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<br />
<br />
=={{header|11l}}==
{{trans|Nim}}
 
<syntaxhighlight lang="11l">F sf(n)
V result = BigInt(1)
L(i) 2 .. n
result *= factorial(i)
R result
 
F hf(n)
V result = BigInt(1)
L(i) 2 .. n
result *= pow(BigInt(i), i)
R result
 
F af(n)
V result = BigInt(0)
V m = ((n [&] 1) << 1) - 1
L(i) 1 .. n
result += m * factorial(i)
m = -m
R result
 
F ef(n)
V result = BigInt(1)
L(k) 2 .. n
result = pow(k, result)
R result
 
F rf(n)
I n == 1
R 0
V result = 1
V p = 1
L p < n
result++
p *= result
I p > n
result = -1
R result
 
V sfs = (0.<10).map(n -> sf(n))
print(‘First ’sfs.len‘ superfactorials: ’sfs.join(‘ ’))
 
V hfs = (0.<10).map(n -> hf(n))
print(‘First ’hfs.len‘ hyperfactorials: ’hfs.join(‘ ’))
 
V afs = (0.<10).map(n -> af(n))
print(‘First ’afs.len‘ alternating factorials: ’afs.join(‘ ’))
 
V efs = (0.<5).map(n -> ef(n))
print(‘First ’efs.len‘ exponential factorials: ’efs.join(‘ ’))
 
print("\nNumber of digits of ef(5): "String(ef(5)).len)
 
print("\nReverse factorials:")
L(n) [1, 2, 6, 24, 119, 120, 720, 5040, 40320, 362880, 3628800]
V r = rf(n)
print(f:‘{n:7}: {I r >= 0 {f:‘{r:2}’} E ‘undefined’}’)</syntaxhighlight>
 
{{out}}
<pre>
First 10 superfactorials: 1 1 2 12 288 34560 24883200 125411328000 5056584744960000 1834933472251084800000
First 10 hyperfactorials: 1 1 4 108 27648 86400000 4031078400000 3319766398771200000 55696437941726556979200000 21577941222941856209168026828800000
First 10 alternating factorials: 0 1 1 5 19 101 619 4421 35899 326981
First 5 exponential factorials: 1 1 2 9 262144
 
Number of digits of ef(5): 183231
 
Reverse factorials:
1: 0
2: 2
6: 3
24: 4
119: undefined
120: 5
720: 6
5040: 7
40320: 8
362880: 9
3628800: 10
</pre>
 
=={{header|ALGOL 68}}==
{{works with|ALGOL 68G|Any - tested with release 2.8.3.win32}}
Uses Algol 68G's LONG LONG INT with default precision, which is long enough for the values needed for the task, except exponential factorial( 5 ).
The reverse factorial function uses a UNION(INT,STRING) for the result, so the result can either be an integer or the string "undefined".
<syntaxhighlight lang="algol68">
BEGIN # show the values of some "special factorials" #
 
# super factorial: returns the product of the factorials up to to n #
PROC sf = ( INT n )LONG LONG INT:
BEGIN
LONG LONG INT f := 1, p := 1;
FOR i TO n DO
f *:= i;
p *:= f
OD;
p
END # sf # ;
# hyper factorial: returns the product of k^k for k up to n #
PROC hf = ( INT n )LONG LONG INT:
BEGIN
LONG LONG INT p := 1;
FOR i TO n DO
TO i DO p *:= i OD
OD;
p
END # hf # ;
# alternating factorial: returns the sum of (-1)^(i-1)*i! for i up to n #
PROC af = ( INT n )LONG LONG INT:
BEGIN
LONG LONG INT s := 0;
LONG LONG INT f := 1;
INT sign := IF ODD n THEN 1 ELSE - 1 FI;
FOR i TO n DO
f *:= i;
s +:= sign * f;
sign := - sign
OD;
s
END # hf # ;
# exponential factorial: returns n^(n-1)^(n-2)... #
PROC xf = ( INT n )LONG LONG INT:
BEGIN
LONG LONG INT x := 1;
FOR i TO n DO
LONG LONG INT ix := 1;
TO SHORTEN SHORTEN x DO ix *:= i OD;
x := ix
OD;
x
END # hf # ;
# reverse factorial: returns k if n = k! for some integer k #
# "undefined" otherwise #
PROC rf = ( LONG LONG INT n )UNION( INT, STRING ):
IF n < 2
THEN 0
ELSE
LONG LONG INT f := 1;
INT i := 1;
WHILE f < n DO
f *:= i;
i +:= 1
OD;
IF f = n THEN i - 1 ELSE "undefined" FI
FI # rf # ;
 
print( ( "super factorials 0..9:", newline, " " ) );
FOR i FROM 0 TO 9 DO print( ( " ", whole( sf( i ), 0 ) ) ) OD;
print( ( newline, "hyper factorials 0..9:", newline, " " ) );
FOR i FROM 0 TO 9 DO print( ( " ", whole( hf( i ), 0 ) ) ) OD;
print( ( newline, "alternating factorials 0..9:", newline, " " ) );
FOR i FROM 0 TO 9 DO print( ( " ", whole( af( i ), 0 ) ) ) OD;
print( ( newline, "exponential factorials 0..4:", newline, " " ) );
FOR i FROM 0 TO 4 DO print( ( " ", whole( xf( i ), 0 ) ) ) OD;
 
