# catanh(3) — Linux manual page

```catanh(3)               Library Functions Manual               catanh(3)
```

## NAME         top

```       catanh, catanhf, catanhl - complex arc tangents hyperbolic
```

## LIBRARY         top

```       Math library (libm, -lm)
```

## SYNOPSIS         top

```       #include <complex.h>

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

## DESCRIPTION         top

```       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         top

```       For an explanation of the terms used in this section, see
attributes(7).
┌─────────────────────────────────────┬───────────────┬─────────┐
│ Interface                           │ Attribute     │ Value   │
├─────────────────────────────────────┼───────────────┼─────────┤
│ catanh(), catanhf(), catanhl()      │ Thread safety │ MT-Safe │
└─────────────────────────────────────┴───────────────┴─────────┘
```

## STANDARDS         top

```       C11, POSIX.1-2008.
```

## HISTORY         top

```       glibc 2.1.  C99, POSIX.1-2001.
```

## EXAMPLES         top

```       /* 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);
}
```

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

## COLOPHON         top

```       This page is part of the man-pages (Linux kernel and C library
user-space interface documentation) project.  Information about
the project can be found at
⟨https://www.kernel.org/doc/man-pages/⟩.  If you have a bug report
for this manual page, see
⟨https://git.kernel.org/pub/scm/docs/man-pages/man-pages.git/tree/CONTRIBUTING⟩.