# Module: Distribution::MathExtension::ApproxFactorial

Defined in:
lib/distribution/math_extension.rb

## Overview

Module to calculate approximated factorial Based (again) on Luschny formula, with 16 digits of precision == Reference

## Class Method Details

### .stieltjes_factorial(x) ⇒ Object

Valid upto 11 digits

 ``` 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157``` ```# File 'lib/distribution/math_extension.rb', line 140 def stieltjes_factorial(x) y = x _p = 1 _p *= y; y += 1 while y < 8 lr = stieltjes_ln_factorial(y) r = Math.exp(lr) if r.infinite? r = BigMath.exp(BigDecimal(lr.to_s), 20) r = (r * x) / (_p * y) if x < 8 r = r.to_i else r = (r * x) / (_p * y) if x < 8 end r end```

### .stieltjes_ln_factorial(z) ⇒ Object

 ``` 118 119 120 121 122 123 124 125 126``` ```# File 'lib/distribution/math_extension.rb', line 118 def stieltjes_ln_factorial(z) a0 = 1.quo(12); a1 = 1.quo(30); a2 = 53.quo(210); a3 = 195.quo(371) a4 = 22_999.quo(22_737); a5 = 29_944_523.quo(19_733_142) a6 = 109_535_241_009.quo(48_264_275_462) zz = z + 1 (1.quo(2)) * Math.log(2 * Math::PI) + (zz - 1.quo(2)) * Math.log(zz) - zz + a0.quo(zz + a1.quo(zz + a2.quo(zz + a3.quo(zz + a4.quo(zz + a5.quo(zz + a6.quo(zz))))))) end```

### .stieltjes_ln_factorial_big(z) ⇒ Object

 ``` 128 129 130 131 132 133 134 135 136 137``` ```# File 'lib/distribution/math_extension.rb', line 128 def stieltjes_ln_factorial_big(z) a0 = 1 / 12.0; a1 = 1 / 30.0; a2 = 53 / 210.0; a3 = 195 / 371.0 a4 = 22_999 / 22_737.0; a5 = 29_944_523 / 19_733_142.0 a6 = 109_535_241_009 / 48_264_275_462.0 zz = z + 1 BigDecimal('0.5') * BigMath.log(BigDecimal('2') * BigMath::PI(20), 20) + BigDecimal((zz - 0.5).to_s) * BigMath.log(BigDecimal(zz.to_s), 20) - BigDecimal(zz.to_s) + BigDecimal(( a0 / (zz + a1 / (zz + a2 / (zz + a3 / (zz + a4 / (zz + a5 / (zz + a6 / zz)))))) ).to_s) end```