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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, (enum toom7_flags) 0, vm2, vm1, v2, vh, 2*s, tp);
}
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