fd1293ba31
cacosh, casin, casinh, catan, and catanh. Thanks to stephen@ and bde@ for working on these. Submitted by: stephen@ Reviewed by: bde
129 lines
3.6 KiB
Groff
129 lines
3.6 KiB
Groff
.\" Copyright (c) 2013 David Schultz <das@FreeBSD.org>
|
|
.\" All rights reserved.
|
|
.\"
|
|
.\" Redistribution and use in source and binary forms, with or without
|
|
.\" modification, are permitted provided that the following conditions
|
|
.\" are met:
|
|
.\" 1. Redistributions of source code must retain the above copyright
|
|
.\" notice, this list of conditions and the following disclaimer.
|
|
.\" 2. Redistributions in binary form must reproduce the above copyright
|
|
.\" notice, this list of conditions and the following disclaimer in the
|
|
.\" documentation and/or other materials provided with the distribution.
|
|
.\"
|
|
.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
|
|
.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
|
.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
|
.\" ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
|
|
.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
|
.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
|
.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
|
.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
|
.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
|
.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
|
.\" SUCH DAMAGE.
|
|
.\"
|
|
.\" $FreeBSD$
|
|
.\"
|
|
.Dd May 27, 2013
|
|
.Dt CACOS 3
|
|
.Os
|
|
.Sh NAME
|
|
.Nm cacos ,
|
|
.Nm cacosf ,
|
|
.Nm cacosh ,
|
|
.Nm cacoshf ,
|
|
.Nm casin ,
|
|
.Nm casinf
|
|
.Nm casinh ,
|
|
.Nm casinhf
|
|
.Nm catan ,
|
|
.Nm catanf
|
|
.Nm catanh ,
|
|
.Nm catanhf
|
|
.Nd complex arc trigonometric and hyperbolic functions
|
|
.Sh LIBRARY
|
|
.Lb libm
|
|
.Sh SYNOPSIS
|
|
.In complex.h
|
|
.Ft double complex
|
|
.Fn cacos "double complex z"
|
|
.Ft float complex
|
|
.Fn cacosf "float complex z"
|
|
.Ft double complex
|
|
.Fn cacosh "double complex z"
|
|
.Ft float complex
|
|
.Fn cacoshf "float complex z"
|
|
.Ft double complex
|
|
.Fn casin "double complex z"
|
|
.Ft float complex
|
|
.Fn casinf "float complex z"
|
|
.Ft double complex
|
|
.Fn casinh "double complex z"
|
|
.Ft float complex
|
|
.Fn casinhf "float complex z"
|
|
.Ft double complex
|
|
.Fn catan "double complex z"
|
|
.Ft float complex
|
|
.Fn catanf "float complex z"
|
|
.Ft double complex
|
|
.Fn catanh "double complex z"
|
|
.Ft float complex
|
|
.Fn catanhf "float complex z"
|
|
.Sh DESCRIPTION
|
|
The
|
|
.Fn cacos ,
|
|
.Fn casin ,
|
|
and
|
|
.Fn catan
|
|
functions compute the principal value of the inverse cosine, sine,
|
|
and tangent of the complex number
|
|
.Fa z ,
|
|
respectively.
|
|
The
|
|
.Fn cacosh ,
|
|
.Fn casinh ,
|
|
and
|
|
.Fn catanh
|
|
functions compute the principal value of the inverse hyperbolic
|
|
cosine, sine, and tangent.
|
|
The
|
|
.Fn cacosf ,
|
|
.Fn casinf ,
|
|
.Fn catanf
|
|
.Fn cacoshf ,
|
|
.Fn casinhf ,
|
|
and
|
|
.Fn catanhf
|
|
functions perform the same operations in
|
|
.Fa float
|
|
precision.
|
|
.Pp
|
|
.ie '\*[.T]'utf8'
|
|
. ds Un \[cu]
|
|
.el
|
|
. ds Un U
|
|
.
|
|
There is no universal convention for defining the principal values of
|
|
these functions. The following table gives the branch cuts, and the
|
|
corresponding ranges for the return values, adopted by the C language.
|
|
.Bl -column ".Sy Function" ".Sy (-\*(If*I, -I) \*(Un (I, \*(If*I)" ".Sy [-\*(Pi/2*I, \*(Pi/2*I]"
|
|
.It Sy Function Ta Sy Branch Cut(s) Ta Sy Range
|
|
.It cacos Ta (-\*(If, -1) \*(Un (1, \*(If) Ta [0, \*(Pi]
|
|
.It casin Ta (-\*(If, -1) \*(Un (1, \*(If) Ta [-\*(Pi/2, \*(Pi/2]
|
|
.It catan Ta (-\*(If*I, -i) \*(Un (I, \*(If*I) Ta [-\*(Pi/2, \*(Pi/2]
|
|
.It cacosh Ta (-\*(If, 1) Ta [-\*(Pi*I, \*(Pi*I]
|
|
.It casinh Ta (-\*(If*I, -i) \*(Un (I, \*(If*I) Ta [-\*(Pi/2*I, \*(Pi/2*I]
|
|
.It catanh Ta (-\*(If, -1) \*(Un (1, \*(If) Ta [-\*(Pi/2*I, \*(Pi/2*I]
|
|
.El
|
|
.Sh SEE ALSO
|
|
.Xr ccos 3 ,
|
|
.Xr ccosh 3 ,
|
|
.Xr complex 3 ,
|
|
.Xr cos 3 ,
|
|
.Xr math 3 ,
|
|
.Xr sin 3 ,
|
|
.Xr tan 3
|
|
.Sh STANDARDS
|
|
These functions conform to
|
|
.St -isoC-99 .
|