Class: Rational

Inherits:
Object
  • Object
show all
Defined in:
lib/include/rational.rb

Class Method Summary collapse

Instance Method Summary collapse

Class Method Details

.one ⇒ Object 



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# File 'lib/include/rational.rb', line 2

def self.one
  return Rational(1, 1)
end

.zero ⇒ Object 



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# File 'lib/include/rational.rb', line 6

def self.zero
  return Rational(0, 1)
end

Instance Method Details

#inverse ⇒ Object 



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# File 'lib/include/rational.rb', line 10

def inverse
  return 1 / self
end

#to_ds(length = 64, base = 10) ⇒ Object

to decimal string

Raises:

  • (ArgumentError) 


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# File 'lib/include/rational.rb', line 91

def to_ds(length = 64, base = 10)
  raise ArgumentError, "invalid radix #{base}" if base < 2 or 36 < base

  # initialize

  quotient = []

  n = numerator.to_s(base).split('').map(&:to_i)
  exp = 0
  while 0 == n.last
    n.pop
    exp += 1
  end
  d = denominator
  loop do
    q, r = d.divmod(base)
    break unless 0 == r
    d = q
    exp -= 1
  end
  t = n[0]

  # division loop

  i = 1
  s = nil
  loop do
    q, r = t.divmod(d)
    t = r * base + n[i].to_i

    s = i - 1 if nil == s and q != 0
    quotient.push([q, nil])

    unless n[i]
      if 0 == t
        quotient.last[1] = 0
        break
      end
      break if s and i - s == length
      quotient.last[1] = t
    end

    i += 1
  end

  # format

  zero_count = 0
  while 0 == quotient[0][0]
    zero_count += 1
    if t == quotient.shift[1]
      # rotate 0

      while 0 == quotient[0][0]
        quotient.push(quotient.shift)
        zero_count += 1
      end
      break
    end
  end
  exp += n.size - zero_count

  convert = "0123456789abcdefghijklmnopqrstuvwxyz"
  rslt = "0." + quotient.map{|q| convert[q[0]]}.inject(&:+)
  rslt +=  "e" + exp.to_s unless 0 == exp

  return rslt
end

#to_rds(base = 10) ⇒ Object

to repeating decimal string

Raises:

  • (ArgumentError) 


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# File 'lib/include/rational.rb', line 15

def to_rds(base = 10)
  raise ArgumentError, "invalid radix #{base}" if base < 2 or 36 < base

  # initialize

  quotient = []

  n = numerator.to_s(base).split('').map(&:to_i)
  exp = 0
  while 0 == n.last
    n.pop
    exp += 1
  end
  d = denominator
  loop do
    q, r = d.divmod(base)
    break unless 0 == r
    d = q
    exp -= 1
  end
  t = n[0]

  # division loop

  i = 1
  loop do
    q, r = t.divmod(d)
    t = r * base + n[i].to_i

    quotient.push([q, nil])

    unless n[i]
      if 0 == t
        quotient.last[1] = 0
        break
      end
      break if quotient.map(&:last).include?(t)
      quotient.last[1] = t
    end

    i += 1
  end

  # format

  rslt = "0."

  zero_count = 0
  while 0 == quotient[0][0]
    zero_count += 1
    if t == quotient.shift[1]
      rslt += '('

      # rotate 0

      while 0 == quotient[0][0]
        quotient.push(quotient.shift)
        zero_count += 1
      end
      break
    end
  end
  exp += n.size - zero_count

  convert = "0123456789abcdefghijklmnopqrstuvwxyz"
  if 0 == quotient.last[1]
    rslt += quotient.map{|q| convert[q[0]]}.inject(&:+)
  else
    quotient.each do |q|
      rslt += convert[q[0]]
      rslt += '(' if t == q[1]
    end
    rslt +=  ")"
  end
  rslt +=  "e" + exp.to_s unless 0 == exp

  return rslt
end