# Implement hyperexponentiation/tetration without the use of '^'

## The Challenge

Implement tetration (aka Power Tower or Hyperexponentiation) with the least amount of characters.

## The Conditions

• Don't use the 'power' operator or its equivalents (such as pow(x,y), x^y, x**y, etc.)
• Input given as: x y (separated by a space)
• x is exponentiated by itself y times.
• Your method must be able to compute at least 4 3 (4 exponentiated by itself 3 times)

## The Scoring

• Lowest score wins: (# of characters)
• Bonus deduction if you do not use the multiplication operator (-5 points).
• No Speed/Memory requirements. Take as long as you want.

## Examples

x, 0 -> 1

2, 2 -> 2^2 = 4

2, 4 -> 2^(2^(2^2)) = 65536

4, 3 -> 4^(4^4) = 4^256 = 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096


Open to suggestions/alterations/questions

• One alteration which I think is fairly important is to replace "* operator" with "multiplication operator". In GolfScript * is multiplication in some contexts, but it's also the simple looping operator: {block}N* is equivalent to C-style for(i=0;i<N;i++){block}. The tricky edge case is string/array multiplication ('a'3* gives 'aaa'), but that's unlikely to be an issue given that an array of 4***3 elements will overflow RAM. – Peter Taylor Apr 19 '12 at 8:38
• Also worth adding a test for the edge case x 0 => 1. My original solution didn't handle that case. – Peter Taylor Apr 19 '12 at 21:20
• The penalty for using multiplication is way too low. (:=bonus for not using it). I made a solution which didn't used it, and had to replace it to avoid stack overflows, and gained a 7 char win for a 5 char bonus loss. – user unknown Apr 20 '12 at 3:32
• @EngineerToast I posted this golf 4 years before the one you linked... – MrZander Sep 19 '17 at 23:13
• The conditions and scoring are kind of strange. You don't allow the use of power operations? Or you do allow them, but they are a +10 point bonus? – Simply Beautiful Art Dec 4 '17 at 23:58

# Racket 58 (no *)

(define(t x y)(if(= y 0)1(for/product([i(t x(- y 1))])x)))

• for/product is walking a fine line on the "no multiplication" rule, haha. – MrZander Sep 18 '14 at 16:17

# Common Lisp, 85 chars

(lambda(b c)(let((r b)u)(dotimes(c c r)(setf u 1 r(dotimes(c b u)(setf u(* u r)))))))


I tried doing the multiplications through repeated addition, but it was way more than 5 characters. Same thing with macrolets, the declarations were not worth the gains.

Another solution, inspired by boothby's python solution. It's 1 character less than the above solution.

(lambda(a b)(eval(*,@(loop for x below b nconc(loop for x below a nconc(,a,a))))))


# Python 3 – 68

(including the 10-point penalty for the power operator)

a,b=input().split()
r=1
exec("r=%s**r;"%a*int(b))
print(r)


# Yabasic, 71 bytes

A function that takes input a and b as a space delimited string.

Input""a,b
d=a^(b>0)
For i=2To b
c=a
For j=2To d
c=c*a
Next
d=c
Next
?d


Try it online!

# R, 71 - 5 = 66 bytes

function(x,y,b=x){for(i in 2:y)b=cumprod(z<-rep(x,b))[sum(z|1)];cat(b)}


Try it online!

-5 for avoiding *, which was harder than I expected. It explodes really fast and won't work (unless it had more memory) but it satisfies all necessary criteria.

# APL(NARS), chars 46, bytes 92

{⍺ ⍺{(a b)←⍺⋄⍵≤1:{⍵:b⋄1}⍵⋄(a,a{×/⍵⍴⍺}b)∇⍵-1}⍵}


test:

  h←{⍺ ⍺{(a b)←⍺⋄⍵≤1:{⍵:b⋄1}⍵⋄(a,a{×/⍵⍴⍺}b)∇⍵-1}⍵}
3 h 0
1
2 h 2
4
2 h 4
65536
4 h 3
1.340780793E154


without the use of pow=* in APL where ⍵>0; but i use multiplication ×...

