expr(3tcl) | Tcl Built-In Commands | expr(3tcl) |

# NAME¶

expr - Evaluate an expression

# SYNOPSIS¶

**expr ***arg *?*arg arg ...*?

# DESCRIPTION¶

The *expr* command concatenates *arg*s, separated by a
space, into an expression, and evaluates that expression, returning its
value. The operators permitted in an expression 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. The value of an expression is often a numeric result, either an
integer or a floating-point value, but may also be a non-numeric value. For
example, the expression

expr8.2 + 6

evaluates to 14.2. Expressions differ from C expressions in the way that operands are specified. Expressions also support non-numeric operands, string comparisons, and some additional operators not found in C.

When an expression evaluates to an integer, the value is the
decimal form of the integer, and when an expression evaluates to a
floating-point number, the value is the form produced by the **%g**
format specifier of Tcl's **format** command.

You can use **#** at any point in the expression (except inside
double quotes or braces) to start a comment. Comments last to the end of the
line or the end of the expression, whichever comes first.

## OPERANDS¶

An expression consists of a combination of operands, operators, parentheses and commas, possibly with whitespace between any of these elements, which is ignored.

An operand 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 variable, using standard
**$**notation. The value of the variable is then the value of the operand. - [4]
- As a string enclosed in double-quotes. Backslash, variable, and command
substitution are performed as described in
**Tcl**. - [5]
- As a string enclosed in braces. The operand is treated as a braced value
as described in
**Tcl**. - [6]
- As a Tcl command enclosed in brackets. Command substitution is performed
as described in
**Tcl**. - [7]
- As a mathematical function such as
**sin($x)**, whose arguments have any of the above forms for operands. See**MATH FUNCTIONS**below for a discussion of how mathematical functions are handled.

Because **expr** parses and performs substitutions on values
that have already been parsed and substituted by **Tcl**, it is usually
best to enclose expressions in braces to avoid the first round of
substitutions by **Tcl**.

Below are some examples of simple expressions where the value of
**a** is 3 and the value of **b** is 6. The command on the left side
of each line produces the value on the right side.

expr{3.1 + $a}6.1expr{2 + "$a.$b"}5.6expr{4*[llength "6 2"]}8expr{{word one} < "word $a"}0

**Integer value**

An integer operand may be specified in decimal (the normal case,
the optional first two characters are **0d**), binary (the first two
characters are **0b**), octal (the first two characters are **0o**),
or hexadecimal (the first two characters are **0x**) form. For

**Floating-point value**

A floating-point number may be specified in any of several common
decimal formats, and may use the decimal point **.**, **e** or
**E** for scientific notation, and the sign characters **+** and
**-**. The following are all valid floating-point numbers: 2.1, 3., 6e4,
7.91e+16. The strings **Inf** and **NaN**, in any combination of case,
are also recognized as floating point values. An operand that doesn't have a
numeric interpretation must be quoted with either braces or with double
quotes.

**Boolean value**

A boolean value may be represented by any of the values **0**,
**false**, **no**, or **off** and any of the values **1**,
**true**, **yes**, or **on**.

**Digit Separator**

Digits in any numeric value may be separated with one or more
underscore characters, "**_**", to improve readability. These
separators may only appear between digits. The separator may not appear at
the start of a numeric value, between the leading 0 and radix specifier, or
at the end of a numeric value. Here are some examples:

expr100_000_000100000000expr0xffff_ffff4294967295format0x%x 0b1111_1110_1101_10110xfedb

## OPERATORS¶

For operators having both a numeric mode and a string mode, the
numeric mode is chosen when all operands have a numeric interpretation. The
integer interpretation of an operand is preferred over the floating-point
interpretation. To ensure string operations on arbitrary values it is
generally a good idea to use **eq**, **ne**, or the **string**
command instead of more versatile operators such as **==**.

Unless otherwise specified, operators accept non-numeric operands.
The value of a boolean operation is 1 if true, 0 otherwise. See also
**string is** **boolean**. The valid operators, most of which are also
available as commands in the **tcl::mathop** namespace (see
**mathop**(3tcl)), are listed below, grouped in decreasing order of
precedence:

**- + ~ !**- Unary minus, unary plus, bit-wise NOT, logical NOT. These operators may only be applied to numeric operands, and bit-wise NOT may only be applied to integers.
******- Exponentiation. Valid for numeric operands. The maximum exponent value that Tcl can handle if the first number is an integer > 1 is 268435455.
*** / %**- Multiply and divide, which are valid for numeric operands, and remainder, which is valid for integers. The remainder, an absolute value smaller than the absolute value of the divisor, has the same sign as the divisor.

When applied to integers, division and remainder can be considered
to partition the number line into a sequence of adjacent non-overlapping
pieces, where each piece is the size of the divisor; the quotient identifies
which piece the dividend lies within, and the remainder identifies where
within that piece the dividend lies. 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 numeric operands.
**<< >>**- Left and right shift. Valid for integers. A right shift always propagates the sign bit.
**< > <= >=**- Boolean numeric-preferring comparisons: less than, greater than, less than or equal, and greater than or equal. If either argument is not numeric, the comparison is done using UNICODE string comparison, as with the string comparison operators below, which have the same precedence.
**lt gt le ge**- Boolean string comparisons: less than, greater than, less than or equal,
and greater than or equal. These always compare values using their UNICODE
strings (also see
**string compare**), unlike with the numeric-preferring comparisons abov, which have the same precedence. **== !=**- Boolean equal and not equal.
**eq ne**- Boolean string equal and string not equal.
**in ni**- List containment and negated list containment. The first argument is
interpreted as a string, the second as a list.
**in**tests for membership in the list, and**ni**is the inverse. **&**- Bit-wise AND. Valid for integer operands.
**^**- Bit-wise exclusive OR. Valid for integer operands.
**|**- Bit-wise OR. Valid for integer operands.
**&&**- Logical AND. If both operands are true, the result is 1, or 0 otherwise. This operator evaluates lazily; it only evaluates its second operand if it must in order to determine its result. This operator evaluates lazily; it only evaluates its second operand if it must in order to determine its result.
**||**- Logical OR. If both operands are false, the result is 0, or 1 otherwise. 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*is false , the result is the value of*y*. Otherwise the result is the value of*z*. This operator evaluates lazily; it evaluates only one of*y*or*z*.