[]INT rf test = ( 1, 2, 6, 24, 119, 120, 720, 5040, 40320, 362880, 3628800 );
print( ( newline, "reverse factorials:", newline ) );
FOR i FROM LWB rf test TO UPB rf test DO
INT tv = rf test[ i ];
print( ( whole( tv, -8 )
, " -> "
, CASE rf( tv )
IN ( INT iv ): whole( iv, 0 )
, ( STRING sv ): sv
OUT "Unexpected value returned by rf( " + whole( tv, 0 ) + " )"
ESAC
, newline
)
)
OD
 
END
</syntaxhighlight>
{{out}}
<pre>
super factorials 0..9:
1 1 2 12 288 34560 24883200 125411328000 5056584744960000 1834933472251084800000
hyper factorials 0..9:
1 1 4 108 27648 86400000 4031078400000 3319766398771200000 55696437941726556979200000 21577941222941856209168026828800000
alternating factorials 0..9:
0 1 1 5 19 101 619 4421 35899 326981
exponential factorials 0..4:
1 1 2 9 262144
reverse factorials:
1 -> 0
2 -> 2
6 -> 3
24 -> 4
119 -> undefined
120 -> 5
720 -> 6
5040 -> 7
40320 -> 8
362880 -> 9
3628800 -> 10
</pre>
 
=={{header|Arturo}}==
 
<syntaxhighlight lang="arturo">super: $ => [fold.seed:1 1..& [x y] -> x * factorial y]
 
hyper: $ => [fold.seed:1 1..& [x y] -> x * y^y]
 
alternating: $[n][
fold 1..n [x y] ->
x + (factorial y) * (neg 1)^n-y
]
 
exponential: $ => [fold.seed:1 0..& [x y] -> y^x]
 
rf: function [n][
if 1 = n -> return 0
b: a: <= 1
while -> n > a [
'b + 1
'a * b
]
if a = n -> return b
return null
]
 
print "First 10 superfactorials:"
print map 0..9 => super
 
print "\nFirst 10 hyperfactorials:"
print map 0..9 => hyper
 
print "\nFirst 10 alternating factorials:"
print map 0..9 => alternating
 
print "\nFirst 5 exponential factorials:"
print map 0..4 => exponential
 
prints "\nNumber of digits in $5: "
print size ~"|exponential 5|"
print ""
 
[1 2 6 24 120 720 5040 40320 362880 3628800 119]
| loop 'x -> print ~"rf(|x|) = |rf x|"</syntaxhighlight>
 
{{out}}
 
<pre>First 10 superfactorials:
1 1 2 12 288 34560 24883200 125411328000 5056584744960000 1834933472251084800000
 
First 10 hyperfactorials:
1 1 4 108 27648 86400000 4031078400000 3319766398771200000 55696437941726556979200000 21577941222941856209168026828800000
 
First 10 alternating factorials:
0.0 1 1 5 19 101 619 4421 35899 326981
 
First 5 exponential factorials:
0 1 2 9 262144
 
Number of digits in $5: 183231
 
rf(1) = 0
rf(2) = 2
rf(6) = 3
rf(24) = 4
rf(120) = 5
rf(720) = 6
rf(5040) = 7
rf(40320) = 8
rf(362880) = 9
rf(3628800) = 10
rf(119) = null</pre>
 
=={{header|Bruijn}}==
 
Implementation for numbers encoded in balanced ternary using Mixfix syntax defined in the Math module:
 
<syntaxhighlight lang="bruijn">
:import std/Combinator .
:import std/List .
:import std/Math .
 
factorial [∏ (+1) → 0 | [0]]
 
superfactorial [∏ (+1) → 0 | factorial]
 
hyperfactorial [∏ (+1) → 0 | [0 ** 0]]
 
alternating-factorial y [[=?0 0 ((factorial 0) - (1 --0))]]
 
exponential-factorial y [[=?0 0 (0 ** (1 --0))]]
 
:test ((factorial (+4)) =? (+24)) ([[1]])
:test ((superfactorial (+4)) =? (+288)) ([[1]])
:test ((hyperfactorial (+4)) =? (+27648)) ([[1]])
:test ((alternating-factorial (+3)) =? (+5)) ([[1]])
:test ((exponential-factorial (+4)) =? (+262144)) ([[1]])
 
invfac y [[[compare-case 1 (2 ++1 0) (-1) 0 (∏ (+0) → --1 | ++‣)]]] (+0)
 
