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Diffstat (limited to 'lib/rational.rb')
| -rw-r--r-- | lib/rational.rb | 361 |
1 files changed, 361 insertions, 0 deletions
diff --git a/lib/rational.rb b/lib/rational.rb new file mode 100644 index 0000000000..d4112c2956 --- /dev/null +++ b/lib/rational.rb @@ -0,0 +1,361 @@ +# +# rational.rb - +# $Release Version: 0.5 $ +# $Revision: 1.1 $ +# $Date: 1996/11/11 04:25:14 $ +# 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 + def Rational.reduce(num, den = 1) + 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 + @denoninator = 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) + 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 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(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 + |