expr(n)
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NAME
expr - Evaluate an expression
SYNOPSIS
expr arg ?arg arg ...?
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DESCRIPTION
Concatenates args (adding separator spaces between them), evaluates the
result as a Tcl expression, and returns the value. The operators per-
mitted in Tcl expressions are a subset of the operators permitted in C
expressions, and they have the same meaning and precedence as the cor-
responding C operators. Expressions almost always yield numeric
results (integer or floating-point values). For example, the expres-
sion
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 opera-
tors 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 speci-
fied 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 with-
out any substitutions.
[6] As a Tcl command enclosed in brackets. The command will be exe-
cuted 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 opera-
tors may be applied to string operands, and remain-
der 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 opera-
tors may be applied to strings as well as numeric
operands, in which case string comparison is used.
== != Boolean equal and not equal. Each operator pro-
duces 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 oper-
ator. 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 evalu-
ate 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] radi-
ans.
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 con-
verts 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 con- |
verted 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 nega-
tive, 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 genera-
tor 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 conver-
sion 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. Float-
ing-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.
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 opera- |
tors. 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 float-
ing-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 val-
ues 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.
PERFORMANCE CONSIDERATIONS
Enclose expressions in braces for the best speed and the smallest stor-
age 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 $a + 2*4.
Most expressions do not require a second round of substitutions.
Either they are enclosed in braces or, if not, their variable and com-
mand substitutions yield numbers or strings that don't themselves
require substitutions. However, because a few unbraced expressions
need two rounds of substitutions, the bytecode compiler must emit addi-
tional instructions to handle this situation. The most expensive code
is required for unbraced expressions that contain command substitu-
tions. These expressions must be implemented by generating new code
each time the expression is executed.
EXAMPLES
Define a procedure that computes an "interesting" mathematical func-
tion:
proc calc {x y} {
expr { ($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(n), for(n), if(n), string(n), Tcl(n), while(n)
KEYWORDS
arithmetic, boolean, compare, expression, fuzzy comparison
Tcl 8.4 expr(n)
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