module Mathematics

# File lib/mathematics.rb, line 50
def self.add *a
  a.reduce :+
end

# File lib/mathematics.rb, line 64
def self.average *a
  1.0 * (a.reduce :+) / a.size
end

# File lib/mathematics.rb, line 68
def self.avg *a
  average *a
end

# File lib/mathematics.rb, line 148
def self.binomial_coefficient n, k
  if k < 0 or k > n
    0
  elsif k == 0 or n == k
    1
  else
    c = 1
    (1..k).each do |i|
      c *= n - k + i
      c /= i
    end
    c
  end
end

# File lib/mathematics.rb, line 176
def self.cos radians
  degrees = (radians / Math::PI * 180) % 360 # think in degrees for ease
  @cos_hash[degrees] || Math.cos(radians)
end

# File lib/mathematics.rb, line 26
def self.desc
  describe
end

# File lib/mathematics.rb, line 22
def self.describe
  "Wrapper around Math module; Has additional methods."
end

# File lib/mathematics.rb, line 128
def self.fact n
  factorial n
end

# File lib/mathematics.rb, line 122
def self.factorial n # uses "Prior Knowledge" paradigm
  h = { 0=>1, 1=>1, 2=>2, 3=>6, 4=>24, 5=>120,
    6=>720, 7=>5040, 8=>40320, 9=>362880, 10=>3628800 }
  n < 0 ? nil : (h[n] || n * factorial(n-1))
end

# File lib/mathematics.rb, line 38
def self.max *a
  a.max
end

# File lib/mathematics.rb, line 72
def self.mean *a
  average *a
end

# File lib/mathematics.rb, line 78
def self.median *a
  a.sort!
  n = a.size
  n.odd? ? a[(n-1)/2] : avg(1.0 * a[n/2], a[n/2-1])
end

# File lib/mathematics.rb, line 197
def self.method_missing m, *a
end

# File lib/mathematics.rb, line 32
def self.min *a
  a.min
end

# File lib/mathematics.rb, line 44
def self.minmax *a
  a.minmax
end

# File lib/mathematics.rb, line 86
def self.mode *a
  h = Hash.new(0)
  a.each { |e| h[e] = h[e] + 1 }
  (h.sort_by &:last).last[0]
end

# File lib/mathematics.rb, line 94
def self.range *a
  (max *a) - (min *a)
end

# File lib/mathematics.rb, line 116
def self.sd *a
  stddev *a
end

# File lib/mathematics.rb, line 167
def self.sin radians
  degrees = (radians / Math::PI * 180) % 360 # think in degrees for ease
  @sin_hash[degrees] || Math.sin(radians)
end

# File lib/mathematics.rb, line 112
def self.stddev *a
  Math.sqrt(variance *a)
end

# File lib/mathematics.rb, line 54
def self.sum *a
  add *a
end

# File lib/mathematics.rb, line 186
def self.tan radians
  degrees = (radians / Math::PI * 180) % 360 # think in degrees for ease
  # to deal with 45, 135, 225, 315 ...
  quantum = 1.0e-12
  degrees = degrees.ceil if degrees.ceil - degrees < quantum
  degrees = degrees.floor if degrees - degrees.floor < quantum
  @tan_hash[degrees] || Math.tan(radians)
end

# File lib/mathematics.rb, line 58
def self.total *a
  add *a
end

# File lib/mathematics.rb, line 142
def self.triangle_number n
  triangular_number n
end

# File lib/mathematics.rb, line 134
def self.triangular_number n # uses "Prior Knowledge" paradigm
  h = { 1=>1, 2=>3, 3=>6, 4=>10, 5=>15, 6=>21,
  7=>28, 8=>36, 9=>45, 10=>55, 11=>66, 12=>78, 13=>91 }
  n < 1 ? nil : (h[n] || n*(n+1)/2)
end

# File lib/mathematics.rb, line 106
def self.var *a
  variance *a
end

# File lib/mathematics.rb, line 100
def self.variance *a
  m = mean *a
  b = a.map { |e| (e-m)*(e-m) } # / a.size
  b.inject { |s,e| s+e } / b.size
end