.\"
.\" Copyright (c) 2006-2007 Donal K. Fellows.
.\"
.\" See the file "license.terms" for information on usage and redistribution
.\" of this file, and for a DISCLAIMER OF ALL WARRANTIES.
.\"
.TH mathop 3tcl 8.5 Tcl "Tcl Mathematical Operator Commands"
.\" 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
.\" Note:  do not modify the .SH NAME line immediately below!
.SH NAME
mathop \- Mathematical operators as Tcl commands
.SH SYNOPSIS
package require \fBTcl 8.5-\fR
.sp
\fB::tcl::mathop::!\fR \fInumber\fR
.br
\fB::tcl::mathop::~\fR \fInumber\fR
.br
\fB::tcl::mathop::+\fR ?\fInumber\fR ...?
.br
\fB::tcl::mathop::\-\fR \fInumber\fR ?\fInumber\fR ...?
.br
\fB::tcl::mathop::*\fR ?\fInumber\fR ...?
.br
\fB::tcl::mathop::/\fR \fInumber\fR ?\fInumber\fR ...?
.br
\fB::tcl::mathop::%\fR \fInumber number\fR
.br
\fB::tcl::mathop::**\fR ?\fInumber\fR ...?
.br
\fB::tcl::mathop::&\fR ?\fInumber\fR ...?
.br
\fB::tcl::mathop::|\fR ?\fInumber\fR ...?
.br
\fB::tcl::mathop::^\fR ?\fInumber\fR ...?
.br
\fB::tcl::mathop::<<\fR \fInumber number\fR
.br
\fB::tcl::mathop::>>\fR \fInumber number\fR
.br
\fB::tcl::mathop::==\fR ?\fIarg\fR ...?
.br
\fB::tcl::mathop::!=\fR \fIarg arg\fR
.br
\fB::tcl::mathop::<\fR ?\fIarg\fR ...?
.br
\fB::tcl::mathop::<=\fR ?\fIarg\fR ...?
.br
\fB::tcl::mathop::>=\fR ?\fIarg\fR ...?
.br
\fB::tcl::mathop::>\fR ?\fIarg\fR ...?
.br
\fB::tcl::mathop::eq\fR ?\fIarg\fR ...?
.br
\fB::tcl::mathop::ne\fR \fIarg arg\fR
.br
.VS "8.7, TIP461"
\fB::tcl::mathop::lt\fR ?\fIarg\fR ...?
.br
\fB::tcl::mathop::le\fR ?\fIarg\fR ...?
.br
\fB::tcl::mathop::gt\fR ?\fIarg\fR ...?
.br
\fB::tcl::mathop::ge\fR ?\fIarg\fR ...?
.VE "8.7, TIP461"
.br
\fB::tcl::mathop::in\fR \fIarg list\fR
.br
\fB::tcl::mathop::ni\fR \fIarg list\fR
.sp
.BE
.SH DESCRIPTION
.PP
The commands in the \fB::tcl::mathop\fR namespace implement the same set of
operations as supported by the \fBexpr\fR command. All are exported from the
namespace, but are not imported into any other namespace by default. Note that
renaming, reimplementing or deleting any of the commands in the namespace does
\fInot\fR alter the way that the \fBexpr\fR command behaves, and nor does
defining any new commands in the \fB::tcl::mathop\fR namespace.
.PP
The following operator commands are supported:
.DS
.ta 2c 4c 6c 8c
\fB~\fR	\fB!\fR	\fB+\fR	\fB\-\fR	\fB*\fR
\fB/\fR	\fB%\fR	\fB**\fR	\fB&\fR	\fB|\fR
\fB^\fR	\fB>>\fR	\fB<<\fR	\fB==\fR	\fBeq\fR
\fB!=\fR	\fBne\fR	\fB<\fR	\fB<=\fR	\fB>\fR
\fB>=\fR	\fBin\fR	\fBni\fR	\fBlt\fR	\fBle\fR
\fBgt\fR	\fBge\fR
.DE
.SS "MATHEMATICAL OPERATORS"
.PP
The behaviors of the mathematical operator commands are as follows:
.TP
\fB!\fR \fIboolean\fR
.
Returns the boolean negation of \fIboolean\fR, where \fIboolean\fR may be any
numeric value or any other form of boolean value (i.e. it returns truth if the
argument is falsity or zero, and falsity if the argument is truth or
non-zero).
.TP
\fB+\fR ?\fInumber\fR ...?
.
Returns the sum of arbitrarily many arguments. Each \fInumber\fR argument may
be any numeric value. If no arguments are given, the result will be zero (the
summation identity).
.TP
\fB\-\fR \fInumber\fR ?\fInumber\fR ...?
.
If only a single \fInumber\fR argument is given, returns the negation of that
numeric value. Otherwise returns the number that results when all subsequent
numeric values are subtracted from the first one. All \fInumber\fR arguments
must be numeric values. At least one argument must be given.
.TP
\fB*\fR ?\fInumber\fR ...?
.
Returns the product of arbitrarily many arguments. Each \fInumber\fR may be
any numeric value. If no arguments are given, the result will be one (the
multiplicative identity).
.TP
\fB/\fR \fInumber\fR ?\fInumber\fR ...?
.
If only a single \fInumber\fR argument is given, returns the reciprocal of that
numeric value (i.e. the value obtained by dividing 1.0 by that value).
Otherwise returns the number that results when the first numeric argument is
divided by all subsequent numeric arguments. All \fInumber\fR arguments must
be numeric values. At least one argument must be given.
.RS
.PP
Note that when the leading values in the list of arguments are integers,
integer division will be used for those initial steps (i.e. the intermediate
results will be as if the functions \fIfloor\fR and \fIint\fR are applied to
them, in that order). If all values in the operation are integers, the result
