HP-UX Reference (11i v2 03/08) - 3 Library Functions A-M (vol 6)

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casinh(3M) casinh(3M)

(Itanium(R)-based System Only)

NAME

casinh( ), casinhf( ), casinhl( ), casinhw( ), casinhq() - complex arc hyperbolic sine functions

SYNOPSIS

#include <complex.h>

double complex casinh(double complex z);

float complex casinhf(float complex z);

long double complex casinhl(long double complex z);

extended complex casinhw(extended complex z);

quad complex casinhq(quad complex z);

DESCRIPTION

These functions are available only for Itanium-based systems.

casinh() returns the complex arc hyperbolic sine of z, in the range of a strip mathematically

unbounded along the real axis and in the interval [-i*Pi/2,+i*Pi/2] along the imaginary axis. Branch cuts

are outside the interval [-i,+i] along the imaginary axis.

casinhf() is a float complex version of casinh(); it takes a float complex argument and

returns a float complex result.

casinhl() is a long double complex version of casinh(); it takes a long double complex

argument and returns a long double complex result.

casinhw() is an extended complex version of casinh(); it takes an extended complex argu-

ment and returns an extended complex result.

casinhq() is equivalent to casinhl() on HP-UX systems.

USAGE

To use these functions, compile with the default

-Ae option. To use casinhw()

or casinhq(), com-

pile with the

-fpwidetypes option. Make sure your program includes <complex.h>. Link in the

math library by specifying -lm on the compiler or linker command line.

RETURN VALUE

casinh(conj(z)) = conj(casinh(z)) and casinh is an odd function.

casinh(+0+i0) returns 0+i0.

casinh(x+iInf) returns +Inf+iPi/2 for positive-signed ﬁnite x.

casinh(x+iNaN) returns NaN+iNaN and may raise the invalid exception for ﬁnite x.

casinh(+Inf+iy) returns +Inf+i0 for positive-signed ﬁnite y.

casinh(+Inf+iInf) returns +Inf+iPi/4.

casinh(+Inf+iNaN) returns +Inf+iNaN.

casinh(NaN+i0) returns NaN+i0.

casinh(NaN+iy) returns NaN+iNaN and may raise the invalid exception for ﬁnite nonzero y.

casinh(NaN+iInf) returns ±Inf+iNaN (where the sign of the real part of the result is unspeciﬁed).

casinh(NaN+iNaN) returns NaN+iNaN.

ERRORS

No errors are deﬁned.