NAME¶
expr - Evaluate an expression
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 floating-point
values). For example, the expression
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'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 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 (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 32-bit systems, integer values MAX_INT (0x7FFFFFFF) and MIN_INT (-0x80000000)
will be represented as 32-bit values, and integer values outside that range
will be represented as 64-bit 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 floating-point.
- [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 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
- [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 + $a 6.1
expr 2 + "$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 operators may be applied to string operands, and bit-wise 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.
- &
- 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 boolean and numeric (integers or
floating-point) operands only.
- ||
- Logical OR. Produces a 0 result if both operands are zero,
1 otherwise. Valid for boolean and numeric (integers or floating-point)
operands only.
- 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 boolean or 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
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
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 floating-point 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 floating-point, 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 floating-point 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 floating-point 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 floating-point value (i.e.
with a zero fractional part) not greater than arg.
- fmod(x, y)
- Returns the floating-point 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 right-angled
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. 32-bits on 32-bit
systems, and 64-bits on 64-bit 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 pseudo-random floating-point 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 one-time 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
non-negative.
- 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 64-bits
wide (by sign-extension if arg is a 32-bit 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 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,
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,
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 floating-point 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 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
eq
or
ne operators, or the
string command instead.
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
$a + 2*4.
Most expressions do not require a second round of substitutions. Either they are
enclosed in braces or, if not, their variable and command substitutions yield
numbers or strings that don't themselves require substitutions. However,
because a few unbraced expressions need two rounds of substitutions, the
bytecode compiler must emit additional instructions to handle this situation.
The most expensive code is required for unbraced expressions that contain
command substitutions. These expressions must be implemented by generating new
code each time the expression is executed.
EXAMPLES¶
Define a procedure that computes an "interesting" mathematical
function:
proc calc {x y} {
expr { ($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()) }]
SEE ALSO¶
array(3tcl), for(3tcl), if(3tcl), string(3tcl), Tcl(3tcl), while(3tcl)
KEYWORDS¶
arithmetic, boolean, compare, expression, fuzzy comparison