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/*
* 2-double floating point numbers
*
* Almost 2 times the precision of double, by using 2 doubles.
*/
/*
Portions from:
Quad Double computation package
Copyright (C) 2003-2012
================================================
Revision date: 13 Mar 2012
Authors:
Yozo Hida U.C. Berkeley yozo@cs.berkeley.edu
Xiaoye S. Li Lawrence Berkeley Natl Lab xiaoye@nersc.gov
David H. Bailey Lawrence Berkeley Natl Lab dhbailey@lbl.gov
C++ usage guide:
Alex Kaiser Lawrence Berkeley Natl Lab adkaiser@lbl.gov
Berkeley Software Distribution Agreement
This License Agreement is entered into by The Regents of the University
of California, Department of Energy contract-operators of the Lawrence
Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720
(“Berkeley Lab”), and the entity listed below (“you” or
"Licensee") having its place of business at the address below:
The parties now agree as follows:
1. Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:
(1) Redistributions of source code must retain the copyright notice,
this list of conditions and the following disclaimer.
(2) Redistributions in binary form must reproduce the copyright notice,
this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
(3) Neither the name of the University of California, Lawrence Berkeley
National Laboratory, U.S. Dept. of Energy nor the names of its
contributors may be used to endorse or promote products derived from
this software without specific prior written permission.
2. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
3. You are under no obligation whatsoever to provide any bug fixes,
patches, or upgrades to the features, functionality or performance of
the source code ("Enhancements") to anyone; however, if you choose to
make your Enhancements available either publicly, or directly to
Lawrence Berkeley National Laboratory, without imposing a separate
written license agreement for such Enhancements, then you hereby grant
the following license: a non-exclusive, royalty-free perpetual license
to install, use, modify, prepare derivative works, incorporate into
other computer software, distribute, and sublicense such enhancements or
derivative works thereof, in binary and source code form.
*/
#ifndef DOUBLEN_H_
#define DOUBLEN_H_
#include <math.h>
typedef struct
{
double x[2];
} double2_t;
static void double2_init(double2_t *a, double y)
{
a->x[0] = y;
a->x[1] = 0;
}
static void double2_init2(double2_t *a, double hi, double lo)
{
a->x[0] = hi;
a->x[1] = lo;
}
static double double_sum_err(double a, double b, double *err)
{
double tmp;
volatile double c, d, e, g, h, f, x;
if (fabs(a) < fabs(b)) {
tmp = b;
b = a;
a = tmp;
}
c = a + b;
e = c - a;
g = c - e;
h = g - a;
f = b - h;
d = f - e;
x = d + e;
if (x != f) {
c = a;
d = b;
}
*err = d;
return c;
}
#define _QD_SPLIT_THRESH 6.69692879491417e+299 /* = 2^996 */
#define _QD_SPLITTER 134217729.0 /* = 2^27 + 1 */
static void double_split(double a, double *hi, double *lo)
{
volatile double b, c;
if (a > _QD_SPLIT_THRESH || a < -_QD_SPLIT_THRESH) {
a *= 3.7252902984619140625e-09; /* 2^-28 */
b = _QD_SPLITTER * a;
c = b - a;
*hi = b - c;
*lo = a - *hi;
*hi *= 268435456.0; /* 2^28 */
*lo *= 268435456.0; /* 2^28 */
} else {
b = _QD_SPLITTER * a;
c = b - a;
*hi = b - c;
*lo = a - *hi;
}
}
static double double_mul_err(double a, double b, double *err)
{
double a_hi, a_lo, b_hi, b_lo;
double p = a * b;
volatile double c, d;
double_split(a, &a_hi, &a_lo);
double_split(b, &b_hi, &b_lo);
c = a_hi * b_hi - p;
d = c + a_hi * b_lo + a_lo * b_hi;
*err = d + a_lo * b_lo;
return p;
}
static void double2_add(double2_t *a, double2_t *b, double2_t *c)
{
double s1, s2, t1, t2;
s1 = double_sum_err(a->x[0], b->x[0], &s2);
t1 = double_sum_err(a->x[1], b->x[1], &t2);
s2 += t1;
s1 = double_sum_err(s1, s2, &s2);
s2 += t2;
s1 = double_sum_err(s1, s2, &s2);
double2_init2(c, s1, s2);
}
static void double2_neg(double2_t *a, double2_t *b)
{
b->x[0] = -a->x[0];
b->x[1] = -a->x[1];
}
static void double2_sub(double2_t *a, double2_t *b, double2_t *c)
{
double2_t d;
double2_neg(b, &d);
double2_add(a, &d, c);
}
static void double2_mul(double2_t *a, double2_t *b, double2_t *c)
{
double p1, p2;
p1 = double_mul_err(a->x[0], b->x[0], &p2);
p2 += (a->x[0] * b->x[1] + a->x[1] * b->x[0]);
p1 = double_sum_err(p1, p2, &p2);
double2_init2(c, p1, p2);
}
static void double2_div(double2_t *a, double2_t *b, double2_t *c)
{
double q1, q2, q3;
double2_t r, e, f;
q1 = a->x[0] / b->x[0]; /* approximate quotient */
double2_init(&f, q1);
double2_mul(&f, b, &e);
double2_sub(a, &e, &r);
q2 = r.x[0] / b->x[0];
double2_init(&f, q2);
double2_mul(&f, b, &e);
double2_sub(&r, &e, &r);
q3 = r.x[0] / b->x[0];
q1 = double_sum_err(q1, q2, &q2);
double2_init2(&e, q1, q2);
double2_init(&f, q3);
double2_add(&e, &f, c);
}
static double double2_double(double2_t *a)
{
return a->x[0] + a->x[1];
}
#endif /* DOUBLE2_H_ */
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