path: root/doc/expr.n

'\"
'\" Copyright (c) 1993 The Regents of the University of California.
'\" Copyright (c) 1994-2000 Sun Microsystems, Inc.
'\" Copyright (c) 2005 by Kevin B. Kenny <kennykb@acm.org>. All rights reserved
'\"
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.TH expr n 8.5 Tcl "Tcl Built-In Commands"
.so man.macros
.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, separated by a space, into an expresion, and evaluates
that expression, returning its value.
The operators permitted in an expression 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.
The value of an expressions is often a numeric result, either an integer or a
floating-point value, but may also be a non-numeric value.
For example, the expression
.PP
.CS
\fBexpr\fR 8.2 + 6
.CE
.PP
evaluates to 14.2.
Expressions differ from C expressions in the way that
operands are specified.  Also, expressions support
non-numeric operands, string comparisons, and some
additional operators not found in C.
.PP
When an expression evaluates to an integer, the value is the decimal form of
the integer, and when an expression evaluates to a floating-point number, the
value is the form produced by the \fB%g\fR format specifier of Tcl's
\fBformat\fR command.
.SS OPERANDS
.PP
An expression consists of a combination of operands, operators, parentheses and
commas, possibly with whitespace between any of these elements, which is
ignored.
An integer operand may be specified in decimal, binary
(the first two characters are \fB0b\fR), octal
(the first two characters are \fB0o\fR), or hexadecimal
(the first two characters are \fB0x\fR) form.  For
compatibility with older Tcl releases, an operand that begins with \fB0\fR is
interpreted as an octal integer even if the second character is not \fBo\fR.
A floating-point number may be specified in any of several
common decimal formats, and may use the decimal point \fB.\fR,
\fBe\fR or \fBE\fR for scientific notation, and
the sign characters \fB+\fR and \fB\-\fR.  The
following are all valid floating-point numbers:  2.1, 3., 6e4, 7.91e+16.
The strings \fBInf\fR
and \fBNaN\fR, in any combination of case, are also recognized as floating point
values.  An operand that doesn't have a numeric interpretation must be quoted
with either braces or with double quotes.
.PP
An operand 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\fR
\fBboolean\fR.
.IP [3]
As a variable, using standard \fB$\fR notation.
The value of the variable is then the value of the operand.
.IP [4]
As a string enclosed in double-quotes.
Backslash, variable, and command substitution are performed as described in
\fBTcl\fR.
.IP [5]
As a string enclosed in braces.
The operand is treated as a braced value as described in \fBTcl\fR.
.IP [6]
As a Tcl command enclosed in brackets.
Command substitution is performed as described in \fBTcl\fR.
.IP [7]
As a mathematical function such as \fBsin($x)\fR, whose arguments have any of the above
forms for operands.  See \fBMATH FUNCTIONS\fR below for
a discussion of how mathematical functions are handled.
.PP
Because \fBexpr\fR parses and performs substitutions on values that have
already been parsed and substituted by \fBTcl\fR, it is usually best to enclose
expressions in braces to avoid the first round of substitutions by
\fBTcl\fR.
.PP
Below are some examples of simple expressions where the value of \fBa\fR is 3
and the value of \fBb\fR is 6.  The command on the left side of each line
produces the value on the right side.
.PP
.CS
.ta 6c
\fBexpr\fR 3.1 + $a	\fI6.1\fR
\fBexpr\fR 2 + "$a.$b"	\fI5.6\fR
\fBexpr\fR 4*[llength "6 2"]	\fI8\fR
\fBexpr\fR {{word one} < "word $a"}	\fI0\fR
.CE
.SS OPERATORS
.PP
For operators having both a numeric mode and a string mode, the numeric mode is
chosen when all operands have a numeric interpretation.  The integer
interpretation of an operand is preferred over the floating-point
interpretation.  To ensure string operations on arbitrary values it is generally a
good idea to use \fBeq\fR, \fBne\fR, or the \fBstring\fR command instead of
more versatile operators such as \fB==\fR.
.PP
Unless otherwise specified, operators accept non-numeric operands.  The value
of a boolean operation is 1 if true, 0 otherwise.  See also \fBstring is\fR
\fBboolean\fR.  The valid operators, most of which are also available as
commands in the \fBtcl::mathop\fR namespace (see \fBmathop\fR(n)), 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.  These operators
may only be applied to numeric operands, and bit-wise NOT may only be
applied to integers.
.TP 20
\fB**\fR
.
Exponentiation.  Valid for numeric operands.
.TP 20
\fB*\0\0/\0\0%\fR
.
