NAME

cacosh — complex inverse hyperbolic cosine function

SYNOPSIS

double complex
cacosh(double complex z);

long double complex
cacoshl(long double complex z);

float complex
cacoshf(float complex z);

DESCRIPTION

cacosh(z) computes the inverse hyperbolic cosine of the complex floating-point number z, with a branch cut on the interval [-inf, 1] along the real axis.

cacosh() returns values in a half-strip of the complex plane with positive real part and imaginary part in the interval [-Pi, Pi].

For all complex floating point numbers z, cacosh(conj(z)) = conj(cacosh(z)).

SPECIAL VALUES

The conjugate symmetry of cacosh() is used to abbreviate the specification of special values.

cacosh(±0 + 0i) returns 0 + Pi/2 i.

cacosh(x + inf i) returns inf + Pi/2 i, for finite x.

cacosh(x + NaN i) returns NaN + NaN i, for finite nonzero x.

cacosh(-inf + yi) returns inf + Pi i, for finite positive-signed y.

cacosh(inf + yi) returns inf + 0i, for finite positive-signed y.

cacosh(-inf + inf i) returns inf + 3Pi/4 i.

cacosh(inf + inf i) returns inf + Pi/4 i.

cacosh(±inf + NaN i) returns inf + NaN i.

cacosh(NaN + yi) returns NaN + NaN i, for finite y.

cacosh(NaN + inf i) returns inf + NaN i.

cacosh(NaN + NaN i) returns NaN + NaN i.

NOTES

STANDARDS