#
# 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 Comparable)
#
# 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::**
# Fixnum::quo
# Bignum::**
# Bignum::quo
#
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, "denominator is zero" 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
private_class_method :new
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, "division by zero" 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)
@numerator == other.numerator and @denominator == other.denominator
elsif other.kind_of?(Integer)
self == Rational.new!(other, 1)
elsif other.kind_of?(Float)
Float(self) == other
else
other == self
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
elsif defined? other.coerce
x, y = other.coerce(self)
return x <=> y
else
return nil
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.hash ^ @denominator.hash
end
attr :numerator
attr :denominator
private :initialize
end
class Integer
def numerator
self
end
def denominator
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
undef quo
def quo(other)
Rational.new!(self,1) / other
end
alias rdiv quo
def rpower (other)
if other >= 0
self.power!(other)
else
Rational.new!(self,1)**other
end
end
unless defined? 1.power!
alias power! **
alias ** rpower
end
end
class Bignum
unless defined? Complex
alias power! **
end
undef quo
def quo(other)
Rational.new!(self,1) / other
end
alias rdiv quo
def rpower (other)
if other >= 0
self.power!(other)
else
Rational.new!(self, 1)**other
end
end
unless defined? Complex
alias ** rpower
end
end