#!/usr/bin/env ruby
# -*- encoding: utf-8 -*-
# Copyright Steffie Dorn <mail@muflax.com>, 2018
# License: GNU APGLv3 (or later) <http://www.gnu.org/copyleft/gpl.html>

module Math
  class << self
    def harmonic n
      (1..n).reduce(0.0){|s, i| s + (1.0 / i)}
    end

    def zipf k, n
      1.0 / (k.to_f * harmonic(n))
    end

    def tolerance total
      θ = total / Math.log(total)
      θ > total ? total : θ.round
    end
    alias :tolerate	:tolerance
    alias :θ       	:tolerance

    # TODO meh iterative solution
    def sufficiency exceptions
      n = 1
      n += 1 while θ(n) < exceptions
      n
    end
    alias :sufficient :sufficiency

    def factorial n
      (2..n).reduce(1){|f, x| f * x}
    end

    def choose k, n
      Math.factorial(n) / (Math.factorial(k) * Math.factorial(n - k))
    end

    def mass_index coeff, mass, height, adjustment=1.0
      h /= 100.0 if (50..300).include? h # cm -> m auto-correction
      adjustment * (mass / (height ** coeff))
    end

    def mass_index_at coeff, index, height, adjustment=1.0
      h /= 100.0 if (50..300).include? h # cm -> m auto-correction
      index * (height ** coeff) / adjustment
    end

    def bmi    	m, h	; mass_index 2.0, m, h     	; end
    def bmi_adj	m, h	; mass_index 2.5, m, h, 1.3	; end
    def bsi    	m, h	; mass_index 3.0, m, h     	; end

    def bmi_at    	i, h	; mass_index_at 2.0, i, h     	; end
    def bmi_adj_at	i, h	; mass_index_at 2.5, i, h, 1.3	; end
    def bsi_at    	i, h	; mass_index_at 3.0, i, h     	; end
  end
end