Exponentiation with infix operators in (or operating on) the base
You are encouraged to solve this task according to the task description, using any language you may know.
(Many programming languages, especially those with extended─precision integer arithmetic, usually
support one of **, ^, ↑ or some such for exponentiation.)
Some languages treat/honor infix operators when performing exponentiation (raising
numbers to some power by the language's exponentiation operator, if the computer
programming language has one).
Other programming languages may make use of the POW or some other BIF
(Built─In Ffunction), or some other library service.
If your language's exponentiation operator is not one of the usual ones, please comment on how to recognize it.
This task will deal with the case where there is some form of an infix operator operating
in (or operating on) the base.
- Example
A negative five raised to the 3rd power could be specified as:
-5 ** 3 or as -(5) ** 3 or as (-5) ** 3 or as something else
(Not all computer programming languages have an exponential operator and/or support these syntax expression(s).
- Task
-
- compute and display exponentiation with a possible infix operator, whether specified and/or implied/inferred.
- Raise the following numbers (integer or real):
- -5 and
- +5
- to the following powers:
- 2nd and
- 3rd
- using the following expressions (if applicable in your language):
- -x**p
- -(x)**p
- (-x)**p
- -(x**p)
- Show here (on this page) the four (or more) types of symbolic expressions for each number and power.
Try to present the results in the same format/manner as the other programming entries to make any differences apparent.
The variables may be of any type(s) that is/are applicable in your language.
- Related tasks
- Exponentiation order
- Exponentiation operator
- Arbitrary-precision integers (included)
- Parsing/RPN to infix conversion
- Operator precedence
- References
Ada
The order of precedence for Ada operators is:
logical_operator ::= and | or | xor relational_operator ::= = | /= | < | <= | > | >= binary_adding_operator ::= + | – | & unary_adding_operator ::= + | – multiplying_operator ::= * | / | mod | rem highest_precedence_operator ::= ** | abs | not
Ada provides an exponentiation operator for integer types and floating point types. <lang Ada>with Ada.Text_IO; use Ada.Text_IO; with Ada.Float_Text_IO; use Ada.Float_Text_IO; with Ada.Integer_Text_IO; use Ada.Integer_Text_IO;
procedure Main is
ivalue : Integer := -5; fvalue : float := -5.0;
begin
Put_Line("Integer exponentiation:");
for i in 1..2 loop
for power in 2..3 loop
Put("x =" & ivalue'image & " p =" & power'image);
Put(" -x ** p ");
Put(item => -ivalue ** power, width => 4);
Put(" -(x) ** p ");
Put(item => -(ivalue) ** power, width => 4);
Put(" (-x) ** p ");
Put(Item => (- ivalue) ** power, Width => 4);
Put(" -(x ** p) ");
Put(Item => -(ivalue ** power), Width => 4);
New_line;
end loop;
ivalue := 5;
fvalue := 5.0;
end loop;
Put_Line("floating point exponentiation:");
ivalue := -5;
fvalue := -5.0;
for i in 1..2 loop
for power in 2..3 loop
Put("x =" & fvalue'image & " p =" & power'image);
Put(" -x ** p ");
Put(item => -fvalue ** power, fore => 4, Aft => 1, Exp => 0);
Put(" -(x) ** p ");
Put(item => -(fvalue) ** power, fore => 4, Aft => 1, Exp => 0);
Put(" (-x) ** p ");
Put(Item => (- fvalue) ** power, fore => 4, Aft => 1, Exp => 0);
Put(" -(x ** p) ");
Put(Item => -(fvalue ** power), fore => 4, Aft => 1, Exp => 0);
New_line;
end loop;
ivalue := 5;
fvalue := 5.0;
end loop;
end Main;
</lang>
- Output:
Integer exponentiation: x =-5 p = 2 -x ** p -25 -(x) ** p -25 (-x) ** p 25 -(x ** p) -25 x =-5 p = 3 -x ** p 125 -(x) ** p 125 (-x) ** p 125 -(x ** p) 125 x = 5 p = 2 -x ** p -25 -(x) ** p -25 (-x) ** p 25 -(x ** p) -25 x = 5 p = 3 -x ** p -125 -(x) ** p -125 (-x) ** p -125 -(x ** p) -125 floating point exponentiation: x =-5.00000E+00 p = 2 -x ** p -25.0 -(x) ** p -25.0 (-x) ** p 25.0 -(x ** p) -25.0 x =-5.00000E+00 p = 3 -x ** p 125.0 -(x) ** p 125.0 (-x) ** p 125.0 -(x ** p) 125.0 x = 5.00000E+00 p = 2 -x ** p -25.0 -(x) ** p -25.0 (-x) ** p 25.0 -(x ** p) -25.0 x = 5.00000E+00 p = 3 -x ** p -125.0 -(x) ** p -125.0 (-x) ** p -125.0 -(x ** p) -125.0
ALGOL 68
In Algol 68, all unary operators have a higher precedence than any binary operator.
