X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/4468424ee46294bb2073ca546d54cced2b9bdf02..908ebb29ff621f582b34d48fd4278b60b78379b6:/mpx-kmul.c diff --git a/mpx-kmul.c b/mpx-kmul.c index d53622b..081de88 100644 --- a/mpx-kmul.c +++ b/mpx-kmul.c @@ -1,13 +1,13 @@ /* -*-c-*- * - * $Id: mpx-kmul.c,v 1.3 1999/12/13 15:35:01 mdw Exp $ + * $Id$ * * Karatsuba's multiplication algorithm * * (c) 1999 Straylight/Edgeware */ -/*----- Licensing notice --------------------------------------------------* +/*----- Licensing notice --------------------------------------------------* * * This file is part of Catacomb. * @@ -15,116 +15,33 @@ * 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 1.3 1999/12/13 15:35:01 mdw - * Simplify and improve. - * - * Revision 1.2 1999/12/11 10:58:02 mdw - * Remove tweakable comments. - * - * Revision 1.1 1999/12/10 23:23:51 mdw - * Karatsuba-Ofman multiplication algorithm. - * - */ - /*----- Header files ------------------------------------------------------*/ #include #include #include "mpx.h" +#include "karatsuba.h" /*----- Tweakables --------------------------------------------------------*/ #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@ --- * @@ -141,9 +58,9 @@ * 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@. + * 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, @@ -165,18 +82,18 @@ 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. @@ -185,7 +102,7 @@ void mpx_kmul(mpw *dv, mpw *dvl, /* --- 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. */ @@ -205,20 +122,17 @@ void mpx_kmul(mpw *dv, mpw *dvl, avm = avl; } - assert(((void)"Destination too small for Karatsuba multiply", - dvl - dv >= 4 * m)); - assert(((void)"Not enough workspace for Karatsuba multiply", - svl - sv >= 4 * m)); - /* --- Sort out the middle term --- */ { 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 > KARATSUBA_CUTOFF) + if (m > MPK_THRESH) mpx_kmul(rdv, rdvl, sv, bsv, bsv, ssv, ssv, svl); else mpx_umul(rdv, rdvl, sv, bsv, bsv, ssv); @@ -234,7 +148,7 @@ void mpx_kmul(mpw *dv, mpw *dvl, if (avl == avm || bvl == bvm) MPX_ZERO(rdv + m + 1, dvl); else { - if (m > KARATSUBA_CUTOFF) + if (m > MPK_THRESH) mpx_kmul(sv, ssv, avm, avl, bvm, bvl, ssv, svl); else mpx_umul(sv, ssv, avm, avl, bvm, bvl); @@ -243,7 +157,7 @@ void mpx_kmul(mpw *dv, mpw *dvl, USUB(tdv, sv, svn); } - if (m > KARATSUBA_CUTOFF) + if (m > MPK_THRESH) mpx_kmul(sv, ssv, av, avm, bv, bvm, ssv, svl); else mpx_umul(sv, ssv, av, avm, bv, bvm); @@ -260,23 +174,21 @@ void mpx_kmul(mpw *dv, mpw *dvl, #include #include -#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)) @@ -304,20 +216,20 @@ static int umul(dstr *v) 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); }