toom33_mul.c
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- /* mpn_toom33_mul -- Multiply {ap,an} and {p,bn} where an and bn are close in
- size. Or more accurately, bn <= an < (3/2)bn.
- Contributed to the GNU project by Torbjorn Granlund.
- Additional improvements 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 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_|
- |b3_|___b2_|___b1_|___b0_|
- <-t-><--n--><--n--><--n-->
- v0 = a0 * b0 # A(0)*B(0)
- v1 = (a0+ a1+ a2)*(b0+ b1+ b2) # A(1)*B(1) ah <= 2 bh <= 2
- vm1 = (a0- a1+ a2)*(b0- b1+ b2) # A(-1)*B(-1) |ah| <= 1 bh <= 1
- v2 = (a0+2a1+4a2)*(b0+2b1+4b2) # A(2)*B(2) ah <= 6 bh <= 6
- vinf= a2 * b2 # A(inf)*B(inf)
- */
- #if TUNE_PROGRAM_BUILD
- #define MAYBE_mul_basecase 1
- #define MAYBE_mul_toom33 1
- #else
- #define MAYBE_mul_basecase
- (MUL_TOOM33_THRESHOLD < 3 * MUL_TOOM22_THRESHOLD)
- #define MAYBE_mul_toom33
- (MUL_TOOM44_THRESHOLD >= 3 * MUL_TOOM33_THRESHOLD)
- #endif
- /* FIXME: TOOM33_MUL_N_REC is not quite right for a balanced
- multiplication at the infinity point. We may have
- MAYBE_mul_basecase == 0, and still get s just below
- MUL_TOOM22_THRESHOLD. If MUL_TOOM33_THRESHOLD == 7, we can even get
- s == 1 and mpn_toom22_mul will crash.
- */
- #define TOOM33_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_toom33
- || BELOW_THRESHOLD (n, MUL_TOOM33_THRESHOLD))
- mpn_toom22_mul (p, a, n, b, n, ws);
- else
- mpn_toom33_mul (p, a, n, b, n, ws);
- } while (0)
- void
- mpn_toom33_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 gp;
- mp_ptr as1, asm1, as2;
- mp_ptr bs1, bsm1, bs2;
- #define a0 ap
- #define a1 (ap + n)
- #define a2 (ap + 2*n)
- #define b0 bp
- #define b1 (bp + n)
- #define b2 (bp + 2*n)
- n = (an + 2) / (size_t) 3;
- s = an - 2 * n;
- t = bn - 2 * n;
- ASSERT (an >= bn);
- ASSERT (0 < s && s <= n);
- ASSERT (0 < t && t <= n);
- as1 = scratch + 4 * n + 4;
- asm1 = scratch + 2 * n + 2;
- as2 = pp + n + 1;
- bs1 = pp;
- bsm1 = scratch + 3 * n + 3; /* we need 4n+4 <= 4n+s+t */
- bs2 = pp + 2 * n + 2;
- gp = scratch;
- vm1_neg = 0;
- /* Compute as1 and asm1. */
- cy = mpn_add (gp, a0, n, a2, s);
- #if HAVE_NATIVE_mpn_add_n_sub_n
- if (cy == 0 && mpn_cmp (gp, a1, n) < 0)
- {
- cy = mpn_add_n_sub_n (as1, asm1, a1, gp, n);
- as1[n] = 0;
- asm1[n] = 0;
- vm1_neg = 1;
- }
- else
- {
- cy2 = mpn_add_n_sub_n (as1, asm1, gp, a1, n);
- as1[n] = cy + (cy2 >> 1);
- asm1[n] = cy - (cy & 1);
- }
- #else
- as1[n] = cy + mpn_add_n (as1, gp, a1, n);
- if (cy == 0 && mpn_cmp (gp, a1, n) < 0)
- {
- mpn_sub_n (asm1, a1, gp, n);
- asm1[n] = 0;
- vm1_neg = 1;
- }
- else
- {
- cy -= mpn_sub_n (asm1, gp, a1, n);
- asm1[n] = cy;
- }
- #endif
- /* Compute as2. */
- #if HAVE_NATIVE_mpn_rsblsh1_n
- cy = mpn_add_n (as2, a2, as1, s);
- if (s != n)
- cy = mpn_add_1 (as2 + s, as1 + s, n - s, cy);
- cy += as1[n];
- cy = 2 * cy + mpn_rsblsh1_n (as2, a0, as2, n);
- #else
- #if HAVE_NATIVE_mpn_addlsh1_n
- cy = mpn_addlsh1_n (as2, a1, a2, s);
- if (s != n)
- cy = mpn_add_1 (as2 + s, a1 + s, n - s, cy);
- cy = 2 * cy + mpn_addlsh1_n (as2, a0, as2, n);
- #else
- cy = mpn_add_n (as2, a2, as1, s);
- if (s != n)
- cy = mpn_add_1 (as2 + s, as1 + s, n - s, cy);
- cy += as1[n];
- cy = 2 * cy + mpn_lshift (as2, as2, n, 1);
- cy -= mpn_sub_n (as2, as2, a0, n);
- #endif
- #endif
- as2[n] = cy;
- /* Compute bs1 and bsm1. */
- cy = mpn_add (gp, b0, n, b2, t);
- #if HAVE_NATIVE_mpn_add_n_sub_n
- if (cy == 0 && mpn_cmp (gp, b1, n) < 0)
- {
- cy = mpn_add_n_sub_n (bs1, bsm1, b1, gp, n);
- bs1[n] = 0;
- bsm1[n] = 0;
- vm1_neg ^= 1;
- }
- else
- {
- cy2 = mpn_add_n_sub_n (bs1, bsm1, gp, b1, n);
- bs1[n] = cy + (cy2 >> 1);
- bsm1[n] = cy - (cy & 1);
- }
- #else
- bs1[n] = cy + mpn_add_n (bs1, gp, b1, n);
- if (cy == 0 && mpn_cmp (gp, b1, n) < 0)
- {
- mpn_sub_n (bsm1, b1, gp, n);
- bsm1[n] = 0;
- vm1_neg ^= 1;
- }
- else
- {
- cy -= mpn_sub_n (bsm1, gp, b1, n);
- bsm1[n] = cy;
- }
- #endif
- /* Compute bs2. */
- #if HAVE_NATIVE_mpn_rsblsh1_n
- cy = mpn_add_n (bs2, b2, bs1, t);
- if (t != n)
- cy = mpn_add_1 (bs2 + t, bs1 + t, n - t, cy);
- cy += bs1[n];
- cy = 2 * cy + mpn_rsblsh1_n (bs2, b0, bs2, n);
- #else
- #if HAVE_NATIVE_mpn_addlsh1_n
- cy = mpn_addlsh1_n (bs2, b1, b2, t);
- if (t != n)
- cy = mpn_add_1 (bs2 + t, b1 + t, n - t, cy);
- cy = 2 * cy + mpn_addlsh1_n (bs2, b0, bs2, n);
- #else
- cy = mpn_add_n (bs2, bs1, b2, t);
- if (t != n)
- cy = mpn_add_1 (bs2 + t, bs1 + t, n - t, cy);
- cy += bs1[n];
- cy = 2 * cy + mpn_lshift (bs2, bs2, n, 1);
- cy -= mpn_sub_n (bs2, bs2, b0, n);
- #endif
- #endif
- bs2[n] = cy;
- ASSERT (as1[n] <= 2);
- ASSERT (bs1[n] <= 2);
- ASSERT (asm1[n] <= 1);
- ASSERT (bsm1[n] <= 1);
- ASSERT (as2[n] <= 6);
- ASSERT (bs2[n] <= 6);
- #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 + 5 * n + 5)
- /* vm1, 2n+1 limbs */
- #ifdef SMALLER_RECURSION
- TOOM33_MUL_N_REC (vm1, asm1, bsm1, n, scratch_out);
- cy = 0;
- if (asm1[n] != 0)
- cy = bsm1[n] + mpn_add_n (vm1 + n, vm1 + n, bsm1, n);
- if (bsm1[n] != 0)
- cy += mpn_add_n (vm1 + n, vm1 + n, asm1, n);
- vm1[2 * n] = cy;
- #else
- TOOM33_MUL_N_REC (vm1, asm1, bsm1, n + 1, scratch_out);
- #endif
- TOOM33_MUL_N_REC (v2, as2, bs2, n + 1, scratch_out); /* v2, 2n+1 limbs */
- /* vinf, s+t limbs */
- if (s > t) mpn_mul (vinf, a2, s, b2, t);
- else TOOM33_MUL_N_REC (vinf, a2, b2, s, scratch_out);
- vinf0 = vinf[0]; /* v1 overlaps with this */
- #ifdef SMALLER_RECURSION
- /* v1, 2n+1 limbs */
- TOOM33_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] != 0)
- {
- #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
- cy = 0;
- if (bs1[n] == 1)
- {
- cy += mpn_add_n (v1 + n, v1 + n, as1, n);
- }
- else if (bs1[n] != 0)
- {
- #if HAVE_NATIVE_mpn_addlsh1_n
- cy += mpn_addlsh1_n (v1 + n, v1 + n, as1, n);
- #else
- cy += mpn_addmul_1 (v1 + n, as1, n, CNST_LIMB(2));
- #endif
- }
- v1[2 * n] = cy;
- #else
- cy = vinf[1];
- TOOM33_MUL_N_REC (v1, as1, bs1, n + 1, scratch_out);
- vinf[1] = cy;
- #endif
- TOOM33_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);
- }