Algol 68 also allows UP and ^ for the exponentiation operator.
<lang algol68>BEGIN
# show the results of exponentiation and unary minus in various combinations #
FOR x FROM -5 BY 10 TO 5 DO
FOR p FROM 2 TO 3 DO
print( ( "x = ", whole( x, -2 ), " p = ", whole( p, 0 ) ) );
print( ( " -x**p ", whole( -x**p, -4 ) ) );
print( ( " -(x)**p ", whole( -(x)**p, -4 ) ) );
print( ( " (-x)**p ", whole( (-x)**p, -4 ) ) );
print( ( " -(x**p) ", whole( -(x**p), -4 ) ) );
print( ( newline ) );
OD
OD
END</lang>
- Output:
x = -5 p = 2 -x**p 25 -(x)**p 25 (-x)**p 25 -(x**p) -25 x = -5 p = 3 -x**p 125 -(x)**p 125 (-x)**p 125 -(x**p) 125 x = 5 p = 2 -x**p 25 -(x)**p 25 (-x)**p 25 -(x**p) -25 x = 5 p = 3 -x**p -125 -(x)**p -125 (-x)**p -125 -(x**p) -125
F#
F# does not support the ** operator for integers but for floats: <lang fsharp> printfn "-5.0**2.0=%f; -(5.0**2.0)=%f" (-5.0**2.0) (-(5.0**2.0)) </lang>
- Output:
-5.0**2.0=25.000000; -(5.0**2.0)=-25.000000
Factor
<lang factor>USING: infix locals prettyprint sequences sequences.generalizations sequences.repeating ;
- row ( x p -- seq )
x p "-x**p" [infix -x**p infix] "-(x)**p" [infix -(x)**p infix] "(-x)**p" [infix (-x)**p infix] "-(x**p)" [infix -(x**p) infix] 10 narray ;
{ "x value" "p value" } { "expression" "result" } 8 cycle append -5 2 row -5 3 row 5 2 row 5 3 row 5 narray simple-table.</lang>
- Output:
x value p value expression result expression result expression result expression result -5 2 -x**p 25 -(x)**p 25 (-x)**p 25 -(x**p) -25 -5 3 -x**p 125 -(x)**p 125 (-x)**p 125 -(x**p) 125 5 2 -x**p 25 -(x)**p 25 (-x)**p 25 -(x**p) -25 5 3 -x**p -125 -(x)**p -125 (-x)**p -125 -(x**p) -125
Go
Go uses the math.Pow function for exponentiation and doesn't support operator overloading at all. Consequently, it is not possible to conjure up an infix operator to do the same job.
Perhaps the closest we can get is to define a derived type (float say) based on float64 and then give it a method with a short name (p say) to provide exponentiation.
This looks odd but is perfectly workable as the following example shows. However, as a method call, x.p is always going to take precedence over the unary minus operator and will always require the exponent to be enclosed in parentheses.
