## expr

expr , a built-in Tcl command, evaluates an expression.

A little math language
Adds features & syntactic sugar to expr.
A real problem
Arbitrary precision math procedures
compute
More syntactic sugar for expr.
Converting numbers from arbitrary bases
DebuggingExprCalls
rwm: Sometimes it is difficult to debug expr calls where the operands are variables. DebuggingExprCalls explains how to wrap expr to help with these cases.
double substitution
exprlex and funclex
Splits expressions and functions into their lexical components.
ycl math =, by PYK
A more concise version of expr. Assigns the result to the given variable. If no variable is provided, The \$expr is used. Makes doing math in Tcl more pleasant. = y {\$m * \$x + \$b} instead of {set y [expr {\$m * \$x + \$b}]}.
Floating-point formatting
Also explains how to format a floating point value without disturbing the disturbing the internal representation.
gotcha
expr figures prominently.
Tcl and octal numbers
The Octal Bug.
expr problems with int
Historical (pre-8.5) information on the limits of number representation (both integer and float) inherited from C.
for
How can I do math in Tcl
if
Importing expr functions
An exploration into using expr functions without explictly calling expr.
infix
A package to facilitate writing sequences of mathematical formulae in the familiar infix form.
in and ni
expr operators to test for list membership.
Math function help
Modeling COND with expr
Braced expressions can span several lines.
Numerical Analysis in Tcl
Sample Math Programs
Extremely simple math examples.
Tcl help
TIP #123
TIP #174
Math Operators as Commands.
TIP #182
TIP #201
Adds the 'in' and ni operators.
TIP #232
TIP #237
while

## Documentation

official reference
mathfunc
mathop man page
tcl_precision
Tcl_GetBoolean man page

## Synopsis

expr arg ?arg arg ...?

## Description

expr concatentates its arguments, evaluates this result as a Tcl expression, and returns the value of the expression.

expr implements a little language that has a syntax separate from Tcl. An expression is composed of values and operators. Like Tcl, it interprets variable substitution, command substitution, double quotes and braces. Unlike Tcl, it interprets anything that looks like a number as a number, anything that looks like boolean as boolean, provides operators and functions, and requires that literal string values be enclosed in double quotes or braces.

A value recognized as boolean by string is boolean... can be used directly, without enclosing it in quotes or braces.

The operators permitted in Tcl expressions include most of the operators permitted in C expressions and a few additional ones. The operators have the same meaning and precedence as the corresponding C operators. Expressions can produce numeric or non-numeric results.

A functions takes the form,

name(argument?)

or

name(argument,argument ...)

The first character of name is a letter, and remaining characters are letters, digits or underscore. I.e. name matches the regular expression, [A-Za-z][A-Za-z0-9_]* .

Each argument to a function is itself a complete expression. For example:

`cos(\$x+\$y)`

## Usage

```set val1 8.2
set val2 6
expr {\$val1 + \$val2}```

Result:

`14.2`

In most cases, it's best to brace or otherwise escape the argument to expr. In particular, the special Tcl characters, \$, [, ", { should normally be escaped:

`expr {\$val1+\$val2}`

This prevents Tcl from performing substitutions on the arguments, leaving it to expr to interpret them as it will. See below for more details.

expr expressions differ from C expressions in the way that operands are specified. They also include some non-numeric operators for strings (comparison) and lists (membership).

## Operators

Since Tcl 8.5, many operators have command equivalents in the ::tcl::mathop namespace.

In spite of the name mathop, some of the operators are string-oriented rather than math-oriented.

The following is a chart of operators in order of precedence (tightest-binding to least-tight associativity):

 - + ~ ! Unary negative, positive, bit-wise NOT (every bit in the input value gets replaced by its inverse), and a logical NOT (non-zero maps to zero, and zero maps to one). ** Exponential power. From Tcl 8.5 on. * / % Multiplication, division and integer remainder. See fmod() below. + - Addition and subtraction. << >> Left and right shift. Equivalent to multiplying or dividing by a suitable power of two and then reducing the result to the range that can be stored as an integer on the host platform. < > <= >= Less than, greater than, less-than or equal, and greater-than or equal. Operands maybe be numeric or non-numeric, but where string comparison is intended it is advisable to use the dedicated string comparison operators, or string compare instead, as those are more predictable in the case of a string that looks like a number. For example, string equal considers "6" and "06" to be different strings, but the == considers them to be numeically equivalent. == != Equality and inequality. Operands may be numeric or non-numeric, but for non-numeric comparisons eq, ne, or string equal are better choices. eq ne String equality and inequality. For example, 6 and 06, are not equal, an neither are 1 and 1.0. Introduced in 8.4. in ni Presence and absence of a string in a list. New in Tcl 8.5. & Bit-wise AND. A bit is set in the result when the corresponding bit is set in both operands. ^ Bit-wise exclusive OR. A bit is set in the result when the corresponding bit is set in precisely one of the operands. | Bit-wise OR. A bit is set in the result when the corresponding bit is set in either of the operands. && Logical AND. The result is 1 when both of the operands are true. and 0 otherwise. This operation is a short-circuiting operation: It only evaluates its second operand when the first is true. If the second operand appears to be evaluated when it shouldn't be, see double substitution. || Logical OR. The result is 0 when both operands are false, and 1 otherwise. This operation is a short-circuiting operation: It only evaluates its second operand when the first is zero. When the second operand appears to be evaluated when it shoudn't be, see double substitution. x ? y : z If-then-else, as in C. x, y, and z are expressions. The result is y if x is true, and z otherwise. This operation is a short-circuiting operation: If x is true, z is not evaluated, and if x is false, y is not evaluated. If an operand appears to be evaluated when it shouldn't be, see double substitution. if is just as perfomant since the generated bytecode is identical.

It would have been better for the bitwise operators to have a higher precedence than the equality operators. The current precedence is inherited from C, which, for idomatic compatiblity with B, gave them a lower precedence.

## Functions

See the mathfunc man page .

The following is a list of builtin functions:

abs(x)
Absolute value (negate if negative).
acos(x)
asin(x)
atan(x)
atan2(y,x)
Inverse tangent. Can handle cases which plain atan() can't due to division by zero, and has a larger output range. The result in radians.
bool(x)
Accepts any valid boolean value and produces the corresponding number 0 or 1.
ceil(x)
Ceiling. Defined over floating point numbers. If the input value is not a whole number, produces the next larger whole number. Surprise: Produces a float, not an integer.
cos(x)
Cosine. x is a radian value.
cosh(x)
Hyperbolic cosine.
double(x)
Produces the floating point representation of a number.
entier(x)
Like int(x) but there is no limit on the size of x.
exp(x)
Exponential function. Produces e to the power of x, where e is the base of natural logarithms.
floor(x)
Floor. Defined over floating-point numbers. If the input value is not a whole number, produces the next smaller whole number as a floating-point number.
fmod(x, y)
Floating-point remainder of x divided by y.
hypot(x,y)
Hypotenuse calculator. Assumes boring old Euclidean geometry. If the projection of a straight line segment onto the X axis is x units long, and the projection of that line segment onto the Y axis is y units long, then the line segment is hypot(x,y) units long. Equivalent to sqrt(x*x+y*y).
int(x)
Convert number to integer by truncation. Limited by the size of long in C.
isqrt(x)
Compute the integer part of the square root of x.
log(x)
Natural logarithm.
log10(x)
Logarithm with respect to base 10.
max(x,...)
The argument with the greatest value.
min(x,...)
The argument with the least value.
pow(x,y)
Power function. x to the power of y.
rand()
Random number. Uses uniform distribution over the range [0,1). Not suitable for cryptographic purposes.
round(x)
Round to nearest whole number. Not suitable for financial rounding.
sin(x)
Sine. x is a radian value.
sinh(x)
Hyperbolic sine.
sqrt(x)
Produces as a real number the square root of the positive number x.
srand(x)
Seeds the random number generator with the integer x. Each interpreter has its own random number generator, which starts out seeded with the current time.
tan(x)
tanh(x)
Hyperbolic tangent.
wide(x)
Produces the lower 64 bits of the number x.

## Mathematical Expressions

`set a [expr {1 + 2}]`

mathematical functions

`set a [expr {sqrt(4)}]`

martin Lemburg: The following returns 1 because " 2 " is interpreted as 2:

`set a [expr {" 2 " == [string trim " 2 "]}]`

To ensure that operators choose real number evaluation, use double() or floor() to produce the numeric real representation of at least one argument:

```set a 1
set b 2
expr {double(\$a)/\$b}```

or, to get an integer:

`expr {entier(\$a/\$b)}`

int() would also have worked, but entier() is more general

## Order of Precedence

The following returns returns 4, rather than -4 as some might expect:

`set a [expr {-2**2}]`

The following returns 1 because 2==2 is evaluated first:

`set a [expr {5&2==2}]`

AMG: The order of bitwise operations (|, &, and ^) may seem totally bogus, but it's inherited from C, which in turn inherited it from an early prototype version of C which lacked separate logical operators (&& and ||) [L1 ]. I wouldn't cry if a new language (not Tcl) decided to break compatibility with C in this respect.

