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4c74403188
Change-Id: Iae65e95cfa0d92091b8b0a424ae36d88efa76aa9 Reviewed-on: https://review.haiku-os.org/c/buildtools/+/3020 Reviewed-by: Adrien Destugues <pulkomandy@gmail.com>
263 lines
8.3 KiB
C
263 lines
8.3 KiB
C
/* Implementation of the multiplication algorithm for Toom-Cook 6.5-way.
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Contributed to the GNU project by Marco Bodrato.
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THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE. IT IS ONLY
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SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
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GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
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Copyright 2009, 2010, 2012 Free Software Foundation, Inc.
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This file is part of the GNU MP Library.
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The GNU MP Library is free software; you can redistribute it and/or modify
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it under the terms of either:
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* the GNU Lesser General Public License as published by the Free
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Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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or
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* the GNU General Public License as published by the Free Software
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Foundation; either version 2 of the License, or (at your option) any
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later version.
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or both in parallel, as here.
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The GNU MP Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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You should have received copies of the GNU General Public License and the
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GNU Lesser General Public License along with the GNU MP Library. If not,
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see https://www.gnu.org/licenses/. */
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#include "gmp-impl.h"
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#if GMP_NUMB_BITS < 21
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#error Not implemented.
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#endif
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#if TUNE_PROGRAM_BUILD
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#define MAYBE_mul_basecase 1
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#define MAYBE_mul_toom22 1
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#define MAYBE_mul_toom33 1
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#define MAYBE_mul_toom6h 1
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#else
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#define MAYBE_mul_basecase \
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(MUL_TOOM6H_THRESHOLD < 6 * MUL_TOOM22_THRESHOLD)
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#define MAYBE_mul_toom22 \
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(MUL_TOOM6H_THRESHOLD < 6 * MUL_TOOM33_THRESHOLD)
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#define MAYBE_mul_toom33 \
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(MUL_TOOM6H_THRESHOLD < 6 * MUL_TOOM44_THRESHOLD)
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#define MAYBE_mul_toom6h \
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(MUL_FFT_THRESHOLD >= 6 * MUL_TOOM6H_THRESHOLD)
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#endif
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#define TOOM6H_MUL_N_REC(p, a, b, f, p2, a2, b2, n, ws) \
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do { \
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if (MAYBE_mul_basecase \
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&& BELOW_THRESHOLD (n, MUL_TOOM22_THRESHOLD)) { \
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mpn_mul_basecase (p, a, n, b, n); \
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if (f) \
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mpn_mul_basecase (p2, a2, n, b2, n); \
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} else if (MAYBE_mul_toom22 \
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&& BELOW_THRESHOLD (n, MUL_TOOM33_THRESHOLD)) { \
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mpn_toom22_mul (p, a, n, b, n, ws); \
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if (f) \
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mpn_toom22_mul (p2, a2, n, b2, n, ws); \
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} else if (MAYBE_mul_toom33 \
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&& BELOW_THRESHOLD (n, MUL_TOOM44_THRESHOLD)) { \
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mpn_toom33_mul (p, a, n, b, n, ws); \
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if (f) \
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mpn_toom33_mul (p2, a2, n, b2, n, ws); \
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} else if (! MAYBE_mul_toom6h \
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|| BELOW_THRESHOLD (n, MUL_TOOM6H_THRESHOLD)) { \
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mpn_toom44_mul (p, a, n, b, n, ws); \
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if (f) \
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mpn_toom44_mul (p2, a2, n, b2, n, ws); \
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} else { \
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mpn_toom6h_mul (p, a, n, b, n, ws); \
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if (f) \
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mpn_toom6h_mul (p2, a2, n, b2, n, ws); \
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} \
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} while (0)
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#define TOOM6H_MUL_REC(p, a, na, b, nb, ws) \
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do { mpn_mul (p, a, na, b, nb); \
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} while (0)
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/* Toom-6.5 , compute the product {pp,an+bn} <- {ap,an} * {bp,bn}
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With: an >= bn >= 46, an*6 < bn * 17.
