From: "正木　功" <GEC01122@...>
Date: 2001-03-02T16:19:18+09:00
Subject: [ruby-list:28415] class Real

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Real.rb
--------
class Sequence
  def initialize(list,*x)
    @list=list
    @x=x
    @proc=eval("proc{"+yield+"}")
  end
  def [](n)
    @list[n] || @list[n]=@proc.call(n,*@x)
  end
  def /(y)
    x=self
    case y
    when Numeric
     Sequence.new([],x,y){"|n,x,y| x[n]/y"}
    else
      Sequence.new([],x,y){"|n,x,y| x[n]/y[n]"}
    end
  end
end
class Real < Sequence
  def +(y)
    x=self
    Real.new([],x,y){"|n,x,y| x[n]+y[n]"}
  end

  def -(y)
    x=self
    Real.new([],x,y){"|n,x,y| x[n]-y[n]"}
  end

  def -@
    x=self
    Real.new([],x){"|n,x| -x[n]"}
  end


  def *(y)
    x=self
    case y
    when Numeric
      Real.new([],x,y){"|n,x,y| x[n]*y"}
    else
      Real.new([],x,y){"|n,x,y| x[n]*y[n]"}
    end
  end

  def /(y)
    x=self
    case y
    when Numeric
      Real.new([],x,y){"|n,x,y| x[n]/y"}
    else
      Real.new([],x,y){"|n,x,y| x[n]/y[n]"}
    end
  end
  def each_index(n=0,m=nil)
    if not m
      i=n
      loop do
	yield(i)
	i+=1
      end
    else
      (n..m).each{|i| yield(i)}
    end
  end
  def succ_each(n=0,m=nil)
    each_index{|i| yield(self[i],self[i+1],i)} 
  end
  def succ_find
    r=nil;succ_each{|x,y,i| if yield(x,y,i) then r=x;break;end};r
  end

  def sqrt
    x=self
    Real.new([Rational(1)],x){"|n,x| a=self[n-1];y=x[n];(a+y/a)/2 "}
  end
  def print(n=16,r=10)
    self.succ_find{|x,y,i| (x-y).abs < Rational(1,r**n)}.printd(n,r)
  end
end

class Object
  def Real(x)
    Real.new([x],x){"|n,x| x"}
  end
end
require "rational.rb"
class Rational
  def to_d(r=10)
    a=@numerator
    b=@denominator
    Sequence.new([a],b,r){"|n,b,r| r*(self[n-1]%b)"}/b
  end
  def printd(n,r)
    s=to_d(r)
    print s[0],"."
    for i in 1..n
      printf("%x",s[i])
    end
  end
end
------
sqrt.rb
------
require "Real.rb"
x=ARGV.shift.to_i
n=ARGV.shift.to_i
r=10
Real(x).sqrt.print(n,r);print "\n"

-----
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time ruby sqrt.rb 2 100
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1.4142135623730950488016887242096980785696718753769480731766797379907324784621
070388503875343276415727

real    0m1.192s
user    0m0.640s
sys     0m0.090s
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