## Composing Expressions

expr tries to interpret operands as numeric values, but doesn't reparse variable substitutions as expressions, so, for example, 2*3 is interpreted as a string:

```set y 2*3; expr {\$y}   ;# ==> 2*3
set y 2*3; expr {\$y+2} ;# ==> can't use non-numeric string as operand of "+"```

To pass a complete expression stored in a variable, omit the braces so that Tcl substitutes the variable before passing it to expr :

```set y 2*3; expr \$y ;#  ==> 6
set y 2*3; puts [expr \$y+2] ;# ==> 8```

But be careful not to introduce an injection attack vulnerability. See double substitution.

## Literal String Operands

expr implements a little language distinct from Tcl itself, which is described in the rules of Tcl. One difference is that expr requires literal strings to be escaped:

```%  if {joe eq mike} {puts wow}
syntax error in expression "joe eq mike": variable references require preceding \$
%  if {"joe" eq "mike"} {puts wow}
%  if {{joe} eq {mike}} {puts wow}```

To insert a literal value when templating an expression, use an identity function like lindex:

```set expr {[lindex @[email protected]] eq [lindex @[email protected]]}
set expr [string map [list @[email protected] [list \$var1] @[email protected] [list \$var2]] \$expr]
expr \$expr```

## Canonical Representation of a Number

expr produces the decimal of a resulting value:

```set val 0x10
puts \$val ;# 0x10
set val [expr {\$val}]
puts \$val ;# 16```
`puts [expr {[join {0 x 1 0} {}]}] ;# 16`

It may be surprising to find that even when no operators are present, the string that expr may not be the string that was passed to it.

## A Logical Conundrum

Consider the following example:

```% expr {1 == true}
0
% expr {1 == !!true}
1```

The logical operators assign numeric interpretations to various values, including true and false. The == operator itself is not a logical operator, and although it inteprets each value as numeric if possible, it it does not consider values like true or false to be numeric, as a logical operator would. In the first expression, "true" is interpreted as a string, but because of a quirk in the implementation of Tcl, unlike other string values, it is not required that it be quoted.

## The Octal Bug

See Tcl and Octal Numbers for details.

rjm: Why does expr return integers with leading zeroes as hex?, e.g.

`expr 0100 ;# -> 64`

AMG: The leading zero makes 0100 octal. The 1 is in the 64's place, hence the result is 64 in decimal. That's not hexadecimal. expr always returns a decimal value; you have to use format if you want it in some other base.

RJM: I came around this as I was going to do calculus on a four-digit formatted number in an entry field. I had to apply scan \$var %d to get rid of the leading zeroes - as would be explicitly necessary in every typed language...

## Floating-Point Arithmetic

expr uses floating point arithmetic, so strings representing decimal fractions that don't have a precise floating-point representation will be given to a close-enough representation. In the following example, 36.37 gets a floating-point representation that approaches 36.37:

`expr {int(36.37*100)}`

If that value is subsequently used as a string, it becomes necessary to somehow produce its string representation. Over the years, the standard string representation has varied. For Tcl version 8.5.13, it looks like

`3636.9999999999995`

RS points out that version 8.4.9 provided the following results, and that that braced or not, expr returns the same (string rep of) double as well as integer, so the issue of bracing one's expressions is not relevant to the issue of floating-point to string conversion.

```% expr 36.37*100
3637.0 ;#-- good enough...
% expr {36.37*100}
3637.0 ;#-- the same
% expr {int(36.37*100)}
3636   ;#-- Hmm
% expr int(36.37*100)
3636   ;#-- the same
% info pa
8.4.9```

One way to get 3637 would be to use round():

`expr {round(36.37*100)}`

format can also be useful, but the main point is to remain aware of the context and decide if and how to use floating-point operations.

LV: My response on comp.lang.tcl was that I thought it was a shame that expr (or perhaps it is Tcl) didn't use the same mechanism for both calculations of 36.37 * 100 ; that way, the results would at least be consistent. Even if they were consistently wrong, one would be able to at least to live within the law of least surprise. As it is, until one experiments, one won't know which way that Tcl is going to round results.

EPSJ: This may be a side effect of the IEEE floating point standard. This is done in hardware to guarantee the convergence in the case of a series of math algorithms. The rule is that the mantissa of a floating point number must be rounded to the nearest even number. As 36.37 cannot be represented exactly in float point it ends up being a small fraction below the intended number. On the other side 36.38 moves on the other direction. Look the following result:

```() 60 % expr int(36.380*100)
3638
() 61 % expr int(36.370*100)
3636```

x86 floating point hardware allows this to be configurable to nearest even, nearest odd, and a few more options. But usually nearest even is the default. The result may seem inconsistent, but it is intentional.

## pow() vs

LES 2005-07-23:

```% expr pow(5,6)
15625.0

% expr 5**6
15625```

Two syntaxes, two slightly different results. Is that intentional?

RS: Yes. While pow() always goes for double logarithms, ** tries to do integer exponentiation where possible.

## String Representation of Floating Point Numbers

The reason that Tcl's float->string and string->float are so very complicated is the combination of (a) 1/2 ulp accuracy through the entire numeric range; (b) lossless conversion (float->string->float always recovers the original number), (c) speed. That's what balloons the conversion from the eight or ten lines that you'll see in an elementary text to a few thousand lines of code, moslly working in bigints.

See kbk, Tcl Chatroom, 2018-11-28

## Precision

davou: What is the precision of functions in expr, and how can it be expanded upon?

Lars H: That's generally determined by the C library functions that implement them. It depends on where (and against what) Tcl is compiled. For real numbers, that means doubles, which are floating-point numbers of typically about 17 decimal digits precision (but how many of these are correct varies between functions and platforms). For integers Tcl has traditionally used longs, which in most cases means 32-bit two's complement integers (\$tcl_platform(wordSize) tells you the actual number of bytes), but as of Tcl 8.5, it supports (almost) arbitrarily large integers (googol magnitude is no problem anymore, whereas googolplex magnitude wouldn't fit in the computer memory anyway). As for extending what the core provides, tcllib provides math::bignum and math::bigfloat.

## Nan and Inf

At least as of Tcl 8.5, NaN and Inf are potential values returning from expr.

Philip Smolen I've never seen expr return NaN. I wish it would!

```[[email protected] ~]\$ tclsh8.6
% expr sqrt(-1)
domain error: argument not in valid range
% ::tcl::mathfunc::sqrt -1
-NaN
% info patchlevel
8.6.4
% expr {Inf+1}
Inf
% ```
```[[email protected] ~]\$ tclsh8.5
% expr sqrt(-1)
domain error: argument not in valid range
% ::tcl::mathfunc::sqrt -1
-NaN
% info patchlevel
8.5.14
% expr {Inf+1}
Inf
% ```

## Interactions with locale

Parsing of decimals in expr may be hampered by locale - you might get syntax error in expression 1.0

## Brace Your Expressions For Syntax

expr concatenates its arguments into an expression. Consider the following error:

`expr 5 > {} ;# -> missing operand at [email protected]_`

The problem in the example above is that expr concatentates the arguments into the expression, 5 >, which is incomplete. Here is another example in which arguments are concatenated, and don't form a correct expression:

```set color1 green
set color2 green

#wrong
expr \$color1 eq \$color2 ;# -> invalid bareword "green"```

Concatenated, the arguments form the script, green eq green, in which the two values are unquoted, which is a syntax error. The following commands both result in correct expressions:

```expr {\$color eq \$color2} ;# -> 1
expr {\$color1} eq {\$color2} ;# -> 1```

But if the arguments are not bracketed, there's a syntax error:

Another example illustrating the same point:

```set a abc
set b [list 123 abcd xyz lmnop]
expr \$a in \$b
# invalid bareword "abc"
# in expression "abc in 123 abcd xyz lmnop";
# should be "\$abc" or "{abc}" or "abc(...)" or ...

