[Python-checkins] CVS: python/nondist/peps pep-0242.txt,NONE,1.1
Barry Warsaw
bwarsaw@users.sourceforge.net
Mon, 19 Mar 2001 21:29:18 -0800
Update of /cvsroot/python/python/nondist/peps
In directory usw-pr-cvs1:/tmp/cvs-serv17967
Added Files:
pep-0242.txt
Log Message:
PEP 242, Numeric Kinds, Paul F. Dubois
(With minor editorial and spelling check pass by Barry)
--- NEW FILE: pep-0242.txt ---
PEP: 242
Title: Numeric Kinds
Version: $Revision: 1.1 $
Author: paul@pfdubois.com (Paul F. Dubois)
Status: Draft
Type: Standards Track
Created: 17-Mar-2001
Python-Version: 2.2
Post-History:
Abstract
This proposal gives the user optional control over the precision
and range of numeric computations so that a computation can be
written once and run anywhere with at least the desired precision
and range. It is backward compatible with existing code. The
meaning of decimal literals is clarified.
Rationale
Currently it is impossible in every language except Fortran 90 to
write a program in a portable way that uses floating point and
gets roughly the same answer regardless of platform -- or refuses
to compile if that is not possible. Python currently has only one
floating point type, equal to a C double in the C implementation.
No type exists corresponding to single or quad floats. It would
complicate the language to try to introduce such types directly
and their subsequent use would not be portable. This proposal is
similar to the Fortran 90 "kind" solution, adapted to the Python
environment. With this facility an entire calculation can be
switched from one level of precision to another by changing a
single line. If the desired precision does not exist on a
particular machine, the program will fail rather than get the
wrong answer. Since coding in this style would involve an early
call to the routine that will fail, this is the next best thing to
not compiling.
Supported Kinds
Each Python compiler may define as many "kinds" of integer and
floating point numbers as it likes, except that it must support at
least two kinds of integer corresponding to the existing int and
long, and must support at least one kind of floating point number,
equivalent to the present float. The range and precision of the
these kinds are processor dependent, as at present, except for the
"long integer" kind, which can hold an arbitrary integer. The
built-in functions int(), float(), long() and complex() convert
inputs to these default kinds as they do at present. (Note that a
Unicode string is actually a different "kind" of string and that a
sufficiently knowledgeable person might be able to expand this PEP
to cover that case.)
Within each type (integer, floating, and complex) the compiler
supports a linearly-ordered set of kinds, with the ordering
determined by the ability to hold numbers of an increased range
and/or precision.
Kind Objects
Three new standard functions are defined in a module named
"kinds". They return callable objects called kind objects. Each
int or floating kind object f has the signature result = f(x), and
each complex kind object has the signature result = f(x, y=0.).
int_kind(n)
For n >= 1, return a callable object whose result is an
integer kind that will hold an integer number in the open
interval (-10**n,10**n). This function always succeeds, since
it can return the 'long' kind if it has to. The kind object
accepts arguments that are integers including longs. If n ==
0, returns the kind object corresponding to long.
float_kind(nd, n)
For nd >= 0 and n >= 1, return a callable object whose result
is a floating point kind that will hold a floating-point
number with at least nd digits of precision and a base-10
exponent in the open interval (-n, n). The kind object
accepts arguments that are integer or real.
complex_kind(nd, n)
Return a callable object whose result is a complex kind that
will will hold a complex number each of whose components
(.real, .imag) is of kind float_kind(nd, n). The kind object
will accept one argument that is integer, real, or complex, or
two arguments, each integer or real.
The compiler will return a kind object corresponding to the least
of its available set of kinds for that type that has the desired
properties. If no kind with the desired qualities exists in a
given implementation an OverflowError exception is thrown. A kind
function converts its argument to the target kind, but if the
result does not fit in the target kind's range, an OverflowError
exception is thrown.
Kind objects also accept a string argument for conversion of
literal notation to their kind.
Besides their callable behavior, kind objects have attributes
giving the traits of the kind in question. The list of traits
needs to be completed.
The Meaning of Literal Values
Literal integer values without a trailing L are of the least
integer kind required to represent them. An integer literal with
a trailing L is a long. Literal decimal values are of the
greatest available binary floating-point kind.
Concerning Infinite Floating Precision
This section makes no proposals and can be omitted from
consideration. It is for illuminating an intentionally
unimplemented 'corner' of the design.
This PEP does not propose the creation of an infinite precision
floating point type, just leaves room for it. Just as int_kind(0)
returns the long kind object, if in the future an infinitely
precise decimal kind is available, float_kind(0,0) could return a
function that converts to that type. Since such a kind function
accepts string arguments, programs could then be written that are
completely precise. Perhaps in analogy to r'a raw string', 1.3r
might be available as syntactic sugar for calling the infinite
floating kind object with argument '1.3'. r could be thought of
as meaning 'rational'.
Complex numbers and kinds
Complex numbers are always pairs of floating-point numbers with
the same kind. A Python compiler must support a complex analog of
each floating point kind it supports, if it supports complex
numbers at all.
Coercion
In an expression, coercion between different kinds is to the
greater kind. For this purpose, all complex kinds are "greater
than" all floating-point kinds, and all floating-point kinds are
"greater than" all integer kinds.
Examples
In module myprecision.py:
import kinds
tinyint = kinds.int_kind(1)
single = kinds.float_kind(6, 90)
double = kinds.float_kind(15, 300)
csingle = kinds.complex_kind(6, 90)
In the rest of my code:
from myprecision import tinyint, single, double, csingle
n = tinyint(3)
x = double(1.e20)
z = 1.2
# builtin float gets you the default float kind, properties unknown
w = x * float(x)
w = x * double(z)
u = csingle(x + z * 1.0j)
u2 = csingle(x+z, 1.0)
Note how that entire code can then be changed to a higher
precision by changing the arguments in myprecision.py.
Comment: note that you aren't promised that single != double; but
you are promised that double(1.e20) will hold a number with 15
decimal digits of precision and a range up to 10**300 or that the
float_kind call will fail.
Open Issues
The assertion that a decimal literal means a binary floating-point
value of the largest available kind is in conflict with other
proposals about Python's numeric model. This PEP asserts that
these other proposals are wrong and that part of them should not
be implemented.
Determine the exact list of traits for integer and floating point
numbers. There are some standard Fortran routines that do this
but I have to track them down. Also there should be information
sufficient to create a Numeric array of an equal or greater kind.
Copyright
This document has been placed in the public domain.
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