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mathop(n) Tcl Mathematical Operator Commands mathop(n) 





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).

  

  
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.

  

  
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).

  

  
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:



  

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

  

  
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







  

    8.5
    Tcl