cacosh, cacoshf, cacoshl — complex arc hyperbolic cosine

## Synopsis

`#include <complex.h>`

`double complex cacosh(double complex z);float complex cacoshf(float complex z);long double complex cacoshl(long double complex z);`

`Link with -lm.`

## Description

These functions calculate the complex arc hyperbolic cosine of z. If y = cacosh(z), then z = ccosh(y). The imaginary part of y is chosen in the interval [-pi,pi]. The real part of y is chosen nonnegative.

One has:

`    cacosh(z) = 2 * clog(csqrt((z + 1) / 2) + csqrt((z - 1) / 2))`

## 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
cacosh(), cacoshf(), cacoshl() Thread safety MT-Safe

## Conforming to

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

## Example

```/* Link with "-lm" */

#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);
exit(EXIT_FAILURE);
}

z = atof(argv) + atof(argv) * I;

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

f = 2 * clog(csqrt((z + 1)/2) + csqrt((z - 1)/2));
printf("formula  = %6.3f %6.3f*i\n", creal(f2), cimag(f2));

exit(EXIT_SUCCESS);
}```