Math functions and constants

Collaboration diagram for Math functions and constants:

Files
file	tsgMathUtils.hpp
	Math functions and constants.

Namespaces
namespace	TasGrid::Maths
	Math functions and constants.

Functions
int	TasGrid::Maths::intlog2 (int i)
	Computes std::floor(std::log2(i)), but uses only integer operations.
int	TasGrid::Maths::int2log2 (int i)
	Computes std::pow(2, std::floor(std::log2(i))), but uses only integer operations.
int	TasGrid::Maths::int3log3 (int i)
	Computes std::pow(3, std::floor(std::log(i) / std::log(2))), but uses only integer operations.
int	TasGrid::Maths::pow2 (int p)
	Computes std::pow(2, p), but uses only integer operations.
int	TasGrid::Maths::pow3 (int p)
	Computes std::pow(3, p), but uses only integer operations.
double	TasGrid::Maths::sign (double p)
	Returns +1 or -1 with the same sign as p.

Variables
constexpr double	TasGrid::Maths::pi = 3.14159265358979323846
	Half-period of the std::sin() and std::cos() functions.
constexpr double	TasGrid::Maths::num_tol = 1.E-12
	Numerical tolerance for various algorithms.

Detailed Description

Variable Documentation

pi

constexpr double TasGrid::Maths::pi = 3.14159265358979323846

constexpr

Half-period of the std::sin() and std::cos() functions.

Borrowed from "math.h", let's hope they don't change the value in a future standard.

num_tol

constexpr double TasGrid::Maths::num_tol = 1.E-12

constexpr

Numerical tolerance for various algorithms.

num_tol is used in many places:

• as a stopping criteria for various iterative schemes (e.g., finding leja points)
• drop criteria for eigenvalue solver related to Gauss rules
• comparison between nodes to detect repeated points in non-nested rules (e.g., all odd Chebyshev rules include zero)
• determining sparse matrix pattern, entries smaller than num_tol will be ignored (for wavelet grids)
• drop criteria in estimating anisotropic coefficients (refinement or just the coefficients) surpluses or Legendre coefficients below 10^3 times num_tol will be ignored