Test data suite for "roots" rubygem written in ruby

rootstest.rb

module Roots
  require 'complex'
  include Math

  def root(n,k=0) # return kth (1..n) value of root n or default for k=0
    raise "Root  n not an integer >  0" unless n.kind_of?(Integer) && n > 0
    raise "Index k not an integer >= 0" unless k.kind_of?(Integer) && k >= 0
    return self if n == 1 || self == 0
    mag = abs**(1.0/n) ; theta = phase/n ; delta = 2*PI/n  # arg <-> phase
    #mag = abs**n**-1 ; theta = arg/n ; delta = 2*PI/n
    return rootn(mag,theta,delta,k>1 ? k-1:0) if kind_of?(Complex)
    return rootn(mag,theta,delta,k-1) if k>0 # kth root of n for any real
    return  mag.round(Roots.digits_to_show) if self > 0 # pos real default
    return -mag.round(Roots.digits_to_show) if n&1 == 1 # neg real default, n odd
    return rootn(mag,theta)    # neg real default, n even, 1st ccw root
  end

  def roots(n,opt=0) #  return array of root n values, [] if no value
    raise "Root n not an integer > 0" unless n.kind_of?(Integer) && n > 0
    raise "Invalid option" unless opt == 0 || opt =~ /^(c|e|i|o|r|C|E|I|O|R)/
    return [self] if n == 1 || self == 0
    mag = abs**(1.0/n) ; theta = phase/n ; delta = 2*PI/n  # arg <-> phase
    #mag = abs**n**-1 ; theta = arg/n ; delta = 2*PI/n
    roots = []
    case opt
    when /^(o|O)/  # odd  roots 1,3,5...
      0.step(n-1,2) {|k| roots << rootn(mag,theta,delta,k)}
    when /^(e|E)/  # even roots 2,4,6...
      1.step(n-1,2) {|k| roots << rootn(mag,theta,delta,k)}
    when /^(r|R)/  # real roots     Complex(x,0) = (x+i0)
      n.times {|k| x=rootn(mag,theta,delta,k); roots << x if x.imag == 0}
    when /^(i|I)/  # imaginry roots Complex(0,y) = (0+iy)
      n.times {|k| x=rootn(mag,theta,delta,k); roots << x if x.real == 0}
    when /^(c|C)/  # complex  roots Complex(x,y) = (x+iy)
      n.times {|k| x=rootn(mag,theta,delta,k); roots << x if x.arg*2 % PI != 0}
    else           # all n roots
      n.times {|k| roots << rootn(mag,theta,delta,k)}
    end
    return roots
  end

  private # not accessible as methods in mixin class
  # Alias sin|cos to fix C lib errors to get 0.0 values for X|Y axis angles.
  def sine(x);   cos(x).abs == 1 ? 0 : sin(x) end
  def cosine(x); sin(x).abs == 1 ? 0 : cos(x) end
  def self.digits_to_show(n = @digits_to_show || 8)
    @digits_to_show = n < 1 ? 1 : n
  end

  def rootn(mag,theta,delta=0,k=0) # root k of n of real|complex
    angle_n = theta + k*delta
    x = mag*Complex(cosine(angle_n),sine(angle_n))
    Complex(x.real.round(Roots.digits_to_show), x.imag.round(Roots.digits_to_show))
  end
end

# Mixin 'root' and 'roots' as methods for all number classes.
class Numeric; include Roots end

puts "------------ Start Tests ------------"

Roots.digits_to_show 8
puts "Digits To Show = #{Roots.digits_to_show}"

puts 13.root 1

puts 2**(-2.0)
puts -2**(-3.0)
puts (-2)**(-3.0)
puts -2**(4)
puts (-2)**(4)
puts 100.root 2

puts 77.root 5
puts 77.root 5,1
puts 77.root 5,2
puts 77.root 5,3
puts 77.root 5,4
puts 77.root 5,5

puts 100.root 2
puts 100.root 2,1
puts 100.root 2,2
p  16.roots 4
p  64.roots 6
puts -8.root 3
p -8.roots 3

puts "------------ 1 ------------"

p (64.0).roots 6
p 64.to_f.roots 6

puts 1838384743734228.root 23
puts 1838384743734228.root 23, 10

p 32313.roots 10, "c"
p 32313.roots 10, "o"
p 32313.roots 10, "e"
p 32313.roots 10, "imag"
p 32313.roots 10, "real"
p 32313.roots 4, "i"

p (b = 4213.roots(8))
p b.map{|i| i.to_s}

puts b[1].class
puts b[3]
puts b[3].to_s

p Complex(1,1).roots(4).map(&:to_s)
puts Complex(3,-9).root(5,3)
puts Complex(3,-9).root(5,3).class
puts Complex(3,19).root 7,4
puts (3 + 19i).root 7,4     # not valid in crystal
puts (3 - 19.i).root 3,2  

puts "------------ 2 ------------"

[2,3.0,-59,911010101113,Complex(-3,48),-97.25].each{|n| p n.root(7)}

p Complex(1,1).roots 4
p Complex(1,1).roots(4).map(&:to_s)
p Complex(1,1).roots(4)[1]
p Complex(1,1).roots 4

#puts 82.root 0
puts 82.root 1, 0
p 82.roots 2, "e"

puts "------------ 3 ------------"

puts 9.root(2)
put -32.root 5,3
puts (-32).root(5,3)
puts 73.root 6
puts 73.root 6,0
puts 73.root 6,1
puts 73.root 6,2
puts 73.root 6,3
puts 73.root 6,4
puts 73.root 6,5
puts 73.root 6,6
puts (-100.43).root 6,6
puts Complex(3,19).root 7,4

puts 625.roots(10,"r")[1]
p 625.roots(10,"c").size

puts "------------ 4 ------------"

p 934813.roots(3)
p 503321.roots 8, "R"
p -89.roots(4,"real")
p (2.2).roots 3,"Im"
p 64.roots 6,"Cmp"
p Complex(23,7.5).roots 3, "odd"
p Complex(3.21,9).roots 5, "evn"

a = Complex(2,0) #503321.roots(8, "R")[1]

puts a*a*a*a*a*a*a*a
puts Complex(2,9).abs

puts "------------ 5 ------------"

puts 10.root(5,3).abs.round 8

puts Roots.digits_to_show
puts 10.root 4
puts Roots.digits_to_show 9
puts 10.root 4
puts Roots.digits_to_show 10
puts 10.root 4
puts Roots.digits_to_show 11
puts 10.root 4
puts Roots.digits_to_show 12
puts 10.root 4
puts -10.root(4)

puts "------------ 6 ------------"

puts (10 ** 0.25).round 5
puts Complex(1.3233439490191, 534).real
puts Complex(1.3233439490191, 534).real.round 1
puts Complex(1.3233439490191, 534).real.round 2
puts Complex(1.3233439490191, 534).real.round 3
puts Complex(1.3233439490191, 534).real.round 4
puts Complex(1.3233439490191, 534).real.round 5
puts Complex(1.3233439490191, 534).real.round 6
puts Complex(1.3233439490191, 534).real.round 7
puts Complex(1.3233439490191, 534).real.round 8
puts Complex(1.3233439490191, 534).real.round 9
puts Complex(1.3233439490191, 534).real.round 10
puts Complex(1.3233439490191, 534).real.round 11
puts Complex(1.3233439490191, 534).real.round 12
puts Complex(1.3233439490191, 534).real.round 13
puts Complex(1.3233439490191, 534).real.round 14