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 Function), 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
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.
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;
- 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
In Algol 68, all unary operators have a higher precedence than any binary operator.
Algol 68 also allows UP and ^ for the exponentiation operator.
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- 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
# syntax: GAWK -f EXPONENTIATION_WITH_INFIX_OPERATORS_IN_OR_OPERATING_ON_THE_BASE.AWK
# converted from FreeBASIC
BEGIN {
print(" x p | -x^p -(x)^p (-x)^p -(x^p)")
print("--------+------------------------------------")
for (x=-5; x<=5; x+=10) {
for (p=2; p<=3; p++) {
printf("%3d %3d | %8d %8d %8d %8d\n",x,p,(-x^p),(-(x)^p),((-x)^p),(-(x^p)))
}
}
exit(0)
}
- Output:
x p | -x^p -(x)^p (-x)^p -(x^p) --------+------------------------------------ -5 2 | -25 -25 25 -25 -5 3 | 125 125 125 125 5 2 | -25 -25 25 -25 5 3 | -125 -125 -125 -125
S$=" ":M$=CHR$(13):?M$" X P -X^P -(X)^P (-X)^P -(X^P)":FORX=-5TO+5STEP10:FORP=2TO3:?M$MID$("+",1+(X<0));X" "PRIGHT$(S$+STR$(-X^P),8)RIGHT$(S$+STR$(-(X)^P),8)RIGHT$(S$+STR$((-X)^P),8)RIGHT$(S$+STR$(-(X^P)),8);:NEXTP,X
- Output:
X P -X^P -(X)^P (-X)^P -(X^P) -5 2 25 25 25 -25 -5 3 125 125 125 125 +5 2 25 25 25 -25 +5 3 -125 -125 -125 -125
print " x p | -x^p -(x)^p (-x)^p -(x^p)"
print ("-"*15); "+"; ("-"*45)
for x = -5 to 5 step 10
for p = 2 to 3
print " "; rjust(x,2); " "; ljust(p,2); " | "; rjust((-x^p),6); " "; rjust((-(x)^p),6); (" "*6); rjust(((-x)^p),6); " "; rjust((-(x^p)),6)
next p
next x- Output:
x p | -x^p -(x)^p (-x)^p -(x^p)
---------------+---------------------------------------------
-5 2 | -25.0 -25.0 25.0 -25.0
-5 3 | 125.0 125.0 125.0 125.0
5 2 | -25.0 -25.0 25.0 -25.0
5 3 | -125.0 -125.0 -125.0 -125.0
Public Sub Main()
Print " x p | -x^p -(x)^p (-x)^p -(x^p)"
Print "----------------+---------------------------------------------"
For x As Integer = -5 To 5 Step 10
For p As Integer = 2 To 3
Print " "; Format$(x, "-#"); " "; Format$(p, "-#"); " | "; Format$((-x ^ p), "-###"); " "; Format$((-(x) ^ p), "-###"); " "; Format$(((-x) ^ p), "-###"); " "; Format$((-(x ^ p)), "-###")
Next
Next
End
- Output:
Same as FreeBASIC entry.
PRINT " x p | -x^p -(x)^p (-x)^p -(x^p)"
PRINT "----------------+---------------------------------------------"
FOR x = -5 TO 5 STEP 10
FOR p = 2 TO 3
PRINT USING " ## ## | #### #### #### ####"; x; p; (-x ^ p); (-(x) ^ p); ((-x) ^ p); (-(x ^ p))
NEXT p
NEXT x
- Output:
Same as FreeBASIC entry.
print " x"; chr$(9); " p"; chr$(9); " | "; chr$(9); "-x^p"; chr$(9); " "; chr$(9); "-(x)^p"; chr$(9); " "; chr$(9); "(-x)^p"; chr$(9); " "; chr$(9); "-(x^p)"
print "----------------------------+-----------------------------------------------------------------"
for x = -5 to 5 step 10
for p = 2 to 3
print " "; x; chr$(9); " "; chr$(9); p; chr$(9); " | "; chr$(9); (-1*x^p); chr$(9); " "; chr$(9); (-1*(x)^p); chr$(9); " "; chr$(9); ((-1*x)^p); chr$(9); " "; chr$(9); (-1*(x^p))
next p
next x
end- Output:
Similar to FreeBASIC entry.
