Comment by bhaney
3 years ago
> For very small numbers (less than about FLT_EPSILON * 0.25) adding 0.5 gives 0.5 exactly, and this then rounds to zero
Is that not correct? Isn't it expected that very small numbers round to zero?
3 years ago
> For very small numbers (less than about FLT_EPSILON * 0.25) adding 0.5 gives 0.5 exactly, and this then rounds to zero
Is that not correct? Isn't it expected that very small numbers round to zero?
The quote is talking about code that is supposed to find the ceiling of a number, and does so by adding 0.5 and then rounding to the nearest value (breaking ties by rounding towards even).
If you have a very small but non-zero positive number, it gets rounded to 0.5 after the addition, and then the second rounding incorrectly rounds toward 0 instead of 1.
The result is that you have a value x such that x > ceil(x), which shouldn't ever happen.
> supposed to find the ceiling
Oh duh. I somehow forgot that over the span of a few sentences. Thanks.
This is in the context of the implementation of a ciel() function: a very small but still positive float should have a ciel() of 1. As said near this part, IEEE default rounding is round half to nearest even: 0.5 rounds to 0, the closest even integer, so if your addition of 0.5 to the argument to ciel() results in exactly 0.5, the result will incorrectly be 0 instead of 1.