8 ms·
The discrepancy with the number in the article is that you're including 2^23 mantissae with exponent 0. In any case, the interesting bit is that half of floats
by surement 10y ago
The discrepancy with the number in the article is that you're including 2^23 mantissae with exponent 0. In any case, the interesting bit is that half of floats are in the interval [-1, 1].
- vog 10y ago> the interesting bit is that half of floats are in the interval [-1, 1] This is not so surprising once you realize that this just means you have the same precision for 1/x as for x, which makes a lot of sense for scientific calculations.
- gugagore 10y agoI'll clarify mostly for my sake (I hadn't thought about this before) f(x) = 1/x takes takes numbers in the range (-1, 1) to numbers outside that range, and vice versa. The representable floats are split evenly between those two sets
- vog 10y agoYes, that was exactly my line of thinking. One minor nitpick: f(x)=1/x maps [-1,1] to [-inf,-1]u[+1,+inf] ... that is, 1 and -1 are in both sets and mapped onto themselves. However, this detail doesn't affect the argument much.