528 lines
12 KiB
Ruby
528 lines
12 KiB
Ruby
#
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# rational.rb -
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# $Release Version: 0.5 $
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# $Revision: 1.7 $
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# $Date: 1999/08/24 12:49:28 $
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# by Keiju ISHITSUKA(SHL Japan Inc.)
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#
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# Documentation by Kevin Jackson and Gavin Sinclair.
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#
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# When you <tt>require 'rational'</tt>, all interactions between numbers
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# potentially return a rational result. For example:
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#
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# 1.quo(2) # -> 0.5
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# require 'rational'
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# 1.quo(2) # -> Rational(1,2)
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#
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# See Rational for full documentation.
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#
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#
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# Creates a Rational number (i.e. a fraction). +a+ and +b+ should be Integers:
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#
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# Rational(1,3) # -> 1/3
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#
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# Note: trying to construct a Rational with floating point or real values
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# produces errors:
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#
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# Rational(1.1, 2.3) # -> NoMethodError
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#
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def Rational(a, b = 1)
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if a.kind_of?(Rational) && b == 1
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a
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else
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Rational.reduce(a, b)
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end
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end
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#
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# Rational implements a rational class for numbers.
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#
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# <em>A rational number is a number that can be expressed as a fraction p/q
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# where p and q are integers and q != 0. A rational number p/q is said to have
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# numerator p and denominator q. Numbers that are not rational are called
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# irrational numbers.</em> (http://mathworld.wolfram.com/RationalNumber.html)
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#
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# To create a Rational Number:
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# Rational(a,b) # -> a/b
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# Rational.new!(a,b) # -> a/b
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#
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# Examples:
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# Rational(5,6) # -> 5/6
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# Rational(5) # -> 5/1
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#
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# Rational numbers are reduced to their lowest terms:
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# Rational(6,10) # -> 3/5
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#
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# But not if you use the unusual method "new!":
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# Rational.new!(6,10) # -> 6/10
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#
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# Division by zero is obviously not allowed:
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# Rational(3,0) # -> ZeroDivisionError
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#
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class Rational < Numeric
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@RCS_ID='-$Id: rational.rb,v 1.7 1999/08/24 12:49:28 keiju Exp keiju $-'
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#
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# Reduces the given numerator and denominator to their lowest terms. Use
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# Rational() instead.
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#
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def Rational.reduce(num, den = 1)
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raise ZeroDivisionError, "denominator is zero" if den == 0
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if den < 0
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num = -num
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den = -den
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end
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gcd = num.gcd(den)
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num = num.div(gcd)
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den = den.div(gcd)
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if den == 1 && defined?(Unify)
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num
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else
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new!(num, den)
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end
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end
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#
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# Implements the constructor. This method does not reduce to lowest terms or
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# check for division by zero. Therefore #Rational() should be preferred in
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# normal use.
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#
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def Rational.new!(num, den = 1)
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new(num, den)
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end
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private_class_method :new
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#
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# This method is actually private.
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#
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def initialize(num, den)
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if den < 0
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num = -num
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den = -den
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end
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if num.kind_of?(Integer) and den.kind_of?(Integer)
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@numerator = num
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@denominator = den
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else
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@numerator = num.to_i
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@denominator = den.to_i
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end
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end
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#
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# Returns the addition of this value and +a+.
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#
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# Examples:
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# r = Rational(3,4) # -> Rational(3,4)
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# r + 1 # -> Rational(7,4)
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# r + 0.5 # -> 1.25
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#
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def + (a)
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if a.kind_of?(Rational)
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num = @numerator * a.denominator
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num_a = a.numerator * @denominator
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Rational(num + num_a, @denominator * a.denominator)
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elsif a.kind_of?(Integer)
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self + Rational.new!(a, 1)
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elsif a.kind_of?(Float)
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Float(self) + a
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else
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x, y = a.coerce(self)
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x + y
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end
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end
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#
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# Returns the difference of this value and +a+.
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# subtracted.
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#
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# Examples:
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# r = Rational(3,4) # -> Rational(3,4)
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# r - 1 # -> Rational(-1,4)
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# r - 0.5 # -> 0.25
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#
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def - (a)
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if a.kind_of?(Rational)
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num = @numerator * a.denominator
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num_a = a.numerator * @denominator
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Rational(num - num_a, @denominator*a.denominator)
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elsif a.kind_of?(Integer)
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self - Rational.new!(a, 1)
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elsif a.kind_of?(Float)
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Float(self) - a
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else
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x, y = a.coerce(self)
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x - y
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end
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end
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#
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# Returns the product of this value and +a+.
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#
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# Examples:
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# r = Rational(3,4) # -> Rational(3,4)
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# r * 2 # -> Rational(3,2)
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# r * 4 # -> Rational(3,1)
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# r * 0.5 # -> 0.375
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# r * Rational(1,2) # -> Rational(3,8)
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#
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def * (a)
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if a.kind_of?(Rational)
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num = @numerator * a.numerator
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den = @denominator * a.denominator
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Rational(num, den)
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elsif a.kind_of?(Integer)
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self * Rational.new!(a, 1)
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elsif a.kind_of?(Float)
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Float(self) * a
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else
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x, y = a.coerce(self)
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x * y
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end
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end
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#
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# Returns the quotient of this value and +a+.
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# r = Rational(3,4) # -> Rational(3,4)
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# r / 2 # -> Rational(3,8)
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# r / 2.0 # -> 0.375
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# r / Rational(1,2) # -> Rational(3,2)
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#
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def / (a)
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if a.kind_of?(Rational)
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num = @numerator * a.denominator
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den = @denominator * a.numerator
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Rational(num, den)
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elsif a.kind_of?(Integer)
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raise ZeroDivisionError, "division by zero" if a == 0
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self / Rational.new!(a, 1)
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elsif a.kind_of?(Float)
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Float(self) / a
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else
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x, y = a.coerce(self)
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x / y
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end
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end
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#
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# Returns this value raised to the given power.
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#
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# Examples:
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# r = Rational(3,4) # -> Rational(3,4)
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# r ** 2 # -> Rational(9,16)
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# r ** 2.0 # -> 0.5625
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# r ** Rational(1,2) # -> 0.866025403784439
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#
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def ** (other)
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if other.kind_of?(Rational)
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Float(self) ** other
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elsif other.kind_of?(Integer)
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if other > 0
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num = @numerator ** other
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den = @denominator ** other
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elsif other < 0
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num = @denominator ** -other
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den = @numerator ** -other
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elsif other == 0
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num = 1
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den = 1
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end
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Rational.new!(num, den)
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elsif other.kind_of?(Float)
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Float(self) ** other
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else
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x, y = other.coerce(self)
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x ** y
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end
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end
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#
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# Returns the remainder when this value is divided by +other+.
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#
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# Examples:
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# r = Rational(7,4) # -> Rational(7,4)
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# r % Rational(1,2) # -> Rational(1,4)
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# r % 1 # -> Rational(3,4)
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# r % Rational(1,7) # -> Rational(1,28)
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# r % 0.26 # -> 0.19
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#
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def % (other)
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value = (self / other).to_i
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return self - other * value
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end
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#
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# Returns the quotient _and_ remainder.
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#
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# Examples:
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# r = Rational(7,4) # -> Rational(7,4)
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# r.divmod Rational(1,2) # -> [3, Rational(1,4)]
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#
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def divmod(other)
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value = (self / other).to_i
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return value, self - other * value
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end
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#
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# Returns the absolute value.
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#
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def abs
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if @numerator > 0
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Rational.new!(@numerator, @denominator)
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else
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Rational.new!(-@numerator, @denominator)
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end
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end
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#
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# Returns +true+ iff this value is numerically equal to +other+.
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#
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# But beware:
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# Rational(1,2) == Rational(4,8) # -> true
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# Rational(1,2) == Rational.new!(4,8) # -> false
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#
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# Don't use Rational.new!
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#
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def == (other)
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if other.kind_of?(Rational)
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@numerator == other.numerator and @denominator == other.denominator
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elsif other.kind_of?(Integer)
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self == Rational.new!(other, 1)
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elsif other.kind_of?(Float)
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Float(self) == other
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else
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other == self
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end
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end
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#
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# Standard comparison operator.
