NAME

catanh — complex inverse hyperbolic tangent function

SYNOPSIS

double complex
catanh(double complex z);

long double complex
catanhl(long double complex z);

float complex
catanhf(float complex z);

DESCRIPTION

catanh(z) computes the inverse hyperbolic tangent of the complex floating-point number z, with branch cuts outside the interval [-1, 1] along the real axis.

catanh() returns values in a strip of the complex plane with imaginary part in the interval [-Pi/2, Pi/2].

For all complex floating point numbers z,

catanh(conj(z)) = conj(catanh(z)).
catanh(-z) = -catanh(z)

SPECIAL VALUES

The symmetries of catanh() are used to abbreviate the specification of special values.

catanh(0 + 0i) returns 0 + 0 i.

catanh(0 + NaN i) returns 0 + NaN i.

catanh(1 + 0i) returns inf + 0i and raises the divide-by-zero flag.

catanh(x + inf i) returns 0 + Pi/2 i, for finite positive-signed x.

catanh(x + NaN i) returns NaN + NaN i, for non-zero finite x.

catanh(inf + yi) returns 0 + Pi/2 i, for finite positive-signed y.

catanh(inf + inf i) returns 0 + Pi/2 i.

catanh(inf + NaN i) returns 0 + NaN i.

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

catanh(NaN + inf i) returns 0 + Pi/2 i.

catanh(NaN + NaN i) returns NaN + NaN i.

NOTES

SEE ALSO

ctanh(3) complex(3)

STANDARDS

The catanh() function conforms to ISO/IEC 9899:2011.