man3/catan.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 CATAN 3 2021-03-22 "Linux man-pages (unreleased)" "Linux Programmer's Manual"
   7 .SH NAME
   8 catan, catanf, catanl \- complex arc tangents
   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 catan(double complex " z );
  17 .BI "float complex catanf(float complex " z );
  18 .BI "long double complex catanl(long double complex " z );
  19 .fi
  20 .SH DESCRIPTION
  21 These functions calculate the complex arc tangent of
  22 .IR z .
  23 If \fIy\~=\~catan(z)\fP, then \fIz\~=\~ctan(y)\fP.
  24 The real part of y is chosen in the interval [\-pi/2,pi/2].
  25 .PP
  26 One has:
  27 .PP
  28 .in +4n
  29 .EX
  30 catan(z) = (clog(1 + i * z) \- clog(1 \- i * z)) / (2 * i)
  31 .EE
  32 .in
  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 catan (),
  47 .BR catanf (),
  48 .BR catanl ()
  49 T}      Thread safety   MT-Safe
  50 .TE
  51 .hy
  52 .ad
  53 .sp 1
  54 .SH STANDARDS
  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     double complex i = I;
  70
  71     if (argc != 3) {
  72         fprintf(stderr, "Usage: %s <real> <imag>\en", argv[0]);
  73         exit(EXIT_FAILURE);
  74     }
  75
  76     z = atof(argv[1]) + atof(argv[2]) * I;
  77
  78     c = catan(z);
  79     printf("catan() = %6.3f %6.3f*i\en", creal(c), cimag(c));
  80
  81     f = (clog(1 + i * z) \- clog(1 \- i * z)) / (2 * i);
  82     printf("formula = %6.3f %6.3f*i\en", creal(f), cimag(f));
  83
  84     exit(EXIT_SUCCESS);
  85 }
  86 .EE
  87 .SH SEE ALSO
  88 .BR ccos (3),
  89 .BR clog (3),
  90 .BR ctan (3),
  91 .BR complex (7)