The value of `one` when using pi and E

When using \pi or \euler with the function one the value is the boolean value: true rather than 1.0. For other irrational values like sqrt(2) the value is 1.0 as it should be. Why is this?

While \sqrt{2} is not rational, sqrt(2) is a floating-point number, thus rational.


1 Like

Yes, I realized after I typed it that sqrt(2) is not irrational in the language. I did an @code_llvm on the call for pi and it seems it is making a distinction between Floats and irrational numbers. But why is this?

true in Julia is numerically equal to 1. It is the most “basic” multiplicative identity the sense that multiplying by any other type will up-promote to the precision of the larger type:

julia> true * 1 # returns Int

julia> true * 1.0 # returns Float64

julia> true * 1.0f0 # returns Float32

I think it is returned as the multiplicative identity for Irrational constants because we’re not sure what other type of 1 to return in that case.

Whereas 1.0 is a Float64 value. This is the multiplicative identity for Float64 types, but you wouldn’t want to use it for arbitrary types because it will cause type promotion to Float64:

julia> 1.0 * 3 # promotes Int to Float64

julia> 1.0 * 3.0f0 # promotes Float32 to Float64

Thank you, that makes sense.

1 Like