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/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001-2013 Free Software Foundation, Inc.
*
* This program 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 2.1 of the License, or
* (at your option) any later version.
*
* This program 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 this program; if not, see <http://www.gnu.org/licenses/>.
*/
/* Define __mul and __sqr and use the rest from generic code. */
#define NO__MUL
#define NO__SQR
#include <sysdeps/ieee754/dbl-64/mpa.c>
/* Multiply *X and *Y and store result in *Z. X and Y may overlap but not X
and Z or Y and Z. For P in [1, 2, 3], the exact result is truncated to P
digits. In case P > 3 the error is bounded by 1.001 ULP. */
void
__mul (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
long i, i1, i2, j, k, k2;
long p2 = p;
double u, zk, zk2;
/* Is z=0? */
if (__glibc_unlikely (X[0] * Y[0] == ZERO))
{
Z[0] = ZERO;
return;
}
/* Multiply, add and carry */
k2 = (p2 < 3) ? p2 + p2 : p2 + 3;
zk = Z[k2] = ZERO;
for (k = k2; k > 1;)
{
if (k > p2)
{
i1 = k - p2;
i2 = p2 + 1;
}
else
{
i1 = 1;
i2 = k;
}
#if 1
/* Rearrange this inner loop to allow the fmadd instructions to be
independent and execute in parallel on processors that have
dual symmetrical FP pipelines. */
if (i1 < (i2 - 1))
{
/* Make sure we have at least 2 iterations. */
if (((i2 - i1) & 1L) == 1L)
{
/* Handle the odd iterations case. */
zk2 = x->d[i2 - 1] * y->d[i1];
}
else
zk2 = 0.0;
/* Do two multiply/adds per loop iteration, using independent
accumulators; zk and zk2. */
for (i = i1, j = i2 - 1; i < i2 - 1; i += 2, j -= 2)
{
zk += x->d[i] * y->d[j];
zk2 += x->d[i + 1] * y->d[j - 1];
}
zk += zk2; /* Final sum. */
}
else
{
/* Special case when iterations is 1. */
zk += x->d[i1] * y->d[i1];
}
#else
/* The original code. */
for (i = i1, j = i2 - 1; i < i2; i++, j--)
zk += X[i] * Y[j];
#endif
u = (zk + CUTTER) - CUTTER;
if (u > zk)
u -= RADIX;
Z[k] = zk - u;
zk = u * RADIXI;
--k;
}
Z[k] = zk;
int e = EX + EY;
/* Is there a carry beyond the most significant digit? */
if (Z[1] == ZERO)
{
for (i = 1; i <= p2; i++)
Z[i] = Z[i + 1];
e--;
}
EZ = e;
Z[0] = X[0] * Y[0];
}
/* Square *X and store result in *Y. X and Y may not overlap. For P in
[1, 2, 3], the exact result is truncated to P digits. In case P > 3 the
error is bounded by 1.001 ULP. This is a faster special case of
multiplication. */
void
__sqr (const mp_no *x, mp_no *y, int p)
{
long i, j, k, ip;
double u, yk;
/* Is z=0? */
if (__glibc_unlikely (X[0] == ZERO))
{
Y[0] = ZERO;
return;
}
/* We need not iterate through all X's since it's pointless to
multiply zeroes. */
for (ip = p; ip > 0; ip--)
if (X[ip] != ZERO)
break;
k = (__glibc_unlikely (p < 3)) ? p + p : p + 3;
while (k > 2 * ip + 1)
Y[k--] = ZERO;
yk = ZERO;
while (k > p)
{
double yk2 = 0.0;
long lim = k / 2;
if (k % 2 == 0)
{
yk += X[lim] * X[lim];
lim--;
}
/* In __mul, this loop (and the one within the next while loop) run
between a range to calculate the mantissa as follows:
Z[k] = X[k] * Y[n] + X[k+1] * Y[n-1] ... + X[n-1] * Y[k+1]
+ X[n] * Y[k]
For X == Y, we can get away with summing halfway and doubling the
result. For cases where the range size is even, the mid-point needs
to be added separately (above). */
for (i = k - p, j = p; i <= lim; i++, j--)
yk2 += X[i] * X[j];
yk += 2.0 * yk2;
u = (yk + CUTTER) - CUTTER;
if (u > yk)
u -= RADIX;
Y[k--] = yk - u;
yk = u * RADIXI;
}
while (k > 1)
{
double yk2 = 0.0;
long lim = k / 2;
if (k % 2 == 0)
{
yk += X[lim] * X[lim];
lim--;
}
/* Likewise for this loop. */
for (i = 1, j = k - 1; i <= lim; i++, j--)
yk2 += X[i] * X[j];
yk += 2.0 * yk2;
u = (yk + CUTTER) - CUTTER;
if (u > yk)
u -= RADIX;
Y[k--] = yk - u;
yk = u * RADIXI;
}
Y[k] = yk;
/* Squares are always positive. */
Y[0] = 1.0;
int e = EX * 2;
/* Is there a carry beyond the most significant digit? */
if (__glibc_unlikely (Y[1] == ZERO))
{
for (i = 1; i <= p; i++)
Y[i] = Y[i + 1];
e--;
}
EY = e;
}
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