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
subset of the operators permitted in C expressions, and
they have the same meaning and precedence as the corre
sponding 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 expres
sions in the way that operands are specified. Also, Tcl
expressions support non-numeric operands and string com
parisons.
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 val
ues 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 suf
fixes 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 interpre
tation 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.
sion 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 substitu
tions.
[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's instruc
tions. 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 vari
able 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 $a"}0
OPERATORS
The valid operators are listed below, grouped in decreas
ing order of precedence:
- + ~ ! Unary minus, unary plus, bit-wise NOT,
logical NOT. None of these operands
may be applied to string operands, and
bit-wise NOT may be applied only to
integers.
* / % Multiply, divide, remainder. None of
these operands may be applied to
string operands, and remainder may be
applied only to integers. The remain
der will always have the same sign as
the divisor and an absolute value
+ - Add and subtract. Valid for any
numeric operands.
<< >> Left and right shift. Valid for inte
ger operands only. A right shift
always propagates the sign bit.
< > <= >= Boolean less, greater, less than or
equal, and greater than or equal.
Each operator produces 1 if the condi
tion is true, 0 otherwise. These
operators may be applied to strings as
well as numeric operands, in which
case string comparison is used.
== != Boolean equal and not equal. Each
operator produces a zero/one result.
Valid for all operand types.
& Bit-wise AND. Valid for integer
operands only.
^ Bit-wise exclusive OR. Valid for
integer operands only.
| Bit-wise OR. Valid for integer
operands only.
&& Logical AND. Produces a 1 result if
both operands are non-zero, 0 other
wise. Valid for boolean and numeric
(integers or floating-point) operands
only.
|| Logical OR. Produces a 0 result if
both operands are zero, 1 otherwise.
Valid for boolean and numeric (inte
gers or floating-point) operands only.
x?y:z If-then-else, as in C. If x evaluates
to non-zero, then the result is the
value of y. Otherwise the result is
the value of z. The x operand must
have a numeric value.
See the C manual for more details on the results produced
by each operator. All of the binary operators group left-
to-right within the same precedence level. For example,
the command
expr 4*2 < 7
returns 0.
just as in C, which means that operands are not evaluated
if they are not needed to determine the outcome. For
example, in the command
expr {$v ? [a] : [b]}
only one of [a] or [b] will actually be evaluated, depend
ing on the value of $v. Note, however, that this is only
true if the entire expression is enclosed in braces; oth
erwise the Tcl parser will evaluate both [a] and [b]
before invoking the expr command.
MATH FUNCTIONS
Tcl supports the following mathematical functions in
expressions:
abs cosh log sqrt
acos double log10 srand
asin exp pow tan
atan floor rand tanh
atan2 fmod round
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(x, y)
Returns the arc tangent of y/x, in the range
[-pi,pi] radians. x and y cannot both be 0.
ceil(arg)
Returns the smallest integer value not less than
arg.
cos(arg)
Returns the cosine of arg, measured in radians.
Returns the hyperbolic cosine of arg. If the
result would cause an overflow, an error is
returned.
double(arg)
If arg is a floating value, returns arg, otherwise
converts arg to floating 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 value not greater than
arg.
fmod(x, y)
Returns the floating-point remainder of the divi
sion 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 (x*x+y*y).
int(arg)
If arg is an integer value, returns arg, otherwise
converts arg to integer 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 floating point number from zero to just
less than one or, in mathematical terms, the range
[0,1). The seed comes from the internal clock of
the machine or may be set manual 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.
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. Returns
the first random number from that seed. Each
interpreter has it's own seed.
tan(arg)
Returns the tangent of arg, measured in radians.
tanh(arg)
Returns the hyperbolic tangent of arg.
In addition to these predefined functions, applications
may define additional functions using Tcl_CreateMath
Func().
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 con
verting 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
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 con
verted back to a string using the C sprintf format speci
fier %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 when
ever possible, it isn't generally a good idea to use oper
ators like == when you really want string comparison and
the values of the operands could be arbitrary; it's bet
ter in these cases to use the string command instead.
PERFORMANCE CONSIDERATIONS
Enclose expressions in braces for the best speed and the
smallest storage requirements. This allows the Tcl byte
code 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 substi
tutions. Either they are enclosed in braces or, if not,
their variable and command substitutions yield numbers or
strings that don't themselves require substitutions. How
ever, 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 substitutions. These expressions must be
implemented by generating new code each time the expres
sion is executed.
arithmetic, boolean, compare, expression, fuzzy comparison
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