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.so man.macros

.TH expr n 8.0 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\fR'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 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, then an operand is left

as a string (and only a limited set of operators may be applied to

it).

.PP

Operands may be specified in any of the following ways:

.IP [1]

As an numeric value, either integer or floating-point.

.IP [2]

As a Tcl variable, using standard \fB$\fR notation.

The variable's value will be used as the operand.

.IP [3]

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 [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 substitutions.

.IP [5]

As a Tcl command enclosed in brackets.

The command will be executed and its result will be used as

the operand.

.IP [6]

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 substitutions occur above (e.g. inside quoted strings), they

are performed by the expression's instructions.

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.

.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 operands

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 operands 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.

.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,

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 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:

.DS

.ta 3c 6c 9c

\fBacos\fR      \fBcos\fR       \fBhypot\fR     \fBsinh\fR

\fBasin\fR      \fBcosh\fR      \fBlog\fR       \fBsqrt\fR

\fBatan\fR      \fBexp\fR       \fBlog10\fR     \fBtan\fR

\fBatan2\fR     \fBfloor\fR     \fBpow\fR       \fBtanh\fR

\fBceil\fR      \fBfmod\fR      \fBsin\fR

.DE

Each of these functions invokes the math library function of the same

name;  see the manual entries for the library functions for details

on what they do.  Tcl also implements the following functions for

conversion between integers and floating-point numbers and the

generation of random numbers:

.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

\fBdouble(\fIarg\fB)\fR

If \fIarg\fR is a floating value, returns \fIarg\fR, otherwise converts

\fIarg\fR to floating and returns the converted value.

.TP

\fBint(\fIarg\fB)\fR

If \fIarg\fR is an integer value, returns \fIarg\fR, otherwise converts

\fIarg\fR to integer by truncation and returns the converted value.

.TP

\fBrand()\fR

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.

.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

\fBsrand(\fIarg\fB)\fR

The \fIarg\fR, 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.

.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.

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 the

\fBstring compare\fR command instead.

.SH "PERFORMANCE CONSIDERATIONS"

.VS

.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.

.VE

.SH KEYWORDS

arithmetic, boolean, compare, expression, fuzzy comparison