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).

       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 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.

       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 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.


SEE ALSO
       array(n), string(n), Tcl(n)


KEYWORDS
