# CATANH

Section: Linux Programmer's Manual (3)
Updated: 2015-04-19
Index

## NAME

catanh, catanhf, catanhl - complex arc tangents hyperbolic

## 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 yis chosen in the interval [-pi/2,pi/2].

One has:

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

## VERSIONS

These functions first appeared in glibc in version 2.1.

## ATTRIBUTES

For an explanation of the terms used in this section, see attributes(7).
 Interface Attribute Value catanh(), catanhf(), catanhl() Thread safety MT-Safe

## CONFORMING TO

C99, POSIX.1-2001, POSIX.1-2008.

## EXAMPLE

#include <complex.h> #include <stdlib.h> #include <unistd.h> #include <stdio.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(f2), cimag(f2));

exit(EXIT_SUCCESS); }

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

NAME
SYNOPSIS
DESCRIPTION
VERSIONS
ATTRIBUTES
CONFORMING TO
EXAMPLE