# NAME

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);
}``````

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