newlib/libm/complex/catan.c

   1 /* $NetBSD: catan.c,v 1.1 2007/08/20 16:01:32 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         <<catan>>, <<catanf>>---complex arc tangent
  38
  39 INDEX
  40         catan
  41 INDEX
  42         catanf
  43
  44 SYNOPSIS
  45        #include <complex.h>
  46        double complex catan(double complex <[z]>);
  47        float complex catanf(float complex <[z]>);
  48
  49
  50 DESCRIPTION
  51         @ifnottex
  52         These functions compute the complex arc tangent of <[z]>,
  53         with branch cuts outside the interval [-i, +i] along the
  54         imaginary axis.
  55         @end ifnottex
  56         @tex
  57         These functions compute the complex arc tangent of <[z]>,
  58         with branch cuts outside the interval [$-i$, $+i$] along the
  59         imaginary axis.
  60         @end tex
  61
  62         <<catanf>> is identical to <<catan>>, except that it performs
  63         its calculations on <<floats complex>>.
  64
  65 RETURNS
  66         @ifnottex
  67         These functions return the complex arc tangent value, in the range
  68         of a strip mathematically  unbounded  along the imaginary axis
  69         and in the interval [-pi/2, +pi/2] along the real axis.
  70         @end ifnottex
  71         @tex
  72         These functions return the complex arc tangent, in the range
  73         of a strip mathematically  unbounded  along the imaginary axis
  74         and in the interval [$-\pi/2$, $+\pi/2$] along the real axis.
  75         @end tex
  76
  77 PORTABILITY
  78         <<catan>> and <<catanf>> are ISO C99
  79
  80 QUICKREF
  81         <<catan>> and <<catanf>> are ISO C99
  82
  83 */
  84
  85
  86 #include <complex.h>
  87 #include <math.h>
  88 #include "cephes_subr.h"
  89
  90 #ifdef __weak_alias
  91 __weak_alias(catan, _catan)
  92 #endif
  93
  94 double complex
  95 catan(double complex z)
  96 {
  97         double complex w;
  98         double a, t, x, x2, y;
  99
 100         x = creal(z);
 101         y = cimag(z);
 102
 103         if ((x == 0.0) && (y > 1.0))
 104                 goto ovrf;
 105
 106         x2 = x * x;
 107         a = 1.0 - x2 - (y * y);
 108
 109         t = 0.5 * atan2(2.0 * x, a);
 110         w = _redupi(t);
 111
 112         t = y - 1.0;
 113         a = x2 + (t * t);
 114         if (a == 0.0)
 115                 goto ovrf;
 116
 117         t = y + 1.0;
 118         a = (x2 + (t * t))/a;
 119         w = w + (0.25 * log(a)) * I;
 120         return w;
 121
 122 ovrf:
 123 #if 0
 124         mtherr ("catan", OVERFLOW);
 125 #endif
 126         w = HUGE_VAL + HUGE_VAL * I;
 127         return w;
 128 }