From 417a0b2848c5016ea3af222a1f52b3b83706e9cf Mon Sep 17 00:00:00 2001
From: Twan Koolen <koolen.twan@gmail.com>
Date: Thu, 14 Sep 2017 13:12:20 -0400
Subject: [PATCH] Add rem2pi. Fix #18.

---
 src/rules.jl       |  1 +
 test/RulesTests.jl | 12 ++++++++++++
 2 files changed, 13 insertions(+)

diff --git a/src/rules.jl b/src/rules.jl
index 5267097..548bc19 100644
--- a/src/rules.jl
+++ b/src/rules.jl
@@ -165,6 +165,7 @@ hasdiffrule(f::Symbol, arity::Int) = in((f, arity), DEFINED_DIFFRULES)
 @define_diffrule hypot(x, y) = :($x / hypot($x, $y)), :($y / hypot($x, $y))
 @define_diffrule mod(x, y)   = :(first(promote(ifelse(isinteger($x / $y), NaN, 1), NaN))), :(z = $x / $y; first(promote(ifelse(isinteger(z), NaN, -floor(z)), NaN)))
 @define_diffrule rem(x, y)   = :(first(promote(ifelse(isinteger($x / $y), NaN, 1), NaN))), :(z = $x / $y; first(promote(ifelse(isinteger(z), NaN, -trunc(z)), NaN)))
+@define_diffrule rem2pi(x, r) = :(first(promote(ifelse(isinteger($x), NaN, 1), NaN))), :NaN
 
 ####################
 # SpecialFunctions #
diff --git a/test/RulesTests.jl b/test/RulesTests.jl
index f874976..fb03d17 100644
--- a/test/RulesTests.jl
+++ b/test/RulesTests.jl
@@ -38,3 +38,15 @@ for f in vcat(RealInterface.BINARY_MATH, RealInterface.BINARY_ARITHMETIC, RealIn
         end
     end
 end
+
+# Treat rem2pi separately because of its non-numeric second argument:
+derivs = DiffBase.diffrule(:rem2pi, :x, :y)
+for mode in [:RoundUp, :RoundDown, :RoundToZero, :RoundNearest]
+    @eval begin
+        x = 5π * (rand() - 0.5)
+        y = $mode
+        dx, dy = $(derivs[1]), $(derivs[2])
+        @test isapprox(dx, finitediff(z -> rem2pi(z, y), x), rtol=0.05)
+        @test isnan(dy)
+    end
+end