lib/libm/complex/cephes_subrf.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_subrf.h"
  36
  37 /* calculate cosh and sinh */
  38
  39 void
  40 _cchshf(float x, float *c, float *s)
  41 {
  42         float e, ei;
  43
  44         if (fabsf(x) <= 0.5f) {
  45                 *c = coshf(x);
  46                 *s = sinhf(x);
  47         } else {
  48                 e = expf(x);
  49                 ei = 0.5f / e;
  50                 e = 0.5f * 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 =  3.140625;
  60 static const double DP2 =  9.67502593994140625E-4;
  61 static const double DP3 =  1.509957990978376432E-7;
  62 #define MACHEPF 3.0e-8
  63
  64 float
  65 _redupif(float x)
  66 {
  67         float t;
  68         long i;
  69
  70         t = x / (float)M_PI;
  71         if (t >= 0.0f)
  72                 t += 0.5f;
  73         else
  74                 t -= 0.5f;
  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 float
  85 _ctansf(float complex z)
  86 {
  87         float f, x, x2, y, y2, rn, t, d;
  88
  89         x = fabsf(2.0f * crealf(z));
  90         y = fabsf(2.0f * cimagf(z));
  91
  92         x = _redupif(x);
  93
  94         x = x * x;
  95         y = y * y;
  96         x2 = 1.0f;
  97         y2 = 1.0f;
  98         f = 1.0f;
  99         rn = 0.0f;
 100         d = 0.0f;
 101         do {
 102                 rn += 1.0f;
 103                 f *= rn;
 104                 rn += 1.0f;
 105                 f *= rn;
 106                 x2 *= x;
 107                 y2 *= y;
 108                 t = y2 + x2;
 109                 t /= f;
 110                 d += t;
 111
 112                 rn += 1.0f;
 113                 f *= rn;
 114                 rn += 1.0f;
 115                 f *= rn;
 116                 x2 *= x;
 117                 y2 *= y;
 118                 t = y2 - x2;
 119                 t /= f;
 120                 d += t;
 121         } while (fabsf(t/d) > MACHEPF);
 122         return d;
 123 }