use SIMD.jl for explicit vectorization of partial operations

.github/workflows/ci.yml

@@ -16,7 +16,6 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - '1.0'
           - '1'
           - 'nightly'
         os:

Project.toml

@@ -12,6 +12,7 @@ NaNMath = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
 Preferences = "21216c6a-2e73-6563-6e65-726566657250"
 Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+SIMD = "fdea26ae-647d-5447-a871-4b548cad5224"
 SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 
@@ -24,9 +25,10 @@ DiffTests = "0.0.1, 0.1"
 LogExpFunctions = "0.3"
 NaNMath = "0.2.2, 0.3"
 Preferences = "1"
+SIMD = "3"
 SpecialFunctions = "0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.10, 1.0"
 StaticArrays = "0.8.3, 0.9, 0.10, 0.11, 0.12, 1.0"
-julia = "1"
+julia = "1.6"
 
 [extras]
 Calculus = "49dc2e85-a5d0-5ad3-a950-438e2897f1b9"

src/partials.jl

@@ -197,29 +197,32 @@ end
     return tupexpr(i -> :(rand(V)), N)
 end
 
-@generated function scale_tuple(tup::NTuple{N}, x) where N
-    return tupexpr(i -> :(tup[$i] * x), N)
-end
-
-@generated function div_tuple_by_scalar(tup::NTuple{N}, x) where N
-    return tupexpr(i -> :(tup[$i] / x), N)
-end
-
-@generated function add_tuples(a::NTuple{N}, b::NTuple{N})  where N
-    return tupexpr(i -> :(a[$i] + b[$i]), N)
-end
 
-@generated function sub_tuples(a::NTuple{N}, b::NTuple{N})  where N
-    return tupexpr(i -> :(a[$i] - b[$i]), N)
-end
-
-@generated function minus_tuple(tup::NTuple{N}) where N
-    return tupexpr(i -> :(-tup[$i]), N)
-end
-
-@generated function mul_tuples(a::NTuple{N}, b::NTuple{N}, afactor, bfactor) where N
-    return tupexpr(i -> :((afactor * a[$i]) + (bfactor * b[$i])), N)
-end
+const SIMDFloat = Union{Float64, Float32}
+const SIMDInt = Union{
+                       Int128, Int64, Int32, Int16, Int8,
+                       UInt128, UInt64, UInt32, UInt16, UInt8,
+                     }
+const SIMDType = Union{SIMDFloat, SIMDInt}
+const NT{N,T} = NTuple{N,T}
+using SIMD
+
+# SIMD implementation
+add_tuples(a::NT{N,T}, b::NT{N,T})               where {N, T<:SIMDType}  = Tuple(Vec(a) + Vec(b))
+sub_tuples(a::NT{N,T}, b::NT{N,T})               where {N, T<:SIMDType}  = Tuple(Vec(a) - Vec(b))
+scale_tuple(tup::NT{N,T}, x::T)                  where {N, T<:SIMDType}  = Tuple(Vec(tup) * x)
+div_tuple_by_scalar(tup::NT{N,T}, x::T)          where {N, T<:SIMDFloat} = Tuple(Vec(tup) / x)
+minus_tuple(tup::NT{N,T})                        where {N, T<:SIMDType}  = Tuple(-Vec(tup))
+mul_tuples(a::NT{N,T}, b::NT{N,T}, af::T, bf::T) where {N, T<:SIMDType}  = Tuple(muladd(Vec{N,T}(af), Vec(a), Vec{N,T}(bf) * Vec(b)))
+
+
+# Fallback implementations
+@generated add_tuples(a::NT{N}, b::NT{N})         where N = tupexpr(i -> :(a[$i] + b[$i]), N)
+@generated sub_tuples(a::NT{N}, b::NT{N})         where N = tupexpr(i -> :(a[$i] - b[$i]), N)
+@generated scale_tuple(tup::NT{N}, x)             where N = tupexpr(i -> :(tup[$i] * x), N)
+@generated div_tuple_by_scalar(tup::NT{N}, x)     where N = tupexpr(i -> :(tup[$i] / x), N)
+@generated minus_tuple(tup::NT{N})                where N = tupexpr(i -> :(-tup[$i]), N)
+@generated mul_tuples(a::NT{N}, b::NT{N}, af, bf) where N = tupexpr(i -> :((af * a[$i]) + (bf * b[$i])), N)
 
 ###################
 # Pretty Printing #

test/PartialsTest.jl

@@ -114,7 +114,7 @@ for N in (0, 3), T in (Int, Float32, Float64)
 
     if N > 0
         @test ForwardDiff._div_partials(PARTIALS, PARTIALS2, X, Y) == ForwardDiff._mul_partials(PARTIALS, PARTIALS2, inv(Y), -X/(Y^2))
-        @test ForwardDiff._mul_partials(PARTIALS, PARTIALS2, X, Y).values == map((a, b) -> (X * a) + (Y * b), VALUES, VALUES2)
+        @test all(isapprox.(ForwardDiff._mul_partials(PARTIALS, PARTIALS2, X, Y).values, map((a, b) -> (X * a) + (Y * b), VALUES, VALUES2)))
         @test ForwardDiff._mul_partials(ZERO_PARTIALS, PARTIALS, X, Y) == Y * PARTIALS
         @test ForwardDiff._mul_partials(PARTIALS, ZERO_PARTIALS, X, Y) == X * PARTIALS