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-.\"
-.\" 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 n 8.5 Tcl "Tcl Mathematical Operator Commands"
-.so man.macros
-.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
-\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
-.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. 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 \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 \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 \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 \fBstring
-compare\fR command should be used instead.
-.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 $x 5]
-
-\fI# Test to see if a list is sorted\fR
-set sorted [\fB<=\fR {*}$list]
-.CE
-.SH "SEE ALSO"
-expr(n), mathfunc(n), namespace(n)
-.SH KEYWORDS
-command, expression, operator
-'\" Local Variables:
-'\" mode: nroff
-'\" End: