Special factorials: Difference between revisions

=={{header|Nim}}==

{{libheader[bignum}}

<lang Nim>import math, strformat, strutils, sugar

import bignum

proc pow(a: int; n: Int): Int =

## Compute a^n for "n" big integer.

var n = n

var a = newInt(a)

if a > 0:

result = newInt(1)

# Start with Int values for "n".

while not n.isZero:

if (n and 1) != 0:

result *= a

n = n shr 1

a *= a

func sf(n: Natural): Int =

result = newInt(1)

for i in 2..n:

result *= fac(i)

func hf(n: Natural): Int =

result = newInt(1)

for i in 2..n:

result *= pow(i, uint(i))

func af(n: Natural): Int =

result = newInt(0)

var m = (n and 1) shl 1 - 1

for i in 1..n:

result += m * fac(i)

m = -m

func ef(n: Natural): Int =

result = newInt(1)

for k in 2..n:

result = pow(k, result)

func rf(n: int | Int): int =

if n == 1: return 0

result = 1

var p = newInt(1)

while p < n:

inc result

p *= result

if p > n: result = -1

let sfs = collect(newSeq, for n in 0..9: sf(n))

echo &"First {sfs.len} superfactorials: ", sfs.join(" ")

let hfs = collect(newSeq, for n in 0..9: hf(n))

echo &"First {hfs.len} hyperfactorials: ", hfs.join(" ")

let afs = collect(newSeq, for n in 0..9: af(n))

echo &"First {afs.len} alternating factorials: ", afs.join(" ")

let efs = collect(newSeq, for n in 0..4: ef(n))

echo &"First {efs.len} exponential factorials: ", efs.join(" ")

echo "\nNumber of digits of ef(5): ", len($ef(5))

echo "\nReverse factorials:"

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"</lang>

{{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>