Added fma, with tests. (#203)

Tests required a third value set (PRIMAL etc) in the testing framework, which was also added.

Fixes issue #202.

Author: tpapp

src/dual.jl

@@ -410,6 +410,38 @@ 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), vx, vy) + partials(z))
+end
+
+@inline function Base.fma(x::Dual, y::Dual, z::Real)
+    vx, vy = value(x), value(y)
+    result = fma(vx, vy, z)
+    return Dual(result, _mul_partials(partials(x), partials(y), vx, vy))
+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))
+end
+
+@inline Base.fma(x::Real, y::Dual, z::Dual) = fma(y, x, z)
+
+@inline function Base.fma(x::Dual, y::Real, z::Real)
+    vx = value(x)
+    return Dual(fma(vx, y, value(z)), partials(x) * y)
+end
+
+@inline Base.fma(x::Real, y::Dual, z::Real) = fma(y, x, z)
+
+@inline function Base.fma(x::Real, y::Real, z::Dual)
+    Dual(fma(x, y, value(z)), partials(z))
+end
+
 ###################
 # Pretty Printing #
 ###################

test/DualTest.jl

@@ -48,6 +48,10 @@ for N in (0,3), M in (0,4), T in (Int, Float32)
     PRIMAL2 = intrand(T)
     FDNUM2 = Dual(PRIMAL2, PARTIALS2)
 
+    PARTIALS3 = Partials{N,T}(ntuple(n -> intrand(T), Val{N}))
+    PRIMAL3 = intrand(T)
+    FDNUM3 = Dual(PRIMAL3, PARTIALS3)
+
     M_PARTIALS = Partials{M,T}(ntuple(m -> intrand(T), Val{M}))
     NESTED_PARTIALS = convert(Partials{N,Dual{M,T}}, PARTIALS)
     NESTED_FDNUM = Dual(Dual(PRIMAL, M_PARTIALS), NESTED_PARTIALS)
@@ -383,6 +387,21 @@ for N in (0,3), M in (0,4), T in (Int, Float32)
 
     @test partials(NaNMath.pow(Dual(-2.0, 1.0), Dual(2.0, 0.0)), 1) == -4.0
 
+    @test fma(FDNUM, FDNUM2, FDNUM3) == Dual(fma(PRIMAL, PRIMAL2, PRIMAL3),
+                                             PRIMAL*PARTIALS2 + PRIMAL2*PARTIALS +
+                                             PARTIALS3)
+    @test fma(FDNUM, FDNUM2, PRIMAL3) == Dual(fma(PRIMAL, PRIMAL2, PRIMAL3),
+                                              PRIMAL*PARTIALS2 + PRIMAL2*PARTIALS)
+    @test fma(PRIMAL, FDNUM2, FDNUM3) == Dual(fma(PRIMAL, PRIMAL2, PRIMAL3),
+                                              PRIMAL*PARTIALS2 + PARTIALS3)
+    @test fma(PRIMAL, FDNUM2, PRIMAL3) == Dual(fma(PRIMAL, PRIMAL2, PRIMAL3),
+                                               PRIMAL*PARTIALS2)
+    @test fma(FDNUM, PRIMAL2, FDNUM3) == Dual(fma(PRIMAL, PRIMAL2, PRIMAL3),
+                                              PRIMAL2*PARTIALS + PARTIALS3)
+    @test fma(FDNUM, PRIMAL2, PRIMAL3) == Dual(fma(PRIMAL, PRIMAL2, PRIMAL3),
+                                               PRIMAL2*PARTIALS)
+    @test fma(PRIMAL, PRIMAL2, FDNUM3) == Dual(fma(PRIMAL, PRIMAL2, PRIMAL3), PARTIALS3)
+
     # Unary Functions #
     #-----------------#