Note that we can't call the method ↑ (or similar) because identifiers in Go must begin with a Unicode letter and using a non-ASCII symbol would be awkward to type on some keyboards in any case. <lang go>package main
import (
"fmt" "math"
)
type float float64
func (f float) p(e float) float { return float(math.Pow(float64(f), float64(e))) }
func main() {
ops := []string{"-x.p(e)", "-(x).p(e)", "(-x).p(e)", "-(x.p(e))"}
for _, x := range []float{float(-5), float(5)} {
for _, e := range []float{float(2), float(3)} {
fmt.Printf("x = %2.0f e = %0.0f | ", x, e)
fmt.Printf("%s = %4.0f | ", ops[0], -x.p(e))
fmt.Printf("%s = %4.0f | ", ops[1], -(x).p(e))
fmt.Printf("%s = %4.0f | ", ops[2], (-x).p(e))
fmt.Printf("%s = %4.0f\n", ops[3], -(x.p(e)))
}
}
}</lang>
- Output:
x = -5 e = 2 | -x.p(e) = -25 | -(x).p(e) = -25 | (-x).p(e) = 25 | -(x.p(e)) = -25 x = -5 e = 3 | -x.p(e) = 125 | -(x).p(e) = 125 | (-x).p(e) = 125 | -(x.p(e)) = 125 x = 5 e = 2 | -x.p(e) = -25 | -(x).p(e) = -25 | (-x).p(e) = 25 | -(x.p(e)) = -25 x = 5 e = 3 | -x.p(e) = -125 | -(x).p(e) = -125 | (-x).p(e) = -125 | -(x.p(e)) = -125
Julia
In Julia, the ^ symbol is the power infix operator. The ^ operator has a higher precedence than the - operator, so -5^2 is -25 and (-5)^2 is 25. <lang julia> for x in [-5, 5], p in [2, 3]
println("x is", lpad(x, 3), ", p is $p, -x^p is", lpad(-x^p, 4), ", -(x)^p is",
lpad(-(x)^p, 5), ", (-x)^p is", lpad((-x)^p, 5), ", -(x^p) is", lpad(-(x^p), 5))
end
</lang>
- Output:
x is -5, p is 2, -x^p is -25, -(x)^p is -25, (-x)^p is 25, -(x^p) is -25 x is -5, p is 3, -x^p is 125, -(x)^p is 125, (-x)^p is 125, -(x^p) is 125 x is 5, p is 2, -x^p is -25, -(x)^p is -25, (-x)^p is 25, -(x^p) is -25 x is 5, p is 3, -x^p is-125, -(x)^p is -125, (-x)^p is -125, -(x^p) is -125
Nim
The infix exponentiation operator is defined in standard module “math”. Its precedence is less than that of unary “-” operator, so -5^2 is 25 and -(5^2) is -25.
<lang Nim>import math, strformat
for x in [-5, 5]:
for p in [2, 3]:
echo &"x is {x:2}, ", &"p is {p:1}, ",
&"-x^p is {-x^p:4}, ", &"-(x)^p is {-(x)^p:4}, ",
&"(-x)^p is {(-x)^p:4}, ", &"-(x^p) is {-(x^p):4}"</lang>
- Output:
x is -5, p is 2, -x^p is 25, -(x)^p is 25, (-x)^p is 25, -(x^p) is -25 x is -5, p is 3, -x^p is 125, -(x)^p is 125, (-x)^p is 125, -(x^p) is 125 x is 5, p is 2, -x^p is 25, -(x)^p is 25, (-x)^p is 25, -(x^p) is -25 x is 5, p is 3, -x^p is -125, -(x)^p is -125, (-x)^p is -125, -(x^p) is -125
Perl
Use the module Sub::Infix to define a custom operator. Note that the bracketing punctuation controls the precedence level. Results structured same as in Raku example. <lang perl>use strict; use warnings; use Sub::Infix;
