NAME

       catanh, catanhf, catanhl - complex arc tangents hyperbolic

LIBRARY

       Math library (libm, -lm)

SYNOPSIS

       #include <complex.h>

       double complex catanh(double complex z);
       float complex catanhf(float complex z);
       long double complex catanhl(long double complex z);

DESCRIPTION

       These functions calculate the complex arc hyperbolic tangent of z.  If y = catanh(z), then
       z = ctanh(y).  The imaginary part of y is chosen in the interval [-pi/2,pi/2].

       One has:

           catanh(z) = 0.5 * (clog(1 + z) - clog(1 - z))

ATTRIBUTES

       For an explanation of the terms used in this section, see attributes(7).

       ┌───────────────────────────────────────────────────────────────┬───────────────┬─────────┐
       │Interface                                                      │ Attribute     │ Value   │
       ├───────────────────────────────────────────────────────────────┼───────────────┼─────────┤
       │catanh(), catanhf(), catanhl()                                 │ Thread safety │ MT-Safe │
       └───────────────────────────────────────────────────────────────┴───────────────┴─────────┘

STANDARDS

       C11, POSIX.1-2008.

HISTORY

       glibc 2.1.  C99, POSIX.1-2001.

EXAMPLES

       /* Link with "-lm" */

       #include <complex.h>
       #include <stdio.h>
       #include <stdlib.h>
       #include <unistd.h>

       int
       main(int argc, char *argv[])
       {
           double complex z, c, f;

           if (argc != 3) {
               fprintf(stderr, "Usage: %s <real> <imag>\n", argv[0]);
               exit(EXIT_FAILURE);
           }

           z = atof(argv[1]) + atof(argv[2]) * I;

           c = catanh(z);
           printf("catanh() = %6.3f %6.3f*i\n", creal(c), cimag(c));

           f = 0.5 * (clog(1 + z) - clog(1 - z));
           printf("formula  = %6.3f %6.3f*i\n", creal(f), cimag(f));

           exit(EXIT_SUCCESS);
       }

SEE ALSO

       atanh(3), cabs(3), cimag(3), ctanh(3), complex(7)