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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).

       On  32-bit  systems, integer values MAX_INT (0x7FFFFFFF) and MIN_INT (-0x80000000) will be |
       represented as 32-bit values, and integer values outside that range will be represented as |
       64-bit values (if that is possible at all.)

       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.				  |

       eq  ne											  |
			   Boolean  string  equal and string not equal.  Each operator produces a |
			   zero/one result.  The operand types are interpreted only as strings.

       &		   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, all of which work solely
       with	    floating-point	   numbers	   unless	  otherwise	   noted:
       abs	   cosh        log	  sqrt		 acos	     double	 log10	    srand
       asin	   exp	       pow	  tan		  atan	      floor	  rand	     tanh
       atan2	   fmod        round	  wide			      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(y, x)
	      Returns the arc tangent of y/x, in the range [-pi,pi] radians.  x and y cannot both
	      be 0.  If x is greater than 0, this is equivalent to atan(y/x).

	      Returns  the  smallest  integral	floating-point value (i.e. with a zero fractional
	      part) 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-point value, returns arg, otherwise converts arg to floating-
	      point 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  floating-point  value (i.e. with a zero fractional
	      part) 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 sqrt(x*x+y*y).

	      If arg is an integer value of the same width as the machine word, returns arg, oth- |
	      erwise converts arg to an integer (of the same size as a machine word, i.e. 32-bits |
	      on  32-bit  systems,  and  64-bits on 64-bit systems) by truncation 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  pseudo-random  floating-point  value in the range (0,1).  The generator
	      algorithm is a simple linear congruential generator that is  not	cryptographically
	      secure.  Each result from rand completely determines all future results from subse-
	      quent calls to rand, so rand should not be used to generate a sequence of  secrets,
	      such  as	one-time  passwords.   The  seed of the generator is initialized from the
	      internal clock of the machine or may be set 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  of  rand.   Returns the first random number (see rand()) from that seed.
	      Each interpreter has its own seed.

	      Returns the tangent of arg, measured in radians.

	      Returns the hyperbolic tangent of arg.

	      Converts arg to an integer value at least 64-bits wide (by sign-extension if arg is |
	      a 32-bit number) if it is not one already.

       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, except in  the |
       case  of  the eq and ne operators.  If one of the operands of a comparison is a string and
       the other has a numeric value, the numeric operand 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 eq or ne opera- |
       tors, or the string command instead.

       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.

       array(n), string(n), Tcl(n)

       arithmetic, boolean, compare, expression, fuzzy comparison

Tcl					       8.4					  expr(n)
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