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\" from: @(#)atan2.3 5.1 (Berkeley) 5/2/91
\" $NetBSD: atan2.3,v 1.19 2017/07/03 21:32:50 wiz 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
> 0,
It Ta sign( Ns Ar y Ns )*(\*(Pi -
Fn atan "\*(Bay/x\*(Ba" ) Ta
if
Ar x
< 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 > 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 .
