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/* mpn_toom33_mul -- Multiply {ap,an} and {p,bn} where an and bn are close in
|
|
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5c3484 |
size. Or more accurately, bn <= an < (3/2)bn.
|
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5c3484 |
|
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5c3484 |
Contributed to the GNU project by Torbjorn Granlund.
|
|
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5c3484 |
Additional improvements by Marco Bodrato.
|
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5c3484 |
|
|
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5c3484 |
THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE. IT IS ONLY
|
|
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5c3484 |
SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
|
|
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5c3484 |
GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
|
|
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5c3484 |
|
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5c3484 |
Copyright 2006-2008, 2010, 2012 Free Software Foundation, Inc.
|
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5c3484 |
|
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5c3484 |
This file is part of the GNU MP Library.
|
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5c3484 |
|
|
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5c3484 |
The GNU MP Library is free software; you can redistribute it and/or modify
|
|
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5c3484 |
it under the terms of either:
|
|
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5c3484 |
|
|
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5c3484 |
* the GNU Lesser General Public License as published by the Free
|
|
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5c3484 |
Software Foundation; either version 3 of the License, or (at your
|
|
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5c3484 |
option) any later version.
|
|
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5c3484 |
|
|
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5c3484 |
or
|
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5c3484 |
|
|
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5c3484 |
* the GNU General Public License as published by the Free Software
|
|
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5c3484 |
Foundation; either version 2 of the License, or (at your option) any
|
|
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5c3484 |
later version.
|
|
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5c3484 |
|
|
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5c3484 |
or both in parallel, as here.
|
|
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5c3484 |
|
|
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5c3484 |
The GNU MP Library is distributed in the hope that it will be useful, but
|
|
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5c3484 |
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
|
|
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5c3484 |
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
|
|
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5c3484 |
for more details.
|
|
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5c3484 |
|
|
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5c3484 |
You should have received copies of the GNU General Public License and the
|
|
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5c3484 |
GNU Lesser General Public License along with the GNU MP Library. If not,
|
|
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5c3484 |
see https://www.gnu.org/licenses/. */
|
|
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5c3484 |
|
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5c3484 |
|
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5c3484 |
#include "gmp.h"
|
|
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5c3484 |
#include "gmp-impl.h"
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5c3484 |
|
|
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5c3484 |
/* Evaluate in: -1, 0, +1, +2, +inf
|
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5c3484 |
|
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5c3484 |
<-s--><--n--><--n-->
|
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5c3484 |
____ ______ ______
|
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5c3484 |
|_a2_|___a1_|___a0_|
|
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5c3484 |
|b2_|___b1_|___b0_|
|
|
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5c3484 |
<-t-><--n--><--n-->
|
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5c3484 |
|
|
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v0 = a0 * b0 # A(0)*B(0)
|
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5c3484 |
v1 = (a0+ a1+ a2)*(b0+ b1+ b2) # A(1)*B(1) ah <= 2 bh <= 2
|
|
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5c3484 |
vm1 = (a0- a1+ a2)*(b0- b1+ b2) # A(-1)*B(-1) |ah| <= 1 bh <= 1
|
|
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5c3484 |
v2 = (a0+2a1+4a2)*(b0+2b1+4b2) # A(2)*B(2) ah <= 6 bh <= 6
|
|
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5c3484 |
vinf= a2 * b2 # A(inf)*B(inf)
|
|
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5c3484 |
*/
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5c3484 |
|
|
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5c3484 |
#if TUNE_PROGRAM_BUILD || WANT_FAT_BINARY
|
|
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5c3484 |
#define MAYBE_mul_basecase 1
|
|
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5c3484 |
#define MAYBE_mul_toom33 1
|
|
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5c3484 |
#else
|
|
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5c3484 |
#define MAYBE_mul_basecase \
|
|
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5c3484 |
(MUL_TOOM33_THRESHOLD < 3 * MUL_TOOM22_THRESHOLD)
|
|
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5c3484 |
#define MAYBE_mul_toom33 \
|
|
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5c3484 |
(MUL_TOOM44_THRESHOLD >= 3 * MUL_TOOM33_THRESHOLD)
|
|
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5c3484 |
#endif
|
|
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5c3484 |
|
|
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/* FIXME: TOOM33_MUL_N_REC is not quite right for a balanced
|
|
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5c3484 |
multiplication at the infinity point. We may have
|
|
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5c3484 |
MAYBE_mul_basecase == 0, and still get s just below
|
|
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5c3484 |
MUL_TOOM22_THRESHOLD. If MUL_TOOM33_THRESHOLD == 7, we can even get
|
|
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5c3484 |
s == 1 and mpn_toom22_mul will crash.
