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