|Title:||IEEE 754 Floating Point Special Values|
|Last-Modified:||2008-01-18 08:36:51 +0000 (Fri, 18 Jan 2008)|
|Author:||Gregory R. Warnes <gregory_r_warnes at groton.pfizer.com> (Pfizer, Inc.)|
This PEP has been rejected. After sitting open for four years, it has failed to generate sufficient community interest.
Several ideas of this PEP were implemented for Python 2.6. float('inf') and repr(float('inf')) are now guaranteed to work on every supported platform with IEEE 754 semantics. However the eval(repr(float('inf'))) roundtrip is still not supported unless you define inf and nan yourself:
>>> inf = float('inf') >>> inf, 1E400 (inf, inf) >>> neginf = float('-inf') >>> neginf, -1E400 (-inf, -inf) >>> nan = float('nan') >>> nan, inf * 0. (nan, nan)
The math and the sys module also have gained additional features, sys.float_info, math.isinf, math.isnan, math.copysign.
This PEP proposes an API and a provides a reference module that generates and tests for IEEE 754 double-precision special values: positive infinity, negative infinity, and not-a-number (NaN).
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, negative infinity, 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
will generate an error when "x" is an IEEE special value.
In the past, some have recommended that programmers use expressions like:
PosInf = 1e300**2 NaN = PosInf/PosInf
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:
PosInf = 1e300000 NaN = PosInf/PosInf
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.
- Non-signalling IEEE 754 "Not a Number" value
- IEEE 754 Positive Infinity value
- IEEE 754 Negative Infinity value
- Determine if the argument is a IEEE 754 NaN (Not a Number) value.
- Determine if the argument is a IEEE 754 positive infinity value.
- Determine if the argument is a IEEE 754 negative infinity value.
- Determine if the argument is an finite IEEE 754 value (i.e., is not NaN, positive, or negative infinity).
- Determine if the argument is an infinite IEEE 754 value (positive or negative infinity)
(Run under Python 2.2.1 on Solaris 8.)
>>> import fpconst >>> val = 1e30000 # should be cause overflow and result in "Inf" >>> val Infinity >>> fpconst.isInf(val) 1 >>> fpconst.PosInf Infinity >>> nval = val/val # should result in NaN >>> nval NaN >>> fpconst.isNaN(nval) 1 >>> fpconst.isNaN(val) 0
The reference implementation is provided in the module "fpconst" , 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.
Patch 1151323 "New fpconst module"  on SourceForge adds the fpconst module to the Python standard library.
See http://babbage.cs.qc.edu/courses/cs341/IEEE-754references.html for reference material on the IEEE 754 floating point standard.
|||Further information on the reference package is available at http://research.warnes.net/projects/rzope/fpconst/|
This document has been placed in the public domain.