Zero to the zero power
Some programming languages are not exactly consistent (with other programming languages) when raising zero to the zeroth power: .
- Task requirements
Show the results of raising zero to the zeroth power.
If your computer language objects to 0**0 at compile time, you may also try something like:
<lang rexx>x = 0
y = 0
z = x**y
··· show the result ···</lang>
Of course, use any symbols or notation that is supported in your computer language for exponentiation.
- See also
- The Wiki entry: Zero to the power of zero.
- The Wiki entry: History of differing points of view.
- The MathWorld™ entry: exponent laws.
- Also, in the above MathWorld™ entry, see formula (9): .
- The OEIS entry: The special case of zero to the zeroth power
Ada
<lang Ada>with Ada.Text_IO, Ada.Integer_Text_IO, Ada.Long_Integer_Text_IO,
Ada.Long_Long_Integer_Text_IO, Ada.Float_Text_IO, Ada.Long_Float_Text_IO, Ada.Long_Long_Float_Text_IO;
use Ada.Text_IO, Ada.Integer_Text_IO, Ada.Long_Integer_Text_IO,
Ada.Long_Long_Integer_Text_IO, Ada.Float_Text_IO, Ada.Long_Float_Text_IO, Ada.Long_Long_Float_Text_IO;
procedure Test5 is
I : Integer := 0; LI : Long_Integer := 0; LLI : Long_Long_Integer := 0; F : Float := 0.0; LF : Long_Float := 0.0; LLF : Long_Long_Float := 0.0; Zero : Natural := 0;
begin
Put ("Integer 0^0 = ");
Put (I ** Zero, 2); New_Line;
Put ("Long Integer 0^0 = ");
Put (LI ** Zero, 2); New_Line;
Put ("Long Long Integer 0^0 = ");
Put (LLI ** Zero, 2); New_Line;
Put ("Float 0.0^0 = ");
Put (F ** Zero); New_Line;
Put ("Long Float 0.0^0 = ");
Put (LF ** Zero); New_Line;
Put ("Long Long Float 0.0^0 = ");
Put (LLF ** Zero); New_Line;
end Test5; </lang>
- Output:
Integer 0^0 = 1 Long Integer 0^0 = 1 Long Long Integer 0^0 = 1 Float 0.0^0 = 1.00000E+00 Long Float 0.0^0 = 1.00000000000000E+00 Long Long Float 0.0^0 = 1.00000000000000000E+00
Applesoft BASIC
]? 0^0 1
Bc
0 ^ 0 1
C
This example uses the standard pow function in the math library. 0^0 is given as 1.
<lang c>#include <stdio.h>
- include <math.h>
- include <complex.h>
int main() { printf("0 ^ 0 = %f\n", pow(0,0));
double complex c = cpow(0,0);
printf("0+0i ^ 0+0i = %f+%fi\n", creal(c), cimag(c)); return 0; }</lang>
- Output:
0 ^ 0 = 1.000000 0+0i ^ 0+0i = nan+nani
C++
<lang cpp>#include <iostream>
- include <cmath>
- include <complex>
int main() {
std::cout << "0 ^ 0 = " << std::pow(0,0) << std::endl; std::cout << "0+0i ^ 0+0i = " << std::pow(std::complex<double>(0),std::complex<double>(0)) << std::endl; return 0;
}</lang>
- Output:
0 ^ 0 = 1 0+0i ^ 0+0i = (nan,nan)
Common Lisp
> (expt 0 0) 1
D
<lang d>void main() {
import std.stdio, std.math, std.bigint, std.complex;
writeln("Int: ", 0 ^^ 0);
writeln("Ulong: ", 0UL ^^ 0UL);
writeln("Float: ", 0.0f ^^ 0.0f);
writeln("Double: ", 0.0 ^^ 0.0);
