mathop(3tcl) Tcl Mathematical Operator Commands mathop(3tcl)
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NAME
mathop - Mathematical operators as Tcl commands
SYNOPSIS
package require Tcl 8.5
::tcl::mathop::! number
::tcl::mathop::~ number
::tcl::mathop::+ ?number ...?
::tcl::mathop::- number ?number ...?
::tcl::mathop::* ?number ...?
::tcl::mathop::/ number ?number ...?
::tcl::mathop::% number number
::tcl::mathop::** ?number ...?
::tcl::mathop::& ?number ...?
::tcl::mathop::| ?number ...?
::tcl::mathop::^ ?number ...?
::tcl::mathop::<< number number
::tcl::mathop::>> number number
::tcl::mathop::== ?arg ...?
::tcl::mathop::!= arg arg
::tcl::mathop::< ?arg ...?
::tcl::mathop::<= ?arg ...?
::tcl::mathop::>= ?arg ...?
::tcl::mathop::> ?arg ...?
::tcl::mathop::eq ?arg ...?
::tcl::mathop::ne arg arg
::tcl::mathop::in arg list
::tcl::mathop::ni arg list
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DESCRIPTION
The commands in the ::tcl::mathop namespace implement the same set of
operations as supported by the expr command. All are exported from the
namespace, but are not imported into any other namespace by default.
Note that renaming, reimplementing or deleting any of the commands in
the namespace does not alter the way that the expr command behaves, and
nor does defining any new commands in the ::tcl::mathop namespace.
The following operator commands are supported:
~ ! + - *
/ % ** & |
^ >> << == eq
!= ne < <= >
>= in ni
MATHEMATICAL OPERATORS
The behaviors of the mathematical operator commands are as follows:
! boolean
Returns the boolean negation of boolean, where boolean may be
any numeric value or any other form of boolean value (i.e. it
returns truth if the argument is falsity or zero, and falsity if
the argument is truth or non-zero).
+ ?number ...?
Returns the sum of arbitrarily many arguments. Each number argu-
ment may be any numeric value. If no arguments are given, the
result will be zero (the summation identity).
- number ?number ...?
If only a single number argument is given, returns the negation
of that numeric value. Otherwise returns the number that results
when all subsequent numeric values are subtracted from the first
one. All number arguments must be numeric values. At least one
argument must be given.
* ?number ...?
Returns the product of arbitrarily many arguments. Each number
may be any numeric value. If no arguments are given, the result
will be one (the multiplicative identity).
/ number ?number ...?
If only a single number argument is given, returns the recipro-
cal of that numeric value (i.e. the value obtained by dividing
1.0 by that value). Otherwise returns the number that results
when the first numeric argument is divided by all subsequent nu-
meric arguments. All number arguments must be numeric values. At
least one argument must be given.
Note that when the leading values in the list of arguments are
integers, integer division will be used for those initial steps
(i.e. the intermediate results will be as if the functions floor
and int are applied to them, in that order). If all values in
the operation are integers, the result will be an integer.
% number number
Returns the integral modulus (i.e., remainder) of the first ar-
gument with respect to the second. Each number must have an in-
tegral value. Also, the sign of the result will be the same as
the sign of the second number, which must not be zero.
Note that Tcl defines this operation exactly even for negative
numbers, so that the following command returns a true value
(omitting the namespace for clarity):
== [* [/ x y] y] [- x [% x y]]
** ?number ...?
Returns the result of raising each value to the power of the re-
sult of recursively operating on the result of processing the
following arguments, so “** 2 3 4” is the same as “** 2 [** 3
4]”. Each number may be any numeric value, though the second
number must not be fractional if the first is negative. The
maximum exponent value that Tcl can handle if the first number
is an integer > 1 is 268435455. If no arguments are given, the
result will be one, and if only one argument is given, the re-
sult will be that argument. The result will have an integral
value only when all arguments are integral values.
COMPARISON OPERATORS
The behaviors of the comparison operator commands (most of which oper-
ate preferentially on numeric arguments) are as follows:
== ?arg ...?
