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'\" t
.\" Copyright 1993 David Metcalfe (david@prism.demon.co.uk)
.\" and Copyright 2008, Linux Foundation, written by Michael Kerrisk
.\" <mtk.manpages@gmail.com>
.\"
.\" SPDX-License-Identifier: Linux-man-pages-copyleft
.\"
.\" References consulted:
.\" Linux libc source code
.\" Lewine's _POSIX Programmer's Guide_ (O'Reilly & Associates, 1991)
.\" 386BSD man pages
.\" Modified 1993-07-24 by Rik Faith (faith@cs.unc.edu)
.\" Modified 2002-07-27 by Walter Harms
.\" (walter.harms@informatik.uni-oldenburg.de)
.\"
.TH atanh 3 2024-05-02 "Linux man-pages (unreleased)"
.SH NAME
atanh, atanhf, atanhl \- inverse hyperbolic tangent function
.SH LIBRARY
Math library
.RI ( libm ", " \-lm )
.SH SYNOPSIS
.nf
.B #include <math.h>
.P
.BI "double atanh(double " x );
.BI "float atanhf(float " x );
.BI "long double atanhl(long double " x );
.P
.fi
.RS -4
Feature Test Macro Requirements for glibc (see
.BR feature_test_macros (7)):
.RE
.P
.BR atanh ():
.nf
_ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
|| _XOPEN_SOURCE >= 500
.\" || _XOPEN_SOURCE && _XOPEN_SOURCE_EXTENDED
|| /* Since glibc 2.19: */ _DEFAULT_SOURCE
|| /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
.fi
.P
.BR atanhf (),
.BR atanhl ():
.nf
_ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
|| /* Since glibc 2.19: */ _DEFAULT_SOURCE
|| /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
.fi
.SH DESCRIPTION
These functions calculate the inverse hyperbolic tangent of
.IR x ;
that is the value whose hyperbolic tangent is
.IR x .
.SH RETURN VALUE
On success, these functions return the inverse hyperbolic tangent of
.IR x .
.P
If
.I x
is a NaN, a NaN is returned.
.P
If
.I x
is +0 (\-0), +0 (\-0) is returned.
.P
If
.I x
is +1 or \-1,
a pole error occurs,
and the functions return
.BR HUGE_VAL ,
.BR HUGE_VALF ,
or
.BR HUGE_VALL ,
respectively, with the mathematically correct sign.
.P
If the absolute value of
.I x
is greater than 1,
a domain error occurs,
and a NaN is returned.
.\"
.\" POSIX.1-2001 documents an optional range error for subnormal x;
.\" glibc 2.8 does not do this.
.SH ERRORS
See
.BR math_error (7)
for information on how to determine whether an error has occurred
when calling these functions.
.P
The following errors can occur:
.TP
Domain error: \fIx\fP less than \-1 or greater than +1
.I errno
is set to
.BR EDOM .
An invalid floating-point exception
.RB ( FE_INVALID )
is raised.
.TP
Pole error: \fIx\fP is +1 or \-1
.I errno
is set to
.B ERANGE
(but see BUGS).
A divide-by-zero floating-point exception
.RB ( FE_DIVBYZERO )
is raised.
.SH ATTRIBUTES
For an explanation of the terms used in this section, see
.BR attributes (7).
.TS
allbox;
lbx lb lb
l l l.
Interface Attribute Value
T{
.na
.nh
.BR atanh (),
.BR atanhf (),
.BR atanhl ()
T} Thread safety MT-Safe
.TE
.SH STANDARDS
C11, POSIX.1-2008.
.SH HISTORY
C99, POSIX.1-2001.
.P
The variant returning
.I double
also conforms to
SVr4, 4.3BSD.
.SH BUGS
In glibc 2.9 and earlier,
.\" Bug: https://www.sourceware.org/bugzilla/show_bug.cgi?id=6759
.\" This can be seen in sysdeps/ieee754/k_standard.c
when a pole error occurs,
.I errno
is set to
.B EDOM
instead of the POSIX-mandated
.BR ERANGE .
Since glibc 2.10, glibc does the right thing.
.SH SEE ALSO
.BR acosh (3),
.BR asinh (3),
.BR catanh (3),
.BR cosh (3),
.BR sinh (3),
.BR tanh (3)
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