:test ((invfac (+1)) =? (+0)) ([[1]])
:test ((invfac (+2)) =? (+2)) ([[1]])
:test ((invfac (+6)) =? (+3)) ([[1]])
:test ((invfac (+24)) =? (+4)) ([[1]])
:test ((invfac (+120)) =? (+5)) ([[1]])
:test ((invfac (+720)) =? (+6)) ([[1]])
:test ((invfac (+5040)) =? (+7)) ([[1]])
:test ((invfac (+40320)) =? (+8)) ([[1]])
:test ((invfac (+362880)) =? (+9)) ([[1]])
:test ((invfac (+3628800)) =? (+10)) ([[1]])
:test ((invfac (+119)) =? (-1)) ([[1]])
 
seq-a [((superfactorial 0) : ((hyperfactorial 0) : {}(alternating-factorial 0)))] <$> (iterate ++‣ (+0))
 
seq-b exponential-factorial <$> (iterate ++‣ (+0))
 
# return first 10/4 elements of both sequences
main [(take (+10) seq-a) : {}(take (+5) seq-b)]
</syntaxhighlight>
 
=={{header|C}}==
<langsyntaxhighlight lang="c">#include <math.h>
#include <stdint.h>
#include <stdio.h>
Line 187 ⟶ 504:
 
return 0;
}</langsyntaxhighlight>
{{out}}
<pre>First 9 super factorials:
Line 215 ⟶ 532:
=={{header|C++}}==
{{trans|C}}
<langsyntaxhighlight lang="cpp">#include <cmath>
#include <cstdint>
#include <iostream>
Line 334 ⟶ 651:
 
return 0;
}</langsyntaxhighlight>
{{out}}
<pre>First 9 super factorials
Line 362 ⟶ 679:
=={{header|Factor}}==
{{works with|Factor|0.99 2021-02-05}}
<langsyntaxhighlight lang="factor">USING: formatting io kernel math math.factorials math.functions
math.parser math.ranges prettyprint sequences sequences.extras ;
IN: rosetta-code.special-factorials
Line 397 ⟶ 714:
 
{ 1 2 6 24 120 720 5040 40320 362880 3628800 119 }
[ dup rf "rf(%d) = %u\n" printf ] each nl</langsyntaxhighlight>
{{out}}
<pre>
Line 429 ⟶ 746:
 
=={{header|Fermat}}==
<syntaxhighlight lang="text">Function Sf(n) = Prod<k=1, n>[k!].
 
Function H(n) = Prod<k=1, n>[k^k].
Line 449 ⟶ 766:
!!' ';
for n=1 to 10 do !!Rf(n!) od;
!!Rf(119)</langsyntaxhighlight>
 
=={{header|FreeBASIC}}==
Only goes up to H(7) due to overflow. Using a library with big int support is possible, but would only add bloat without being illustrative.
<langsyntaxhighlight lang="freebasic">function factorial(n as uinteger) as ulongint
if n<2 then return 1 else return n*factorial(n-1)
end function
Line 506 ⟶ 823:
print rf(factorial(n));" ";
next n
print rf(119)</langsyntaxhighlight>
 
=={{header|Go}}==
{{trans|Wren}}
<langsyntaxhighlight lang="go">package main
 
import (
Line 620 ⟶ 937:
fmt.Printf("%4s <- rf(%d)\n", srfact, fact)
}
}</langsyntaxhighlight>
 
{{out}}
Line 669 ⟶ 986:
none <- rf(119)
</pre>
 
=={{header|jq}}==
{{trans|Wren}}
'''Works with gojq, the Go implementation of jq'''
 
The standard version of jq does not maintain integer precision sufficiently for
some of the specific tasks (some of the hyperfactorials and the computation of 5$)
but can otherwise be used.
<syntaxhighlight lang="jq">
# for integer precision:
def power($b): . as $a | reduce range(0;$b) as $i (1; . * $a);
 
def sf:
. as $n
| if $n < 2 then 1
else {sfact: 1, fact: 1}
| reduce range (2;1+$n) as $i (.;
.fact *= $i
| .sfact *= .fact)
| .sfact
end;
 
def H:
. as $n
| if $n < 2 then 1
else
reduce range(2;1+$n) as $i ( {hfact: 1};
.hfact *= ($i | power($i)))
| .hfact
end;
 
def af:
. as $n
| if $n < 1 then 0
else {afact: 0, fact: 1, sign: (if $n%2 == 0 then -1 else 1 end)}
| reduce range(1; 1+$n) as $i (.;
.fact *= $i
| .afact += .fact * .sign
| .sign *= -1)
| .afact
end;
def ef: # recursive
. as $n
| if $n < 1 then 1
else $n | power( ($n-1)|ef )
end;
def rf:
. as $n
| {i: 0, fact: 1}
| until( .fact >= $n;
.i += 1
| .fact = .fact * .i)
| if .fact > $n then null else .i end;</syntaxhighlight>
''' The tasks:'''
<syntaxhighlight lang="jq">
"First 10 superfactorials:",
(range(0;10) | sf),
"\nFirst 10 hyperfactorials:",
(range(0; 10) | H),
"\nFirst 10 alternating factorials:",
(range(0;10) | af),
"\n\nFirst 5 exponential factorials:",
(range(0;5) | ef),
 
