130 lines
4.0 KiB
Plaintext
130 lines
4.0 KiB
Plaintext
PEP: 228
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Title: Reworking Python's Numeric Model
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Version: $Revision$
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Author: pep@zadka.site.co.il (Moshe Zadka)
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Status: Draft
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Type: Standards Track
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Python-Version: ??
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Created: 4-Nov-2000
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Post-History:
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Abstract
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Today, Python's numerical model is similar to the C numeric model:
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there are several unrelated numerical types, and when operations
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between numerical types are requested, coercions happen. While
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the C rationale for the numerical model is that it is very similar
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to what happens at the hardware level, that rationale does not
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apply to Python. So, while it is acceptable to C programmers that
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2/3 == 0, it is surprising to Python programmers.
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Rationale
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In usability studies, one of the least usable aspect of Python was
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the fact that integer division returns the floor of the division.
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This makes it hard to program correctly, requiring casts to
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float() in various parts through the code. Python's numerical
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model stems from C, while an model that might be easier to work with
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can be based on the mathematical understanding of numbers.
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Other Numerical Models
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Perl's numerical model is that there is one type of numbers --
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floating point numbers. While it is consistent and superficially
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non-surprising, it tends to have subtle gotchas. One of these is
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that printing numbers is very tricky, and requires correct
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rounding. In Perl, there is also a mode where all numbers are
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integers. This mode also has its share of problems, which arise
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from the fact that there is not even an approximate way of
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dividing numbers and getting meaningful answers.
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Suggested Interface For Python's Numerical Model
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While coercion rules will remain for add-on types and classes, the
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built in type system will have exactly one Python type -- a
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number. There are several things which can be considered "number
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methods":
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1. isnatural()
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2. isintegral()
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3. isrational()
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4. isreal()
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5. iscomplex()
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a. isexact()
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Obviously, a number which answers true to a question from 1 to 5, will
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also answer true to any following question. If "isexact()" is not true,
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then any answer might be wrong.
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(But not horribly wrong: it's close to the truth.)
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Now, there is two thing the models promises for the field operations
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(+, -, /, *):
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- If both operands satisfy isexact(), the result satisfies
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isexact().
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- All field rules are true, except that for not-isexact() numbers,
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they might be only approximately true.
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One consequence of these two rules is that all exact calcutions
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are done as (complex) rationals: since the field laws must hold,
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then
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(a/b)*b == a
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must hold.
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There is built-in function, inexact() which takes a number
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and returns an inexact number which is a good approximation.
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Inexact numbers must be as least as accurate as if they were
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using IEEE-754.
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Several of the classical Python functions will return exact numbers
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even when given inexact numbers: e.g, int().
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Coercion
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The number type does not define nb_coerce
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Any numeric operation slot, when receiving something other then PyNumber,
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refuses to implement it.
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Inexact Operations
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The functions in the "math" module will be allowed to return
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inexact results for exact values. However, they will never return
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a non-real number. The functions in the "cmath" module are also
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allowed to return an inexact result for an exact argument, and are
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furthermore allowed to return a complex result for a real
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argument.
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Numerical Python Issues
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People who use Numerical Python do so for high-performance vector
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operations. Therefore, NumPy should keep its hardware based
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numeric model.
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Unresolved Issues
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Which number literals will be exact, and which inexact?
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How do we deal with IEEE 754 operations? (probably, isnan/isinf should
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be methods)
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Copyright
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This document has been placed in the public domain.
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Local Variables:
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mode: indented-text
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indent-tabs-mode: nil
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End:
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