`mod` is JIT-ed to HLO operator with the semantic of Julia's `rem`

[giordano]

The fact that Base.mod and Base.rem both are lowered to the same HLO operator looks very fishy since they have different semantics in Julia.

https://openxla.org/xla/operation_semantics#element-wise_binary_arithmetic_operations

When Op is Rem, the sign of the result is taken from the dividend, and the absolute value of the result is always less than the divisor's absolute value.

This is the semantic of Julia's rem, the opposite of mod. See also https://openxla.org/stablehlo/spec#remainder for more details about the operator.

Originally posted by @giordano in #754 (comment)

[giordano]

I didn't find an HLO function for this operation in https://openxla.org/stablehlo/spec. If we have to roll our own, a possible implementation of mod could be

# Based on https://github.com/JuliaLang/julia/blob/39255d47db7657950ff1c82137ecec5a70bae622/base/float.jl#L608-L617
function Base.mod(@nospecialize(x::Reactant.TracedRNumber{T}), @nospecialize(y::Reactant.TracedRNumber{T})) where {T}
    r = rem(x, y)
    return ifelse(r == 0, copysign(r, y), ifelse((r > 0) ⊻ (y > 0), r + y, r))
end

but we don't have a method for copysign. How do I find the HLO function for this operation? Google is failing me.

[mofeing]

https://openxla.org/stablehlo/spec#sign

[giordano]

That's not exactly the same thing.

[giordano]

You can implement copysign(a, b) = sign(b) * abs(a), but this is likely going to be much less efficient than a proper builtin implementation. LLVM has a specific intrinsic for example.

[mofeing]

yep, but stablehlo has a limited amount of ops, and the only op close to it is that one. not even CHLO has one like this https://github.com/openxla/stablehlo/blob/main/stablehlo/dialect/ChloOps.td

You can implement copysign(a, b) = sign(b) * abs(a), but this is likely going to be much less efficient than a proper builtin implementation. LLVM has a specific intrinsic for example.

remember that this are very high-level ops, so probably XLA can optimize it if we express it well enough.

[giordano]

You can implement copysign(a, b) = sign(b) * abs(a)

That's not true, sign is the completely wrong function to use here.