  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

### 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 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

    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.

### 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 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 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 f, F, l, and L 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).

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.)

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 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

### OPERATORS

The valid operators 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.

* / %
  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.

&
  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. 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

Tcl supports the following mathematical functions in expressions, all of which work solely with floating-point 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 floating-point, 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 floating-point 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 floating-point value, returns arg, otherwise converts arg to floating-point 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 floating-point value (i.e. with a zero fractional part) not greater than arg.

fmod(x, y)
  Returns the floating-point 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 right-angled 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. 32-bits on 32-bit systems, and 64-bits on 64-bit 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 pseudo-random floating-point 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 one-time 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 non-negative.

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 64-bits wide (by sign-extension if arg is a 32-bit number) if it is not one already.

In addition to these predefined functions, applications may define additional functions using Tcl_CreateMathFunc().

### TYPES, OVERFLOW, AND PRECISION

All internal computations involving integers are done with the C type long, and 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 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.

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, 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 floating-point 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 after the second operand is converted to the string 18. 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.

### 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 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.

### EXAMPLES

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()) }]

### SEE ALSO

array, for, if, string, Tcl, while

### KEYWORDS

arithmetic, boolean, compare, expression, fuzzy comparison

    Copyright © 1993 The Regents of the University of California.
    Copyright © 1994-2000 Sun Microsystems, Inc.
    Copyright © 1995-1997 Roger E. Critchlow Jr.