"\nThe number of digits in 5$ is \(5 | ef | tostring | length)",
 
"\nReverse factorials:",
( 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 119 | "\(rf) <- rf(\(.))")
</syntaxhighlight>
{{out}}
Invocation: gojq -nr -f special-factorials.jq
 
The output is essentially as for [[#Wren|Wren]] and so is not repeated here.
 
=={{header|Julia}}==
No recursion.
<langsyntaxhighlight lang="julia">superfactorial(n) = n < 1 ? 1 : mapreduce(factorial, *, 1:n)
sf(n) = superfactorial(n)
 
Line 713 ⟶ 1,108:
println(rpad(n, 10), rf(n))
end
</langsyntaxhighlight>{{out}}
<pre>
N Superfactorial Hyperfactorial Alternating Factorial Exponential Factorial
Line 748 ⟶ 1,143:
=={{header|Kotlin}}==
{{trans|C}}
<langsyntaxhighlight lang="scala">import java.math.BigInteger
import java.util.function.Function
 
Line 863 ⟶ 1,258:
testInverse(3628800)
testInverse(119)
}</langsyntaxhighlight>
{{out}}
<pre>First 10 super factorials:
Line 891 ⟶ 1,286:
=={{header|Lua}}==
{{trans|C}}
<langsyntaxhighlight lang="lua">-- n! = 1 * 2 * 3 * ... * n-1 * n
function factorial(n)
local result = 1
Line 997 ⟶ 1,392:
test_inverse(362880)
test_inverse(3628800)
test_inverse(119)</langsyntaxhighlight>
{{out}}
<pre>First 9 super factorials
Line 1,022 ⟶ 1,417:
rf(3628800 = 10
rf(119 = No Solution</pre>
 
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">ClearAll[sf, expf]
sf[n_] := BarnesG[2 + n]
expf[n_] := Power @@ Range[n, 1, -1]
 
sf /@ Range[0, 9]
Hyperfactorial /@ Range[0, 9]
AlternatingFactorial /@ Range[0, 9]
expf /@ Range[0, 4]</syntaxhighlight>
{{out}}
<pre>{1, 1, 2, 12, 288, 34560, 24883200, 125411328000, 5056584744960000, 1834933472251084800000}
{1, 1, 4, 108, 27648, 86400000, 4031078400000, 3319766398771200000, 55696437941726556979200000, 21577941222941856209168026828800000}
{0, 1, 1, 5, 19, 101, 619, 4421, 35899, 326981}
{1, 1, 2, 9, 262144}</pre>
 
=={{header|Nim}}==
{{libheader[|bignum}}
<langsyntaxhighlight Nimlang="nim">import math, strformat, strutils, sugar
import bignum
 
Line 1,089 ⟶ 1,499:
for n in [1, 2, 6, 24, 119, 120, 720, 5040, 40320, 362880, 3628800]:
let r = rf(n)
echo &"{n:7}: ", if r >= 0: &"{r:2}" else: "undefined"</langsyntaxhighlight>
 
{{out}}
Line 1,114 ⟶ 1,524:
=={{header|Perl}}==
{{libheader|ntheory}}
<langsyntaxhighlight lang="perl">use strict;
use warnings;
use feature qw<signatures say>;
Line 1,137 ⟶ 1,547:
say '5$ has ' . length(5**4**3**2) . ' digits';
say 'rf : ' . join ' ', map { rf $_ } <1 2 6 24 120 720 5040 40320 362880 3628800>;
say 'rf(119) = ' . rf(119);</langsyntaxhighlight>
{{out}}
<pre>sf : 1 1 2 12 288 34560 24883200 125411328000 5056584744960000 1834933472251084800000
Line 1,152 ⟶ 1,562:
which means sf/H/af/ef aren't usable independently as-is, but reconstitution should be easy enough
(along with somewhat saner and thread-safe routine-local vars).
<!--<langsyntaxhighlight Phixlang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
Line 1,212 ⟶ 1,622:
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Reverse factorials: %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">({</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">24</span><span style="color: #0000FF;">,</span><span style="color: #000000;">120</span><span style="color: #0000FF;">,</span><span style="color: #000000;">720</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5040</span><span style="color: #0000FF;">,</span><span style="color: #000000;">40320</span><span style="color: #0000FF;">,</span><span style="color: #000000;">362880</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3628800</span><span style="color: #0000FF;">,</span><span style="color: #000000;">119</span><span style="color: #0000FF;">},</span><span style="color: #000000;">rf</span><span style="color: #0000FF;">))})</span>
<!--</langsyntaxhighlight>-->
{{out}}
<pre>
Line 1,221 ⟶ 1,631:
Number of digits in 5$: 183,231
Reverse factorials: 0 2 3 4 5 6 7 8 9 10 undefined
</pre>
 