Multiply and divide, which are valid for numeric operands, and remainder, which
is valid for integers.  The remainder, an absolute value smaller than the
absolute value of the divisor, has the same sign as the divisor.
.RS
.PP
When applied to integers, division and remainder can be
considered to partition the number line into a sequence of 
adjacent non-overlapping pieces, where each piece is the size of the divisor;
the quotient identifies which piece the dividend lies within, and the
remainder identifies where within that piece the dividend lies. A
consequence of this is that the result of
.QW "-57 \fB/\fR 10"
is always -6, and the result of
.QW "-57 \fB%\fR 10"
is always 3.
.RE
.TP 20
\fB+\0\0\-\fR
.
Add and subtract.  Valid for numeric operands.
.TP 20
\fB<<\0\0>>\fR
.
Left and right shift.  Valid for integers.
A right shift always propagates the sign bit.
.TP 20
\fB<\0\0>\0\0<=\0\0>=\fR
.
Boolean less than, greater than, less than or equal, and greater than or equal.
.TP 20
\fB==\0\0!=\fR
.
Boolean equal and not equal.
.TP 20
\fBeq\0\0ne\fR
.
Boolean string equal and string not equal.
.TP 20
\fBin\0\0ni\fR
.
List containment and negated list containment.  The first argument is
interpreted as a string, the second as a list.  \fBin\fR tests for membership
in the list, and \fBni\fR is the inverse.
.TP 20
\fB&\fR
.
Bit-wise AND.  Valid for integer operands.
.TP 20
\fB^\fR
.
Bit-wise exclusive OR.  Valid for integer operands.
.TP 20
\fB|\fR
.
Bit-wise OR.  Valid for integer operands.
.TP 20
\fB&&\fR
.
Logical AND.  If both operands are true, the result is 1, or 0 otherwise.

.TP 20
\fB||\fR
.
Logical OR.  If both operands are false, the result is 0, or 1 otherwise.
.TP 20
\fIx\fB?\fIy\fB:\fIz\fR
.
If-then-else, as in C.  If \fIx\fR is false , the result is the value of
\fIy\fR.  Otherwise the result is the value of \fIz\fR.
.PP
The exponentiation operator promotes types in the same way as the multiply 
and divide operators, and the result is is the same as the result of 
\fBpow\fR.
exponentiation groups right-to-left within a precedence level. Other binary 
operators group left-to-right.  For example, the value of
.PP
.CS
\fBexpr\fR {4*2 < 7}
.CE
.PP
is 0, while the value of
.PP
.CS
\fBexpr\fR {2**3**2}
.CE
.PP
is 512.
.PP
\fB&&\fR, \fB||\fR, and \fB?:\fR feature 
.QW "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
.PP
.CS
\fBexpr\fR {$v ? [a] : [b]}
.CE
.PP
only one of \fB[a]\fR or \fB[b]\fR is evaluated,
depending on the value of \fB$v\fR.  This is not true of the normal Tcl parser,
so it is normally recommended to enclose the arguments to \fBexpr\fR in braces.
Without braces, as in
\fBexpr\fR $v ? [a] : [b]
both \fB[a]\fR and \fB[b]\fR are evaluated before \fBexpr\fR is even called.
.PP
For more details on the results
produced by each operator, see the documentation for C.
.SS "MATH FUNCTIONS"
.PP
A mathematical function such as \fBsin($x)\fR is replaced with a call to an ordinary
Tcl command in the \fBtcl::mathfunc\fR namespace.  The evaluation
of an expression such as
.PP
.CS
\fBexpr\fR {sin($x+$y)}
.CE
.PP
is the same in every way as the evaluation of
.PP
.CS
\fBexpr\fR {[tcl::mathfunc::sin [\fBexpr\fR {$x+$y}]]}
.CE
.PP
which in turn is the same as the evaluation of
.PP
.CS
tcl::mathfunc::sin [\fBexpr\fR {$x+$y}]
.CE
.PP
\fBtcl::mathfunc::sin\fR is resolved as described in
\fBNAMESPACE RESOLUTION\fR in the \fBnamespace\fR documentation.   Given the
default value of \fBnamespace path\fR, \fB[namespace
current]::tcl::mathfunc::sin\fR or \fB::tcl::mathfunc::sin\fR are the typical
resolutions.
.PP
As in C, a mathematical function may accept multiple arguments separated by commas. Thus,
.PP
.CS
\fBexpr\fR {hypot($x,$y)}
.CE
.PP
becomes
.PP
.CS
tcl::mathfunc::hypot $x $y
.CE
.PP
See the \fBmathfunc\fR(n) documentation for the math functions that are
available by default.
