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.so man.macros
.TH expr n 8.4 Tcl "Tcl Built-In Commands"
.BS
'\" Note:  do not modify the .SH NAME line immediately below!
.SH NAME
expr \- Evaluate an expression
.SH SYNOPSIS
\fBexpr \fIarg \fR?\fIarg arg ...\fR?
.BE

.SH DESCRIPTION
.PP
Concatenates \fIarg\fRs (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
.CS
\fBexpr 8.2 + 6\fR
.CE
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.
.SH OPERANDS
.PP
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 \fB0\fR), or in hexadecimal (if the first
two characters of the operand are \fB0x\fR).
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
\fBf\fR, \fBF\fR, \fBl\fR, and \fBL\fR 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).
.PP
.VS 8.4
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.)
.VE 8.4
.PP
Operands may be specified in any of the following ways:
.IP [1]
As a numeric value, either integer or floating-point.
.IP [2]
As a boolean value, using any form understood by \fBstring is boolean\fR.
.IP [3]
As a Tcl variable, using standard \fB$\fR notation.
The variable's value will be used as the operand.
.IP [4]
As a string enclosed in double-quotes.
The expression parser will perform backslash, variable, and
command substitutions on the information between the quotes,
and use the resulting value as the operand
.IP [5]
As a string enclosed in braces.
The characters between the open brace and matching close brace
will be used as the operand without any substitutions.
.IP [6]
As a Tcl command enclosed in brackets.
The command will be executed and its result will be used as
the operand.
.IP [7]
As a mathematical function whose arguments have any of the above
forms for operands, such as \fBsin($x)\fR.  See below for a list of defined
functions.
.LP
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.
.PP
For some examples of simple expressions, suppose the variable
\fBa\fR has the value 3 and
the variable \fBb\fR 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:
.CS
.ta 6c
\fBexpr 3.1 + $a	6.1
expr 2 + "$a.$b"	5.6
expr 4*[llength "6 2"]	8
expr {{word one} < "word $a"}	0\fR
.CE
.SH OPERATORS
.PP
The valid operators are listed below, grouped in decreasing order
of precedence:
.TP 20
\fB\-\0\0+\0\0~\0\0!\fR
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.
.TP 20
\fB*\0\0/\0\0%\fR
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.
.TP 20
\fB+\0\0\-\fR
Add and subtract.  Valid for any numeric operands.
.TP 20
\fB<<\0\0>>\fR
Left and right shift.  Valid for integer operands only.
A right shift always propagates the sign bit.
.TP 20
\fB<\0\0>\0\0<=\0\0>=\fR
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.
.TP 20
\fB==\0\0!=\fR
Boolean equal and not equal.  Each operator produces a zero/one result.
Valid for all operand types.
.VS 8.4
.TP 20
\fBeq\0\0ne\fR
Boolean string equal and string not equal.  Each operator produces a
zero/one result.  The operand types are interpreted only as strings.
.VE 8.4
.TP 20
\fB&\fR
Bit-wise AND.  Valid for integer operands only.
.TP 20
\fB^\fR
Bit-wise exclusive OR.  Valid for integer operands only.
.TP 20
\fB|\fR
Bit-wise OR.  Valid for integer operands only.
.TP 20
\fB&&\fR
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.
.TP 20
\fB||\fR
Logical OR.  Produces a 0 result if both operands are zero, 1 otherwise.
Valid for boolean and numeric (integers or floating-point) operands only.
.TP 20
\fIx\fB?\fIy\fB:\fIz\fR
If-then-else, as in C.  If \fIx\fR
evaluates to non-zero, then the result is the value of \fIy\fR.
Otherwise the result is the value of \fIz\fR.
The \fIx\fR operand must have a boolean or numeric value.
.LP
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
.CS
\fBexpr 4*2 < 7\fR
.CE
returns 0.
.PP
The \fB&&\fR, \fB||\fR, and \fB?:\fR 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
.CS
\fBexpr {$v ? [a] : [b]}\fR
.CE
only one of \fB[a]\fR or \fB[b]\fR will actually be evaluated,
depending on the value of \fB$v\fR.  Note, however, that this is
only true if the entire expression is enclosed in braces;  otherwise
the Tcl parser will evaluate both \fB[a]\fR and \fB[b]\fR before
invoking the \fBexpr\fR command.
.SH "MATH FUNCTIONS"
.PP
Tcl supports the following mathematical functions in expressions, all
of which work solely with floating-point numbers unless otherwise noted:
.DS
.ta 3c 6c 9c
\fBabs\fR	\fBcosh\fR	\fBlog\fR	\fBsqrt\fR
\fBacos\fR	\fBdouble\fR	\fBlog10\fR	\fBsrand\fR
\fBasin\fR	\fBexp\fR	\fBpow\fR	\fBtan\fR
\fBatan\fR	\fBfloor\fR	\fBrand\fR	\fBtanh\fR
\fBatan2\fR	\fBfmod\fR	\fBround\fR	\fBwide\fR
\fBceil\fR	\fBhypot\fR	\fBsin\fR
\fBcos\fR	\fBint\fR	\fBsinh\fR
.DE
.PP
.TP
\fBabs(\fIarg\fB)\fR
Returns the absolute value of \fIarg\fR.  \fIArg\fR may be either
integer or floating-point, and the result is returned in the same form.
