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

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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

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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 names-
       pace.

       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 argu-
	      ments. 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 opera-
	      tion are integers, the result will be an integer.

       % number number
	      Returns the integral modulus of the first argument with respect to the second.  Each number must have an integral value.	Note  that
	      Tcl defines this operation exactly even for negative numbers, so that the following equality holds true:
		     (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 follow-
	      ing 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  com-
	      parison 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  argu-
	      ments 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(n), mathfunc(n), namespace(n)

KEYWORDS

       command, expression, operator

Tcl									8.5								 mathop(n)