will be an integer.
.RE
.TP
\fB%\fR \fInumber number\fR
.
Returns the integral modulus (i.e., remainder) of the first argument
with respect to the second.
Each \fInumber\fR must have an integral value.
Also, the sign of the result will be the same as the sign of the second
\fInumber\fR, which must not be zero.
.RS
.PP
Note that Tcl defines this operation exactly even for negative numbers, so
that the following command returns a true value (omitting the namespace for
clarity):
.PP
.CS
\fB==\fR [\fB*\fR [\fB/\fI x y\fR] \fIy\fR] [\fB\-\fI x\fR [\fB%\fI x y\fR]]
.CE
.RE
.TP
\fB**\fR ?\fInumber\fR ...?
.
Returns the result of raising each value to the power of the result of
recursively operating on the result of processing the following arguments, so
.QW "\fB** 2 3 4\fR"
is the same as
.QW "\fB** 2 [** 3 4]\fR" .
Each \fInumber\fR may be
any numeric value, though the second number must not be fractional if the
first is negative.  The maximum exponent value that Tcl can handle if the
first number is an integer > 1 is 268435455. If no arguments are given,
the result will be one, and if only one argument is given, the result will
be that argument. The result will have an integral value only when all
arguments are integral values.
.SS "COMPARISON OPERATORS"
.PP
The behaviors of the comparison operator commands (most of which operate
preferentially on numeric arguments) are as follows:
.TP
\fB==\fR ?\fIarg\fR ...?
.
Returns whether each argument is equal to the arguments on each side of it in
the sense of the \fBexpr\fR == operator (\fIi.e.\fR, numeric comparison if
possible, exact string comparison otherwise). If fewer than two arguments
are given, this operation always returns a true value.
.TP
\fBeq\fR ?\fIarg\fR ...?
.
Returns whether each argument is equal to the arguments on each side of it
using exact string comparison. If fewer than two arguments are given, this
operation always returns a true value.
.TP
\fB!=\fR \fIarg arg\fR
.
Returns whether the two arguments are not equal to each other, in the sense of
the \fBexpr\fR != operator (\fIi.e.\fR, numeric comparison if possible, exact
string comparison otherwise).
.TP
\fBne\fR \fIarg arg\fR
.
Returns whether the two arguments are not equal to each other using exact
string comparison.
.TP
\fB<\fR ?\fIarg\fR ...?
.
Returns whether the arbitrarily-many arguments are ordered, with each argument
after the first having to be strictly more than the one preceding it.
Comparisons are performed preferentially on the numeric values, and are
otherwise performed using UNICODE string comparison. If fewer than two
arguments are present, this operation always returns a true value. When the
arguments are numeric but should be compared as strings, the \fBlt\fR
operator or the \fBstring compare\fR command should be used instead.
.TP
\fB<=\fR ?\fIarg\fR ...?
.
Returns whether the arbitrarily-many arguments are ordered, with each argument
after the first having to be equal to or more than the one preceding it.
Comparisons are performed preferentially on the numeric values, and are
otherwise performed using UNICODE string comparison. If fewer than two
arguments are present, this operation always returns a true value. When the
arguments are numeric but should be compared as strings,  the \fBle\fR
operator or the \fBstring compare\fR command should be used instead.
.TP
\fB>\fR ?\fIarg\fR ...?
.
Returns whether the arbitrarily-many arguments are ordered, with each argument
after the first having to be strictly less than the one preceding it.
Comparisons are performed preferentially on the numeric values, and are
otherwise performed using UNICODE string comparison. If fewer than two
arguments are present, this operation always returns a true value. When the
arguments are numeric but should be compared as strings, the \fBgt\fR
operator or the \fBstring compare\fR command should be used instead.
.TP
\fB>=\fR ?\fIarg\fR ...?
.
Returns whether the arbitrarily-many arguments are ordered, with each argument
after the first having to be equal to or less than the one preceding it.
Comparisons are performed preferentially on the numeric values, and are
otherwise performed using UNICODE string comparison. If fewer than two
arguments are present, this operation always returns a true value. When the
