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

______________________________________________________________________________

NAME
       expr - Evaluate an expression

SYNOPSIS
       expr arg ?arg arg ...?
_________________________________________________________________

DESCRIPTION
       Concatenates args (adding separator spaces between them), evaluates the
       result as a Tcl expression, and returns the value.  The operators  per-
       mitted  in Tcl expressions are a subset of the operators permitted in C
       expressions, and they have the same meaning and precedence as the  cor-
       responding  C  operators.   Expressions	almost	always	yield  numeric
       results (integer or floating-point values).  For example,  the  expres-
       sion
	      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.

OPERANDS
       A  Tcl expression consists of a combination of operands, operators, and
       parentheses.  White space may be used between the operands  and	opera-
       tors  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 character 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 speci-
       fied 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 (note that all literal operands that	 are  not  numeric  or
       boolean	must be quoted with either braces or with double quotes), 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 a numeric value, either integer or floating-point.

       [2]    As a boolean value, using	 any  form  understood	by  string  is
	      boolean.

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

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

       [5]    As a string enclosed in braces.  The characters between the open
	      brace and matching close brace will be used as the operand with-
	      out any substitutions.

       [6]    As a Tcl command enclosed in brackets.  The command will be exe-
	      cuted and its result will be used as the operand.

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

       Where the above substitutions occur (e.g. inside quoted strings),  they
       are  performed  by the expression's instructions.  However, the command
       parser may already have performed one round of substitution before  the
       expression  processor  was  called.   As discussed 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

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

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

       *  /  %		   Multiply, divide, remainder.	 None of these	opera-
			   tors may be applied to string operands, and remain-
			   der may be applied only to integers.	 The remainder
			   will	 always	 have the same sign as the divisor and
			   an absolute 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 opera-
			   tors may be applied to strings as well  as  numeric
			   operands,  in which case string comparison is used.

       ==  !=		   Boolean equal and not equal.	  Each	operator  pro-
			   duces  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	 otherwise.   Valid  for  boolean  and
			   numeric (integers or floating-point) operands 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 operand must  have
			   a boolean or numeric value.

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

       The  &&,	 ||,  and ?: operators have ``lazy evaluation'', just as in C,
       which means that operands 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 evalu-
       ate both [a] and [b] before invoking the expr command.

MATH FUNCTIONS
       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

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

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

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

       atan(arg)
	      Returns  the arc tangent of arg, in the range [-pi/2,pi/2] radi-
	      ans.

       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).

       ceil(arg)
	      Returns the smallest integral floating-point value (i.e. with  a
	      zero fractional part) not less than arg.

       cos(arg)
	      Returns the cosine of arg, measured in radians.

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

       double(arg)
	      If arg is a floating-point value, returns	 arg,  otherwise  con-
	      verts arg to floating-point and returns the converted value.

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

       floor(arg)
	      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).

       int(arg)
	      If  arg  is  an  integer	value of the same width as the machine |
	      word, returns arg, otherwise 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  con- |
	      verted value.

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

       log10(arg)
	      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 nega-
	      tive, 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 genera-
	      tor that is not cryptographically secure.	 Each result from rand
	      completely  determines  all future results from subsequent 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.

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

       sin(arg)
	      Returns the sine of arg, measured in radians.

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

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

       srand(arg)
	      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.

       tan(arg)
	      Returns the tangent of arg, measured in radians.

       tanh(arg)
	      Returns the hyperbolic tangent of arg.

       wide(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().

TYPES, OVERFLOW, AND PRECISION
       All internal computations involving integers are done with the  C  type
       long,  and  all internal computations involving floating-point are done
       with the C type double.	When converting a  string  to  floating-point,
       exponent	 overflow is detected and results in a Tcl error.  For conver-
       sion 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.	Float-
       ing-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 example,
	      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 OPERATIONS
       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	opera- |
       tors.  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 float-
       ing-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 val-
       ues 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 operators, or the string command instead.

PERFORMANCE CONSIDERATIONS
       Enclose expressions in braces for the best speed and the smallest stor-
       age  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  com-
       mand  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 addi-
       tional instructions to handle this situation.  The most expensive  code
       is  required  for  unbraced  expressions that contain command substitu-
       tions.  These expressions must be implemented by	 generating  new  code
       each time the expression is executed.

EXAMPLES
       Define  a  procedure  that computes an "interesting" mathematical func-
       tion:
	      proc calc {x y} {
		  expr { ($x*$x - $y*$y) / exp($x*$x + $y*$y) }
	      }

       Convert polar coordinates into cartesian coordinates:
	      # convert from ($radius,$angle)
	      set x [expr { $radius * cos($angle) }]
	      set y [expr { $radius * sin($angle) }]

       Convert cartesian coordinates into polar coordinates:
	      # convert from ($x,$y)
	      set radius [expr { hypot($y, $x) }]
	      set angle	 [expr { atan2($y, $x) }]

       Print a message describing the relationship of  two  string  values  to
       each other:
	      puts "a and b are [expr {$a eq $b ? {equal} : {different}}]"

       Set  a  variable	 to whether an environment variable is both defined at
       all and also set to a true boolean value:
	      set isTrue [expr {
		  [info exists ::env(SOME_ENV_VAR)] &&
		  [string is true -strict $::env(SOME_ENV_VAR)]
	      }]

       Generate a random integer in the range 0..99 inclusive:
	      set randNum [expr { int(100 * rand()) }]

SEE ALSO
       array(n), for(n), if(n), string(n), Tcl(n), while(n)

KEYWORDS
       arithmetic, boolean, compare, expression, fuzzy comparison

Tcl				      8.4			       expr(n)
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