use sincos in rules for sin and cos (#296)

* use `sincos` in rules for `sin` and `cos`

* add rules for `sin` and `cos` to fastmath_able

* conjugte the rrule derivative values but not the frule derivatives

Project.toml

@@ -1,6 +1,6 @@
 name = "ChainRules"
 uuid = "082447d4-558c-5d27-93f4-14fc19e9eca2"
-version = "0.7.31"
+version = "0.7.32"
 
 [deps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"

src/rulesets/Base/fastmath_able.jl

@@ -5,8 +5,33 @@ let
     # e.g. do not add `foo` unless `Base.FastMath.foo_fast` exists.
     fastable_ast = quote
         #  Trig-Basics
-        @scalar_rule cos(x) -(sin(x))
-        @scalar_rule sin(x) cos(x)
+        ## use `sincos` to compute `sin` and `cos` at the same time
+        ## for the rules for `sin` and `cos`
+        ## See issue: https://github.com/JuliaDiff/ChainRules.jl/issues/291
+        ## sin
+        function rrule(::typeof(sin), x::Number)
+            sinx, cosx = sincos(x)
+            sin_pullback(Δy) = (NO_FIELDS, cosx' * Δy)
+            return (sinx, sin_pullback)
+        end
+
+        function frule((_, Δx), ::typeof(sin), x::Number)
+            sinx, cosx = sincos(x)
+            return (sinx, cosx * Δx)
+        end
+
+        ## cos
+        function rrule(::typeof(cos), x::Number)
+            sinx, cosx = sincos(x)
+            cos_pullback(Δy) = (NO_FIELDS, -sinx' * Δy)
+            return (cosx, cos_pullback)
+        end
+
+        function frule((_, Δx), ::typeof(cos), x::Number)
+            sinx, cosx = sincos(x)
+            return (cosx, -sinx * Δx)
+        end
+
         @scalar_rule tan(x) 1 + Ω ^ 2