Add rem2pi

[tkoolen]

Fixes #18.

Unlike rem, I don't think it makes sense to add rem2pi to RealInterface.BINARY_MATH, because e.g. https://github.com/JuliaDiff/ForwardDiff.jl/blob/18b46471e4bb3d36633058267606767246b3e931/src/dual.jl#L420 won't do the right thing for this case. Same thing for the standard tests in RulesTests.jl.

Please advise on how to handle this: should there be a new category in RealInterface containing only this function, or should this just be special cased directly in ForwardDiff and other RealInterface dependents?

[jrevels]

Please advise on how to handle this: should there be a new category in RealInterface containing only this function, or should this just be special cased directly in ForwardDiff and other RealInterface dependents?

I think we can fix this by just adding Any to ForwardDiff's type ambiguity list (the REAL_TYPES const). EDIT: And we'll also have to add a special test case for rem2pi in ForwardDiff, but that's not too bad.

Instead of this PR, could you open a similar PR in https://github.com/JuliaDiff/DiffRules.jl instead? Sorry for the inconvenience - my plan is to archive DiffBase and RealInterface after JuliaDiff/ForwardDiff.jl#262 is merged.

[tkoolen]

See JuliaDiff/DiffRules.jl#2.

[rdeits]

Adding Any to the REAL_TYPES results in some new ambiguities in the tests:

Testing Dual...
  ...testing Dual{TestTag(),Int64,0} and Dual{TestTag(),Dual{TestTag(),Int64,0},0}
Error During Test
  Test threw an exception of type MethodError
  Expression: dual_isapprox(PRIMAL / NESTED_FDNUM, Dual{TestTag()}(PRIMAL / value(NESTED_FDNUM), (-PRIMAL / value(NESTED_FDNUM) ^ 2) * partials(NESTED_FDNUM)))
  MethodError: *(::ForwardDiff.Dual{DualTest.TestTag(),Float64,0}, ::ForwardDiff.Partials{0,ForwardDiff.Dual{DualTest.TestTag(),Int64,0}}) is ambiguous. Candidates:                                                                            
    *(x::ForwardDiff.Dual{Tx,V,N} where N where V<:Real, y) where Tx in ForwardDiff at /home/rdeits/Downloads/packages/v0.6/ForwardDiff/src/dual.jl:104                                                                                         
    *(x::Real, partials::ForwardDiff.Partials{0,V}) where V in ForwardDiff at /home/rdeits/Downloads/packages/v0.6/ForwardDiff/src/partials.jl:134                                                                                              
  Possible fix, define                                                                                                  
    *(::ForwardDiff.Dual{Tx,V,N} where N where V<:Real, ::ForwardDiff.Partials{0,V})                                    
  Stacktrace:
   [1] /(::Int64, ::ForwardDiff.Dual{DualTest.TestTag(),ForwardDiff.Dual{DualTest.TestTag(),Int64,0},0}) at /home/rdeits/Downloads/packages/v0.6/ForwardDiff/src/dual.jl:373
   [2] macro expansion at /home/rdeits/Downloads/packages/v0.6/ForwardDiff/test/DualTest.jl:373 [inlined]

[jrevels]

Thanks for looking into this. Simplest solution then might be to add the strictest supertype necessary to resolve the ambiguity (for this case, RoundingMode).