cacosh(3)

complex arc hyperbolic cosine

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Description

cacosh

NAME

cacosh, cacoshf, cacoshl - complex arc hyperbolic cosine

LIBRARY

Math library (libm, -lm)

SYNOPSIS

#include <complex.h>

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

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 were added in glibc 2.1.

ATTRIBUTES

For an explanation of the terms used in this section, see attributes(7).

Image grohtml-9157-1.png

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 = 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(f), cimag(f));

exit(EXIT_SUCCESS);
}