catanh(3) Library Functions Manual catanh(3)

# 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))
```

# VERSIONS¶

These functions were added in glibc 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

# STANDARDS¶

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

# 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);
}
```