writeln("Real: ", 0.0L ^^ 0.0L);
writeln("pow: ", pow(0, 0));
writeln("BigInt: ", 0.BigInt ^^ 0);
writeln("Complex: ", complex(0.0, 0.0) ^^ 0);
}</lang>
- Output:
Int: 1 Ulong: 1 Float: 1 Double: 1 Real: 1 pow: 1 BigInt: 1 Complex: 1+0i
Go
Go does not have an exponentiation operator but has functions in the standard library for three types, float64, complex128, and big.Int. The functions for float64 and big.Int are documented to return 1. The function for complex128 does not have the special case documented. <lang go>package main
import (
"fmt" "math" "math/big" "math/cmplx"
)
func main() {
fmt.Println("float64: ", math.Pow(0, 0))
var b big.Int
fmt.Println("big integer:", b.Exp(&b, &b, nil))
fmt.Println("complex: ", cmplx.Pow(0, 0))
}</lang>
- Output:
float64: 1 big integer: 1 complex: (0+0i)
Haskell
<lang haskell>import Data.Complex
main = do
print $ 0 ^ 0 print $ 0.0 ^ 0 print $ 0 ^^ 0 print $ 0 ** 0 print $ (0 :+ 0) ^ 0 print $ (0 :+ 0) ** (0 :+ 0)</lang>
- Output:
1 1.0 1.0 1.0 1.0 :+ 0.0 NaN :+ NaN
J
<lang j> 0 ^ 0 1</lang>
Java
<lang java>System.out.println(Math.pow(0, 0));</lang>
- Output:
1.0
JavaScript
In interactive mode: <lang javascript>> Math.pow(0, 0); 1</lang>
OCaml
In the interpreter:
# 0.0 ** 0.0;;
- : float = 1.
# Complex.pow Complex.zero Complex.zero;;
- : Complex.t = {Complex.re = nan; Complex.im = nan}
# #load "nums.cma";;
# open Num;;
# Int 0 **/ Int 0;;
- : Num.num = Int 1
PARI/GP
<lang parigp>0^0</lang>
- Output:
%1 = 1
Perl
<lang perl>print 0 ** 0, "\n";
use Math::Complex;
print cplx(0,0) ** cplx(0,0), "\n";</lang>
- Output:
1 1
Perl 6
Translation of REXX.
<lang perl 6>say '0 ** 0 (zero to the zeroth power) ───► ', 0**0</lang>
- Output:
0 ** 0 (zero to the zeroth power) ───► 1
PHP
<lang PHP><?php echo pow(0,0);</lang>
- Output:
1
PL/I
<lang pli> zhz: Proc Options(Main);
Dcl a dec float(10) Init(1);
Dcl b dec float(10) Init(0);
Put skip list('1**0=',a**b);
Put skip list('0**1=',b**a);
Put skip list('0**0=',b**b);
End;</lang>
- Output:
1**0= 1.000000000E+0000 0**1= 0.000000000E+0000 0**0= IBM0682I ONCODE=1553 X in EXPONENT(X) was invalid. At offset +0000025B in procedure with entry ZHZ
PowerShell
<lang PowerShell>[math]::pow(0,0)</lang>
Python
<lang python>from decimal import Decimal from fractions import Fraction for n in (Decimal(0), Fraction(0, 1), complex(0), float(0), int(0)): try: n1 = n**n except: n1 = '<Raised exception>' try: n2 = pow(n, n) except: n2 = '<Raised exception>' print('%8s: ** -> %r; pow -> %r' % (n.__class__.__name__, n1, n2))</lang>
- Output:
Decimal: ** -> '<Raised exception>'; pow -> '<Raised exception>'
Fraction: ** -> Fraction(1, 1); pow -> Fraction(1, 1)
complex: ** -> (1+0j); pow -> (1+0j)
float: ** -> 1.0; pow -> 1.0
int: ** -> 1; pow -> 1
Racket
<lang racket>#lang racket
- as many zeros as I can think of...
