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Avoid overflow in gamma_inc derivatives #862

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Avoid overflow in gamma_inc derivatives #862

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8 changes: 7 additions & 1 deletion src/dual.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -878,7 +878,13 @@ end
function SpecialFunctions.gamma_inc(a::Real, d::Dual{T,<:Real}, ind::Integer) where {T}
x = value(d)
p, q = SpecialFunctions.gamma_inc(a, x, ind)
∂p = exp(-x) * x^(a - 1) / SpecialFunctions.gamma(a) * partials(d)
logx = log(x)
if isfinite(logx)
∂p = exp(-x + (a - 1) * logx - SpecialFunctions.loggamma(a)) * partials(d)
else
# Preserve the power rule at zero for higher-order derivatives.
∂p = exp(-x) * x^(a - 1) / SpecialFunctions.gamma(a) * partials(d)
end
return (Dual{T}(p, ∂p), Dual{T}(q, -∂p))
end

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12 changes: 12 additions & 0 deletions test/DualTest.jl
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Expand Up @@ -667,6 +667,18 @@ end
# bug fixes #
#############

@testset "gamma_inc derivatives" begin
for V in (Float32, Float64), (a, x) in ((150, 150), (200, 200), (1, 0), (2, 0)), ind in 0:2
# Compute the reference in arbitrary precision to avoid overflowing intermediates.
expected = V(exp(-big(x)) * big(x)^(a - 1) / factorial(big(a - 1)))
p, q = gamma_inc(V(a), Dual{TestTag}(V(x), one(V)), ind)
@test partials(p, 1) ≈ expected
@test partials(q, 1) ≈ -expected
end
@test ForwardDiff.derivative(x -> ForwardDiff.derivative(y -> gamma_inc(2.0, y, 0)[1], x), 0.0) ≈ 1.0
@test ForwardDiff.derivative(x -> ForwardDiff.derivative(y -> gamma_inc(2.0, y, 0)[2], x), 0.0) ≈ -1.0
end

@testset "Exponentiation of zero" begin
x0 = 0.0
x1 = Dual{:t1}(x0, 1.0)
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