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1.\" Copyright (c) 2006 Apple Computer
2.\"
3.Dd December 11, 2006
4.Dt CATANH 3
5.Os BSD 4
6.Sh NAME
7.Nm catanh
8.Nd complex inverse hyperbolic tangent function
9.Sh SYNOPSIS
10.Ft double complex
11.Fn catanh "double complex z"
12.Ft long double complex
13.Fn catanhl "long double complex z"
14.Ft float complex
15.Fn catanhf "float complex z"
16.Sh DESCRIPTION
17.Fn catanh "z"
18computes the inverse hyperbolic tangent of the complex floating-point number
19.Fa z ,
20with branch cuts outside the interval
21.Bq -1, 1
22along the real axis.
23.Pp
24.Fn catanh
25returns values in a strip of the complex plane with imaginary part in the interval
26.Bq -Pi/2 , Pi/2 .
27.Pp
28For all complex floating point numbers z,
29.Bd -literal -offset indent
30catanh(conj(z)) = conj(catanh(z)).
31catanh(-z) = -catanh(z)
32.Ed
33.Sh SPECIAL VALUES
34The symmetries of catanh() are used to abbreviate the specification of special values.
35.Pp
36.Fn catanh "0 + 0i"
37returns 0 + 0 i.
38.Pp
39.Fn catanh "0 + NaN i"
40returns 0 + NaN i.
41.Pp
42.Fn catanh "1 + 0i"
43returns inf + 0i and raises the divide-by-zero flag.
44.Pp
45.Fn catanh "x + inf i"
46returns 0 + Pi/2 i, for finite positive-signed x.
47.Pp
48.Fn catanh "x + NaN i"
49returns NaN + NaN i, for non-zero finite x.
50.Pp
51.Fn catanh "inf + yi"
52returns 0 + Pi/2 i, for finite positive-signed y.
53.Pp
54.Fn catanh "inf + inf i"
55returns 0 + Pi/2 i.
56.Pp
57.Fn catanh "inf + NaN i"
58returns 0 + NaN i.
59.Pp
60.Fn catanh "NaN + yi"
61returns NaN + NaN i, for finite y.
62.Pp
63.Fn catanh "NaN + inf i"
64returns 0 + Pi/2 i.
65.Pp
66.Fn catanh "NaN + NaN i"
67returns NaN + NaN i.
68.Sh NOTES
69.Sh SEE ALSO
70.Xr ctanh 3
71.Xr complex 3
72.Sh STANDARDS
73The
74.Fn catanh
75function conforms to ISO/IEC 9899:1999(E).