Provided by: tcl8.6-doc_8.6.10+dfsg-1_all bug


       expr - Evaluate an expression


       expr arg ?arg arg ...?


       Concatenates  args  (adding  separator spaces between them), evaluates the result as a Tcl
       expression, and returns the value.  The operators permitted in Tcl expressions  include  a
       subset  of  the  operators permitted in C expressions.  For those operators common to both
       Tcl and C, Tcl applies the same meaning and precedence 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, as
       well as some additional operators not found in C.

       A Tcl expression consists of a combination of operands, operators, parentheses and commas.
       White space may be used between the operands and operators and parentheses (or commas); 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 binary
       (if the first two characters of the operand are 0b), in octal (if the first two characters
       of  the operand are 0o), or in hexadecimal (if the first two characters of the operand are
       0x).  For compatibility with older Tcl releases, an octal integer value is also  indicated
       simply  when  the first character of the operand is 0, whether or not the second character
       is also o.  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 several common formats making use of the decimal digits,  the  decimal
       point  .,  the characters e or E indicating scientific notation, and the sign characters +
       or -.  For example, all of the following are valid floating-point numbers:  2.1, 3.,  6e4,
       7.91e+16.  Also recognized as floating point values are the strings Inf and NaN making use
       of any case for each character.  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).

       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 without any substitutions.

       [6]    As a Tcl command enclosed in brackets.  The command will be executed 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  MATH  FUNCTIONS  below for a discussion of how
              mathematical functions are handled.

       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

       The valid operators (most of which are also  available  as  commands  in  the  tcl::mathop
       namespace;  see  the  mathop(3tcl)  manual  page for details) 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.

       **                  Exponentiation.  Valid for any numeric operands.  The maximum exponent
                           value  that  Tcl  can  handle if the first number is an integer > 1 is

       *  /  %             Multiply, divide, remainder.  None of these operators 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 absolute value of the divisor.

                           When  applied to integers, the division and remainder operators can be
                           considered to partition the number line into a sequence of equal-sized
                           adjacent  non-overlapping  pieces  where each piece is the size of the
                           divisor; the division result identifies which piece  the  divisor  lay
                           within,  and  the  remainder result identifies where within that piece
                           the divisor lay. A consequence of this is that the result  of  “-57  /
                           10” is always -6, and the result of “-57 % 10” is always 3.

       +  -                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.

       in  ni              List containment and negated list containment.  Each operator produces
                           a zero/one result and treats its first argument as a  string  and  its
                           second  argument as a Tcl list.  The in operator indicates whether the
                           first argument is a  member  of  the  second  argument  list;  the  ni
                           operator inverts the sense of the result.

       &                   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.  This operator evaluates lazily; it only evaluates its
                           second operand if it must in order to determine its result.

       ||                  Logical OR.  Produces  a  0  result  if  both  operands  are  zero,  1
                           otherwise.  Valid for boolean and numeric (integers or floating-point)
                           operands only.  This operator evaluates lazily; it only evaluates  its
                           second operand if it must in order to determine its result.

       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.  This operator evaluates
                           lazily; it evaluates only one of y or z.

       See the C manual for  more  details  on  the  results  produced  by  each  operator.   The
       exponentiation  operator  promotes  types  like  the  multiply  and  divide operators, and
       produces a result that is the same as the output of  the  pow  function  (after  any  type
       conversions.)   All  of the binary operators but exponentiation group left-to-right within
       the same precedence level; exponentiation groups right-to-left.  For example, the command

              expr {4*2 < 7}

       returns 0, while

              expr {2**3**2}

       returns 512.

       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 evaluate both “[a]”  and  “[b]”  before  invoking  the  expr

       When the expression parser encounters a mathematical function such as sin($x), it replaces
       it with a call to an ordinary Tcl command in the tcl::mathfunc namespace.  The  processing
       of an expression such as:

              expr {sin($x+$y)}

       is the same in every way as the processing of:

              expr {[tcl::mathfunc::sin [expr {$x+$y}]]}

       which in turn is the same as the processing of:

              tcl::mathfunc::sin [expr {$x+$y}]

       The  executor  will  search  for  tcl::mathfunc::sin  using  the usual rules for resolving
       functions     in     namespaces.     Either     ::tcl::mathfunc::sin     or     [namespace
       current]::tcl::mathfunc::sin  will  satisfy the request, and others may as well (depending
       on the current namespace path setting).

       Some mathematical functions have several arguments, separated by commas like in C. Thus:

              expr {hypot($x,$y)}

       ends up as

              tcl::mathfunc::hypot $x $y

       See the mathfunc(3tcl) manual page for the math functions that are available by default.

       All internal computations involving integers are done calling on the  LibTomMath  multiple
       precision  integer  library  as  required  so  that all integer calculations are performed
       exactly.  Note that in Tcl releases prior to 8.5, integer calculations were performed with
       one  of  the  C  types long int or Tcl_WideInt, causing implicit range truncation in those
       calculations where values overflowed the range of those types.  Any code  that  relied  on
       these  implicit  truncations will need to explicitly add int() or wide() function calls to
       expressions at the points where such truncation is required to take place.

       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 the
       double value of Inf or -Inf as appropriate.  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

              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, i.e., when all
       arguments  to the operator allow numeric interpretations, 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, a canonical string representation of the numeric operand value is generated
       to compare with the string operand.  Canonical string representation for integer values is
       a  decimal  string  format.   Canonical string representation for floating-point values is
       that produced by the %g format specifier  of  Tcl's  format  command.   For  example,  the

              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.  Because of  Tcl's  tendency  to  treat  values  as  numbers
       whenever  possible,  it  is  not  generally  a good idea to use operators like == when you
       really want string comparison and the values of the operands could be  arbitrary;   it  is
       better in these cases to use the eq or ne operators, 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 do not 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.

       If it is necessary to include a non-constant expression string within the wider context of
       an  otherwise-constant expression, the most efficient technique is to put the varying part
       inside a recursive expr, as this at least allows for the compilation of  the  outer  part,
       though  it  does  mean  that  the  varying  part  must  itself  be evaluated as a separate
       expression. Thus, in this example the result is 20 and the outer expression benefits  from
       fully cached bytecode compilation.

              set a 3
              set b {$a + 2}
              expr {[expr $b] * 4}

       When  the  expression  is  unbraced  to  allow the substitution of a function or operator,
       consider using the commands documented in the mathfunc(3tcl) or mathop(3tcl) manual  pages
       directly instead.


       Define a procedure that computes an “interesting” mathematical function:

              proc tcl::mathfunc::calc {x y} {
                  expr { ($x**2 - $y**2) / exp($x**2 + $y**2) }

       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()) }]


       array(3tcl),   for(3tcl),   if(3tcl),   mathfunc(3tcl),   mathop(3tcl),   namespace(3tcl),
       proc(3tcl), string(3tcl), Tcl(3tcl), while(3tcl)


       arithmetic, boolean, compare, expression, fuzzy comparison


       Copyright (c) 1993 The Regents of the University of California.
       Copyright (c) 1994-2000 Sun Microsystems Incorporated.
       Copyright (c) 2005 by Kevin B. Kenny <>. All rights reserved.