# APL (Dyalog Classic), 23 bytes

f←{⍵=0:1⋄⊃⌽{×/⍵⍴⍺}\⍵⍴⍺}


Try it online!

# Ruby, 43 39 points

->a,b{c=1;eval"c=eval('a*'*~-c+?a);"*b}


Try it online

# Ruby, also 43 39 points

t=->a,b{b<1?1:eval("a*"*~-t[a,b-1]+?a)}


Try it online

The following are no longer valid(?)

# Ruby, 26 + (1 power operation)*10 points

t=->a,b{b<1?1:a**t[a,b-1]}


Try it online

# Ruby, 28 + (1 power operation)*10 points

->a,b{c=1;b.times{c=a**c};c}


Try it online

# PHP, 139 125 bytes

function f($x,$y){return gmp_strval($y?(function($x,$y){for($a=1;$i<$y;$i++)$a=gmp_mul($x,$a);return$a;})($x,f($x,$y-1)):1);}


Uses GMP library for the arbitrary-length math. It does compute the result instantly and able to solve 2***5 as well.

The longer (198 bytes - 5 = 193) version that does not multiply:

function f($x,$y){return gmp_strval($y?(function($x,$y,$a=1){for(;$i<$y;$i++)$a=(function($x,$y){$a=0;for(;$i<gmp_intval($y);$i++)$a=gmp_add($x,$a);return$a;})($x,$a);return$a;})($x,f($x,$y-1)):1);}


Output Tests:

2, 0 -> 1
Exec time 0.00009513 seconds
2, 2 -> 4
Exec time 0.00006819 seconds
2, 4 -> 65536
Exec time 0.00002694 seconds
4, 3 -> 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096
Exec time 0.00011992 seconds


If you were curious the result of 2***5, here it is:

2, 5 -> 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Exec time 0.11125493 seconds


# JavaScript, 85 bytes

function(s){for(s=s.split(" "),a=b=s[0],i=0;++i<s[1];)for(j=a,a=b;--j;)a*=b;return a}


# JavaScript (ES6), 83 bytes

r=f=>(i,n,j=i)=>--n?j:r(f)(i,n,f(i,j));s=>r(r((a,b)=>a*b),(s=s.split(" "))[0],s[1])


# APL (Dyalog Unicode), 14 12 bytes (SBCS)

f←(×/⍴⍨)/1,⍨⍴⍨


Try it online!

### Without multiplication, 19 17 - 5 = 12

f←((+/⍴⍨)/⍴⍨)/1,⍨⍴⍨


Try it online!

This is practically the same thing as above, but much, much slower. This time, since we can't have multiplication either, there's (+/⍴⍨).

### With exponentiation operator (*), 4 bytes

*/⍴⍨


Try it online!

# Whispers v3, $$\39 - 5 = 34\$$ bytes

> Input
> Input
>> 1↑↑2
>> Output 3


This uses the tetration builtin

# Perl 5-Mbigint -pa, 51 46 bytes

for$i(0..<>){$_=1;for$b(1..$e){$_*="@F"}$e=\$_}


Try it online!

In Python 3:

pow = 1
for i in range(n):
pow=pow**a


where a is the base and n is the height

• Welcome to Code Golf! Nice first answer. – Redwolf Programs Mar 2 at 20:22

# Javascript (ES6), 24 + 10 bytes:

h=(a,n)=>n?a**h(a,--n):1

# Without **, 50 bytes:

e=(n,p)=>p?e(n,--p)*n:1;h=(a,n)=>n?e(a,h(a,--n)):1

# Without *, 77 - 5 bytes:

m=(n,p)=>p?n+m(n,--p):0;e=(n,p)=>p?m(e(n,--p),n):1;h=(a,n)=>n?e(a,h(a,--n)):1

There's got to be a better way to do this than create recursive helpers, but until then...

h is the main function, the others are recursive helpers.

• These only compute the exponent, you need to go one level deeper. Compare your results with the test cases provided in the question. – MrZander Feb 12 at 17:10