lib/libm/complex/casin.c

   1 /* $NetBSD$ */
   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
  32 #include "../src/namespace.h"
  33 #include <complex.h>
  34 #include <math.h>
  35
  36 #ifdef __weak_alias
  37 __weak_alias(casin, _casin)
  38 #endif
  39
  40 double complex
  41 casin(double complex z)
  42 {
  43         double complex w;
  44         double complex ca, ct, zz, z2;
  45         double x, y;
  46
  47         x = creal(z);
  48         y = cimag(z);
  49
  50 #if 0 /* MD: test is incorrect, casin(>1) is defined */
  51         if (y == 0.0) {
  52                 if (fabs(x) > 1.0) {
  53                         w = M_PI_2 + 0.0 * I;
  54 #if 0
  55                         mtherr ("casin", DOMAIN);
  56 #endif
  57                 } else {
  58                         w = asin(x) + 0.0 * I;
  59                 }
  60                 return w;
  61         }
  62 #endif
  63
  64 /* Power series expansion */
  65 /*
  66 b = cabs(z);
  67 if( b < 0.125 )
  68 {
  69 z2.r = (x - y) * (x + y);
  70 z2.i = 2.0 * x * y;
  71
  72 cn = 1.0;
  73 n = 1.0;
  74 ca.r = x;
  75 ca.i = y;
  76 sum.r = x;
  77 sum.i = y;
  78 do
  79         {
  80         ct.r = z2.r * ca.r  -  z2.i * ca.i;
  81         ct.i = z2.r * ca.i  +  z2.i * ca.r;
  82         ca.r = ct.r;
  83         ca.i = ct.i;
  84
  85         cn *= n;
  86         n += 1.0;
  87         cn /= n;
  88         n += 1.0;
  89         b = cn/n;
  90
  91         ct.r *= b;
  92         ct.i *= b;
  93         sum.r += ct.r;
  94         sum.i += ct.i;
  95         b = fabs(ct.r) + fabs(ct.i);
  96         }
  97 while( b > MACHEP );
  98 w->r = sum.r;
  99 w->i = sum.i;
 100 return;
 101 }
 102 */
 103
 104
 105         ca = x + y * I;
 106         ct = ca * I;
 107         /* sqrt( 1 - z*z) */
 108         /* cmul( &ca, &ca, &zz ) */
 109         /*x * x  -  y * y */
 110         zz = (x - y) * (x + y) + (2.0 * x * y) * I;
 111
 112         zz = 1.0 - creal(zz) - cimag(zz) * I;
 113         z2 = csqrt(zz);
 114
 115         zz = ct + z2;
 116         zz = clog(zz);
 117         /* multiply by 1/i = -i */
 118         w = zz * (-1.0 * I);
 119         return w;
 120 }