X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/1b756626c7f156b987666eb548132f7bf0c161dc..6ec3a4cf4aaa7cd375e1aa18f85861986259b8e5:/mpx-kmul.c diff --git a/mpx-kmul.c b/mpx-kmul.c index 7bb4f40..081de88 100644 --- a/mpx-kmul.c +++ b/mpx-kmul.c @@ -1,13 +1,13 @@ /* -*-c-*- * - * $Id: mpx-kmul.c,v 1.2 1999/12/11 10:58:02 mdw Exp $ + * $Id$ * * Karatsuba's multiplication algorithm * * (c) 1999 Straylight/Edgeware */ -/*----- Licensing notice --------------------------------------------------* +/*----- Licensing notice --------------------------------------------------* * * This file is part of Catacomb. * @@ -15,112 +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 1.2 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@ --- * @@ -137,9 +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, @@ -161,18 +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. @@ -181,7 +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. */ @@ -201,64 +122,48 @@ void mpx_kmul(mpw *dv, mpw *dvl, 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); } } @@ -269,23 +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)) @@ -313,20 +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); }