newlib/libm/complex/casin.c

   1 /* $NetBSD: casin.c,v 1.1 2007/08/20 16:01:31 drochner Exp $ */
   2
   3 /*-
   4  * Copyright (c) 2007 The NetBSD Foundation, Inc.
   5  * All rights reserved.
   6  *
   7  * This code is derived from software written by Stephen L. Moshier.
   8  * It is redistributed by the NetBSD Foundation by permission of the author.
   9  *
  10  * Redistribution and use in source and binary forms, with or without
  11  * modification, are permitted provided that the following conditions
  12  * are met:
  13  * 1. Redistributions of source code must retain the above copyright
  14  *    notice, this list of conditions and the following disclaimer.
  15  * 2. Redistributions in binary form must reproduce the above copyright
  16  *    notice, this list of conditions and the following disclaimer in the
  17  *    documentation and/or other materials provided with the distribution.
  18  *
  19  * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS
  20  * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
  21  * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
  22  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS
  23  * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
  24  * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
  25  * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
  26  * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
  27  * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  28  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
  29  * POSSIBILITY OF SUCH DAMAGE.
  30  *
  31  * imported and modified include for newlib 2010/10/03
  32  * Marco Atzeri <marco_atzeri@yahoo.it>
  33  */
  34
  35 /*
  36 FUNCTION
  37         <<casin>>, <<casinf>>---complex arc sine
  38
  39 INDEX
  40         casin
  41 INDEX
  42         casinf
  43
  44 SYNOPSIS
  45        #include <complex.h>
  46        double complex casin(double complex <[z]>);
  47        float complex casinf(float complex <[z]>);
  48
  49
  50 DESCRIPTION
  51         These functions compute the complex arc sine of <[z]>,
  52         with branch cuts outside the interval [-1, +1] along the real axis.
  53
  54         <<casinf>> is identical to <<casin>>, except that it performs
  55         its calculations on <<floats complex>>.
  56
  57 RETURNS
  58         @ifnottex
  59         These functions return the complex arc sine value, in the range
  60         of a strip mathematically  unbounded  along the imaginary axis
  61         and in the interval [-pi/2, +pi/2] along the real axis.
  62         @end ifnottex
  63         @tex
  64         These functions return the complex arc sine value, in the range
  65         of a strip mathematically  unbounded  along the imaginary axis
  66         and in the interval [$-\pi/2$, $+\pi/2$] along the real axis.
  67         @end tex
  68
  69 PORTABILITY
  70         <<casin>> and <<casinf>> are ISO C99
  71
  72 QUICKREF
  73         <<casin>> and <<casinf>> are ISO C99
  74
  75 */
  76
  77
  78 #include <complex.h>
  79 #include <math.h>
  80
  81 #ifdef __weak_alias
  82 __weak_alias(casin, _casin)
  83 #endif
  84
  85 double complex
  86 casin(double complex z)
  87 {
  88         double complex w;
  89         double complex ca, ct, zz, z2;
  90         double x, y;
  91
  92         x = creal(z);
  93         y = cimag(z);
  94
  95 #if 0 /* MD: test is incorrect, casin(>1) is defined */
  96         if (y == 0.0) {
  97                 if (fabs(x) > 1.0) {
  98                         w = M_PI_2 + 0.0 * I;
  99 #if 0
 100                         mtherr ("casin", DOMAIN);
 101 #endif
 102                 } else {
 103                         w = asin(x) + 0.0 * I;
 104                 }
 105                 return w;
 106         }
 107 #endif
 108
 109 /* Power series expansion */
 110 /*
 111 b = cabs(z);
 112 if( b < 0.125 )
 113 {
 114 z2.r = (x - y) * (x + y);
 115 z2.i = 2.0 * x * y;
 116
 117 cn = 1.0;
 118 n = 1.0;
 119 ca.r = x;
 120 ca.i = y;
 121 sum.r = x;
 122 sum.i = y;
 123 do
 124         {
 125         ct.r = z2.r * ca.r  -  z2.i * ca.i;
 126         ct.i = z2.r * ca.i  +  z2.i * ca.r;
 127         ca.r = ct.r;
 128         ca.i = ct.i;
 129
 130         cn *= n;
 131         n += 1.0;
 132         cn /= n;
 133         n += 1.0;
 134         b = cn/n;
 135
 136         ct.r *= b;
 137         ct.i *= b;
 138         sum.r += ct.r;
 139         sum.i += ct.i;
 140         b = fabs(ct.r) + fabs(ct.i);
 141         }
 142 while( b > MACHEP );
 143 w->r = sum.r;
 144 w->i = sum.i;
 145 return;
 146 }
 147 */
 148
 149
 150         ca = x + y * I;
 151         ct = ca * I;
 152         /* sqrt( 1 - z*z) */
 153         /* cmul( &ca, &ca, &zz ) */
 154         /*x * x  -  y * y */
 155         zz = (x - y) * (x + y) + (2.0 * x * y) * I;
 156
 157         zz = 1.0 - creal(zz) - cimag(zz) * I;
 158         z2 = csqrt(zz);
 159
 160         zz = ct + z2;
 161         zz = clog(zz);
 162         /* multiply by 1/i = -i */
 163         w = zz * (-1.0 * I);
 164         return w;
 165 }