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expr(n) 			      Tcl Built-In Commands				  expr(n)


       expr - Evaluate an expression

       expr arg ?arg arg ...?

       Concatenates  arg's  (adding separator spaces between them), evaluates the result as a Tcl
       expression, and returns the value.  The operators permitted in Tcl expressions are a  sub-
       set of the operators permitted in C expressions, and they have the same meaning and prece-
       dence as the corresponding C operators.	Expressions almost always yield  numeric  results
       (integer or floating-point values).  For example, the expression
	      expr 8.2 + 6
       evaluates to 14.2.  Tcl expressions differ from C expressions in the way that operands are
       specified.  Also, Tcl expressions support non-numeric operands and string comparisons.

       A Tcl expression consists of a combination of operands, operators, and parentheses.  White
       space may be used between the operands and operators and parentheses; it is ignored by the
       expression's instructions.  Where possible, operands are interpreted  as  integer  values.
       Integer values may be specified in decimal (the normal case), in octal (if the first char-
       acter of the operand is 0), or in hexadecimal (if the first two characters of the  operand
       are  0x).   If an operand does not have one of the integer formats given above, then it is
       treated as a floating-point number if that is possible.	 Floating-point  numbers  may  be
       specified  in any of the ways accepted by an ANSI-compliant C compiler (except that the f,
       F, l, and L suffixes will not be permitted in most installations).  For	example,  all  of
       the  following  are  valid floating-point numbers:  2.1, 3., 6e4, 7.91e+16.  If no numeric
       interpretation is possible, then an operand is left as a string (and only a limited set of
       operators may be applied to it).

       Operands may be specified in any of the following ways:

       [1]    As an numeric value, either integer or floating-point.

       [2]    As a Tcl variable, using standard $ notation.  The variable's value will be used as
	      the operand.

       [3]    As a string enclosed in double-quotes.  The expression parser  will  perform  back-
	      slash,  variable,  and command substitutions on the information between the quotes,
	      and use the resulting value as the operand

       [4]    As a string enclosed in braces.  The characters between the open brace and matching
	      close brace will be used as the operand without any substitutions.

       [5]    As a Tcl command enclosed in brackets.  The command will be executed and its result
	      will be used as the operand.

       [6]    As a mathematical function whose arguments have any of the above	forms  for  oper-
	      ands, such as sin($x).  See below for a list of defined functions.

       Where  substitutions  occur  above (e.g. inside quoted strings), they are performed by the
       expression's instructions.  However, an additional layer of substitution may already  have
       been  performed by the command parser before the expression processor was called.  As dis-
       cussed below, it is usually best to enclose expressions in braces to prevent  the  command
       parser from performing substitutions on the contents.

       For  some  examples  of simple expressions, suppose the variable a has the value 3 and the
       variable b has the value 6.  Then the command on the left side of each of the lines  below
       will produce the value on the right side of the line:
	      expr 3.1 + $a	      6.1
	      expr 2 + "$a.$b"	      5.6
	      expr 4*[llength "6 2"]  8
	      expr {{word one} < "word $a"}0

       The valid operators are listed below, grouped in decreasing order of precedence:

       -  +  ~	!	   Unary minus, unary plus, bit-wise NOT, logical NOT.	None of these op-
			   erands may be applied to string operands,  and  bit-wise  NOT  may  be
			   applied only to integers.

       *  /  %		   Multiply, divide, remainder.  None of these operands may be applied to
			   string operands, and remainder may be applied only to  integers.   The
			   remainder  will  always have the same sign as the divisor and an abso-
			   lute value smaller than the divisor.

       +  -		   Add and subtract.  Valid for any numeric operands.

       <<  >>		   Left and right shift.  Valid for integer operands only.  A right shift
			   always propagates the sign bit.

       <  >  <=  >=	   Boolean  less, greater, less than or equal, and greater than or equal.
			   Each operator produces 1 if the condition is true, 0 otherwise.  These
			   operators  may  be  applied to strings as well as numeric operands, in
			   which case string comparison is used.

       ==  !=		   Boolean equal and  not  equal.   Each  operator  produces  a  zero/one
			   result.  Valid for all operand types.

       &		   Bit-wise AND.  Valid for integer operands only.

       ^		   Bit-wise exclusive OR.  Valid for integer operands only.

       |		   Bit-wise OR.  Valid for integer operands only.

       &&		   Logical  AND.   Produces  a	1 result if both operands are non-zero, 0
			   otherwise.  Valid for boolean and numeric (integers or floating-point)
			   operands only.

       ||		   Logical  OR.   Produces a 0 result if both operands are zero, 1 other-
			   wise.  Valid for boolean and numeric (integers or floating-point)  op-
			   erands only.

       x?y:z		   If-then-else, as in C.  If x evaluates to non-zero, then the result is
			   the value of y.  Otherwise the result is the value of z.  The x  oper-
			   and must have a numeric value.

       See  the  C  manual for more details on the results produced by each operator.  All of the
       binary operators group left-to-right within the same precedence level.  For  example,  the
	      expr 4*2 < 7
       returns 0.

       The  &&, ||, and ?: operators have ``lazy evaluation'', just as in C, which means that op-
       erands are not evaluated if they are not needed to determine the outcome.  For example, in
       the command
	      expr {$v ? [a] : [b]}
       only  one  of  [a] or [b] will actually be evaluated, depending on the value of $v.  Note,
       however, that this is only true if the entire expression is enclosed in braces;	otherwise
       the Tcl parser will evaluate both [a] and [b] before invoking the expr command.

