## Tcl8.6.0/Tk8.6.0 Documentation > Tcl Commands, version 8.6.0 > mathop

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  NAME
    mathop — Mathematical operators as Tcl commands
  SYNOPSIS
  DESCRIPTION
  MATHEMATICAL OPERATORS
    ! boolean
    + ?number ...?
    - number ?number ...?
    * ?number ...?
    / number ?number ...?
    % number number
    ** ?number ...?
  COMPARISON OPERATORS
    == ?arg ...?
    eq ?arg ...?
    != arg arg
    ne arg arg
    < ?arg ...?
    <= ?arg ...?
    > ?arg ...?
    >= ?arg ...?
  BIT-WISE OPERATORS
    ~ number
    & ?number ...?
    | ?number ...?
    ^ ?number ...?
    << number number
    >> number number
  LIST OPERATORS
    in arg list
    ni arg list
  EXAMPLES
  SEE ALSO
  KEYWORDS

### 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 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. 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, mathfunc, namespace

### KEYWORDS

command, expression, operator