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