Re: Lissajous curves

I always chuckle at:

sub pie() {
    2 * atan2(1, 0);
}
[download]

as in "compute pi/2, then double it", instead of just computing pi directly:

sub pi () {
  atan2(0, -1);
}
[download]

-- Randal L. Schwartz, Perl hacker

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Re^2: Lissajous curves by ambrus (Abbot) on Jun 14, 2007 at 15:58 UTC
Sure you can, but atan2 has a branch cut there so you have to know that it returns pi, not minus pi which would also make sense to me (though the IEEE 754 committee might have had a reason). Update 2011-04-18: in fact, appendix F of the C99 standard states that atan2 with zero first argument and negative second argument gives pi with the sign copied from the zero. This guarantees that atan2(-1,0) must return positive pi. You can see that indeed perl will give negative pi for a negative zero first argument: `$ perl -wE '$x = -1; $x/=2 for 1..9999; $,=" "; say $x, atan2($x,-1), +atan2(0,-1);' -0 -3.14159265358979 3.14159265358979` [download]	[reply] [d/l]

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Re^2: Lissajous curves
by ambrus (Abbot) on Jun 14, 2007 at 15:58 UTC

Sure you can, but atan2 has a branch cut there so you have to know that it returns pi, not minus pi which would also make sense to me (though the IEEE 754 committee might have had a reason).

Update 2011-04-18: in fact, appendix F of the C99 standard states that atan2 with zero first argument and negative second argument gives pi with the sign copied from the zero. This guarantees that atan2(-1,0) must return positive pi. You can see that indeed perl will give negative pi for a negative zero first argument:

$ perl -wE '$x = -1; $x/=2 for 1..9999; $,=" "; say $x, atan2($x,-1), 
+atan2(0,-1);'
-0 -3.14159265358979 3.14159265358979
[download]

[reply]
[d/l]