compiler/stdc/math/s_ctan.c

   1 /*      $OpenBSD: s_ctan.c,v 1.6 2013/07/03 04:46:36 espie Exp $        */
   2 /*
   3  * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
   4  *
   5  * Permission to use, copy, modify, and distribute this software for any
   6  * purpose with or without fee is hereby granted, provided that the above
   7  * copyright notice and this permission notice appear in all copies.
   8  *
   9  * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
  10  * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
  11  * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
  12  * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
  13  * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
  14  * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
  15  * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
  16  */
  17
  18 /*                                                      ctan()
  19  *
  20  *      Complex circular tangent
  21  *
  22  *
  23  *
  24  * SYNOPSIS:
  25  *
  26  * double complex ctan();
  27  * double complex z, w;
  28  *
  29  * w = ctan (z);
  30  *
  31  *
  32  *
  33  * DESCRIPTION:
  34  *
  35  * If
  36  *     z = x + iy,
  37  *
  38  * then
  39  *
  40  *           sin 2x  +  i sinh 2y
  41  *     w  =  --------------------.
  42  *            cos 2x  +  cosh 2y
  43  *
  44  * On the real axis the denominator is zero at odd multiples
  45  * of PI/2.  The denominator is evaluated by its Taylor
  46  * series near these points.
  47  *
  48  * ctan(z) = -i ctanh(iz).
  49  *
  50  * ACCURACY:
  51  *
  52  *                      Relative error:
  53  * arithmetic   domain     # trials      peak         rms
  54  *    DEC       -10,+10      5200       7.1e-17     1.6e-17
  55  *    IEEE      -10,+10     30000       7.2e-16     1.2e-16
  56  * Also tested by ctan * ccot = 1 and catan(ctan(z))  =  z.
  57  */
  58
  59 #include <float.h>
  60 #include <complex.h>
  61 #include "math.h"
  62 #include "math_private.h"
  63
  64 double complex
  65 ctan(double complex z)
  66 {
  67
  68         /* ctan(z) = -I * ctanh(I * z) = I * conj(ctanh(I * conj(z))) */
  69         z = ctanh(CMPLX(cimag(z), creal(z)));
  70         return (CMPLX(cimag(z), creal(z)));
  71 }
  72
  73 #if     LDBL_MANT_DIG == DBL_MANT_DIG
  74 AROS_MAKE_ASM_SYM(typeof(ctanl), ctanl, AROS_CSYM_FROM_ASM_NAME(ctanl), AROS_CSYM_FROM_ASM_NAME(ctan));
  75 AROS_EXPORT_ASM_SYM(AROS_CSYM_FROM_ASM_NAME(ctanl));
  76 #endif  /* LDBL_MANT_DIG == DBL_MANT_DIG */