|
|
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5c3484 |
*/
|
|
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5c3484 |
|
|
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5c3484 |
#define TOOM33_MUL_N_REC(p, a, b, n, ws) \
|
|
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5c3484 |
do { \
|
|
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5c3484 |
if (MAYBE_mul_basecase \
|
|
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5c3484 |
&& BELOW_THRESHOLD (n, MUL_TOOM22_THRESHOLD)) \
|
|
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5c3484 |
mpn_mul_basecase (p, a, n, b, n); \
|
|
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5c3484 |
else if (! MAYBE_mul_toom33 \
|
|
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5c3484 |
|| BELOW_THRESHOLD (n, MUL_TOOM33_THRESHOLD)) \
|
|
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5c3484 |
mpn_toom22_mul (p, a, n, b, n, ws); \
|
|
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5c3484 |
else \
|
|
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5c3484 |
mpn_toom33_mul (p, a, n, b, n, ws); \
|
|
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5c3484 |
} while (0)
|
|
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5c3484 |
|
|
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5c3484 |
void
|
|
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5c3484 |
mpn_toom33_mul (mp_ptr pp,
|
|
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5c3484 |
mp_srcptr ap, mp_size_t an,
|
|
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5c3484 |
mp_srcptr bp, mp_size_t bn,
|
|
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5c3484 |
mp_ptr scratch)
|
|
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5c3484 |
{
|
|
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5c3484 |
const int __gmpn_cpuvec_initialized = 1;
|
|
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5c3484 |
mp_size_t n, s, t;
|
|
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5c3484 |
int vm1_neg;
|
|
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5c3484 |
mp_limb_t cy, vinf0;
|
|
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5c3484 |
mp_ptr gp;
|
|
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5c3484 |
mp_ptr as1, asm1, as2;
|
|
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5c3484 |
mp_ptr bs1, bsm1, bs2;
|
|
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5c3484 |
|
|
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5c3484 |
#define a0 ap
|
|
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5c3484 |
#define a1 (ap + n)
|
|
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5c3484 |
#define a2 (ap + 2*n)
|
|
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5c3484 |
#define b0 bp
|
|
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5c3484 |
#define b1 (bp + n)
|
|
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5c3484 |
#define b2 (bp + 2*n)
|
|
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5c3484 |
|
|
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5c3484 |
n = (an + 2) / (size_t) 3;
|
|
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5c3484 |
|
|
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5c3484 |
s = an - 2 * n;
|
|
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5c3484 |
t = bn - 2 * n;
|
|
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5c3484 |
|
|
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5c3484 |
ASSERT (an >= bn);
|
|
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5c3484 |
|
|
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5c3484 |
ASSERT (0 < s && s <= n);
|
|
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5c3484 |
ASSERT (0 < t && t <= n);
|
|
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5c3484 |
|
|
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5c3484 |
as1 = scratch + 4 * n + 4;
|
|
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5c3484 |
asm1 = scratch + 2 * n + 2;
|
|
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5c3484 |
as2 = pp + n + 1;
|
|
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5c3484 |
|
|
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5c3484 |
bs1 = pp;
|
|
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5c3484 |
bsm1 = scratch + 3 * n + 3; /* we need 4n+4 <= 4n+s+t */
|
|
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5c3484 |
bs2 = pp + 2 * n + 2;
|
|
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5c3484 |
|
|
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5c3484 |
gp = scratch;
|
|
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5c3484 |
|
|
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5c3484 |
vm1_neg = 0;
|
|
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5c3484 |
|
|
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5c3484 |
/* Compute as1 and asm1. */
|
|
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5c3484 |
cy = mpn_add (gp, a0, n, a2, s);
|
|
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5c3484 |
#if HAVE_NATIVE_mpn_add_n_sub_n
|
|
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5c3484 |
if (cy == 0 && mpn_cmp (gp, a1, n) < 0)
|
|
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5c3484 |
{
|
|
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5c3484 |
cy = mpn_add_n_sub_n (as1, asm1, a1, gp, n);
|
|
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5c3484 |
as1[n] = cy >> 1;
|
|
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5c3484 |
asm1[n] = 0;
|
|
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5c3484 |
vm1_neg = 1;
|
|
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5c3484 |
}
|
|
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5c3484 |
else
|
|
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5c3484 |
{
|
|
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5c3484 |
mp_limb_t cy2;
|
|
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5c3484 |
cy2 = mpn_add_n_sub_n (as1, asm1, gp, a1, n);
|
|
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5c3484 |
as1[n] = cy + (cy2 >> 1);
|
|
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5c3484 |
asm1[n] = cy - (cy2 & 1);
|
|
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5c3484 |
}
|
|
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5c3484 |
#else
|
|
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5c3484 |
as1[n] = cy + mpn_add_n (as1, gp, a1, n);
|
|
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5c3484 |
if (cy == 0 && mpn_cmp (gp, a1, n) < 0)
|
|
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5c3484 |
{
|
|
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5c3484 |
mpn_sub_n (asm1, a1, gp, n);
|
|
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5c3484 |
asm1[n] = 0;
|
|
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5c3484 |
vm1_neg = 1;
|
|
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5c3484 |
}
|
|
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5c3484 |
else
|
|
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5c3484 |
{
|
|
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5c3484 |
cy -= mpn_sub_n (asm1, gp, a1, n);
|
|
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5c3484 |
asm1[n] = cy;
|
|
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5c3484 |
}
|
|
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5c3484 |
#endif
|
|
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5c3484 |
|
|
Packit |
5c3484 |
/* Compute as2. */
|
|
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5c3484 |
#if HAVE_NATIVE_mpn_rsblsh1_n
|
|
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5c3484 |
cy = mpn_add_n (as2, a2, as1, s);
|
|
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5c3484 |
if (s != n)
|
|
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5c3484 |
cy = mpn_add_1 (as2 + s, as1 + s, n - s, cy);
|
|
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5c3484 |
cy += as1[n];
|
|
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5c3484 |
cy = 2 * cy + mpn_rsblsh1_n (as2, a0, as2, n);
|
|
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5c3484 |
#else
|
|
Packit |
5c3484 |
#if HAVE_NATIVE_mpn_addlsh1_n
|
|
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5c3484 |
cy = mpn_addlsh1_n (as2, a1, a2, s);
|
|
Packit |
5c3484 |
if (s != n)
|
|
Packit |
5c3484 |
