/* Implementation of the multiplication algorithm for Toom-Cook 8.5-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 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 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. 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 Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */ #include "gmp.h" #include "gmp-impl.h" #if GMP_NUMB_BITS < 29 #error Not implemented. #endif #if GMP_NUMB_BITS < 43 #define BIT_CORRECTION 1 #define CORRECTION_BITS GMP_NUMB_BITS #else #define BIT_CORRECTION 0 #define CORRECTION_BITS 0 #endif #if TUNE_PROGRAM_BUILD #define MAYBE_mul_basecase 1 #define MAYBE_mul_toom22 1 #define MAYBE_mul_toom33 1 #define MAYBE_mul_toom44 1 #define MAYBE_mul_toom8h 1 #else #define MAYBE_mul_basecase \ (MUL_TOOM8H_THRESHOLD < 8 * MUL_TOOM22_THRESHOLD) #define MAYBE_mul_toom22 \ (MUL_TOOM8H_THRESHOLD < 8 * MUL_TOOM33_THRESHOLD) #define MAYBE_mul_toom33 \ (MUL_TOOM8H_THRESHOLD < 8 * MUL_TOOM44_THRESHOLD) #define MAYBE_mul_toom44 \ (MUL_TOOM8H_THRESHOLD < 8 * MUL_TOOM6H_THRESHOLD) #define MAYBE_mul_toom8h \ (MUL_FFT_THRESHOLD >= 8 * MUL_TOOM8H_THRESHOLD) #endif #define TOOM8H_MUL_N_REC(p, a, b, n, ws) \ do { \ if (MAYBE_mul_basecase \ && BELOW_THRESHOLD (n, MUL_TOOM22_THRESHOLD)) \ mpn_mul_basecase (p, a, n, b, n); \ else if (MAYBE_mul_toom22 \ && BELOW_THRESHOLD (n, MUL_TOOM33_THRESHOLD)) \ mpn_toom22_mul (p, a, n, b, n, ws); \ else if (MAYBE_mul_toom33 \ && BELOW_THRESHOLD (n, MUL_TOOM44_THRESHOLD)) \ mpn_toom33_mul (p, a, n, b, n, ws); \ else if (MAYBE_mul_toom44 \ && BELOW_THRESHOLD (n, MUL_TOOM6H_THRESHOLD)) \ mpn_toom44_mul (p, a, n, b, n, ws); \ else if (! MAYBE_mul_toom8h \ || BELOW_THRESHOLD (n, MUL_TOOM8H_THRESHOLD)) \ mpn_toom6h_mul (p, a, n, b, n, ws); \ else \ mpn_toom8h_mul (p, a, n, b, n, ws); \ } while (0) #define TOOM8H_MUL_REC(p, a, na, b, nb, ws) \ do { mpn_mul (p, a, na, b, nb); \ } while (0) /* Toom-8.5 , compute the product {pp,an+bn} <- {ap,an} * {bp,bn} With: an >= bn >= 86, an*5 < bn * 11. It _may_ work with bn<=?? and bn*?? < an*? < bn*?? Evaluate in: infinity, +8,-8,+4,-4,+2,-2,+1,-1,+1/2,-1/2,+1/4,-1/4,+1/8,-1/8,0. */ /* Estimate on needed scratch: S(n) <= (n+7)\8*13+5+MAX(S((n+7)\8),1+2*(n+7)\8), since n>80; S(n) <= ceil(log(n/10)/log(8))*(13+5)+n*15\8 < n*15\8 + lg2(n)*6 */ void mpn_toom8h_mul (mp_ptr pp, mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn, mp_ptr scratch) { mp_size_t n, s, t; int p, q, half; int sign; /***************************** decomposition *******************************/ ASSERT (an >= bn); /* Can not handle too small operands */ ASSERT (bn >= 86); /* Can not handle too much unbalancement */ ASSERT (an*4 <= bn*13); ASSERT (GMP_NUMB_BITS > 12*3 || an*4 <= bn*12); ASSERT (GMP_NUMB_BITS > 11*3 || an*5 <= bn*11); ASSERT (GMP_NUMB_BITS > 10*3 || an*6 <= bn*10); ASSERT (GMP_NUMB_BITS > 9*3 || an*7 <= bn* 9); /* Limit num/den is a rational number between (16/15)^(log(6)/log(2*6-1)) and (16/15)^(log(8)/log(2*8-1)) */ #define LIMIT_numerator (21) #define LIMIT_denominat (20) if (LIKELY (an == bn) || an * (LIMIT_denominat>>1) < LIMIT_numerator * (bn>>1) ) /* is 8*... < 8*... */ { half = 0; n = 1 + ((an - 1)>>3); p = q = 7; s = an - p * n; t = bn - q * n; } else { if (an * 13 < 16 * bn) /* (an*7*LIMIT_numerator>1) < (LIMIT_numerator/7*9) * (bn>>1)) { p = 9; q = 7; } else if (an * 10 < 33 * (bn>>1)) /* (an*3*LIMIT_numerator= p * bn ? (an - 1) / (size_t) p : (bn - 1) / (size_t) q); p--; q--; s = an - p * n; t = bn - q * n; if(half) { /* Recover from badly chosen splitting */ if (s<1) {p--; s+=n; half=0;} else if (t<1) {q--; t+=n; half=0;} } } #undef LIMIT_numerator #undef LIMIT_denominat ASSERT (0 < s && s <= n); ASSERT (0 < t && t <= n); ASSERT (half || s + t > 3); ASSERT (n > 2); #define r6 (pp + 3 * n) /* 3n+1 */ #define r4 (pp + 7 * n) /* 3n+1 */ #define r2 (pp +11 * n) /* 3n+1 */ #define r0 (pp +15 * n) /* s+t <= 2*n */ #define r7 (scratch) /* 3n+1 */ #define r5 (scratch + 3 * n + 1) /* 3n+1 */ #define r3 (scratch + 6 * n + 2) /* 3n+1 */ #define r1 (scratch + 9 * n + 3) /* 3n+1 */ #define v0 (pp +11 * n) /* n+1 */ #define v1 (pp +12 * n+1) /* n+1 */ #define v2 (pp +13 * n+2) /* n+1 */ #define v3 (scratch +12 * n + 4) /* n+1 */ #define wsi (scratch +12 * n + 4) /* 3n+1 */ #define wse (scratch +13 * n + 5) /* 2n+1 */ /* Alloc also 3n+1 limbs for wsi... toom_interpolate_16pts may need all of them */ /* if (scratch == NULL) */ /* scratch = TMP_SALLOC_LIMBS(mpn_toom8_sqr_itch(n * 8)); */ ASSERT (15 * n + 6 <= mpn_toom8h_mul_itch (an, bn)); ASSERT (15 * n + 6 <= mpn_toom8_sqr_itch (n * 8)); /********************** evaluation and recursive calls *********************/ /* $\pm1/8$ */ sign = mpn_toom_eval_pm2rexp (v2, v0, p, ap, n, s, 3, pp) ^ mpn_toom_eval_pm2rexp (v3, v1, q, bp, n, t, 3, pp); TOOM8H_MUL_N_REC(pp, v0, v1, n + 1, wse); /* A(-1/8)*B(-1/8)*8^. */ TOOM8H_MUL_N_REC(r7, v2, v3, n + 1, wse); /* A(+1/8)*B(+1/8)*8^. */ mpn_toom_couple_handling (r7, 2 * n + 1 + BIT_CORRECTION, pp, sign, n, 3*(1+half), 3*(half)); /* $\pm1/4$ */ sign = mpn_toom_eval_pm2rexp (v2, v0, p, ap, n, s, 2, pp) ^ mpn_toom_eval_pm2rexp (v3, v1, q, bp, n, t, 2, pp); TOOM8H_MUL_N_REC(pp, v0, v1, n + 1, wse); /* A(-1/4)*B(-1/4)*4^. */ TOOM8H_MUL_N_REC(r5, v2, v3, n + 1, wse); /* A(+1/4)*B(+1/4)*4^. */ mpn_toom_couple_handling (r5, 2 * n + 1, pp, sign, n, 2*(1+half), 2*(half)); /* $\pm2$ */ sign = mpn_toom_eval_pm2 (v2, v0, p, ap, n, s, pp) ^ mpn_toom_eval_pm2 (v3, v1, q, bp, n, t, pp); TOOM8H_MUL_N_REC(pp, v0, v1, n + 1, wse); /* A(-2)*B(-2) */ TOOM8H_MUL_N_REC(r3, v2, v3, n + 1, wse); /* A(+2)*B(+2) */ mpn_toom_couple_handling (r3, 2 * n + 1, pp, sign, n, 1, 2); /* $\pm8$ */ sign = mpn_toom_eval_pm2exp (v2, v0, p, ap, n, s, 3, pp) ^ mpn_toom_eval_pm2exp (v3, v1, q, bp, n, t, 3, pp); TOOM8H_MUL_N_REC(pp, v0, v1, n + 1, wse); /* A(-8)*B(-8) */ TOOM8H_MUL_N_REC(r1, v2, v3, n + 1, wse); /* A(+8)*B(+8) */ mpn_toom_couple_handling (r1, 2 * n + 1 + BIT_CORRECTION, pp, sign, n, 3, 6); /* $\pm1/2$ */ sign = mpn_toom_eval_pm2rexp (v2, v0, p, ap, n, s, 1, pp) ^ mpn_toom_eval_pm2rexp (v3, v1, q, bp, n, t, 1, pp); TOOM8H_MUL_N_REC(pp, v0, v1, n + 1, wse); /* A(-1/2)*B(-1/2)*2^. */ TOOM8H_MUL_N_REC(r6, v2, v3, n + 1, wse); /* A(+1/2)*B(+1/2)*2^. */ mpn_toom_couple_handling (r6, 2 * n + 1, pp, sign, n, 1+half, half); /* $\pm1$ */ sign = mpn_toom_eval_pm1 (v2, v0, p, ap, n, s, pp); if (q == 3) sign ^= mpn_toom_eval_dgr3_pm1 (v3, v1, bp, n, t, pp); else sign ^= mpn_toom_eval_pm1 (v3, v1, q, bp, n, t, pp); TOOM8H_MUL_N_REC(pp, v0, v1, n + 1, wse); /* A(-1)*B(-1) */ TOOM8H_MUL_N_REC(r4, v2, v3, n + 1, wse); /* A(1)*B(1) */ mpn_toom_couple_handling (r4, 2 * n + 1, pp, sign, n, 0, 0); /* $\pm4$ */ sign = mpn_toom_eval_pm2exp (v2, v0, p, ap, n, s, 2, pp) ^ mpn_toom_eval_pm2exp (v3, v1, q, bp, n, t, 2, pp); TOOM8H_MUL_N_REC(pp, v0, v1, n + 1, wse); /* A(-4)*B(-4) */ TOOM8H_MUL_N_REC(r2, v2, v3, n + 1, wse); /* A(+4)*B(+4) */ mpn_toom_couple_handling (r2, 2 * n + 1, pp, sign, n, 2, 4); #undef v0 #undef v1 #undef v2 #undef v3 #undef wse /* A(0)*B(0) */ TOOM8H_MUL_N_REC(pp, ap, bp, n, wsi); /* Infinity */ if( half != 0) { if(s>t) { TOOM8H_MUL_REC(r0, ap + p * n, s, bp + q * n, t, wsi); } else { TOOM8H_MUL_REC(r0, bp + q * n, t, ap + p * n, s, wsi); }; }; mpn_toom_interpolate_16pts (pp, r1, r3, r5, r7, n, s+t, half, wsi); #undef r0 #undef r1 #undef r2 #undef r3 #undef r4 #undef r5 #undef r6 #undef wsi } #undef TOOM8H_MUL_N_REC #undef TOOM8H_MUL_REC #undef MAYBE_mul_basecase #undef MAYBE_mul_toom22 #undef MAYBE_mul_toom33 #undef MAYBE_mul_toom44 #undef MAYBE_mul_toom8h