/* -*-c-*-
*
- * $Id: mpx-kmul.c,v 1.1 1999/12/10 23:23:51 mdw Exp $
+ * $Id$
*
* Karatsuba's multiplication algorithm
*
* (c) 1999 Straylight/Edgeware
*/
-/*----- Licensing notice --------------------------------------------------*
+/*----- Licensing notice --------------------------------------------------*
*
* This file is part of Catacomb.
*
* 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 <assert.h>
#include <stdio.h>
#include "mpx.h"
+#include "karatsuba.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
+# undef MPK_THRESH
+# define MPK_THRESH 4 /* Smallest possible correct value */
#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@ --- *
* 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'.)
+ * The destination must be three times as large as the larger
+ * argument. The scratch space must be five times as large as
+ * the larger argument.
*/
void mpx_kmul(mpw *dv, mpw *dvl,
MPX_SHRINK(av, avl);
MPX_SHRINK(bv, bvl);
- if (avl - av <= KARATSUBA_CUTOFF || bvl - bv <= KARATSUBA_CUTOFF) {
+ if (avl - av <= MPK_THRESH || bvl - bv <= MPK_THRESH) {
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 %$yv$%
+ * 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
+ * of the larger one, since this minimizes the amount of work I have to do
* most effectively.
*/
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.
- */
+ /* --- Sort out the middle term --- */
{
- 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)
+ mpw *bsv = sv + m + 1, *ssv = bsv + m + 1;
+ mpw *rdv = dv + m, *rdvl = rdv + 2 * (m + 2);
+
+ assert(rdvl <= dvl);
+ assert(ssv <= svl);
+ UADD2(sv, bsv, av, avm, avm, avl);
+ UADD2(bsv, ssv, bv, bvm, bvm, bvl);
+ if (m > MPK_THRESH)
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 *svm = sv + m, *svn = svm + m, *ssv = svn + 4;
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)
+ if (avl == avm || bvl == bvm)
+ MPX_ZERO(rdv + m + 1, dvl);
+ else {
+ if (m > MPK_THRESH)
+ mpx_kmul(sv, ssv, avm, avl, bvm, bvl, ssv, svl);
+ else
+ mpx_umul(sv, ssv, avm, avl, bvm, bvl);
+ MPX_COPY(rdv + m + 1, dvl, svm + 1, svn);
+ UADD(rdv, sv, svm + 1);
+ USUB(tdv, sv, svn);
+ }
+
+ if (m > MPK_THRESH)
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);
+ MPX_COPY(dv, tdv, sv, svm);
+ USUB(tdv, sv, svn);
+ UADD(tdv, svm, svn);
}
}
#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; \
+#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; \
+#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))
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);
+ ALLOC(d, dl, 3 * m);
+ ALLOC(s, sl, 5 * m);
mpx_kmul(d, dl, a, al, b, bl, s, sl);
- if (MPX_UCMP(d, dl, !=, c, cl)) {
+ if (!mpx_ueq(d, dl, c, cl)) {
fprintf(stderr, "\n*** umul failed\n");
- dumpmp(" a", a, al);
- dumpmp(" b", b, bl);
+ 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);
+ xfree(a); xfree(b); xfree(c); xfree(d); xfree(s);
return (ok);
}
projects / u / mdw / catacomb / blobdiff