PRINT " x p | -x^p -(x)^p (-x)^p -(x^p)"
PRINT "----------------+---------------------------------------------"
FOR x = -5 TO 5 STEP 10
FOR p = 2 TO 3
PRINT USING " ## ## | #### #### #### ####": x, p, (-x^p), (-(x)^p), ((-x)^p), (-(x^p))
NEXT p
NEXT x
END
- Output:
Same as FreeBASIC entry.
OpenConsole()
PrintN(" x p | -x^p -(x)^p (-x)^p -(x^p)")
PrintN("----------------+---------------------------------------")
For x.i = -5 To 5 Step 10
For p.i = 2 To 3
PrintN(" " + Str(x) + " " + Str(p) + " | " + StrD(Pow(-x,p),0) + #TAB$ + StrD(Pow(-1*(x),p),0) + #TAB$ + StrD(Pow((-x),p),0) + #TAB$ + " " + StrD(-1*Pow(x,p),0))
Next p
Next x
Input()
CloseConsole()
- Output:
x p | -x^p -(x)^p (-x)^p -(x^p)
----------------+---------------------------------------
-5 2 | 25 25 25 -25
-5 3 | 125 125 125 125
5 2 | 25 25 25 -25
5 3 | -125 -125 -125 -125
PROGRAM "Exponentiation with infix operators in (or operating on) the base"
DECLARE FUNCTION Entry ()
FUNCTION Entry ()
PRINT " x p | -x**p -(x)**p (-x)**p -(x**p)"
PRINT "----------------+-----------------------------------------------"
FOR x = -5 TO 5 STEP 10
FOR p = 2 TO 3
PRINT " "; FORMAT$("##",x); " "; FORMAT$("##",p); " | "; FORMAT$("######",(-x**p)); " "; FORMAT$("######",(-(x)**p)); " "; FORMAT$("######",((-x)**p)); " "; FORMAT$("######",(-(x**p)))
NEXT p
NEXT x
END FUNCTION
END PROGRAM
- Output:
Similar to FreeBASIC entry.
print " x p | -x^p -(x)^p (-x)^p -(x^p)"
print "----------------+---------------------------------------------"
for x = -5 to 5 step 10
for p = 2 to 3
print " ", x using "##", " ", p using "##", " | ", (-x^p) using "####", " ", (-(x)^p) using "####", " ", ((-x)^p) using "####", " ", (-(x^p)) using "####"
next p
next x- Output:
Same as FreeBASIC entry.
Indexable.each_cartesian([[-5, 5], [2, 3]]).each do |(x, p)|
printf "x =%2d p=%2d ", x, p
[{"-x**p", -x**p}, {"-(x)**p", -(x)**p},
{"(-x)**p", (-x)**p}, {"-(x**p)", -(x**p)}].each do |sr|
print "%s %4d " % sr
end
puts
end
- 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
for x in [ -5 5 ]
for p in [ 2 3 ]
print x & "^" & p & " = " & pow x p
.
.
F# does not support the ** operator for integers but for floats:
printfn "-5.0**2.0=%f; -(5.0**2.0)=%f" (-5.0**2.0) (-(5.0**2.0))
- Output:
-5.0**2.0=25.000000; -(5.0**2.0)=-25.000000
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.
- 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
In Fortran the exponentiation operator ** has a higher precedence than the unary minus sign operator. Consequently, -x**2 is calculated as -(x*x), in case x=-5, the result is -25. This default behaviour can be changed by using parentheses: (-x)**2 is (-x) * (-x), which is 25 if x is -5 or 5
! Exponentiation with infix operators in (or operating on) the base
! tested with Intel ifx (IFX) 2025.2.1 20250806 on Kubuntu 25.10
! GNU Fortran (Ubuntu 15.2.0-4ubuntu4) 15.2.0 on Kubuntu 25.10
! VSI Fortran x86-64 V8.7-001 on OpenVMS x86_64 V9.2-3
! No Non-standard features used, should compile on any fairly recent Fortran.
