rem and div overflow unexpectedly for Rational

[simeonschaub]

These probably shouldn't overflow:

julia> rem(1//typemax(Int), 2)
ERROR: OverflowError: 9223372036854775807 * 2 overflowed for type Int64
Stacktrace:
 [1] throw_overflowerr_binaryop(::Symbol, ::Int64, ::Int64) at ./checked.jl:173
 [2] checked_mul at ./checked.jl:307 [inlined]
 [3] rem(::Rational{Int64}, ::Int64) at ./rational.jl:288
 [4] top-level scope at REPL[9]:1

julia> div(1//typemax(Int), 2)
ERROR: OverflowError: 9223372036854775807 * 2 overflowed for type Int64
Stacktrace:
 [1] throw_overflowerr_binaryop(::Symbol, ::Int64, ::Int64) at ./checked.jl:173
 [2] checked_mul at ./checked.jl:307 [inlined]
 [3] div(::Rational{Int64}, ::Int64, ::RoundingMode{:ToZero}) at ./rational.jl:407
 [4] div(::Rational{Int64}, ::Int64) at ./rational.jl:425
 [5] top-level scope at REPL[10]:1

Maybe a it's enough to just check if the first argument is smaller than the second one, and in that case just return the first argument/0.

[StefanKarpinski]

The denominator in the div case is too large to be represented. The rem operation could be made to work.

[simeonschaub]

div(1//typemax(Int), 2) ist just 0, no?

[StefanKarpinski]

Ah, true. I was thinking (1//typemax(Int))/2 which is not zero, of course. Carry on!