newlib/libm/complex/cacosh.c

   1 /* $NetBSD: cacosh.c,v 1.2 2009/08/03 19:41:32 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 /*
  36 FUNCTION
  37         <<cacosh>>, <<cacoshf>>---complex arc hyperbolic cosine
  38
  39 INDEX
  40         cacosh
  41 INDEX
  42         cacoshf
  43
  44 SYNOPSIS
  45        #include <complex.h>
  46        double complex cacosh(double complex <[z]>);
  47        float complex cacoshf(float complex <[z]>);
  48
  49
  50 DESCRIPTION
  51         These functions compute the complex arc hyperbolic cosine of <[z]>,
  52         with a branch cut at values less than 1 along the real axis.
  53
  54         <<cacoshf>> is identical to <<cacosh>>, except that it performs
  55         its calculations on <<floats complex>>.
  56
  57 RETURNS
  58         @ifnottex
  59         These functions return the complex arc hyperbolic cosine value,
  60         in the range of a half-strip of non-negative values along the
  61         real axis and in the interval [-i * pi, +i * pi] along the
  62         imaginary axis.
  63         @end ifnottex
  64         @tex
  65         These functions return the complex arc hyperbolic cosine value,
  66         in the range of a half-strip of non-negative values along the
  67         real axis and in the interval [$-i\pi$, $+i\pi$] along the
  68         imaginary axis.
  69         @end tex
  70
  71 PORTABILITY
  72         <<cacosh>> and <<cacoshf>> are ISO C99
  73
  74 QUICKREF
  75         <<cacosh>> and <<cacoshf>> are ISO C99
  76
  77 */
  78
  79
  80 #include <complex.h>
  81
  82 double complex
  83 cacosh(double complex z)
  84 {
  85         double complex w;
  86
  87 #if 0 /* does not give the principal value */
  88         w = I * cacos(z);
  89 #else
  90         w = clog(z + csqrt(z + 1) * csqrt(z - 1));
  91 #endif
  92         return w;
  93 }