arguments are numeric but should be compared as strings, the \fBge\fR
operator or the \fBstring compare\fR command should be used instead.
.TP
\fBlt\fR ?\fIarg\fR ...?
.VS "8.7, TIP461"
Returns whether the arbitrarily-many arguments are ordered, with each argument
after the first having to be strictly more than the one preceding it.
Comparisons are performed using UNICODE string comparison. If fewer than two
arguments are present, this operation always returns a true value.
.VE "8.7, TIP461"
.TP
\fBle\fR ?\fIarg\fR ...?
.VS "8.7, TIP461"
Returns whether the arbitrarily-many arguments are ordered, with each argument
after the first having to be equal to or strictly more than the one preceding it.
Comparisons are performed using UNICODE string comparison. If fewer than two
arguments are present, this operation always returns a true value.
.VE "8.7, TIP461"
.TP
\fBgt\fR ?\fIarg\fR ...?
.VS "8.7, TIP461"
Returns whether the arbitrarily-many arguments are ordered, with each argument
after the first having to be strictly less than the one preceding it.
Comparisons are performed using UNICODE string comparison. If fewer than two
arguments are present, this operation always returns a true value.
.VE "8.7, TIP461"
.TP
\fBge\fR ?\fIarg\fR ...?
.VS "8.7, TIP461"
Returns whether the arbitrarily-many arguments are ordered, with each argument
after the first having to be equal to or strictly less than the one preceding it.
Comparisons are performed using UNICODE string comparison. If fewer than two
arguments are present, this operation always returns a true value.
.VE "8.7, TIP461"
.SS "BIT-WISE OPERATORS"
.PP
The behaviors of the bit-wise operator commands (all of which only operate on
integral arguments) are as follows:
.TP
\fB~\fR \fInumber\fR
.
Returns the bit-wise negation of \fInumber\fR. \fINumber\fR may be an integer
of any size. Note that the result of this operation will always have the
opposite sign to the input \fInumber\fR.
.TP
\fB&\fR ?\fInumber\fR ...?
.
Returns the bit-wise AND of each of the arbitrarily many arguments. Each
\fInumber\fR must have an integral value. If no arguments are given, the
result will be minus one.
.TP
\fB|\fR ?\fInumber\fR ...?
.
Returns the bit-wise OR of each of the arbitrarily many arguments. Each
\fInumber\fR must have an integral value. If no arguments are given, the
result will be zero.
.TP
\fB^\fR ?\fInumber\fR ...?
.
Returns the bit-wise XOR of each of the arbitrarily many arguments. Each
\fInumber\fR must have an integral value. If no arguments are given, the
result will be zero.
.TP
\fB<<\fR \fInumber number\fR
.
Returns the result of bit-wise shifting the first argument left by the
number of bits specified in the second argument. Each \fInumber\fR
must have an integral value.
.TP
\fB>>\fR \fInumber number\fR
.
Returns the result of bit-wise shifting the first argument right by
the number of bits specified in the second argument. Each \fInumber\fR
must have an integral value.
.SS "LIST OPERATORS"
.PP
The behaviors of the list-oriented operator commands are as follows:
.TP
\fBin\fR \fIarg list\fR
.
Returns whether the value \fIarg\fR is present in the list \fIlist\fR
(according to exact string comparison of elements).
.TP
\fBni\fR \fIarg list\fR
.
Returns whether the value \fIarg\fR is not present in the list \fIlist\fR
(according to exact string comparison of elements).
.SH EXAMPLES
.PP
The simplest way to use the operators is often by using \fBnamespace path\fR
to make the commands available. This has the advantage of not affecting the
set of commands defined by the current namespace.
.PP
.CS
namespace path {\fB::tcl::mathop\fR ::tcl::mathfunc}

\fI# Compute the sum of some numbers\fR
set sum [\fB+\fR 1 2 3]

\fI# Compute the average of a list\fR
set list {1 2 3 4 5 6}
set mean [\fB/\fR [\fB+\fR {*}$list] [double [llength $list]]]

\fI# Test for list membership\fR
set gotIt [\fBin\fR 3 $list]

\fI# Test to see if a value is within some defined range\fR
set inRange [\fB<=\fR 1 $x 5]

\fI# Test to see if a list is numerically sorted\fR
set sorted [\fB<=\fR {*}$list]

\fI# Test to see if a list is lexically sorted\fR
set alphaList {a b c d e f}
set sorted [\fBle\fR {*}$alphaList]
.CE
.SH "SEE ALSO"
expr(3tcl), mathfunc(3tcl), namespace(3tcl)
.SH KEYWORDS
command, expression, operator
'\" Local Variables:
'\" mode: nroff
'\" End: