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143 lines
4.3 KiB
C
143 lines
4.3 KiB
C
/* Implementation of the algorithm for Toom-Cook 4.5-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, 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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/* Toom-4.5, the splitting 5x4 unbalanced version.
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Evaluate in: infinity, +4, -4, +2, -2, +1, -1, 0.
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<--s-><--n--><--n--><--n--><--n-->
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____ ______ ______ ______ ______
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|_a4_|__a3__|__a2__|__a1__|__a0__|
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|b3_|__b2__|__b1__|__b0__|
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<-t-><--n--><--n--><--n-->
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*/
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#define TOOM_54_MUL_N_REC(p, a, b, n, ws) \
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do { mpn_mul_n (p, a, b, n); \
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} while (0)
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#define TOOM_54_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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void
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mpn_toom54_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 sign;
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/***************************** decomposition *******************************/
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#define a4 (ap + 4 * n)
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#define b3 (bp + 3 * n)
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ASSERT (an >= bn);
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n = 1 + (4 * an >= 5 * bn ? (an - 1) / (size_t) 5 : (bn - 1) / (size_t) 4);
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s = an - 4 * n;
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t = bn - 3 * n;
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ASSERT (0 < s && s <= n);
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ASSERT (0 < t && t <= n);
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/* Required by mpn_toom_interpolate_8pts. */
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ASSERT ( s + t >= n );
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ASSERT ( s + t > 4);
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ASSERT ( n > 2);
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#define r8 pp /* 2n */
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#define r7 scratch /* 3n+1 */
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#define r5 (pp + 3*n) /* 3n+1 */
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#define v0 (pp + 3*n) /* n+1 */
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#define v1 (pp + 4*n+1) /* n+1 */
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#define v2 (pp + 5*n+2) /* n+1 */
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#define v3 (pp + 6*n+3) /* n+1 */
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#define r3 (scratch + 3 * n + 1) /* 3n+1 */
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#define r1 (pp + 7*n) /* s+t <= 2*n */
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#define ws (scratch + 6 * n + 2) /* ??? */
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/* Alloc also 3n+1 limbs for ws... mpn_toom_interpolate_8pts may
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need all of them, when DO_mpn_sublsh_n usea a scratch */
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/********************** evaluation and recursive calls *********************/
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/* $\pm4$ */
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sign = mpn_toom_eval_pm2exp (v2, v0, 4, ap, n, s, 2, pp)
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^ mpn_toom_eval_pm2exp (v3, v1, 3, bp, n, t, 2, pp);
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TOOM_54_MUL_N_REC(pp, v0, v1, n + 1, ws); /* A(-4)*B(-4) */
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TOOM_54_MUL_N_REC(r3, v2, v3, n + 1, ws); /* A(+4)*B(+4) */
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mpn_toom_couple_handling (r3, 2*n+1, pp, sign, n, 2, 4);
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/* $\pm1$ */
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sign = mpn_toom_eval_pm1 (v2, v0, 4, ap, n, s, pp)
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^ mpn_toom_eval_dgr3_pm1 (v3, v1, bp, n, t, pp);
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TOOM_54_MUL_N_REC(pp, v0, v1, n + 1, ws); /* A(-1)*B(-1) */
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TOOM_54_MUL_N_REC(r7, v2, v3, n + 1, ws); /* A(1)*B(1) */
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mpn_toom_couple_handling (r7, 2*n+1, pp, sign, n, 0, 0);
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/* $\pm2$ */
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sign = mpn_toom_eval_pm2 (v2, v0, 4, ap, n, s, pp)
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^ mpn_toom_eval_dgr3_pm2 (v3, v1, bp, n, t, pp);
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TOOM_54_MUL_N_REC(pp, v0, v1, n + 1, ws); /* A(-2)*B(-2) */
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TOOM_54_MUL_N_REC(r5, v2, v3, n + 1, ws); /* A(+2)*B(+2) */
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mpn_toom_couple_handling (r5, 2*n+1, pp, sign, n, 1, 2);
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/* A(0)*B(0) */
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TOOM_54_MUL_N_REC(pp, ap, bp, n, ws);
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/* Infinity */
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if (s > t) {
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TOOM_54_MUL_REC(r1, a4, s, b3, t, ws);
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} else {
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TOOM_54_MUL_REC(r1, b3, t, a4, s, ws);
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};
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mpn_toom_interpolate_8pts (pp, n, r3, r7, s + t, ws);
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#undef a4
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#undef b3
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#undef r1
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#undef r3
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#undef r5
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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 r7
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#undef r8
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#undef ws
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}
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