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 floatingpoint 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 nonnumeric 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 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, 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:

As an numeric value, either integer or floatingpoint.

As a Tcl variable, using standard $ notation. The variable's value will be used as the operand.

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

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.

As a Tcl command enclosed in brackets. The command will be executed and its result will be used as the operand.

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 (for example, 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 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
OPERATORS
The valid operators are listed below, grouped in decreasing order of precedence:
  + ~ !

Unary minus, unary plus, bitwise NOT, logical NOT. None of these operands may be applied to string operands, and bitwise 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 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.
 &

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 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
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 evaluate 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 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(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 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 (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 negative, 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 manually 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. 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
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
returns 1, while
expr 5 / 4.0 expr 5 / ( [string length "abcd"] + 0.0 )
both return 1.25. Floatingpoint 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 floatingpoint 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 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"}
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 values 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 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 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.
PORTABILITY
Windows 8.1. Windows Server 2012 R2. Windows 10. Windows Server 2016. Windows Server 2019. Windows 11. Windows Server 2022.
AVAILABILITY
PTC MKS Toolkit for Power Users
PTC MKS Toolkit for System Administrators
PTC MKS Toolkit for Developers
PTC MKS Toolkit for Interoperability
PTC MKS Toolkit for Professional Developers
PTC MKS Toolkit for Enterprise Developers
PTC MKS Toolkit for Enterprise Developers 64Bit Edition
PTC MKS Toolkit 10.4 Documentation Build 39.