cy = mpn_add_1 (as2 + s, a1 + s, n - s, cy);
|
|
Packit |
5c3484 |
cy = 2 * cy + mpn_addlsh1_n (as2, a0, as2, n);
|
|
Packit |
5c3484 |
#else
|
|
Packit |
5c3484 |
cy = mpn_add_n (as2, a2, as1, s);
|
|
Packit |
5c3484 |
if (s != n)
|
|
Packit |
5c3484 |
cy = mpn_add_1 (as2 + s, as1 + s, n - s, cy);
|
|
Packit |
5c3484 |
cy += as1[n];
|
|
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5c3484 |
cy = 2 * cy + mpn_lshift (as2, as2, n, 1);
|
|
Packit |
5c3484 |
cy -= mpn_sub_n (as2, as2, a0, n);
|
|
Packit |
5c3484 |
#endif
|
|
Packit |
5c3484 |
#endif
|
|
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5c3484 |
as2[n] = cy;
|
|
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5c3484 |
|
|
Packit |
5c3484 |
/* Compute bs1 and bsm1. */
|
|
Packit |
5c3484 |
cy = mpn_add (gp, b0, n, b2, t);
|
|
Packit |
5c3484 |
#if HAVE_NATIVE_mpn_add_n_sub_n
|
|
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5c3484 |
if (cy == 0 && mpn_cmp (gp, b1, n) < 0)
|
|
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5c3484 |
{
|
|
Packit |
5c3484 |
cy = mpn_add_n_sub_n (bs1, bsm1, b1, gp, n);
|
|
Packit |
5c3484 |
bs1[n] = cy >> 1;
|
|
Packit |
5c3484 |
bsm1[n] = 0;
|
|
Packit |
5c3484 |
vm1_neg ^= 1;
|
|
Packit |
5c3484 |
}
|
|
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5c3484 |
else
|
|
Packit |
5c3484 |
{
|
|
Packit |
5c3484 |
mp_limb_t cy2;
|
|
Packit |
5c3484 |
cy2 = mpn_add_n_sub_n (bs1, bsm1, gp, b1, n);
|
|
Packit |
5c3484 |
bs1[n] = cy + (cy2 >> 1);
|
|
Packit |
5c3484 |
bsm1[n] = cy - (cy2 & 1);
|
|
Packit |
5c3484 |
}
|
|
Packit |
5c3484 |
#else
|
|
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5c3484 |
bs1[n] = cy + mpn_add_n (bs1, gp, b1, n);
|
|
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5c3484 |
if (cy == 0 && mpn_cmp (gp, b1, n) < 0)
|
|
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5c3484 |
{
|
|
Packit |
5c3484 |
mpn_sub_n (bsm1, b1, gp, n);
|
|
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5c3484 |
bsm1[n] = 0;
|
|
Packit |
5c3484 |
vm1_neg ^= 1;
|
|
Packit |
5c3484 |
}
|
|
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5c3484 |
else
|
|
Packit |
5c3484 |
{
|
|
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5c3484 |
cy -= mpn_sub_n (bsm1, gp, b1, n);
|
|
Packit |
5c3484 |
bsm1[n] = cy;
|
|
Packit |
5c3484 |
}
|
|
Packit |
5c3484 |
#endif
|
|
Packit |
5c3484 |
|
|
Packit |
5c3484 |
/* Compute bs2. */
|
|
Packit |
5c3484 |
#if HAVE_NATIVE_mpn_rsblsh1_n
|
|
Packit |
5c3484 |
cy = mpn_add_n (bs2, b2, bs1, t);
|
|
Packit |
5c3484 |
if (t != n)
|
|
Packit |
5c3484 |
cy = mpn_add_1 (bs2 + t, bs1 + t, n - t, cy);
|
|
Packit |
5c3484 |
cy += bs1[n];
|
|
Packit |
5c3484 |
cy = 2 * cy + mpn_rsblsh1_n (bs2, b0, bs2, n);
|
|
Packit |
5c3484 |
#else
|
|
Packit |
5c3484 |
#if HAVE_NATIVE_mpn_addlsh1_n
|
|
Packit |
5c3484 |
cy = mpn_addlsh1_n (bs2, b1, b2, t);
|
|
Packit |
5c3484 |
if (t != n)
|
|
Packit |
5c3484 |
cy = mpn_add_1 (bs2 + t, b1 + t, n - t, cy);
|
|
Packit |
5c3484 |
cy = 2 * cy + mpn_addlsh1_n (bs2, b0, bs2, n);
|
|
Packit |
5c3484 |
#else
|
|
Packit |
5c3484 |
cy = mpn_add_n (bs2, bs1, b2, t);
|
|
Packit |
5c3484 |
if (t != n)
|
|
Packit |
5c3484 |
cy = mpn_add_1 (bs2 + t, bs1 + t, n - t, cy);
|
|
Packit |
5c3484 |
cy += bs1[n];
|
|
Packit |
5c3484 |
cy = 2 * cy + mpn_lshift (bs2, bs2, n, 1);
|
|
Packit |
5c3484 |
cy -= mpn_sub_n (bs2, bs2, b0, n);
|
|
Packit |
5c3484 |
#endif
|
|
Packit |
5c3484 |
#endif
|
|
Packit |
5c3484 |
bs2[n] = cy;
|
|
Packit |
5c3484 |
|
|
Packit |
5c3484 |
ASSERT (as1[n] <= 2);
|
|
Packit |
5c3484 |
ASSERT (bs1[n] <= 2);
|
|
Packit |
5c3484 |
ASSERT (asm1[n] <= 1);
|
|
Packit |
5c3484 |
ASSERT (bsm1[n] <= 1);
|
|
Packit |
5c3484 |
ASSERT (as2[n] <= 6);
|
|
Packit |
5c3484 |
ASSERT (bs2[n] <= 6);
|
|
Packit |
5c3484 |
|
|
Packit |
5c3484 |
#define v0 pp /* 2n */
|
|
Packit |
5c3484 |
#define v1 (pp + 2 * n) /* 2n+1 */
|
|
Packit |
5c3484 |
#define vinf (pp + 4 * n) /* s+t */
|
|
Packit |
5c3484 |
#define vm1 scratch /* 2n+1 */
|
|
Packit |
5c3484 |
#define v2 (scratch + 2 * n + 1) /* 2n+2 */
|
|
Packit |
5c3484 |
#define scratch_out (scratch + 5 * n + 5)
|
|
Packit |
5c3484 |
|
|
Packit |
5c3484 |
/* vm1, 2n+1 limbs */