.TP
\fBacos(\fIarg\fB)\fR
Returns the arc cosine of \fIarg\fR, in the range [\fI0\fR,\fIpi\fR]
radians. \fIArg\fR should be in the range [\fI-1\fR,\fI1\fR].
.TP
\fBasin(\fIarg\fB)\fR
Returns the arc sine of \fIarg\fR, in the range [\fI-pi/2\fR,\fIpi/2\fR]
radians.  \fIArg\fR should be in the range [\fI-1\fR,\fI1\fR].
.TP
\fBatan(\fIarg\fB)\fR
Returns the arc tangent of \fIarg\fR, in the range [\fI-pi/2\fR,\fIpi/2\fR]
radians.
.TP
\fBatan2(\fIy, x\fB)\fR
Returns the arc tangent of \fIy\fR/\fIx\fR, in the range [\fI-pi\fR,\fIpi\fR]
radians.  \fIx\fR and \fIy\fR cannot both be 0.  If \fIx\fR is greater
than \fI0\fR, this is equivalent to \fBatan(\fIy/x\fB)\fR.
.TP
\fBceil(\fIarg\fB)\fR
Returns the smallest integral floating-point value (i.e. with a zero
fractional part) not less than \fIarg\fR.
.TP
\fBcos(\fIarg\fB)\fR
Returns the cosine of \fIarg\fR, measured in radians.
.TP
\fBcosh(\fIarg\fB)\fR
Returns the hyperbolic cosine of \fIarg\fR.  If the result would cause
an overflow, an error is returned.
.TP
\fBdouble(\fIarg\fB)\fR
If \fIarg\fR is a floating-point value, returns \fIarg\fR, otherwise converts
\fIarg\fR to floating-point and returns the converted value.
.TP
\fBexp(\fIarg\fB)\fR
Returns the exponential of \fIarg\fR, defined as \fIe\fR**\fIarg\fR.
If the result would cause an overflow, an error is returned.
.TP
\fBfloor(\fIarg\fB)\fR
Returns the largest integral floating-point value (i.e. with a zero
fractional part) not greater than \fIarg\fR.
.TP
\fBfmod(\fIx, y\fB)\fR
Returns the floating-point remainder of the division of \fIx\fR by
\fIy\fR.  If \fIy\fR is 0, an error is returned.
.TP
\fBhypot(\fIx, y\fB)\fR
Computes the length of the hypotenuse of a right-angled triangle
\fBsqrt(\fIx\fR*\fIx\fR+\fIy\fR*\fIy\fB)\fR.
.TP
\fBint(\fIarg\fB)\fR
.VS 8.4
If \fIarg\fR is an integer value of the same width as the machine
word, returns \fIarg\fR, otherwise
converts \fIarg\fR 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.
.VE 8.4
.TP
\fBlog(\fIarg\fB)\fR
Returns the natural logarithm of \fIarg\fR.  \fIArg\fR must be a
positive value.
.TP
\fBlog10(\fIarg\fB)\fR
Returns the base 10 logarithm of \fIarg\fR.  \fIArg\fR must be a
positive value.
.TP
\fBpow(\fIx, y\fB)\fR
Computes the value of \fIx\fR raised to the power \fIy\fR.  If \fIx\fR
is negative, \fIy\fR must be an integer value.
.TP
\fBrand()\fR
Returns a pseudo-random floating-point value in the range (\fI0\fR,\fI1\fR).  
The generator algorithm is a simple linear congruential generator that
is not cryptographically secure.  Each result from \fBrand\fR completely
determines all future results from subsequent calls to \fBrand\fR, so
\fBrand\fR 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 \fBsrand\fR function.
.TP
\fBround(\fIarg\fB)\fR
If \fIarg\fR is an integer value, returns \fIarg\fR, otherwise converts
\fIarg\fR to integer by rounding and returns the converted value.
.TP
\fBsin(\fIarg\fB)\fR
Returns the sine of \fIarg\fR, measured in radians.
.TP
\fBsinh(\fIarg\fB)\fR
Returns the hyperbolic sine of \fIarg\fR.  If the result would cause
an overflow, an error is returned.
.TP
\fBsqrt(\fIarg\fB)\fR
Returns the square root of \fIarg\fR.  \fIArg\fR must be non-negative.
.TP
\fBsrand(\fIarg\fB)\fR
The \fIarg\fR, which must be an integer, is used to reset the seed for
the random number generator of \fBrand\fR.  Returns the first random
number (see \fBrand()\fR) from that seed.  Each interpreter has its own seed.
