`'''[http://www.tcl.tk/man/tcl/TclCmd/expr.htm%|%expr]'''`, a [TclCommands%|%built-in] [Tcl] command, evaluates an expression.
** See Also **
[A little math language]: adds features & sugar to `expr`
[A real problem]:
[Additional math functions]:
[Arbitrary precision math procedures]:
[Brace your expr-essions]:
[compute]: more 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]:
`[cmdSplit%|%exprlex]` and `[cmdSplit%|%funclex]`: Split expressions and functions into their lexical components.
[Floating-point formatting]: including how to format a floating point value without causing it to [shimmer]
[gotcha]: where `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]: use `expr`'s functions without explicitly calling that, see [Importing expr functions].
[infix]: a package to facilitate writing sequences of mathematical formulae in the familiar infix form
[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]:
[http://tip.tcl.tk/123%|%TIP #123]: Adding an Exponentiation Operator to `expr`
[http://tip.tcl.tk/174%|%TIP #174]: [Math Operators as Commands]
[http://tip.tcl.tk/182%|%TIP #182]: Add 'expr bool' Math Function
[http://tip.tcl.tk/201%|%TIP #201]: Add 'in' Operator to expr
[http://tip.tcl.tk/232%|%TIP #201]: Creating New Math Functions for `expr` ([tcl::mathfunc])
[http://tip.tcl.tk/237%|%TIP #237]: Arbitrary-Precision Integers for Tcl
[while]:
** Documentation **
[http://www.tcl.tk/man/tcl/TclCmd/expr.htm%|%officieal reference]:
[tcl::mathfunc%|%mathfunc]:
[tcl::mathop%|%mathop man page]:
[tcl_precision]:
[http://www.tcl.tk/man/tcl/TclLib/GetInt.htm%|%Tcl_GetBoolean man page]:
** Synopsis **
'''expr''' ''arg'' ?''arg arg ...''?
** Description **
`expr` [concat%|%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
yield numeric or non-numeric results.
Functions take 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
'''`[[A-Za-z]][[A-Za-z0-9_]]*`''' . Each ''argument'' is itself a complete
expression.
Each ''argument'' is itself a Tcl expression. For example:
======
cos($x+$y)
======
** Usage **
======
set val1 8.2
set val2 6
expr {$val1 + $val2}
======
Result:
======
14.2
======
In most cases, it's best to [Brace your Expr-essions%|%brace] or otherwise
escape the argument to `[expr]`. In particular, the special Tcl characters,
`$`, `[`, `"`, `{` should normally be escaped:
======
expr {$val1+$val2}
======
This allows `expr` to do the interpretation, rather than having Tcl interpret
them first and then having `expr` interpret them again. 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 operators; specifically a negation operation, a non-negation operation, a bit-wise NOT operation (every bit in the input value gets replaced by its inverse) and a logical NOT operation (non-zero maps to zero, and zero maps to one). |&
&| [**] | exponential. From Tcl 8.5 on. |&
&| [+] [-] | 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 representable in an integer on the host platform. |&
&| [<] [>] [<=] [>=] | Ordering relations: less than, greater than, less than or equal, greater than or equal. These operations work on strings as well as numbers, but where string comparison is intended, it is advisable to use the dedicated string comparison operators or [string compare] or [string equal] 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 `expr`' operator `==` considers them to be equivalent numbers.|&
&| [==] [!=] | Equality and inequality. These operations work on strings as well as numbers, but see the description equality operators for notes about string comparison. |&
&| [eq] [ne] | Since Tcl 8.4, these are string-comparison operators. "6" and "06", as well as 1 and 1.0, will compare unequal. |&
&| [in] [ni] | checks for occurrence of an item in a list. New in Tcl 8.5. |&
&| [**] | exponential. From Tcl 8.5 on. |&
&| [&] | Bit-wise AND. A bit is set in the result when the corresponding bit is set in both the arguments. |&
&| [^] | Bit-wise exclusive OR. A bit is set in the result when the corresponding bit is set in ''precisely one'' of the arguments. |&
&| [<>] | Bit-wise OR. A bit is set in the result when the corresponding bit is set in either of the arguments. |&
&| [&&] | Logical AND. The result is `1` when both of the arguments true. and `0` otherwise. This operation is a ''short-circuiting'' operation, and will only evaluate its second argument when the first argument is non-zero. This includes the expansion of Tcl commands in square brackets. Where Tcl seems not to be behaving as describe here, see [double substitution]. |&
&| [<><>] | Logical OR. The result is `0` when both of the arguments are false, and `1` otherwise. This operation is a ''short-circuiting'' operation, and will only evaluate its second argument when the first argument is zero. Where Tcl seems not to be behaving as describe here, 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` will not be evaluated, and if `x` is false, `y` will not be evaluated. Where Tcl seems not to be behaving as describe here, see [double substitution]. `[if]` performs just as well as this construct. The generated bytecode is identical. |&
** Functions **
See the [http://www.tcl.tk/man/tcl/TclCmd/mathfunc.htm%|%mathfunc man page].
