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/* mpn_toom53_mul -- Multiply {ap,an} and {bp,bn} where an is nominally 5/3
|
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5c3484 |
times as large as bn. Or more accurately, (4/3)bn < an < (5/2)bn.
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5c3484 |
|
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5c3484 |
Contributed to the GNU project by Torbjorn Granlund and Marco Bodrato.
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5c3484 |
|
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5c3484 |
The idea of applying toom to unbalanced multiplication is due to Marco
|
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5c3484 |
Bodrato and Alberto Zanoni.
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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, 2012, 2014 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: 0, +1, -1, +2, -2, 1/2, +inf
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5c3484 |
|
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5c3484 |
<-s-><--n--><--n--><--n--><--n-->
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5c3484 |
___ ______ ______ ______ ______
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5c3484 |
|a4_|___a3_|___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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5c3484 |
v0 = a0 * b0 # A(0)*B(0)
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5c3484 |
v1 = ( a0+ a1+ a2+ a3+ a4)*( b0+ b1+ b2) # A(1)*B(1) ah <= 4 bh <= 2
|
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5c3484 |
vm1 = ( a0- a1+ a2- a3+ a4)*( b0- b1+ b2) # A(-1)*B(-1) |ah| <= 2 bh <= 1
|
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5c3484 |
v2 = ( a0+2a1+4a2+8a3+16a4)*( b0+2b1+4b2) # A(2)*B(2) ah <= 30 bh <= 6
|
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5c3484 |
vm2 = ( a0-2a1+4a2-8a3+16a4)*( b0-2b1+4b2) # A(2)*B(2) -9<=ah<=20 -1<=bh<=4
|
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5c3484 |
vh = (16a0+8a1+4a2+2a3+ a4)*(4b0+2b1+ b2) # A(1/2)*B(1/2) ah <= 30 bh <= 6
|
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5c3484 |
vinf= a4 * b2 # A(inf)*B(inf)
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5c3484 |
*/
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5c3484 |
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5c3484 |
void
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5c3484 |
mpn_toom53_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 |
mp_size_t n, s, t;
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5c3484 |
mp_limb_t cy;
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5c3484 |
mp_ptr gp;
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5c3484 |
mp_ptr as1, asm1, as2, asm2, ash;
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5c3484 |
mp_ptr bs1, bsm1, bs2, bsm2, bsh;
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5c3484 |
mp_ptr tmp;
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5c3484 |
enum toom7_flags flags;
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5c3484 |
TMP_DECL;
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5c3484 |
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5c3484 |
#define a0 ap
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#define a1 (ap + n)
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5c3484 |
#define a2 (ap + 2*n)
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5c3484 |
#define a3 (ap + 3*n)
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5c3484 |
#define a4 (ap + 4*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 = 1 + (3 * an >= 5 * bn ? (an - 1) / (size_t) 5 : (bn - 1) / (size_t) 3);
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5c3484 |
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5c3484 |
s = an - 4 * n;
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5c3484 |
t = bn - 2 * n;
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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 |
TMP_MARK;
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5c3484 |
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5c3484 |
tmp = TMP_ALLOC_LIMBS (10 * (n + 1));
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5c3484 |
as1 = tmp; tmp += n + 1;
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5c3484 |
