newlib/libm/complex/cephes_subrf.c

   1 /* $NetBSD: cephes_subrf.c,v 1.1 2007/08/20 16:01:34 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_subrf.h"
  38
  39 /* calculate cosh and sinh */
  40
  41 void
  42 _cchshf(float x, float *c, float *s)
  43 {
  44         float e, ei;
  45
  46         if (fabsf(x) <= 0.5f) {
  47                 *c = coshf(x);
  48                 *s = sinhf(x);
  49         } else {
  50                 e = expf(x);
  51                 ei = 0.5f / e;
  52                 e = 0.5f * 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 =  3.140625;
  62 static const double DP2 =  9.67502593994140625E-4;
  63 static const double DP3 =  1.509957990978376432E-7;
  64 #define MACHEPF 3.0e-8
  65
  66 float
  67 _redupif(float x)
  68 {
  69         float t;
  70         long i;
  71
  72         t = x / (float)M_PI;
  73         if (t >= 0.0f)
  74                 t += 0.5f;
  75         else
  76                 t -= 0.5f;
  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 float
  87 _ctansf(float complex z)
  88 {
  89         float f, x, x2, y, y2, rn, t, d;
  90
  91         x = fabsf(2.0f * crealf(z));
  92         y = fabsf(2.0f * cimagf(z));
  93
  94         x = _redupif(x);
  95
  96         x = x * x;
  97         y = y * y;
  98         x2 = 1.0f;
  99         y2 = 1.0f;
 100         f = 1.0f;
 101         rn = 0.0f;
 102         d = 0.0f;
 103         do {
 104                 rn += 1.0f;
 105                 f *= rn;
 106                 rn += 1.0f;
 107                 f *= rn;
 108                 x2 *= x;
 109                 y2 *= y;
 110                 t = y2 + x2;
 111                 t /= f;
 112                 d += t;
 113
 114                 rn += 1.0f;
 115                 f *= rn;
 116                 rn += 1.0f;
 117                 f *= rn;
 118                 x2 *= x;
 119                 y2 *= y;
 120                 t = y2 - x2;
 121                 t /= f;
 122                 d += t;
 123         } while (fabsf(t/d) > MACHEPF);
 124         return d;
 125 }