From: Mark Hubbart <discordantus@...>
Date: 2005-10-19T18:18:46+09:00
Subject: Re: Integer#** weirdness

On 10/17/05, Peter Vanbroekhoven <calamitates@gmail.com> wrote:
> Hello,
>
> I've encountered a bit of a problem when I was trying out Ruby's numeric
> coercion:
>
>     class SomeNumberLikeThing
>
>       attr :value
>
>       def initialize(value)
>         @value = value
>       end
>
>       def **(other)
>         SomeNumberLikeThing.new(value ** other.value)
>       end
>
>       def coerce(other)
>         [SomeNumberLikeThing.new(other), self]
>       end
>
>     end
>
>     p 2.0 ** SomeNumberLikeThing.new(2)
>       # OK, returns #<SomeNumberLikeThing:0x4021c32c @value=4.0>
>     p 2 ** SomeNumberLikeThing.new(2)
>       # ERROR: /home/peterv/local/lib/ruby/1.8/rational.rb:339:in `**':
>            undefined method `>=' for #<SomeNumberLikeThing:0x4021c2dc
>            @value=2> (NoMethodError)
>
> Seems that Integer#** tries to compare its argument to zero before
> coercing. Problem is that I don't want this SomeNumberLikeThing to be
> comparable. This is not something very exotic, as not all "number-like"
> things are (totally) ordered, e.g., polynomials, matrices and complex
> numbers. So IMO Integer#** should coerce before doing anything else with
> its argument.

Note that the error is generated in rational.rb. Rational.rb does the
comparison so that it can trap negative exponents and give a rational
result:

irb> [2 ** -1, 2 ** -2]
    ==>[Rational(1, 2), Rational(1, 4)]

Try not requiring rational.rb, and your code works perfectly. So this
is actually a problem with the rational library. It appears that it
does the comparison to gain speed when rational division isn't needed.

A possible fix to this: change the Integer#rpower method definition in
rational.rb from

  def rpower (other)
    if other >= 0
      self.power!(other)
    else
      Rational.new!(self,1)**other
    end
  end

to:

  def rpower (other)
    me, you = other.coerce(self)
    return me**you unless me == self
    if other >= 0
      self.power!(other)
    else
      Rational.new!(self,1)**other
    end
  end

This seems to fix your problem, while still letting Rational do its
rational thing:

p 2 ** SomeNumberLikeThing.new(2)
p 2 ** SomeNumberLikeThing.new(-3)
p 2 ** -3

#<SomeNumberLikeThing:0x1c2e14 @value=4>
#<SomeNumberLikeThing:0x1c2e14 @value=Rational(1, 8)>
Rational(1, 8)

There seems to be a very small performance hit for this:

mark@eMac% ruby -rbenchmark -rrational
-e'Benchmark.bm(10){|x|x.report("modified"){100000.times{|n|2**(-n)}}}'
                user     system      total        real
modified   23.220000   0.400000  23.620000 ( 27.584483)
mark@eMac% ruby -rbenchmark -rrational
-e'Benchmark.bm(10){|x|x.report("original"){100000.times{|n|2**(-n)}}}'
                user     system      total        real
original   22.400000   0.400000  22.800000 ( 26.598195)


... but these benchmarks are not necessarily conclusive.  I may be
missing something big there.

cheers,
Mark

> As a side note, Complex#<=> is defined, but it violates the definition of
> an order: Complex(1, 1) >= Complex(1, -1) and Complex(1, 1) <= Complex(1,
> -1) but not Complex(1, 1) == Complex(1, -1), which is a violation of the
> antisymmetry law.
>
> Peter
>
>