Returns whether each argument is equal to the arguments on each
side of it in the sense of the expr == operator (i.e., numeric
comparison if possible, exact string comparison otherwise). If
fewer than two arguments are given, this operation always re-
turns a true value.
eq ?arg ...?
Returns whether each argument is equal to the arguments on each
side of it using exact string comparison. If fewer than two ar-
guments are given, this operation always returns a true value.
!= arg arg
Returns whether the two arguments are not equal to each other,
in the sense of the expr != operator (i.e., numeric comparison
if possible, exact string comparison otherwise).
ne arg arg
Returns whether the two arguments are not equal to each other
using exact string comparison.
< ?arg ...?
Returns whether the arbitrarily-many arguments are ordered, with
each argument after the first having to be strictly more than
the one preceding it. Comparisons are performed preferentially
on the numeric values, and are otherwise performed using UNICODE
string comparison. If fewer than two arguments are present, this
operation always returns a true value. When the arguments are
numeric but should be compared as strings, the string compare
command should be used instead.
<= ?arg ...?
Returns whether the arbitrarily-many arguments are ordered, with
each argument after the first having to be equal to or more than
the one preceding it. Comparisons are performed preferentially
on the numeric values, and are otherwise performed using UNICODE
string comparison. If fewer than two arguments are present, this
operation always returns a true value. When the arguments are
numeric but should be compared as strings, the string compare
command should be used instead.
> ?arg ...?
Returns whether the arbitrarily-many arguments are ordered, with
each argument after the first having to be strictly less than
the one preceding it. Comparisons are performed preferentially
on the numeric values, and are otherwise performed using UNICODE
string comparison. If fewer than two arguments are present, this
operation always returns a true value. When the arguments are
numeric but should be compared as strings, the string compare
command should be used instead.
>= ?arg ...?
Returns whether the arbitrarily-many arguments are ordered, with
each argument after the first having to be equal to or less than
the one preceding it. Comparisons are performed preferentially
on the numeric values, and are otherwise performed using UNICODE
string comparison. If fewer than two arguments are present, this
operation always returns a true value. When the arguments are
numeric but should be compared as strings, the string compare
command should be used instead.
BIT-WISE OPERATORS
The behaviors of the bit-wise operator commands (all of which only op-
erate on integral arguments) are as follows:
~ number
Returns the bit-wise negation of number. Number may be an inte-
ger of any size. Note that the result of this operation will al-
ways have the opposite sign to the input number.
& ?number ...?
Returns the bit-wise AND of each of the arbitrarily many argu-
ments. Each number must have an integral value. If no arguments
are given, the result will be minus one.
| ?number ...?
Returns the bit-wise OR of each of the arbitrarily many argu-
ments. Each number must have an integral value. If no arguments
are given, the result will be zero.
^ ?number ...?
Returns the bit-wise XOR of each of the arbitrarily many argu-
ments. Each number must have an integral value. If no arguments
are given, the result will be zero.
<< number number
Returns the result of bit-wise shifting the first argument left
by the number of bits specified in the second argument. Each
number must have an integral value.
>> number number
Returns the result of bit-wise shifting the first argument right
by the number of bits specified in the second argument. Each
number must have an integral value.
LIST OPERATORS
The behaviors of the list-oriented operator commands are as follows:
in arg list
Returns whether the value arg is present in the list list (ac-
cording to exact string comparison of elements).
ni arg list
Returns whether the value arg is not present in the list list
(according to exact string comparison of elements).
EXAMPLES
The simplest way to use the operators is often by using namespace path
to make the commands available. This has the advantage of not affecting
the set of commands defined by the current namespace.
namespace path {::tcl::mathop ::tcl::mathfunc}
# Compute the sum of some numbers
set sum [+ 1 2 3]
# Compute the average of a list
set list {1 2 3 4 5 6}
set mean [/ [+ {*}$list] [double [llength $list]]]
# Test for list membership
set gotIt [in 3 $list]
# Test to see if a value is within some defined range
set inRange [<= 1 $x 5]
# Test to see if a list is sorted
set sorted [<= {*}$list]
SEE ALSO
expr(3tcl), mathfunc(3tcl), namespace(3tcl)
KEYWORDS
command, expression, operator
Tcl 8.5 mathop(3tcl)
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