X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/4468424ee46294bb2073ca546d54cced2b9bdf02..6a7dce9165a4a707382e49877334353618fcad9a:/mpx-ksqr.c diff --git a/mpx-ksqr.c b/mpx-ksqr.c index 3ca145d..ba7aa18 100644 --- a/mpx-ksqr.c +++ b/mpx-ksqr.c @@ -1,13 +1,13 @@ /* -*-c-*- * - * $Id: mpx-ksqr.c,v 1.2 1999/12/13 15:35:01 mdw Exp $ + * $Id$ * * Karatsuba-based squaring algorithm * * (c) 1999 Straylight/Edgeware */ -/*----- Licensing notice --------------------------------------------------* +/*----- Licensing notice --------------------------------------------------* * * This file is part of Catacomb. * @@ -15,79 +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-ksqr.c,v $ - * Revision 1.2 1999/12/13 15:35:01 mdw - * Simplify and improve. - * - * Revision 1.1 1999/12/11 10:57:43 mdw - * Karatsuba squaring 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 #endif -/*----- Addition macros ---------------------------------------------------*/ - -#define ULSL1(dv, av, avl) do { \ - mpw *_dv = (dv); \ - const mpw *_av = (av), *_avl = (avl); \ - mpw _c = 0; \ - \ - while (_av < _avl) { \ - mpw _x = *_av++; \ - *_dv++ = MPW(_c | (_x << 1)); \ - _c = MPW(_x >> (MPW_BITS - 1)); \ - } \ - *_dv++ = _c; \ -} while (0) - -#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) - /*----- Main code ---------------------------------------------------------*/ /* --- @mpx_ksqr@ --- * @@ -104,9 +58,9 @@ * large numbers, although more expensive on small ones, and * rather simpler than full-blown Karatsuba multiplication. * - * The destination must be twice as large as the argument. The - * scratch space must be twice as large as the 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_ksqr(mpw *dv, mpw *dvl, @@ -126,17 +80,17 @@ void mpx_ksqr(mpw *dv, mpw *dvl, MPX_SHRINK(av, avl); - if (avl - av <= KARATSUBA_CUTOFF) { + if (avl - av <= MPK_THRESH) { mpx_usqr(dv, dvl, av, avl); return; } /* --- How the algorithm works --- * * - * Unlike Karatsuba's identity for multiplication which isn't particularly - * obvious, the identity for multiplication is known to all schoolchildren. - * Let %$A = xb + y$%. Then %$A^2 = x^2 b^x + 2 x y b + y^2$%. So now I - * have three multiplications, each four times easier, and that's a win. + * The identity for squaring is known to all schoolchildren. + * Let %$A = xb + y$%. Then %$A^2 = x^2 b^2 + 2 x y b + y^2$%. Now, + * %$(x + y)^2 - x^2 - y^2 = 2 x y$%, which means I only need to do three + * squarings. */ /* --- First things --- * @@ -147,11 +101,6 @@ void mpx_ksqr(mpw *dv, mpw *dvl, m = (avl - av + 1) >> 1; avm = av + m; - assert(((void)"Destination too small for Karatsuba square", - dvl - dv >= 4 * m)); - assert(((void)"Not enough workspace for Karatsuba square", - svl - sv >= 4 * m)); - /* --- Sort out everything --- */ { @@ -159,31 +108,29 @@ void mpx_ksqr(mpw *dv, mpw *dvl, mpw *tdv = dv + m; mpw *rdv = tdv + m; - /* --- The cross term in the middle needs a multiply --- * - * - * This isn't actually true, since %$x y = ((x + y)^2 - (x - y)^2)/4%. - * But that's two squarings, versus one multiplication. - */ - - if (m > KARATSUBA_CUTOFF) - mpx_kmul(sv, ssv, av, avm, avm, avl, ssv, svl); + assert(rdv + m + 4 < dvl); + assert(ssv < svl); + UADD2(sv, svm, av, avm, avm, avl); + if (m > MPK_THRESH) + mpx_ksqr(tdv, rdv + m + 4, sv, svm + 1, ssv, svl); else - mpx_umul(sv, ssv, av, avm, avm, avl); - ULSL1(tdv, sv, svn); + mpx_usqr(tdv, rdv + m + 4, sv, svm + 1); - if (m > KARATSUBA_CUTOFF) + if (m > MPK_THRESH) mpx_ksqr(sv, ssv, avm, avl, ssv, svl); else mpx_usqr(sv, ssv, avm, avl); MPX_COPY(rdv + m + 1, dvl, svm + 1, svn); UADD(rdv, sv, svm + 1); - - if (m > KARATSUBA_CUTOFF) + USUB(tdv, sv, svn); + + if (m > MPK_THRESH) mpx_ksqr(sv, ssv, av, avm, ssv, svl); else mpx_usqr(sv, ssv, av, avm); MPX_COPY(dv, tdv, sv, svm); UADD(tdv, svm, svn); + USUB(tdv, sv, svn); } } @@ -194,23 +141,21 @@ void mpx_ksqr(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)) @@ -236,19 +181,19 @@ static int usqr(dstr *v) LOAD(a, al, &v[0]); LOAD(c, cl, &v[1]); m = al - a + 1; - ALLOC(d, dl, 2 * m); - ALLOC(s, sl, 2 * m + 32); + ALLOC(d, dl, 3 * m); + ALLOC(s, sl, 5 * m); mpx_ksqr(d, dl, a, al, s, sl); - if (MPX_UCMP(d, dl, !=, c, cl)) { + if (!mpx_ueq(d, dl, c, cl)) { fprintf(stderr, "\n*** usqr failed\n"); - dumpmp(" a", a, al); + dumpmp(" a", a, al); dumpmp("expected", c, cl); dumpmp(" result", d, dl); ok = 0; } - free(a); free(c); free(d); free(s); + xfree(a); xfree(c); xfree(d); xfree(s); return (ok); }