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240 lines
7.8 KiB
C
240 lines
7.8 KiB
C
/* mpn_toom44_mul -- Multiply {ap,an} and {bp,bn} where an and bn are close in
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size. Or more accurately, bn <= an < (4/3)bn.
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Contributed to the GNU project by Torbjorn Granlund and 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 2006-2008, 2013 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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/* Evaluate in: 0, +1, -1, +2, -2, 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+ a3)*( b0+ b1+ b2+ b3) # A(1)*B(1) ah <= 3 bh <= 3
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vm1 = ( a0- a1+ a2- a3)*( b0- b1+ b2- b3) # A(-1)*B(-1) |ah| <= 1 |bh| <= 1
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v2 = ( a0+2a1+4a2+8a3)*( b0+2b1+4b2+8b3) # A(2)*B(2) ah <= 14 bh <= 14
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vm2 = ( a0-2a1+4a2-8a3)*( b0-2b1+4b2-8b3) # A(-2)*B(-2) |ah| <= 9 |bh| <= 9
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vh = (8a0+4a1+2a2+ a3)*(8b0+4b1+2b2+ b3) # A(1/2)*B(1/2) ah <= 14 bh <= 14
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vinf= a3 * 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_toom22 1
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#define MAYBE_mul_toom44 1
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#else
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#define MAYBE_mul_basecase \
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(MUL_TOOM44_THRESHOLD < 4 * MUL_TOOM22_THRESHOLD)
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#define MAYBE_mul_toom22 \
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(MUL_TOOM44_THRESHOLD < 4 * MUL_TOOM33_THRESHOLD)
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#define MAYBE_mul_toom44 \
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(MUL_TOOM6H_THRESHOLD >= 4 * MUL_TOOM44_THRESHOLD)
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#endif
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#define TOOM44_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_toom22 \
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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 if (! MAYBE_mul_toom44 \
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|| BELOW_THRESHOLD (n, MUL_TOOM44_THRESHOLD)) \
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mpn_toom33_mul (p, a, n, b, n, ws); \
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else \
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mpn_toom44_mul (p, a, n, b, n, ws); \
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} while (0)
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/* Use of scratch space. In the product area, we store
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___________________
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|vinf|____|_v1_|_v0_|
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s+t 2n-1 2n+1 2n
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The other recursive products, vm1, v2, vm2, vh are stored in the
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scratch area. When computing them, we use the product area for
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intermediate values.
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Next, we compute v1. We can store the intermediate factors at v0
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and at vh + 2n + 2.
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Finally, for v0 and vinf, factors are parts of the input operands,
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and we need scratch space only for the recursive multiplication.
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In all, if S(an) is the scratch need, the needed space is bounded by
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S(an) <= 4 (2*ceil(an/4) + 1) + 1 + S(ceil(an/4) + 1)
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which should give S(n) = 8 n/3 + c log(n) for some constant c.
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*/
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void
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mpn_toom44_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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mp_limb_t cy;
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enum toom7_flags flags;
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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 a3 (ap + 3*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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#define b3 (bp + 3*n)
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ASSERT (an >= bn);
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n = (an + 3) >> 2;
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s = an - 3 * 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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ASSERT (s >= t);
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/* NOTE: The multiplications to v2, vm2, vh and vm1 overwrites the
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* following limb, so these must be computed in order, and we need a
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* one limb gap to tp. */
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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 + 6 * n) /* s+t */
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#define v2 scratch /* 2n+1 */
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#define vm2 (scratch + 2 * n + 1) /* 2n+1 */
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#define vh (scratch + 4 * n + 2) /* 2n+1 */
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#define vm1 (scratch + 6 * n + 3) /* 2n+1 */
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#define tp (scratch + 8*n + 5)
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/* apx and bpx must not overlap with v1 */
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#define apx pp /* n+1 */
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#define amx (pp + n + 1) /* n+1 */
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#define bmx (pp + 2*n + 2) /* n+1 */
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#define bpx (pp + 4*n + 2) /* n+1 */
