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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 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/. */
/*
Things to work on:
1. Trim allocation. The allocations for as1, asm1, bs1, and bsm1 could be
avoided by instead reusing the pp area and the scratch area.
2. Use new toom functions for the recursive calls.
*/
#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_|
|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
vh = (8a0+4a1+2a2+ a3)*(8b0+4b1+2b2+ b3) # A(1/2)*B(1/2) ah <= 14 bh <= 14
vmh = (8a0-4a1+2a2- a3)*(8b0-4b1+2b2- b3) # A(-1/2)*B(-1/2) -4<=ah<=9 -4<=bh<=9
vinf= a3 * b2 # A(inf)*B(inf)
*/
#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_KARATSUBA_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_N_REC(p, a, n, ws) \
do { \
if (MAYBE_sqr_basecase \
&& BELOW_THRESHOLD (n, SQR_KARATSUBA_THRESHOLD)) \
mpn_sqr_basecase (p, a, n); \
else if (MAYBE_sqr_toom2 \
&& BELOW_THRESHOLD (n, SQR_TOOM3_THRESHOLD)) \
mpn_kara_sqr_n (p, a, n, ws); \
else if (! MAYBE_sqr_toom4 \
|| BELOW_THRESHOLD (n, SQR_TOOM4_THRESHOLD)) \
mpn_toom3_sqr_n (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;
mp_ptr gp, hp;
mp_ptr as1, asm1, as2, ash, asmh;
TMP_DECL;
#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);
TMP_MARK;
as1 = TMP_SALLOC_LIMBS (n + 1);
asm1 = TMP_SALLOC_LIMBS (n + 1);
as2 = TMP_SALLOC_LIMBS (n + 1);
ash = TMP_SALLOC_LIMBS (n + 1);
asmh = TMP_SALLOC_LIMBS (n + 1);
gp = pp;
hp = pp + n + 1;
/* Compute as1 and asm1. */
gp[n] = mpn_add_n (gp, a0, a2, n);
hp[n] = mpn_add (hp, a1, n, a3, s);
#if HAVE_NATIVE_mpn_addsub_n
if (mpn_cmp (gp, hp, n + 1) < 0)
{
mpn_addsub_n (as1, asm1, hp, gp, n + 1);
}
else
{
mpn_addsub_n (as1, asm1, gp, hp, n + 1);
}
#else
mpn_add_n (as1, gp, hp, n + 1);
if (mpn_cmp (gp, hp, n + 1) < 0)
{
mpn_sub_n (asm1, hp, gp, n + 1);
}
else
{
mpn_sub_n (asm1, gp, hp, n + 1);
}
#endif
/* Compute as2. */
#if HAVE_NATIVE_mpn_addlsh1_n
cy = mpn_addlsh1_n (as2, a2, a3, s);
if (s != n)
cy = mpn_add_1 (as2 + s, a2 + s, n - s, cy);
cy = 2 * cy + mpn_addlsh1_n (as2, a1, as2, n);
cy = 2 * cy + mpn_addlsh1_n (as2, a0, as2, n);
#else
cy = mpn_lshift (as2, a3, s, 1);
cy += mpn_add_n (as2, a2, as2, s);
if (s != n)
cy = mpn_add_1 (as2 + s, a2 + s, n - s, cy);
cy = 2 * cy + mpn_lshift (as2, as2, n, 1);
cy += mpn_add_n (as2, a1, as2, n);
cy = 2 * cy + mpn_lshift (as2, as2, n, 1);
cy += mpn_add_n (as2, a0, as2, n);
#endif
as2[n] = cy;
/* Compute ash and asmh. */
cy = mpn_lshift (gp, a0, n, 3); /* 8a0 */
#if HAVE_NATIVE_mpn_addlsh1_n
gp[n] = cy + mpn_addlsh1_n (gp, gp, a2, n); /* 8a0 + 2a2 */
#else
cy += mpn_lshift (hp, a2, n, 1); /* 2a2 */
gp[n] = cy + mpn_add_n (gp, gp, hp, n); /* 8a0 + 2a2 */
#endif
cy = mpn_lshift (hp, a1, n, 2); /* 4a1 */
hp[n] = cy + mpn_add (hp, hp, n, a3, s); /* 4a1 + a3 */
#if HAVE_NATIVE_mpn_addsub_n
if (mpn_cmp (gp, hp, n + 1) < 0)
{
mpn_addsub_n (ash, asmh, hp, gp, n + 1);
}
else
{
mpn_addsub_n (ash, asmh, gp, hp, n + 1);
}
#else
mpn_add_n (ash, gp, hp, n + 1);
if (mpn_cmp (gp, hp, n + 1) < 0)
{
mpn_sub_n (asmh, hp, gp, n + 1);
}
else
{
mpn_sub_n (asmh, gp, hp, n + 1);
}
#endif
ASSERT (as1[n] <= 3);
ASSERT (asm1[n] <= 1);
ASSERT (as2[n] <= 14);
ASSERT (ash[n] <= 14);
ASSERT (asmh[n] <= 9);
#define v0 pp /* 2n */
#define v1 (scratch + 6 * n + 6) /* 2n+1 */
#define vm1 scratch /* 2n+1 */
#define v2 (scratch + 2 * n + 2) /* 2n+1 */
#define vinf (pp + 6 * n) /* s+t */
#define vh (pp + 2 * n) /* 2n+1 */
#define vmh (scratch + 4 * n + 4)
#define scratch_out (scratch + 8 * n + 8)
/* vm1, 2n+1 limbs */
TOOM4_SQR_N_REC (vm1, asm1, n + 1, scratch_out); /* vm1, 2n+1 limbs */
TOOM4_SQR_N_REC (v2 , as2 , n + 1, scratch_out); /* v2, 2n+1 limbs */
TOOM4_SQR_N_REC (vinf, a3 , s, scratch_out); /* vinf, 2s limbs */
TOOM4_SQR_N_REC (v1 , as1 , n + 1, scratch_out); /* v1, 2n+1 limbs */
TOOM4_SQR_N_REC (vh , ash , n + 1, scratch_out);
TOOM4_SQR_N_REC (vmh, asmh, n + 1, scratch_out);
TOOM4_SQR_N_REC (v0 , ap , n , scratch_out); /* v0, 2n limbs */
mpn_toom_interpolate_7pts (pp, n, 0, vmh, vm1, v1, v2, s + s, scratch_out);
TMP_FREE;
}
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