'\" '\" Generated from file 'constants\&.man' by tcllib/doctools with format 'nroff' '\" Copyright (c) 2004 Arjen Markus '\" .TH "math::constants" 3tcl 1\&.0\&.2 tcllib "Tcl Math Library" .\" The -*- nroff -*- definitions below are for supplemental macros used .\" in Tcl/Tk manual entries. .\" .\" .AP type name in/out ?indent? .\" Start paragraph describing an argument to a library procedure. .\" type is type of argument (int, etc.), in/out is either "in", "out", .\" or "in/out" to describe whether procedure reads or modifies arg, .\" and indent is equivalent to second arg of .IP (shouldn't ever be .\" needed; use .AS below instead) .\" .\" .AS ?type? ?name? .\" Give maximum sizes of arguments for setting tab stops. Type and .\" name are examples of largest possible arguments that will be passed .\" to .AP later. If args are omitted, default tab stops are used. .\" .\" .BS .\" Start box enclosure. From here until next .BE, everything will be .\" enclosed in one large box. .\" .\" .BE .\" End of box enclosure. .\" .\" .CS .\" Begin code excerpt. .\" .\" .CE .\" End code excerpt. .\" .\" .VS ?version? ?br? .\" Begin vertical sidebar, for use in marking newly-changed parts .\" of man pages. The first argument is ignored and used for recording .\" the version when the .VS was added, so that the sidebars can be .\" found and removed when they reach a certain age. If another argument .\" is present, then a line break is forced before starting the sidebar. .\" .\" .VE .\" End of vertical sidebar. .\" .\" .DS .\" Begin an indented unfilled display. .\" .\" .DE .\" End of indented unfilled display. .\" .\" .SO ?manpage? .\" Start of list of standard options for a Tk widget. The manpage .\" argument defines where to look up the standard options; if .\" omitted, defaults to "options". The options follow on successive .\" lines, in three columns separated by tabs. .\" .\" .SE .\" End of list of standard options for a Tk widget. .\" .\" .OP cmdName dbName dbClass .\" Start of description of a specific option. cmdName gives the .\" option's name as specified in the class command, dbName gives .\" the option's name in the option database, and dbClass gives .\" the option's class in the option database. .\" .\" .UL arg1 arg2 .\" Print arg1 underlined, then print arg2 normally. .\" .\" .QW arg1 ?arg2? .\" Print arg1 in quotes, then arg2 normally (for trailing punctuation). .\" .\" .PQ arg1 ?arg2? .\" Print an open parenthesis, arg1 in quotes, then arg2 normally .\" (for trailing punctuation) and then a closing parenthesis. .\" .\" # Set up traps and other miscellaneous stuff for Tcl/Tk man pages. .if t .wh -1.3i ^B .nr ^l \n(.l .ad b .\" # Start an argument description .de AP .ie !"\\$4"" .TP \\$4 .el \{\ . ie !"\\$2"" .TP \\n()Cu . el .TP 15 .\} .ta \\n()Au \\n()Bu .ie !"\\$3"" \{\ \&\\$1 \\fI\\$2\\fP (\\$3) .\".b .\} .el \{\ .br .ie !"\\$2"" \{\ \&\\$1 \\fI\\$2\\fP .\} .el \{\ \&\\fI\\$1\\fP .\} .\} .. .\" # define tabbing values for .AP .de AS .nr )A 10n .if !"\\$1"" .nr )A \\w'\\$1'u+3n .nr )B \\n()Au+15n .\" .if !"\\$2"" .nr )B \\w'\\$2'u+\\n()Au+3n .nr )C \\n()Bu+\\w'(in/out)'u+2n .. .AS Tcl_Interp Tcl_CreateInterp in/out .\" # BS - start boxed text .\" # ^y = starting y location .\" # ^b = 1 .de BS .br .mk ^y .nr ^b 1u .if n .nf .if n .ti 0 .if n \l'\\n(.lu\(ul' .if n .fi .. .