newlib/libm/complex/casinl.c

   1 /* $NetBSD: casinl.c,v 1.1 2014/10/10 00:48:18 christos 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
  32 #include <complex.h>
  33 #include <math.h>
  34
  35 #ifdef __weak_alias
  36 __weak_alias(casinl, _casinl)
  37 #endif
  38
  39 long double complex
  40 casinl(long double complex z)
  41 {
  42         long double complex w;
  43         long double complex ca, ct, zz, z2;
  44         long double x, y;
  45
  46         x = creall(z);
  47         y = cimagl(z);
  48
  49 #if 0 /* MD: test is incorrect, casin(>1) is defined */
  50         if (y == 0.0L) {
  51                 if (fabsl(x) > 1.0L) {
  52                         w = M_PI_2L + 0.0L * I;
  53 #if 0
  54                         mtherr ("casinl", DOMAIN);
  55 #endif
  56                 } else {
  57                         w = asinl(x) + 0.0L * I;
  58                 }
  59                 return w;
  60         }
  61 #endif
  62
  63 /* Power series expansion */
  64 /*
  65 b = cabsl(z);
  66 if( b < 0.125L )
  67 {
  68 z2.r = (x - y) * (x + y);
  69 z2.i = 2.0L * x * y;
  70
  71 cn = 1.0L;
  72 n = 1.0L;
  73 ca.r = x;
  74 ca.i = y;
  75 sum.r = x;
  76 sum.i = y;
  77 do
  78         {
  79         ct.r = z2.r * ca.r  -  z2.i * ca.i;
  80         ct.i = z2.r * ca.i  +  z2.i * ca.r;
  81         ca.r = ct.r;
  82         ca.i = ct.i;
  83
  84         cn *= n;
  85         n += 1.0;
  86         cn /= n;
  87         n += 1.0;
  88         b = cn/n;
  89
  90         ct.r *= b;
  91         ct.i *= b;
  92         sum.r += ct.r;
  93         sum.i += ct.i;
  94         b = fabsl(ct.r) + fabsl(ct.i);
  95         }
  96 while( b > MACHEPL );
  97 w->r = sum.r;
  98 w->i = sum.i;
  99 return;
 100 }
 101 */
 102
 103
 104         ca = x + y * I;
 105         ct = ca * I;
 106         /* sqrtl( 1 - z*z) */
 107         /* cmull( &ca, &ca, &zz ) */
 108         /*x * x  -  y * y */
 109         zz = (x - y) * (x + y) + (2.0L * x * y) * I;
 110
 111         zz = 1.0L - creall(zz) - cimagl(zz) * I;
 112         z2 = csqrtl(zz);
 113
 114         zz = ct + z2;
 115         zz = clogl(zz);
 116         /* multiply by 1/i = -i */
 117         w = zz * (-1.0L * I);
 118         return w;
 119 }
 120