I’ve seen a tweet from David Amos explaining this case where sum in Python fails miserably. The example is taken from BINARY FLOATING POINT SUMMATION ACCURATE TO FULL PRECISION (PYTHON RECIPE) . Julia fails too: julia> sum([1.0, 1e100, 1.0, -1e100]) 0.0 What would be the easiest way to avoid this …

In general, this is not a language issue. Python is not “failing”, nor is Julia. You’ll get exactly the same thing if you just use + in any language using double-precision floating-point arithmetic (the default precision in most languages). As another example, sum([1e-100, 1.0, 1e-100, -1.0]) al…

float(sum(Rational.(BigFloat[1.0, 1e100, 1.0, -1e100]))) 2.0

julia> sum(sort([1.0, 1e100, 1.0, -1e100],by=abs,rev=true)) 2.0 (“easiest” here may mean many things… these are just tricks to get the idea of floating point summation. If that was an actual problem, one would need to check exactly what is the purpose of the calculation to see what to do)

Relevant? [image] Julia equivalent of Python's "fsum" for floating point summation General Usage I have been looking for a Julia equivalent of Python’s fsum and have thus far been unable to find one. Is there an implementation already available? If not I will write my own…

A third one if the problem are supposed to have “nice” integer numbers, just use BigInts. sum([1, BigInt(10)^100, 1, -BigInt(10)^100])

[image] rafael.guerra: Rational that’s kind of cheating… might as well just use more precision? julia> setprecision(800) do # you can do this globally sum(BigFloat[1.0, 1e100, 1.0, -1e100]) end 2.0

[image] runjaj: sum([1.0, 1e100, 1.0, -1e100]) Try using KahanSummation sum_kbn([1.0, 1e100, 1.0, -1e100]) which was earlier in Base IIUC. Related thread . Edit: you’ll also find AccurateArithmetics and the interesting task to extend error-free transformations.

[image] runjaj: In Python, fsum gives the correct answer. The direct analogue of fsum in Julia is Xsum.jl , not Kahan/compensated summation (which is very accurate, but is not exactly rounded in general).

[image] stevengj: The direct analogue of fsum in Julia is Xsum.jl , not Kahan/compensated summation (which is very accurate, but is not exactly rounded in general). This looks like it is working with a double precision compensated sum?

[image] stevengj: In general, this is not a language issue. Agreed. But this could be about language guarantees like speed vs. accuracy (discussions, which we had before about for example checked integer arithmetic or signalling NaN’s).

People have mentioned this problem before. This is NOT a problem with the programming language. This is the LIMITATION of the Float64 binary floating point representation of REAL NUMBERS There is only so much precision in Float64, if you add a small number with a big number, you can only represe…

"sum([1.0, 1e100, 1.0, -1e100])" fails

General Usage

johnmyleswhite February 15, 2022, 6:46pm 4

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"sum([1.0, 1e100, 1.0, -1e100])" fails

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