toom42_mul.c
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- /* mpn_toom42_mul -- Multiply {ap,an} and {bp,bn} where an is nominally twice
- as large as bn. Or more accurately, (3/2)bn < an < 4bn.
- Contributed to the GNU project by Torbjorn Granlund.
- Additional improvements by Marco Bodrato.
- The idea of applying toom to unbalanced multiplication is due to Marco
- Bodrato and Alberto Zanoni.
- 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 2006, 2007, 2008 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"
- /* Evaluate in: -1, 0, +1, +2, +inf
- <-s-><--n--><--n--><--n-->
- ___ ______ ______ ______
- |a3_|___a2_|___a1_|___a0_|
- |_b1_|___b0_|
- <-t--><--n-->
- v0 = a0 * b0 # A(0)*B(0)
- v1 = (a0+ a1+ a2+ a3)*(b0+ b1) # A(1)*B(1) ah <= 3 bh <= 1
- vm1 = (a0- a1+ a2- a3)*(b0- b1) # A(-1)*B(-1) |ah| <= 1 bh = 0
- v2 = (a0+2a1+4a2+8a3)*(b0+2b1) # A(2)*B(2) ah <= 14 bh <= 2
- vinf= a3 * b1 # A(inf)*B(inf)
- */
- #define TOOM42_MUL_N_REC(p, a, b, n, ws)
- do {
- mpn_mul_n (p, a, b, n);
- } while (0)
- void
- mpn_toom42_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 vm1_neg;
- mp_limb_t cy, vinf0;
- mp_ptr a0_a2, a1_a3;
- mp_ptr as1, asm1, as2;
- mp_ptr bs1, bsm1, bs2;
- TMP_DECL;
- #define a0 ap
- #define a1 (ap + n)
- #define a2 (ap + 2*n)
- #define a3 (ap + 3*n)
- #define b0 bp
- #define b1 (bp + n)
- n = an >= 2 * bn ? (an + 3) >> 2 : (bn + 1) >> 1;
- s = an - 3 * n;
- t = bn - n;
- ASSERT (0 < s && s <= n);
- ASSERT (0 < t && t <= n);
- TMP_MARK;
- as1 = TMP_SALLOC_LIMBS (n + 1);
- asm1 = TMP_SALLOC_LIMBS (n + 1);
- as2 = TMP_SALLOC_LIMBS (n + 1);
- bs1 = TMP_SALLOC_LIMBS (n + 1);
- bsm1 = TMP_SALLOC_LIMBS (n);
- bs2 = TMP_SALLOC_LIMBS (n + 1);
- a0_a2 = pp;
- a1_a3 = pp + n + 1;
- /* Compute as1 and asm1. */
- vm1_neg = mpn_toom_eval_dgr3_pm1 (as1, asm1, ap, n, s, a0_a2) & 1;
- /* Compute as2. */
- #if HAVE_NATIVE_mpn_addlsh1_n
- cy = mpn_addlsh1_n (as2, a2, a3, s);
- if (s != n)
- cy = mpn_add_1 (as2 + s, a2 + s, n - s, cy);
- cy = 2 * cy + mpn_addlsh1_n (as2, a1, as2, n);
- cy = 2 * cy + mpn_addlsh1_n (as2, a0, as2, n);
- #else
- cy = mpn_lshift (as2, a3, s, 1);
- cy += mpn_add_n (as2, a2, as2, s);
- if (s != n)
- cy = mpn_add_1 (as2 + s, a2 + s, n - s, cy);
- cy = 2 * cy + mpn_lshift (as2, as2, n, 1);
- cy += mpn_add_n (as2, a1, as2, n);
- cy = 2 * cy + mpn_lshift (as2, as2, n, 1);