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It _may_ work with bn<=46 and bn*17 < an*6 < bn*18
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Evaluate in: infinity, +4, -4, +2, -2, +1, -1, +1/2, -1/2, +1/4, -1/4, 0.
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*/
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/* Estimate on needed scratch:
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S(n) <= (n+5)\6*10+4+MAX(S((n+5)\6),1+2*(n+5)\6),
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since n>42; S(n) <= ceil(log(n)/log(6))*(10+4)+n*12\6 < n*2 + lg2(n)*6
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*/
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void
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mpn_toom6h_mul (mp_ptr pp,
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mp_srcptr ap, mp_size_t an,
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mp_srcptr bp, mp_size_t bn, mp_ptr scratch)
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{
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mp_size_t n, s, t;
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int p, q, half;
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int sign;
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/***************************** decomposition *******************************/
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ASSERT (an >= bn);
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/* Can not handle too much unbalancement */
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ASSERT (bn >= 42);
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/* Can not handle too much unbalancement */
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ASSERT ((an*3 < bn * 8) || (bn >= 46 && an * 6 < bn * 17));
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/* Limit num/den is a rational number between
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(12/11)^(log(4)/log(2*4-1)) and (12/11)^(log(6)/log(2*6-1)) */
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#define LIMIT_numerator (18)
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#define LIMIT_denominat (17)
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if (LIKELY (an * LIMIT_denominat < LIMIT_numerator * bn)) /* is 6*... < 6*... */
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{
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n = 1 + (an - 1) / (size_t) 6;
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p = q = 5;
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half = 0;
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s = an - 5 * n;
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t = bn - 5 * n;
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}
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else {
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if (an * 5 * LIMIT_numerator < LIMIT_denominat * 7 * bn)
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{ p = 7; q = 6; }
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else if (an * 5 * LIMIT_denominat < LIMIT_numerator * 7 * bn)
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{ p = 7; q = 5; }
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else if (an * LIMIT_numerator < LIMIT_denominat * 2 * bn) /* is 4*... < 8*... */
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{ p = 8; q = 5; }
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else if (an * LIMIT_denominat < LIMIT_numerator * 2 * bn) /* is 4*... < 8*... */
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{ p = 8; q = 4; }
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else
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{ p = 9; q = 4; }
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half = (p ^ q) & 1;
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n = 1 + (q * an >= p * bn ? (an - 1) / (size_t) p : (bn - 1) / (size_t) q);
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p--; q--;
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s = an - p * n;
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t = bn - q * n;
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/* With LIMIT = 16/15, the following recover is needed only if bn<=73*/
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if (half) { /* Recover from badly chosen splitting */
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if (UNLIKELY (s<1)) {p--; s+=n; half=0;}
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else if (UNLIKELY (t<1)) {q--; t+=n; half=0;}
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}
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}
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#undef LIMIT_numerator
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#undef LIMIT_denominat
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ASSERT (0 < s && s <= n);
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ASSERT (0 < t && t <= n);
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ASSERT (half || s + t > 3);
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ASSERT (n > 2);
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#define r4 (pp + 3 * n) /* 3n+1 */
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#define r2 (pp + 7 * n) /* 3n+1 */
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#define r0 (pp +11 * n) /* s+t <= 2*n */
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#define r5 (scratch) /* 3n+1 */
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#define r3 (scratch + 3 * n + 1) /* 3n+1 */
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#define r1 (scratch + 6 * n + 2) /* 3n+1 */
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#define v0 (pp + 7 * n) /* n+1 */
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#define v1 (pp + 8 * n+1) /* n+1 */
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#define v2 (pp + 9 * n+2) /* n+1 */
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#define v3 (scratch + 9 * n + 3) /* n+1 */
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#define wsi (scratch + 9 * n + 3) /* 3n+1 */
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#define wse (scratch +10 * n + 4) /* 2n+1 */