! U.B., February 2026
!=========================================================================================
program Expo
implicit none
integer:: x, p
write (*,'(2x,a,2x,a,2x,a,2x,a,2x,a,2x,a,2x,a)') 'x', 'p', '-x**p', '-(x)**p', '(-x)**p', '-(x**p)'
do x=-5,5,10
do p=2, 3
write (*, '(i3, i3, 2 (i7), 2x, 2 (i7,x))') x, p, -x**p, -(x)**p, (-x)**p, -(x**p)
end do
end do
end program Expo
- Output:
x p -x**p -(x)**p (-x)**p -(x**p) -5 2 -25 -25 25 -25 -5 3 125 125 125 125 5 2 -25 -25 25 -25 5 3 -125 -125 -125 -125
print " x p | -x^p -(x)^p (-x)^p -(x^p)"
print "----------------+---------------------------------------------"
for x as integer = -5 to 5 step 10
for p as integer = 2 to 3
print using " ## ## | #### #### #### ####";_
x;p;(-x^p);(-(x)^p);((-x)^p);(-(x^p))
next p
next x
- Output:
x p | -x^p -(x)^p (-x)^p -(x^p)----------------+---------------------------------------------
-5 2 | -25 -25 25 -25 -5 3 | 125 125 125 125 5 2 | -25 -25 25 -25 5 3 | -125 -125 -125 -125
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.
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)))
}
}
}
- 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
--https://wiki.haskell.org/Power_function
main = do
print [-5^2,-(5)^2,(-5)^2,-(5^2)] --Integer
print [-5^^2,-(5)^^2,(-5)^^2,-(5^^2)] --Fractional
print [-5**2,-(5)**2,(-5)**2,-(5**2)] --Real
print [-5^3,-(5)^3,(-5)^3,-(5^3)] --Integer
print [-5^^3,-(5)^^3,(-5)^^3,-(5^^3)] --Fractional
print [-5**3,-(5)**3,(-5)**3,-(5**3)] --Real
- Output:
[-25,-25,25,-25] [-25.0,-25.0,25.0,-25.0] [-25.0,-25.0,25.0,-25.0] [-125,-125,-125,-125] [-125.0,-125.0,-125.0,-125.0] [-125.0,-125.0,-125.0,-125.0]
In both languages all unary operators have higher precedence than binary operators so -5^2 is equivalent to (-5)x(-5) = 25. The program here works in both languages.
procedure main()
every (b := -5|5, e := 2|3) do {
writes(left(" -"||b||"^"||e,8)," -> ",right(-b^e,4)," ")
writes(left(" -("||b||")^"||e,8)," -> ",right(-(b)^e,4)," ")
writes(left(" (-"||b||")^"||e,8)," -> ",right((-b)^e,4)," ")
write(left(" -("||b||"^"||e,8),") -> ",right(-(b^e),4))
}
end
Output:
--5^2 -> 25 -(-5)^2 -> 25 (--5)^2 -> 25 -(-5^2 ) -> -25 --5^3 -> 125 -(-5)^3 -> 125 (--5)^3 -> 125 -(-5^3 ) -> 125 -5^2 -> 25 -(5)^2 -> 25 (-5)^2 -> 25 -(5^2 ) -> -25 -5^3 -> -125 -(5)^3 -> -125 (-5)^3 -> -125 -(5^3 ) -> -125
APLs use a negative sign distinguished from minus as a different character. Underscore followed by a number specifies a negative number. APLs also process the operations from right to left, evaluating parenthesized expressions when the interpreter comes to them. In J, unary plus returns complex conjugate, which won't affect the outcome of this experiment.
format=: ''&$: :([: ; (a: , [: ":&.> [) ,. '{}' ([ (E. <@}.;._1 ]) ,) ])
S=: 'x = {} p = {} -x^p {} -(x)^p {} (-x)^p {} -(x^p) {}'
explicit=: dyad def 'S format~ 2 2 4 4 4 4 ":&> x,y,(-x^y),(-(x)^y),((-x)^y),(-(x^y))'
tacit=: S format~ 2 2 4 4 4 4 ":&> [`]`([:-^)`([:-^)`((^~-)~)`([:-^)`:0
_2 explicit/\_5 2 _5 3 5 2 5 3
x = _5 p = 2 -x^p _25 -(x)^p _25 (-x)^p 25 -(x^p) _25
x = _5 p = 3 -x^p 125 -(x)^p 125 (-x)^p 125 -(x^p) 125
x = 5 p = 2 -x^p _25 -(x)^p _25 (-x)^p 25 -(x^p) _25
x = 5 p = 3 -x^p _125 -(x)^p _125 (-x)^p _125 -(x^p) _125
-:/ 1 0 2 |: _2(tacit ,: explicit)/\_5 2 _5 3 5 2 5 3 NB. the verbs produce matching results
1
JavaScript doesn't allow ambiguous expressions like -x ** p or -(x) ** p - both of them throw syntax errors, regardless of whether x is positive or negative.
