cc6f4bacb26e42cf92f6e4494e03c990e;
+
+ # --- Larger number tests for Karatsuba ---
+
+ 416e63549e2cf08fb225058b3545cb4a47cbf9
+ de38c473c27f7bdef02a084192b3e17f435cf7
+ 38cc3c7f360737411df7b52a222a3672c6e0d39f0a868479176a6143e1129d44d5aa61be493f;
+
+ aa20b1355073f21c57530d2f90bc40e47ac463
+ 8315dfa60e97ff3dab7a6f61fcec2cd5b6f127
+ 571d43fda6ce14a78534ac72c50b58738d62630766a59a7cec1a63433e499b1b5eac5ef71e15;
+
+ f641594177c8c364d922c659a8f7ae0460c7d74b266c8cc258ad5f
+ 5948dd29fc5172c37c31da6957779a1bebe452d8deba26c5d3d390
+ 55e2cf27aa49f938584dca4044d944077e226206c6f8c7688e8760f3b5c106413fd0ef4b63a97991da86fd113ff4822a41f76913d270;
+
+ a4170f55dfa135c4bdd3a921a8c1567eebc6b799fb62b0dd27b089
+ 7b7d619e07a5d01427348c05605f67196b2923b074787c375977ac
+ 4f277232c75290f0c5fed384dba2aaa23fe4a360ea63ee45fb6c0134b36a09a9163f3c767d498b8dcd31e5deaef386d4a9b7d85b4b0c;
+
+ 250e7a0c7035df81429572d3f772720e723b710d54b9eb5f16814117980f0559bf12b82e00c5b3904e
+ 1be3c88b01ce53a70c12f74dcc247823846ac6c06a9cb41b86794900006045f05e29da23b81523aa9f
+ 04097fbcf75616fef7b6b91680963f7e0cf1bf72bc5f453e46136fc92b20ae8a30d7ae7965f8271de854442b93562ebaa9ee09fba4a7b79ef8b26718b12424419dc301496dc0d6cfb04e4f7a3a3729046c72;
+
+ af3148a72dcf1340f6b5a3b2fc1cacd7e6f9e60a13de5c91c37bb850f0e930683c2dc96882a9f62b76
+ 48603cc656908b34c70ed826da8c3414d5845100f53cb6f9f370a4c7708a9b8ffd787537048f89493a
+ 3187b8818bf644805c880d189bbf606ca23e01431cf5b3b633db48a1202aa346f6a0e3958c7264fa1de2d92660345e820f4f3659cf0040a28fb9b725f7ab83610c9c056062326f776ce871696eede0507ebc;
+
+ 0b1cc934a2f6244b93c8ac10881de20349d133642ac19fa0be3acacbf4429d0ec7bbad2f41534a693647b7c02e683cde249e36f008fb68e96de65c8a268eb1ea
+ 12444899c13f0ee85a4f47024f06d8a5746f0d9fec02e57c6d87a7bba17c1454fe6387bff5b96e38ce6142b9eebe249865c52b617b8966e6f93b16f612a91155
+ cafcf1ea9f16a56f9ac4635d58992a789c51b6d7e53b5e1d8b59d5c1850c5c6ac2297839af44b29d5cf440772f98fd9d090ccec2d56adeb113bd3459d620b0b02679b72f3170ea8e2bd4486eebf2496d8be01cfe86923e5bbeb6f91582dfb95c6ef0a52cbc068081dc363b31dbd2ed80e3267d973ea39f82e276002eab9cb2;
+
+ 3ba5a9c550b8cf6c3b87cc106b6551221a0dc90ac193ebcc526e4e5f53cf012fa6e05b155dcb3c4c0e1a90a01062a67ec434f6744195349194770711ea836a8b
+ 54f04f121d22db842523e9bf75727d5b0e9ef17e6d727918894927fade87ceeb2106684c4af7c49653425e29f7a91abf8adec4de2ca499df2534644397e454ac
+ 13ca59703f4c087c16a9a7bc7022904a37a469c1d0fd9fa7ffabe8f7d887fe1572c0bf5c75fde6913b565f8106bba9c26c9bbce190a9b8967112d74c0ac3d4ff9d2a385b96833e3c456d5601c74d8d2c9fff35abc60e7cc15d7c680f20757c13a415f1b8fbe3c6c32434aa36c528473dd20ea39f0e5ee22d1cd23040900d3164;
+
}
usqr {
projects / u / mdw / catacomb / commitdiff