#207, but rebased against master (#214)

* fix wrong partials multiplied in FMA

* use more fma

Author: jrevels

src/dual.jl

@@ -410,11 +410,13 @@ end
 @ambiguous @inline Base.atan2(y::Real, x::Dual) = calc_atan2(y, x)
 @ambiguous @inline Base.atan2(y::Dual, x::Real) = calc_atan2(y, x)
 
-@inline function Base.fma(x::Dual, y::Dual, z::Dual)
-    vx, vy = value(x), value(y)
-    result = fma(vx, vy, value(z))
-    return Dual(result,
-                _mul_partials(partials(x), partials(y), vy, vx) + partials(z))
+@generated function Base.fma{N}(x::Dual{N}, y::Dual{N}, z::Dual{N})
+    ex = Expr(:tuple, [:(fma(value(x), partials(y)[$i], fma(value(y), partials(x)[$i], partials(z)[$i]))) for i in 1:N]...)
+    return quote
+        $(Expr(:meta, :inline))
+        v = fma(value(x), value(y), value(z))
+        Dual(v, $ex)
+    end
 end
 
 @inline function Base.fma(x::Dual, y::Dual, z::Real)
@@ -423,10 +425,13 @@ end
     return Dual(result, _mul_partials(partials(x), partials(y), vy, vx))
 end
 
-@inline function Base.fma(x::Dual, y::Real, z::Dual)
-    vx = value(x)
-    result = fma(vx, y, value(z))
-    return Dual(result, partials(x) * y + partials(z))
+@generated function Base.fma{N}(x::Dual{N}, y::Real, z::Dual{N})
+    ex = Expr(:tuple, [:(fma(partials(x)[$i], y,  partials(z)[$i])) for i in 1:N]...)
+    return quote
+        $(Expr(:meta, :inline))
+        v = fma(value(x), y, value(z))
+        Dual(v, $ex)
+    end
 end
 
 @inline Base.fma(x::Real, y::Dual, z::Dual) = fma(y, x, z)