Floating-point glitches with the math module. Bug? Or am I missing something?

Jeff Epler jepler at unpythonic.net
Tue Sep 21 02:03:57 CEST 2004


If it's any consolation, I get similar problems in C.  Whenever Python
does floating point math, it thinly wraps your C compiler's math
library.

$ cat > metzler.c <<EOF
> #include <math.h>
> 
> double x, y, z;
> double cos_gamma3, gamma3;
> 
> int main(void) {
>     x = 0.999999;
>     y = 0.999997;
>     z = 1e-08;
> 
>     cos_gamma3 = cos(x - y) - sin(x)*sin(y)*(1.0 - cos(z));
>     gamma3 = acos(cos_gamma3);
> 
>     printf("This shold be positive:  %g\n", gamma3 - fabs(x-y));
>     return 0;
> }
> EOF
$ gcc metzler.c -lm -o metzler
$ ./metzler
This shold be positive:  -2.21218e-11

acos(cos(d)) for small d gives fairly large errors on my system:
>>> d = .999999 - .9999977
>>> acos(cos(d)), d 
(1.2999928800133351e-06,
 1.2999999999818712e-06)
>>> #   ^ First difference here
a half dozen correct digits isn't great, but it's all my platform's trig
functions seem to give me.  And you're trying to make a silk purse out
of a sow's ear...

Incidentally, the second part of your expression goes to 0 here, with
the given values:
>>> cos(z) == 1.0
True
>>> sin(x)*sin(y)*(1-cos(z))
0.0
>>> _ == 0
True

Jeff
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