asm1 = tmp; tmp += n + 1;
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5c3484 |
as2 = tmp; tmp += n + 1;
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5c3484 |
asm2 = tmp; tmp += n + 1;
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5c3484 |
ash = tmp; tmp += n + 1;
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5c3484 |
bs1 = tmp; tmp += n + 1;
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5c3484 |
bsm1 = tmp; tmp += n + 1;
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5c3484 |
bs2 = tmp; tmp += n + 1;
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5c3484 |
bsm2 = tmp; tmp += n + 1;
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5c3484 |
bsh = tmp; tmp += n + 1;
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5c3484 |
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5c3484 |
gp = pp;
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5c3484 |
|
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5c3484 |
/* Compute as1 and asm1. */
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|
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flags = (enum toom7_flags) (toom7_w3_neg & mpn_toom_eval_pm1 (as1, asm1, 4, ap, n, s, gp));
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5c3484 |
|
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5c3484 |
/* Compute as2 and asm2. */
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5c3484 |
flags = (enum toom7_flags) (flags | (toom7_w1_neg & mpn_toom_eval_pm2 (as2, asm2, 4, ap, n, s, gp)));
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5c3484 |
|
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5c3484 |
/* Compute ash = 16 a0 + 8 a1 + 4 a2 + 2 a3 + a4
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5c3484 |
= 2*(2*(2*(2*a0 + a1) + a2) + a3) + a4 */
|
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5c3484 |
#if HAVE_NATIVE_mpn_addlsh1_n
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5c3484 |
cy = mpn_addlsh1_n (ash, a1, a0, n);
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5c3484 |
cy = 2*cy + mpn_addlsh1_n (ash, a2, ash, n);
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5c3484 |
cy = 2*cy + mpn_addlsh1_n (ash, a3, ash, n);
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5c3484 |
if (s < n)
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5c3484 |
{
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5c3484 |
mp_limb_t cy2;
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5c3484 |
cy2 = mpn_addlsh1_n (ash, a4, ash, s);
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5c3484 |
ash[n] = 2*cy + mpn_lshift (ash + s, ash + s, n - s, 1);
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5c3484 |
MPN_INCR_U (ash + s, n+1-s, cy2);
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5c3484 |
}
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5c3484 |
else
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5c3484 |
ash[n] = 2*cy + mpn_addlsh1_n (ash, a4, ash, n);
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5c3484 |
#else
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5c3484 |
cy = mpn_lshift (ash, a0, n, 1);
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5c3484 |
cy += mpn_add_n (ash, ash, a1, n);
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5c3484 |
cy = 2*cy + mpn_lshift (ash, ash, n, 1);
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5c3484 |
cy += mpn_add_n (ash, ash, a2, n);
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5c3484 |
cy = 2*cy + mpn_lshift (ash, ash, n, 1);
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5c3484 |
cy += mpn_add_n (ash, ash, a3, n);
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5c3484 |
cy = 2*cy + mpn_lshift (ash, ash, n, 1);
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5c3484 |
ash[n] = cy + mpn_add (ash, ash, n, a4, s);
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5c3484 |
#endif
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5c3484 |
|
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5c3484 |
/* Compute bs1 and bsm1. */
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5c3484 |
bs1[n] = mpn_add (bs1, b0, n, b2, t); /* b0 + b2 */
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5c3484 |
#if HAVE_NATIVE_mpn_add_n_sub_n
