newlib/libm/complex/cephes_subrl.c

   1 /* $NetBSD: cephes_subrl.c,v 1.2 2014/10/10 14:06:40 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 #include "cephes_subrl.h"
  35
  36 /* calculate cosh and sinh */
  37
  38 /* On platforms where long double is as wide as double.  */
  39 #ifdef _LDBL_EQ_DBL
  40 void
  41 _cchshl(long double x, long double *c, long double *s)
  42 {
  43         long double e, ei;
  44
  45         if (fabsl(x) <= 0.5L) {
  46                 *c = coshl(x);
  47                 *s = sinhl(x);
  48         } else {
  49                 e = expl(x);
  50                 ei = 0.5L / e;
  51                 e = 0.5L * e;
  52                 *s = e - ei;
  53                 *c = e + ei;
  54         }
  55 }
  56 #endif
  57
  58 /* Program to subtract nearest integer multiple of PI */
  59
  60 /* extended precision value of PI: */
  61 static const long double DP1 = 3.14159265358979323829596852490908531763125L;
  62 static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L;
  63 #ifndef __vax__
  64 static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L;
  65 #define MACHEPL 1.1e-38L
  66 #else
  67 static const long double DP3 = 0L;
  68 #define MACHEPL 1.1e-19L
  69 #endif
  70
  71 long double
  72 _redupil(long double x)
  73 {
  74         long double t;
  75         long long i;
  76
  77         t = x / M_PIL;
  78         if (t >= 0.0L)
  79                 t += 0.5L;
  80         else
  81                 t -= 0.5L;
  82
  83         i = t;  /* the multiple */
  84         t = i;
  85         t = ((x - t * DP1) - t * DP2) - t * DP3;
  86         return t;
  87 }
  88
  89 /* Taylor series expansion for cosh(2y) - cos(2x) */
  90
  91 /* On platforms where long double is as wide as double.  */
  92 #ifdef _LDBL_EQ_DBL
  93 long double
  94 _ctansl(long double complex z)
  95 {
  96         long double f, x, x2, y, y2, rn, t;
  97         long double d;
  98
  99         x = fabsl(2.0L * creall(z));
 100         y = fabsl(2.0L * cimagl(z));
 101
 102         x = _redupil(x);
 103
 104         x = x * x;
 105         y = y * y;
 106         x2 = 1.0;
 107         y2 = 1.0;
 108         f = 1.0;
 109         rn = 0.0;
 110         d = 0.0;
 111         do {
 112                 rn += 1.0L;
 113                 f *= rn;
 114                 rn += 1.0L;
 115                 f *= rn;
 116                 x2 *= x;
 117                 y2 *= y;
 118                 t = y2 + x2;
 119                 t /= f;
 120                 d += t;
 121
 122                 rn += 1.0L;
 123                 f *= rn;
 124                 rn += 1.0L;
 125                 f *= rn;
 126                 x2 *= x;
 127                 y2 *= y;
 128                 t = y2 - x2;
 129                 t /= f;
 130                 d += t;
 131         } while (fabsl(t/d) > MACHEPL);
 132         return d;
 133 }
 134 #endif