7e6cabd06e
Renumber cluase 4 to 3, per what everybody else did when BSD granted them permission to remove clause 3. My insistance on keeping the same numbering for legal reasons is too pedantic, so give up on that point. Submitted by: Jan Schaumann <jschauma@stevens.edu> Pull Request: https://github.com/freebsd/freebsd/pull/96
226 lines
5.0 KiB
Groff
226 lines
5.0 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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.\" $FreeBSD$
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.\"
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.Dd July 31, 2008
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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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.Nm atan2l ,
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.Nm carg ,
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.Nm cargf ,
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.Nm cargl
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.Nd arc tangent and complex phase angle functions
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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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.Ft long double
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.Fn atan2l "long double y" "long double x"
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.In complex.h
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.Ft double
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.Fn carg "double complex z"
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.Ft float
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.Fn cargf "float complex z"
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.Ft long double
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.Fn cargl "long double complex z"
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.Sh DESCRIPTION
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The
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.Fn atan2 ,
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.Fn atan2f ,
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and
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.Fn atan2l
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functions compute the principal value of the arc tangent of
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.Fa 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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.Pp
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The
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.Fn carg ,
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.Fn cargf ,
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and
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.Fn cargl
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functions compute the complex argument (or phase angle) of
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.Fa z .
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The complex argument is the number theta such that
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.Li z = r * e^(I * theta) ,
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where
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.Li r = cabs(z) .
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The call
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.Li carg(z)
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is equivalent to
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.Li atan2(cimag(z), creal(z)) ,
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and similarly for
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.Fn cargf
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and
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.Fn cargl .
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.Sh RETURN VALUES
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The
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.Fn atan2 ,
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.Fn atan2f ,
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and
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.Fn atan2l
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functions, if successful,
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return the arc tangent of
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.Fa 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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Here are some of the special cases:
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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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> 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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< 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 > 0,"
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.Fn atan2 0 0
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= 0 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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In general, conversions to polar coordinates
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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 cabs 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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.Fn atan2f ,
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.Fn atan2l ,
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.Fn carg ,
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.Fn cargf ,
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and
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.Fn cargl
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functions conform to
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.St -isoC-99 .
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