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5c3484 |
if (bs1[n] == 0 && mpn_cmp (bs1, b1, n) < 0)
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5c3484 |
{
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5c3484 |
bs1[n] = mpn_add_n_sub_n (bs1, bsm1, b1, bs1, n) >> 1;
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5c3484 |
bsm1[n] = 0;
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5c3484 |
flags = (enum toom7_flags) (flags ^ toom7_w3_neg);
|
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5c3484 |
}
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5c3484 |
else
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5c3484 |
{
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5c3484 |
cy = mpn_add_n_sub_n (bs1, bsm1, bs1, b1, n);
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5c3484 |
bsm1[n] = bs1[n] - (cy & 1);
|
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5c3484 |
bs1[n] += (cy >> 1);
|
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5c3484 |
}
|
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5c3484 |
#else
|
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5c3484 |
if (bs1[n] == 0 && mpn_cmp (bs1, b1, n) < 0)
|
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5c3484 |
{
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5c3484 |
mpn_sub_n (bsm1, b1, bs1, n);
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5c3484 |
bsm1[n] = 0;
|
|
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5c3484 |
flags = (enum toom7_flags) (flags ^ toom7_w3_neg);
|
|
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5c3484 |
}
|
|
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5c3484 |
else
|
|
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5c3484 |
{
|
|
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5c3484 |
bsm1[n] = bs1[n] - mpn_sub_n (bsm1, bs1, b1, n);
|
|
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5c3484 |
}
|
|
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5c3484 |
bs1[n] += mpn_add_n (bs1, bs1, b1, n); /* b0+b1+b2 */
|
|
Packit |
5c3484 |
#endif
|
|
Packit |
5c3484 |
|
|
Packit |
5c3484 |
/* Compute bs2 and bsm2. */
|
|
Packit |
5c3484 |
#if HAVE_NATIVE_mpn_addlsh_n || HAVE_NATIVE_mpn_addlsh2_n
|
|
Packit |
5c3484 |
#if HAVE_NATIVE_mpn_addlsh2_n
|
|
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5c3484 |
cy = mpn_addlsh2_n (bs2, b0, b2, t);
|
|
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5c3484 |
#else /* HAVE_NATIVE_mpn_addlsh_n */
|
|
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5c3484 |
cy = mpn_addlsh_n (bs2, b0, b2, t, 2);
|
|
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5c3484 |
#endif
|
|
Packit |
5c3484 |
if (t < n)
|
|
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5c3484 |
cy = mpn_add_1 (bs2 + t, b0 + t, n - t, cy);
|
|
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5c3484 |
bs2[n] = cy;
|
|
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5c3484 |
#else
|
|
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5c3484 |
cy = mpn_lshift (gp, b2, t, 2);
|
|
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5c3484 |
bs2[n] = mpn_add (bs2, b0, n, gp, t);
|
|
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5c3484 |
MPN_INCR_U (bs2 + t, n+1-t, cy);
|
|
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5c3484 |
#endif
|
|
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5c3484 |
|
|
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5c3484 |
gp[n] = mpn_lshift (gp, b1, n, 1);
|
|
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5c3484 |
|
|
Packit |
5c3484 |
#if HAVE_NATIVE_mpn_add_n_sub_n
|
|
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5c3484 |
if (mpn_cmp (bs2, gp, n+1) < 0)
|
|
Packit |
5c3484 |
{
|
|
Packit |
5c3484 |
ASSERT_NOCARRY (mpn_add_n_sub_n (bs2, bsm2, gp, bs2, n+1));
|
|
Packit |
5c3484 |
flags = (enum toom7_flags) (flags ^ toom7_w1_neg);
|
|
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5c3484 |
}
|
|
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5c3484 |
else
|
|
Packit |
5c3484 |
{
|
|
Packit |
5c3484 |
ASSERT_NOCARRY (mpn_add_n_sub_n (bs2, bsm2, bs2, gp, n+1));
|
|
Packit |
5c3484 |
}
|
|
Packit |
5c3484 |
#else
|
|
Packit |
5c3484 |
if (mpn_cmp (bs2, gp, n+1) < 0)
|
|
Packit |
5c3484 |
{
|
|
Packit |
5c3484 |
ASSERT_NOCARRY (mpn_sub_n (bsm2, gp, bs2, n+1));