expr {\$a in \$b} ;#-> 0

expr {\$a ni \$b} ;#-> 1```
```% expr \$a eq "foo" ? true : false
invalid bareword "abc"
% expr {\$a eq "foo" ? true : false}
false```

## Brace Your Expressions for Performance

When exactly one unconcatenated value is passed to expr, the argument can be compiled to bytecode, which is much more efficient. "Unconcatenated" means that the argument must not contain multiple substitutions or be the concatenation of substitutions and literal text. The goal is for there to be a persistent Tcl_Obj in which to store the compiled math expression. If expr has to concatenate its arguments (i.e. it is passed more than one argument), or if Tcl has to concatenate the results of multiple substitutions and literal substrings, then the math expression will be in a temporary Tcl_Obj which must be regenerated every time expr is called.

Fast:

```expr {2 + 2}         ; # Preferred
expr 2+2             ; # Valid but lazy (1)
expr "2 + 2"         ; # Valid but not preferred (2)
expr 2\ +\ 2         ; # Valid but ugly (3)
expr \$expression     ; # Valid
expr [expression]    ; # Valid```

(1) This style is easy to type and is fine for interactive use, but you will lose performance (and correctness and security) if you use this notation in combination with variable and script substitutions.

(2) Same problems as (1). Use braces instead.

(3) Same problems as (1), plus you might forget a backslash before a space, thereby forcing expr to concatenate its arguments.

Slow:

```expr 2 + 2           ; # Slow since [expr] must concatenate its arguments
expr 2 + \$x          ; # Slow since [expr] must concatenate its arguments, also unsafe
expr 2+\$x            ; # Slow since Tcl must concatenate to determine argument, also unsafe
expr "2 + \$x"        ; # Slow since Tcl must concatenate to determine argument, also unsafe```

## Brace Your Expressions for Security

AMG: The security problems of unbraced expressions are very similar to SQL injection attacks. Notice how sqlite's Tcl binding does its own variable expansion to avoid this very problem. Many, many sh scripts have this problem as well because the default is to apply multiple passes of interpretation.

## Remember if, for, and while

AMG: The above speed and security concerns also apply to if, for, and while since they share the expression engine with expr.

Additionally, for and while really do need their expressions to be braced. In order for the loop to execute a nonzero but finite number of times, the expression's value must not be constant; but if they're not braced, their value is determined before the loop can begin.

The exception is when the expression (as opposed to value) is contained in a variable, in which case it must not be brace-quoted, or else the command would try to treat the expression as a (string) value and almost certainly fail to convert it to a boolean value.

DKF: But even then, for if, for and while you must still brace the expression to avoid being stuck in the compilation slow lane. Putting an expr inside can help:

```set ex {\$f > 42}
while {[expr \$ex]} {
puts "This is the body: f is now [incr f -1]"
}```

Consider what would happen if this script were actually working with user input:

```#DON'T EXECUTE THIS SCRIPT!!!
set x {[exec format C:\\]}
set j {[puts Sucker!]}
#C:\ get formatted in the next command
set k [expr \$x / \$j.]```

On the other hand,

`set k [expr { \$x / double(\$j) }]`

gives a much more reasonable result:

```argument to math function didn't have numeric value
while executing
"expr { \$x / double(\$y) }"
invoked from within
"set k [expr { \$x / double(\$y) }]
"
(file "foo.tcl" line 3)
```

## Concise Assignment

expr is usually used to assign a result to a variable:

`set m [expr {0.5 * \$width * \$radius}]`

A small procedure makes it possible to write this instead:

`= m {0.5 * \$width * \$radius}`

here is the procedure:

```proc = {name args} {
::tailcall try "::set [list \$name] \[::expr \$args]"
}```

## The 'Dot' Trick for Unbraced Expressions

Unless you know exactly what you are doing, unbraced expressions are not recommended. Nevertheles...

With unbraced expressions, . (\x2e) can be appended to a variable to get expr to interpret the value as a float, but double() is a better alternative:

```set x 1; set j 2

# works (but don't do this)
expr \$x/\$j.

#an accepted way to do it
expr {double(\$x)/\$j}

# error: syntax error in expression "\$x/\$j."  (expr parser)
expr {\$x/\$j.}```

It's faster, too:

```set script1 {
set x 1
set j 2
set k [expr \$x / \$j.]
}
set script2 {
set x 1
set j 2
set k [expr { \$x / double(\$j) }]
}
foreach v {script1 script2} {
puts "\$v: [time [set \$v] 10000]"
}

