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PEP 228 -- Reworking Python's Numeric Model

PEP:228
Title:Reworking Python's Numeric Model
Author:moshez at zadka.site.co.il (Moshe Zadka), guido at python.org (Guido van Rossum)
Status:Withdrawn
Type:Standards Track
Created:4-Nov-2000
Post-History:

Withdrawal

This PEP has been withdrawn in favor of PEP 3141.

Abstract

Today, Python's numerical model is similar to the C numeric model: there are several unrelated numerical types, and when operations between numerical types are requested, coercions happen. While the C rationale for the numerical model is that it is very similar to what happens at the hardware level, that rationale does not apply to Python. So, while it is acceptable to C programmers that 2/3 == 0, it is surprising to many Python programmers.

NOTE: in the light of recent discussions in the newsgroup, the motivation in this PEP (and details) need to be extended.

Rationale

In usability studies, one of the least usable aspect of Python was the fact that integer division returns the floor of the division. This makes it hard to program correctly, requiring casts to float() in various parts through the code. Python's numerical model stems from C, while a model that might be easier to work with can be based on the mathematical understanding of numbers.

Other Numerical Models

Perl's numerical model is that there is one type of numbers -- floating point numbers. While it is consistent and superficially non-surprising, it tends to have subtle gotchas. One of these is that printing numbers is very tricky, and requires correct rounding. In Perl, there is also a mode where all numbers are integers. This mode also has its share of problems, which arise from the fact that there is not even an approximate way of dividing numbers and getting meaningful answers.

Suggested Interface For Python's Numerical Model

While coercion rules will remain for add-on types and classes, the built in type system will have exactly one Python type -- a number. There are several things which can be considered "number methods":

  1. isnatural()
  2. isintegral()
  3. isrational()
  4. isreal()
  5. iscomplex()
  6. isexact()

Obviously, a number which answers true to a question from 1 to 5, will also answer true to any following question. If isexact() is not true, then any answer might be wrong. (But not horribly wrong: it's close to the truth.)

Now, there is two thing the models promises for the field operations (+, -, /, *):

  • If both operands satisfy isexact(), the result satisfies isexact().
  • All field rules are true, except that for not-isexact() numbers, they might be only approximately true.

One consequence of these two rules is that all exact calcutions are done as (complex) rationals: since the field laws must hold, then

(a/b)*b == a

must hold.

There is built-in function, inexact() which takes a number and returns an inexact number which is a good approximation. Inexact numbers must be as least as accurate as if they were using IEEE-754.

Several of the classical Python functions will return exact numbers even when given inexact numbers: e.g, int().

Coercion

The number type does not define nb_coerce Any numeric operation slot, when receiving something other then PyNumber, refuses to implement it.

Inexact Operations

The functions in the math module will be allowed to return inexact results for exact values. However, they will never return a non-real number. The functions in the cmath module are also allowed to return an inexact result for an exact argument, and are furthermore allowed to return a complex result for a real argument.

Numerical Python Issues

People who use Numerical Python do so for high-performance vector operations. Therefore, NumPy should keep its hardware based numeric model.

Unresolved Issues

Which number literals will be exact, and which inexact?

How do we deal with IEEE 754 operations? (probably, isnan/isinf should be methods)

On 64-bit machines, comparisons between ints and floats may be broken when the comparison involves conversion to float. Ditto for comparisons between longs and floats. This can be dealt with by avoiding the conversion to float. (Due to Andrew Koenig.)

Source: https://github.com/python/peps/blob/master/pep-0228.txt