math::constants - Mathematical and numerical constants
This package defines some common mathematical and numerical constants. By using the package you get consistent values for numbers like pi and ln(10).
It defines two commands:
One for importing the constants
One for reporting which constants are defined and what values they actually have.
The motivation for this package is that quite often, with (mathematical) computations, you need a good approximation to, say, the ratio of degrees to radians. You can, of course, define this like:
variable radtodeg [expr {180.0/(4.0*atan(1.0))}]
and use the variable radtodeg whenever you need the conversion.
This has two drawbacks:
You need to remember the proper formula or value and that is error-prone.
Especially with the use of mathematical functions like atan you assume that they have been accurately implemented. This is seldom or never the case and for each platform you can get subtle differences.
Here is the way you can do it with the math::constants package:
package require math::constants ::math::constants::constants radtodeg degtorad
which creates two variables, radtodeg and (its reciprocal) degtorad in the calling namespace.
Constants that have been defined (their values are mostly taken from mathematical tables with more precision than usually can be handled) include:
basic constants like pi, e, gamma (Euler's constant)
derived values like ln(10) and sqrt(2)
purely numerical values such as 1/3 that are included for convenience and for the fact that certain seemingly trivial computations like:
set value [expr {3.0*$onethird}]
give exactly the value you expect (if IEEE arithmetic is available).
The full set of named constants is listed in section Constants.
The package defines the following public procedures:
Import the constants whose names are given as arguments
Print the constants whose names are given as arguments on the screen (name, value and description) or, if no arguments are given, print all defined constants. This is mainly a convenience procedure.
Ratio of circle circumference to diameter
Base for natural logarithm
Natural logarithm of 10
Golden ratio
Euler's constant
Square root of 2
One-third power of 2
Square root of 3
Conversion from radians to degrees
Conversion from degrees to radians
One third (0.3333....)
Two thirds (0.6666....)
One sixth (0.1666....)
(Approximately) largest number
(Approximately) smallest number not equal zero
Smallest number such that 1+eps != 1
This document, and the package it describes, will undoubtedly contain bugs and other problems. Please report such in the category math :: constants of the Tcllib Trackers. Please also report any ideas for enhancements you may have for either package and/or documentation.
When proposing code changes, please provide unified diffs, i.e the output of diff -u.
Note further that attachments are strongly preferred over inlined patches. Attachments can be made by going to the Edit form of the ticket immediately after its creation, and then using the left-most button in the secondary navigation bar.
Mathematics
Copyright © 2004 Arjen Markus <[email protected]>