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Diffstat (limited to 'lib/rational.rb')
| -rw-r--r-- | lib/rational.rb | 528 |
1 files changed, 10 insertions, 518 deletions
diff --git a/lib/rational.rb b/lib/rational.rb index 59588528ab..b12bf7ef38 100644 --- a/lib/rational.rb +++ b/lib/rational.rb @@ -1,469 +1,23 @@ -# -# rational.rb - -# $Release Version: 0.5 $ -# $Revision: 1.7 $ -# by Keiju ISHITSUKA(SHL Japan Inc.) -# -# Documentation by Kevin Jackson and Gavin Sinclair. -# -# When you <tt>require 'rational'</tt>, all interactions between numbers -# potentially return a rational result. For example: -# -# 1.quo(2) # -> 0.5 -# require 'rational' -# 1.quo(2) # -> Rational(1,2) -# -# See Rational for full documentation. -# - -# -# Creates a Rational number (i.e. a fraction). +a+ and +b+ should be Integers: -# -# Rational(1,3) # -> 1/3 -# -# Note: trying to construct a Rational with floating point or real values -# produces errors: -# -# Rational(1.1, 2.3) # -> NoMethodError -# -def Rational(a, b = 1) - if a.kind_of?(Rational) && b == 1 - a - else - Rational.reduce(a, b) - end -end - -# -# Rational implements a rational class for numbers. -# -# <em>A rational number is a number that can be expressed as a fraction p/q -# where p and q are integers and q != 0. A rational number p/q is said to have -# numerator p and denominator q. Numbers that are not rational are called -# irrational numbers.</em> (http://mathworld.wolfram.com/RationalNumber.html) -# -# To create a Rational Number: -# Rational(a,b) # -> a/b -# Rational.new!(a,b) # -> a/b -# -# Examples: -# Rational(5,6) # -> 5/6 -# Rational(5) # -> 5/1 -# -# Rational numbers are reduced to their lowest terms: -# Rational(6,10) # -> 3/5 -# -# But not if you use the unusual method "new!": -# Rational.new!(6,10) # -> 6/10 -# -# Division by zero is obviously not allowed: -# Rational(3,0) # -> ZeroDivisionError -# -class Rational < Numeric - @RCS_ID='-$Id: rational.rb,v 1.7 1999/08/24 12:49:28 keiju Exp keiju $-' - - # - # Reduces the given numerator and denominator to their lowest terms. Use - # Rational() instead. - # - 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 - - # - # Implements the constructor. This method does not reduce to lowest terms or - # check for division by zero. Therefore #Rational() should be preferred in - # normal use. - # - def Rational.new!(num, den = 1) - new(num, den) - end - - private_class_method :new - - # - # This method is actually private. - # - 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 - - # - # Returns the addition of this value and +a+. - # - # Examples: - # r = Rational(3,4) # -> Rational(3,4) - # r + 1 # -> Rational(7,4) - # r + 0.5 # -> 1.25 - # - 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 - - # - # Returns the difference of this value and +a+. - # subtracted. - # - # Examples: - # r = Rational(3,4) # -> Rational(3,4) - # r - 1 # -> Rational(-1,4) - # r - 0.5 # -> 0.25 - # - 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 - - # - # Returns the product of this value and +a+. - # - # Examples: - # r = Rational(3,4) # -> Rational(3,4) - # r * 2 # -> Rational(3,2) - # r * 4 # -> Rational(3,1) - # r * 0.5 # -> 0.375 - # r * Rational(1,2) # -> Rational(3,8) - # - 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 - - # - # Returns the quotient of this value and +a+. - # r = Rational(3,4) # -> Rational(3,4) - # r / 2 # -> Rational(3,8) - # r / 2.0 # -> 0.375 - # r / Rational(1,2) # -> Rational(3,2) - # - 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 - - # - # Returns this value raised to the given power. - # - # Examples: - # r = Rational(3,4) # -> Rational(3,4) - # r ** 2 # -> Rational(9,16) - # r ** 2.0 # -> 0.5625 - # r ** Rational(1,2) # -> 0.866025403784439 - # - 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 div(other) - (self / other).floor - end - - # - # Returns the remainder when this value is divided by +other+. - # - # Examples: - # r = Rational(7,4) # -> Rational(7,4) - # r % Rational(1,2) # -> Rational(1,4) - # r % 1 # -> Rational(3,4) - # r % Rational(1,7) # -> Rational(1,28) - # r % 0.26 # -> 0.19 - # - def % (other) - value = (self / other).floor - return self - other * value - end - - # - # Returns the quotient _and_ remainder. - # - # Examples: - # r = Rational(7,4) # -> Rational(7,4) - # r.divmod Rational(1,2) # -> [3, Rational(1,4)] - # - def divmod(other) - value = (self / other).floor - return value, self - other * value - end - - # - # Returns the absolute value. - # - def abs - if @numerator > 0 - self - else - Rational.new!