|
|
Packit |
5c3484 |
flags = (enum toom7_flags) (flags ^ toom7_w1_neg);
|
|
Packit |
5c3484 |
}
|
|
Packit |
5c3484 |
else
|
|
Packit |
5c3484 |
{
|
|
Packit |
5c3484 |
ASSERT_NOCARRY (mpn_sub_n (bsm2, bs2, gp, n+1));
|
|
Packit |
5c3484 |
}
|
|
Packit |
5c3484 |
mpn_add_n (bs2, bs2, gp, n+1);
|
|
Packit |
5c3484 |
#endif
|
|
Packit |
5c3484 |
|
|
Packit |
5c3484 |
/* Compute bsh = 4 b0 + 2 b1 + b2 = 2*(2*b0 + b1)+b2. */
|
|
Packit |
5c3484 |
#if HAVE_NATIVE_mpn_addlsh1_n
|
|
Packit |
5c3484 |
cy = mpn_addlsh1_n (bsh, b1, b0, n);
|
|
Packit |
5c3484 |
if (t < n)
|
|
Packit |
5c3484 |
{
|
|
Packit |
5c3484 |
mp_limb_t cy2;
|
|
Packit |
5c3484 |
cy2 = mpn_addlsh1_n (bsh, b2, bsh, t);
|
|
Packit |
5c3484 |
bsh[n] = 2*cy + mpn_lshift (bsh + t, bsh + t, n - t, 1);
|
|
Packit |
5c3484 |
MPN_INCR_U (bsh + t, n+1-t, cy2);
|
|
Packit |
5c3484 |
}
|
|
Packit |
5c3484 |
else
|
|
Packit |
5c3484 |
bsh[n] = 2*cy + mpn_addlsh1_n (bsh, b2, bsh, n);
|
|
Packit |
5c3484 |
#else
|
|
Packit |
5c3484 |
cy = mpn_lshift (bsh, b0, n, 1);
|
|
Packit |
5c3484 |
cy += mpn_add_n (bsh, bsh, b1, n);
|
|
Packit |
5c3484 |
cy = 2*cy + mpn_lshift (bsh, bsh, n, 1);
|
|
Packit |
5c3484 |
bsh[n] = cy + mpn_add (bsh, bsh, n, b2, t);
|
|
Packit |
5c3484 |
#endif
|
|
Packit |
5c3484 |
|
|
Packit |
5c3484 |
ASSERT (as1[n] <= 4);
|
|
Packit |
5c3484 |
ASSERT (bs1[n] <= 2);
|
|
Packit |
5c3484 |
ASSERT (asm1[n] <= 2);
|
|
Packit |
5c3484 |
ASSERT (bsm1[n] <= 1);
|
|
Packit |
5c3484 |
ASSERT (as2[n] <= 30);
|
|
Packit |
5c3484 |
ASSERT (bs2[n] <= 6);
|
|
Packit |
5c3484 |
ASSERT (asm2[n] <= 20);
|
|
Packit |
5c3484 |
ASSERT (bsm2[n] <= 4);
|
|
Packit |
5c3484 |
ASSERT (ash[n] <= 30);
|
|
Packit |
5c3484 |
ASSERT (bsh[n] <= 6);
|
|
Packit |
5c3484 |
|
|
Packit |
5c3484 |
#define v0 pp /* 2n */
|
|
Packit |
5c3484 |
#define v1 (pp + 2 * n) /* 2n+1 */
|
|
Packit |
5c3484 |
#define vinf (pp + 6 * n) /* s+t */
|
|
Packit |
5c3484 |
#define v2 scratch /* 2n+1 */
|
|
Packit |
5c3484 |
#define vm2 (scratch + 2 * n + 1) /* 2n+1 */
|
|
Packit |
5c3484 |
#define vh (scratch + 4 * n + 2) /* 2n+1 */
|
|
Packit |
5c3484 |
#define vm1 (scratch + 6 * n + 3) /* 2n+1 */
|
|
Packit |
5c3484 |
#define scratch_out (scratch + 8 * n + 4) /* 2n+1 */
|
|
Packit |
5c3484 |
/* Total scratch need: 10*n+5 */
|
|
Packit |
5c3484 |
|
|
Packit |
5c3484 |
/* Must be in allocation order, as they overwrite one limb beyond
|
|
Packit |
5c3484 |
* 2n+1. */
|
|
Packit |
5c3484 |
mpn_mul_n (v2, as2, bs2, n + 1); /* v2, 2n+1 limbs */
|
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Packit |
5c3484 |
mpn_mul_n (vm2, asm2, bsm2, n + 1); /* vm2, 2n+1 limbs */
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5c3484 |
mpn_mul_n (vh, ash, bsh, n + 1); /* vh, 2n+1 limbs */
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5c3484 |
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5c3484 |
/* vm1, 2n+1 limbs */
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5c3484 |
#ifdef SMALLER_RECURSION
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5c3484 |
mpn_mul_n (vm1, asm1, bsm1, n);
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5c3484 |
if (asm1[n] == 1)
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5c3484 |
{
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5c3484 |
cy = bsm1[n] + mpn_add_n (vm1 + n, vm1 + n, bsm1, n);
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5c3484 |
}
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5c3484 |
else if (asm1[n] == 2)
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5c3484 |
{
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5c3484 |
#if HAVE_NATIVE_mpn_addlsh1_n
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5c3484 |
cy = 2 * bsm1[n] + mpn_addlsh1_n (vm1 + n, vm1 + n, bsm1, n);
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5c3484 |
#else
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5c3484 |
cy = 2 * bsm1[n] + mpn_addmul_1 (vm1 + n, bsm1, n, CNST_LIMB(2));
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5c3484 |
#endif
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5c3484 |
}
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5c3484 |
else
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5c3484 |
cy = 0;
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Packit |
5c3484 |
if (bsm1[n] != 0)
