source: trunk/libs/newlib/src/newlib/libm/complex/cephes_subrl.c @ 452

/* $NetBSD: cephes_subrl.c,v 1.2 2014/10/10 14:06:40 christos 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 <complex.h>
#include <math.h>
#include "cephes_subrl.h"

/* calculate cosh and sinh */

void
_cchshl(long double x, long double *c, long double *s)
{
        long double e, ei;

        if (fabsl(x) <= 0.5L) {
                *c = coshl(x);
                *s = sinhl(x);
        } else {
                e = expl(x);
                ei = 0.5L / e;
                e = 0.5L * e;
                *s = e - ei;
                *c = e + ei;
        }
}

/* Program to subtract nearest integer multiple of PI */

/* extended precision value of PI: */
static const long double DP1 = 3.14159265358979323829596852490908531763125L;
static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L;
#ifndef __vax__
static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L;
#define MACHEPL 1.1e-38L
#else
static const long double DP3 = 0L;
#define MACHEPL 1.1e-19L
#endif

long double
_redupil(long double x)
{
        long double t;
        long long i;

        t = x / M_PIL;
        if (t >= 0.0L)
                t += 0.5L;
        else
                t -= 0.5L;

        i = t;  /* the multiple */
        t = i;
        t = ((x - t * DP1) - t * DP2) - t * DP3;
        return t;
}

/* Taylor series expansion for cosh(2y) - cos(2x) */

long double
_ctansl(long double complex z)
{
        long double f, x, x2, y, y2, rn, t;
        long double d;

        x = fabsl(2.0L * creall(z));
        y = fabsl(2.0L * cimagl(z));

        x = _redupil(x);

        x = x * x;
        y = y * y;
        x2 = 1.0;
        y2 = 1.0;
        f = 1.0;
        rn = 0.0;
        d = 0.0;
        do {
                rn += 1.0L;
                f *= rn;
                rn += 1.0L;
                f *= rn;
                x2 *= x;
                y2 *= y;
                t = y2 + x2;
                t /= f;
                d += t;

                rn += 1.0L;
                f *= rn;
                rn += 1.0L;
                f *= rn;
                x2 *= x;
                y2 *= y;
                t = y2 - x2;
                t /= f;
                d += t;
        } while (fabsl(t/d) > MACHEPL);
        return d;
}