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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 argu‐
	      ment  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  recipro‐
	      cal  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	 oper‐
       ate 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 inte‐
	      ger 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 argu‐
	      ments. 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 argu‐
	      ments. 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 argu‐
	      ments. 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)
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