TIP: | 123 |

Title: | Adding an Exponentiation Operator to the [expr] Command |

Version: | $Revision: 1.6 $ |

Authors: |
Arjen Markus <arjen dot markus at wldelft dot nl> Donal K. Fellows <donal dot k dot fellows at man dot ac dot uk> |

State: | Final |

Type: | Project |

Tcl-Version: | 8.5 |

Vote: | Done |

Created: | Monday, 16 December 2002 |

Keywords: | mathematics, evaluation |

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.

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

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 0if

*y < 0*, the result is an errorif

*y == 0*, the result is 1

If

*x*has the value 1, then the result is always 1If

*y*has the value 0, the result is always 1If

*x*has a negative value lower than -1 and*y < 0*, the result is 0If

*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.

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

This document is placed in the public domain.

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