0dc9e0996a
As the current libc includes a libm implementation, with the new libc this is needed. Unneeded (for the moment) archs have been removed.
193 lines
4.5 KiB
Groff
193 lines
4.5 KiB
Groff
.\" Copyright (c) 1991 The Regents of the University of California.
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.\" All rights reserved.
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.\"
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.\" Redistribution and use in source and binary forms, with or without
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.\" modification, are permitted provided that the following conditions
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.\" are met:
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.\" 1. Redistributions of source code must retain the above copyright
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.\" notice, this list of conditions and the following disclaimer.
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.\" 2. Redistributions in binary form must reproduce the above copyright
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.\" notice, this list of conditions and the following disclaimer in the
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.\" documentation and/or other materials provided with the distribution.
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.\" 3. Neither the name of the University nor the names of its contributors
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.\" may be used to endorse or promote products derived from this software
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.\" without specific prior written permission.
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.\"
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.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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.\" SUCH DAMAGE.
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.\"
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.\" from: @(#)atan2.3 5.1 (Berkeley) 5/2/91
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.\" $NetBSD: atan2.3,v 1.16 2003/08/07 16:44:46 agc Exp $
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.\"
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.Dd May 2, 1991
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.Dt ATAN2 3
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.Os
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.Sh NAME
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.Nm atan2 ,
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.Nm atan2f
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.Nd arc tangent function of two variables
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.Sh LIBRARY
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.Lb libm
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.Sh SYNOPSIS
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.In math.h
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.Ft double
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.Fn atan2 "double y" "double x"
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.Ft float
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.Fn atan2f "float y" "float x"
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.Sh DESCRIPTION
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The
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.Fn atan2
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and
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.Fn atan2f
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functions compute the principal value of the arc tangent of
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.Ar y/ Ns Ar x ,
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using the signs of both arguments to determine the quadrant of
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the return value.
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.Sh RETURN VALUES
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The
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.Fn atan2
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function, if successful,
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returns the arc tangent of
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.Ar y/ Ns Ar x
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in the range
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.Bk -words
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.Bq \&- Ns \*(Pi , \&+ Ns \*(Pi
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.Ek
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radians.
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If both
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.Ar x
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and
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.Ar y
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are zero, the global variable
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.Va errno
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is set to
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.Er EDOM .
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On the
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.Tn VAX :
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.Bl -column atan_(y,x)_:=____ sign(y)_(Pi_atan2(Xy_xX))___
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.It Fn atan2 y x No := Ta
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.Fn atan y/x Ta
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if
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.Ar x
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\*[Gt] 0,
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.It Ta sign( Ns Ar y Ns )*(\*(Pi -
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.Fn atan "\\*(Bay/x\\*(Ba" ) Ta
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if
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.Ar x
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\*[Lt] 0,
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.It Ta
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.No 0 Ta
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if x = y = 0, or
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.It Ta
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.Pf sign( Ar y Ns )*\\*(Pi/2 Ta
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if
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.Ar x
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= 0 \*(!=
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.Ar y .
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.El
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.Sh NOTES
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The function
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.Fn atan2
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defines "if x \*[Gt] 0,"
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.Fn atan2 0 0
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= 0 on a
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.Tn VAX
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despite that previously
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.Fn atan2 0 0
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may have generated an error message.
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The reasons for assigning a value to
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.Fn atan2 0 0
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are these:
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.Bl -enum -offset indent
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.It
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Programs that test arguments to avoid computing
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.Fn atan2 0 0
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must be indifferent to its value.
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Programs that require it to be invalid are vulnerable
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to diverse reactions to that invalidity on diverse computer systems.
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.It
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The
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.Fn atan2
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function is used mostly to convert from rectangular (x,y)
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to polar
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.if n\
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(r,theta)
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.if t\
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(r,\(*h)
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coordinates that must satisfy x =
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.if n\
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r\(**cos theta
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.if t\
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r\(**cos\(*h
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and y =
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.if n\
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r\(**sin theta.
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.if t\
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r\(**sin\(*h.
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These equations are satisfied when (x=0,y=0)
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is mapped to
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.if n \
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(r=0,theta=0)
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.if t \
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(r=0,\(*h=0)
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on a VAX.
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In general, conversions to polar coordinates should be computed thus:
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.Bd -unfilled -offset indent
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.if n \{\
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r := hypot(x,y); ... := sqrt(x\(**x+y\(**y)
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theta := atan2(y,x).
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.\}
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.if t \{\
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r := hypot(x,y); ... := \(sr(x\u\s82\s10\d+y\u\s82\s10\d)
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\(*h := atan2(y,x).
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.\}
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.Ed
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.It
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The foregoing formulas need not be altered to cope in a
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reasonable way with signed zeros and infinities
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on a machine that conforms to
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.Tn IEEE 754 ;
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the versions of
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.Xr hypot 3
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and
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.Fn atan2
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provided for
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such a machine are designed to handle all cases.
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That is why
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.Fn atan2 \(+-0 \-0
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= \(+-\*(Pi
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for instance.
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In general the formulas above are equivalent to these:
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.Bd -unfilled -offset indent
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.if n \
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r := sqrt(x\(**x+y\(**y); if r = 0 then x := copysign(1,x);
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.if t \
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r := \(sr(x\(**x+y\(**y);\0\0if r = 0 then x := copysign(1,x);
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.Ed
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.El
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.Sh SEE ALSO
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.Xr acos 3 ,
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.Xr asin 3 ,
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.Xr atan 3 ,
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.Xr cos 3 ,
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.Xr cosh 3 ,
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.Xr math 3 ,
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.Xr sin 3 ,
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.Xr sinh 3 ,
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.Xr tan 3 ,
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.Xr tanh 3
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.Sh STANDARDS
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The
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.Fn atan2
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function conforms to
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.St -ansiC .
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