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b58ddff026
* merged mpfr 3.0.0 and gmp 5.0.1 in buildtools trunk git-svn-id: file:///srv/svn/repos/haiku/buildtools/trunk@37378 a95241bf-73f2-0310-859d-f6bbb57e9c96
303 lines
7.8 KiB
C
303 lines
7.8 KiB
C
/* mpn_toom33_mul -- Multiply {ap,an} and {p,bn} where an and bn are close in
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size. Or more accurately, bn <= an < (3/2)bn.
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Contributed to the GNU project by Torbjorn Granlund.
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Additional improvements 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 2006, 2007, 2008 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 the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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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 Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
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#include "gmp.h"
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#include "gmp-impl.h"
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/* Evaluate in: -1, 0, +1, +2, +inf
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<-s--><--n--><--n--><--n-->
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____ ______ ______ ______
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|_a3_|___a2_|___a1_|___a0_|
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|b3_|___b2_|___b1_|___b0_|
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<-t-><--n--><--n--><--n-->
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v0 = a0 * b0 # A(0)*B(0)
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v1 = (a0+ a1+ a2)*(b0+ b1+ b2) # A(1)*B(1) ah <= 2 bh <= 2
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vm1 = (a0- a1+ a2)*(b0- b1+ b2) # A(-1)*B(-1) |ah| <= 1 bh <= 1
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v2 = (a0+2a1+4a2)*(b0+2b1+4b2) # A(2)*B(2) ah <= 6 bh <= 6
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vinf= a2 * b2 # A(inf)*B(inf)
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*/
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#if TUNE_PROGRAM_BUILD
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#define MAYBE_mul_basecase 1
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#define MAYBE_mul_toom33 1
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#else
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#define MAYBE_mul_basecase \
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(MUL_TOOM33_THRESHOLD < 3 * MUL_TOOM22_THRESHOLD)
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#define MAYBE_mul_toom33 \
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(MUL_TOOM44_THRESHOLD >= 3 * MUL_TOOM33_THRESHOLD)
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#endif
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/* FIXME: TOOM33_MUL_N_REC is not quite right for a balanced
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multiplication at the infinity point. We may have
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MAYBE_mul_basecase == 0, and still get s just below
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MUL_TOOM22_THRESHOLD. If MUL_TOOM33_THRESHOLD == 7, we can even get
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s == 1 and mpn_toom22_mul will crash.
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*/
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#define TOOM33_MUL_N_REC(p, a, b, 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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else if (! MAYBE_mul_toom33 \
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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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else \
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mpn_toom33_mul (p, a, n, b, n, ws); \
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} while (0)
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void
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mpn_toom33_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,
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mp_ptr scratch)
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{
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mp_size_t n, s, t;
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int vm1_neg;
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mp_limb_t cy, vinf0;
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mp_ptr gp;
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mp_ptr as1, asm1, as2;
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mp_ptr bs1, bsm1, bs2;
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#define a0 ap
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#define a1 (ap + n)
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#define a2 (ap + 2*n)
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#define b0 bp
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#define b1 (bp + n)
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#define b2 (bp + 2*n)
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n = (an + 2) / (size_t) 3;
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s = an - 2 * n;
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t = bn - 2 * n;
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ASSERT (an >= bn);
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ASSERT (0 < s && s <= n);
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ASSERT (0 < t && t <= n);
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as1 = scratch + 4 * n + 4;
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asm1 = scratch + 2 * n + 2;
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as2 = pp + n + 1;
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bs1 = pp;
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bsm1 = scratch + 3 * n + 3; /* we need 4n+4 <= 4n+s+t */
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bs2 = pp + 2 * n + 2;
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gp = scratch;
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vm1_neg = 0;
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/* Compute as1 and asm1. */
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cy = mpn_add (gp, a0, n, a2, s);
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#if HAVE_NATIVE_mpn_add_n_sub_n
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if (cy == 0 && mpn_cmp (gp, a1, n) < 0)
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{
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cy = mpn_add_n_sub_n (as1, asm1, a1, gp, n);
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as1[n] = 0;
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asm1[n] = 0;
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vm1_neg = 1;
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}
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else
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{
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cy2 = mpn_add_n_sub_n (as1, asm1, gp, a1, n);
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as1[n] = cy + (cy2 >> 1);
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asm1[n] = cy - (cy & 1);
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}
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#else
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as1[n] = cy + mpn_add_n (as1, gp, a1, n);
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if (cy == 0 && mpn_cmp (gp, a1, n) < 0)
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{
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mpn_sub_n (asm1, a1, gp, n);
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asm1[n] = 0;
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vm1_neg = 1;
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}
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else
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{
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cy -= mpn_sub_n (asm1, gp, a1, n);
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asm1[n] = cy;
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}
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#endif
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/* Compute as2. */
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#if HAVE_NATIVE_mpn_rsblsh1_n
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cy = mpn_add_n (as2, a2, as1, s);
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if (s != n)
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cy = mpn_add_1 (as2 + s, as1 + s, n - s, cy);
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cy += as1[n];
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cy = 2 * cy + mpn_rsblsh1_n (as2, a0, as2, n);
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#else
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#if HAVE_NATIVE_mpn_addlsh1_n
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cy = mpn_addlsh1_n (as2, a1, a2, s);
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if (s != n)
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cy = mpn_add_1 (as2 + s, a1 + s, n - s, cy);
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cy = 2 * cy + mpn_addlsh1_n (as2, a0, as2, n);
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#else
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cy = mpn_add_n (as2, a2, as1, s);
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if (s != n)
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cy = mpn_add_1 (as2 + s, as1 + s, n - s, cy);
