TIP 123: Adding an Exponentiation Operator to the [expr] Command

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by Aug 21.
Author:         Arjen Markus <arjen.markus@wldelft.nl>
Author:         Donal K. Fellows <donal.k.fellows@man.ac.uk>
State:          Final
Type:           Project
Vote:           Done
Created:        16-Dec-2002
Post-History:   
Keywords:       mathematics,evaluation
Tcl-Version:    8.5

Abstract

This TIP proposes to add a new operator to the operators recognised by the [expr] command: the exponentiation operator. This operator will enhance the functionality of the current pow() function by returning a result that depends on the type of its operands. It will also make complicated formulae more readable.

Introduction

Currently Tcl's [expr] command uses the exponentiation function pow() to calculate such expressions as "2 to the power 10". The drawback of this is twofold:

Other languages, like for instance FORTRAN, use an operator instead of a function. Two operators are commonly found: ** and ^. As the latter already has a meaning within the [expr] command, we propose to add the "**" operator instead. The above example would become:

 2.0*$x**3 - 1.2*$x**2 + 3.0*$x + 4.0

Mathematical Details

The implementation of the exponentiation operator will have the following properties (below we refer to the expression $x**$y):

If x and y are both integers (ordinary or wide):

If either x or y is a double, the C function pow() is used to compute the result.

The following expressions are parsed and evaluated in accordance with all other operators:

 $x ** $y ** $z ==> ($x ** $y ) ** $z
 $x ** -1       ==> ($x ** (-1))

The precedence of the exponentiation operator is thus higher than the multiplication, division and remainder operations and lower than the unary operations, in accordance with common definitions.

Sample Implementation

http://sf.net/tracker/?func=detail&aid=655176&group\_id=10894&atid=310894

Copyright

This document is placed in the public domain.

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