.TP
\fBtan(\fIarg\fB)\fR
Returns the tangent of \fIarg\fR, measured in radians.
.TP
\fBtanh(\fIarg\fB)\fR
Returns the hyperbolic tangent of \fIarg\fR.
.TP
\fBwide(\fIarg\fB)\fR
.VS 8.4
Converts \fIarg\fR to an integer value at least 64-bits wide (by sign-extension
if \fIarg\fR is a 32-bit number) if it is not one already.
.VE 8.4
.PP
In addition to these predefined functions, applications may
define additional functions using \fBTcl_CreateMathFunc\fR().
.SH "TYPES, OVERFLOW, AND PRECISION"
.PP
All internal computations involving integers are done with the C type
\fIlong\fR, and all internal computations involving floating-point are
done with the C type \fIdouble\fR.
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.
.PP
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,
.CS
\fBexpr 5 / 4\fR
.CE
returns 1, while
.CS
\fBexpr 5 / 4.0\fR
\fBexpr 5 / ( [string length "abcd"] + 0.0 )\fR
.CE
both return 1.25.
Floating-point values are always returned with a ``\fB.\fR''
or an \fBe\fR so that they will not look like integer values.  For
example,
.CS
\fBexpr 20.0/5.0\fR
.CE
returns \fB4.0\fR, not \fB4\fR.
.SH "STRING OPERATIONS"
.PP
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,
.VS 8.4
except in the case of the \fBeq\fR and \fBne\fR operators.
.VE 8.4
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 \fIsprintf\fR format specifier
\fB%d\fR for integers and \fB%g\fR for floating-point values.
For example, the commands
.CS
\fBexpr {"0x03" > "2"}\fR
\fBexpr {"0y" < "0x12"}\fR
.CE
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 \fB18\fR.
Because of Tcl's tendency to treat values as numbers whenever
possible, it isn't generally a good idea to use operators like \fB==\fR
when you really want string comparison and the values of the
operands could be arbitrary;  it's better in these cases to use
.VS 8.4
the \fBeq\fR or \fBne\fR operators, or
.VE 8.4
the \fBstring\fR command instead.

.SH "PERFORMANCE CONSIDERATIONS"
.PP
Enclose expressions in braces for the best speed and the smallest
storage requirements.
This allows the Tcl bytecode compiler to generate the best code.
.PP
As mentioned above, expressions are substituted twice:
once by the Tcl parser and once by the \fBexpr\fR command.
For example, the commands
.CS
\fBset a 3\fR
\fBset b {$a + 2}\fR
\fBexpr $b*4\fR
.CE
return 11, not a multiple of 4.
This is because the Tcl parser will first substitute \fB$a + 2\fR for
the variable \fBb\fR,
then the \fBexpr\fR command will evaluate the expression \fB$a + 2*4\fR.
.PP
Most expressions do not require a second round of substitutions.
Either they are enclosed in braces or, if not,
their variable and command substitutions yield numbers or strings
that don't themselves require substitutions.
However, because a few unbraced expressions 
need two rounds of substitutions,
the bytecode compiler must emit
additional instructions to handle this situation.
The most expensive code is required for
unbraced expressions that contain command substitutions.
These expressions must be implemented by generating new code
each time the expression is executed.
.SH EXAMPLES
Define a procedure that computes an "interesting" mathematical
function:
.CS
proc calc {x y} {
    \fBexpr\fR { ($x*$x - $y*$y) / exp($x*$x + $y*$y) }
}
.CE
.PP
Convert polar coordinates into cartesian coordinates:
.CS
# convert from ($radius,$angle)
set x [\fBexpr\fR { $radius * cos($angle) }]
set y [\fBexpr\fR { $radius * sin($angle) }]
.CE
.PP
Convert cartesian coordinates into polar coordinates:
.CS
# convert from ($x,$y)
set radius [\fBexpr\fR { hypot($y, $x) }]
set angle  [\fBexpr\fR { atan2($y, $x) }]
.CE
.PP
Print a message describing the relationship of two string values to
each other:
.CS
puts "a and b are [\fBexpr\fR {$a eq $b ? {equal} : {different}}]"
.CE
.PP
Set a variable to whether an environment variable is both defined at
all and also set to a true boolean value:
.CS
set isTrue [\fBexpr\fR {
    [info exists ::env(SOME_ENV_VAR)] &&
    [string is true -strict $::env(SOME_ENV_VAR)]
}]
.CE
.PP
Generate a random integer in the range 0..99 inclusive:
.CS
set randNum [\fBexpr\fR { int(100 * rand()) }]
.CE

.SH "SEE ALSO"
array(n), for(n), if(n), string(n), Tcl(n), while(n)

.SH KEYWORDS
arithmetic, boolean, compare, expression, fuzzy comparison
