PEP: 754
Title: IEEE 754 Floating Point Special Values
Version: $Revision$
Last-Modified: $Date$
Author: Gregory R. Warnes <warnes@users.sourceforge.net>
Status: Draft
Type: Standard Track
Content-Type: text/x-rst
Created: 28-Mar-2003
Python-Version: 2.3
Post-History:


Abstract
========

This PEP proposes an API and a provides a reference module that
generates and tests for IEEE 754 double-precision special values:
positive infinity (Inf), negative infinity (-Inf), and not-a-number
(NaN).


Rationale
=========

The IEEE 754 standard defines a set of binary representations and
algorithmic rules for floating point arithmetic.  Included in the
standard is a set of constants for representing special values,
including positive infinity (Inf), negative infinity (-Inf), and
indeterminate or non-numeric results (NaN).  Most modern CPUs
implement the IEEE 754 standard, including the (Ultra)SPARC, PowerPC,
and x86 processor series.

Currently, the handling of IEEE 754 special values in Python depends
on the underlying C library.  Unfortunately, there is little
consistency between C libraries in how or whether these values are
handled.  For instance, on some systems "float('Inf')" will properly
return the IEEE 754 constant for positive infinity.  On many systems,
however, this expression will instead generate an error message.

The output string representation for an IEEE 754 special value also
varies by platform.  For example, the expression "float(1e3000)",
which is large enough to generate an overflow, should return a string
representation corresponding to IEEE 754 positive infinity.  Python
2.1.3 on x86 Debian Linux returns "inf".  On Sparc Solaris 8 with
Python 2.2.1, this same expression returns "Infinity", and on
MS-Windows 2000 with Active Python 2.2.1, it returns "1.#INF".

Adding to the confusion, some platforms generate one string on
conversion from floating point and accept a different string for
conversion to floating point.  On these systems ::

    float(str(x))

will generate an error when "x" is an IEEE special value.

In the past, some have recommended that programmers use expressions
like::

    Inf = 1e300**2
    NaN = Inf/Inf

to obtain positive infinity and not-a-number constants.  However, the
first expression generates an error on current Python interpreters.  A
possible alternative is to use::

    Inf = 1e300000
    NaN = Inf/Inf

While this does not generate an error with current Python
interpreters, it is still an ugly and potentially non-portable hack.
In addition, defining NaN in this way does solve the problem of
detecting such values.  First, the IEEE 754 standard provides for an
entire set of constant values for Not-a-Number.  Second, the standard
requires that ::

    NaN != X

for all possible values of X, including NaN.  As a consequence ::

    NaN == NaN

should always evaluate to false.  However, this behavior also is not
consistently implemented.  [e.g. Cygwin Python 2.2.2]

Due to the many platform and library inconsistencies in handling IEEE
special values, it is impossible to consistently set or detect IEEE
754 floating point values in normal Python code without resorting to
directly manipulating bit-patterns.

This PEP proposes a standard Python API and provides a reference
module implementation which allows for consistent handling of IEEE 754
special values on all supported platforms.


API Definition
==============

Constants
---------

NaN
    IEEE 754 "Not a Number" value

Inf, PosInf
    IEEE 754 Positive Infinity value

NegInf
    IEEE 754 Negative Infinity value


Functions
---------

is_NaN(value)
    Determine if the argument is a IEEE 754 NaN (Not a Number) value.

is_Inf(value), is_PosInf(value)
    Determine if the argument is a IEEE 754 positive infinity value

is_NegInf(value)
    Determine if the argument is a IEEE 754 negative infinity value

is_Finite(value)
    Determine if the argument is an finite IEEE 754 value (i.e., is
    not NaN, positive or negative infinity)

is_Infinite(value)
    Determine if the argument is an infinite IEEE 754 value (positive
    or negative infinity)


Example
-------

(Run under Python 2.2.1 on Solaris 8.)

>>> import fpconst
>>> val = 1e30000 # should be cause overflow and result in "Inf"
>>> val
Infinity
>>> fpconst.is_Inf(val)
1
>>> fpconst.Inf
Infinity
>>> nval = val/val # should result in NaN
>>> nval
NaN
>>> fpconst.is_NaN(nval)
1
>>> fpconst.is_NaN(val)
0


Implementation
--------------

The reference implementation is provided in the module "fpconst" [1]_,
which is written in pure Python by taking advantage of the "struct"
standard module to directly set or test for the bit patterns that
define IEEE 754 special values.  Care has been taken to generate
proper results on both big-endian and little-endian machines.

The current implementation is pure Python, but some efficiency could
be gained by translating the core routines into C.


References
==========

See http://babbage.cs.qc.edu/courses/cs341/IEEE-754references.html for
reference material on the IEEE 754 floating point standard.

.. [1] Further information on the reference package is available at
   http://software.biostat.washington.edu/statsoft/snake/fpconst.


Copyright
=========

This document has been placed in the public domain.


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