=={{header|PureBasic}}==
{{trans|FreeBASIC}}
<syntaxhighlight lang="purebasic">Procedure.q factorial(n.i)
If n < 2
ProcedureReturn 1
Else
ProcedureReturn n * Factorial(n - 1)
EndIf
EndProcedure
 
Procedure.q sf(n.i)
p.i = 1
For k.i = 1 To n
p = p * factorial(k)
Next k
ProcedureReturn p
EndProcedure
 
Procedure.q H(n.i)
p.i = 1
For k.i = 1 To n
p = p * Pow(k, k)
Next k
ProcedureReturn p
EndProcedure
 
Procedure.q af(n.i)
s.i = 0
For i.i = 1 To n
s = s + Pow((-1), (n-i)) * factorial(i)
Next i
ProcedureReturn s
EndProcedure
 
Procedure.q ef(n.i)
If n < 2
ProcedureReturn 1
Else
ProcedureReturn Pow(n, ef(n-1))
EndIf
EndProcedure
 
Procedure.i rf(n.i)
r.i = 0
While #True
rr.i = factorial(r)
If rr > n : ProcedureReturn -1 : EndIf
If rr = n : ProcedureReturn r : EndIf
r + 1
Wend
EndProcedure
 
OpenConsole()
PrintN("First 8 ...")
PrintN(" superfactorials hyperfactorials alternating factorials")
For n.i = 0 To 7 ;con 8 o más necesitaríamos BigInt
PrintN(RSet(Str(sf(n)),16) + " " + RSet(Str(H(n)),19) + " " + RSet(Str(af(n)),19))
Next n
 
PrintN(#CRLF$ + #CRLF$ + "First 5 exponential factorials:")
For n.i = 0 To 4
Print(Str(ef(n)) + " ")
Next n
 
PrintN(#CRLF$ + #CRLF$ + "Reverse factorials:")
For n.i = 1 To 10
PrintN(RSet(Str(rf(factorial(n))),2) + " <- rf(" + Str(factorial(n)) + ")")
Next n
PrintN(RSet(Str(rf(factorial(119))),2) + " <- rf(119)")
 
PrintN(#CRLF$ + "Press ENTER to exit"): Input()
CloseConsole()</syntaxhighlight>
 
=={{header|Python}}==
Writing a custom factorial instead of math.prod is trivial but using a standard library tool is always a nice change.
 
It also means less code :)
<syntaxhighlight lang="python">
#Aamrun, 5th October 2021
 
from math import prod
 
def superFactorial(n):
return prod([prod(range(1,i+1)) for i in range(1,n+1)])
 
def hyperFactorial(n):
return prod([i**i for i in range(1,n+1)])
 
def alternatingFactorial(n):
return sum([(-1)**(n-i)*prod(range(1,i+1)) for i in range(1,n+1)])
 
def exponentialFactorial(n):
if n in [0,1]:
return 1
else:
return n**exponentialFactorial(n-1)
def inverseFactorial(n):
i = 1
while True:
if n == prod(range(1,i)):
return i-1
elif n < prod(range(1,i)):
return "undefined"
i+=1
 
print("Superfactorials for [0,9] :")
print({"sf(" + str(i) + ") " : superFactorial(i) for i in range(0,10)})
 
print("\nHyperfactorials for [0,9] :")
print({"H(" + str(i) + ") " : hyperFactorial(i) for i in range(0,10)})
 
print("\nAlternating factorials for [0,9] :")
print({"af(" + str(i) + ") " : alternatingFactorial(i) for i in range(0,10)})
 
print("\nExponential factorials for [0,4] :")
print({str(i) + "$ " : exponentialFactorial(i) for i in range(0,5)})
 
print("\nDigits in 5$ : " , len(str(exponentialFactorial(5))))
 
factorialSet = [1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800]
 
print("\nInverse factorials for " , factorialSet)
print({"rf(" + str(i) + ") ":inverseFactorial(i) for i in factorialSet})
 
print("\nrf(119) : " + inverseFactorial(119))
</syntaxhighlight>
{{out}}
<pre>
Superfactorials for [0,9] :
{'sf(0) ': 1, 'sf(1) ': 1, 'sf(2) ': 2, 'sf(3) ': 12, 'sf(4) ': 288, 'sf(5) ': 34560, 'sf(6) ': 24883200, 'sf(7) ': 125411328000, 'sf(8) ': 5056584744960000, 'sf(9) ': 1834933472251084800000}
 
