Provided by: tcl8.6-doc_8.6.12+dfsg-1build1_all 
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
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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 non-zero).
+ ?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. 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.
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 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 string compare command should be used instead.
<= ?arg ...?
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 string compare command should be used instead.
> ?arg ...?
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 string compare command should be used instead.
>= ?arg ...?
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 string compare command should be used instead.
BIT-WISE OPERATORS
The behaviors of the bit-wise operator commands (all of which only operate on integral
arguments) are as follows:
~ number
Returns the bit-wise 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 bit-wise 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 bit-wise 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 bit-wise 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 bit-wise 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 bit-wise 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 list-oriented 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(3tcl), mathfunc(3tcl), namespace(3tcl)
KEYWORDS
command, expression, operator