BEGIN { *e = infix { $_[0] ** $_[1] } }; # operator needs to be defined at compile time
my @eqns = ('1 + -$xOP$p', '1 + (-$x)OP$p', '1 + (-($x)OP$p)', '(1 + -$x)OP$p', '1 + -($xOP$p)');
for my $op ('**', '/e/', '|e|') {
for ( [-5, 2], [-5, 3], [5, 2], [5, 3] ) {
my( $x, $p, $eqn ) = @$_;
printf 'x: %2d p: %2d |', $x, $p;
$eqn = s/OP/$op/gr and printf '%17s %4d |', $eqn, eval $eqn for @eqns;
print "\n";
}
print "\n";
}</lang>
- Output:
x: -5 p: 2 | 1 + -$x**$p -24 | 1 + (-$x)**$p 26 | 1 + (-($x)**$p) -24 | (1 + -$x)**$p 36 | 1 + -($x**$p) -24 | x: -5 p: 3 | 1 + -$x**$p 126 | 1 + (-$x)**$p 126 | 1 + (-($x)**$p) 126 | (1 + -$x)**$p 216 | 1 + -($x**$p) 126 | x: 5 p: 2 | 1 + -$x**$p -24 | 1 + (-$x)**$p 26 | 1 + (-($x)**$p) -24 | (1 + -$x)**$p 16 | 1 + -($x**$p) -24 | x: 5 p: 3 | 1 + -$x**$p -124 | 1 + (-$x)**$p -124 | 1 + (-($x)**$p) -124 | (1 + -$x)**$p -64 | 1 + -($x**$p) -124 | x: -5 p: 2 | 1 + -$x/e/$p 26 | 1 + (-$x)/e/$p 26 | 1 + (-($x)/e/$p) 26 | (1 + -$x)/e/$p 36 | 1 + -($x/e/$p) -24 | x: -5 p: 3 | 1 + -$x/e/$p 126 | 1 + (-$x)/e/$p 126 | 1 + (-($x)/e/$p) 126 | (1 + -$x)/e/$p 216 | 1 + -($x/e/$p) 126 | x: 5 p: 2 | 1 + -$x/e/$p 26 | 1 + (-$x)/e/$p 26 | 1 + (-($x)/e/$p) 26 | (1 + -$x)/e/$p 16 | 1 + -($x/e/$p) -24 | x: 5 p: 3 | 1 + -$x/e/$p -124 | 1 + (-$x)/e/$p -124 | 1 + (-($x)/e/$p) -124 | (1 + -$x)/e/$p -64 | 1 + -($x/e/$p) -124 | x: -5 p: 2 | 1 + -$x|e|$p 36 | 1 + (-$x)|e|$p 36 | 1 + (-($x)|e|$p) 26 | (1 + -$x)|e|$p 36 | 1 + -($x|e|$p) -24 | x: -5 p: 3 | 1 + -$x|e|$p 216 | 1 + (-$x)|e|$p 216 | 1 + (-($x)|e|$p) 126 | (1 + -$x)|e|$p 216 | 1 + -($x|e|$p) 126 | x: 5 p: 2 | 1 + -$x|e|$p 16 | 1 + (-$x)|e|$p 16 | 1 + (-($x)|e|$p) 26 | (1 + -$x)|e|$p 16 | 1 + -($x|e|$p) -24 | x: 5 p: 3 | 1 + -$x|e|$p -64 | 1 + (-$x)|e|$p -64 | 1 + (-($x)|e|$p) -124 | (1 + -$x)|e|$p -64 | 1 + -($x|e|$p) -124 |
Phix
Phix has a power() function instead of an infix operator, hence there are only two possible syntaxes, with the obvious outcomes.
(Like Go, Phix does not support operator overloading or definition at all.)
<lang Phix>for x=-5 to 5 by 10 do
for p=2 to 3 do
printf(1,"x = %2d, p = %d, power(-x,p) = %4d, -power(x,p) = %4d\n",{x,p,power(-x,p),-power(x,p)})
end for
end for</lang>
- Output:
x = -5, p = 2, power(-x,p) = 25, -power(x,p) = -25 x = -5, p = 3, power(-x,p) = 125, -power(x,p) = 125 x = 5, p = 2, power(-x,p) = 25, -power(x,p) = -25 x = 5, p = 3, power(-x,p) = -125, -power(x,p) = -125
Raku
In Raku by default, infix exponentiation binds tighter than unary negation. It is trivial however to define your own infix operators with whatever precedence level meets the needs of your program.
