From 11da511c784eca003deb90c23570f0873954e0de Mon Sep 17 00:00:00 2001 From: Duncan Wilkie Date: Sat, 18 Nov 2023 06:11:09 -0600 Subject: Initial commit. --- gmp-6.3.0/mpn/generic/toom_interpolate_12pts.c | 374 +++++++++++++++++++++++++ 1 file changed, 374 insertions(+) create mode 100644 gmp-6.3.0/mpn/generic/toom_interpolate_12pts.c (limited to 'gmp-6.3.0/mpn/generic/toom_interpolate_12pts.c') diff --git a/gmp-6.3.0/mpn/generic/toom_interpolate_12pts.c b/gmp-6.3.0/mpn/generic/toom_interpolate_12pts.c new file mode 100644 index 0000000..6273466 --- /dev/null +++ b/gmp-6.3.0/mpn/generic/toom_interpolate_12pts.c @@ -0,0 +1,374 @@ +/* Interpolation for the algorithm Toom-Cook 6.5-way. + + Contributed to the GNU project by Marco Bodrato. + + THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE. IT IS ONLY + SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST + GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE. + +Copyright 2009, 2010, 2012, 2015, 2020 Free Software Foundation, Inc. + +This file is part of the GNU MP Library. + +The GNU MP Library is free software; you can redistribute it and/or modify +it under the terms of either: + + * the GNU Lesser General Public License as published by the Free + Software Foundation; either version 3 of the License, or (at your + option) any later version. + +or + + * the GNU General Public License as published by the Free Software + Foundation; either version 2 of the License, or (at your option) any + later version. + +or both in parallel, as here. + +The GNU MP Library 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 General Public License +for more details. + +You should have received copies of the GNU General Public License and the +GNU Lesser General Public License along with the GNU MP Library. If not, +see https://www.gnu.org/licenses/. */ + + +#include "gmp-impl.h" + + +#if GMP_NUMB_BITS < 21 +#error Not implemented: Both sublsh_n(,,,20) should be corrected. +#endif + +#if GMP_NUMB_BITS < 16 +#error Not implemented: divexact_by42525 needs splitting. +#endif + +#if GMP_NUMB_BITS < 12 +#error Not implemented: Hard to adapt... +#endif + + +/* FIXME: tuneup should decide the best variant */ +#ifndef AORSMUL_FASTER_AORS_AORSLSH +#define AORSMUL_FASTER_AORS_AORSLSH 1 +#endif +#ifndef AORSMUL_FASTER_AORS_2AORSLSH +#define AORSMUL_FASTER_AORS_2AORSLSH 1 +#endif +#ifndef AORSMUL_FASTER_2AORSLSH +#define AORSMUL_FASTER_2AORSLSH 1 +#endif +#ifndef AORSMUL_FASTER_3AORSLSH +#define AORSMUL_FASTER_3AORSLSH 1 +#endif + + +#if HAVE_NATIVE_mpn_sublsh_n +#define DO_mpn_sublsh_n(dst,src,n,s,ws) mpn_sublsh_n(dst,dst,src,n,s) +#else +static mp_limb_t +DO_mpn_sublsh_n(mp_ptr dst, mp_srcptr src, mp_size_t n, unsigned int s, mp_ptr ws) +{ +#if USE_MUL_1 && 0 + return mpn_submul_1(dst,src,n,CNST_LIMB(1) <<(s)); +#else + mp_limb_t __cy; + __cy = mpn_lshift(ws,src,n,s); + return __cy + mpn_sub_n(dst,dst,ws,n); +#endif +} +#endif + +#if HAVE_NATIVE_mpn_addlsh_n +#define DO_mpn_addlsh_n(dst,src,n,s,ws) mpn_addlsh_n(dst,dst,src,n,s) +#else +#if !defined (AORSMUL_FASTER_2AORSLSH) && !defined (AORSMUL_FASTER_AORS_2AORSLSH) +static mp_limb_t +DO_mpn_addlsh_n(mp_ptr dst, mp_srcptr src, mp_size_t n, unsigned int s, mp_ptr ws) +{ +#if USE_MUL_1 && 0 + return mpn_addmul_1(dst,src,n,CNST_LIMB(1) <<(s)); +#else + mp_limb_t __cy; + __cy = mpn_lshift(ws,src,n,s); + return __cy + mpn_add_n(dst,dst,ws,n); +#endif +} +#endif +#endif + +#if HAVE_NATIVE_mpn_subrsh +#define DO_mpn_subrsh(dst,nd,src,ns,s,ws) mpn_subrsh(dst,nd,src,ns,s) +#else +/* FIXME: This is not a correct definition, it assumes no carry */ +#define DO_mpn_subrsh(dst,nd,src,ns,s,ws) \ +do { \ + mp_limb_t __cy; \ + MPN_DECR_U (dst, nd, src[0] >> s); \ + __cy = DO_mpn_sublsh_n (dst, src + 1, ns - 1, GMP_NUMB_BITS - s, ws); \ + MPN_DECR_U (dst + ns - 1, nd - ns + 1, __cy); \ +} while (0) +#endif + + +#define BINVERT_9 \ + ((((GMP_NUMB_MAX / 9) << (6 - GMP_NUMB_BITS % 6)) * 8 & GMP_NUMB_MAX) | 0x39) + +#define BINVERT_255 \ + (GMP_NUMB_MAX - ((GMP_NUMB_MAX / 255) << (8 - GMP_NUMB_BITS % 8))) + + /* FIXME: find some more general expressions for 2835^-1, 42525^-1 */ +#if GMP_LIMB_BITS == 32 +#define BINVERT_2835 (GMP_NUMB_MASK & CNST_LIMB(0x53E3771B)) +#define BINVERT_42525 (GMP_NUMB_MASK & CNST_LIMB(0x9F314C35)) +#else +#if GMP_LIMB_BITS == 64 +#define BINVERT_2835 (GMP_NUMB_MASK & CNST_LIMB(0x938CC70553E3771B)) +#define BINVERT_42525 (GMP_NUMB_MASK & CNST_LIMB(0xE7B40D449F314C35)) +#endif +#endif + +#ifndef mpn_divexact_by255 +#if GMP_NUMB_BITS % 8 == 0 +#define mpn_divexact_by255(dst,src,size) \ + (255 & 1 * mpn_bdiv_dbm1 (dst, src, size, __GMP_CAST (mp_limb_t, GMP_NUMB_MASK / 255))) +#else +#if HAVE_NATIVE_mpn_pi1_bdiv_q_1 +#define mpn_divexact_by255(dst,src,size) mpn_pi1_bdiv_q_1(dst,src,size,CNST_LIMB(255),BINVERT_255,0) +#else +#define mpn_divexact_by255(dst,src,size) mpn_divexact_1(dst,src,size,CNST_LIMB(255)) +#endif +#endif +#endif + +#ifndef mpn_divexact_by9x4 +#if HAVE_NATIVE_mpn_pi1_bdiv_q_1 +#define mpn_divexact_by9x4(dst,src,size) mpn_pi1_bdiv_q_1(dst,src,size,CNST_LIMB(9),BINVERT_9,2) +#else +#define mpn_divexact_by9x4(dst,src,size) mpn_divexact_1(dst,src,size,CNST_LIMB(9)<<2) +#endif +#endif + +#ifndef mpn_divexact_by42525 +#if HAVE_NATIVE_mpn_pi1_bdiv_q_1 && defined(BINVERT_42525) +#define mpn_divexact_by42525(dst,src,size) mpn_pi1_bdiv_q_1(dst,src,size,CNST_LIMB(42525),BINVERT_42525,0) +#else +#define mpn_divexact_by42525(dst,src,size) mpn_divexact_1(dst,src,size,CNST_LIMB(42525)) +#endif +#endif + +#ifndef mpn_divexact_by2835x4 +#if HAVE_NATIVE_mpn_pi1_bdiv_q_1 && defined(BINVERT_2835) +#define mpn_divexact_by2835x4(dst,src,size) mpn_pi1_bdiv_q_1(dst,src,size,CNST_LIMB(2835),BINVERT_2835,2) +#else +#define mpn_divexact_by2835x4(dst,src,size) mpn_divexact_1(dst,src,size,CNST_LIMB(2835)<<2) +#endif +#endif + +/* Interpolation for Toom-6.5 (or Toom-6), using the evaluation + points: infinity(6.5 only), +-4, +-2, +-1, +-1/4, +-1/2, 0. More precisely, + we want to compute f(2^(GMP_NUMB_BITS * n)) for a polynomial f of + degree 11 (or 10), given the 12 (rsp. 11) values: + + r0 = limit at infinity of f(x) / x^11, + r1 = f(4),f(-4), + r2 = f(2),f(-2), + r3 = f(1),f(-1), + r4 = f(1/4),f(-1/4), + r5 = f(1/2),f(-1/2), + r6 = f(0). + + All couples of the form f(n),f(-n) must be already mixed with + toom_couple_handling(f(n),...,f(-n),...) + + The result is stored in {pp, spt + 7*n (or 6*n)}. + At entry, r6 is stored at {pp, 2n}, + r4 is stored at {pp + 3n, 3n + 1}. + r2 is stored at {pp + 7n, 3n + 1}. + r0 is stored at {pp +11n, spt}. + + The other values are 3n+1 limbs each (with most significant limbs small). + + Negative intermediate results are stored two-complemented. + Inputs are destroyed. +*/ + +void +mpn_toom_interpolate_12pts (mp_ptr pp, mp_ptr r1, mp_ptr r3, mp_ptr r5, + mp_size_t n, mp_size_t spt, int half, mp_ptr wsi) +{ + mp_limb_t cy; + mp_size_t n3; + mp_size_t n3p1; + n3 = 3 * n; + n3p1 = n3 + 1; + +#define r4 (pp + n3) /* 3n+1 */ +#define r2 (pp + 7 * n) /* 3n+1 */ +#define r0 (pp +11 * n) /* s+t <= 2*n */ + + /******************************* interpolation *****************************/ + if (half != 0) { + cy = mpn_sub_n (r3, r3, r0, spt); + MPN_DECR_U (r3 + spt, n3p1 - spt, cy); + + cy = DO_mpn_sublsh_n (r2, r0, spt, 10, wsi); + MPN_DECR_U (r2 + spt, n3p1 - spt, cy); + DO_mpn_subrsh(r5, n3p1, r0, spt, 2, wsi); + + cy = DO_mpn_sublsh_n (r1, r0, spt, 