function exp_test(x, p) {
const syntax = ["-x ** p", "-(x) ** p", "(-x) ** p", "-(x ** p)"];
for (let i = 0; i < 4; i++) {
console.log(`${syntax[i]}, x = ${x}, p = ${p}:`);
try {
console.log(eval(syntax[i]));
} catch {
console.log("Not syntactically valid");
}
}
}
const xa = [5, -5, 5, -5];
const pa = [2, 2, 3, 3];
for (let i = 0; i < 4; i++) {
exp_test(xa[i], pa[i]);
}
- Output:
-x ** p, x = 5, p = 2: Not syntactically valid -(x) ** p, x = 5, p = 2: Not syntactically valid (-x) ** p, x = 5, p = 2: 25 -(x ** p), x = 5, p = 2: -25 -x ** p, x = -5, p = 2: Not syntactically valid -(x) ** p, x = -5, p = 2: Not syntactically valid (-x) ** p, x = -5, p = 2: 25 -(x ** p), x = -5, p = 2: -25 -x ** p, x = 5, p = 3: Not syntactically valid -(x) ** p, x = 5, p = 3: Not syntactically valid (-x) ** p, x = 5, p = 3: -125 -(x ** p), x = 5, p = 3: -125 -x ** p, x = -5, p = 3: Not syntactically valid -(x) ** p, x = -5, p = 3: Not syntactically valid (-x) ** p, x = -5, p = 3: 125 -(x ** p), x = -5, p = 3: 125
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.
for x in [-5, 5], p in [2, 3]
println("x is", lpad(x, 3), ", p is $p, -x^p is", lpad(-x^p, 4), ", -(x)^p is",
lpad(-(x)^p, 5), ", (-x)^p is", lpad((-x)^p, 5), ", -(x^p) is", lpad(-(x^p), 5))
end
- Output:
x is -5, p is 2, -x^p is -25, -(x)^p is -25, (-x)^p is 25, -(x^p) is -25 x is -5, p is 3, -x^p is 125, -(x)^p is 125, (-x)^p is 125, -(x^p) is 125 x is 5, p is 2, -x^p is -25, -(x)^p is -25, (-x)^p is 25, -(x^p) is -25 x is 5, p is 3, -x^p is-125, -(x)^p is -125, (-x)^p is -125, -(x^p) is -125
writeln [-5^2, -(5)^2, (-5)^2, -(5^2)]
writeln [-5^3, -(5)^3, (-5)^3, -(5^3)]- Output:
[-25, -25, 25, -25] [-125, -125, -125, -125]
Lua < 5.3 has a single double-precision numeric type. Lua >= 5.3 adds an integer numeric type. "^" is supported as an infix exponentiation operator for both types.
