In Julia, if I write Int8(127) + 1 I get 128 as an answer (and not an overflow), because the two numbers are promoted to Int before performing the addition. The same promotion occurs for other operations like -, *, and /, but not for ^. I’ve read in promotion.jl that ^(x::Number, y::Number) = ^(pro…

julia> @which x^y # https://github.com/JuliaLang/julia/tree/5e7b6dd090791ca545897d9625a82cae34c116b1/base/intfuncs.jl#L299 ^(x::Number, p::Integer) in Base at intfuncs.jl:299

I believe promotion is explicitly defined here ?

Ahh, I see. Indeed, if I extend Base.^ by saying ^(x::Number, p::Integer) = ^(promote(x,p)...), then ^(Int8(127), Int64(2)) yields 16129 of type Int64. But why is ^ different from other operators in this respect? I’ve read some comments in the code about letting the compiler optimise the operation a…

Mhh, thanks! but why is ^ treated differently from the other operators in this snippet?

that’s for literal? from an implementation perspective, power by squaring simply does this: while p>1 x *= x p -= 1 end which is why there’s no promotion because x only multiplies with its own type. We can change this behavior if we promote it before the loop. Idk what’s the ramification of t…

[image] Federico_Marotta: Mhh, thanks! but why is ^ treated differently from the other operators in this snippet? I don’t know, but I could imagine the reason being that the adequate target type of the promotion is dependent of the (value of the) exponent.

[image] Federico_Marotta: but why is ^ treated differently from the other operators in this snippet? I would imagine it would be unacceptable from a performance point of view if x^2 is calculated as pow(x, 2.0) instead of as x*x. Promoting the exponent to a float would be pretty bad.

That’s exactly what happens, though: if we specify either the base or the exponent as a float, promotion occurs. E.g. 3^2.0 == 9.0 or 3.0^2 == 9.0. This is also what I would expect after reading the documentation. But the problem is just for integers of different sizes (no need to involve floats or …

[image] Federico_Marotta: That’s exactly what happens, though: if we specify either the base or the exponent as a float, promotion occurs. E.g. 3^2.0 == 9.0 or 3.0^2 == 9.0 . No, promotion does not happen for 3.0^2, it just turns into 3.0*3.0, as you actually note later in your post. [ima…

Pardon my poor choice of words, what I mean is the following. In the case of 3.0^2, the result is of type Float, the ‘common type’ between Float and Int. Similarly, in the case of Int8(3) + Int64(2), the result is of type Int64, the ‘common type’ between Int8 and Int64. From my point of view, the…

Why doesn't `^` promote its arguments?

General Usage

heliosdrm February 15, 2022, 11:03am 13

Related, with full discusion of why Julia does as it does:

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Automatic conversion of ^ to repeated * without applying promotion rule Numerics	7	797	July 13, 2019
Integer type promotion behavior New to Julia question	4	222	March 20, 2024
Built in exponentiation for `Any` type Internals & Design question	11	1347	April 8, 2020
Should large exponentials not yield Inf? General Usage question , numerics , integer-overflow	15	1455	May 23, 2022
Weird result in power operator New to Julia	13	3182	June 6, 2020

Why doesn't `^` promote its arguments?

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