man3/catanh.3

   1 .\" Copyright 2002 Walter Harms (walter.harms@informatik.uni-oldenburg.de)
   2 .\" and Copyright (C) 2011 Michael Kerrisk <mtk.manpages@gmail.com>
   3 .\"
   4 .\" SPDX-License-Identifier: GPL-1.0-or-later
   5 .\"
   6 .TH CATANH 3 2021-03-22 "" "Linux Programmer's Manual"
   7 .SH NAME
   8 catanh, catanhf, catanhl \- complex arc tangents hyperbolic
   9 .SH LIBRARY
  10 Math library
  11 .RI ( libm ", " \-lm )
  12 .SH SYNOPSIS
  13 .nf
  14 .B #include <complex.h>
  15 .PP
  16 .BI "double complex catanh(double complex " z );
  17 .BI "float complex catanhf(float complex " z );
  18 .BI "long double complex catanhl(long double complex " z );
  19 .fi
  20 .SH DESCRIPTION
  21 These functions calculate the complex arc hyperbolic tangent of
  22 .IR z .
  23 If \fIy\ =\ catanh(z)\fP, then \fIz\ =\ ctanh(y)\fP.
  24 The imaginary part of
  25 .I y
  26 is chosen in the interval [\-pi/2,pi/2].
  27 .PP
  28 One has:
  29 .PP
  30 .nf
  31     catanh(z) = 0.5 * (clog(1 + z) \- clog(1 \- z))
  32 .fi
  33 .SH VERSIONS
  34 These functions first appeared in glibc in version 2.1.
  35 .SH ATTRIBUTES
  36 For an explanation of the terms used in this section, see
  37 .BR attributes (7).
  38 .ad l
  39 .nh
  40 .TS
  41 allbox;
  42 lbx lb lb
  43 l l l.
  44 Interface       Attribute       Value
  45 T{
  46 .BR catanh (),
  47 .BR catanhf (),
  48 .BR catanhl ()
  49 T}      Thread safety   MT-Safe
  50 .TE
  51 .hy
  52 .ad
  53 .sp 1
  54 .SH CONFORMING TO
  55 C99, POSIX.1-2001, POSIX.1-2008.
  56 .SH EXAMPLES
  57 .EX
  58 /* Link with "\-lm" */
  59
  60 #include <complex.h>
  61 #include <stdlib.h>
  62 #include <unistd.h>
  63 #include <stdio.h>
  64
  65 int
  66 main(int argc, char *argv[])
  67 {
  68     double complex z, c, f;
  69
  70     if (argc != 3) {
  71         fprintf(stderr, "Usage: %s <real> <imag>\en", argv[0]);
  72         exit(EXIT_FAILURE);
  73     }
  74
  75     z = atof(argv[1]) + atof(argv[2]) * I;
  76
  77     c = catanh(z);
  78     printf("catanh() = %6.3f %6.3f*i\en", creal(c), cimag(c));
  79
  80     f = 0.5 * (clog(1 + z) \- clog(1 \- z));
  81     printf("formula  = %6.3f %6.3f*i\en", creal(f2), cimag(f2));
  82
  83     exit(EXIT_SUCCESS);
  84 }
  85 .EE
  86 .SH SEE ALSO
  87 .BR atanh (3),
  88 .BR cabs (3),
  89 .BR cimag (3),
  90 .BR ctanh (3),
  91 .BR complex (7)