compiler/stdc/math/s_casin.c

   1 /*      $OpenBSD: s_casin.c,v 1.6 2013/07/03 04:46:36 espie Exp $       */
   2 /*
   3  * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
   4  *
   5  * Permission to use, copy, modify, and distribute this software for any
   6  * purpose with or without fee is hereby granted, provided that the above
   7  * copyright notice and this permission notice appear in all copies.
   8  *
   9  * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
  10  * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
  11  * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
  12  * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
  13  * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
  14  * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
  15  * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
  16  */
  17
  18 /*                                                      casin()
  19  *
  20  *      Complex circular arc sine
  21  *
  22  *
  23  *
  24  * SYNOPSIS:
  25  *
  26  * double complex casin();
  27  * double complex z, w;
  28  *
  29  * w = casin (z);
  30  *
  31  *
  32  *
  33  * DESCRIPTION:
  34  *
  35  * Inverse complex sine:
  36  *
  37  *                               2
  38  * w = -i clog( iz + csqrt( 1 - z ) ).
  39  *
  40  * casin(z) = -i casinh(iz)
  41  *
  42  * ACCURACY:
  43  *
  44  *                      Relative error:
  45  * arithmetic   domain     # trials      peak         rms
  46  *    DEC       -10,+10     10100       2.1e-15     3.4e-16
  47  *    IEEE      -10,+10     30000       2.2e-14     2.7e-15
  48  * Larger relative error can be observed for z near zero.
  49  * Also tested by csin(casin(z)) = z.
  50  */
  51
  52 #include <float.h>
  53 #include <complex.h>
  54 #include "math.h"
  55
  56 double complex
  57 casin(double complex z)
  58 {
  59         double complex w;
  60         double complex ca, ct, zz, z2;
  61         double x, y;
  62
  63         x = creal (z);
  64         y = cimag (z);
  65
  66         if (y == 0.0) {
  67                 if (fabs(x) > 1.0) {
  68                         w = M_PI_2 + 0.0 * I;
  69                         /*mtherr ("casin", DOMAIN);*/
  70                 }
  71                 else {
  72                         w = asin (x) + 0.0 * I;
  73                 }
  74                 return (w);
  75         }
  76
  77         /* Power series expansion */
  78         /*
  79         b = cabs(z);
  80         if( b < 0.125 ) {
  81                 z2.r = (x - y) * (x + y);
  82                 z2.i = 2.0 * x * y;
  83
  84                 cn = 1.0;
  85                 n = 1.0;
  86                 ca.r = x;
  87                 ca.i = y;
  88                 sum.r = x;
  89                 sum.i = y;
  90                 do {
  91                         ct.r = z2.r * ca.r  -  z2.i * ca.i;
  92                         ct.i = z2.r * ca.i  +  z2.i * ca.r;
  93                         ca.r = ct.r;
  94                         ca.i = ct.i;
  95
  96                         cn *= n;
  97                         n += 1.0;
  98                         cn /= n;
  99                         n += 1.0;
 100                         b = cn/n;
 101
 102                         ct.r *= b;
 103                         ct.i *= b;
 104                         sum.r += ct.r;
 105                         sum.i += ct.i;
 106                         b = fabs(ct.r) + fabs(ct.i);
 107                 }
 108                 while( b > MACHEP );
 109                 w->r = sum.r;
 110                 w->i = sum.i;
 111                 return;
 112         }
 113         */
 114
 115         ca = x + y * I;
 116         ct = ca * I;
 117         /* sqrt( 1 - z*z) */
 118         /* cmul( &ca, &ca, &zz ) */
 119         /*x * x  -  y * y */
 120         zz = (x - y) * (x + y) + (2.0 * x * y) * I;
 121
 122         zz = 1.0 - creal(zz) - cimag(zz) * I;
 123         z2 = csqrt (zz);
 124
 125         zz = ct + z2;
 126         zz = clog (zz);
 127         /* multiply by 1/i = -i */
 128         w = zz * (-1.0 * I);
 129         return (w);
 130 }
 131
 132 #if     LDBL_MANT_DIG == DBL_MANT_DIG
 133 AROS_MAKE_ASM_SYM(typeof(casinl), casinl, AROS_CSYM_FROM_ASM_NAME(casinl), AROS_CSYM_FROM_ASM_NAME(casin));
 134 AROS_EXPORT_ASM_SYM(AROS_CSYM_FROM_ASM_NAME(casinl));
 135 #endif  /* LDBL_MANT_DIG == DBL_MANT_DIG */