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diff --git a/tcllib/idoc/man/files/modules/math/constants.n b/tcllib/idoc/man/files/modules/math/constants.n new file mode 100644 index 0000000..b05b417 --- /dev/null +++ b/tcllib/idoc/man/files/modules/math/constants.n @@ -0,0 +1,430 @@ +'\" +'\" Generated from file 'constants\&.man' by tcllib/doctools with format 'nroff' +'\" Copyright (c) 2004 Arjen Markus <arjenmarkus@users\&.sourceforge\&.net> +'\" +.TH "math::constants" n 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\&. +.SH KEYWORDS +constants, degrees, e, math, pi, radians +.SH CATEGORY +Mathematics +.SH COPYRIGHT +.nf +Copyright (c) 2004 Arjen Markus <arjenmarkus@users\&.sourceforge\&.net> + +.fi
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