I am curious about the decision to have 1/5 == 1//5 return false. I’m assuming there is a rationale (pun intended) and would like to understand why. Note that 1/2 == 1//2 returns true. This make sense in so far as some rational numbers can be represented exactly in binary, but mathematically it fee…

Fundamentally the reason this returns false is that they aren’t the same number. This isn’t really any different than 1/5 == Float32(1/5) returning false.

It’s also exactly the same reason that 2/3 != 2//3. That one seems more obvious because two thirds isn’t represented exactly in either base 10 (0.666666…) or base 2 (0.1010101010…). While one fifth is exactly representable in base 10, it’s not in base 2. It’s a repeating fraction just like two th…

Another reason to use strict equality is that anything (?) else creates a tangled web of paradoxes. For example, even if we made 1/5 == 1//5 we would still struggle with the famous (and non-Julia-specific) julia> 1/10 + 2/10 0.30000000000000004 julia> 1/10 + 2/10 - 3/10 5.551115123125783e-17 If w…

You can also look at it the other way around — there does exist a rational number that exactly equals the Float64 that 1/5 evaluates to: julia> r = 0b0011001100110011001100110011001100110011001100110011010// 0b10000000000000000000000000000000000000000000000000000000 0x000ccccccccccccd//0x…

[image] PSA: floating-point arithmetic Offtopic 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 2.2204460492503…

Thanks all. I was aware that floating point is not exact, but I see the appeal of having == only be true if the equality is exact. And this is an option: julia> 1/3 ≈ 1//3 true

[image] mikmoore: and then round the result to the best representable value according to the floating point rounding configuration (usually “round to nearest, ties prefer even”). Yes, you can choose non-default (even stochastic rounding with a package), but that’s for operations, for literals…

Rounding of basic hardware arithmetic is controlled by the floating point environment , which is set via processor flags. Julia has a stub function for this, setrounding, but it’s currently (v1.9) not supported for any types except BigFloat. I’m saying that it’s good to be explicit about what you me…

[image] mikmoore: or checks for equality with zero. Then ≈ doesn’t apply (nor ==), I mean for relative tolerance, since it’s infinite. So when do you use == or ≈ in real-world float code (I only see it useful for informal (test) code, or in tests)? I suppose you could use isapprox for the abs…

big"0.2" is equivalent to @big_str("0.2") (and any xyz"content" is equivalent to @xyz_str("content")). You can @edit big"0.2" to see the macro source code, but the short version is that it uses tryparse to parse the content of the string as a BigInt or BigFloat at parse time. The reason this macro d…

Why is `1/5` not equal to `1//5`?

Internals & Design

John_Gibson May 15, 2023, 7:20pm 6

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Why is `1/5` not equal to `1//5`?

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