From: Jim Weirich <jim@...>
Date: 2005-05-27T12:38:35+09:00
Subject: Re: A different perspective on Ruby.

On Thursday 26 May 2005 04:11 pm, Glenn Parker wrote:
> I can't think of any unary
> mathematical operations that are naturally postfix, 

Factorial !

> One justification for sqrt(5) would be that "sqrt", works on more than
> one class of objects (Fixnum, Bignum, Rational, etc). �So does "abs" for
> that matter, and I'm not crazy about 5.abs. �As a method, sqrt would
> have to be defined in every applicable class, either with new code or as
> an included module. �This spreads the definition out, which complicates
> maintainence.

Actually, I think you have this backwards.  It would be much more convenient 
to have sqrt as a member function in order to implement it differently in 
different classes.  Numeric could hold the standard definition, but if a 
subclass needed to redefine it, it could do so with little effort.

Look at the code in complex.rb to see how it handles enhancing sqrt to handle 
complex numbers:

  alias sqrt! sqrt
  # ...
  def sqrt(z)
    if Complex.generic?(z)
      if z >= 0
        sqrt!(z)
      else
        Complex(0,sqrt!(-z))
      end
    else
      if z.image < 0
        sqrt(z.conjugate).conjugate
      else
        r = z.abs
        x = z.real
        Complex( sqrt!((r+x)/2), sqrt!((r-x)/2) )
      end
    end
  end

If sqrt were a member function, the generic test could be completely avoided.
Although the original sqrt would still have to be enhanced to handle negative 
values, it would only have to test for < 0, rather than the rather fragile 
test for Integer, Float and Rational.  

-- 
-- Jim Weirich    jim@weirichhouse.org     http://onestepback.org
-----------------------------------------------------------------
"Beware of bugs in the above code; I have only proved it correct, 
not tried it." -- Donald Knuth (in a memo to Peter van Emde Boas)