Merge pull request JuliaDiff#79 from YingboMa/myb/atan

Fix atan2 rules

Author: oxinabox

src/rulesets/Base/base.jl

@@ -64,7 +64,7 @@
 @scalar_rule(csch(x), -coth(x) * Ω)
 @scalar_rule(hypot(x, y), (x / Ω, y / Ω))
 @scalar_rule(sincos(x), @setup((sinx, cosx) = Ω), cosx, -sinx)
-@scalar_rule(atan(y, x), @setup(u = hypot(x, y)), (x / u, y / u))
+@scalar_rule(atan(x, y), @setup(u = x^2 + y^2), (y / u, -x / u))
 @scalar_rule(max(x, y), @setup(gt = x > y), (gt, !gt))
 @scalar_rule(min(x, y), @setup(gt = x > y), (!gt, gt))
 @scalar_rule(mod(x, y), @setup((u, nan) = promote(x / y, NaN16)),

test/rulesets/Base/base.jl

@@ -62,7 +62,27 @@ end
             test_scalar(acscd, x -> -180 / π / abs(x) / sqrt(x^2 - 1), x)
             test_scalar(acotd, x -> -180 / π / (1 + x^2), x)
         end
-        # TODO: atan2 sincos
+        @testset "Multivariate" begin
+            x, y = rand(2)
+            ratan = atan(x, y) # https://en.wikipedia.org/wiki/Atan2
+            u = x^2 + y^2
+            datan = y/u - 2x/u
+            r, df = frule(atan, x, y)
+            @test r === ratan
+            @test df(1, 2) === datan
+            r, (df1, df2) = rrule(atan, x, y)
+            @test r === ratan
+            @test df1(1) + df2(2) === datan
+
+            rsincos = sincos(x)
+            dsincos = cos(x) - 2sin(x)
+            r, (df1, df2) = frule(sincos, x)
+            @test r === rsincos
+            @test df1(1) + df2(2) === dsincos
+            r, df = rrule(sincos, x)
+            @test r === rsincos
+            @test df(1, 2) === dsincos
+        end
     end
     @testset "Misc. Tests" begin
         @testset "*(x, y)" begin