# # rational.rb - # \$Release Version: 0.5 \$ # \$Revision: 1.7 \$ # \$Date: 1999/08/24 12:49:28 \$ # by Keiju ISHITSUKA(SHL Japan Inc.) # # -- # Usage: # class Rational < Numeric # (include Compareable) # # Rational(a, b) --> a/b # # Rational::+ # Rational::- # Rational::* # Rational::/ # Rational::** # Rational::% # Rational::divmod # Rational::abs # Rational::<=> # Rational::to_i # Rational::to_f # Rational::to_s # # Integer::gcd # Integer::lcm # Integer::gcdlcm # Integer::to_r # # Fixnum::** # Bignum::** # # def Rational(a, b = 1) if a.kind_of?(Rational) && b == 1 a else Rational.reduce(a, b) end end class Rational < Numeric @RCS_ID='-\$Id: rational.rb,v 1.7 1999/08/24 12:49:28 keiju Exp keiju \$-' def Rational.reduce(num, den = 1) raise ZeroDivisionError, "denometor is 0" if den == 0 if den < 0 num = -num den = -den end gcd = num.gcd(den) num = num.div(gcd) den = den.div(gcd) if den == 1 && defined?(Unify) num else new!(num, den) end end def Rational.new!(num, den = 1) new(num, den) end def initialize(num, den) if den < 0 num = -num den = -den end if num.kind_of?(Integer) and den.kind_of?(Integer) @numerator = num @denominator = den else @numerator = num.to_i @denominator = den.to_i end end def + (a) if a.kind_of?(Rational) num = @numerator * a.denominator num_a = a.numerator * @denominator Rational(num + num_a, @denominator * a.denominator) elsif a.kind_of?(Integer) self + Rational.new!(a, 1) elsif a.kind_of?(Float) Float(self) + a else x , y = a.coerce(self) x + y end end def - (a) if a.kind_of?(Rational) num = @numerator * a.denominator num_a = a.numerator * @denominator Rational(num - num_a, @denominator*a.denominator) elsif a.kind_of?(Integer) self - Rational.new!(a, 1) elsif a.kind_of?(Float) Float(self) - a else x , y = a.coerce(self) x - y end end def * (a) if a.kind_of?(Rational) num = @numerator * a.numerator den = @denominator * a.denominator Rational(num, den) elsif a.kind_of?(Integer) self * Rational.new!(a, 1) elsif a.kind_of?(Float) Float(self) * a else x , y = a.coerce(self) x * y end end def / (a) if a.kind_of?(Rational) num = @numerator * a.denominator den = @denominator * a.numerator Rational(num, den) elsif a.kind_of?(Integer) raise ZeroDivisionError, "devided by 0" if a == 0 self / Rational.new!(a, 1) elsif a.kind_of?(Float) Float(self) / a else x , y = a.coerce(self) x / y end end def ** (other) if other.kind_of?(Rational) Float(self) ** other elsif other.kind_of?(Integer) if other > 0 num = @numerator ** other den = @denominator ** other elsif other < 0 num = @denominator ** -other den = @numerator ** -other elsif other == 0 num = 1 den = 1 end Rational.new!(num, den) elsif other.kind_of?(Float) Float(self) ** other else x , y = other.coerce(self) x ** y end end def % (other) value = (self / other).to_i return self - other * value end def divmod(other) value = (self / other).to_i return value, self - other * value end def abs if @numerator > 0 Rational.new!(@numerator, @denominator) else Rational.new!(-@numerator, @denominator) end end def <=> (other) if other.kind_of?(Rational) num = @numerator * other.denominator num_a = other.numerator * @denominator v = num - num_a if v > 0 return 1 elsif v < 0 return -1 else return 0 end elsif other.kind_of?(Integer) return self <=> Rational.new!(other, 1) elsif other.kind_of?(Float) return Float(self) <=> other else x , y = other.coerce(self) return x <=> y end end def coerce(other) if other.kind_of?(Float) return other, self.to_f elsif other.kind_of?(Integer) return Rational.new!(other, 1), self else super end end def to_i Integer(@numerator.div(@denominator)) end def to_f @numerator.to_f/@denominator.to_f end def to_s if @denominator == 1 @numerator.to_s else @numerator.to_s+"/"+@denominator.to_s end end def to_r self end def inspect sprintf("Rational(%s, %s)", @numerator.inspect, @denominator.inspect) end def hash @numerator ^ @denominator end attr :numerator attr :denominator private :initialize end class Integer def numerator self end def denomerator 1 end def to_r Rational(self, 1) end def gcd(n) m = self.abs n = n.abs return n if m == 0 return m if n == 0 b = 0 while n[0] == 0 && m[0] == 0 b += 1; n >>= 1; m >>= 1 end m >>= 1 while m[0] == 0 n >>= 1 while n[0] == 0 while m != n m, n = n, m if n > m m -= n; m >>= 1 while m[0] == 0 end m << b end def gcd2(int) a = self.abs b = int.abs a, b = b, a if a < b while b != 0 void, a = a.divmod(b) a, b = b, a end return a end def lcm(int) a = self.abs b = int.abs gcd = a.gcd(b) (a.div(gcd)) * b end def gcdlcm(int) a = self.abs b = int.abs gcd = a.gcd(b) return gcd, (a.div(gcd)) * b end end class Fixnum alias div! /; def div(other) if other.kind_of?(Fixnum) self.div!(other) elsif other.kind_of?(Bignum) x, y = other.coerce(self) x.div!(y) else x, y = other.coerce(self) x / y end end # alias divmod! divmod if not defined? Complex alias power! **; end # def rdiv(other) # if other.kind_of?(Fixnum) # Rational(self, other) # elsif # x, y = other.coerce(self) # if defined?(x.div()) # x.div(y) # else # x / y # end # end # end def rdiv(other) Rational.new!(self,1) / other end def rpower (other) if other >= 0 self.power!(other) else Rational.new!(self,1)**other end end if not defined? Complex alias ** rpower end end class Bignum alias div! /; alias div /; alias divmod! divmod if not defined? power! alias power! ** end def rdiv(other) Rational.new!(self,1) / other end def rpower (other) if other >= 0 self.power!(other) else Rational.new!(self, 1)**other end end if not defined? Complex alias ** rpower end end