NAME

ctanh — complex hyperbolic tangent function

SYNOPSIS

double complex
ctanh(double complex z);

long double complex
ctanhl(long double complex z);

float complex
ctanhf(float complex z);

ctanh(z) computes the hyperbolic tangent of the complex floating-point number z.

For all complex floating point numbers z,

ctanh(conj(z)) = conj(ctanh(z)),
ctanh(-z) = -ctanh(z).

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

ctanh(0 + 0i) returns 0 + 0i.

ctanh(0 + inf i) returns NaN + NaN i, and raises the invalid flag.

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

ctanh(x + inf i) returns NaN + NaN i, and raises the invalid flag, for finite nonzero x.

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

ctanh(inf + 0i) returns 1 + 0i.

ctanh(inf + yi) returns 1 ± 0i, for finite positive y, with the sign chosen to match the sign of sin(2y).

ctanh(inf + inf i) returns 1 + 0i.

ctanh(inf + NaN i) returns 1 + 0i.

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

ctanh(NaN + yi) returns NaN + NaN i, for nonzero numbers y.

ctanh(NaN + NaN i) returns NaN + NaN i.

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