NAME
       expr - Evaluate an expression

SYNOPSIS
       expr arg ?arg arg ...?


DESCRIPTION
       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 subset of the operators permitted in
       C expressions, and they have the same meaning  and  precedence  as  the
       corresponding  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, 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  backslash, 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 with-
              out any substitutions.

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

       [6]    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 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 discussed below,
       it is usually best to enclose expressions in braces to prevent the com-
       mand 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 operands 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  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.

       &                   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 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:

              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



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

       ceil(arg)
              Returns the smallest integer value 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 value, returns arg, otherwise converts  arg
              to floating 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 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).

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

       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.  Returns the  first  random  number
              from that seed.  Each interpreter has it's own seed.

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

       tanh(arg)
              Returns the hyperbolic tangent of arg.

       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.  If one of the operands of a comparison  is
       a string and the other has a numeric value, the numeric operand is con-
       verted 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 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 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.


KEYWORDS
