166 lines
4.0 KiB
C
166 lines
4.0 KiB
C
/* $NetBSD: casin.c,v 1.1 2007/08/20 16:01:31 drochner Exp $ */
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/*-
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* Copyright (c) 2007 The NetBSD Foundation, Inc.
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* All rights reserved.
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*
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* This code is derived from software written by Stephen L. Moshier.
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* It is redistributed by the NetBSD Foundation by permission of the author.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS
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* ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
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* TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS
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* BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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* POSSIBILITY OF SUCH DAMAGE.
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*
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* imported and modified include for newlib 2010/10/03
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* Marco Atzeri <marco_atzeri@yahoo.it>
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*/
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/*
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FUNCTION
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<<casin>>, <<casinf>>---complex arc sine
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INDEX
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casin
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INDEX
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casinf
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ANSI_SYNOPSIS
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#include <complex.h>
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double complex casin(double complex <[z]>);
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float complex casinf(float complex <[z]>);
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DESCRIPTION
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These functions compute the complex arc sine of <[z]>,
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with branch cuts outside the interval [-1, +1] along the real axis.
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<<casinf>> is identical to <<casin>>, except that it performs
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its calculations on <<floats complex>>.
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RETURNS
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@ifnottex
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These functions return the complex arc sine value, in the range
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of a strip mathematically unbounded along the imaginary axis
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and in the interval [-pi/2, +pi/2] along the real axis.
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@end ifnottex
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@tex
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These functions return the complex arc sine value, in the range
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of a strip mathematically unbounded along the imaginary axis
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and in the interval [$-\pi/2$, $+\pi/2$] along the real axis.
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@end tex
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PORTABILITY
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<<casin>> and <<casinf>> are ISO C99
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QUICKREF
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<<casin>> and <<casinf>> are ISO C99
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*/
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#include <complex.h>
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#include <math.h>
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#ifdef __weak_alias
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__weak_alias(casin, _casin)
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#endif
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double complex
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casin(double complex z)
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{
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double complex w;
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double complex ca, ct, zz, z2;
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double x, y;
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x = creal(z);
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y = cimag(z);
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#if 0 /* MD: test is incorrect, casin(>1) is defined */
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if (y == 0.0) {
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if (fabs(x) > 1.0) {
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w = M_PI_2 + 0.0 * I;
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#if 0
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mtherr ("casin", DOMAIN);
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#endif
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} else {
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w = asin(x) + 0.0 * I;
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}
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return w;
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}
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#endif
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/* Power series expansion */
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/*
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b = cabs(z);
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if( b < 0.125 )
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{
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z2.r = (x - y) * (x + y);
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z2.i = 2.0 * x * y;
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cn = 1.0;
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n = 1.0;
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ca.r = x;
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ca.i = y;
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sum.r = x;
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sum.i = y;
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do
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{
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ct.r = z2.r * ca.r - z2.i * ca.i;
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ct.i = z2.r * ca.i + z2.i * ca.r;
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ca.r = ct.r;
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ca.i = ct.i;
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cn *= n;
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n += 1.0;
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cn /= n;
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n += 1.0;
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b = cn/n;
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ct.r *= b;
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ct.i *= b;
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sum.r += ct.r;
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sum.i += ct.i;
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b = fabs(ct.r) + fabs(ct.i);
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}
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while( b > MACHEP );
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w->r = sum.r;
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w->i = sum.i;
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return;
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}
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*/
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ca = x + y * I;
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ct = ca * I;
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/* sqrt( 1 - z*z) */
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/* cmul( &ca, &ca, &zz ) */
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/*x * x - y * y */
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zz = (x - y) * (x + y) + (2.0 * x * y) * I;
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zz = 1.0 - creal(zz) - cimag(zz) * I;
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z2 = csqrt(zz);
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zz = ct + z2;
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zz = clog(zz);
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/* multiply by 1/i = -i */
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w = zz * (-1.0 * I);
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return w;
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}
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