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FMA all the way down #207

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8ee80d1
fix wrong partials multiplied in FMA
KristofferC Mar 18, 2017
2a6d95a
use more fma
KristofferC Mar 18, 2017
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25 changes: 15 additions & 10 deletions src/dual.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -410,23 +410,28 @@ 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))
@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)
vx, vy = value(x), value(y)
result = fma(vx, vy, z)
return Dual(result, _mul_partials(partials(x), partials(y), vx, vy))
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)
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28 changes: 15 additions & 13 deletions test/DualTest.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -15,6 +15,8 @@ samerng() = MersenneTwister(1)
# exponent by one
intrand(T) = T == Int ? rand(2:10) : rand(T)

dualapprox(A, B) = value(A) ≈ value(B) && partials(A) ≈ partials(B)

# fix testing issue with Base.hypot(::Int...) undefined in 0.4
if v"0.4" <= VERSION < v"0.5"
Base.hypot(x::Int, y::Int) = Base.hypot(Float64(x), Float64(y))
Expand Down Expand Up @@ -387,20 +389,20 @@ 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),
@test dualapprox(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)
PARTIALS3))
@test dualapprox(fma(FDNUM, FDNUM2, PRIMAL3), Dual(fma(PRIMAL, PRIMAL2, PRIMAL3),
PRIMAL*PARTIALS2 + PRIMAL2*PARTIALS))
@test dualapprox(fma(PRIMAL, FDNUM2, FDNUM3), Dual(fma(PRIMAL, PRIMAL2, PRIMAL3),
PRIMAL*PARTIALS2 + PARTIALS3))
@test dualapprox(fma(PRIMAL, FDNUM2, PRIMAL3), Dual(fma(PRIMAL, PRIMAL2, PRIMAL3),
PRIMAL*PARTIALS2))
@test dualapprox(fma(FDNUM, PRIMAL2, FDNUM3), Dual(fma(PRIMAL, PRIMAL2, PRIMAL3),
PRIMAL2*PARTIALS + PARTIALS3))
@test dualapprox(fma(FDNUM, PRIMAL2, PRIMAL3), Dual(fma(PRIMAL, PRIMAL2, PRIMAL3),
PRIMAL2*PARTIALS))
@test dualapprox(fma(PRIMAL, PRIMAL2, FDNUM3), Dual(fma(PRIMAL, PRIMAL2, PRIMAL3), PARTIALS3))

# Unary Functions #
#-----------------#
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