A slight departure from the task specs. Use 1 + {expression} rather than just {expression} to better demonstrate the relative precedence levels. Where {expression} is one of:
-x{exponential operator}p-(x){exponential operator}p((-x){exponential operator}p)-(x{exponential operator}p)
Also add a different grouping: (1 + -x){exponential operator}p
<lang perl6>sub infix:<↑> is looser(&prefix:<->) { $^a ** $^b } sub infix:<^> is looser(&infix:<->) { $^a ** $^b }
use MONKEY;
for 'Default precedence: infix exponentiation is tighter (higher) precedence than unary negation.',
('1 + -$x**$p', '1 + (-$x)**$p', '1 + (-($x)**$p)', '(1 + -$x)**$p', '1 + -($x**$p)'),
"\nEasily modified: custom loose infix exponentiation is looser (lower) precedence than unary negation.",
('1 + -$x↑$p ', '1 + (-$x)↑$p ', '1 + (-($x)↑$p) ', '(1 + -$x)↑$p ', '1 + -($x↑$p) '),
"\nEven moreso: custom looser infix exponentiation is looser (lower) precedence than infix subtraction.",
('1 + -$x^$p ', '1 + (-$x)^$p ', '1 + (-($x)^$p) ', '(1 + -$x)^$p ', '1 + -($x^$p) ')
-> $message, $ops {
say $message;
for -5, 5 X 2, 3 -> ($x, $p) {
printf "x = %2d p = %d", $x, $p;
-> $op { printf " │ %s = %4d", $op, EVAL $op } for |$ops;
print "\n";
}
}</lang>
- Output:
Default precedence: infix exponentiation is tighter (higher) precedence than unary negation. x = -5 p = 2 │ 1 + -$x**$p = -24 │ 1 + (-$x)**$p = 26 │ 1 + (-($x)**$p) = -24 │ (1 + -$x)**$p = 36 │ 1 + -($x**$p) = -24 x = -5 p = 3 │ 1 + -$x**$p = 126 │ 1 + (-$x)**$p = 126 │ 1 + (-($x)**$p) = 126 │ (1 + -$x)**$p = 216 │ 1 + -($x**$p) = 126 x = 5 p = 2 │ 1 + -$x**$p = -24 │ 1 + (-$x)**$p = 26 │ 1 + (-($x)**$p) = -24 │ (1 + -$x)**$p = 16 │ 1 + -($x**$p) = -24 x = 5 p = 3 │ 1 + -$x**$p = -124 │ 1 + (-$x)**$p = -124 │ 1 + (-($x)**$p) = -124 │ (1 + -$x)**$p = -64 │ 1 + -($x**$p) = -124 Easily modified: custom loose infix exponentiation is looser (lower) precedence than unary negation. x = -5 p = 2 │ 1 + -$x↑$p = 26 │ 1 + (-$x)↑$p = 26 │ 1 + (-($x)↑$p) = 26 │ (1 + -$x)↑$p = 36 │ 1 + -($x↑$p) = -24 x = -5 p = 3 │ 1 + -$x↑$p = 126 │ 1 + (-$x)↑$p = 126 │ 1 + (-($x)↑$p) = 126 │ (1 + -$x)↑$p = 216 │ 1 + -($x↑$p) = 126 x = 5 p = 2 │ 1 + -$x↑$p = 26 │ 1 + (-$x)↑$p = 26 │ 1 + (-($x)↑$p) = 26 │ (1 + -$x)↑$p = 16 │ 1 + -($x↑$p) = -24 x = 5 p = 3 │ 1 + -$x↑$p = -124 │ 1 + (-$x)↑$p = -124 │ 1 + (-($x)↑$p) = -124 │ (1 + -$x)↑$p = -64 │ 1 + -($x↑$p) = -124 Even moreso: custom looser infix exponentiation is looser (lower) precedence than infix subtraction. x = -5 p = 2 │ 1 + -$x^$p = 36 │ 1 + (-$x)^$p = 36 │ 1 + (-($x)^$p) = 26 │ (1 + -$x)^$p = 36 │ 1 + -($x^$p) = -24 x = -5 p = 3 │ 1 + -$x^$p = 216 │ 1 + (-$x)^$p = 216 │ 1 + (-($x)^$p) = 126 │ (1 + -$x)^$p = 216 │ 1 + -($x^$p) = 126 x = 5 p = 2 │ 1 + -$x^$p = 16 │ 1 + (-$x)^$p = 16 │ 1 + (-($x)^$p) = 26 │ (1 + -$x)^$p = 16 │ 1 + -($x^$p) = -24 x = 5 p = 3 │ 1 + -$x^$p = -64 │ 1 + (-$x)^$p = -64 │ 1 + (-($x)^$p) = -124 │ (1 + -$x)^$p = -64 │ 1 + -($x^$p) = -124
REXX
<lang rexx>/*REXX program shows exponentition with an infix operator (implied and/or specified).*/ _= '─'; ! = '║'; mJunct= '─╫─'; bJunct= '─╨─' /*define some special glyphs. */