Hyperfactorials for [0,9] :
{'H(0) ': 1, 'H(1) ': 1, 'H(2) ': 4, 'H(3) ': 108, 'H(4) ': 27648, 'H(5) ': 86400000, 'H(6) ': 4031078400000, 'H(7) ': 3319766398771200000, 'H(8) ': 55696437941726556979200000, 'H(9) ': 21577941222941856209168026828800000}
 
Alternating factorials for [0,9] :
{'af(0) ': 0, 'af(1) ': 1, 'af(2) ': 1, 'af(3) ': 5, 'af(4) ': 19, 'af(5) ': 101, 'af(6) ': 619, 'af(7) ': 4421, 'af(8) ': 35899, 'af(9) ': 326981}
 
Exponential factorials for [0,4] :
{'0$ ': 1, '1$ ': 1, '2$ ': 2, '3$ ': 9, '4$ ': 262144}
 
Digits in 5$ : 183231
 
Inverse factorials for [1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800]
{'rf(1) ': 0, 'rf(2) ': 2, 'rf(6) ': 3, 'rf(24) ': 4, 'rf(120) ': 5, 'rf(720) ': 6, 'rf(5040) ': 7, 'rf(40320) ': 8, 'rf(362880) ': 9, 'rf(3628800) ': 10}
 
rf(119) : undefined
</pre>
 
=={{header|Quackery}}==
 
<syntaxhighlight lang="Quackery">
[ 1 & ] is odd ( n --> b )
 
[ 1 swap
[ 10 / dup 0 > while
dip 1+ again ]
drop ] is digitcount ( n --> n )
 
[ 1 1 rot times
[ i^ 1+ *
tuck * swap ]
drop ] is s! ( n --> n )
 
[ 1 swap times
[ i^ 1+ dup ** * ] ] is h! ( n --> n )
 
[ 0 1 rot times
[ i^ 1+ * tuck
i odd iff - else +
swap ]
drop ] is a! ( n --> n )
 
[ dup 0 = if done
dup 1 - recurse ** ] is **! ( n --> n )
 
[ this ] is undefined ( --> t )
 
[ dup 1 = iff
[ drop 0 ] done
1 swap
[ over /mod 0 != iff
[ drop undefined
swap ]
done
dip 1+
dup 1 = until
dip [ 1 - ] ]
drop ] is i! ( n --> n )
 
 
say "Superfactorials:" sp
10 times [ i^ s! echo sp ]
cr cr
say "Hyperfactorials:" sp
10 times [ i^ h! echo sp ]
cr cr
say "Alternating factorials: "
10 times [ i^ a! echo sp ]
cr cr
say "Exponential factorials: "
5 times [ i^ **! echo sp ]
cr cr
say "Number of digits in $5: "
5 **! digitcount echo
cr cr
say "Inverse factorials: "
' [ 1 2 6 24 119 120 720 5040
40320 362880 3628800 ]
witheach [ i! echo sp ]</syntaxhighlight>
 
{{out}}
 
<pre>Superfactorials: 1 1 2 12 288 34560 24883200 125411328000 5056584744960000 1834933472251084800000
 
Hyperfactorials: 1 1 4 108 27648 86400000 4031078400000 3319766398771200000 55696437941726556979200000 21577941222941856209168026828800000
 
Alternating factorials: 0 1 1 5 19 101 619 4421 35899 326981
 
Exponential factorials: 0 1 2 9 262144
 
Number of digits in $5: 183231
 
Inverse factorials: 0 2 3 4 undefined 5 6 7 8 9 10
</pre>
 
=={{header|Raku}}==
<syntaxhighlight lang="raku" perl6line>sub postfix:<!> ($n) { [*] 1 .. $n }
sub postfix:<$> ($n) { [R**] 1 .. $n }
 
Line 1,243 ⟶ 1,879:
 
say 'rf : ', map &rf, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800;
say 'rf(119) = ', rf(119).raku;</langsyntaxhighlight>
{{out}}
<pre>
Line 1,255 ⟶ 1,891:
 