\" # BE - end boxed text (draw box now) .de BE .nf .ti 0 .mk ^t .ie n \l'\\n(^lu\(ul' .el \{\ .\" Draw four-sided box normally, but don't draw top of .\" box if the box started on an earlier page. .ie !\\n(^b-1 \{\ \h'-1.5n'\L'|\\n(^yu-1v'\l'\\n(^lu+3n\(ul'\L'\\n(^tu+1v-\\n(^yu'\l'|0u-1.5n\(ul' .\} .el \}\ \h'-1.5n'\L'|\\n(^yu-1v'\h'\\n(^lu+3n'\L'\\n(^tu+1v-\\n(^yu'\l'|0u-1.5n\(ul' .\} .\} .fi .br .nr ^b 0 .. .\" # VS - start vertical sidebar .\" # ^Y = starting y location .\" # ^v = 1 (for troff; for nroff this doesn't matter) .de VS .if !"\\$2"" .br .mk ^Y .ie n 'mc \s12\(br\s0 .el .nr ^v 1u .. .\" # VE - end of vertical sidebar .de VE .ie n 'mc .el \{\ .ev 2 .nf .ti 0 .mk ^t \h'|\\n(^lu+3n'\L'|\\n(^Yu-1v\(bv'\v'\\n(^tu+1v-\\n(^Yu'\h'-|\\n(^lu+3n' .sp -1 .fi .ev .\} .nr ^v 0 .. .\" # Special macro to handle page bottom: finish off current .\" # box/sidebar if in box/sidebar mode, then invoked standard .\" # page bottom macro. .de ^B .ev 2 'ti 0 'nf .mk ^t .if \\n(^b \{\ .\" Draw three-sided box if this is the box's first page, .\" draw two sides but no top otherwise. .ie !\\n(^b-1 \h'-1.5n'\L'|\\n(^yu-1v'\l'\\n(^lu+3n\(ul'\L'\\n(^tu+1v-\\n(^yu'\h'|0u'\c .el \h'-1.5n'\L'|\\n(^yu-1v'\h'\\n(^lu+3n'\L'\\n(^tu+1v-\\n(^yu'\h'|0u'\c .\} .if \\n(^v \{\ .nr ^x \\n(^tu+1v-\\n(^Yu \kx\h'-\\nxu'\h'|\\n(^lu+3n'\ky\L'-\\n(^xu'\v'\\n(^xu'\h'|0u'\c .\} .bp 'fi .ev .if \\n(^b \{\ .mk ^y .nr ^b 2 .\} .if \\n(^v \{\ .mk ^Y .\} .. .\" # DS - begin display .de DS .RS .nf .sp .. .\" # DE - end display .de DE .fi .RE .sp .. .\" # SO - start of list of standard options .de SO 'ie '\\$1'' .ds So \\fBoptions\\fR 'el .ds So \\fB\\$1\\fR .SH "STANDARD OPTIONS" .LP .nf .ta 5.5c 11c .ft B .. .\" # SE - end of list of standard options .de SE .fi .ft R .LP See the \\*(So manual entry for details on the standard options. .. .\" # OP - start of full description for a single option .de OP .LP .nf .ta 4c Command-Line Name: \\fB\\$1\\fR Database Name: \\fB\\$2\\fR Database Class: \\fB\\$3\\fR .fi .IP .. .\" # CS - begin code excerpt .de CS .RS .nf .ta .25i .5i .75i 1i .. .\" # CE - end code excerpt .de CE .fi .RE .. .\" # UL - underline word .de UL \\$1\l'|0\(ul'\\$2 .. .\" # QW - apply quotation marks to word .de QW .ie '\\*(lq'"' ``\\$1''\\$2 .\"" fix emacs highlighting .el \\*(lq\\$1\\*(rq\\$2 .. .\" # PQ - apply parens and quotation marks to word .de PQ .ie '\\*(lq'"' (``\\$1''\\$2)\\$3 .\"" fix emacs highlighting .el (\\*(lq\\$1\\*(rq\\$2)\\$3 .. .\" # QR - quoted range .de QR .ie '\\*(lq'"' ``\\$1''\\-``\\$2''\\$3 .\"" fix emacs highlighting .el \\*(lq\\$1\\*(rq\\-\\*(lq\\$2\\*(rq\\$3 .. .\" # MT - "empty" string .de MT .QW "" .. .BS .SH NAME math::constants \- Mathematical and numerical constants .SH SYNOPSIS package require \fBTcl ?8\&.3?\fR .sp package require \fBmath::constants ?1\&.0\&.2?