say @(' x ', 5) @(" p ", 5) ! say @('value', 5) @("value", 5) copies(! @('expression',10) @("result",6)" ", 4) say @( , 5, _) @("", 5, _)copies(mJunct || @(, 10, _) @("", 6, _) , 4)
do x=-5 to 5 by 10 /*assign -5 and 5 to X. */
do p= 2 to 3 /*assign 2 and 3 to P. */
a = -x**p ; b = -(x)**p ; c = (-x)**p ; d = -(x**p)
ae= '-x**p'; be= "-(x)**p"; ce= '(-x)**p'; de= "-(x**p)"
say @(x,5) @(p,5) ! @(ae, 10) right(a, 5)" " ,
! @(be, 10) right(b, 5)" " ,
! @(ce, 10) right(c, 5)" " ,
! @(de, 10) right(d, 5)
end /*p*/
end /*x*/
say @( , 5, _) @(, 5, _)copies(bJunct || @(, 10, _) @(, 6, _) , 4) exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ @: parse arg txt, w, fill; if fill== then fill= ' '; return center( txt, w, fill) </lang>
- output when using the internal default input:
x p ║ value value ║ expression result ║ expression result ║ expression result ║ expression result ───── ──────╫─────────── ───────╫─────────── ───────╫─────────── ───────╫─────────── ────── -5 2 ║ -x**p 25 ║ -(x)**p 25 ║ (-x)**p 25 ║ -(x**p) -25 -5 3 ║ -x**p 125 ║ -(x)**p 125 ║ (-x)**p 125 ║ -(x**p) 125 5 2 ║ -x**p 25 ║ -(x)**p 25 ║ (-x)**p 25 ║ -(x**p) -25 5 3 ║ -x**p -125 ║ -(x)**p -125 ║ (-x)**p -125 ║ -(x**p) -125 ───── ──────╨─────────── ───────╨─────────── ───────╨─────────── ───────╨─────────── ──────
Python
<lang python>from itertools import product
xx = '-5 +5'.split() pp = '2 3'.split() texts = '-x**p -(x)**p (-x)**p -(x**p)'.split()
print('Integer variable exponentiation') for x, p in product(xx, pp):
print(f' x,p = {x:2},{p}; ', end=' ')
x, p = int(x), int(p)
print('; '.join(f"{t} =={eval(t):4}" for t in texts))
print('\nBonus integer literal exponentiation') X, P = 'xp' xx.insert(0, ' 5') texts.insert(0, 'x**p') for x, p in product(xx, pp):
texts2 = [t.replace(X, x).replace(P, p) for t in texts]
print(' ', '; '.join(f"{t2} =={eval(t2):4}" for t2 in texts2))</lang>
- Output:
Integer variable exponentiation x,p = -5,2; -x**p == -25; -(x)**p == -25; (-x)**p == 25; -(x**p) == -25 x,p = -5,3; -x**p == 125; -(x)**p == 125; (-x)**p == 125; -(x**p) == 125 x,p = +5,2; -x**p == -25; -(x)**p == -25; (-x)**p == 25; -(x**p) == -25 x,p = +5,3; -x**p ==-125; -(x)**p ==-125; (-x)**p ==-125; -(x**p) ==-125 Bonus integer literal exponentiation 5**2 == 25; - 5**2 == -25; -( 5)**2 == -25; (- 5)**2 == 25; -( 5**2) == -25 5**3 == 125; - 5**3 ==-125; -( 5)**3 ==-125; (- 5)**3 ==-125; -( 5**3) ==-125 -5**2 == -25; --5**2 == 25; -(-5)**2 == -25; (--5)**2 == 25; -(-5**2) == 25 -5**3 ==-125; --5**3 == 125; -(-5)**3 == 125; (--5)**3 == 125; -(-5**3) == 125 +5**2 == 25; -+5**2 == -25; -(+5)**2 == -25; (-+5)**2 == 25; -(+5**2) == -25 +5**3 == 125; -+5**3 ==-125; -(+5)**3 ==-125; (-+5)**3 ==-125; -(+5**3) ==-125
Smalltalk
