toom22_mul.c
上传用户:qaz666999
上传日期:2022-08-06
资源大小:2570k
文件大小:5k
- /* mpn_toom22_mul -- Multiply {ap,an} and {bp,bn} where an >= bn. Or more
- accurately, bn <= an < 2bn.
- Contributed to the GNU project by Torbjorn Granlund.
- 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, 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"
- /* Evaluate in: -1, 0, +inf
- <-s--><--n-->
- ____ ______
- |_a1_|___a0_|
- |b1_|___b0_|
- <-t-><--n-->
- v0 = a0 * b0 # A(0)*B(0)
- vm1 = (a0- a1)*(b0- b1) # A(-1)*B(-1)
- vinf= a1 * b1 # A(inf)*B(inf)
- */
- #if TUNE_PROGRAM_BUILD
- #define MAYBE_mul_toom22 1
- #else
- #define MAYBE_mul_toom22
- (MUL_TOOM33_THRESHOLD >= 2 * MUL_TOOM22_THRESHOLD)
- #endif
- #define TOOM22_MUL_N_REC(p, a, b, n, ws)
- do {
- if (! MAYBE_mul_toom22
- || BELOW_THRESHOLD (n, MUL_TOOM22_THRESHOLD))
- mpn_mul_basecase (p, a, n, b, n);
- else
- mpn_toom22_mul (p, a, n, b, n, ws);
- } while (0)
- /* Normally, this calls mul_basecase or toom22_mul. But when when the fraction
- MUL_TOOM33_THRESHOLD / MUL_TOOM22_THRESHOLD is large, an initially small
- relative unbalance will become a larger and larger relative unbalance with
- each recursion (the difference s-t will be invariant over recursive calls).
- Therefore, we need to call toom32_mul. FIXME: Suppress depending on
- MUL_TOOM33_THRESHOLD / MUL_TOOM22_THRESHOLD and on MUL_TOOM22_THRESHOLD. */
- #define TOOM22_MUL_REC(p, a, an, b, bn, ws)
- do {
- if (! MAYBE_mul_toom22
- || BELOW_THRESHOLD (bn, MUL_TOOM22_THRESHOLD))
- mpn_mul_basecase (p, a, an, b, bn);
- else if (4 * an < 5 * bn)
- mpn_toom22_mul (p, a, an, b, bn, ws);
- else
- mpn_toom32_mul (p, a, an, b, bn, ws);
- } while (0)
- void
- mpn_toom22_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, cy2;
- mp_ptr asm1;
- mp_ptr bsm1;
- #define a0 ap
- #define a1 (ap + n)
- #define b0 bp
- #define b1 (bp + n)
- s = an >> 1;
- n = an - s;
- t = bn - n;
- ASSERT (an >= bn);
- ASSERT (0 < s && s <= n);
- ASSERT (0 < t && t <= s);
- asm1 = pp;
- bsm1 = pp + n;
- vm1_neg = 0;
- /* Compute asm1. */
- if (s == n)
- {
- if (mpn_cmp (a0, a1, n) < 0)
- {
- mpn_sub_n (asm1, a1, a0, n);
- vm1_neg = 1;
- }
- else
- {
- mpn_sub_n (asm1, a0, a1, n);
- }
- }
- else
- {
- if (mpn_zero_p (a0 + s, n - s) && mpn_cmp (a0, a1, s) < 0)
- {
- mpn_sub_n (asm1, a1, a0, s);
- MPN_ZERO (asm1 + s, n - s);
- vm1_neg = 1;
- }
- else
- {
- mpn_sub (asm1, a0, n, a1, s);
- }
- }
- /* Compute bsm1. */
- if (t == 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);
- }
- }
- else
- {
- 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);
- }
- }
- #define v0 pp /* 2n */
- #define vinf (pp + 2 * n) /* s+t */
- #define vm1 scratch /* 2n */
- #define scratch_out scratch + 2 * n
- /* vm1, 2n limbs */
- TOOM22_MUL_N_REC (vm1, asm1, bsm1, n, scratch_out);
- if (s > t) TOOM22_MUL_REC (vinf, a1, s, b1, t, scratch_out);
- else TOOM22_MUL_N_REC (vinf, a1, b1, s, scratch_out);
- /* v0, 2n limbs */
- TOOM22_MUL_N_REC (v0, ap, bp, n, scratch_out);
- /* H(v0) + L(vinf) */
- cy = mpn_add_n (pp + 2 * n, v0 + n, vinf, n);
- /* L(v0) + H(v0) */
- cy2 = cy + mpn_add_n (pp + n, pp + 2 * n, v0, n);
- /* L(vinf) + H(vinf) */
- cy += mpn_add (pp + 2 * n, pp + 2 * n, n, vinf + n, s + t - n);
- if (vm1_neg)
- cy += mpn_add_n (pp + n, pp + n, vm1, 2 * n);
- else
- cy -= mpn_sub_n (pp + n, pp + n, vm1, 2 * n);
- ASSERT (cy + 1 <= 3);
- ASSERT (cy2 <= 2);
- mpn_incr_u (pp + 2 * n, cy2);
- if (LIKELY (cy <= 2))
- mpn_incr_u (pp + 3 * n, cy);
- else
- mpn_decr_u (pp + 3 * n, 1);
- }