gamma.h File Reference

Packet-type friendly implementation of: More...

#include <numeric>
#include "util/poly.h"
#include "util/named.h"

Go to the source code of this file.

Namespaces
namespace	bbm

Functions
template<typename TA , typename TX , size_t MaxTerm = 100>
auto	tgamma_lower (const TA &a, const TX &x)
	Unnormalized incomplete lower gamma function.
template<typename TA , typename TX , size_t MaxTerm = 100>
auto	gamma_p (const TA &a, const TX &x)
	Normalized incomplete lower gamma function.
template<typename TA , typename TX , size_t MaxTerm = 100>
auto	tgamma (const TA &a, const TX &x)
	Unnormalized incomplete upper gamma function.
template<typename TA , typename TX , size_t MaxTerm = 100>
auto	gamma_q (const TA &a, const TX &x)
	Normalized incomplete upper gamma function.
template<typename TA , typename TX , size_t MaxTerm = 100>
auto	gamma_pq (const TA &a, const TX &x)
	Normalized incomplete upper and lower gamma function.

Detailed Description

Packet-type friendly implementation of:

• tgamma_lower : lower unnormalized incomplete gamma
• tgamma : upper unnormalized incomplete gamma
• gamma_p : lower nornalized incomplete gamma
• gamma_q : upper normalized incomplete gamma
• gamma_pq : upper and lower normalized incomplete gamma

Follows for (a < 20) "Numerical Recipes in C++, The Art of Scientific Computing, 2nd ed.", Press et al., p 221, Sec. 6.2.

and

Follow for (a > 20): "The asymptotic expansion of the incomplete gamma functions", Temme [1979]: https://doi.org/10.1137/0510071

The accuracy for x < 1.1 is not optimal, and higher accuracy can be achieved following the additional steps described at https://www.boost.org/doc/libs/1_64_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html