mathtype = math.type or type -- polyfill <5.3
function test(xs, ps)
for _,x in ipairs(xs) do
for _,p in ipairs(ps) do
print(string.format("%2.f %7s %2.f %7s %4.f %4.f %4.f %4.f", x, mathtype(x), p, mathtype(p), -x^p, -(x)^p, (-x)^p, -(x^p)))
end
end
end
print(" x type(x) p type(p) -x^p -(x)^p (-x)^p -(x^p)")
print("-- ------- -- ------- ------ ------ ------ ------")
test( {-5.,5.}, {2.,3.} ) -- "float" (or "number" if <5.3)
if math.type then -- if >=5.3
test( {-5,5}, {2,3} ) -- "integer"
end
- Output:
x type(x) p type(p) -x^p -(x)^p (-x)^p -(x^p) -- ------- -- ------- ------ ------ ------ ------ -5 float 2 float -25 -25 25 -25 -5 float 3 float 125 125 125 125 5 float 2 float -25 -25 25 -25 5 float 3 float -125 -125 -125 -125 -5 integer 2 integer -25 -25 25 -25 -5 integer 3 integer 125 125 125 125 5 integer 2 integer -25 -25 25 -25 5 integer 3 integer -125 -125 -125 -125
[-5**2,-(5)**2,(-5)**2,-(5**2)];
[-25, -25, 25, -25]
[-5**3,-(5)**3,(-5)**3,-(5**3)];
[-125, -125, -125, -125]
{-5^2, -(5)^2, (-5)^2, -(5^2)}
{-5^3, -(5)^3, (-5)^3, -(5^3)}
- Output:
{-25, -25, 25, -25}
{-125, -125, -125, -125}
syntax: ["-x^p", "-(x)^p", "(-x)^p", "-(x^p)"]$
exp_test(x, p) := block(
sprint("| x =", x, ",", "p =", p, ":"),
newline(),
for i from 1 thru 4 do(
sprint("|", syntax[i], "=", eval_string(syntax[i]))
),
newline()
)$
x: [5, -5, 5, -5]$
p: [2, 2, 3, 3]$
for i from 1 thru 4 do(exp_test(x[i], p[i]))$
- Output:
| x = 5 , p = 2 : | -x^p = -25 | -(x)^p = -25 | (-x)^p = 25 | -(x^p) = -25 | 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 = 3 : | -x^p = 125 | -(x)^p = 125 | (-x)^p = 125 | -(x^p) = 125
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.
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}"
- 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
Apart from the built-in (prefix) functions sqr (exponent = 2) and sqrt (exponent = 0.5) already defined in Standard “Unextended” Pascal (ISO standard 7185), Extended Pascal (ISO standard 10206) defines following additional (infix) operators:
program exponentiationWithInfixOperatorsInTheBase(output);
const
minimumWidth = 7;
fractionDigits = minimumWidth div 4 + 1;
procedure testIntegerPower(
{ `pow` can in fact accept `integer`, `real` and `complex`. }
protected base: integer;
{ For `pow` the `exponent` _has_ to be an `integer`. }
protected exponent: integer
);
begin
writeLn('=====> testIntegerPower <=====');
writeLn(' base = ', base:minimumWidth);
writeLn(' exponent = ', exponent:minimumWidth);
{ Note: `exponent` may not be negative if `base` is zero! }
writeLn(' -base pow exponent = ', -base pow exponent:minimumWidth);
writeLn('-(base) pow exponent = ', -(base) pow exponent:minimumWidth);
writeLn('(-base) pow exponent = ', (-base) pow exponent:minimumWidth);
writeLn('-(base pow exponent) = ', -(base pow exponent):minimumWidth)
end;
procedure testRealPower(
{ `**` actually accepts all data types (`integer`, `real`, `complex`). }
protected base: real;
{ The `exponent` in an `**` expression will be, if applicable, }
{ _promoted_ to a `real` value approximation. }
protected exponent: integer
);
begin
writeLn('======> testRealPower <======');
writeLn(' base = ', base:minimumWidth:fractionDigits);
writeLn(' exponent = ', exponent:pred(minimumWidth, succ(fractionDigits)));
if base > 0.0 then
begin
{ The result of `base ** exponent` is a `complex` value }
{ `base` is a `complex` value, `real` otherwise. }
writeLn(' -base ** exponent = ', -base ** exponent:minimumWidth:fractionDigits);
writeLn('-(base) ** exponent = ', -(base) ** exponent:minimumWidth:fractionDigits);
writeLn('(-base) ** exponent = illegal');
writeLn('-(base ** exponent) = ', -(base ** exponent):minimumWidth:fractionDigits)
end
else
begin
{ “negative” zero will not alter the sign of the value. }
writeLn(' -base ** exponent = ', -base pow exponent:minimumWidth:fractionDigits);
writeLn('-(base) ** exponent = ', -(base) pow exponent:minimumWidth:fractionDigits);
writeLn('(-base) ** exponent = ', (-base) pow exponent:minimumWidth:fractionDigits);
writeLn('-(base ** exponent) = ', -(base pow exponent):minimumWidth:fractionDigits)
end
end;
{ === MAIN =================================================================== }
begin
testIntegerPower(-5, 2);
testIntegerPower(+5, 2);
testIntegerPower(-5, 3);
testIntegerPower( 5, 3);
testRealPower(-5.0, 2);
testRealPower(+5.0, 2);
testRealPower(-5E0, 3);
testRealPower(+5E0, 3)
end.
