[comment {-*- tcl -*- doctools manpage}]
[vset VERSION 1.0.2]
[manpage_begin math::constants n [vset VERSION]]
[keywords constants]
[keywords degrees]
[keywords e]
[keywords math]
[keywords pi]
[keywords radians]
[copyright {2004 Arjen Markus <arjenmarkus@users.sourceforge.net>}]
[moddesc   {Tcl Math Library}]
[titledesc {Mathematical and numerical constants}]
[category  Mathematics]
[require Tcl [opt 8.3]]
[require math::constants [opt [vset VERSION]]]

[description]
[para]
This package defines some common mathematical and numerical constants.
By using the package you get consistent values for numbers like pi and
ln(10).

[para]
It defines two commands:

[list_begin itemized]
[item]
One for importing the constants

[item]
One for reporting which constants are defined and what values they
actually have.

[list_end]

[para]
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:
[example {
    variable radtodeg [expr {180.0/(4.0*atan(1.0))}]
}]
and use the variable radtodeg whenever you need the conversion.

[para]
This has two drawbacks:

[list_begin itemized]
[item]
You need to remember the proper formula or value and that is
error-prone.

[item]
Especially with the use of mathematical functions like [emph 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.

[list_end]

Here is the way you can do it with the [emph math::constants] package:
[example {
    package require math::constants
    ::math::constants::constants radtodeg degtorad
}]
which creates two variables, radtodeg and (its reciprocal) degtorad
in the calling namespace.

[para]
Constants that have been defined (their values are mostly taken
from mathematical tables with more precision than usually can be
handled) include:

[list_begin itemized]
[item]
basic constants like pi, e, gamma (Euler's constant)

[item]
derived values like ln(10) and sqrt(2)

[item]
purely numerical values such as 1/3 that are included for convenience
and for the fact that certain seemingly trivial computations like:
[example {
    set value [expr {3.0*$onethird}]
}]
give [emph exactly] the value you expect (if IEEE arithmetic is
available).

[list_end]

The full set of named constants is listed in section [sectref Constants].

[section "PROCEDURES"]

The package defines the following public procedures:

[list_begin definitions]

[call [cmd ::math::constants::constants] [arg args]]

Import the constants whose names are given as arguments

[para]

[call [cmd ::math::constants::print-constants] [arg args]]

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.

[list_end]

[section "Constants"]
[list_begin definitions]
[def [const pi]]       Ratio of circle circumference to diameter
[def [const e]]	       Base for natural logarithm
[def [const ln10]]     Natural logarithm of 10
[def [const phi]]      Golden ratio
[def [const gamma]]    Euler's constant
[def [const sqrt2]]    Square root of 2
[def [const thirdrt2]] One-third power of 2
[def [const sqrt3]]    Square root of 3
[def [const radtodeg]] Conversion from radians to degrees
[def [const degtorad]] Conversion from degrees to radians
[def [const onethird]] One third (0.3333....)
[def [const twothirds]]Two thirds (0.6666....)
[def [const onesixth]] One sixth (0.1666....)
[def [const huge]]     (Approximately) largest number
[def [const tiny]]     (Approximately) smallest number not equal zero
[def [const eps]]      Smallest number such that 1+eps != 1
[list_end]

[vset CATEGORY {math :: constants}]
[include ../common-text/feedback.inc]
[manpage_end]
