TIP #123: ADDING AN EXPONENTIATION OPERATOR TO THE [EXPR] COMMAND =================================================================== Version: $Revision: 1.6 $ Author: Arjen Markus Donal K. Fellows State: Final Type: Project Tcl-Version: 8.5 Vote: Done Created: Monday, 16 December 2002 URL: https://tip.tcl-lang.org123.html Post-History: ------------------------------------------------------------------------- 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: * Expressions using several exponentiations become difficult to read. For instance, a third-degree polynomial looks like: 2.0*pow($x,3) - 1.2*pow($x,2) + 3.0*$x + 4.0 or: 2.0*$x*$x*$x - 1.2*$x*$x + 3.0*$x + 4.0 * The result of raising an integer to an integer power is a double: 2 to the power 10 is 1024.0, not 1024. Other languages, like for instance FORTRAN, use an operator instead of a function. Two operators are commonly found: ** and ^. As the latter already has a meaning within the [expr] command, we propose to add the "**" operator instead. The above example would become: 2.0*$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): * The result is of the same type as the widest operand * An error is raised if the operation makes no mathematical sense, /0**(-1)/ for instance. * If /x/ has the value 0, then: * if /y > 0/, the result is 0 * if /y < 0/, the result is an error * if /y == 0/, the result is 1 * If /x/ has the value 1, then the result is always 1 * If /y/ has the value 0, the result is always 1 * If /x/ has a negative value lower than -1 and /y < 0/, the result is 0 * If /x/ has the value -1, then depending on whether /y/ is even or odd, the result is 1 or -1 (respectively.) * For all other combinations, the value is "/x/ raised to the power /y/" * When evaluating this, no attention is paid to overflow, even though the result might fit into a wide integer (though of course the result will be a wide integer if either operand was wide.) This is in accordance with the type model used in other [expr] operators. 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 ======================= COPYRIGHT =========== This document is placed in the public domain. ------------------------------------------------------------------------- TIP AutoGenerator - written by Donal K. Fellows