(-@numerator, @denominator) - end - end - - # - # Returns +true+ iff this value is numerically equal to +other+. - # - # But beware: - # Rational(1,2) == Rational(4,8) # -> true - # Rational(1,2) == Rational.new!(4,8) # -> false - # - # Don't use Rational.new! - # - 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 - - # - # Standard comparison operator. - # - 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 - - # - # Converts the rational to an Integer. Not the _nearest_ integer, the - # truncated integer. Study the following example carefully: - # Rational(+7,4).to_i # -> 1 - # Rational(-7,4).to_i # -> -2 - # (-1.75).to_i # -> -1 - # - # In other words: - # Rational(-7,4) == -1.75 # -> true - # Rational(-7,4).to_i == (-1.75).to_i # false - # - - def floor() - @numerator.div(@denominator) - end - - def ceil() - -((-@numerator).div(@denominator)) - end - - def truncate() - if @numerator < 0 - return -((-@numerator).div(@denominator)) - end - @numerator.div(@denominator) - end - - alias_method :to_i, :truncate - - def round() - if @numerator < 0 - num = -@numerator - num = num * 2 + @denominator - den = @denominator * 2 - -(num.div(den)) - else - num = @numerator * 2 + @denominator - den = @denominator * 2 - num.div(den) - end - end +class Fixnum - # - # Converts the rational to a Float. - # - def to_f - @numerator.quof(@denominator) - end + alias quof fdiv - # - # Returns a string representation of the rational number. - # - # Example: - # Rational(3,4).to_s # "3/4" - # Rational(8).to_s # "8" - # - def to_s - if @denominator == 1 - @numerator.to_s - else - @numerator.to_s+"/"+@denominator.to_s - end - end + alias power! ** + alias rpower ** - # - # Returns +self+. - # - def to_r - self - end +end - # - # Returns a reconstructable string representation: - # - # Rational(5,8).inspect # -> "Rational(5, 8)" - # - def inspect - sprintf("Rational(%s, %s)", @numerator.inspect, @denominator.inspect) - end +class Bignum - # - # Returns a hash code for the object. - # - def hash - @numerator.hash ^ @denominator.hash - end + alias quof fdiv - attr :numerator - attr :denominator + alias power! ** + alias rpower ** - private :initialize end class Integer - # - # In an integer, the value _is_ the numerator of its rational equivalent. - # Therefore, this method returns +self+. - # - def numerator - self - end - - # - # In an integer, the denominator is 1. Therefore, this method returns 1. - # - def denominator - 1 - end - # - # Returns a Rational representation of this integer. - # - def to_r - Rational(self, 1) - end - - # - # Returns the <em>greatest common denominator</em> of the two numbers (+self+ - # and +n+). - # - # Examples: - # 72.gcd 168 # -> 24 - # 19.gcd 36 # -> 1 - # - # The result is positive, no matter the sign of the arguments. - # def gcd(other) min = self.abs max = other.abs @@ -475,10 +29,6 @@ class Integer max end - # Examples: - # 6.lcm 7 # -> 42 - # 6.lcm 9 # -> 18 - # def lcm(other) if self.zero? or other.zero? 0 @@ -486,15 +36,7 @@ class Integer (self.div(self.gcd(other)) * other).abs end end - - # - # Returns the GCD _and_ the LCM (see #gcd and #lcm) of the two arguments - # (+self+ and +other+). This is more efficient than calculating them - # separately. - # - # Example: - # 6.gcdlcm 9 # -> [3, 18] - # + def gcdlcm(other) gcd = self.gcd(other) if self.zero? or other.zero? @@ -503,55 +45,5 @@ class Integer [gcd, (self.div(gcd) * other).abs] end end -end - -class Fixnum - alias quof quo - remove_method :quo - - # If Rational is defined, returns a Rational number instead of a Float. - def quo(other) - Rational.new!(self, 1) / other - end - alias rdiv quo - # Returns a Rational number if the result is in fact rational (i.e. +other+ < 0). - def rpower (other) - if other >= 0 - self.power!(other) - else - Rational.new!(self, 1)**other - end - end -end - -class Bignum - alias quof quo - remove_method :quo - - # If Rational is defined, returns a Rational number instead of a Float. - def quo(other) - Rational.new!(self, 1) / other - end - alias rdiv quo - - # Returns a Rational number if the result is in fact rational (i.e. +other+ < 0). - def rpower (other) - if other >= 0 - self.power!(other) - else - Rational.new!(self, 1)**other - end - end -end - -unless defined? 1.power! - class Fixnum - alias power! ** - alias ** rpower - end - class Bignum - alias power! ** - alias ** rpower - end end |