mathop
Section: Tcl Mathematical Operator Commands (n)
Updated: 8.5
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NAME
mathop  Mathematical operators as Tcl commands
SYNOPSIS
package require
Tcl 8.5
::tcl::mathop::! number
::tcl::mathop::~ number
::tcl::mathop::+ ?number ...?
::tcl::mathop:: number ?number ...?
::tcl::mathop::* ?number ...?
::tcl::mathop::/ number ?number ...?
::tcl::mathop::% number number
::tcl::mathop::** ?number ...?
::tcl::mathop::& ?number ...?
::tcl::mathop:: ?number ...?
::tcl::mathop::^ ?number ...?
::tcl::mathop::<< number number
::tcl::mathop::>> number number
::tcl::mathop::== ?arg ...?
::tcl::mathop::!= arg arg
::tcl::mathop::< ?arg ...?
::tcl::mathop::<= ?arg ...?
::tcl::mathop::>= ?arg ...?
::tcl::mathop::> ?arg ...?
::tcl::mathop::eq ?arg ...?
::tcl::mathop::ne arg arg
::tcl::mathop::in arg list
::tcl::mathop::ni arg list
DESCRIPTION
The commands in the ::tcl::mathop namespace implement the same set of
operations as supported by the expr 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
not alter the way that the expr command behaves, and nor does
defining any new commands in the ::tcl::mathop namespace.
The following operator commands are supported:

~ ! +  *
/ % ** &
^ >> <<==eq
!= ne <<=>
>= in ni
MATHEMATICAL OPERATORS
The behaviors of the mathematical operator commands are as follows:
 ! boolean

Returns the boolean negation of boolean, where boolean 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
nonzero).
 + ?number ...?

Returns the sum of arbitrarily many arguments. Each number argument may
be any numeric value. If no arguments are given, the result will be zero (the
summation identity).
  number ?number ...?

If only a single number 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 number arguments
must be numeric values. At least one argument must be given.
 * ?number ...?

Returns the product of arbitrarily many arguments. Each number may be
any numeric value. If no arguments are given, the result will be one (the
multiplicative identity).
 / number ?number ...?

If only a single number 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 number arguments must
be numeric values. At least one argument must be given.

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 floor and int are applied to
them, in that order). If all values in the operation are integers, the result
will be an integer.
 % number number

Returns the integral modulus (i.e., remainder) of the first argument
with respect to the second.
Each number must have an integral value.
Also, the sign of the result will be the same as the sign of the second
number, which must not be zero.

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):

== [* [/ x y] y] [ x [% x y]]
 ** ?number ...?

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
``** 2 3 4''
is the same as
``** 2 [** 3 4]''.
Each number 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.
COMPARISON OPERATORS
The behaviors of the comparison operator commands (most of which operate
preferentially on numeric arguments) are as follows:
 == ?arg ...?

Returns whether each argument is equal to the arguments on each side of it in
the sense of the expr == operator (i.e., numeric comparison if
possible, exact string comparison otherwise). If fewer than two arguments
are given, this operation always returns a true value.
 eq ?arg ...?

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.
 != arg arg

Returns whether the two arguments are not equal to each other, in the sense of
the expr != operator (i.e., numeric comparison if possible, exact
string comparison otherwise).
 ne arg arg

Returns whether the two arguments are not equal to each other using exact
string comparison.
 < ?arg ...?

Returns whether the arbitrarilymany 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 string
compare command should be used instead.
 <= ?arg ...?

Returns whether the arbitrarilymany 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 string
compare command should be used instead.
 > ?arg ...?

Returns whether the arbitrarilymany 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 string
compare command should be used instead.
 >= ?arg ...?

Returns whether the arbitrarilymany 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 string
compare command should be used instead.
BITWISE OPERATORS
The behaviors of the bitwise operator commands (all of which only operate on
integral arguments) are as follows:
 ~ number

Returns the bitwise negation of number. Number may be an integer
of any size. Note that the result of this operation will always have the
opposite sign to the input number.
 & ?number ...?

Returns the bitwise AND of each of the arbitrarily many arguments. Each
number must have an integral value. If no arguments are given, the
result will be minus one.
  ?number ...?

Returns the bitwise OR of each of the arbitrarily many arguments. Each
number must have an integral value. If no arguments are given, the
result will be zero.
 ^ ?number ...?

Returns the bitwise XOR of each of the arbitrarily many arguments. Each
number must have an integral value. If no arguments are given, the
result will be zero.
 << number number

Returns the result of bitwise shifting the first argument left by the
number of bits specified in the second argument. Each number
must have an integral value.
 >> number number

Returns the result of bitwise shifting the first argument right by
the number of bits specified in the second argument. Each number
must have an integral value.
LIST OPERATORS
The behaviors of the listoriented operator commands are as follows:
 in arg list

Returns whether the value arg is present in the list list
(according to exact string comparison of elements).
 ni arg list

Returns whether the value arg is not present in the list list
(according to exact string comparison of elements).
EXAMPLES
The simplest way to use the operators is often by using namespace path
to make the commands available. This has the advantage of not affecting the
set of commands defined by the current namespace.

namespace path {::tcl::mathop ::tcl::mathfunc}
# Compute the sum of some numbers
set sum [+ 1 2 3]
# Compute the average of a list
set list {1 2 3 4 5 6}
set mean [/ [+ {*}$list] [double [llength $list]]]
# Test for list membership
set gotIt [in 3 $list]
# Test to see if a value is within some defined range
set inRange [<= 1 $x 5]
# Test to see if a list is sorted
set sorted [<= {*}$list]
SEE ALSO
expr(n),
mathfunc(n),
namespace(n)
KEYWORDS
command, expression, operator