`InexactError` when comparing `Int8` with `UInt9`

[matthias314]

julia> @emulate UInt9

julia> Int8(-1) < UInt9(0)
ERROR: InexactError: trunc(UInt16, -1)
Stacktrace:
  [1] throw_inexacterror(func::Symbol, to::Type, val::Int8)
    @ Core ./boot.jl:815
  [2] check_sign_bit
    @ ./boot.jl:821 [inlined]
  [3] toUInt16
    @ ./boot.jl:907 [inlined]
  [4] UInt16
    @ ./boot.jl:960 [inlined]
  [5] convert
    @ ./number.jl:7 [inlined]
  [6] Type
    @ ~/.julia/packages/EmulatedBitIntegers/IFk3G/src/interface.jl:3 [inlined]
  [7] convert
    @ ./number.jl:7 [inlined]
  [8] _promote
    @ ./promotion.jl:379 [inlined]
  [9] promote
    @ ./promotion.jl:404 [inlined]
 [10] <(x::Int8, y::UInt9)
    @ Base ./promotion.jl:488
 [11] top-level scope
    @ REPL[3]:1

Tested with Julia 1.12.7 and EmulatedBitIntegers v0.4.2.

[matthias314]

The following InexactError might be related to this:

julia> @emulate UInt65

julia> BigInt(UInt65(0))
ERROR: InexactError: trunc(UInt128, -9223372036854775808)
Stacktrace:
  [1] throw_inexacterror(func::Symbol, to::Type, val::Int64)
    @ Core ./boot.jl:815
  [2] check_sign_bit
    @ ./boot.jl:821 [inlined]
  [3] toUInt128
    @ ./boot.jl:943 [inlined]
  [4] UInt128
    @ ./boot.jl:963 [inlined]
  [5] convert
    @ ./number.jl:7 [inlined]
  [6] Type
    @ ~/.julia/packages/EmulatedBitIntegers/IFk3G/src/interface.jl:3 [inlined]
  [7] convert
    @ ./number.jl:7 [inlined]
  [8] _promote
    @ ./promotion.jl:379 [inlined]
  [9] promote
    @ ./promotion.jl:404 [inlined]
 [10] <=
    @ ./promotion.jl:489 [inlined]
 [11] BigInt(x::UInt65)
    @ Base.GMP ./gmp.jl:333
 [12] top-level scope
    @ REPL[3]:1

[matthias314]

I think the root problem are the promotions inside various functions in Julia Base,
see https://github.com/JuliaLang/julia/blob/c9c281e7938df9c5ec82ea6758966755fabb7127/base/promotion.jl#L516-L526

==(x::Number, y::Number) = (==)(promote(x,y)...)
<( x::Real, y::Real)     = (< )(promote(x,y)...)
<=(x::Real, y::Real)     = (<=)(promote(x,y)...)

rem(x::Real, y::Real) = rem(promote(x,y)...)
mod(x::Real, y::Real) = mod(promote(x,y)...)
mod1(x::Real, y::Real) = mod1(promote(x,y)...)

max(x::Real, y::Real) = max(promote(x,y)...)
min(x::Real, y::Real) = min(promote(x,y)...)
minmax(x::Real, y::Real) = minmax(promote(x, y)...)

[PatrickHaecker]

Thanks, Matthias, for the report and the detailed description how to tackle this.