The following is a list of builtin functions:
'''[abs]'''(x): Absolute value (negate if negative).
'''[acos]'''(x): Inverse cosine (result in radians).
'''[asin]'''(x): Inverse sine (result in radians).
'''[atan]'''(x): Inverse tangent (result in radians).
'''[atan2]'''(y,x): Inverse tangent. Can handle cases which plain `atan()` can't (due to division by zero) and has a larger output range (result in radians).
'''[bool]'''(x): Accepts any valid boolean value and returns the corresponding boolean value `0` or `1`.
'''[ceil]'''(x): Ceiling (defined over floating point numbers.) If the input value is not a whole number, return the next ''larger'' whole number. '''Surprise''': The return value is a float, not an integer.
'''[cos]'''(x): Cosine (input in radians).
'''[cosh function%|%cosh]'''(x): Hyperbolic cosine.
'''[double]'''(x): Convert number to floating point.
'''[entier]'''(x): Like `int(x)`, but there is no limit to the input or output value.
'''[exp]'''(x): Exponential function. Returns ''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, return 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). ''This RNG is not suitable for cryptography.''
'''[round]'''(x): Round to nearest whole number. ''Not suitable for financial rounding.''
'''[sin]'''(x): Sine (input in radians).
'''[sinh]'''(x): Hyperbolic sine.
'''[sqrt]'''(x): Square root (well, the positive square root only. And Tcl doesn't do complex math, so the input had better be positive).
'''[srand]'''(x): Seeds the random number generator with the given value. Each interpreter has its own random number generator, which starts out seeded with the current time.
'''[tan]'''(x): Tangent (input in radians.)
'''[tanh]'''(x): Hyperbolic tangent.kjh
'''[wide]'''(x): Take any numeric value, and return the low order 64 bits of the integer value of the argument
** Mathematical Expressions **
Simple addition:
======
set a [expr {1 + 2}]
======
mathematical functions
======
set a [expr {sqrt(4)}]
======
[martin Lemburg]: The following returns `1` because `" 2 "` will be interpreted
as `2`:
======
set a [expr {" 2 " == [string trim " 2 "]}]
======
To ensure that expression evaluates to a floating point number, use `double()`
or `floor()`:
======
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 `||`) [http://cm.bell-labs.com/who/dmr/chist.html]. 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 parse
variable values as expressions, so a value `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
[double substitution%|%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 the language described in [dodekalogue%|%the rules of Tcl]. One
difference is that `expr` requires literal strings to be quoted:
======none
% 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 @val1@] eq [lindex @val2@]}
set expr [string map [list @val@ [list $var1] @val2@ [list $var2]] $expr]
expr $expr
======
** Canonical Number Form **
If the return value of `expr` is numeric, it is transformed into a canonical
numeric form:
======
set val 0x10
puts $val ;# 0x10
set val [expr {$val}]
puts $val ;# 16
======
======
puts [expr {[join {0 x 1 0} {}]}] ;# 16
======
In other words, `expr` may mutate strings that can be interpreted as
numbers, which is a potential [gotcha] when using string functionality
of `expr` while not considering that they may have a numeric
interpretation.