\fR .sp \fB::math::constants::constants\fR \fIargs\fR .sp \fB::math::constants::print-constants\fR \fIargs\fR .sp .BE .SH DESCRIPTION .PP This package defines some common mathematical and numerical constants\&. By using the package you get consistent values for numbers like pi and ln(10)\&. .PP It defines two commands: .IP \(bu One for importing the constants .IP \(bu One for reporting which constants are defined and what values they actually have\&. .PP .PP 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: .CS variable radtodeg [expr {180\&.0/(4\&.0*atan(1\&.0))}] .CE and use the variable radtodeg whenever you need the conversion\&. .PP This has two drawbacks: .IP \(bu You need to remember the proper formula or value and that is error-prone\&. .IP \(bu Especially with the use of mathematical functions like \fIatan\fR you assume that they have been accurately implemented\&. This is seldom or never the case and for each platform you can get subtle differences\&. .PP Here is the way you can do it with the \fImath::constants\fR package: .CS package require math::constants ::math::constants::constants radtodeg degtorad .CE which creates two variables, radtodeg and (its reciprocal) degtorad in the calling namespace\&. .PP Constants that have been defined (their values are mostly taken from mathematical tables with more precision than usually can be handled) include: .IP \(bu basic constants like pi, e, gamma (Euler's constant) .IP \(bu derived values like ln(10) and sqrt(2) .IP \(bu purely numerical values such as 1/3 that are included for convenience and for the fact that certain seemingly trivial computations like: .CS set value [expr {3\&.0*$onethird}] .CE .IP give \fIexactly\fR the value you expect (if IEEE arithmetic is available)\&. .PP The full set of named constants is listed in section \fBConstants\fR\&. .SH PROCEDURES The package defines the following public procedures: .TP \fB::math::constants::constants\fR \fIargs\fR Import the constants whose names are given as arguments .sp .TP \fB::math::constants::print-constants\fR \fIargs\fR 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\&. .PP .SH CONSTANTS .TP \fBpi\fR Ratio of circle circumference to diameter .TP \fBe\fR Base for natural logarithm .TP \fBln10\fR Natural logarithm of 10 .TP \fBphi\fR Golden ratio .TP \fBgamma\fR Euler's constant .TP \fBsqrt2\fR Square root of 2 .TP \fBthirdrt2\fR One-third power of 2 .TP \fBsqrt3\fR Square root of 3 .TP \fBradtodeg\fR Conversion from radians to degrees .TP \fBdegtorad\fR Conversion from degrees to radians .TP \fBonethird\fR One third (0\&.3333\&.\&.\&.\&.) .TP \fBtwothirds\fR Two thirds (0\&.6666\&.\&.\&.\&.) .TP \fBonesixth\fR One sixth (0\&.1666\&.\&.\&.\&.) .TP \fBhuge\fR (Approximately) largest number .TP \fBtiny\fR (Approximately) smallest number not equal zero .TP \fBeps\fR Smallest number such that 1+eps != 1 .PP .SH "BUGS, IDEAS, FEEDBACK" This document, and the package it describes, will undoubtedly contain bugs and other problems\&. Please report such in the category \fImath :: constants\fR of the \fITcllib Trackers\fR [http://core\&.tcl\&.tk/tcllib/reportlist]\&. Please also report any ideas for enhancements you may have for either package and/or documentation\&. .PP When proposing code changes, please provide \fIunified diffs\fR, i\&.e the output of \fBdiff -u\fR\&. .PP Note further that \fIattachments\fR are strongly preferred over inlined patches\&. Attachments can be made by going to the \fBEdit\fR form of the ticket immediately after its creation, and then using the left-most button in the secondary navigation bar\&. .SH KEYWORDS constants, degrees, e, math, pi, radians .SH CATEGORY Mathematics .SH COPYRIGHT .nf Copyright (c) 2004 Arjen Markus .fi