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1.\" Copyright (c) 2006 Apple Computer
2.\"
3.Dd December 11, 2006
4.Dt CACOSH 3
5.Os BSD 4
6.Sh NAME
7.Nm cacosh
8.Nd complex inverse hyperbolic cosine function
9.Sh SYNOPSIS
10.Ft double complex
11.Fn cacosh "double complex z"
12.Ft long double complex
13.Fn cacoshl "long double complex z"
14.Ft float complex
15.Fn cacoshf "float complex z"
16.Sh DESCRIPTION
17.Fn cacosh "z"
18computes the inverse hyperbolic cosine of the complex floating-point number
19.Fa z ,
20with a branch cut on the interval
21.Bq -inf, 1
22along the real axis.
23.Pp
24.Fn cacosh
25returns values in a half-strip of the complex plane with positive real part and imaginary part in the interval
26.Bq -Pi , Pi .
27.Pp
28For all complex floating point numbers z, cacosh(conj(z)) = conj(cacosh(z)).
29.Sh SPECIAL VALUES
30The conjugate symmetry of cacosh() is used to abbreviate the specification of special values.
31.Pp
32.Fn cacosh "�0 + 0i"
33returns 0 + Pi/2 i.
34.Pp
35.Fn cacosh "x + inf i"
36returns inf + Pi/2 i, for finite x.
37.Pp
38.Fn cacosh "x + NaN i"
39returns NaN + NaN i, for finite nonzero x.
40.Pp
41.Fn cacosh "-inf + yi"
42returns inf + Pi i, for finite positive-signed y.
43.Pp
44.Fn cacosh "inf + yi"
45returns inf + 0i, for finite positive-signed y.
46.Pp
47.Fn cacosh "-inf + inf i"
48returns inf + 3Pi/4 i.
49.Pp
50.Fn cacosh "inf + inf i"
51returns inf + Pi/4 i.
52.Pp
53.Fn cacosh "�inf + NaN i"
54returns inf + NaN i.
55.Pp
56.Fn cacosh "NaN + yi"
57returns NaN + NaN i, for finite y.
58.Pp
59.Fn cacosh "NaN + inf i"
60returns inf + NaN i.
61.Pp
62.Fn cacosh "NaN + NaN i"
63returns NaN + NaN i.
64.Sh NOTES
65.Sh SEE ALSO
66.Xr ccosh 3
67.Xr complex 3
68.Sh STANDARDS
69The
70.Fn cacosh
71function conforms to ISO/IEC 9899:1999(E).