X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/5bf74deaebe06922cc0e03bd9118f207b31f211e..c760149fcb65296defd1af967fbfa098bd83143a:/mpx-ksqr.c diff --git a/mpx-ksqr.c b/mpx-ksqr.c index 45c49c9..226b99a 100644 --- a/mpx-ksqr.c +++ b/mpx-ksqr.c @@ -1,6 +1,6 @@ /* -*-c-*- * - * $Id: mpx-ksqr.c,v 1.1 1999/12/11 10:57:43 mdw Exp $ + * $Id: mpx-ksqr.c,v 1.3 2000/06/17 11:42:54 mdw Exp $ * * Karatsuba-based squaring algorithm * @@ -30,6 +30,14 @@ /*----- Revision history --------------------------------------------------* * * $Log: mpx-ksqr.c,v $ + * Revision 1.3 2000/06/17 11:42:54 mdw + * Moved the Karatsuba macros into a separate file for better sharing. + * Fixed some comments. Use an improved technique so that all the + * operations are squarings. + * + * 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. * @@ -37,9 +45,11 @@ /*----- Header files ------------------------------------------------------*/ +#include #include #include "mpx.h" +#include "mpx-kmac.h" /*----- Tweakables --------------------------------------------------------*/ @@ -48,42 +58,6 @@ # define KARATSUBA_CUTOFF 2 #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@ --- * @@ -129,10 +103,10 @@ void mpx_ksqr(mpw *dv, mpw *dvl, /* --- 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 --- * @@ -143,38 +117,39 @@ 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 --- */ { - mpw *ssv = sv + 2 * m; + mpw *svm = sv + m, *svn = svm + m, *ssv = svn + 4; 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. - */ - + UADD2(sv, svm, av, avm, avm, avl); if (m > KARATSUBA_CUTOFF) - mpx_kmul(sv, ssv, av, avm, avm, avl, ssv, svl); + mpx_ksqr(tdv, rdv + m + 4, sv, svm + 1, ssv, svl); else - mpx_umul(sv, ssv, av, avm, avm, avl); - ULSL1(tdv, sv, ssv); - MPX_ZERO(dv, tdv); - MPX_ZERO(rdv + m + 1, dvl); + mpx_usqr(tdv, rdv + m + 4, sv, svm + 1); if (m > KARATSUBA_CUTOFF) mpx_ksqr(sv, ssv, avm, avl, ssv, svl); else mpx_usqr(sv, ssv, avm, avl); - UADD(rdv, sv, ssv); + MPX_COPY(rdv + m + 1, dvl, svm + 1, svn); + UADD(rdv, sv, svm + 1); + USUB(tdv, sv, svn); if (m > KARATSUBA_CUTOFF) mpx_ksqr(sv, ssv, av, avm, ssv, svl); else mpx_usqr(sv, ssv, av, avm); - UADD(dv, sv, ssv); + MPX_COPY(dv, tdv, sv, svm); + UADD(tdv, svm, svn); + USUB(tdv, sv, svn); } }