(define zeros (list
0 ; unspecified number type
0. ; hinted as float
#e0 ; explicitly exact
#i0 ; explicitly inexact
0+0i ; exact complex
0.+0.i ; float inexact
))
(for*((z zeros) (p zeros))
(printf "(~a)^(~a) = ~s~%" z p (with-handlers [(exn:fail:contract:divide-by-zero? exn-message)] (expt z p))))</lang>
- Output:
(0)^(0) = 1 (0)^(0.0) = 1.0 (0)^(0) = 1 (0)^(0.0) = 1.0 (0)^(0) = 1 (0)^(0.0+0.0i) = "expt: undefined for 0 and 0.0+0.0i" (0.0)^(0) = 1 (0.0)^(0.0) = 1.0 (0.0)^(0) = 1 (0.0)^(0.0) = 1.0 (0.0)^(0) = 1 (0.0)^(0.0+0.0i) = +nan.0+nan.0i (0)^(0) = 1 (0)^(0.0) = 1.0 (0)^(0) = 1 (0)^(0.0) = 1.0 (0)^(0) = 1 (0)^(0.0+0.0i) = "expt: undefined for 0 and 0.0+0.0i" (0.0)^(0) = 1 (0.0)^(0.0) = 1.0 (0.0)^(0) = 1 (0.0)^(0.0) = 1.0 (0.0)^(0) = 1 (0.0)^(0.0+0.0i) = +nan.0+nan.0i (0)^(0) = 1 (0)^(0.0) = 1.0 (0)^(0) = 1 (0)^(0.0) = 1.0 (0)^(0) = 1 (0)^(0.0+0.0i) = "expt: undefined for 0 and 0.0+0.0i" (0.0+0.0i)^(0) = 1 (0.0+0.0i)^(0.0) = 1.0+0.0i (0.0+0.0i)^(0) = 1 (0.0+0.0i)^(0.0) = 1.0+0.0i (0.0+0.0i)^(0) = 1 (0.0+0.0i)^(0.0+0.0i) = +nan.0+nan.0i
REXX
<lang rexx>/*REXX program shows the results of raising zero to the zeroth power.*/
say '0 ** 0 (zero to the zeroth power) ───► ' 0**0</lang>
using PC/REXX
using Personal REXX
using REGINA
output
0 ** 0 (zero to the zeroth power) ───► 1
using R4
output
Error 26 : Invalid whole number (SYNTAX) Information: 0 ** 0 is undefined Error occurred in statement# 2 Statement source: say '0 ** 0 (zero to the zeroth power) ───► ' 0**0 Statement context: C:\ZERO_TO0.REX, procedure: ZERO_TO0
using ROO
output
Error 26 : Invalid whole number (SYNTAX) Information: 0 ** 0 is undefined Error occurred in statement# 2 Statement source: say '0 ** 0 (zero to the zeroth power) ───► ' 0**0 Statement context: C:\ZERO_TO0.REX, procedure: ZERO_TO0
Ruby
<lang ruby>require 'complex' require 'rational' require 'bigdecimal'
[0, 0.0, Complex(0), Rational(0), BigDecimal.new("0")].each {|n|
printf "%10s: ** -> %s\n" % [n.class, n**n]
}</lang>
- Output:
Fixnum: ** -> 1
Float: ** -> 1.0
Complex: ** -> 1+0i
Rational: ** -> 1/1
BigDecimal: ** -> 0.1E1
Scheme
<lang scheme>(display (expt 0 0)) (newline) (display (expt 0.0 0.0)) (newline) (display (expt 0+0i 0+0i)) (newline)</lang>
- Output:
1 1.0 1.0
Standard ML
In the interpreter:
- Math.pow (0.0, 0.0); val it = 1.0 : real
Tcl
Interactively… <lang tcl>% expr 0**0 1 % expr 0.0**0.0 1.0</lang>
zkl
<lang zkl>(0.0).pow(0) //--> 1.0 var BN=Import("zklBigNum"); // big ints BN(0).pow(0) //--> 1</lang>