.SS "TYPES, OVERFLOW, AND PRECISION"
.PP
When needed to guarantee exact performance, internal computations involving
integers use the LibTomMath multiple precision integer library.  In Tcl releases
prior to 8.5, integer calculations were performed using one of the C types
\fIlong int\fR or \fITcl_WideInt\fR, causing implicit range truncation
in those calculations where values overflowed the range of those types.
Any code that relied on these implicit truncations should instead call
\fBint()\fR or \fBwide()\fR, which do truncate.
.PP
Internal floating-point computations are
performed using the C type \fIdouble\fR.
When converting a string to floating-point, exponent overflow is
detected and results in the \fIdouble\fR value of \fBInf\fR or
\fB\-Inf\fR as appropriate.  Floating-point overflow and underflow
are detected to the degree supported by the hardware, which is generally
fairly 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 values are used.  For example,
.PP
.CS
\fBexpr\fR {5 / 4}
.CE
.PP
returns 1, while
.PP
.CS
\fBexpr\fR {5 / 4.0}
\fBexpr\fR {5 / ( [string length "abcd"] + 0.0 )}
.CE
.PP
both return 1.25.
A floating-point result can be distinguished from an integer result by the
presence of either
.QW \fB.\fR
or
.QW \fBe\fR
.PP
. For example,
.PP
.CS
\fBexpr\fR {20.0/5.0}
.CE
.PP
returns \fB4.0\fR, not \fB4\fR.
.SH "PERFORMANCE CONSIDERATIONS"
.PP
Where an expression contains syntax that Tcl would otherwise perform
substitutions on, enclosing an expression in braces or otherwise quoting it
so that it's a static value allows the Tcl compiler to generate bytecode for
the expression, resulting in better speed and smaller storage requirements.
This also avoids issues that can arise if Tcl is allowed to perform
substitution on the value before \fBexpr\fR is called.
.PP
In the following example, the value of the expression is 11 because the Tcl parser first
substitutes \fB$b\fR and \fBexpr\fR then substitutes \fB$a\fR.  Enclosing the
expression in braces would result in a syntax error.
.CS
set a 3
set b {$a + 2}
\fBexpr\fR $b*4
.CE
.PP

When an expression is generated at runtime, like the one above is, the bytcode
compiler must ensure that new code is generated each time the expression
is evaluated.  This is the most costly kind of expression from a performance
perspective.  In such cases, consider directly using the commands described in
the \fBmathfunc\fR(n) or \fBmathop\fR(n) documentation instead of \fBexpr\fR.

Most expressions are not formed at runtime, but are literal strings or contain
substitutions that don't introduce other substitutions.  To allow the bytecode
compiler to work with an expression as a string literal at compilation time,
ensure that it contains no substitutions or that it is enclosed in braces or
otherwise quoted to prevent Tcl from performing substitutions, allowing
\fBexpr\fR to perform them instead.
.SH EXAMPLES
.PP
A numeric comparison whose result is 1:
.CS
\fBexpr\fR {"0x03" > "2"}
.CE
.PP
A string comparison whose result is 1:
.CS
\fBexpr\fR {"0y" > "0x12"}
.CE
.PP
Define a procedure that computes an
.QW interesting
mathematical function:
.PP
.CS
proc tcl::mathfunc::calc {x y} {
    \fBexpr\fR { ($x**2 - $y**2) / exp($x**2 + $y**2) }
}
.CE
.PP
Convert polar coordinates into cartesian coordinates:
.PP
.CS
# convert from ($radius,$angle)
set x [\fBexpr\fR { $radius * cos($angle) }]
set y [\fBexpr\fR { $radius * sin($angle) }]
.CE
.PP
Convert cartesian coordinates into polar coordinates:
.PP
.CS
# convert from ($x,$y)
set radius [\fBexpr\fR { hypot($y, $x) }]
set angle  [\fBexpr\fR { atan2($y, $x) }]
.CE
.PP
Print a message describing the relationship of two string values to
each other:
.PP
.CS
puts "a and b are [\fBexpr\fR {$a eq $b ? {equal} : {different}}]"
.CE
.PP
Set a variable indicating whether an environment variable is defined and has
value of true:
.PP
.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:
.PP
.CS
set randNum [\fBexpr\fR { int(100 * rand()) }]
.CE
.SH "SEE ALSO"
array(n), for(n), if(n), mathfunc(n), mathop(n), namespace(n), proc(n),
string(n), Tcl(n), while(n)
.SH KEYWORDS
arithmetic, boolean, compare, expression, fuzzy comparison
.SH COPYRIGHT
.nf
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.
.fi
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