
expr(n) Tcl BuiltIn Commands expr(n)
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NAME
expr  Evaluate an expression
SYNOPSIS
expr arg ?arg arg ...?
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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 sub
set of the operators permitted in C expressions, and they have the same meaning and prece
dence 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 char
acter 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).
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 an numeric value, either integer or floatingpoint.
[2] As a Tcl variable, using standard $ notation. The variable's value will be used as
the operand.
[3] As a string enclosed in doublequotes. The expression parser will perform back
slash, 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 oper
ands, 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's instructions. However, an additional layer of substitution may already have
been performed by the command parser before the expression processor was called. As dis
cussed 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 op
erands 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 abso
lute 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 other
wise. Valid for boolean and numeric (integers or floatingpoint) op
erands 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 oper
and 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 op
erands 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, all of which work solely
with floatingpoint numbers unless otherwise noted:
abs cosh log sqrt acos double log10 srand
asin exp pow tan atan floor rand tanh
atan2 fmod round wide 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(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 floating
point 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, oth 
erwise 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 subse
quent 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 inter
nal computations involving floatingpoint are done with the C type double. When convert
ing 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 exam
ple,
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, 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"}
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 eq or ne opera 
tors, or 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.
SEE ALSO
array(n), string(n), Tcl(n)
KEYWORDS
arithmetic, boolean, compare, expression, fuzzy comparison
Tcl 8.4 expr(n) 
