newlib/libm/complex/cephes_subr.c

   1 /* $NetBSD: cephes_subr.c,v 1.1 2007/08/20 16:01:33 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 #include <complex.h>
  36 #include <math.h>
  37 #include "cephes_subr.h"
  38
  39 /* calculate cosh and sinh */
  40
  41 void
  42 _cchsh(double x, double *c, double *s)
  43 {
  44         double e, ei;
  45
  46         if (fabs(x) <= 0.5) {
  47                 *c = cosh(x);
  48                 *s = sinh(x);
  49         } else {
  50                 e = exp(x);
  51                 ei = 0.5 / e;
  52                 e = 0.5 * e;
  53                 *s = e - ei;
  54                 *c = e + ei;
  55         }
  56 }
  57
  58 /* Program to subtract nearest integer multiple of PI */
  59
  60 /* extended precision value of PI: */
  61 static const double DP1 = 3.14159265160560607910E0;
  62 static const double DP2 = 1.98418714791870343106E-9;
  63 static const double DP3 = 1.14423774522196636802E-17;
  64 #define MACHEP 1.1e-16
  65
  66 double
  67 _redupi(double x)
  68 {
  69         double t;
  70         long i;
  71
  72         t = x / M_PI;
  73         if (t >= 0.0)
  74                 t += 0.5;
  75         else
  76                 t -= 0.5;
  77
  78         i = t;  /* the multiple */
  79         t = i;
  80         t = ((x - t * DP1) - t * DP2) - t * DP3;
  81         return t;
  82 }
  83
  84 /* Taylor series expansion for cosh(2y) - cos(2x) */
  85
  86 double
  87 _ctans(double complex z)
  88 {
  89         double f, x, x2, y, y2, rn, t;
  90         double d;
  91
  92         x = fabs(2.0 * creal(z));
  93         y = fabs(2.0 * cimag(z));
  94
  95         x = _redupi(x);
  96
  97         x = x * x;
  98         y = y * y;
  99         x2 = 1.0;
 100         y2 = 1.0;
 101         f = 1.0;
 102         rn = 0.0;
 103         d = 0.0;
 104         do {
 105                 rn += 1.0;
 106                 f *= rn;
 107                 rn += 1.0;
 108                 f *= rn;
 109                 x2 *= x;
 110                 y2 *= y;
 111                 t = y2 + x2;
 112                 t /= f;
 113                 d += t;
 114
 115                 rn += 1.0;
 116                 f *= rn;
 117                 rn += 1.0;
 118                 f *= rn;
 119                 x2 *= x;
 120                 y2 *= y;
 121                 t = y2 - x2;
 122                 t /= f;
 123                 d += t;
 124         } while (fabs(t/d) > MACHEP);
 125         return d;
 126 }