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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 nu-
	      meric 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  ar-
	      gument with respect to the second.  Each number must have	an in-
	      tegral 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 re-
	      sult 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 ar-
	      gument  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 re-
	      turns 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 ar-
	      guments 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 op-
       erate 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 al-
	      ways 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  (ac-
	      cording 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)

NAME | SYNOPSIS | DESCRIPTION | EXAMPLES | SEE ALSO | KEYWORDS

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