=={{header|REXX}}==
<syntaxhighlight lang="rexx">
<lang rexx>/*REXX program to compute some special factorials: superfactorials, hyperfactorials,*/
/* REXX program to calculate Special factorials */
/*───────────────────────────────────── alternating factorials, exponential factorials.*/
numeric digits 100 /*allows humongous results to be shown.*/
call hdr 'super'; do j=0 to 9; $= $ sf(j); end; call tell
call hdr 'hyper'; do j=0 to 9; $= $ hf(j); end; call tell
call hdr 'alternating '; do j=0 to 9; $= $ af(j); end; call tell
call hdr 'exponential '; do j=0 to 5; $= $ ef(j); end; call tell
@= 'the number of decimal digits in the exponential factorial of '
say @ 5 " is:"; $= ' 'commas( efn( ef(5) ) ); call tell
@= 'the inverse factorial of'
do j=1 for 10; say @ right(!(j), 8) " is: " rf(!(j))
end /*j*/
say @ right(119, 8) " is: " rf(119)
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
!: procedure; parse arg x; != 1; do #=2 to x; != ! * #; end; return !
af: procedure; parse arg x; if x==0 then return 0; prev= 0; call af!; return !
af!: do #=1 for x; != !(#) - prev; prev= !; end; return !
commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?
ef: procedure; parse arg x; if x==0 | x==1 then return 1; return x**ef(x-1)
efn: procedure; parse arg x; numeric digits 9; x= x; parse var x 'E' d; return d+1
sf: procedure; parse arg x; != 1; do #=2 to x; != ! * !(#); end; return !
hf: procedure; parse arg x; != 1; do #=2 to x; != ! * #**#; end; return !
rf: procedure; parse arg x; do #=0 until f>=x; f=!(#); end; return rfr()
rfr: if x==f then return #; ?= 'undefined'; return ?
hdr: parse arg ?,,$; say 'the first ten '?"factorials:"; return
tell: say substr($, 2); say; $=; return</lang>
{{out|output|text=&nbsp; when using the internal default input:}}
<pre>
the first 10 superfactorials:
1 1 2 12 288 34560 24883200 125411328000 5056584744960000 1834933472251084800000
 
numeric digits 35
the first 10 hyperfactorials:
1 1 4 108 27648 86400000 4031078400000 3319766398771200000 55696437941726556979200000 21577941222941856209168026828800000
 
line = "superfactorials 0-9: "
the first 10 alternating factorials:
do n = 0 to 9
0 1 1 5 19 101 619 4421 35899 326981
line = line superfactorial(n)
end
say line
 
line = "hyperfactorials 0-9: "
the first 5 exponential factorials:
1do 1n 2= 90 262144to 9
line = line hyperfactorial(n)
end
say line
 
line = "alternating factorials 0-9:"
the number of decimal digits in the exponential factorial of 5 is:
do n = 0 to 9
183,231
line = line alternatingfactorial(n)
end
say line
 
line = "exponential factorials 0-4:"
the inverse factorial of 1 is: 0
do n = 0 to 4
the inverse factorial of 2 is: 2
line = line exponentialfactorial(n)
the inverse factorial of 6 is: 3
end
the inverse factorial of 24 is: 4
say line
the inverse factorial of 120 is: 5
 
the inverse factorial of 720 is: 6
thesay inverse"exponential factorial of5: 5040 is: 7",
length(format(exponentialfactorial(5), , , 0)) "digits"
the inverse factorial of 40320 is: 8
 
the inverse factorial of 362880 is: 9
theline = "inverse factorialfactorials: of 3628800 is: 10"
numbers = "1 2 6 24 120 720 5040 40320 362880 3628800 119"
the inverse factorial of 119 is: undefined
do i = 1 to words(numbers)
line = line inversefactorial(word(numbers,i))
end
say line
 
return
 
 
superfactorial: procedure
parse arg n
sf = 1
f = 1
do k = 1 to n
f = f * k
sf = sf * f
end
return sf
 
hyperfactorial: procedure
parse arg n
hf = 1
do k = 1 to n
hf = hf * k ** k
end
return hf
 
alternatingfactorial: procedure
parse arg n
af = 0
f = 1
do i = 1 to n
f = f * i
af = af + (-1) ** (n - i) * f
end
return af
 
exponentialfactorial: procedure
parse arg n
ef = 1
do i = 1 to n
ef = i ** ef
end
return ef
 
inversefactorial: procedure
parse arg f
n = 1
do i = 2 while n < f
n = n * i
end
if n = f then
if i > 2 then
return i - 1
else
return 0
else
return "undefined"
</syntaxhighlight>
{{out}}
<pre>
superfactorials 0-9: 1 1 2 12 288 34560 24883200 125411328000 5056584744960000 1834933472251084800000
hyperfactorials 0-9: 1 1 4 108 27648 86400000 4031078400000 3319766398771200000 55696437941726556979200000 21577941222941856209168026828800000
alternating factorials 0-9: 0 1 1 5 19 101 619 4421 35899 326981
exponential factorials 0-4: 1 1 2 9 262144
exponential factorial 5: 183231 digits
inverse factorials: 0 2 3 4 5 6 7 8 9 10 undefined
</pre>
 
=={{header|RPL}}==
Super factorial:
≪ 1 1 ROT '''FOR''' j j FACT * '''NEXT'''
≫ '<span style="color:blue">SFACT</span>' STO
Hyper factorial:
≪ 1 1 ROT '''FOR''' j j DUP ^ * '''NEXT'''
≫ '<span style="color:blue">HFACT</span>' STO
Alternating factorial:
≪ → n
≪ 0 '''IF''' n '''THEN'''
1 n '''FOR''' j -1 n j - ^ j FACT * + '''NEXT'''
≫ ≫ '<span style="color:blue">AFACT</span>' STO
Exponential factorial:
≪ '''IF''' DUP '''THEN'''
DUP 1 - 1 '''FOR''' j j ^ -1 '''STEP'''
'''ELSE''' NOT '''END'''
≫ '<span style="color:blue">EFACT</span>' STO
Inverse factorial - this function actually inverses Gamma(x+1), so its result is always defined:
≪ 'FACT(x)' OVER - 'x' ROT LN ROOT 'x' PURGE
≫ '<span style="color:blue">IFACT</span>' STO
 