#script1: 38 microseconds per iteration
#script2: 9 microseconds per iteration

#[pyk] 2012-11-28: what a difference a few years makes (an "old" 3.06Ghz Intel Core 2 Duo):
#script1: 4.4767364 microseconds per iteration
#script2: 0.7374299 microseconds per iteration```

RS: This was just to demonstrate the differences between the regular Tcl parser and the parser for expr', not recommended practice. Another example is substitution of operators:

```set op +
expr 4 \$op 5
9
expr {4 \$op 5}
syntax error in expression "4 \$op 5"```

See the for page on a case where that helped.

## Bytecode compilation and performance

AMG: When expr's argument is properly braced, the expression can be bytecoded for significant performance gains. However, the performance is not always quite as good as one would hope. Use tcl::unsupported::disassemble to see this in action:

```% tcl::unsupported::disassemble script {expr {4 / 3. * acos(-1) * \$r ** 3}}
ByteCode 0x00000000025FADB0, refCt 1, epoch 16, interp 0x00000000026365B0 (epoch 16)
Source "expr {4 / 3. * acos(-1) * \$r ** 3}"
Cmds 1, src 34, inst 17, litObjs 5, aux 0, stkDepth 3, code/src 0.00
Commands 1:
1: pc 0-15, src 0-33
Command 1: "expr {4 / 3. * acos(-1) * \$r ** 3}"
(0) push1 0         # "1.3333333333333333"
(2) push1 1         # "tcl::mathfunc::acos"
(4) push1 2         # "-1"
(6) invokeStk1 2
(8) mult
(9) push1 3         # "r"
(12) push1 4         # "3"
(14) expon
(15) mult
(16) done ```

This shows that 4 / 3. is precomputed to 1.3333333333333333, but acos(-1) is not precomputed to 3.141592653589793. While it would seem ideal to fold the constants together into 4.1887902047863905, doing so would skip invoking , which might have a trace on it. Tcl optimizations always favor correctness over speed, so this shortcut is not available.

Here's the above again, but with local variables which provide a large speed boost by avoiding looking up the variable by name:

```% tcl::unsupported::disassemble lambda {{} {expr {4 / 3. * acos(-1) * \$r ** 3}}}
ByteCode 0x00000000027A1080, refCt 1, epoch 16, interp 0x00000000026E65B0 (epoch 16)
Source "expr {4 / 3. * acos(-1) * \$r ** 3}"
Cmds 1, src 34, inst 16, litObjs 4, aux 0, stkDepth 3, code/src 0.00
Proc 0x00000000026A8620, refCt 1, args 0, compiled locals 1
slot 0, scalar, "r"
Commands 1:
1: pc 0-14, src 0-33
Command 1: "expr {4 / 3. * acos(-1) * \$r ** 3}"
(0) push1 0         # "1.3333333333333333"
(2) push1 1         # "tcl::mathfunc::acos"
(4) push1 2         # "-1"
(6) invokeStk1 2
(8) mult
(9) loadScalar1 %v0         # var "r"
(11) push1 3         # "3"
(13) expon
(14) mult
(15) done ```

(For disassembly readouts, it's not necessary to list the variables as arguments to the lambda. They'll be assigned slots in the compiled locals table either way. You're not actually running the code, so it doesn't matter if the variable exists.)

Common subexpressions cannot be optimized because this would bypass some potential traces on variable access and procedure invocation. If expr could know in advance that particular procedures and variables don't have traces, it would have greater freedom to perform common subexpression elimination. Knowing that a procedure is a pure function (its result depends only on its arguments), plus knowing that its definition will not change throughout the execution of the program, would let expr treat acos(-1) as a constant.

Now rearrange the expression to put the division at the end. Algebraically, this should produce an identical result. But because of potential floating point precision issues (non-commutativity of operations), Tcl must play it safe and do the operations in the order specified:

```% tcl::unsupported::disassemble script {expr {4 * acos(-1) * \$r ** 3 / 3.}}
ByteCode 0x00000000025F91B0, refCt 1, epoch 16, interp 0x00000000026365B0 (epoch 16)
Source "expr {4 * acos(-1) * \$r ** 3 / 3.}"
Cmds 1, src 34, inst 20, litObjs 6, aux 0, stkDepth 3, code/src 0.00
Commands 1:
1: pc 0-18, src 0-33
Command 1: "expr {4 * acos(-1) * \$r ** 3 / 3.}"
(0) push1 0         # "4"
(2) push1 1         # "tcl::mathfunc::acos"
(4) push1 2         # "-1"
(6) invokeStk1 2
(8) mult
(9) push1 3         # "r"
(12) push1 4         # "3"
(14) expon
(15) mult
(16) push1 5         # "3."
(18) div
(19) done ```

