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 Summary collapse

Class Method Details

.stieltjes_factorial(x) ⇒ Object

Valid upto 11 digits



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# File 'lib/distribution/math_extension.rb', line 187

def self.stieltjes_factorial(x)
 y = x; _p = 1;
   while y < 8 do 
     _p = _p*y; y = y+1
   end
 lr= stieltjes_ln_factorial(y)
 r = Math.exp(lr)
 #puts "valid: #{5/2.0+(13/2.0)*Math::log(x)}" 
 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 



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# File 'lib/distribution/math_extension.rb', line 163

def self.stieltjes_ln_factorial(z)
 
  a0 = 1.quo(12); a1 = 1.quo(30); a2 = 53.quo(210); a3 = 195.quo(371);
  a4 = 22999.quo(22737); a5 = 29944523.quo(19733142);
  a6 = 109535241009.quo(48264275462);
  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 



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# File 'lib/distribution/math_extension.rb', line 174

def self.stieltjes_ln_factorial_big(z)
 
  a0 = 1/12.0; a1 = 1/30.0; a2 = 53/210.0; a3 = 195/371.0;
  a4 = 22999/22737.0; a5 = 29944523/19733142.0;
  a6 = 109535241009/48264275462.0;
  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