# cacosh.3   [plain text]

```.\" Copyright (c) 2006 Apple Computer
.\"
.Dd December 11, 2006
.Dt CACOSH 3
.Os BSD 4
.Sh NAME
.Nm cacosh
.Nd complex inverse hyperbolic cosine function
.Sh SYNOPSIS
.Ft double complex
.Fn cacosh "double complex z"
.Ft long double complex
.Fn cacoshl "long double complex z"
.Ft float complex
.Fn cacoshf "float complex z"
.Sh DESCRIPTION
.Fn cacosh "z"
computes the inverse hyperbolic cosine of the complex floating-point number
.Fa z ,
with a branch cut on the interval
.Bq -inf, 1
along the real axis.
.Pp
.Fn cacosh
returns values in a half-strip of the complex plane with positive real part and imaginary part in the interval
.Bq -Pi , Pi .
.Pp
For all complex floating point numbers z, cacosh(conj(z)) = conj(cacosh(z)).
.Sh SPECIAL VALUES
The conjugate symmetry of cacosh() is used to abbreviate the specification of special values.
.Pp
.Fn cacosh "±0 + 0i"
returns 0 + Pi/2 i.
.Pp
.Fn cacosh "x + inf i"
returns inf + Pi/2 i, for finite x.
.Pp
.Fn cacosh "x + NaN i"
returns NaN + NaN i, for finite nonzero x.
.Pp
.Fn cacosh "-inf + yi"
returns inf + Pi i, for finite positive-signed y.
.Pp
.Fn cacosh "inf + yi"
returns inf + 0i, for finite positive-signed y.
.Pp
.Fn cacosh "-inf + inf i"
returns inf + 3Pi/4 i.
.Pp
.Fn cacosh "inf + inf i"
returns inf + Pi/4 i.
.Pp
.Fn cacosh "±inf + NaN i"
returns inf + NaN i.
.Pp
.Fn cacosh "NaN + yi"
returns NaN + NaN i, for finite y.
.Pp
.Fn cacosh "NaN + inf i"
returns inf + NaN i.
.Pp
.Fn cacosh "NaN + NaN i"
returns NaN + NaN i.
.Sh NOTES
.Xr ccosh 3
.Xr complex 3
.Sh STANDARDS
The
.Fn cacosh
function conforms to ISO/IEC 9899:1999(E).```