NAME
       expr - Evalue 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 corre-
       sponding 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  expres-
       sions  in  the way that operands are specified.  Also, Tcl
       expressions support non-numeric operands and  string  com-
       parisons.

OPERANDS
       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  processor.   Where  possible,
       operands  are interpreted as integer values.  Integer val-
       ues 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 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 installa-
       tions).   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 expres-
              sion 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 without any substitu-
              tions.

       [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  operands,  such  as
              ``sin($x)''.  See below for a list of defined func-
              tions.

       Where   substitutions  occur  above  (e.g.  inside  quoted
       strings), they are performed by the expression  processor.
       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  pre-
       vent  the  command parser from performing substitutions on
       the contents.

       For some examples of simple expressions, suppose the vari-
       able 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  decreas-
       ing order of precedence:

       -  ~  !             Unary  minus,  bit-wise  NOT,  logical
                           NOT.  None of these  operands  may  be
                           applied  to  string operands, and bit-
                           wise NOT may be applied only to  inte-
                           gers.

       *  /  %             Multiply,  divide, remainder.  None of
                           these  operands  may  be  applied   to
                           string  operands, and remainder may be
                           applied only to integers.  The remain-
                           der  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 inte-
                           ger operands only.

       <  >  <=  >=        Boolean  less,  greater,  less than or
                           equal,  and  greater  than  or  equal.
                           Each operator produces 1 if the condi-
                           tion  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 other-
                           wise.  Valid for numeric operands only
                           (integers or floating-point).

       ||                  Logical  OR.   Produces  a 0 result if
                           both operands are zero,  1  otherwise.
                           Valid for numeric operands only (inte-
                           gers or floating-point).

       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 operator.  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, depend-
       ing  on the value of $v.  Note, however, that this is only
       true if the entire expression is enclosed in braces;  oth-
       erwise  the  Tcl  parser  will  evaluate  both [a] and [b]
       before invoking the expr command.

MATH FUNCTIONS
       Tcl  supports  the  following  mathematical  functions  in
       expressions:

              acos        cos         hypot      sinh
              asin        cosh        log        sqrt
              atan        exp         log10      tan
              atan2       floor       pow        tanh
              ceil        fmod        sin
       Each  of these functions invokes the math library function
       of the same name;  see the manual entries for the  library
       functions  for  details  on what they do.  Tcl also imple-
       ments the following functions for conversion between inte-
       gers and floating-point numbers:

       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.

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

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

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

       In  addition  to  these predifined 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 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 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''.    The   global   variable
       tcl_precision  determines  the  the  number of significant
       digits that are retained when  floating  values  are  con-
       verted  to  strings (except that trailing zeroes are omit-
       ted).  If tcl_precision is unset then 6 digits  of  preci-
       sion  are  used.  To retain all of the significant bits of
       an IEEE floating-point number set tcl_precision to 17;  if
       a value is converted to string with 17 digits of precision
       and then converted back to binary for some later  calcula-
       tion, the resulting binary value is guaranteed to be iden-
       tical to the original one.


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 speci-
       fier %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''.


KEYWORDS
       arithmetic, boolean, compare, expression
