--- /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 -------------------------------------------------*/
projects / u / mdw / catacomb / blobdiff