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5c3484 |
cy += mpn_add_n (vm1 + n, vm1 + n, asm1, n);
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5c3484 |
vm1[2 * n] = cy;
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5c3484 |
#else /* SMALLER_RECURSION */
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5c3484 |
vm1[2 * n] = 0;
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Packit |
5c3484 |
mpn_mul_n (vm1, asm1, bsm1, n + ((asm1[n] | bsm1[n]) != 0));
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Packit |
5c3484 |
#endif /* SMALLER_RECURSION */
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Packit |
5c3484 |
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Packit |
5c3484 |
/* v1, 2n+1 limbs */
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Packit |
5c3484 |
#ifdef SMALLER_RECURSION
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Packit |
5c3484 |
mpn_mul_n (v1, as1, bs1, n);
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Packit |
5c3484 |
if (as1[n] == 1)
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Packit |
5c3484 |
{
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Packit |
5c3484 |
cy = bs1[n] + mpn_add_n (v1 + n, v1 + n, bs1, n);
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Packit |
5c3484 |
}
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Packit |
5c3484 |
else if (as1[n] == 2)
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Packit |
5c3484 |
{
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Packit |
5c3484 |
#if HAVE_NATIVE_mpn_addlsh1_n
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Packit |
5c3484 |
cy = 2 * bs1[n] + mpn_addlsh1_n (v1 + n, v1 + n, bs1, n);
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5c3484 |
#else
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Packit |
5c3484 |
cy = 2 * bs1[n] + mpn_addmul_1 (v1 + n, bs1, n, CNST_LIMB(2));
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Packit |
5c3484 |
#endif
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Packit |
5c3484 |
}
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Packit |
5c3484 |
else if (as1[n] != 0)
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Packit |
5c3484 |
{
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Packit |
5c3484 |
cy = as1[n] * bs1[n] + mpn_addmul_1 (v1 + n, bs1, n, as1[n]);
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Packit |
5c3484 |
}
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Packit |
5c3484 |
else
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Packit |
5c3484 |
cy = 0;
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Packit |
5c3484 |
if (bs1[n] == 1)
|
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Packit |
5c3484 |
{
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Packit |
5c3484 |
cy += mpn_add_n (v1 + n, v1 + n, as1, n);
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Packit |
5c3484 |
}
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Packit |
5c3484 |
else if (bs1[n] == 2)
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Packit |
5c3484 |
{
|
|
Packit |
5c3484 |
#if HAVE_NATIVE_mpn_addlsh1_n
|
|
Packit |
5c3484 |
cy += mpn_addlsh1_n (v1 + n, v1 + n, as1, n);
|
|
Packit |
5c3484 |
#else
|
|
Packit |
5c3484 |
cy += mpn_addmul_1 (v1 + n, as1, n, CNST_LIMB(2));
|
|
Packit |
5c3484 |
#endif
|
|
Packit |
5c3484 |
}
|
|
Packit |
5c3484 |
v1[2 * n] = cy;
|
|
Packit |
5c3484 |
#else /* SMALLER_RECURSION */
|
|
Packit |
5c3484 |
v1[2 * n] = 0;
|
|
Packit |
5c3484 |
mpn_mul_n (v1, as1, bs1, n + ((as1[n] | bs1[n]) != 0));
|
|
Packit |
5c3484 |
#endif /* SMALLER_RECURSION */
|
|
Packit |
5c3484 |
|
|
Packit |
5c3484 |
mpn_mul_n (v0, a0, b0, n); /* v0, 2n limbs */
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|
Packit |
5c3484 |
|
|
Packit |
5c3484 |
/* vinf, s+t limbs */
|
|
Packit |
5c3484 |
if (s > t) mpn_mul (vinf, a4, s, b2, t);
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Packit |
5c3484 |
else mpn_mul (vinf, b2, t, a4, s);
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Packit |
5c3484 |
|
|
Packit |
5c3484 |
mpn_toom_interpolate_7pts (pp, n, flags, vm2, vm1, v2, vh, s + t,
|
|
Packit |
5c3484 |
scratch_out);
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|
Packit |
5c3484 |
|
|
Packit |
5c3484 |
TMP_FREE;
|
|
Packit |
5c3484 |
}
|