Add rem2pi (#2)

Transplanted from JuliaAttic/DiffBase.jl#19.

src/rules.jl

@@ -72,6 +72,7 @@
 @define_diffrule Base.hypot(x, y) = :( $x / hypot($x, $y)                                      ), :(  $y / hypot($x, $y)                                                     )
 @define_diffrule Base.mod(x, y)   = :( first(promote(ifelse(isinteger($x / $y), NaN, 1), NaN)) ), :(  z = $x / $y; first(promote(ifelse(isinteger(z), NaN, -floor(z)), NaN)) )
 @define_diffrule Base.rem(x, y)   = :( first(promote(ifelse(isinteger($x / $y), NaN, 1), NaN)) ), :(  z = $x / $y; first(promote(ifelse(isinteger(z), NaN, -trunc(z)), NaN)) )
+@define_diffrule Base.rem2pi(x, r) = :(1), :NaN
 
 ####################
 # SpecialFunctions #

test/runtests.jl

@@ -9,7 +9,11 @@ function finitediff(f, x)
     return (f(x + ϵ) - f(x - ϵ)) / (ϵ + ϵ)
 end
 
+
+non_numeric_arg_functions = [(:Base, :rem2pi, 2)]
+
 for (M, f, arity) in DiffRules.diffrules()
+    (M, f, arity) ∈ non_numeric_arg_functions && continue
     if arity == 1
         @test DiffRules.hasdiffrule(M, f, 1)
         deriv = DiffRules.diffrule(M, f, :x)
@@ -33,3 +37,17 @@ for (M, f, arity) in DiffRules.diffrules()
         end
     end
 end
+
+# Treat rem2pi separately because of its non-numeric second argument:
+derivs = DiffRules.diffrule(:Base, :rem2pi, :x, :y)
+for xtype in [:Float64, :BigFloat, :Int64]
+    for mode in [:RoundUp, :RoundDown, :RoundToZero, :RoundNearest]
+        @eval begin
+            x = $xtype(rand(1 : 10))
+            y = $mode
+            dx, dy = $(derivs[1]), $(derivs[2])
+            @test isapprox(dx, finitediff(z -> rem2pi(z, y), float(x)), rtol=0.05)
+            @test isnan(dy)
+        end
+    end
+end