- cy += mpn_add_n (as2, a0, as2, n);
- #endif
- as2[n] = cy;
- /* Compute bs1 and bsm1. */
- if (t == n)
- {
- #if HAVE_NATIVE_mpn_add_n_sub_n
- if (mpn_cmp (b0, b1, n) < 0)
- {
- cy = mpn_add_n_sub_n (bs1, bsm1, b1, b0, n);
- vm1_neg ^= 1;
- }
- else
- {
- cy = mpn_add_n_sub_n (bs1, bsm1, b0, b1, n);
- }
- bs1[n] = cy >> 1;
- #else
- bs1[n] = mpn_add_n (bs1, b0, b1, n);
- if (mpn_cmp (b0, b1, n) < 0)
- {
- mpn_sub_n (bsm1, b1, b0, n);
- vm1_neg ^= 1;
- }
- else
- {
- mpn_sub_n (bsm1, b0, b1, n);
- }
- #endif
- }
- else
- {
- bs1[n] = mpn_add (bs1, b0, n, b1, t);
- if (mpn_zero_p (b0 + t, n - t) && mpn_cmp (b0, b1, t) < 0)
- {
- mpn_sub_n (bsm1, b1, b0, t);
- MPN_ZERO (bsm1 + t, n - t);
- vm1_neg ^= 1;
- }
- else
- {
- mpn_sub (bsm1, b0, n, b1, t);
- }
- }
- /* Compute bs2, recycling bs1. bs2=bs1+b1 */
- mpn_add (bs2, bs1, n + 1, b1, t);
- ASSERT (as1[n] <= 3);
- ASSERT (bs1[n] <= 1);
- ASSERT (asm1[n] <= 1);
- /*ASSERT (bsm1[n] == 0);*/
- ASSERT (as2[n] <= 14);
- ASSERT (bs2[n] <= 2);
- #define v0 pp /* 2n */
- #define v1 (pp + 2 * n) /* 2n+1 */
- #define vinf (pp + 4 * n) /* s+t */
- #define vm1 scratch /* 2n+1 */
- #define v2 (scratch + 2 * n + 1) /* 2n+2 */
- #define scratch_out scratch + 4 * n + 4 /* Currently unused. */
- /* vm1, 2n+1 limbs */
- TOOM42_MUL_N_REC (vm1, asm1, bsm1, n, scratch_out);
- cy = 0;
- if (asm1[n] != 0)
- cy = mpn_add_n (vm1 + n, vm1 + n, bsm1, n);
- vm1[2 * n] = cy;
- TOOM42_MUL_N_REC (v2, as2, bs2, n + 1, scratch_out); /* v2, 2n+1 limbs */
- /* vinf, s+t limbs */
- if (s > t) mpn_mul (vinf, a3, s, b1, t);
- else mpn_mul (vinf, b1, t, a3, s);
- vinf0 = vinf[0]; /* v1 overlaps with this */
- /* v1, 2n+1 limbs */
- TOOM42_MUL_N_REC (v1, as1, bs1, n, scratch_out);
- if (as1[n] == 1)
- {
- cy = bs1[n] + mpn_add_n (v1 + n, v1 + n, bs1, n);
- }
- else if (as1[n] == 2)
- {
- #if HAVE_NATIVE_mpn_addlsh1_n
- cy = 2 * bs1[n] + mpn_addlsh1_n (v1 + n, v1 + n, bs1, n);
- #else
- cy = 2 * bs1[n] + mpn_addmul_1 (v1 + n, bs1, n, CNST_LIMB(2));
- #endif
- }
- else if (as1[n] == 3)
- {
- cy = 3 * bs1[n] + mpn_addmul_1 (v1 + n, bs1, n, CNST_LIMB(3));
- }
- else
- cy = 0;
- if (bs1[n] != 0)
- cy += mpn_add_n (v1 + n, v1 + n, as1, n);
- v1[2 * n] = cy;
- TOOM42_MUL_N_REC (v0, ap, bp, n, scratch_out); /* v0, 2n limbs */
- mpn_toom_interpolate_5pts (pp, v2, vm1, n, s + t, vm1_neg, vinf0);
- TMP_FREE;
- }