toom44_mul.c
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- /* mpn_toom44_mul -- Multiply {ap,an} and {bp,bn} where an and bn are close in
- size. Or more accurately, bn <= an < (4/3)bn.
- Contributed to the GNU project by Torbjorn Granlund and 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: 0, +1, -1, +2, -2, 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+ a3)*( b0+ b1+ b2+ b3) # A(1)*B(1) ah <= 3 bh <= 3
- vm1 = ( a0- a1+ a2- a3)*( b0- b1+ b2- b3) # A(-1)*B(-1) |ah| <= 1 |bh| <= 1
- v2 = ( a0+2a1+4a2+8a3)*( b0+2b1+4b2+8b3) # A(2)*B(2) ah <= 14 bh <= 14
- vm2 = ( a0-2a1+4a2-8a3)*( b0-2b1+4b2-8b3) # A(2)*B(2) ah <= 9 |bh| <= 9
- vh = (8a0+4a1+2a2+ a3)*(8b0+4b1+2b2+ b3) # A(1/2)*B(1/2) ah <= 14 bh <= 14
- vinf= a3 * b2 # A(inf)*B(inf)
- */
- #if TUNE_PROGRAM_BUILD
- #define MAYBE_mul_basecase 1
- #define MAYBE_mul_toom22 1
- #define MAYBE_mul_toom44 1
- #else
- #define MAYBE_mul_basecase
- (MUL_TOOM44_THRESHOLD < 4 * MUL_TOOM22_THRESHOLD)
- #define MAYBE_mul_toom22
- (MUL_TOOM44_THRESHOLD < 4 * MUL_TOOM33_THRESHOLD)
- #define MAYBE_mul_toom44
- (MUL_FFT_THRESHOLD >= 4 * MUL_TOOM44_THRESHOLD)
- #endif
- #define TOOM44_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_toom22
- && BELOW_THRESHOLD (n, MUL_TOOM33_THRESHOLD))
- mpn_toom22_mul (p, a, n, b, n, ws);
- else if (! MAYBE_mul_toom44
- || BELOW_THRESHOLD (n, MUL_TOOM44_THRESHOLD))
- mpn_toom33_mul (p, a, n, b, n, ws);
- else
- mpn_toom44_mul (p, a, n, b, n, ws);
- } while (0)
- /* Use of scratch space. In the product area, we store
- ___________________
- |vinf|____|_v1_|_v0_|
- s+t 2n-1 2n+1 2n
- The other recursive products, vm1, v2, vm2, vh are stored in the
- scratch area. When computing them, we use the product area for
- intermediate values.
- Next, we compute v1. We can store the intermediate factors at v0
- and at vh + 2n + 2.
- Finally, for v0 and vinf, factors are parts of the input operands,
- and we need scratch space only for the recursive multiplication.
- In all, if S(an) is the scratch need, the needed space is bounded by
- S(an) <= 4 (2*ceil(an/4) + 1) + 1 + S(ceil(an/4) + 1)
- which should give S(n) = 8 n/3 + c log(n) for some constant c.
- */
- void
- mpn_toom44_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;
- mp_limb_t cy;
- enum toom7_flags flags;
- #define a0 ap
- #define a1 (ap + n)
- #define a2 (ap + 2*n)
- #define a3 (ap + 3*n)
- #define b0 bp
- #define b1 (bp + n)
- #define b2 (bp + 2*n)
- #define b3 (bp + 3*n)
- ASSERT (an >= bn);
- n = (an + 3) >> 2;
- s = an - 3 * n;
- t = bn - 3 * n;
- ASSERT (0 < s && s <= n);
- ASSERT (0 < t && t <= n);
- ASSERT (s >= t);
- /* NOTE: The multiplications to v2, vm2, vh and vm1 overwrites the
- * following limb, so these must be computed in order, and we need a
- * one limb gap to tp. */
- #define v0 pp /* 2n */
- #define v1 (pp + 2 * n) /* 2n+1 */
- #define vinf (pp + 6 * n) /* s+t */
- #define v2 scratch /* 2n+1 */
- #define vm2 (scratch + 2 * n + 1) /* 2n+1 */
- #define vh (scratch + 4 * n + 2) /* 2n+1 */
