On Tue, Apr 16, 2013 at 6:10 PM, Hugo Arts <hugo.yo...@gmail.com> wrote: >>>> i = 0 >>>> for _ in range(1000): > i += 0.1 > >>>> i > 99.9999999999986 > > That should, by all the laws of math, be 100. But it isn't. Because the > computer can't store 0.1 in a float, so it stores the closest possible > number it can instead. The value stored in a above is not actually 0.1, it's > closer to: > > 0.1000000000000000055511151231257827021181583404541015625
Now you have to explain how the summation ends up as less than 100. ;) That really gets to the heart of error introduced by intermediate rounding with fixed-precision arithmetic. This is a more important point than the fact that 0.1 doesn't have an exact representation in binary floating point. Python's floats are limited to hardware precision, which is 53 bits or floor(53*log10(2)) == 15 decimal digits. There's no option to extend the precision arbitrarily as is possible with the Decimal type. BTW, did you know Decimal got a C implementation in 3.3? It's a lot faster than the pure Python implementation in previous versions, but still not as fast as hardware floats. _______________________________________________ Tutor maillist - Tutor@python.org To unsubscribe or change subscription options: http://mail.python.org/mailman/listinfo/tutor
