 NAME
 expr  Evaluate an expression
 SYNOPSIS
 expr arg ?arg arg ...?
 DESCRIPTION
 OPERANDS
 OPERATORS
  + ~ !
 * / %
 + 
 << >>
 < > <= >=
 == !=
 eq ne
 &
 ^
 
 &&
 
 x?y:z
 MATH FUNCTIONS
 abs(arg)
 acos(arg)
 asin(arg)
 atan(arg)
 atan2(y, x)
 ceil(arg)
 cos(arg)
 cosh(arg)
 double(arg)
 exp(arg)
 floor(arg)
 fmod(x, y)
 hypot(x, y)
 int(arg)
 log(arg)
 log10(arg)
 pow(x, y)
 rand()
 round(arg)
 sin(arg)
 sinh(arg)
 sqrt(arg)
 srand(arg)
 tan(arg)
 tanh(arg)
 wide(arg)
 TYPES, OVERFLOW, AND PRECISION
 STRING OPERATIONS
 PERFORMANCE CONSIDERATIONS
 EXAMPLES
 SEE ALSO
 KEYWORDS
expr  Evaluate an expression
expr arg ?arg arg ...?
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 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.
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 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 (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 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 a numeric value, either integer or floatingpoint.
 [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 doublequotes.
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
The valid operators are listed below, grouped in decreasing order
of precedence:
  + ~ !

Unary minus, unary plus, bitwise NOT, logical NOT. None of these operators
may be applied to string operands, and bitwise 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.
 &

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 otherwise.
Valid for boolean and numeric (integers or floatingpoint) operands 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 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 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 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.
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 floatingpoint 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, otherwise
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 subsequent 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().
All internal computations involving integers are done with the C type
long, and all internal computations involving floatingpoint are
done with the C type double.
When converting 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 example,
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 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,
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, 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.
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 $a + 2*4.
Most expressions do not require a second round of substitutions.
Either they are enclosed in braces or, if not,
their variable and command substitutions yield numbers or strings
that don't themselves require substitutions.
However, because a few unbraced expressions
need two rounds of substitutions,
the bytecode compiler must emit
additional instructions to handle this situation.
The most expensive code is required for
unbraced expressions that contain command substitutions.
These expressions must be implemented by generating new code
each time the expression is executed.
Define a procedure that computes an "interesting" mathematical
function:
proc calc {x y} {
expr { ($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()) }]
array, for, if, string, Tcl, while
arithmetic, boolean, compare, expression, fuzzy comparison
Copyright © 1993 The Regents of the University of California.
Copyright © 19942000 Sun Microsystems, Inc.
Copyright © 19951997 Roger E. Critchlow Jr.