- #define vm1 (scratch + 6 * n + 3) /* 2n+1 */
- #define tp (scratch + 8*n + 5)
- /* apx and bpx must not overlap with v1 */
- #define apx pp /* n+1 */
- #define amx (pp + n + 1) /* n+1 */
- #define bmx (pp + 2*n + 2) /* n+1 */
- #define bpx (pp + 4*n + 2) /* n+1 */
- /* Total scratch need: 8*n + 5 + scratch for recursive calls. This
- gives roughly 32 n/3 + log term. */
- /* Compute apx = a0 + 2 a1 + 4 a2 + 8 a3 and amx = a0 - 2 a1 + 4 a2 - 8 a3. */
- flags = toom7_w1_neg & mpn_toom_eval_dgr3_pm2 (apx, amx, ap, n, s, tp);
- /* Compute bpx = b0 + 2 b1 + 4 b2 + 8 b3 and bmx = b0 - 2 b1 + 4 b2 - 8 b3. */
- flags ^= toom7_w1_neg & mpn_toom_eval_dgr3_pm2 (bpx, bmx, bp, n, t, tp);
- TOOM44_MUL_N_REC (v2, apx, bpx, n + 1, tp); /* v2, 2n+1 limbs */
- TOOM44_MUL_N_REC (vm2, amx, bmx, n + 1, tp); /* vm2, 2n+1 limbs */
- /* Compute apx = 8 a0 + 4 a1 + 2 a2 + a3 = (((2*a0 + a1) * 2 + a2) * 2 + a3 */
- #if HAVE_NATIVE_mpn_addlsh1_n
- cy = mpn_addlsh1_n (apx, a1, a0, n);
- cy = 2*cy + mpn_addlsh1_n (apx, a2, apx, n);
- if (s < n)
- {
- mp_limb_t cy2;
- cy2 = mpn_addlsh1_n (apx, a3, apx, s);
- apx[n] = 2*cy + mpn_lshift (apx + s, apx + s, n - s, 1);
- MPN_INCR_U (apx + s, n+1-s, cy2);
- }
- else
- apx[n] = 2*cy + mpn_addlsh1_n (apx, a3, apx, n);
- #else
- cy = mpn_lshift (apx, a0, n, 1);
- cy += mpn_add_n (apx, apx, a1, n);
- cy = 2*cy + mpn_lshift (apx, apx, n, 1);
- cy += mpn_add_n (apx, apx, a2, n);
- cy = 2*cy + mpn_lshift (apx, apx, n, 1);
- apx[n] = cy + mpn_add (apx, apx, n, a3, s);
- #endif
- /* Compute bpx = 8 b0 + 4 b1 + 2 b2 + b3 = (((2*b0 + b1) * 2 + b2) * 2 + b3 */
- #if HAVE_NATIVE_mpn_addlsh1_n
- cy = mpn_addlsh1_n (bpx, b1, b0, n);
- cy = 2*cy + mpn_addlsh1_n (bpx, b2, bpx, n);
- if (t < n)
- {
- mp_limb_t cy2;
- cy2 = mpn_addlsh1_n (bpx, b3, bpx, t);
- bpx[n] = 2*cy + mpn_lshift (bpx + t, bpx + t, n - t, 1);
- MPN_INCR_U (bpx + t, n+1-t, cy2);
- }
- else
- bpx[n] = 2*cy + mpn_addlsh1_n (bpx, b3, bpx, n);
- #else
- cy = mpn_lshift (bpx, b0, n, 1);
- cy += mpn_add_n (bpx, bpx, b1, n);
- cy = 2*cy + mpn_lshift (bpx, bpx, n, 1);
- cy += mpn_add_n (bpx, bpx, b2, n);
- cy = 2*cy + mpn_lshift (bpx, bpx, n, 1);
- bpx[n] = cy + mpn_add (bpx, bpx, n, b3, t);
- #endif
- ASSERT (apx[n] < 15);
- ASSERT (bpx[n] < 15);
- TOOM44_MUL_N_REC (vh, apx, bpx, n + 1, tp); /* vh, 2n+1 limbs */
- /* Compute apx = a0 + a1 + a2 + a3 and amx = a0 - a1 + a2 - a3. */
- flags |= toom7_w3_neg & mpn_toom_eval_dgr3_pm1 (apx, amx, ap, n, s, tp);
- /* Compute bpx = b0 + b1 + b2 + b3 bnd bmx = b0 - b1 + b2 - b3. */
- flags ^= toom7_w3_neg & mpn_toom_eval_dgr3_pm1 (bpx, bmx, bp, n, t, tp);
- TOOM44_MUL_N_REC (vm1, amx, bmx, n + 1, tp); /* vm1, 2n+1 limbs */
- /* Clobbers amx, bmx. */
- TOOM44_MUL_N_REC (v1, apx, bpx, n + 1, tp); /* v1, 2n+1 limbs */
- TOOM44_MUL_N_REC (v0, a0, b0, n, tp);
- if (s > t)
- mpn_mul (vinf, a3, s, b3, t);
- else
- TOOM44_MUL_N_REC (vinf, a3, b3, s, tp); /* vinf, s+t limbs */
- mpn_toom_interpolate_7pts (pp, n, flags, vm2, vm1, v2, vh, s + t, tp);
- }