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Implemented large a series expansion

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This commit is contained in:
Jacob Hass
2026-01-12 18:04:17 -08:00
parent 1d670c85b4
commit 9086171934
1 changed files with 66 additions and 0 deletions
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66
include/boost/math/special_functions/gamma.hpp
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@@ -1290,6 +1290,33 @@ BOOST_MATH_GPU_ENABLED T incomplete_tgamma_large_x(const T& a, const T& x, const
return result;
}
template <class T>
struct incomplete_tgamma_lower_large_a_series
{
typedef T result_type;
BOOST_MATH_GPU_ENABLED incomplete_tgamma_lower_large_a_series(const T& a, const T& x)
: a_poch(a + 1), z(x), term(1 / a) {}
BOOST_MATH_GPU_ENABLED T operator()()
{
T result = term;
term *= z / a_poch;
a_poch += 1;
return result;
}
T a_poch, z, term;
};
template <class T, class Policy>
T incomplete_tgamma_lower_large_a(const T& a, const T&x, const Policy & pol)
{
BOOST_MATH_STD_USING
incomplete_tgamma_lower_large_a_series<T> s(a, x);
boost::math::uintmax_t max_iter = boost::math::policies::get_max_series_iterations<Policy>();
T result = boost::math::tools::sum_series(s, boost::math::policies::get_epsilon<T, Policy>(), max_iter);
boost::math::policies::check_series_iterations<T>("boost::math::tgamma_p<%1%>(%1%,%1%)", max_iter, pol);
return result;
}
//
// Main incomplete gamma entry point, handles all four incomplete gamma's:
@@ -1813,6 +1840,45 @@ BOOST_MATH_GPU_ENABLED T lgamma_incomplete_imp(T a, T x, const Policy& pol)
return log(gamma_q(a, x, pol));
}
// Calculate log of incomplete gamma function
template <class T, class Policy>
BOOST_MATH_GPU_ENABLED T lgamma_incomplete_lower_imp(T a, T x, const Policy& pol)
{
using namespace boost::math; // temporary until we're in the right namespace
BOOST_MATH_STD_USING_CORE
// Check for invalid inputs (a < 0 or x < 0)
constexpr auto function = "boost::math::lgamma_p<%1%>(%1%, %1%)";
if(a <= 0)
return policies::raise_domain_error<T>(function, "Argument a to the incomplete gamma function must be greater than zero (got a=%1%).", a, pol);
if(x < 0)
return policies::raise_domain_error<T>(function, "Argument x to the incomplete gamma function must be >= 0 (got x=%1%).", x, pol);
// Need to change this to be more appropriate!
if (a > 100){
return log(detail::incomplete_tgamma_lower_large_a(a, x, pol)) + a * log(x) - x - lgamma(a, pol);
}
//
// Can't do better than taking the log of P, but...
//
// Figure out whether we need P or Q, since if we calculate P and it's too close to unity
// we will lose precision in the result, selection logic here is extracted from gamma_incomplete_imp_final:
//
bool need_p = false;
if ((x < 0.5) && (T(-0.4) / log(x) < a))
need_p = true;
else if ((x < 1.1) && (x >= 0.5) && (x * 0.75f < a))
need_p = true;
else if ((x < a) && (x >= 1.1))
need_p = true;
if (need_p)
return log(gamma_p(a, x, pol));
return log1p(-gamma_q(a, x, pol), pol);
}
//
// Ratios of two gamma functions:
//