About Rational Number (PEP 239/PEP 240)

[Steven D'Aprano]

On Sat, 15 Dec 2007 15:44:26 -0800, Arnaud Delobelle wrote:

> Rationals are not that simple.
> 
> * Unless you are working under very controlled conditions, rationals
> very quickly grow enormous numerators and denominators, hence require
> arbitrary precision integers (which, I concede, are part of Python).

Come now. Rationals aren't living things that grow if you sit them in the 
corner and provide them air and light. Whether the numerator and 
denominator grow depends on what you do with them. If you wish to say 
that they *can* grow enormous numerators and denominators, I won't argue, 
but implying that *must* and will *always* grow is misleading. It's pure 
propaganda.

And if they do... well, longs can also "quickly grow enormous". That 
hasn't stopped Python integrating ints and longs. The programmer is 
expected to deal with it. Integrating floats and rationals isn't even on 
the table for discussion. Anyone using rationals is making a conscious 
choice to do so and can deal with the consequences.


> * In order to have a canonical representation of integers, they need to
> be kept in normalised form.

Oh noes! Not normalised form!!!

Is this supposed to be an objection?


> * Nobody uses big fractions apart from mathematicians (and maybe
> bookmakers?).

Putting the cart before the horse. Nobody uses rationals because 
rationals aren't available!

Nobody uses complex numbers except for mathematicians, and maybe a few 
electrical engineers, and they're a built in. Nobody uses math functions 
like sin and cos except for mathematicians and engineers, and they're 
available.

The Forth programming language didn't even support floating point for 
many years. Programmers were expected to use the equivalent of rationals 
using integers. This was very successful, and avoided the gotchas that 
you get with floats. For example, with floats it is unavoidable to have 
unintuitive results like (x + y) - x != y and it isn't even very hard to 
find an example. 

>>> 3.1 + 0.7 - 3.1 == 0.7
False

Such a bizarre result shouldn't happen with any non-buggy rational 
representation:

31/10 + 7/10 - 31/10 => 38/10 - 31/10 => 7/10

In the real world, people use fractions all the time, e.g. plumbers. (Not 
that I'm expecting plumbers to start taking laptops out to the building 
site in order to calculate pipe sizes.)

 
> * Having yet another numerical type would make it difficult what type to
> expect from a calculation.

I simply don't believe that at all. It's not like calculations will 
suddenly start returning rationals unexpectedly, any more than they 
suddenly started returning Decimals unexpectedly.

I find it bizarre that the simple to implement, simple to understand 
rational data type was rejected while the hard to implement, hard to 
understand Decimal was accepted.


-- 
Steven