expr(3tcl)
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 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. 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 expressions in the
way that operands are specified. Also, Tcl expressions support non-
numeric operands and string comparisons, as well as some additional
operators not found in C.
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 binary (if the first two characters of the operand are 0b), in octal
(if the first two characters of the operand are 0o), or in hexadecimal
(if the first two characters of the operand are 0x). For compatibility
with older Tcl releases, an octal integer value is also indicated
simply when the first character of the operand is 0, whether or not the
second character is also o. 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 several common formats making use of the decimal digits, the
decimal point ., the characters e or E indicating scientific notation,
and the sign characters + or -. For example, all of the following are
valid floating-point numbers: 2.1, 3., 6e4, 7.91e+16. Also recognized
as floating point values are the strings Inf and NaN making use of any
case for each character. 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).
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 MATH FUNCTIONS below
for a discussion of how mathematical functions are handled.
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 (most of which are also available as commands in
the tcl::mathop namespace; see the mathop(3tcl) manual page for
details) 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.
** Exponentiation. Valid for any numeric operands.
* / % 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
absolute value of the divisor.
When applied to integers, the division and
remainder operators can be considered to partition
the number line into a sequence of equal-sized
adjacent non-overlapping pieces where each piece is
the size of the divisor; the division result
identifies which piece the divisor lay within, and
the remainder result identifies where within that
piece the divisor lay. 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 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.
in ni List containment and negated list containment.
Each operator produces a zero/one result and treats
its first argument as a string and its second
argument as a Tcl list. The in operator indicates
whether the first argument is a member of the
second argument list; the ni operator inverts the
sense of the result.
& 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. The exponentiation operator promotes types like the multiply
and divide operators, and produces a result that is the same as the
output of the pow function (after any type conversions.) 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 $v. Note, however, that this is only true if the entire
expression is enclosed in braces; otherwise the Tcl parser will
evaluate both "[a]" and "[b]" before invoking the expr command.
MATH FUNCTIONS
When the expression parser encounters a mathematical function such as
sin($x), it replaces it with a call to an ordinary Tcl function in the
tcl::mathfunc namespace. The processing of an expression such as:
expr {sin($x+$y)}
is the same in every way as the processing of:
expr {[tcl::mathfunc::sin [expr {$x+$y}]]}
which in turn is the same as the processing of:
tcl::mathfunc::sin [expr {$x+$y}]
The executor will search for tcl::mathfunc::sin using the usual rules
for resolving functions in namespaces. Either ::tcl::mathfunc::sin or
[namespace current]::tcl::mathfunc::sin will satisfy the request, and
others may as well (depending on the current namespace path setting).
See the mathfunc(3tcl) manual page for the math functions that are
available by default.
TYPES, OVERFLOW, AND PRECISION
All internal computations involving integers are done calling on the
LibTomMath multiple precision integer library as required so that all
integer calculations are performed exactly. Note that in Tcl releases
prior to 8.5, integer calculations were performed with 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 will need to
explicitly add int() or wide() function calls to expressions at the
points where such truncation is required to take place.
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 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 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, i.e., when all arguments to the operator
allow numeric interpretations, 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, a canonical string representation of the
numeric operand value is generated to compare with the string operand.
Canonical string representation for integer values is a decimal string
format. Canonical string representation for floating-point values is
that produced by the %g format specifier of Tcl's format command. 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. Because of Tcl's
tendency to treat values as numbers whenever possible, it is not
generally a good idea to use operators like == when you really want
string comparison and the values of the operands could be arbitrary;
it is 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
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 $a + 2*4.
Most expressions do not require a second round of substitutions.
Either they are enclosed in braces or, if not, their variable and
command substitutions yield numbers or strings that do not themselves
require substitutions. However, because a few unbraced expressions
need two rounds of substitutions, the bytecode compiler must emit
additional instructions to handle this situation. The most expensive
code is required for unbraced expressions that contain command
substitutions. These expressions must be implemented by generating new
code each time the expression is executed. When the expression is
unbraced to allow the substitution of a function or operator, consider
using the commands documented in the mathfunc(3tcl) or mathop(3tcl)
manual pages directly instead.
EXAMPLES
Define a procedure that computes an "interesting" mathematical
function:
proc tcl::mathfunc::calc {x y} {
expr { ($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 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), mathfunc(3tcl), mathop(3tcl), namespace(3tcl), proc(3tcl), string(3tcl), Tcl(3tcl), while(3tcl)
KEYWORDS
arithmetic, boolean, compare, expression, fuzzy comparison
COPYRIGHT
Copyright (c) 1993 The Regents of the University of California. Copyright (c) 1994-2000 Sun Microsystems Incorporated. Copyright (c) 2005 by Kevin B. Kenny <kennykb@acm.org>. All rights reserved.
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