TIP: 123 Title: Adding an Exponentiation Operator to the [expr] Command Version: $Revision: 1.6 $ Author: Arjen Markus Author: Donal K. Fellows 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: * 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 http://sf.net/tracker/?func=detail&aid=655176&group_id=10894&atid=310894 ~ Copyright This document is placed in the public domain.