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/* Alloc also 3n+1 limbs for wsi... toom_interpolate_12pts may
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need all of them */
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/* if (scratch == NULL) */
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/* scratch = TMP_SALLOC_LIMBS(mpn_toom6_sqr_itch(n * 6)); */
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ASSERT (12 * n + 6 <= mpn_toom6h_mul_itch(an,bn));
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ASSERT (12 * n + 6 <= mpn_toom6_sqr_itch(n * 6));
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/********************** evaluation and recursive calls *********************/
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/* $\pm1/2$ */
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sign = mpn_toom_eval_pm2rexp (v2, v0, p, ap, n, s, 1, pp) ^
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mpn_toom_eval_pm2rexp (v3, v1, q, bp, n, t, 1, pp);
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/* A(-1/2)*B(-1/2)*2^. */ /* A(+1/2)*B(+1/2)*2^. */
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TOOM6H_MUL_N_REC(pp, v0, v1, 2, r5, v2, v3, n + 1, wse);
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mpn_toom_couple_handling (r5, 2 * n + 1, pp, sign, n, 1+half , half);
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/* $\pm1$ */
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sign = mpn_toom_eval_pm1 (v2, v0, p, ap, n, s, pp);
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if (UNLIKELY (q == 3))
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sign ^= mpn_toom_eval_dgr3_pm1 (v3, v1, bp, n, t, pp);
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else
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sign ^= mpn_toom_eval_pm1 (v3, v1, q, bp, n, t, pp);
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/* A(-1)*B(-1) */ /* A(1)*B(1) */
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TOOM6H_MUL_N_REC(pp, v0, v1, 2, r3, v2, v3, n + 1, wse);
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mpn_toom_couple_handling (r3, 2 * n + 1, pp, sign, n, 0, 0);
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/* $\pm4$ */
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sign = mpn_toom_eval_pm2exp (v2, v0, p, ap, n, s, 2, pp) ^
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mpn_toom_eval_pm2exp (v3, v1, q, bp, n, t, 2, pp);
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/* A(-4)*B(-4) */
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TOOM6H_MUL_N_REC(pp, v0, v1, 2, r1, v2, v3, n + 1, wse); /* A(+4)*B(+4) */
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mpn_toom_couple_handling (r1, 2 * n + 1, pp, sign, n, 2, 4);
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/* $\pm1/4$ */
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sign = mpn_toom_eval_pm2rexp (v2, v0, p, ap, n, s, 2, pp) ^
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mpn_toom_eval_pm2rexp (v3, v1, q, bp, n, t, 2, pp);
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/* A(-1/4)*B(-1/4)*4^. */ /* A(+1/4)*B(+1/4)*4^. */
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TOOM6H_MUL_N_REC(pp, v0, v1, 2, r4, v2, v3, n + 1, wse);
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mpn_toom_couple_handling (r4, 2 * n + 1, pp, sign, n, 2*(1+half), 2*(half));
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/* $\pm2$ */
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sign = mpn_toom_eval_pm2 (v2, v0, p, ap, n, s, pp) ^
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mpn_toom_eval_pm2 (v3, v1, q, bp, n, t, pp);
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/* A(-2)*B(-2) */ /* A(+2)*B(+2) */
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TOOM6H_MUL_N_REC(pp, v0, v1, 2, r2, v2, v3, n + 1, wse);
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mpn_toom_couple_handling (r2, 2 * n + 1, pp, sign, n, 1, 2);
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#undef v0
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#undef v1
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#undef v2
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#undef v3
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#undef wse
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/* A(0)*B(0) */
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TOOM6H_MUL_N_REC(pp, ap, bp, 0, pp, ap, bp, n, wsi);
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/* Infinity */
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if (UNLIKELY (half != 0)) {
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if (s > t) {
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TOOM6H_MUL_REC(r0, ap + p * n, s, bp + q * n, t, wsi);
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} else {
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TOOM6H_MUL_REC(r0, bp + q * n, t, ap + p * n, s, wsi);
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};
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};
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mpn_toom_interpolate_12pts (pp, r1, r3, r5, n, s+t, half, wsi);
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#undef r0
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#undef r1
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#undef r2
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#undef r3
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#undef r4
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#undef r5
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#undef wsi
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}
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#undef TOOM6H_MUL_N_REC
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#undef TOOM6H_MUL_REC
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#undef MAYBE_mul_basecase
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#undef MAYBE_mul_toom22
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#undef MAYBE_mul_toom33
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#undef MAYBE_mul_toom6h
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