20, wsi); + MPN_DECR_U (r1 + spt, n3p1 - spt, cy); + DO_mpn_subrsh(r4, n3p1, r0, spt, 4, wsi); + }; + + r4[n3] -= DO_mpn_sublsh_n (r4 + n, pp, 2 * n, 20, wsi); + DO_mpn_subrsh(r1 + n, 2 * n + 1, pp, 2 * n, 4, wsi); + +#if HAVE_NATIVE_mpn_add_n_sub_n + mpn_add_n_sub_n (r1, r4, r4, r1, n3p1); +#else + ASSERT_NOCARRY(mpn_add_n (wsi, r1, r4, n3p1)); + mpn_sub_n (r4, r4, r1, n3p1); /* can be negative */ + MP_PTR_SWAP(r1, wsi); +#endif + + r5[n3] -= DO_mpn_sublsh_n (r5 + n, pp, 2 * n, 10, wsi); + DO_mpn_subrsh(r2 + n, 2 * n + 1, pp, 2 * n, 2, wsi); + +#if HAVE_NATIVE_mpn_add_n_sub_n + mpn_add_n_sub_n (r2, r5, r5, r2, n3p1); +#else + mpn_sub_n (wsi, r5, r2, n3p1); /* can be negative */ + ASSERT_NOCARRY(mpn_add_n (r2, r2, r5, n3p1)); + MP_PTR_SWAP(r5, wsi); +#endif + + r3[n3] -= mpn_sub_n (r3+n, r3+n, pp, 2 * n); + +#if AORSMUL_FASTER_AORS_AORSLSH + mpn_submul_1 (r4, r5, n3p1, 257); /* can be negative */ +#else + mpn_sub_n (r4, r4, r5, n3p1); /* can be negative */ + DO_mpn_sublsh_n (r4, r5, n3p1, 8, wsi); /* can be negative */ +#endif + /* A division by 2835x4 follows. Warning: the operand can be negative! */ + mpn_divexact_by2835x4(r4, r4, n3p1); + if ((r4[n3] & (GMP_NUMB_MAX << (GMP_NUMB_BITS-3))) != 0) + r4[n3] |= (GMP_NUMB_MAX << (GMP_NUMB_BITS-2)); + +#if AORSMUL_FASTER_2AORSLSH + mpn_addmul_1 (r5, r4, n3p1, 60); /* can be negative */ +#else + DO_mpn_sublsh_n (r5, r4, n3p1, 2, wsi); /* can be negative */ + DO_mpn_addlsh_n (r5, r4, n3p1, 6, wsi); /* can give a carry */ +#endif + mpn_divexact_by255(r5, r5, n3p1); + + ASSERT_NOCARRY(DO_mpn_sublsh_n (r2, r3, n3p1, 5, wsi)); + +#if AORSMUL_FASTER_3AORSLSH + ASSERT_NOCARRY(mpn_submul_1 (r1, r2, n3p1, 100)); +#else + ASSERT_NOCARRY(DO_mpn_sublsh_n (r1, r2, n3p1, 6, wsi)); + ASSERT_NOCARRY(DO_mpn_sublsh_n (r1, r2, n3p1, 5, wsi)); + ASSERT_NOCARRY(DO_mpn_sublsh_n (r1, r2, n3p1, 2, wsi)); +#endif + ASSERT_NOCARRY(DO_mpn_sublsh_n (r1, r3, n3p1, 9, wsi)); + mpn_divexact_by42525(r1, r1, n3p1); + +#if AORSMUL_FASTER_AORS_2AORSLSH + ASSERT_NOCARRY(mpn_submul_1 (r2, r1, n3p1, 225)); +#else + ASSERT_NOCARRY(mpn_sub_n (r2, r2, r1, n3p1)); + ASSERT_NOCARRY(DO_mpn_addlsh_n (r2, r1, n3p1, 5, wsi)); + ASSERT_NOCARRY(DO_mpn_sublsh_n (r2, r1, n3p1, 8, wsi)); +#endif + mpn_divexact_by9x4(r2, r2, n3p1); + + ASSERT_NOCARRY(mpn_sub_n (r3, r3, r2, n3p1)); + +#ifdef HAVE_NATIVE_mpn_rsh1sub_n + mpn_rsh1sub_n (r4, r2, r4, n3p1); + r4 [n3p1 - 1] &= GMP_NUMB_MASK >> 1; +#else + mpn_sub_n (r4, r2, r4, n3p1); + ASSERT_NOCARRY(mpn_rshift(r4, r4, n3p1, 1)); +#endif + ASSERT_NOCARRY(mpn_sub_n (r2, r2, r4, n3p1)); + +#ifdef HAVE_NATIVE_mpn_rsh1add_n + mpn_rsh1add_n (r5, r5, r1, n3p1); + r5 [n3p1 - 1] &= GMP_NUMB_MASK >> 1; +#else + mpn_add_n (r5, r5, r1, n3p1); + ASSERT_NOCARRY(mpn_rshift(r5, r5, n3p1, 1)); +#endif + + /* last interpolation steps... */ + ASSERT_NOCARRY(mpn_sub_n (r3, r3, r1, n3p1)); + ASSERT_NOCARRY(mpn_sub_n (r1, r1, r5, n3p1)); + /* ... could be mixed with recomposition + ||H-r5|M-r5|L-r5| ||H-r1|M-r1|L-r1| + */ + + /***************************** recomposition *******************************/ + /* + pp[] prior to operations: + |M r0|L r0|___||H r2|M r2|L r2|___||H r4|M r4|L r4|____|H_r6|L r6|pp + + summation scheme for remaining operations: + |__12|n_11|n_10|n__9|n__8|n__7|n__6|n__5|n__4|n__3|n__2|n___|n___|pp + |M r0|L r0|___||H r2|M r2|L r2|___||H r4|M r4|L r4|____|H_r6|L r6|pp + ||H r1|M r1|L r1| ||H r3|M r3|L r3| ||H_r5|M_r5|L_r5| + */ + + cy = mpn_add_n (pp + n, pp + n, r5, n); + cy = mpn_add_1 (pp + 2 * n, r5 + n, n, cy); +#if HAVE_NATIVE_mpn_add_nc + cy = r5[n3] + mpn_add_nc(pp + n3, pp + n3, r5 + 2 * n, n, cy); +#else + MPN_INCR_U (r5 + 2 * n, n + 1, cy); + cy = r5[n3] + mpn_add_n (pp + n3, pp + n3, r5 + 2 * n, n); +#endif + MPN_INCR_U (pp + n3 + n, 2 * n + 1, cy); + + pp[2 * n3]+= mpn_add_n (pp + 5 * n, pp + 5 * n, r3, n); + cy = mpn_add_1 (pp + 2 * n3, r3 + n, n, pp[2 * n3]); +#if HAVE_NATIVE_mpn_add_nc + cy = r3[n3] + mpn_add_nc(pp + 7 * n, pp + 7 * n, r3 + 2 * n, n, cy); +#else + MPN_INCR_U (r3 + 2 * n, n + 1, cy); + cy = r3[n3] + mpn_add_n (pp + 7 * n, pp + 7 * n, r3 + 2 * n, n); +#endif + MPN_INCR_U (pp + 8 * n, 2 * n + 1, cy); + + pp[10*n]+=mpn_add_n (pp + 9 * n, pp + 9 * n, r1, n); + if (half) { + cy = mpn_add_1 (pp + 10 * n, r1 + n, n, pp[10 * n]); +#if HAVE_NATIVE_mpn_add_nc + if (LIKELY (spt > n)) { + cy = r1[n3] + mpn_add_nc(pp + 11 * n, pp + 11 * n, r1 + 2 * n, n, cy); + MPN_INCR_U (pp + 4 * n3, spt - n, cy); + } else { + ASSERT_NOCARRY(mpn_add_nc(pp + 11 * n, pp + 11 * n, r1 + 2 * n, spt, cy)); + } +#else + MPN_INCR_U (r1 + 2 * n, n + 1, cy); + if (LIKELY (spt > n)) { + cy = r1[n3] + mpn_add_n (pp + 11 * n, pp + 11 * n, r1 + 2 * n, n); + MPN_INCR_U (pp + 4 * n3, spt - n, cy); + } else { + ASSERT_NOCARRY(mpn_add_n (pp + 11 * n, pp + 11 * n, r1 + 2 * n, spt)); + } +#endif + } else { + ASSERT_NOCARRY(mpn_add_1 (pp + 10 * n, r1 + n, spt, pp[10 * n])); + } + +#undef r0 +#undef r2 +#undef r4 +} -- cgit v1.2.3