From: Kent Dahl <kentda@...>
Date: 2001-07-29T22:29:43+09:00
Subject: [ruby-talk:18741] Re: Numbers classes.. Rational number? [was: Ruby as opposed to Python?]

Kero van Gelder wrote:
> 1 Dutch guilder is wordt 2.20something Euro.
> 
> that's a float :)

It looks like a float, but are you sure 2.20 can be represent accurately
using a float, or is that an approximation?

2.20 == 2 + 1/5

Unfortunately, floating-point formats can't store fiths. Here the
approximation doesn't pose a problem, but once you've got one hundre
billion and a 1/5 dollars, you've got a problem.


> I'd like Rationals in Ruby, but a few divisions can run into huge
> BixNums for denominator and whatstheothercalled. That can be an
> unexpected speed slowdown. Guess you'd get:
> 
>   5 / 2     => Rational(5, 2)
>   5.0 / 2   => Float(2.5)

.... for some reason the Java touting "operator-overloading is evil"
mantra springs to mind here :-) But even if I'd have to use some
explisit verbose "divide" method, I think that it is worth adding.
As for huge Bignums for denominator and divisor(or is it dividend?),
perhaps one could do some normalization of the Rational? Ie,
Rational(100,200) == Rational(1,2)? Some clever bitwise and-ing and
shifting would probably do the trick.


My take on it is this: A float is basically a rational. 
Or a subset of rational, since Rational can represent any number Float
can, but not
the other way.
The only floatingpoint formats I've seen (up close) use something like: 
	a * 2^b
Which is basically a rational: (a * 2^b) == (a / 2^-b)

The reason for most of the approximation losses of floats, is the range
restrictions of a and b. (The tying to base 2 also has impact)
After seeing the light that is Bignum, it seems naturally to also have a
Bigfloat ( basically a float with a and b that can be Bignums) and a
Rational ( where the divisor is any possible Bignum, and not a multiple
of 2)

> which raises the question:
> 
>   Rational(5, 2) / 3.0  => Rational? Float?

(5/2) / (3/1) == (5/2) * (1/3) = (5*1/2*3) == (5/6) if my math skills
don't fail me.

In this case I would assume the Rational / operator did the honorable
thing, and preserved as much information as possible, despite slowness.
If I wanted a float, I would do:
	Rational(5,2).to_f / 3.0

Assuming that the internal data for the float (a and b) can be
extracted, the Rational class has no problem dividing, multiplying or
adding with a float, since it basically treats it like Rational.

As for slowness, Float already seems somewhat plagued since its not an
immediate value (but thats more a GC thing). However, I do strongly
believe that accuracy and information preservation is more paramount
than speed. I'd rather have the operators be slow and correct, and have
some alternative, verbose and fast methods, doing the same but giving a
rats behind about accuracy.

....

While I'm ranting about numbers: Is there any plans to have "bang"
versions of numeric operators?

<SNIP>
irb(main):077:0> a = b = 5.0
5.0
irb(main):078:0>
irb(main):079:0* a *=2
10.0
irb(main):080:0> b
5.0
</SNIP>

This seems to indicate that a*=b is just syntactic sugar for a=a+b,
which is probably the element of least surprise, atleast when converting
Java / C++ programmers more familiar with by-value semantics. But if I
put my OO-purist cap on and start chanting, I feel like the *= operator
violates the object-message paradigm: I would assume the object is
changed inplace.

So, how about mul!, div!, plus! and minus! to complement (and imitate
for immediate types) the operators *=, /=, += and -= that yields this
functionality:
	a = b = 5.0	#=> 5.0
	a.mul! 2	#=> 10.0
	b		#=> 10.0

On numeric objects that are real (and bother the GC), I think this might
help on efficiency, avoiding the creation of an object. 

The only real problem I see, is the confusion it could lead to when
working with immediate values that _may_ turn into true objects due to a
call:
	a = b = 5	#=> 5
	a.mul! 2	#=> 10
	b		#=> 5    # immediate value, therefore not changed
versus
	a = b = myLargeNumber	# myLargeNumber could be Fixnum, Bignum, Float
etc
	a.mul! 2		#=> myLargeNumber*2
	b			# Just what is b now?
where b would be myLargeNumber if it was a Fixnum, but would be
myLargeNumber*2 if
it was a true object (Bignum, Float, etc)

Have I gone completely mad, missed something obvious or? Comments?

-- 
<[ Kent Dahl ]>================<[ http://www.stud.ntnu.no/~kentda/ ]>
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 \"nor the frontal lobe of my left cerebral hemisphere.           "/