The exponentiation operator promotes types in the same way that
the multiply and divide operators do, and the result is is the same as the
result of **pow**. Exponentiation groups right-to-left within a
precedence level. Other binary operators group left-to-right. For example,
the value of

expr{4*2 < 7}

is 0, while the value of

expr{2**3**2}

is 512.

As in C, **&&**, **||**, and **?:** feature
“lazy evaluation”, which means that operands are not evaluated
if they are not needed to determine the outcome. For example, in

expr{$v?[a]:[b]}

only one of **[a]** or **[b]** is evaluated, depending on
the value of **$v**. This is not true of the normal Tcl parser, so it is
normally recommended to enclose the arguments to **expr** in braces.
Without braces, as in **expr** $v ? [a] : [b] both **[a]** and
**[b]** are evaluated before **expr** is even called.

For more details on the results produced by each operator, see the documentation for C.

## MATH FUNCTIONS¶

A mathematical function such as **sin($x)** is replaced with a
call to an ordinary Tcl command in the **tcl::mathfunc** namespace. The
evaluation of an expression such as

expr{sin($x+$y)}

is the same in every way as the evaluation of

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

which in turn is the same as the evaluation of

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

**tcl::mathfunc::sin** is resolved as described in **NAMESPACE
RESOLUTION** in the **namespace**(3tcl) documentation. Given the
default value of **namespace path**, **[namespace**
**current]::tcl::mathfunc::sin** or **::tcl::mathfunc::sin** are the
typical resolutions.

As in C, a mathematical function may accept multiple arguments separated by commas. Thus,

expr{hypot($x,$y)}

becomes

tcl::mathfunc::hypot $x $y

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

## TYPES, OVERFLOW, AND PRECISION¶

When needed to guarantee exact performance, internal computations
involving integers use the LibTomMath multiple precision integer library. In
Tcl releases prior to 8.5, integer calculations were performed using 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 should instead
call **int()** or **wide()**, which do truncate.

Internal floating-point computations are performed using the
*double* C type. When converting a string to floating-point value,
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 fairly 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 values are used. For example,

expr{5 / 4}

returns 1, while

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

both return 1.25. A floating-point result can be distinguished
from an integer result by the presence of either “**.**” or
“**e**”

expr{20.0/5.0}

returns **4.0**, not **4**.

# PERFORMANCE CONSIDERATIONS¶

Where an expression contains syntax that Tcl would otherwise
perform substitutions on, enclosing an expression in braces or otherwise
quoting it so that it's a static value allows the Tcl compiler to generate
bytecode for the expression, resulting in better speed and smaller storage
requirements. This also avoids issues that can arise if Tcl is allowed to
perform substitution on the value before **expr** is called.

In the following example, the value of the expression is 11
because the Tcl parser first substitutes **$b** and **expr** then
substitutes **$a** as part of evaluating the expression “$a +
2*4”. Enclosing the expression in braces would result in a syntax
error as **$b** does not evaluate to a numeric value.

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

When an expression is generated at runtime, like the one above is,
the bytecode compiler must ensure that new code is generated each time the
expression is evaluated. This is the most costly kind of expression from a
performance perspective. In such cases, consider directly using the commands
described in the **mathfunc**(3tcl) or **mathop**(3tcl) documentation
instead of **expr**.

Most expressions are not formed at runtime, but are literal
strings or contain substitutions that don't introduce other substitutions.
To allow the bytecode compiler to work with an expression as a string
literal at compilation time, ensure that it contains no substitutions or
that it is enclosed in braces or otherwise quoted to prevent Tcl from
performing substitutions, allowing **expr** to perform them instead.

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}

In general, you should enclose your expression in braces wherever
possible, and where not possible, the argument to **expr** should be an
expression defined elsewhere as simply as possible. It is usually more
efficient and safer to use other techniques (e.g., the commands in the
**tcl::mathop** namespace) than it is to do complex expression
generation.

# EXAMPLES¶

A numeric comparison whose result is 1:

expr{"0x03" > "2"}

A string comparison whose result is 1:

expr{"0y" > "0x12"}

A forced string comparison whose result is 0:

expr{"0x03" gt "2"}

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 indicating whether an environment variable is defined and has value of true:

set isTrue [expr{

# Does the environment variable exist, and...

[info exists ::env(SOME_ENV_VAR)] &&

# ...does it contain a proper true value?

[string is true -strict $::env(SOME_ENV_VAR)] }]

Generate a random integer in the range 0..99 inclusive:

set randNum [expr{ int(100 * rand()) }]

# SEE ALSO¶

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

# KEYWORDS¶

arithmetic, boolean, compare, expression, fuzzy comparison, integer value

# COPYRIGHT¶

Copyright © 1993 The Regents of the University of California. Copyright © 1994-2000 Sun Microsystems Incorporated. Copyright © 2005 Kevin B. Kenny <kennykb@acm.org>. All rights reserved.

8.5 | Tcl |