Smalltalk has no prefix operator for negation. To negate, you have to send the number a "negated" message, which has higher precedence than any binary message. Literal constants may have a sign (which is not an operation, but part of the constant). <lang smalltalk>a := 2. b := 3. Transcript show:'-5**2 => '; showCR: -5**2. Transcript show:'-5**a => '; showCR: -5**a. Transcript show:'-5**b => '; showCR: -5**b. Transcript show:'5**2 => '; showCR: 5**2. Transcript show:'5**a => '; showCR: 5**a. Transcript show:'5**b => '; showCR: 5**b. " Transcript show:'-(5**b) => '; showCR: -(5**b). -- invalid: syntax error " " Transcript show:'5**-b => '; showCR: 5**-b. -- invalid: syntax error "</lang> Using the "negated" message: <lang smalltalk>Transcript show:'5 negated**2 => '; showCR: 5 negated**2. "negates 5" Transcript show:'5 negated**3 => '; showCR: 5 negated**3. Transcript show:'5**2 negated => '; showCR: 5**2 negated. "negates 2" Transcript show:'5**3 negated => '; showCR: 5**3 negated. "negates 3" Transcript show:'5 negated**a => '; showCR: 5 negated**a. Transcript show:'5 negated**b => '; showCR: 5 negated**b. Transcript show:'5**a negated => '; showCR: 5**a negated. Transcript show:'5**b negated => '; showCR: 5**b negated. Transcript show:'(5**a) negated => '; showCR: (5**a) negated. Transcript show:'(5**b) negated => '; showCR: (5**b) negated. Transcript show:'(-5**a) negated => '; showCR: (-5**a) negated. Transcript show:'(-5**b) negated => '; showCR: (-5**b) negated. Transcript show:'-5 negated**2 => '; showCR: -5 negated**2. "negates the negative 5" Transcript show:'-5 negated**3 => '; showCR: -5 negated**3.</lang>
- Output:
-5**2 => 25 -5**a => 25 -5**b => -125 5**2 => 25 5**a => 25 5**b => 125 5 negated**2 => 25 5 negated**3 => -125 5**2 negated => (1/25) 5**3 negated => (1/125) 5 negated**a => 25 5 negated**b => -125 5**a negated => (1/25) 5**b negated => (1/125) (5**a) negated => -25 (5**b) negated => -125 (-5**a) negated => -25 (-5**b) negated => 125 -5 negated**2 => 25 -5 negated**3 => 125
Wren
Wren uses the pow() method for exponentiation of numbers and, whilst it supports operator overloading, there is no way of adding a suitable infix operator to the existing Num class.
Also inheriting from the Num class is not recommended and will probably be banned altogether from the next version.
However, what we can do is to wrap Num objects in a new Num2 class and then add exponentiation and unary minus operators to that.
Ideally what we'd like to do is to use a new operator such as '**' for exponentiation (because '^' is the bitwise exclusive or operator) but we can only overload existing operators with their existing precedence and so, for the purposes of this task, '^' is the only realistic choice. <lang ecmascript>import "/fmt" for Fmt
class Num2 {
construct new(n) { _n = n }
n { _n}
^(exp) {
if (exp is Num2) exp = exp.n
return Num2.new(_n.pow(exp))
}
- { Num2.new(-_n) }
toString { _n.toString }
}
var ops = ["-x^p", "-(x)^p", "(-x)^p", "-(x^p)"] for (x in [Num2.new(-5), Num2.new(5)]) {
for (p in [Num2.new(2), Num2.new(3)]) {
Fmt.write("x = $2s p = $s | ", x, p)
Fmt.write("$s = $4s | ", ops[0], -x^p)
Fmt.write("$s = $4s | ", ops[1], -(x)^p)
Fmt.write("$s = $4s | ", ops[2], (-x)^p)
Fmt.print("$s = $4s", ops[3], -(x^p))
}
}</lang>
- Output:
x = -5 p = 2 | -x^p = 25 | -(x)^p = 25 | (-x)^p = 25 | -(x^p) = -25 x = -5 p = 3 | -x^p = 125 | -(x)^p = 125 | (-x)^p = 125 | -(x^p) = 125 x = 5 p = 2 | -x^p = 25 | -(x)^p = 25 | (-x)^p = 25 | -(x^p) = -25 x = 5 p = 3 | -x^p = -125 | -(x)^p = -125 | (-x)^p = -125 | -(x^p) = -125