- Output:
=====> testIntegerPower <=====
base = -5
exponent = 2
-base pow exponent = -25
-(base) pow exponent = -25
(-base) pow exponent = 25
-(base pow exponent) = -25
=====> testIntegerPower <=====
base = 5
exponent = 2
-base pow exponent = -25
-(base) pow exponent = -25
(-base) pow exponent = 25
-(base pow exponent) = -25
=====> testIntegerPower <=====
base = -5
exponent = 3
-base pow exponent = 125
-(base) pow exponent = 125
(-base) pow exponent = 125
-(base pow exponent) = 125
=====> testIntegerPower <=====
base = 5
exponent = 3
-base pow exponent = -125
-(base) pow exponent = -125
(-base) pow exponent = -125
-(base pow exponent) = -125
======> testRealPower <======
base = -5.00
exponent = 2
-base ** exponent = -25.00
-(base) ** exponent = -25.00
(-base) ** exponent = 25.00
-(base ** exponent) = -25.00
======> testRealPower <======
base = 5.00
exponent = 2
-base ** exponent = -25.00
-(base) ** exponent = -25.00
(-base) ** exponent = illegal
-(base ** exponent) = -25.00
======> testRealPower <======
base = -5.00
exponent = 3
-base ** exponent = 125.00
-(base) ** exponent = 125.00
(-base) ** exponent = 125.00
-(base ** exponent) = 125.00
======> testRealPower <======
base = 5.00
exponent = 3
-base ** exponent = -125.00
-(base) ** exponent = -125.00
(-base) ** exponent = illegal
-(base ** exponent) = -125.00
Since there are two different power operators available, both accepting operands of different data types, having different limits, and yielding different data types, it was not sensible to produce a table similar to other entries on this page.
##
foreach var x in |-5, 5| do
foreach var p in |2, 3| do
writeln('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);
- 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
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.
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 $eqn for @eqns;
print "\n";
}
print "\n";
}
- Output:
x: -5 p: 2 | 1 + -$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 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.)
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
- 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
Pluto does have the integer exponentiation operator '**'. This has higher priority than the unary minus operator, hence the results for the first two expressions below.
local fmt = require "fmt"
local expr = {"-x**p", "-(x)**p", "(-x)**p", "-(x**p)"}
for {-5, 5} as x do
for {2, 3} as p do
fmt.write("x = %2d p = %d | ", x, p)
fmt.write("%s = %4d | ", expr[1], -x ** p)
fmt.write("%s = %4d | ", expr[2], -(x) ** p)
fmt.write("%s = %4d | ", expr[3], (-x) ** p)
fmt.print("%s = %4d", expr[4], -(x ** p))
end
end
- 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
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))
- 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
For x = -5 To 5 Step 10
For p = 2 To 3
Print "x = "; x; " p ="; p; " ";
Print Using "-x^p is ####"; -x ^ p;
Print Using ", -(x)^p is ####"; -(x) ^ p;
Print Using ", (-x)^p is ####"; (-x) ^ p;
Print Using ", -(x^p) is ####"; -(x ^ p)
Next
Next- Output:
x = -5 p = 2 -x^p is -25, -(x)^p is -25, (-x)^p is 25, -(x^p) is -25 x = -5 p = 3 -x^p is 125, -(x)^p is 125, (-x)^p is 125, -(x^p) is 125 x = 5 p = 2 -x^p is -25, -(x)^p is -25, (-x)^p is 25, -(x^p) is -25 x = 5 p = 3 -x^p is -125, -(x)^p is -125, (-x)^p is -125, -(x^p) is -125
expressions <- alist(-x ^ p, -(x) ^ p, (-x) ^ p, -(x ^ p))
x <- c(-5, -5, 5, 5)
