[expr {atan2($y, $x)}]

    ($y / $x)

RS notes (testing functional imaging): Contrary to the above claim, on Sun computers the call atan2(0,0) raises the error:

 % expr atan2(0,0)
 domain error: argument not in valid range

Fix: check that at least one coordinate is non-zero:

 proc toPolars p {
    foreach {x y} $p break
    # for Sun, we have to make sure atan2 gets no two 0's
    list [expr {hypot($x,$y)}] [expr {$x||$y? atan2($y,$x): 0}]
 }

Arjen Markus I tested this feature in a small C program on an HPUX and a SGI machine with native compilers. The results were quite similar:

• HPUX reports a Nan and errno = 0
• SGI reports a value 0.0 and a Domain error.

Tcl 8.3.1 on SGI responds with a domain error as well, so that is quite consistent!

AMG: GNU (glibc) atan2() is defined [1] to return 0 when both arguments are 0.

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The most common use of atan2 is in Converting between rectangular and polar co-ordinates.

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atan2 is also available as a command in Tclx.

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AM (28 april 2008) Interesting feature:

• atan2(y,x) will give the mathematical angle, that is, the angle with the positive x axis, oriented counter-clockwise
• atan2(x,y) (so the arguments in just the opposite order) will give the nautical angle, that is, the angle with the positive y-axis, oriented clockwise (or if you like: the angle on the compass)

AMG: When dealing with maps and geospatial data, I greatly prefer to orient north along the positive X axis and east along the positive Y axis. This way atan2(y,x) gives me a compass heading. Well, atan2(y,x)*180/acos(-1) does. :^) I am told this is standard GIS convention.

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GWM (28 april 2008) note that Excel uses the reverse convention from C, Fortran, Tcl (and probably most other languages),

 atan2(0,1) = 0; atan2(1,0) = 1.570796 etc.

Have all other spreadsheets been infected by Excel? Does SLK insist on Excel ordered atan2? Take care when translating a formula that works in Excel to other languages (and vice versa).

AMG: OpenOffice.org Calc uses the same backwards convention. Sigh. It stinks when the de facto standard is exactly backwards from the de jure standard. (Maybe I should say "du jour standard", hehehe.)

RS 2015-11-26 I see the same behavior, so what is "backwards"?:

 $  tclsh
 % info pa
 8.5.9
 % expr atan2(1,0)
 1.5707963267948966
 % expr atan2(0,1)
 0.0

But while we're at it, the Tcl manpage mathfunc has a bug there:

atan arg

Returns the arc tangent of arg, in the range [-pi/2,pi/2] radians.

atan2 y x

Returns the arc tangent of y/x, in the range [-pi,pi] radians. x and y cannot both be 0. If x is greater than 0, this is equivalent to “atan [expr {y/x}]”.

...

To be equivalent (which I tested), the range of atan2 is equally -pi/2...pi/2.

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DKF: Tcl just uses the same convention as C, because it uses the same function.

AMG: Which explains why it accepts two arguments.