minix/lib/libm/man/atan2.3
Lionel Sambuc 84d9c625bf Synchronize on NetBSD-CVS (2013/12/1 12:00:00 UTC)
- Fix for possible unset uid/gid in toproto
 - Fix for default mtree style
 - Update libelf
 - Importing libexecinfo
 - Resynchronize GCC, mpc, gmp, mpfr
 - build.sh: Replace params with show-params.
     This has been done as the make target has been renamed in the same
     way, while a new target named params has been added. This new
     target generates a file containing all the parameters, instead of
     printing it on the console.
 - Update test48 with new etc/services (Fix by Ben Gras <ben@minix3.org)
     get getservbyport() out of the inner loop

Change-Id: Ie6ad5226fa2621ff9f0dee8782ea48f9443d2091
2014-07-28 17:05:06 +02:00

196 lines
4.6 KiB
Groff

.\" Copyright (c) 1991 The Regents of the University of California.
.\" 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.
.\" 3. Neither the name of the University nor the names of its contributors
.\" may be used to endorse or promote products derived from this software
.\" without specific prior written permission.
.\"
.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS 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 REGENTS 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.
.\"
.\" from: @(#)atan2.3 5.1 (Berkeley) 5/2/91
.\" $NetBSD: atan2.3,v 1.18 2013/04/26 18:18:22 njoly Exp $
.\"
.Dd January 29, 2013
.Dt ATAN2 3
.Os
.Sh NAME
.Nm atan2 ,
.Nm atan2f ,
.Nm atan2l
.Nd arc tangent function of two variables
.Sh LIBRARY
.Lb libm
.Sh SYNOPSIS
.In math.h
.Ft double
.Fn atan2 "double y" "double x"
.Ft float
.Fn atan2f "float y" "float x"
.Ft long double
.Fn atan2l "long double y" "long double x"
.Sh DESCRIPTION
The
.Fn atan2 ,
.Fn atan2f ,
and
.Fn atan2l
functions compute the principal value of the arc tangent of
.Ar y/ Ns Ar x ,
using the signs of both arguments to determine the quadrant of
the return value.
.Sh RETURN VALUES
The
.Fn atan2
function, if successful,
returns the arc tangent of
.Ar y/ Ns Ar x
in the range
.Bk -words
.Bq \&- Ns \*(Pi , \&+ Ns \*(Pi
.Ek
radians.
If both
.Ar x
and
.Ar y
are zero, the global variable
.Va errno
is set to
.Er EDOM .
On the
.Tn VAX :
.Bl -column atan_(y,x)_:=____ sign(y)_(Pi_atan2(Xy_xX))___
.It Fn atan2 y x No := Ta
.Fn atan y/x Ta
if
.Ar x
\*[Gt] 0,
.It Ta sign( Ns Ar y Ns )*(\*(Pi -
.Fn atan "\*(Bay/x\*(Ba" ) Ta
if
.Ar x
\*[Lt] 0,
.It Ta
.No 0 Ta
if x = y = 0, or
.It Ta
.Pf sign( Ar y Ns )*\*(Pi/2 Ta
if
.Ar x
= 0 \*(!=
.Ar y .
.El
.Sh NOTES
The function
.Fn atan2
defines "if x \*[Gt] 0,"
.Fn atan2 0 0
= 0 on a
.Tn VAX
despite that previously
.Fn atan2 0 0
may have generated an error message.
The reasons for assigning a value to
.Fn atan2 0 0
are these:
.Bl -enum -offset indent
.It
Programs that test arguments to avoid computing
.Fn atan2 0 0
must be indifferent to its value.
Programs that require it to be invalid are vulnerable
to diverse reactions to that invalidity on diverse computer systems.
.It
The
.Fn atan2
function is used mostly to convert from rectangular (x,y)
to polar
.if n\
(r,theta)
.if t\
(r,\(*h)
coordinates that must satisfy x =
.if n\
r\(**cos theta
.if t\
r\(**cos\(*h
and y =
.if n\
r\(**sin theta.
.if t\
r\(**sin\(*h.
These equations are satisfied when (x=0,y=0)
is mapped to
.if n \
(r=0,theta=0)
.if t \
(r=0,\(*h=0)
on a VAX.
In general, conversions to polar coordinates should be computed thus:
.Bd -unfilled -offset indent
.if n \{\
r := hypot(x,y); ... := sqrt(x\(**x+y\(**y)
theta := atan2(y,x).
.\}
.if t \{\
r := hypot(x,y); ... := \(sr(x\u\s82\s10\d+y\u\s82\s10\d)
\(*h := atan2(y,x).
.\}
.Ed
.It
The foregoing formulas need not be altered to cope in a
reasonable way with signed zeros and infinities
on a machine that conforms to
.Tn IEEE 754 ;
the versions of
.Xr hypot 3
and
.Fn atan2
provided for
such a machine are designed to handle all cases.
That is why
.Fn atan2 \(+-0 \-0
= \(+-\*(Pi
for instance.
In general the formulas above are equivalent to these:
.Bd -unfilled -offset indent
.if n \
r := sqrt(x\(**x+y\(**y); if r = 0 then x := copysign(1,x);
.if t \
r := \(sr(x\(**x+y\(**y);\0\0if r = 0 then x := copysign(1,x);
.Ed
.El
.Sh SEE ALSO
.Xr acos 3 ,
.Xr asin 3 ,
.Xr atan 3 ,
.Xr cos 3 ,
.Xr cosh 3 ,
.Xr math 3 ,
.Xr sin 3 ,
.Xr sinh 3 ,
.Xr tan 3 ,
.Xr tanh 3
.Sh STANDARDS
The
.Fn atan2
function conforms to
.St -isoC-99 .