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 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 floatingpoint values). For example, the expression

expr 8.2 + 6
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'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 floatingpoint number if that is possible. Floatingpoint numbers may be specified in any of the ways accepted by an ANSIcompliant 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 floatingpoint 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 32bit systems, integer values MAX_INT (0x7FFFFFFF) and MIN_INT (0x80000000) will be represented as 32bit values, and integer values outside that range will be represented as 64bit 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 floatingpoint.
 [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 doublequotes. 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 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 + $a6.1 expr 2 + "$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, bitwise NOT, logical NOT. None of these operators may be applied to string operands, and bitwise NOT may be applied only to integers.
 * / %
 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 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 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.
 &
 Bitwise AND. Valid for integer operands only.
 ^
 Bitwise exclusive OR. Valid for integer operands only.
 
 Bitwise OR. Valid for integer operands only.
 &&
 Logical AND. Produces a 1 result if both operands are nonzero, 0 otherwise. Valid for boolean and numeric (integers or floatingpoint) operands only.
 
 Logical OR. Produces a 0 result if both operands are zero, 1 otherwise. Valid for boolean and numeric (integers or floatingpoint) operands only.
 x?y:z
 Ifthenelse, as in C. If x evaluates to nonzero, 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 operator. All of the binary operators group lefttoright within the same precedence level. For example, the command

expr 4*2 < 7
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]}
MATH FUNCTIONS
Tcl supports the following mathematical functions in expressions, all of which work solely with floatingpoint numbers unless otherwise noted:

abs coshlogsqrt acos doublelog10srand asin exppowtan atan floorrandtanh atan2 fmodroundwide ceil hypotsin cos intsinh
 abs(arg)
 Returns the absolute value of arg. Arg may be either integer or floatingpoint, 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] radians.
 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 floatingpoint 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 floatingpoint value, returns arg, otherwise converts arg to floatingpoint 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 floatingpoint value (i.e. with a zero fractional part) not greater than arg.
 fmod(x, y)
 Returns the floatingpoint 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 rightangled 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. 32bits on 32bit systems, and 64bits on 64bit systems) 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 negative, y must be an integer value.
 rand()
 Returns a pseudorandom floatingpoint value in the range (0,1). The generator algorithm is a simple linear congruential generator 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 onetime 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 nonnegative.
 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 64bits wide (by signextension if arg is a 32bit 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 floatingpoint are done with the C type double. When converting a string to floatingpoint, 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. Floatingpoint overflow and underflow are detected to the degree supported by the hardware, which is generally pretty reliable.
Conversion among internal representations for integer, floatingpoint, and string operands is done automatically as needed. For arithmetic computations, integers are used until some floatingpoint number is introduced, after which floatingpoint is used. For example,

expr 5 / 4

expr 5 / 4.0 expr 5 / ( [string length "abcd"] + 0.0 )

expr 20.0/5.0
STRING OPERATIONS
String values may be used as operands of the comparison operators, although the expression evaluator tries to do comparisons as integer or floatingpoint 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, the numeric operand is converted back to a string using the C sprintf format specifier %d for integers and %g for floatingpoint values. For example, the commands

expr {"0x03" > "2"} expr {"0y" > "0x12"}
PERFORMANCE CONSIDERATIONS
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 $b*4
Most expressions do not require a second round of substitutions. Either they are enclosed in braces or, if not, their variable and command substitutions yield numbers or strings that don't themselves require substitutions. However, because a few unbraced expressions need two rounds of substitutions, the bytecode compiler must emit additional instructions to handle this situation. The most expensive code is required for unbraced expressions that contain command substitutions. These expressions must be implemented by generating new code each time the expression is executed.
EXAMPLES
Define a procedure that computes an "interesting" mathematical function:
proc calc {x y} { expr { ($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()) }]
KEYWORDS
arithmetic, boolean, compare, expression, fuzzy comparison