≪ { } 0 9 FOR j j <span style="color:blue">SFACT</span> + NEXT ≫ EVAL
≪ { } 0 9 FOR j j <span style="color:blue">HFACT</span> + NEXT ≫ EVAL
≪ { } 0 9 FOR j j <span style="color:blue">AFACT</span> + NEXT ≫ EVAL
≪ { } 0 4 FOR j j <span style="color:blue">EFACT</span> + NEXT ≫ EVAL
3628800 <span style="color:blue">IFACT</span>
119 <span style="color:blue">IFACT</span>
{{out}}
<pre>
6: { 1 1 2 12 288 34560 24883200 125411328000 5.05658474496E+15 1.83493347225E+21 }
5: { 1 1 4 108 27648 86400000 4.0310784E+12 3.31976639877E+18 5.56964379417E+25 2.15779412229E+34 }
4: { 0 1 1 5 19 101 619 4421 35899 326981 }
3: { 0 1 2 9 262144 }
2: 10
1: 4.99509387149
</pre>
 
=={{header|Seed7}}==
<langsyntaxhighlight lang="seed7">$ include "seed7_05.s7i";
include "bigint.s7i";
 
Line 1,406 ⟶ 2,124:
writeln("invFactorial(" <& n <& ") = " <& invFactorial(n));
end for;
end func;</langsyntaxhighlight>
{{out}}
<pre>
Line 1,432 ⟶ 2,150:
invFactorial(3628800) = 10
invFactorial(119) = -1
</pre>
 
=={{header|Sidef}}==
<syntaxhighlight lang="ruby">func sf(n) { 1..n -> prod {|k| k! } }
func H(n) { 1..n -> prod {|k| k**k } }
func af(n) { 1..n -> sum {|k| (-1)**(n-k) * k! } }
func ef(n) { 1..n -> reduce({|a,b| b**a }, 1) }
 
func factorial_valuation(n,p) {
(n - n.sumdigits(p)) / (p-1)
}
 
func p_adic_inverse (p, k) {
 
var n = (k * (p - 1))
 
while (factorial_valuation(n, p) < k) {
n -= (n % p)
n += p
}
 
return n
}
 
func rf(f) {
 
return nil if (f < 0)
return 0 if (f <= 1)
 
var t = valuation(f, 2) || return nil
var n = p_adic_inverse(2, t)
var d = factor(n + 1)[-1]
 
if (f.valuation(d) == factorial_valuation(n+1, d)) {
++n
}
 
for p in (primes(2, n)) {
var v = factorial_valuation(n, p)
f.valuation(p) == v || return nil
f /= p**v
}
 
(f == 1) ? n : nil
}
 
say ('sf : ', 10.of(sf).join(' '))
say ('H : ', 10.of(H).join(' '))
say ('af : ', 10.of(af).join(' '))
say ('ef : ', 5.of(ef).join(' '))
 
say "ef(5) has #{ef(5).len} digits"
 
say ('rf : ', [1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800].map(rf))
say ('rf(119) = ', rf(119) \\ 'nil')
say ('rf is defined for: ', 8.by { defined(rf(_)) }.join(', ' ) + ', ...')</syntaxhighlight>
{{out}}
<pre>
sf : 1 1 2 12 288 34560 24883200 125411328000 5056584744960000 1834933472251084800000
H : 1 1 4 108 27648 86400000 4031078400000 3319766398771200000 55696437941726556979200000 21577941222941856209168026828800000
af : 0 1 1 5 19 101 619 4421 35899 326981
ef : 1 1 2 9 262144
ef(5) has 183231 digits
rf : [0, 2, 3, 4, 5, 6, 7, 8, 9, 10]
rf(119) = nil
rf is defined for: 0, 1, 2, 6, 24, 120, 720, 5040, ...
</pre>
 
Line 1,438 ⟶ 2,222:
{{libheader|Wren-fmt}}
We've little choice but to use BigInt here as Wren can only deal natively with integers up to 2^53.
<langsyntaxhighlight ecmascriptlang="wren">import "./big" for BigInt
import "./fmt" for Fmt
 
var sf = Fn.new { |n|
Line 1,506 ⟶ 2,290:
System.print("Reverse factorials:")
var facts = [1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 119]
for (fact in facts) Fmt.print("$4s <- rf($d)", rf.call(fact), fact)</langsyntaxhighlight>
 
{{out}}
Marvin
55

edits

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