p <- c(2, 3, 2, 3)
output <- data.frame(x,
p,
setNames(lapply(expressions, eval), sapply(expressions, deparse)),
check.names = FALSE)
print(output, row.names = FALSE)
- Output:
x p -x^p -(x)^p (-x)^p -(x^p) -5 2 -25 -25 25 -25 -5 3 125 125 125 125 5 2 -25 -25 25 -25 5 3 -125 -125 -125 -125
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
sub infix:<↑> is looser(&prefix:<->) { $^a ** $^b }
sub infix:<∧> is looser(&infix:<->) { $^a ** $^b }
for
('Default precedence: infix exponentiation is tighter (higher) precedence than unary negation.',
'1 + -$x**$p', {1 + -$^a**$^b}, '1 + (-$x)**$p', {1 + (-$^a)**$^b}, '1 + (-($x)**$p)', {1 + (-($^a)**$^b)},
'(1 + -$x)**$p', {(1 + -$^a)**$^b}, '1 + -($x**$p)', {1 + -($^a**$^b)}),
("\nEasily modified: custom loose infix exponentiation is looser (lower) precedence than unary negation.",
'1 + -$x↑$p ', {1 + -$^a↑$^b}, '1 + (-$x)↑$p ', {1 + (-$^a)↑$^b}, '1 + (-($x)↑$p) ', {1 + (-($^a)↑$^b)},
'(1 + -$x)↑$p ', {(1 + -$^a)↑$^b}, '1 + -($x↑$p) ', {1 + -($^a↑$^b)}),
("\nEven more so: custom looser infix exponentiation is looser (lower) precedence than infix subtraction.",
'1 + -$x∧$p ', {1 + -$^a∧$^b}, '1 + (-$x)∧$p ', {1 + (-$^a)∧$^b}, '1 + (-($x)∧$p) ', {1 + (-($^a)∧$^b)},
'(1 + -$x)∧$p ', {(1 + -$^a)∧$^b}, '1 + -($x∧$p) ', {1 + -($^a∧$^b)})
-> $case {
my ($title, @operations) = $case<>;
say $title;
for -5, 5 X 2, 3 -> ($x, $p) {
printf "x = %2d p = %d", $x, $p;
for @operations -> $label, &code { print " │ $label = " ~ $x.&code($p).fmt('%4d') }
say ''
}
}
- 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 more so: 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 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)
- 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 ───── ──────╨─────────── ───────╨─────────── ───────╨─────────── ───────╨─────────── ──────
« { 'x' 'p' '-x^p' '-(x)^p' '(-x)^p' '-(x^p)' } → exp
« exp
{ { -5 2 } { -5 3 } { 5 2 } { 5 3 } }
1 « EVAL → x p « exp « EVAL » DOLIST » » DOLIST
EVAL
» » 'TASK' STO
- Output:
5: { x p '-x^p' '-x^p' '(-x)^p' '-x^p' }
4: { -5 2 -25 -25 25 -25 }
3: { -5 3 125 125 125 125 }
2: { 5 2 -25 -25 25 -25 }
1:{ 5 3 -125 -125 -125 -125 }
nums = [-5, 5]
pows = [2, 3]
nums.product(pows) do |x, p|
puts "x = #{x} p = #{p}\t-x**p #{-x**p}\t-(x)**p #{-(x)**p}\t(-x)**p #{ (-x)**p}\t-(x**p) #{-(x**p)}"
end
- 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
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).
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 "
Using the "negated" message:
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.
- 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
import math
fn main() {
xs := [-5, 5]
ps := [2, 3]
for x in xs {
for p in ps {
print('x =${x:2d} p=${p:2d} ')
// compute powers
x_pow_p := int(math.pow(f64(x), f64(p)))
neg_x_pow_p := -x_pow_p
neg_x := -x
neg_x_pow_p_paren := int(math.pow(f64(neg_x), f64(p)))
// hash map of `string: value`
sr := {
'-x**p': neg_x_pow_p
'-(x)**p': neg_x_pow_p
'(-x)**p': neg_x_pow_p_paren
'-(x**p)': neg_x_pow_p
}
for key, val in sr {
print('${key} ${val:4d} ')
}
println('')
}
}
}
- 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
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 or inheriting from that class.
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.
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))
}
}
- 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
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