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Special case x^0 #331

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Merged
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Jul 19, 2018
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Special case x^0 #331

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8 changes: 6 additions & 2 deletions src/dual.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -408,8 +408,12 @@ for f in (:(Base.:^), :(NaNMath.pow))
begin
v = value(x)
expv = ($f)(v, y)
deriv = y * ($f)(v, y - 1)
return Dual{Tx}(expv, deriv * partials(x))
if y == zero(y)
new_partials = zero(partials(x))
else
new_partials = partials(x) * y * ($f)(v, y - 1)
end
return Dual{Tx}(expv, new_partials)
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Looks good. I think the main concern here is performance/SIMDability.

A cleaner way to write this that might be easier on the compiler is

new_partials = ifelse(iszero(y), zero(partials(x)), partials(x) * y * ($f)(v, y - 1))

It'd be worth benchmarking this/looking at generated LLVM code to ensure there aren't any substantial regressions.

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Sure, I'll do some benchmarks.

I guess we can also define Base.literal_pow to do the branching at the compile time for some extra boost. Though it only works for the case exponent is an integer literal.

end,
begin
v = value(y)
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10 changes: 10 additions & 0 deletions test/DualTest.jl
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Expand Up @@ -455,4 +455,14 @@ for N in (0,3), M in (0,4), V in (Int, Float32)
end
end

@testset "Exponentiation of zero" begin
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I thought to mix this with the rest of the test but then can't think of a good way to turn this into a random test. So I created a separated testset. I also noticed that @testset is not used anywhere but I assumed that's only because ForwardDiff.jl predates @testset. I hope using @testset is OK.

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Yup, that's fine.

x0 = 0.0
x1 = Dual{:t1}(x0, 1.0)
x2 = Dual{:t2}(x1, 1.0)
x3 = Dual{:t3}(x2, 1.0)
@test x3^2 === x3 * x3
@test x2^1 === x2
@test x1^0 === Dual{:t1}(1.0, 0.0)
end

end # module