How many floating-point numbers are in the interval [0,1]?
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Re: How many floating-point numbers are in the interval [0,1]?
#2He references one of my favorite functions, 'nextafter'.
http://en.cppreference.com/w/cpp/numeric/math/nextafter
I'm the kind of person who understands floats by looking at the underlying bit patterns, and nextafter makes it easy to traverse the integers.
Re: How many floating-point numbers are in the interval [0,1]?
#3What about nan? The test '!(x 1)' will say yes, while 'x >= 0 && x Or -0 for that matter.
Re: How many floating-point numbers are in the interval [0,1]?
#4for many applications, consider randomizing in [1,2) and then subtracting one. Although many of the fp values in [0,1) will be inaccessible, you are guaranteed uniformity, and also the lattice that you're drawing from will be fixed.
Re: How many floating-point numbers are in the interval [0,1]?
#5What about nan? The test '!(x 1)' will say yes, while 'x >= 0 && x Or -0 for that matter.
Common sense approach: like the name says, NaN is not a number. The question was about floating point numbers, not floating point values. So I suppose we shouldn't count NaN. Further, -0 (an arbitrarily small number less than 0) doesn't logically fall in the range [0, 1], so it is excluded.
Re: How many floating-point numbers are in the interval [0,1]?
#6Article says 1,056,964,609 / 1,056,964,610
Quick Java program says 1,065,353,216 / 1,065,353,217
Which one is right? Or are Java floats just "different"?
static {
float a = 0;
long count = 0;
while (a Re: How many floating-point numbers are in the interval [0,1]?
#7Article says 1,056,964,609 / 1,056,964,610 Quick Java program says 1,065,353,216 / 1,065,353,217 Which one is right? Or are Java floats just "different"? static { float a = 0; long count = 0; while (a
It might depend on the precise representation. This has become increasingly standardized lately which is why those numbers are really close and not wildly off.
Re: How many floating-point numbers are in the interval [0,1]?
#8> Of all the float-pointing point numbers your computer can represent, a quarter of them lie in [0,1].
Many people think floating point numbers are magically precise. They're not. They're far more accurate at lower magnitudes and precision fades as you work with larger values.
Re: How many floating-point numbers are in the interval [0,1]?
#9Asking how many "are" in the interval implies that these numbers exist in some sense in that interval.
A clearer way to phrase the question might be: "How many floating-point numbers between 0 and 1 can be generated without duplicates?"
Re: How many floating-point numbers are in the interval [0,1]?
#10Article says 1,056,964,609 / 1,056,964,610 Quick Java program says 1,065,353,216 / 1,065,353,217 Which one is right? Or are Java floats just "different"? static { float a = 0; long count = 0; while (a
nextAfter is probably also including the denormals (an additional 2^23 values near 0).