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Adjust recursion when using the Bessel function approximation with large z.

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Avoids hitting tgamma on a negative integer, also improves accuracy when b-a-0.5 is close to a negative integer.
Fixes https://github.com/boostorg/math/issues/1034.
This commit is contained in:
jzmaddock
2023-10-11 11:45:33 +01:00
parent 1722ef9261
commit 2dbd7698cc
2 changed files with 8 additions and 1 deletions
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2
include/boost/math/special_functions/detail/hypergeometric_1F1_large_abz.hpp
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@@ -393,6 +393,8 @@
// So shift b to match a (b shifting seems to be more stable via method of ratios).
//
int b_shift = itrunc(b - a);
if (b_shift < 0)
b_shift -= 2; // Make sure b - a - 0.5 > 0
T b_local = b - b_shift;
T h = boost::math::detail::hypergeometric_1F1_AS_13_3_6(a, b_local, z, T(b_local - a), pol, log_scaling);
return hypergeometric_1F1_shift_on_b(h, a, b_local, z, b_shift, pol, log_scaling);

7
test/test_1F1.hpp
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@@ -162,7 +162,7 @@ void test_spots5(T, const char* type_name)
template <class T>
void test_spots6(T, const char* type_name)
{
static const std::array<std::array<T, 4>, 183> hypergeometric_1F1_bugs = { {
static const std::array<std::array<T, 4>, 186> hypergeometric_1F1_bugs = { {
{ { static_cast<double>(17955.561660766602), static_cast<double>(9.6968994205831605e-09), static_cast<double>(-82.406154185533524), SC_(6.98056008378736714088730927132364938220428678e-11) }},
{ { static_cast<double>(17955.561660766602), static_cast<double>(-9.6968994205831605e-09), static_cast<double>(-82.406154185533524), SC_(-6.98055306629610746072607353939306734740549551e-11) }},
{ { static_cast<double>(-17955.561660766602), static_cast<double>(-9.6968994205831605e-09), static_cast<double>(82.406154185533524), SC_(-42897094853118832762870100.8669248353530950866) }} ,
@@ -390,6 +390,11 @@ void test_spots6(T, const char* type_name)
{ { -28, 28, 28, SC_(-6.2125286411657869483728921158018766e-9) } },
{ { -29, 29, 29, SC_(-1.3521578972057573423569167878458172e-9) } },
{{ -30, 30, 30, SC_(8.2238878884841599031462003461115991e-10) } },
// https://github.com/boostorg/math/issues/1034
{{ 13, 1.5f, 61, SC_(1.35508577094765660270265300640877455638098585524020525369044e39)}},
{{ 13, 1.5f - T(1)/128, 61, SC_(1.40067238333701986992154961431485209677766220602448290643906e39)}},
{{ 13, 1.5f + T(1)/128, 61, SC_(1.31105748771677778012064837998217769289913724450105998963999e39)}},
} };
static const std::array<std::array<T, 4>, 2> hypergeometric_1F1_big_bugs = { {
#if DBL_MAX_EXP == LDBL_MAX_EXP