127 lines
3.0 KiB
C
127 lines
3.0 KiB
C
|
/* $NetBSD: cephes_subr.c,v 1.1 2007/08/20 16:01:33 drochner Exp $ */
|
||
|
|
|
||
|
|
/*-
|
||
|
|
* Copyright (c) 2007 The NetBSD Foundation, Inc.
|
||
|
|
* All rights reserved.
|
||
|
|
*
|
||
|
|
* This code is derived from software written by Stephen L. Moshier.
|
||
|
|
* It is redistributed by the NetBSD Foundation by permission of the author.
|
||
|
|
*
|
||
|
|
* 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 above copyright
|
||
|
|
* notice, this list of conditions and the following disclaimer.
|
||
|
|
* 2. Redistributions in binary form must reproduce the above copyright
|
||
|
|
* notice, this list of conditions and the following disclaimer in the
|
||
|
|
* documentation and/or other materials provided with the distribution.
|
||
|
|
*
|
||
|
|
* THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. 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 FOUNDATION 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.
|
||
|
|
*
|
||
|
|
* imported and modified include for newlib 2010/10/03
|
||
|
|
* Marco Atzeri <marco_atzeri@yahoo.it>
|
||
|
|
*/
|
||
|
|
|
||
|
|
#include <complex.h>
|
||
|
|
#include <math.h>
|
||
|
|
#include "cephes_subr.h"
|
||
|
|
|
||
|
|
/* calculate cosh and sinh */
|
||
|
|
|
||
|
|
void
|
||
|
|
_cchsh(double x, double *c, double *s)
|
||
|
|
{
|
||
|
|
double e, ei;
|
||
|
|
|
||
|
|
if (fabs(x) <= 0.5) {
|
||
|
|
*c = cosh(x);
|
||
|
|
*s = sinh(x);
|
||
|
|
} else {
|
||
|
|
e = exp(x);
|
||
|
|
ei = 0.5 / e;
|
||
|
|
e = 0.5 * e;
|
||
|
|
*s = e - ei;
|
||
|
|
*c = e + ei;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Program to subtract nearest integer multiple of PI */
|
||
|
|
|
||
|
|
/* extended precision value of PI: */
|
||
|
|
static const double DP1 = 3.14159265160560607910E0;
|
||
|
|
static const double DP2 = 1.98418714791870343106E-9;
|
||
|
|
static const double DP3 = 1.14423774522196636802E-17;
|
||
|
|
#define MACHEP 1.1e-16
|
||
|
|
|
||
|
|
double
|
||
|
|
_redupi(double x)
|
||
|
|
{
|
||
|
|
double t;
|
||
|
|
long i;
|
||
|
|
|
||
|
|
t = x / M_PI;
|
||
|
|
if (t >= 0.0)
|
||
|
|
t += 0.5;
|
||
|
|
else
|
||
|
|
t -= 0.5;
|
||
|
|
|
||
|
|
i = t; /* the multiple */
|
||
|
|
t = i;
|
||
|
|
t = ((x - t * DP1) - t * DP2) - t * DP3;
|
||
|
|
return t;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Taylor series expansion for cosh(2y) - cos(2x) */
|
||
|
|
|
||
|
|
double
|
||
|
|
_ctans(double complex z)
|
||
|
|
{
|
||
|
|
double f, x, x2, y, y2, rn, t;
|
||
|
|
double d;
|
||
|
|
|
||
|
|
x = fabs(2.0 * creal(z));
|
||
|
|
y = fabs(2.0 * cimag(z));
|
||
|
|
|
||
|
|
x = _redupi(x);
|
||
|
|
|
||
|
|
x = x * x;
|
||
|
|
y = y * y;
|
||
|
|
x2 = 1.0;
|
||
|
|
y2 = 1.0;
|
||
|
|
f = 1.0;
|
||
|
|
rn = 0.0;
|
||
|
|
d = 0.0;
|
||
|
|
do {
|
||
|
|
rn += 1.0;
|
||
|
|
f *= rn;
|
||
|
|
rn += 1.0;
|
||
|
|
f *= rn;
|
||
|
|
x2 *= x;
|
||
|
|
y2 *= y;
|
||
|
|
t = y2 + x2;
|
||
|
|
t /= f;
|
||
|
|
d += t;
|
||
|
|
|
||
|
|
rn += 1.0;
|
||
|
|
f *= rn;
|
||
|
|
rn += 1.0;
|
||
|
|
f *= rn;
|
||
|
|
x2 *= x;
|
||
|
|
y2 *= y;
|
||
|
|
t = y2 - x2;
|
||
|
|
t /= f;
|
||
|
|
d += t;
|
||
|
|
} while (fabs(t/d) > MACHEP);
|
||
|
|
return d;
|
||
|
|
}
|