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Ensure Igamma does not NaN or Inf for large values.

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This commit is contained in:
Srinivas Vasudevan
2020-01-14 21:32:48 +00:00
committed by Rasmus Munk Larsen
parent 6601abce86
commit f6c6de5d63
2 changed files with 48 additions and 5 deletions
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38
unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsImpl.h
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@@ -713,6 +713,18 @@ struct cephes_helper<double> {
enum IgammaComputationMode { VALUE, DERIVATIVE, SAMPLE_DERIVATIVE };
template <typename Scalar>
static EIGEN_STRONG_INLINE Scalar main_igamma_term(Scalar a, Scalar x) {
/* Compute x**a * exp(-x) / gamma(a) */
Scalar logax = a * numext::log(x) - x - lgamma_impl<Scalar>::run(a);
if (logax < -numext::log(NumTraits<Scalar>::highest()) ||
// Assuming x and a aren't Nan.
(numext::isnan)(logax)) {
return Scalar(0);
}
return numext::exp(logax);
}
template <typename Scalar, IgammaComputationMode mode>
EIGEN_DEVICE_FUNC
int igamma_num_iterations() {
@@ -755,6 +767,15 @@ struct igammac_cf_impl {
return zero;
}
Scalar ax = main_igamma_term<Scalar>(a, x);
// This is independent of mode. If this value is zero,
// then the function value is zero. If the function value is zero,
// then we are in a neighborhood where the function value evalutes to zero,
// so the derivative is zero.
if (ax == zero) {
return zero;
}
// continued fraction
Scalar y = one - a;
Scalar z = x + y + one;
@@ -825,9 +846,7 @@ struct igammac_cf_impl {
}
/* Compute x**a * exp(-x) / gamma(a) */
Scalar logax = a * numext::log(x) - x - lgamma_impl<Scalar>::run(a);
Scalar dlogax_da = numext::log(x) - digamma_impl<Scalar>::run(a);
Scalar ax = numext::exp(logax);
Scalar dax_da = ax * dlogax_da;
switch (mode) {
@@ -858,6 +877,18 @@ struct igamma_series_impl {
const Scalar one = 1;
const Scalar machep = cephes_helper<Scalar>::machep();
Scalar ax = main_igamma_term<Scalar>(a, x);
// This is independent of mode. If this value is zero,
// then the function value is zero. If the function value is zero,
// then we are in a neighborhood where the function value evalutes to zero,
// so the derivative is zero.
if (ax == zero) {
return zero;
}
ax /= a;
/* power series */
Scalar r = a;
Scalar c = one;
@@ -886,10 +917,7 @@ struct igamma_series_impl {
}
}
/* Compute x**a * exp(-x) / gamma(a + 1) */
Scalar logax = a * numext::log(x) - x - lgamma_impl<Scalar>::run(a + one);
Scalar dlogax_da = numext::log(x) - digamma_impl<Scalar>::run(a + one);
Scalar ax = numext::exp(logax);
Scalar dax_da = ax * dlogax_da;
switch (mode) {