The following remainder calculations are a bit surprising to me, as I’d expect to get a remainder of 0 (or something like ~1e-18) in each case. I guess there is some floating point issue: julia> rem(500,0.625) 0.0 julia> rem(50,0.0625) 0.0 julia> rem(5,0.00625) 0.006249999999999723 julia> rem(…

[image] _bernhard: This is exactly what happens in your example - the divisor (and dividend) is rounded to the nearest float In particular, 0.00625 is not exactly representable in binary floating point, so it is rounded to a slightly larger value: julia> big(0.00625) 0.0062500000000000003469…

One would expect the remainder to either be very close to 0.0 or very close to 0.0...625, depending on whether it’s slightly bigger or smaller than a multiple. Or rather, whether the floating point roundoffs pull in one direction or the other.

This is an issue with floating point numbers in general. in contrast to integers floats are (for most values) not exact, but rounded to the nearest value that can be represented. This is exactly what happens in your example - the divisor (and dividend) is rounded to the nearest float and depending …

The documentation hints that rem(x,y,r) is the same as x - y*round(x/y,r). For x = 5 and y = 0.00625 this actually returns 0. So maybe a bug is hiding somewhere?

The comments above about floating point roundoffs are what I was alluding to as “floating point issues”. If the remainder value is e.g. 2e-18, that’s clearly roundoff. However, @natlampen hits the nail on the head - when the “remainder” value is essentially equal to the divisor, it seems like this …

Thanks @stevengj this is a very clear example. Again, the general issues with floating point representation are clear - in fact I tried t=displaying values following more or less the logic you did. The mistake I made was to try to use @printf and I stopped a few digits short; next time I will use b…

[image] lwhitefox: It would be useful to include a 1-line example like this in the docs just to help make clear what the implications of “exact” might be Sure, but realize also that this is not specific to Julia. The same floating-point standard is followed by essentially all modern languag…

Calculation of remainder, floating point issues

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Calculation of remainder, floating point issues

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