Back to common subexpression elimination: It may seem that the solution is for the programmer to manually precompute common subexpressions and reference their values via variables. This generally helps, so long as the subexpressions aren't too simple, but you must use local variables or else performance will suffer:

```% proc a {x} {expr {cos(\$x * acos(-1)) + sin(\$x * acos(-1))}}
% proc b {x} {set y [expr {\$x * acos(-1)}]; expr {cos(\$y) + sin(\$y)}}
% proc c {x} {set ::y [expr {\$x * acos(-1)}]; expr {cos(\$::y) + sin(\$::y)}}
% set x 12.3
% time {a \$x} 1000000
1.536581 microseconds per iteration
% time {b \$x} 1000000
1.333106 microseconds per iteration
% time {c \$x} 1000000
1.994305 microseconds per iteration```

## History

In Embedded vs. separate commands , 1992-12-38, JO published the voting results 37:8 in favor of embedded functions() vs. separate [commands]

## (Tcl 8.4 and older) 32-bit integer limitations

```% expr (1<<31)-1
2147483647

% expr 2147483647 + 2147483647
-2```

Multiplication

```% expr sqrt((1<<31)-1)
46340.9500011

expr 46341*46341
-2147479015```

These are results of Tcl 8.4 and older versions using a 32-bit representation for integers.

Tcl 8.5 features abritrary-precision integers. See TIP #237 .

## Suggestion to Reparse expr Variables

RS suggests that arguments to expr could be reparsed so that full mathematical expressions in variable values would interpreted as such

RS 2003-04-24: Here's a tiny wrapper for friends of infix assignment:

```proc let {var = args} {
uplevel 1 set \$var \[expr \$args\]
} ;#RS```
```% let i = 1
1
% let j = \$i + 1
2
% let k = {\$i + \$j}
3```
`set y 2*3; puts [expr \$y+0] ;# ==> 6`

AM: The problem with variables whose values are actually expressions is that they change the whole expression in which they are used. The performance gain for caching the parsed expression will then be lost.

AMG: This reopens the door to all the security, performance, and correctness problems solved by bracing one's expressions.

## Unsuitability of expr for time offset calculations

Wookie: I had some trouble recently using expr to calculate time offsets. I had 2 time stamps in the form hh:mm

So I had 4 variables h1, m1, h2, m2 and one of my expr functions was

`set result [expr {\$m1 + \$m2}]`

As many of you may be thinking, you fool! what about 08 and 09, which will get treated as invalid octal. So after some grumbling I thought okay so I have to trimleft them. Bit verbose but who cares:

```set m1 [string trimleft \$m1 0]
set m2 [string trimleft \$m2 0]
set result [expr (\$m1 + \$m2)]```

Now what could possibly go wrong with that... well obviously 00 becomes the empty string, which causes unexpected closed parameter in the expression. So now I have to check for the empty string. So...

```set m1 [string trimleft \$m1 0]
if {\$m1=={}} {set m1 0}

set m2 [string trimleft \$m2 0]
if {\$m2=={}} {set m2 0}

set result [expr {\$m1 + \$m2}]```

... and then repeat it for the hours. It all seemed very clumsy. So I came up with this, which may solve many of the conversion issues in this section.

```scan "\$h1:\$m1 \$h2:\$m2" "%d:%d %d:%d" h1 m1 h2 m2
set result [expr {\$m1 + \$m2}]```

All the conversions to int have been done and leading 0's have been stripped and returns 0 if the value is all 0s. This works for float and probably double (though I've not tried). Can anyone see any problems with this approach?

glennj: No, scan is definitely the way to parse numbers out of dates and times. However, for date arithmetic, nothing beats clock.

```# adding a delta to a time
set h1 12; set m1 45
set h2 3; set m2 30
clock format [clock add [clock scan "\$h1:\$m1" -format "%H:%M"] \$h2 hours \$m2 minutes] -format %T ;# ==> 16:15:00```

What are you trying to do with your two times?

## Page Authors

AMG
PYK

 Arts and Crafts of Tcl-Tk Programming Tcl syntax Category Command Category Mathematics expr]''', a [Tcl Commands