|
|
Packit |
5c3484 |
#ifdef SMALLER_RECURSION
|
|
Packit |
5c3484 |
TOOM33_MUL_N_REC (vm1, asm1, bsm1, n, scratch_out);
|
|
Packit |
5c3484 |
cy = 0;
|
|
Packit |
5c3484 |
if (asm1[n] != 0)
|
|
Packit |
5c3484 |
cy = bsm1[n] + mpn_add_n (vm1 + n, vm1 + n, bsm1, n);
|
|
Packit |
5c3484 |
if (bsm1[n] != 0)
|
|
Packit |
5c3484 |
cy += mpn_add_n (vm1 + n, vm1 + n, asm1, n);
|
|
Packit |
5c3484 |
vm1[2 * n] = cy;
|
|
Packit |
5c3484 |
#else
|
|
Packit |
5c3484 |
TOOM33_MUL_N_REC (vm1, asm1, bsm1, n + 1, scratch_out);
|
|
Packit |
5c3484 |
#endif
|
|
Packit |
5c3484 |
|
|
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5c3484 |
TOOM33_MUL_N_REC (v2, as2, bs2, n + 1, scratch_out); /* v2, 2n+1 limbs */
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/* vinf, s+t limbs */
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if (s > t) mpn_mul (vinf, a2, s, b2, t);
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else TOOM33_MUL_N_REC (vinf, a2, b2, s, scratch_out);
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vinf0 = vinf[0]; /* v1 overlaps with this */
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#ifdef SMALLER_RECURSION
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/* v1, 2n+1 limbs */
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TOOM33_MUL_N_REC (v1, as1, bs1, n, scratch_out);
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if (as1[n] == 1)
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{
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cy = bs1[n] + mpn_add_n (v1 + n, v1 + n, bs1, n);
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}
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else if (as1[n] != 0)
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{
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#if HAVE_NATIVE_mpn_addlsh1_n
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cy = 2 * bs1[n] + mpn_addlsh1_n (v1 + n, v1 + n, bs1, n);
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#else
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cy = 2 * bs1[n] + mpn_addmul_1 (v1 + n, bs1, n, CNST_LIMB(2));
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#endif
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}
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else
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cy = 0;
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if (bs1[n] == 1)
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{
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cy += mpn_add_n (v1 + n, v1 + n, as1, n);
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}
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else if (bs1[n] != 0)
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{
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#if HAVE_NATIVE_mpn_addlsh1_n
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cy += mpn_addlsh1_n (v1 + n, v1 + n, as1, n);
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#else
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5c3484 |
cy += mpn_addmul_1 (v1 + n, as1, n, CNST_LIMB(2));
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#endif
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}
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v1[2 * n] = cy;
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#else
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cy = vinf[1];
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5c3484 |
TOOM33_MUL_N_REC (v1, as1, bs1, n + 1, scratch_out);
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5c3484 |
vinf[1] = cy;
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5c3484 |
#endif
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5c3484 |
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5c3484 |
TOOM33_MUL_N_REC (v0, ap, bp, n, scratch_out); /* v0, 2n limbs */
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5c3484 |
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5c3484 |
mpn_toom_interpolate_5pts (pp, v2, vm1, n, s + t, vm1_neg, vinf0);
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5c3484 |
}
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