       Tcl     supports     the     following	  mathematical	  functions    in    expressions:
       abs	   cosh        log	  sqrt		 acos	     double	 log10	    srand
       asin	   exp	       pow	  tan		  atan	      floor	  rand	     tanh
       atan2	   fmod        round ceil	 hypot	     sin cos	     int	 sinh

	      Returns the absolute value of arg.  Arg may be either  integer  or  floating-point,
	      and the result is returned in the same form.

	      Returns  the  arc  cosine of arg, in the range [0,pi] radians. Arg should be in the
	      range [-1,1].

	      Returns the arc sine of arg, in the range [-pi/2,pi/2] radians.  Arg should  be  in
	      the range [-1,1].

	      Returns the arc tangent of arg, in the range [-pi/2,pi/2] radians.

       atan2(x, y)
	      Returns the arc tangent of y/x, in the range [-pi,pi] radians.  x and y cannot both
	      be 0.

	      Returns the smallest integer value not less than arg.

	      Returns the cosine of arg, measured in radians.

	      Returns the hyperbolic cosine of arg.  If the result would cause	an  overflow,  an
	      error is returned.

	      If  arg  is  a  floating value, returns arg, otherwise converts arg to floating and
	      returns the converted value.

	      Returns the exponential of arg, defined as e**arg.  If the result  would	cause  an
	      overflow, an error is returned.

	      Returns the largest integral value not greater than arg.

       fmod(x, y)
	      Returns  the  floating-point  remainder  of  the division of x by y.  If y is 0, an
	      error is returned.

       hypot(x, y)
	      Computes the length of the hypotenuse of a right-angled triangle (x*x+y*y).

	      If arg is an integer value, returns arg, otherwise converts arg to integer by trun-
	      cation and returns the converted value.

	      Returns the natural logarithm of arg.  Arg must be a positive value.

	      Returns the base 10 logarithm of arg.  Arg must be a positive value.

       pow(x, y)
	      Computes	the  value  of	x  raised to the power y.  If x is negative, y must be an
	      integer value.

       rand() Returns a floating point number from zero to just less than one or, in mathematical
	      terms,  the  range [0,1).  The seed comes from the internal clock of the machine or
	      may be set manual with the srand function.

	      If arg is an integer value, returns arg,	otherwise  converts  arg  to  integer  by
	      rounding and returns the converted value.

	      Returns the sine of arg, measured in radians.

	      Returns  the  hyperbolic	sine  of  arg.	If the result would cause an overflow, an
	      error is returned.

	      Returns the square root of arg.  Arg must be non-negative.

	      The arg, which must be an integer, is used to reset the seed for the random  number
	      generator.   Returns  the first random number from that seed.  Each interpreter has
	      it's own seed.

	      Returns the tangent of arg, measured in radians.

	      Returns the hyperbolic tangent of arg.

       In addition to these predefined functions, applications may  define  additional	functions
       using Tcl_CreateMathFunc().

       All internal computations involving integers are done with the C type long, and all inter-
       nal computations involving floating-point are done with the C type double.  When  convert-
       ing  a string to floating-point, exponent overflow is detected and results in a Tcl error.
       For conversion to integer from string, detection of overflow depends on	the  behavior  of
       some  routines  in  the	local  C library, so it should be regarded as unreliable.  In any
       case, integer overflow and underflow are generally not detected reliably for  intermediate
       results.   Floating-point  overflow  and underflow are detected to the degree supported by
       the hardware, which is generally pretty reliable.

       Conversion among internal representations for integer, floating-point, and string operands
       is  done  automatically	as  needed.  For arithmetic computations, integers are used until
       some floating-point number is introduced, after which floating-point is used.   For  exam-
	      expr 5 / 4
       returns 1, while
	      expr 5 / 4.0
	      expr 5 / ( [string length "abcd"] + 0.0 )
       both return 1.25.  Floating-point values are always returned with a ``.''  or an e so that
       they will not look like integer values.	For example,
	      expr 20.0/5.0
       returns 4.0, not 4.

       String values may be used as operands of the comparison operators, although the expression
       evaluator tries to do comparisons as integer or floating-point when it can.  If one of the
       operands of a comparison is a string and the other has a numeric value, the numeric  oper-
       and is converted back to a string using the C sprintf format specifier %d for integers and
       %g for floating-point values.  For example, the commands
	      expr {"0x03" > "2"}
	      expr {"0y" < "0x12"}
       both return 1.  The first comparison is done using integer comparison, and the  second  is
       done  using  string  comparison	after  the  second operand is converted to the string 18.
       Because of Tcl's tendency to treat values as numbers whenever possible, it isn't generally
       a good idea to use operators like == when you really want string comparison and the values
       of the operands could be arbitrary;  it's better in these cases to use the string  command

       Enclose	expressions  in  braces for the best speed and the smallest storage requirements.
       This allows the Tcl bytecode compiler to generate the best code.

       As mentioned above, expressions are substituted twice: once by the Tcl parser and once  by
       the expr command.  For example, the commands
	      set a 3
	      set b {$a + 2}
	      expr $b*4
       return 11, not a multiple of 4.	This is because the Tcl parser will first substitute $a +
       2 for the variable b, then the expr command will evaluate the expression $a + 2*4.

       Most expressions do not require a second round of substitutions.  Either they are enclosed
       in  braces  or,	if not, their variable and command substitutions yield numbers or strings
       that don't themselves require substitutions.  However, because a few unbraced  expressions
       need  two rounds of substitutions, the bytecode compiler must emit additional instructions
       to handle this situation.  The most expensive code is required  for  unbraced  expressions
       that  contain  command substitutions.  These expressions must be implemented by generating
       new code each time the expression is executed.

       arithmetic, boolean, compare, expression, fuzzy comparison

Tcl					       8.3					  expr(n)
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