toom4_sqr.c
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- /* mpn_toom4_sqr -- Square {ap,an}.
- 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, 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, -1/2, 0, +1/2, +1, +2, +inf
- <-s--><--n--><--n--><--n-->
- ____ ______ ______ ______
- |_a3_|___a2_|___a1_|___a0_|
- v0 = a0 ^2 # A(0)^2
- v1 = ( a0+ a1+ a2+ a3)^2 # A(1)^2 ah <= 3
- vm1 = ( a0- a1+ a2- a3)^2 # A(-1)^2 |ah| <= 1
- v2 = ( a0+2a1+4a2+8a3)^2 # A(2)^2 ah <= 14
- vh = (8a0+4a1+2a2+ a3)^2 # A(1/2)^2 ah <= 14
- vmh = (8a0-4a1+2a2- a3)^2 # A(-1/2)^2 -4<=ah<=9
- vinf= a3 ^2 # A(inf)^2
- */
- #if TUNE_PROGRAM_BUILD
- #define MAYBE_sqr_basecase 1
- #define MAYBE_sqr_toom2 1
- #define MAYBE_sqr_toom4 1
- #else
- #define MAYBE_sqr_basecase
- (SQR_TOOM4_THRESHOLD < 4 * SQR_TOOM2_THRESHOLD)
- #define MAYBE_sqr_toom2
- (SQR_TOOM4_THRESHOLD < 4 * SQR_TOOM3_THRESHOLD)
- #define MAYBE_sqr_toom4
- (SQR_FFT_THRESHOLD >= 4 * SQR_TOOM4_THRESHOLD)
- #endif
- #define TOOM4_SQR_REC(p, a, n, ws)
- do {
- if (MAYBE_sqr_basecase
- && BELOW_THRESHOLD (n, SQR_TOOM2_THRESHOLD))
- mpn_sqr_basecase (p, a, n);
- else if (MAYBE_sqr_toom2
- && BELOW_THRESHOLD (n, SQR_TOOM3_THRESHOLD))
- mpn_toom2_sqr (p, a, n, ws);
- else if (! MAYBE_sqr_toom4
- || BELOW_THRESHOLD (n, SQR_TOOM4_THRESHOLD))
- mpn_toom3_sqr (p, a, n, ws);
- else
- mpn_toom4_sqr (p, a, n, ws);
- } while (0)
- void
- mpn_toom4_sqr (mp_ptr pp,
- mp_srcptr ap, mp_size_t an,
- mp_ptr scratch)
- {
- mp_size_t n, s;
- mp_limb_t cy;
- #define a0 ap
- #define a1 (ap + n)
- #define a2 (ap + 2*n)
- #define a3 (ap + 3*n)
- n = (an + 3) >> 2;
- s = an - 3 * n;
- ASSERT (0 < s && s <= n);
- /* 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)
- /* No overlap with v1 */
- #define apx pp /* n+1 */
- #define amx (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. */
- mpn_toom_eval_dgr3_pm2 (apx, amx, ap, n, s, tp);
- TOOM4_SQR_REC (v2, apx, n + 1, tp); /* v2, 2n+1 limbs */
- TOOM4_SQR_REC (vm2, amx, 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
- ASSERT (apx[n] < 15);
- TOOM4_SQR_REC (vh, apx, n + 1, tp); /* vh, 2n+1 limbs */
- /* Compute apx = a0 + a1 + a2 + a3 and amx = a0 - a1 + a2 - a3. */
- mpn_toom_eval_dgr3_pm1 (apx, amx, ap, n, s, tp);
- TOOM4_SQR_REC (v1, apx, n + 1, tp); /* v1, 2n+1 limbs */
- TOOM4_SQR_REC (vm1, amx, n + 1, tp); /* vm1, 2n+1 limbs */
- TOOM4_SQR_REC (v0, a0, n, tp);
- TOOM4_SQR_REC (vinf, a3, s, tp); /* vinf, 2s limbs */
- mpn_toom_interpolate_7pts (pp, n, 0, vm2, vm1, v2, vh, 2*s, tp);
- }