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/* mpn_toom22_mul -- Multiply {ap,an} and {bp,bn} where an >= bn. Or more
accurately, bn <= an < 2bn.
Contributed to the GNU project by Torbjorn Granlund.
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 2006-2010, 2012, 2014, 2018, 2020 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 either:
* 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.
or
* the GNU General Public License as published by the Free Software
Foundation; either version 2 of the License, or (at your option) any
later version.
or both in parallel, as here.
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 General Public License
for more details.
You should have received copies of the GNU General Public License and the
GNU Lesser General Public License along with the GNU MP Library. If not,
see https://www.gnu.org/licenses/. */
#include "gmp-impl.h"
/* Evaluate in: -1, 0, +inf
<-s--><--n-->
____ ______
|_a1_|___a0_|
|b1_|___b0_|
<-t-><--n-->
v0 = a0 * b0 # A(0)*B(0)
vm1 = (a0- a1)*(b0- b1) # A(-1)*B(-1)
vinf= a1 * b1 # A(inf)*B(inf)
*/
#if TUNE_PROGRAM_BUILD || WANT_FAT_BINARY
#define MAYBE_mul_toom22 1
#else
#define MAYBE_mul_toom22 \
(MUL_TOOM33_THRESHOLD >= 2 * MUL_TOOM22_THRESHOLD)
#endif
#define TOOM22_MUL_N_REC(p, a, b, n, ws) \
do { \
if (! MAYBE_mul_toom22 \
|| BELOW_THRESHOLD (n, MUL_TOOM22_THRESHOLD)) \
mpn_mul_basecase (p, a, n, b, n); \
else \
mpn_toom22_mul (p, a, n, b, n, ws); \
} while (0)
/* Normally, this calls mul_basecase or toom22_mul. But when when the fraction
MUL_TOOM33_THRESHOLD / MUL_TOOM22_THRESHOLD is large, an initially small
relative unbalance will become a larger and larger relative unbalance with
each recursion (the difference s-t will be invariant over recursive calls).
Therefore, we need to call toom32_mul. FIXME: Suppress depending on
MUL_TOOM33_THRESHOLD / MUL_TOOM22_THRESHOLD and on MUL_TOOM22_THRESHOLD. */
#define TOOM22_MUL_REC(p, a, an, b, bn, ws) \
do { \
if (! MAYBE_mul_toom22 \
|| BELOW_THRESHOLD (bn, MUL_TOOM22_THRESHOLD)) \
mpn_mul_basecase (p, a, an, b, bn); \
else if (4 * an < 5 * bn) \
mpn_toom22_mul (p, a, an, b, bn, ws); \
else \
mpn_toom32_mul (p, a, an, b, bn, ws); \
} while (0)
void
mpn_toom22_mul (mp_ptr pp,
mp_srcptr ap, mp_size_t an,
mp_srcptr bp, mp_size_t bn,
mp_ptr scratch)
{
const int __gmpn_cpuvec_initialized = 1;
mp_size_t n, s, t;
int vm1_neg;
mp_limb_t cy, cy2;
mp_ptr asm1;
mp_ptr bsm1;
#define a0 ap
#define a1 (ap + n)
#define b0 bp
#define b1 (bp + n)
s = an >> 1;
n = an - s;
t = bn - n;
ASSERT (an >= bn);
ASSERT (0 < s && s <= n && (n - s) == (an & 1));
ASSERT (0 < t && t <= s);
asm1 = pp;
bsm1 = pp + n;
vm1_neg = 0;
/* Compute asm1. */
if ((an & 1) == 0) /* s == n */
{
if (mpn_cmp (a0, a1, n) < 0)
{
mpn_sub_n (asm1, a1, a0, n);
vm1_neg = 1;
}
else
{
mpn_sub_n (asm1, a0, a1, n);
}
}
else /* n - s == 1 */
{
if (a0[s] == 0 && mpn_cmp (a0, a1, s) < 0)
{
mpn_sub_n (asm1, a1, a0, s);
asm1[s] = 0;
vm1_neg = 1;
}
else
{
asm1[s] = a0[s] - mpn_sub_n (asm1, a0, a1, s);
}
}
/* Compute bsm1. */
if (t == n)
{
if (mpn_cmp (b0, b1, n) < 0)
{
mpn_sub_n (bsm1, b1, b0, n);
vm1_neg ^= 1;
}
else
{
mpn_sub_n (bsm1, b0, b1, n);
}
}
else
{
if (mpn_zero_p (b0 + t, n - t) && mpn_cmp (b0, b1, t) < 0)
{
mpn_sub_n (bsm1, b1, b0, t);
MPN_ZERO (bsm1 + t, n - t);
vm1_neg ^= 1;
}
else
{
mpn_sub (bsm1, b0, n, b1, t);
}
}
#define v0 pp /* 2n */
#define vinf (pp + 2 * n) /* s+t */
#define vm1 scratch /* 2n */
#define scratch_out scratch + 2 * n
/* vm1, 2n limbs */
TOOM22_MUL_N_REC (vm1, asm1, bsm1, n, scratch_out);
if (s > t) TOOM22_MUL_REC (vinf, a1, s, b1, t, scratch_out);
else TOOM22_MUL_N_REC (vinf, a1, b1, s, scratch_out);
/* v0, 2n limbs */
TOOM22_MUL_N_REC (v0, ap, bp, n, scratch_out);
/* H(v0) + L(vinf) */
cy = mpn_add_n (pp + 2 * n, v0 + n, vinf, n);
/* L(v0) + (H(v0) + L(vinf)) */
cy2 = cy + mpn_add_n (pp + n, pp + 2 * n, v0, n);
/* (H(v0) + L(vinf)) + H(vinf) */
cy += mpn_add (pp + 2 * n, pp + 2 * n, n, vinf + n, s + t - n);
if (vm1_neg)
cy += mpn_add_n (pp + n, pp + n, vm1, 2 * n);
else {
cy -= mpn_sub_n (pp + n, pp + n, vm1, 2 * n);
if (UNLIKELY (cy + 1 == 0)) { /* cy is negative */
/* The total contribution of v0+vinf-vm1 can not be negative. */
#if WANT_ASSERT
/* The borrow in cy stops the propagation of the carry cy2, */
ASSERT (cy2 == 1);
cy += mpn_add_1 (pp + 2 * n, pp + 2 * n, n, cy2);
ASSERT (cy == 0);
#else
/* we simply fill the area with zeros. */
MPN_FILL (pp + 2 * n, n, 0);
/* ASSERT (s + t == n || mpn_zero_p (pp + 3 * n, s + t - n)); */
#endif
return;
}
}
ASSERT (cy <= 2);
ASSERT (cy2 <= 2);
MPN_INCR_U (pp + 2 * n, s + t, cy2);
/* if s+t==n, cy is zero, but we should not access pp[3*n] at all. */
MPN_INCR_U (pp + 3 * n, s + t - n, cy);
}
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