** The Octal Bug **
** [Tcl and Octal Numbers%|%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
convert it. Over the years, the default string conversion has varied. For Tcl
version 8.5.13, it looks like
======none
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.
======none
% 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:
======none
() 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:
======none
% 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.
** 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 '''double'''s, 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 '''long'''s, 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!
======
[phil@harvey ~]$ 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
%
======
======
[phil@becca ~]$ 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 expr-essions%|%Brace Your Expressions%|%] For Syntax **
`expr` concatenates its arguments into an expression. Consider the following
`expr` resolves variables in the context of its caller, and each variable
value becomes exactly one operand in the expression. Consider the following:
======
expr 5 > {} ;# -> missing operand at _@_
set color2 green
expr {$color1} eq {$color2} ;# 1
Concatenated, the arguments form the script, `green eq green`, in which the two
Another example illustrating the same point:
======
#wrong
expr $color1 eq $color2
======
======none
invalid bareword "green"
in expression "green eq green";
should be "$green" or "{green}" or "green(...)" or ...
======
This is because in `expr` syntax, strings should be quoted or bracketed
======
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 expr-essions%|%Brace Your Expressions%|%] for Performance **
When exactly one unconcatenated value is passed to `expr`, the argument can be
`expr` is much more performant when it has exactly one argument. The
argument must either be brace-quoted or be a single variable substitution,
since this allows byte-compilation.
[AMG]: More precisely, the argument must not contain multiple substitutions or
be the concatenation of substitutions and literal text. The goal is for there
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 + $x" ; # Slow since Tcl must concatenate to determine argument, also unsafe
======
** [Brace your expr-essions%|%Brace Your Expressions%|%] for Security **
[AMG]: The security problems of unbraced `expr`essions are very similar to
[SQL] [injection attack%|%injection attacks]. Notice how [sqlite]'s [Tcl] binding does its own
variable expansion to avoid this very problem. Many, many [sh] scripts have
this problem as well because the default is to apply multiple passes of
interpretation.
See also [double substitution].
** Remember `[if]`, `[for]`, and `[while]` **
[AMG]: The above speed and security concerns also apply to `[if]`,
`[for]`, and `[while]` since they share the expression engine with
`expr`.
Additionally, `[for]` and `[while]` really do need their expressions to
be braced. In order for the loop to execute a nonzero but finite number of
times, the expression's value must not be constant; but if they're not braced,
their value is determined before the loop can begin.
The exception is when the ''expression'' (as opposed to value) is contained in
a variable, in which case it must not be brace-quoted, or else the command
would try to treat the expression as a (string) value and almost certainly fail
to convert it to a boolean value.
[DKF]: But even then, for `if`, `for` and `while` you must still brace the expression to avoid being stuck in the compilation slow lane. Putting an `expr` inside can help:
======
set ex {$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:
======none
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)
======
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:
======none
% 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"
(11) loadStk
(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 `[tcl::mathfunc]::[acos]`, 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:
======none
% 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:
======none
% 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) * $r ** 3 / 3.}"
(0) push1 0 # "4"
(2) push1 1 # "tcl::mathfunc::acos"
(4) push1 2 # "-1"
(6) invokeStk1 2
(8) mult
(9) push1 3 # "r"
(11) loadStk
(12) push1 4 # "3"
(14) expon
(15) mult
(16) push1 5 # "3."
(18) div
(19) done
======
Back to common subexpression elimination: It may seem that the solution is for the programmer to manually precompute common subexpressions and reference their values via variables. This generally helps, so long as the subexpressions aren't too simple, but you must use local variables or else performance will suffer:
======
% proc a {x} {expr {cos($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 [http://groups.google.com/group/comp.lang.tcl/browse_thread/thread/f873d6fab9f0e304%|%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 **
Addition
======none
% expr (1<<31)-1
2147483647
% expr 2147483647 + 2147483647
-2
======
Multiplication
======none
% 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
[http://www.tcl.tk/cgi-bin/tct/tip/237.html%|%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:
======none
proc let {var = args} {
uplevel 1 set $var \[expr $args\]
} ;#RS
======
======none
% 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 `expr`ession.
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?