PEP: 242 Title: Numeric Kinds Version: $Revision$ 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. Local Variables: mode: indented-text indent-tabs-mode: nil End: