```
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
Tcl-Ticket: 655176
```

# 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 1If

*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.

# Sample Implementation

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

# Copyright

This document is placed in the public domain.