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#
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def <=> (other)
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if other.kind_of?(Rational)
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num = @numerator * other.denominator
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num_a = other.numerator * @denominator
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v = num - num_a
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if v > 0
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return 1
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elsif v < 0
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return -1
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else
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return 0
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end
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elsif other.kind_of?(Integer)
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return self <=> Rational.new!(other, 1)
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elsif other.kind_of?(Float)
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return Float(self) <=> other
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elsif defined? other.coerce
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x, y = other.coerce(self)
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return x <=> y
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else
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return nil
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end
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end
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def coerce(other)
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if other.kind_of?(Float)
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return other, self.to_f
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elsif other.kind_of?(Integer)
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return Rational.new!(other, 1), self
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else
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super
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end
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end
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#
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# Converts the rational to an Integer. Not the _nearest_ integer, the
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# truncated integer. Study the following example carefully:
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# Rational(+7,4).to_i # -> 1
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# Rational(-7,4).to_i # -> -2
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# (-1.75).to_i # -> -1
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#
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# In other words:
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# Rational(-7,4) == -1.75 # -> true
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# Rational(-7,4).to_i == (-1.75).to_i # false
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#
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def to_i
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Integer(@numerator.div(@denominator))
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end
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#
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# Converts the rational to a Float.
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#
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def to_f
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@numerator.quof(@denominator)
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end
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#
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# Returns a string representation of the rational number.
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#
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# Example:
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# Rational(3,4).to_s # "3/4"
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# Rational(8).to_s # "8"
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#
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def to_s
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if @denominator == 1
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@numerator.to_s
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else
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@numerator.to_s+"/"+@denominator.to_s
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end
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end
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#
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# Returns +self+.
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#
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def to_r
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self
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end
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#
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# Returns a reconstructable string representation:
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#
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# Rational(5,8).inspect # -> "Rational(5, 8)"
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#
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def inspect
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sprintf("Rational(%s, %s)", @numerator.inspect, @denominator.inspect)
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end
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#
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# Returns a hash code for the object.
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#
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def hash
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@numerator.hash ^ @denominator.hash
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end
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attr :numerator
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attr :denominator
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private :initialize
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end
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class Integer
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#
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# In an integer, the value _is_ the numerator of its rational equivalent.
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# Therefore, this method returns +self+.
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#
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def numerator
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self
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end
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#
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# In an integer, the denominator is 1. Therefore, this method returns 1.
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#
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def denominator
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1
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end
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#
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# Returns a Rational representation of this integer.
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#
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def to_r
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Rational(self, 1)
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end
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#
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# Returns the <em>greatest common denominator</em> of the two numbers (+self+
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# and +n+).
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#
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# Examples:
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# 72.gcd 168 # -> 24
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# 19.gcd 36 # -> 1
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#
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# The result is positive, no matter the sign of the arguments.
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#
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def gcd(other)
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min = self.abs
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max = other.abs
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while min > 0
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tmp = min
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min = max % min
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max = tmp
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end
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max
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end
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# Examples:
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# 6.lcm 7 # -> 42
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# 6.lcm 9 # -> 18
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#
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def lcm(other)
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if self.zero? or other.zero?
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0
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else
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(self.div(self.gcd(other)) * other).abs
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end
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end
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#
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# Returns the GCD _and_ the LCM (see #gcd and #lcm) of the two arguments
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# (+self+ and +other+). This is more efficient than calculating them
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# separately.
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#
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# Example:
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# 6.gcdlcm 9 # -> [3, 18]
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#
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def gcdlcm(other)
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gcd = self.gcd(other)
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if self.zero? or other.zero?
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[gcd, 0]
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else
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[gcd, (self.div(gcd) * other).abs]
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end
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end
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end
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class Fixnum
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alias quof quo
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undef quo
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# If Rational is defined, returns a Rational number instead of a Fixnum.
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def quo(other)
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Rational.new!(self,1) / other
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end
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alias rdiv quo
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# Returns a Rational number if the result is in fact rational (i.e. +other+ < 0).
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def rpower (other)
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if other >= 0
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self.power!(other)
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else
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Rational.new!(self,1)**other
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end
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end
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unless defined? 1.power!
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alias power! **
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alias ** rpower
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end
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end
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class Bignum
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unless defined? Complex
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alias power! **
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end
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alias quof quo
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undef quo
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# If Rational is defined, returns a Rational number instead of a Bignum.
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def quo(other)
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Rational.new!(self,1) / other
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end
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alias rdiv quo
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# Returns a Rational number if the result is in fact rational (i.e. +other+ < 0).
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def rpower (other)
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if other >= 0
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self.power!(other)
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else
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Rational.new!(self, 1)**other
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end
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end
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unless defined? Complex
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alias ** rpower
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end
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end
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