From: Albert Chou <achou@...>
Date: 2003-04-20T23:12:11+09:00
Subject: Float.to_rational

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I thought it would be nice to be able to convert Floats to Rationals, so
I went through the exercise of figuring out how to do it, even though
it's (by the nature of floating point arithmetic) an inexact science.
Here's my extension to class Float.  The main feature is the to_rational
instance method, but you can also get the maximum number of decimal
digits representable by a Float on your computer by using the
max_precision instance and/or class methods.


class Float
  require 'rational'

  @@max_num_significant_digits_minus_1 =3D nil
  @@scaling_factor =3D nil

  def to_rational
    unless ! @@max_num_significant_digits_minus_1.nil?
      Float.calculate_max_num_significant_digits
    end

    Rational( (self * @@scaling_factor).to_i, @@scaling_factor )
  end

  def Float.calculate_max_num_significant_digits
    i =3D j =3D 0

    until 1.0 - i =3D=3D 0.0
      j +=3D 1
      i =3D 1.0 + 0.1**j
    end

    @@max_num_significant_digits_minus_1 =3D j - 1
    @@scaling_factor =3D 10**@@max_num_significant_digits_minus_1
  end

  def Float.max_precision
    @@max_num_significant_digits_minus_1 + 1
  end

  def max_precision
    Float.max_precision
  end
end



Al

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<TITLE>Float.to_rational</TITLE>
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<P><FONT SIZE=3D2>I thought it would be nice to be able to convert =
Floats to Rationals, so I went through the exercise of figuring out how =
to do it, even though it's (by the nature of floating point arithmetic) =
an inexact science.&nbsp; Here's my extension to class Float.&nbsp; The =
main feature is the to_rational instance method, but you can also get =
the maximum number of decimal digits representable by a Float on your =
computer by using the max_precision instance and/or class methods.<BR>
<BR>
<BR>
class Float<BR>
&nbsp; require 'rational'<BR>
<BR>
&nbsp; @@max_num_significant_digits_minus_1 =3D nil<BR>
&nbsp; @@scaling_factor =3D nil<BR>
<BR>
&nbsp; def to_rational<BR>
&nbsp;&nbsp;&nbsp; unless ! =
@@max_num_significant_digits_minus_1.nil?<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =
Float.calculate_max_num_significant_digits<BR>
&nbsp;&nbsp;&nbsp; end<BR>
<BR>
&nbsp;&nbsp;&nbsp; Rational( (self * @@scaling_factor).to_i, =
@@scaling_factor )<BR>
&nbsp; end<BR>
<BR>
&nbsp; def Float.calculate_max_num_significant_digits<BR>
&nbsp;&nbsp;&nbsp; i =3D j =3D 0<BR>
<BR>
&nbsp;&nbsp;&nbsp; until 1.0 - i =3D=3D 0.0<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; j +=3D 1<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; i =3D 1.0 + 0.1**j<BR>
&nbsp;&nbsp;&nbsp; end<BR>
<BR>
&nbsp;&nbsp;&nbsp; @@max_num_significant_digits_minus_1 =3D j - 1<BR>
&nbsp;&nbsp;&nbsp; @@scaling_factor =3D =
10**@@max_num_significant_digits_minus_1<BR>
&nbsp; end<BR>
<BR>
&nbsp; def Float.max_precision<BR>
&nbsp;&nbsp;&nbsp; @@max_num_significant_digits_minus_1 + 1<BR>
&nbsp; end<BR>
<BR>
&nbsp; def max_precision<BR>
&nbsp;&nbsp;&nbsp; Float.max_precision<BR>
&nbsp; end<BR>
end<BR>
<BR>
<BR>
<BR>
Al</FONT>
</P>

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