# 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 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.

## 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 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 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 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).

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 without any substitutions.

[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 functions.

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 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, 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.

< > <= >=
  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.

&
  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 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 (integers 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, 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:

    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 implements the following functions for conversion between integers 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 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 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 converted to strings (except that trailing zeroes are omitted). If tcl_precision is unset then 6 digits of precision 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 calculation, the resulting binary value is guaranteed to be identical 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 converted back to a string using the C sprintf format specifier %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''. 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 compare command instead.

## KEYWORDS

arithmetic, boolean, compare, expression