[ruby-dev:33662] rational, complex and mathn

rational は floor、truncate、ceil、round を定義していません。Numeric 
のまま提供しています。しかし、Numeric のものは、浮動小数点数に変換して
しまうためまともな結果が得られるとは限りません。[ruby-dev:32201]

現状、floor のかわりに to_i をつかって問題がないのは、to_i の定義が 
floor になっているからです。Float#to_i の定義から、Numeric の to_i は 
truncate であるべきだと思います。

Complex(1,2).numerator がエラーになります。rational を読んでいるとエラー
になりません。

$ ruby19  -r complex -e 'Complex(1,2).numerator'
/usr/local/ruby19/lib/ruby/1.9.0/complex.rb:345:in `denominator': undefined method `denominator' for 1:Fixnum (NoMethodError)
        from /usr/local/ruby19/lib/ruby/1.9.0/complex.rb:352:in `numerator'
        from -e:1:in `<main>'

Complex#quo が機能しません。普通に整数割りしてしまいます。

$ ruby19  -r complex -e 'p Complex(1,2).quo(2)'
Complex(0, 1)

$ ruby19  -r complex -r rational -e 'p Complex(1,2).quo(2)'
Complex(0, 1)

complex では、不要に思えるメソッドが放置してあります。>、>=、<、<=、
between?、floor、ceil、round、truncate など。1.8 では、step、<=> も。
あと、% は意味があるのでしょうか。

mathn で、Rational#inspect を書き換えているが、さすがに余計なお世話の
ような気もします。どうしてもしたければ、そういうことは、irb などアプリ
ケーション側でやればいいような気がします。

以下修正案。floor、ceil、truncate、round は原さんの rational からパク
りました。


Index: lib/rational.rb
===================================================================
--- lib/rational.rb	(revision 15409)
+++ lib/rational.rb	(working copy)
@@ -238,6 +238,10 @@
     end
   end
 
+  def div(other)
+    (self / other).floor
+  end
+
   #
   # Returns the remainder when this value is divided by +other+.
   #
@@ -249,7 +253,7 @@
   #   r % 0.26             # -> 0.19
   #
   def % (other)
-    value = (self / other).to_i
+    value = (self / other).floor
     return self - other * value
   end
 
@@ -261,7 +265,7 @@
   #   r.divmod Rational(1,2)   # -> [3, Rational(1,4)]
   #
   def divmod(other)
-    value = (self / other).to_i
+    value = (self / other).floor
     return value, self - other * value
   end
 
@@ -270,7 +274,7 @@
   #
   def abs
     if @numerator > 0
-      Rational.new!(@numerator, @denominator)
+      self
     else
       Rational.new!(-@numerator, @denominator)
     end
@@ -345,10 +349,37 @@
   #   Rational(-7,4) == -1.75                 # -> true
   #   Rational(-7,4).to_i == (-1.75).to_i     # false
   #
-  def to_i
-    Integer(@numerator.div(@denominator))
+
+  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
+
   #
   # Converts the rational to a Float.
   #
@@ -476,10 +507,11 @@
 
 class Fixnum
   alias quof quo
-  undef quo
-  # If Rational is defined, returns a Rational number instead of a Fixnum.
+  remove_method :quo
+
+  # If Rational is defined, returns a Rational number instead of a Float.
   def quo(other)
-    Rational.new!(self,1) / other
+    Rational.new!(self, 1) / other
   end
   alias rdiv quo
 
@@ -488,26 +520,18 @@
     if other >= 0
       self.power!(other)
     else
-      Rational.new!(self,1)**other
+      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
+  alias quof quo
+  remove_method :quo
 
-  alias quof quo
-  undef quo
-  # If Rational is defined, returns a Rational number instead of a Bignum.
+  # If Rational is defined, returns a Rational number instead of a Float.
   def quo(other)
-    Rational.new!(self,1) / other
+    Rational.new!(self, 1) / other
   end
   alias rdiv quo
 
@@ -519,8 +543,15 @@
       Rational.new!(self, 1)**other
     end
   end
+end
 
-  unless defined? Complex
+unless defined? 1.power!
+  class Fixnum
+    alias power! **
     alias ** rpower
   end
+  class Bignum
+    alias power! **
+    alias ** rpower
+  end
 end
Index: lib/mathn.rb
===================================================================
--- lib/mathn.rb	(revision 15409)
+++ lib/mathn.rb	(working copy)
@@ -121,11 +121,6 @@
 class Rational
   Unify = true
 
-  remove_method :inspect
-  def inspect
-    format "%s/%s", numerator.inspect, denominator.inspect
-  end
-
   alias power! **
 
   def ** (other)
Index: lib/complex.rb
===================================================================
--- lib/complex.rb	(revision 15409)
+++ lib/complex.rb	(working copy)
@@ -104,6 +104,10 @@
   @RCS_ID='-$Id: complex.rb,v 1.3 1998/07/08 10:05:28 keiju Exp keiju $-'
 
   undef step
+  undef <, <=, <=>, >, >=
+  undef between?
+  undef divmod, modulo
+  undef floor, truncate, ceil, round
 
   def scalar?
     false
@@ -199,6 +203,10 @@
       x/y
     end
   end
+
+  def quo(other)
+    Complex(@real.quo(1), @image.quo(1)) / other
+  end
   
   #
   # Raise this complex number to the given (real or complex) power.
@@ -248,6 +256,8 @@
   #
   # Remainder after division by a real or complex number.
   #
+
+=begin
   def % (other)
     if other.kind_of?(Complex)
       Complex(@real % other.real, @image % other.image)
@@ -258,7 +268,8 @@
       x % y
     end
   end
-  
+=end
+
 #--
 #    def divmod(other)
 #      if other.kind_of?(Complex)
@@ -312,8 +323,6 @@
   end
   alias conj conjugate
 
-  undef <=>
-  
   #
   # Test for numerical equality (<tt>a == a + 0<i>i</i></tt>).
   #
@@ -410,9 +419,35 @@
   
 end
 
+class Integer
 
+  unless defined?(1.numerator) # temporal
+    def numerator() self end
+    def denominator() 1 end
 
+    def gcd(other)
+      min = self.abs
+      max = other.abs
+      while min > 0
+        tmp = min
+        min = max % min
+        max = tmp
+      end
+      max
+    end
 
+    def lcm(other)
+      if self.zero? or other.zero?
+        0
+      else
+        (self.div(self.gcd(other)) * other).abs
+      end
+    end
+
+  end
+
+end
+
 module Math
   alias sqrt! sqrt
   alias exp! exp