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cy += as1[n];
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cy = 2 * cy + mpn_lshift (as2, as2, n, 1);
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cy -= mpn_sub_n (as2, as2, a0, n);
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#endif
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#endif
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as2[n] = cy;
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/* Compute bs1 and bsm1. */
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cy = mpn_add (gp, b0, n, b2, t);
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#if HAVE_NATIVE_mpn_add_n_sub_n
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if (cy == 0 && mpn_cmp (gp, b1, n) < 0)
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{
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cy = mpn_add_n_sub_n (bs1, bsm1, b1, gp, n);
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bs1[n] = 0;
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bsm1[n] = 0;
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vm1_neg ^= 1;
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}
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else
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{
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cy2 = mpn_add_n_sub_n (bs1, bsm1, gp, b1, n);
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bs1[n] = cy + (cy2 >> 1);
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bsm1[n] = cy - (cy & 1);
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}
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#else
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bs1[n] = cy + mpn_add_n (bs1, gp, b1, n);
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if (cy == 0 && mpn_cmp (gp, b1, n) < 0)
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{
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mpn_sub_n (bsm1, b1, gp, n);
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bsm1[n] = 0;
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vm1_neg ^= 1;
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}
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else
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{
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cy -= mpn_sub_n (bsm1, gp, b1, n);
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bsm1[n] = cy;
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}
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#endif
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/* Compute bs2. */
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#if HAVE_NATIVE_mpn_rsblsh1_n
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cy = mpn_add_n (bs2, b2, bs1, t);
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if (t != n)
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cy = mpn_add_1 (bs2 + t, bs1 + t, n - t, cy);
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cy += bs1[n];
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cy = 2 * cy + mpn_rsblsh1_n (bs2, b0, bs2, n);
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#else
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#if HAVE_NATIVE_mpn_addlsh1_n
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cy = mpn_addlsh1_n (bs2, b1, b2, t);
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if (t != n)
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cy = mpn_add_1 (bs2 + t, b1 + t, n - t, cy);
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cy = 2 * cy + mpn_addlsh1_n (bs2, b0, bs2, n);
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#else
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cy = mpn_add_n (bs2, bs1, b2, t);
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if (t != n)
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cy = mpn_add_1 (bs2 + t, bs1 + t, n - t, cy);
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cy += bs1[n];
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cy = 2 * cy + mpn_lshift (bs2, bs2, n, 1);
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cy -= mpn_sub_n (bs2, bs2, b0, n);
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#endif
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#endif
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bs2[n] = cy;
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ASSERT (as1[n] <= 2);
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ASSERT (bs1[n] <= 2);
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ASSERT (asm1[n] <= 1);
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ASSERT (bsm1[n] <= 1);
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ASSERT (as2[n] <= 6);
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ASSERT (bs2[n] <= 6);
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#define v0 pp /* 2n */
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#define v1 (pp + 2 * n) /* 2n+1 */
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#define vinf (pp + 4 * n) /* s+t */
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#define vm1 scratch /* 2n+1 */
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#define v2 (scratch + 2 * n + 1) /* 2n+2 */
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#define scratch_out (scratch + 5 * n + 5)
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/* vm1, 2n+1 limbs */
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#ifdef SMALLER_RECURSION
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TOOM33_MUL_N_REC (vm1, asm1, bsm1, n, scratch_out);
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cy = 0;
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if (asm1[n] != 0)
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cy = bsm1[n] + mpn_add_n (vm1 + n, vm1 + n, bsm1, n);
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if (bsm1[n] != 0)
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cy += mpn_add_n (vm1 + n, vm1 + n, asm1, n);
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vm1[2 * n] = cy;
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#else
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TOOM33_MUL_N_REC (vm1, asm1, bsm1, n + 1, scratch_out);
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#endif
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TOOM33_MUL_N_REC (v2, as2, bs2, n + 1, scratch_out); /* v2, 2n+1 limbs */
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/* vinf, s+t limbs */
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if (s > t) mpn_mul (vinf, a2, s, b2, t);
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else TOOM33_MUL_N_REC (vinf, a2, b2, s, scratch_out);
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vinf0 = vinf[0]; /* v1 overlaps with this */
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#ifdef SMALLER_RECURSION
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/* v1, 2n+1 limbs */
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TOOM33_MUL_N_REC (v1, as1, bs1, n, scratch_out);
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if (as1[n] == 1)
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{
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cy = bs1[n] + mpn_add_n (v1 + n, v1 + n, bs1, n);
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}
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else if (as1[n] != 0)
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{
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#if HAVE_NATIVE_mpn_addlsh1_n
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cy = 2 * bs1[n] + mpn_addlsh1_n (v1 + n, v1 + n, bs1, n);
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#else
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cy = 2 * bs1[n] + mpn_addmul_1 (v1 + n, bs1, n, CNST_LIMB(2));
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#endif
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}
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else
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cy = 0;
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if (bs1[n] == 1)
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{
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cy += mpn_add_n (v1 + n, v1 + n, as1, n);
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}
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else if (bs1[n] != 0)
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{
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#if HAVE_NATIVE_mpn_addlsh1_n
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cy += mpn_addlsh1_n (v1 + n, v1 + n, as1, n);
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#else
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cy += mpn_addmul_1 (v1 + n, as1, n, CNST_LIMB(2));
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#endif
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}
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v1[2 * n] = cy;
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#else
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cy = vinf[1];
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TOOM33_MUL_N_REC (v1, as1, bs1, n + 1, scratch_out);
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vinf[1] = cy;
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#endif
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TOOM33_MUL_N_REC (v0, ap, bp, n, scratch_out); /* v0, 2n limbs */
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mpn_toom_interpolate_5pts (pp, v2, vm1, n, s + t, vm1_neg, vinf0);
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}
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