man3/cacosh.3

   1 '\" t
   2 .\" Copyright 2002 Walter Harms(walter.harms@informatik.uni-oldenburg.de)
   3 .\" and Copyright (C) 2011 Michael Kerrisk <mtk.manpages@gmail.com>
   4 .\"
   5 .\" SPDX-License-Identifier: GPL-1.0-or-later
   6 .\"
   7 .TH cacosh 3 (date) "Linux man-pages (unreleased)"
   8 .SH NAME
   9 cacosh, cacoshf, cacoshl \- complex arc hyperbolic cosine
  10 .SH LIBRARY
  11 Math library
  12 .RI ( libm ", " \-lm )
  13 .SH SYNOPSIS
  14 .nf
  15 .B #include <complex.h>
  16 .PP
  17 .BI "double complex cacosh(double complex " z );
  18 .BI "float complex cacoshf(float complex " z );
  19 .BI "long double complex cacoshl(long double complex " z );
  20 .fi
  21 .SH DESCRIPTION
  22 These functions calculate the complex arc hyperbolic cosine of
  23 .IR z .
  24 If \fIy\ =\ cacosh(z)\fP, then \fIz\ =\ ccosh(y)\fP.
  25 The imaginary part of
  26 .I y
  27 is chosen in the interval [\-pi,pi].
  28 The real part of
  29 .I y
  30 is chosen nonnegative.
  31 .PP
  32 One has:
  33 .PP
  34 .nf
  35     cacosh(z) = 2 * clog(csqrt((z + 1) / 2) + csqrt((z \- 1) / 2))
  36 .fi
  37 .SH ATTRIBUTES
  38 For an explanation of the terms used in this section, see
  39 .BR attributes (7).
  40 .TS
  41 allbox;
  42 lbx lb lb
  43 l l l.
  44 Interface       Attribute       Value
  45 T{
  46 .na
  47 .nh
  48 .BR cacosh (),
  49 .BR cacoshf (),
  50 .BR cacoshl ()
  51 T}      Thread safety   MT-Safe
  52 .TE
  53 .sp 1
  54 .SH STANDARDS
  55 C11, POSIX.1-2008.
  56 .SH HISTORY
  57 C99, POSIX.1-2001.
  58 glibc 2.1.
  59 .SH EXAMPLES
  60 .\" SRC BEGIN (cacosh.c)
  61 .EX
  62 /* Link with "\-lm" */
  63 \&
  64 #include <complex.h>
  65 #include <stdio.h>
  66 #include <stdlib.h>
  67 #include <unistd.h>
  68 \&
  69 int
  70 main(int argc, char *argv[])
  71 {
  72     double complex z, c, f;
  73 \&
  74     if (argc != 3) {
  75         fprintf(stderr, "Usage: %s <real> <imag>\en", argv[0]);
  76         exit(EXIT_FAILURE);
  77     }
  78 \&
  79     z = atof(argv[1]) + atof(argv[2]) * I;
  80 \&
  81     c = cacosh(z);
  82     printf("cacosh() = %6.3f %6.3f*i\en", creal(c), cimag(c));
  83 \&
  84     f = 2 * clog(csqrt((z + 1)/2) + csqrt((z \- 1)/2));
  85     printf("formula  = %6.3f %6.3f*i\en", creal(f), cimag(f));
  86 \&
  87     exit(EXIT_SUCCESS);
  88 }
  89 .EE
  90 .\" SRC END
  91 .SH SEE ALSO
  92 .BR acosh (3),
  93 .BR cabs (3),
  94 .BR ccosh (3),
  95 .BR cimag (3),
  96 .BR complex (7)