Why does Julia say 1/26=0.038461538461538464

[a-boy]

julia> BigFloat(1/26)
0.0384615384615384636735058165868395008146762847900390625

julia> 1/26
0.038461538461538464

In fact, 1/26=0.0384615[384615]… 384615 as a decimal cycle section. So I doubt the value of BigFloat(1/26) and 1/26 giving by Julia are not correct. What happened？

[jling]

What’s the problem/question here? Floating point numbers have limited precisions, they can’t losslessly represent all real numbers

[Sukera]

PSA: floating-point arithmetic

Sometimes people are surprised by the results of floating-point calculations such as julia> 5/6 0.8333333333333334 # shouldn't the last digit be 3? julia> 2.6 - 0.7 - 1.9 2.220446049250313e-16 # shouldn't the answer be 0? These are not bugs in Julia. They’re consequences of the IEEE-standard 64-bit binary representation of floating-point numbers that is burned into computer hardware, which Julia and many other languages use by default. Brief explanation You can t…

[dlakelan]

@a-boy

julia> BigFloat(1/26)

julia> BigFloat(1)/BigFloat(26)
0.03846153846153846153846153846153846153846153846153846153846153846153846153846162

The code BigFloat(1/26) first computes 1/26 which becomes a Float64 and then converts that to a BigFloat.

[dlakelan]

Yes or BigFloat(1//26) which takes the exact rational 1//26 and converts it to BigFloat.

@a-boy

why the output of 1/26 is 0.038461538461538464, not 0.038461538461538462?

I’m going to assume there are no bugs in the Intel/AMD chips etc, so the number it gives must be the closest 64 bit binary floating point number to the correct value. Let’s see:

julia> eps(1/26)
6.938893903907228e-18

julia> 1/26 + eps(1/26)
0.03846153846153847

julia> 1/26 - eps(1/26)
0.03846153846153846

It looks like it was rounded right I guess.

[giordano]

@dlakelan

julia> 1/26 + eps(1/26)
0.03846153846153847

julia> 1/26 - eps(1/26)
0.03846153846153846

You usually want to use prevfloat/nextfloat, eps is the maximum of the distances to the two adjacent floating point numbers, which is not always the same between the two of them (otherwise it’d be the same for all numbers)