math::constants(3tcl)

💖 math::constants — the Tcl Math Library's little box of ✨famous numbers✨

okay so bestie, this is math::constants(3tcl) from the Tcl Math Library, and it's basically a snack drawer full of math constants so you never have to type 4.0*atan(1.0) ever again 🫶

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🌸 NAME 🌸

math::constants — mathematical and numerical constants, but make it convenient 💅

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✨ SYNOPSIS ✨

package require Tcl ?8.3?

package require math::constants ?1.0.4?

::math::constants::constants args

::math::constants::print-constants args

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🦋 DESCRIPTION 🦋

So this package defines some common mathematical and numerical constants. The whole point: by using it, you get consistent values for numbers like pi and ln(10). No cap, consistency is the vibe here.

It defines two commands:

• One for importing the constants 📥
• One for reporting which constants are defined and what values they actually have 📢

The motivation — and honestly this is so real — is that with (mathematical) computations, you very often need a good approximation to, say, the ratio of degrees to radians. Like, you could just define it yourself:

variable radtodeg [expr {180.0/(4.0*atan(1.0))}]

and then use the variable radtodeg whenever you need the conversion. Sure. But this has two drawbacks:

• You need to remember the proper formula or value and that is error-prone. Not the moment, bestie.
• 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. It's giving chaos across platforms 😭

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. Iconic behaviour, honestly 🌈

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). chef's kiss 👑

The full set of named constants is listed in section Constants below, bestie, don't worry, we got you 💜

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🎀 PROCEDURES 🎀

The package defines the following public procedures:

• ::math::constants::constants args — import the constants whose names are given as arguments 🌟
• ::math::constants::print-constants 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 💅

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👑 CONSTANTS 👑

The full roster, no gatekeeping:

• pi — ratio of circle circumference to diameter 🥧
• e — base for natural logarithm
• ln10 — natural logarithm of 10
• phi — golden ratio ✨
• gamma — Euler's constant
• sqrt2 — square root of 2
• thirdrt2 — one-third power of 2
• sqrt3 — square root of 3
• radtodeg — conversion from radians to degrees
• degtorad — conversion from degrees to radians
• onethird — one third (0.3333....)
• twothirds — two thirds (0.6666....)
• onesixth — one sixth (0.1666....)
• huge — (approximately) largest number
• tiny — (approximately) smallest number not equal zero
• eps — smallest number such that 1+eps != 1

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💀 BUGS, IDEAS, FEEDBACK 💀

This document, and the package it describes, will undoubtedly contain bugs and other problems. Not me being honest about it 😭 Please report such in the category math :: constants of the Tcllib Trackers [http://core.tcl.tk/tcllib/reportlist]. Please also report any ideas for enhancements you may have for either package and/or documentation. We love ideas fr fr 🫶

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.

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🔥 KEYWORDS 🔥

constants, degrees, e, math, pi, radians

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🌈 CATEGORY 🌈

Mathematics

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💖 COPYRIGHT 💖

Copyright (c) 2004 Arjen Markus <arjenmarkus@users.sourceforge.net>

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okay that's the whole thing bestie, you ate it, go import some constants 💅✨

this has been math::constants, version 1.0.4, brought to you by tcllib — mwah, ily, go compute something gorgeous 🦋🌸💜