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/* Total scratch need: 8*n + 5 + scratch for recursive calls. This
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gives roughly 32 n/3 + log term. */
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/* Compute apx = a0 + 2 a1 + 4 a2 + 8 a3 and amx = a0 - 2 a1 + 4 a2 - 8 a3. */
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flags = (enum toom7_flags) (toom7_w1_neg & mpn_toom_eval_dgr3_pm2 (apx, amx, ap, n, s, tp));
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/* Compute bpx = b0 + 2 b1 + 4 b2 + 8 b3 and bmx = b0 - 2 b1 + 4 b2 - 8 b3. */
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flags = (enum toom7_flags) (flags ^ (toom7_w1_neg & mpn_toom_eval_dgr3_pm2 (bpx, bmx, bp, n, t, tp)));
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TOOM44_MUL_N_REC (v2, apx, bpx, n + 1, tp); /* v2, 2n+1 limbs */
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TOOM44_MUL_N_REC (vm2, amx, bmx, n + 1, tp); /* vm2, 2n+1 limbs */
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/* Compute apx = 8 a0 + 4 a1 + 2 a2 + a3 = (((2*a0 + a1) * 2 + a2) * 2 + a3 */
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#if HAVE_NATIVE_mpn_addlsh1_n
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cy = mpn_addlsh1_n (apx, a1, a0, n);
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cy = 2*cy + mpn_addlsh1_n (apx, a2, apx, n);
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if (s < n)
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{
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mp_limb_t cy2;
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cy2 = mpn_addlsh1_n (apx, a3, apx, s);
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apx[n] = 2*cy + mpn_lshift (apx + s, apx + s, n - s, 1);
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MPN_INCR_U (apx + s, n+1-s, cy2);
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}
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else
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apx[n] = 2*cy + mpn_addlsh1_n (apx, a3, apx, n);
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#else
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cy = mpn_lshift (apx, a0, n, 1);
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cy += mpn_add_n (apx, apx, a1, n);
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cy = 2*cy + mpn_lshift (apx, apx, n, 1);
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cy += mpn_add_n (apx, apx, a2, n);
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cy = 2*cy + mpn_lshift (apx, apx, n, 1);
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apx[n] = cy + mpn_add (apx, apx, n, a3, s);
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#endif
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/* Compute bpx = 8 b0 + 4 b1 + 2 b2 + b3 = (((2*b0 + b1) * 2 + b2) * 2 + b3 */
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#if HAVE_NATIVE_mpn_addlsh1_n
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cy = mpn_addlsh1_n (bpx, b1, b0, n);
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cy = 2*cy + mpn_addlsh1_n (bpx, b2, bpx, n);
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if (t < n)
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{
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mp_limb_t cy2;
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cy2 = mpn_addlsh1_n (bpx, b3, bpx, t);
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bpx[n] = 2*cy + mpn_lshift (bpx + t, bpx + t, n - t, 1);
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MPN_INCR_U (bpx + t, n+1-t, cy2);
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}
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else
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bpx[n] = 2*cy + mpn_addlsh1_n (bpx, b3, bpx, n);
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#else
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cy = mpn_lshift (bpx, b0, n, 1);
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cy += mpn_add_n (bpx, bpx, b1, n);
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cy = 2*cy + mpn_lshift (bpx, bpx, n, 1);
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cy += mpn_add_n (bpx, bpx, b2, n);
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cy = 2*cy + mpn_lshift (bpx, bpx, n, 1);
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bpx[n] = cy + mpn_add (bpx, bpx, n, b3, t);
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#endif
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ASSERT (apx[n] < 15);
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ASSERT (bpx[n] < 15);
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TOOM44_MUL_N_REC (vh, apx, bpx, n + 1, tp); /* vh, 2n+1 limbs */
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/* Compute apx = a0 + a1 + a2 + a3 and amx = a0 - a1 + a2 - a3. */
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flags = (enum toom7_flags) (flags | (toom7_w3_neg & mpn_toom_eval_dgr3_pm1 (apx, amx, ap, n, s, tp)));
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/* Compute bpx = b0 + b1 + b2 + b3 and bmx = b0 - b1 + b2 - b3. */
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flags = (enum toom7_flags) (flags ^ (toom7_w3_neg & mpn_toom_eval_dgr3_pm1 (bpx, bmx, bp, n, t, tp)));
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ASSERT (amx[n] <= 1);
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ASSERT (bmx[n] <= 1);
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vm1 [2 * n] = 0;
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TOOM44_MUL_N_REC (vm1, amx, bmx, n + (bmx[n] | amx[n]), tp); /* vm1, 2n+1 limbs */
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/* Clobbers amx, bmx. */
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TOOM44_MUL_N_REC (v1, apx, bpx, n + 1, tp); /* v1, 2n+1 limbs */
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TOOM44_MUL_N_REC (v0, a0, b0, n, tp);
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if (s > t)
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mpn_mul (vinf, a3, s, b3, t);
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else
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TOOM44_MUL_N_REC (vinf, a3, b3, s, tp); /* vinf, s+t limbs */
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mpn_toom_interpolate_7pts (pp, n, flags, vm2, vm1, v2, vh, s + t, tp);
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}
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