sortix--sortix/libm/complex/cephes_subr.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.
 */

#include "../src/namespace.h"
#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;
}