Module: MoreMath::Constants::FunctionsConstants

Included in:: NormalDistribution

Defined in:: lib/more_math/constants/functions_constants.rb

Overview

Module containing mathematical constants used in function implementations

Constant Summary collapse

LANCZOS_COEFFICIENTS =

Note:

These values are precomputed for optimal accuracy in the Lanczos approximation algorithm

Lanczos coefficients for gamma function approximation

These coefficients are part of the Lanczos approximation formula, which provides a highly accurate method for computing the logarithm of the gamma function. The Lanczos method is particularly effective for maintaining numerical stability across a wide range of inputs.

[
  0.99999999999999709182,
  57.156235665862923517,
  -59.597960355475491248,
  14.136097974741747174,
  -0.49191381609762019978,
  0.33994649984811888699e-4,
  0.46523628927048575665e-4,
  -0.98374475304879564677e-4,
  0.15808870322491248884e-3,
  -0.21026444172410488319e-3,
  0.21743961811521264320e-3,
  -0.16431810653676389022e-3,
  0.84418223983852743293e-4,
  -0.26190838401581408670e-4,
  0.36899182659531622704e-5,
]

HALF_LOG_2_PI =

Note:

This value appears in the Lanczos approximation formula and other mathematical identities involving the gamma function

Precomputed value of half the natural logarithm of 2π

This constant is used in Stirling’s approximation and various statistical calculations. It’s computed as:

0.5 * Math.log(2 * Math::PI)

0.5 * Math.log(2 * Math::PI)

ERF_A = Parameter for error function approximation This constant is used in the rational approximation of the error function. It’s derived from the relationship: ERF_A = -8 * (Math::PI - 3) / (3 * Math::PI * (Math::PI - 4)) The value helps optimize the accuracy of the erf approximation for a wide range of input values

-8 * (Math::PI - 3) / (3 * Math::PI * (Math::PI - 4))

ROOT2 = Square root of 2 This constant is frequently used in statistics and probability, particularly in the normal distribution and error function calculations.

Math.sqrt(2)