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))

ATTRIBUTES¶

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

STANDARDS¶

C11, POSIX.1-2008.

HISTORY¶

C99, POSIX.1-2001. glibc 2.1.

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);
}

SEE ALSO¶

acosh(3), cabs(3), ccosh(3), cimag(3), complex(7)