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Floats have a fixed accuracy everywhere. Ints have a variable accuracy across their range. When you convert from int to float, the number stays accurate to howe

Floats have a fixed accuracy everywhere. Ints have a variable accuracy across their range. When you convert from int to float, the number stays accurate to however many digits, say 8 digits for single precision. Ints have a fixed precision everywhere, whereas for floats it varies. A given float might be accurate to one part in 10^30. When you cast to int, you get accuracy to within 1 part in 1. So you lose far more orders of magnitude of precision converting from float to int then you lose in order of magnitude of accuracy converting from int to float.

titzer 1y ago
> When you convert from int to float, the number stays accurate to however many digits The point of the article is that this "however many digits" actually implies rounding many numbers that aren't that big. A single precision (i.e. 32-bit) float cannot exactly represent some 32-bit integers. For example 1_234_567_891f is actually rounded to 1_234_567_936. This is because there are only 23 bits of fraction available (https://en.wikipedia.org/wiki/Single-precision_floating-point_format https://en.wikipedia.org/wiki/Single-precision_floating-poin...).
tomtom1337 1y ago
You have a typo: In your last sentence you effectively wrote «from int to float» twice in contradicting ways. «To float from int than (…) from int to float».
- nofriend 1y ago
  there was an error made when I went back to edit what I wrote...
dmurray 1y ago
Floats have the same accuracy everywhere when measured in relative error, ints have the same accuracy everywhere when measuring absolutely. Which of those is better? It depends on the application. All you can do is hope the person who gave you the numbers chose the more appropriate representation, the less painful way to lose fidelity in a representation of the real world. By converting to the other representation you now have lost that fidelity in both ways. Again, by a similar argument to above, something like this has to be true. You have exactly 32 bits of information either way, and both conversions lose the same amount of information - you end up with a 32-bit representation, but it only represents a domain of 2^27 (or whatever it is) distinct numbers.
- nofriend 1y ago
  >both conversions lose the same amount of information This is exactly what's untrue. I said "orders of magnitude", but I could have said bits - they're analogous concepts. Ints with the high 9 bits set to zero lose no information when converting to single precision floating point. The rest lose progressively more information, concentrated in the low order bits, up to 8 bits. Certainly regrettable, but usually manageable. Converting from floats to ints might be representable exactly, but if the number is, say, near 1, then it will be rounded to 1, losing 23 bits of information. If the number is near 0 then it will be rounded to 0, losing 31 bits of information.

titzer 1y ago

> When you convert from int to float, the number stays accurate to however many digits The point of the article is that this "however many digits" actually implies rounding many numbers that aren't that big. A single precision (i.e. 32-bit) float cannot exactly represent some 32-bit integers. For example 1_234_567_891f is actually rounded to 1_234_567_936. This is because there are only 23 bits of fraction available (https://en.wikipedia.org/wiki/Single-precision_floating-point_format https://en.wikipedia.org/wiki/Single-precision_floating-poin...).

tomtom1337 1y ago

You have a typo: In your last sentence you effectively wrote «from int to float» twice in contradicting ways. «To float from int than (…) from int to float».

nofriend 1y ago
there was an error made when I went back to edit what I wrote...

dmurray 1y ago

Floats have the same accuracy everywhere when measured in relative error, ints have the same accuracy everywhere when measuring absolutely. Which of those is better? It depends on the application. All you can do is hope the person who gave you the numbers chose the more appropriate representation, the less painful way to lose fidelity in a representation of the real world. By converting to the other representation you now have lost that fidelity in both ways. Again, by a similar argument to above, something like this has to be true. You have exactly 32 bits of information either way, and both conversions lose the same amount of information - you end up with a 32-bit representation, but it only represents a domain of 2^27 (or whatever it is) distinct numbers.

nofriend 1y ago
>both conversions lose the same amount of information This is exactly what's untrue. I said "orders of magnitude", but I could have said bits - they're analogous concepts. Ints with the high 9 bits set to zero lose no information when converting to single precision floating point. The rest lose progressively more information, concentrated in the low order bits, up to 8 bits. Certainly regrettable, but usually manageable. Converting from floats to ints might be representable exactly, but if the number is, say, near 1, then it will be rounded to 1, losing 23 bits of information. If the number is near 0 then it will be rounded to 0, losing 31 bits of information.