Why… NaN*(0/0)*false gives 0.0, (0/0)*NaN*false gives -0.0, and: false*(0/0)*NaN false*NaN*(0/0) NaN*false*(0/0) (0/0)*false*NaN all give NaN? :thinking: Because changing false by true we get always the same result: NaN

Multiplication happens left to right. False* Nan is 0 (or negative 0). Thus multiplying that by a Nan yields a Nan.

[image] aerdely: NaN*(0/0)*false gives 0.0 , Interesting, it seems to be intentional. # make `false` a "strong zero": false*NaN == 0.0 function *(x::Bool, y::T)::promote_type(Bool,T) where T<:AbstractFloat return ifelse(x, y, copysign(zero(y), y)) end

Ok, but how would you explain -0.0 instead of 0.0 and the cases when we get NaN?

Follow my first link and read the explanations from last time you asked that question.

But how does that explain the cases when we get NaN?

Your four last cases all boil down to false (strong zero) times anything becoming an ordinary 0, and ordinary 0 times NaN becoming NaN. Well, that and left-associativity of multiplication.

julia> false * NaN 0.0 julia> NaN * false 0.0 Saying I’m surprising with this is to say the least. For me ANY operation involving a NaN must be a NaN

[image] joa-quim: For me ANY operation involving a NaN must be a NaN See Knuth’s paper linked by @GunnarFarneback , for me after thinking it up it makes sense to treat false as super strong 0 to suport Iverson’s bracket convention.

[image] joa-quim: For me ANY operation involving a NaN must be a NaN Pop-quiz, in C++ what would the following result in: std::max(Nan,x) std::max(x,NaN) fmax(Nan,x) fmax(x,NaN) And what about in Julia?

I’ve not present what they do in C++ (I deal quite a bit with NaNs in C but use isnan() to detect and deal with them). In Julia they do the right thing julia> max(NaN,8.0) NaN julia> max(NaN,8.0,NaN) NaN julia> maximum([1.1 5 7 9 NaN]) NaN but the right thing is not always what we want. For exa…

About NaN, 0/0 and false

Specific Domains Numerics

GunnarFarneback February 6, 2020, 9:31pm 3

Cf Inconsistency of NaN.

Regarding false as strong zero, see Knuth’s writings at [math/9205211] Two notes on notation.

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About NaN, 0/0 and false

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