Special factorials: Difference between revisions
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=={{header|REXX}}== |
=={{header|REXX}}== |
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<syntaxhighlight lang="rexx"> |
<syntaxhighlight lang="rexx"> |
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/* REXX program to calculate Special factorials */ |
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/*───────────────────────────────────── alternating factorials, exponential factorials.*/ |
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numeric digits 1000 /*allows humongous results to be shown.*/ |
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call hdr 'super'; do j=0 to 9; $= $ sf(j); end; call tell |
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call hdr 'hyper'; do j=0 to 9; $= $ hf(j); end; call tell |
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call hdr 'alternating '; do j=0 to 9; $= $ af(j); end; call tell |
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call hdr 'exponential '; do j=0 to 5; $= $ ef(j); end; call tell |
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@= 'the number of decimal digits in the exponential factorial of ' |
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say @ 5 " is:"; $= ' 'commas( efn( ef(5) ) ); call tell |
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@= 'the inverse factorial of' |
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do j=1 for 10; say @ right(!(j), 8) " is: " rf(!(j)) |
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end /*j*/ |
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say @ right(119, 8) " is: " rf(119) |
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exit 0 /*stick a fork in it, we're all done. */ |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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!: procedure; parse arg x; != 1; do #=2 to x; != ! * #; end; return ! |
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af: procedure; parse arg x; if x==0 then return 0; prev= 0; call af!; return ! |
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af!: do #=1 for x; != !(#) - prev; prev= !; end; return ! |
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commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ? |
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ef: procedure; parse arg x; if x==0 | x==1 then return 1; return x**ef(x-1) |
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efn: procedure; parse arg x; numeric digits 9; x= x; parse var x 'E' d; return d+1 |
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sf: procedure; parse arg x; != 1; do #=2 to x; != ! * !(#); end; return ! |
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hf: procedure; parse arg x; != 1; do #=2 to x; != ! * #**#; end; return ! |
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rf: procedure; parse arg x; do #=0 until f>=x; f=!(#); end; return rfr() |
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rfr: if x==f then return #; ?= 'undefined'; return ? |
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hdr: parse arg ?,,$; say 'the first ten '?"factorials:"; return |
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tell: say substr($, 2); say; $=; return</syntaxhighlight> |
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{{out|output|text= when using the internal default input:}} |
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<pre> |
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the first 10 superfactorials: |
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1 1 2 12 288 34560 24883200 125411328000 5056584744960000 1834933472251084800000 |
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numeric digits 35 |
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the first 10 hyperfactorials: |
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1 1 4 108 27648 86400000 4031078400000 3319766398771200000 55696437941726556979200000 21577941222941856209168026828800000 |
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line = "superfactorials 0-9: " |
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the first 10 alternating factorials: |
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do n = 0 to 9 |
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0 1 1 5 19 101 619 4421 35899 326981 |
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line = line superfactorial(n) |
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end |
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say line |
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line = "hyperfactorials 0-9: " |
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the first 5 exponential factorials: |
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do n = 0 to 9 |
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line = line hyperfactorial(n) |
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end |
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say line |
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line = "alternating factorials 0-9:" |
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the number of decimal digits in the exponential factorial of 5 is: |
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do n = 0 to 9 |
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183,231 |
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line = line alternatingfactorial(n) |
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end |
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say line |
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line = "exponential factorials 0-4:" |
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the inverse factorial of 1 is: 0 |
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do n = 0 to 4 |
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the inverse factorial of 2 is: 2 |
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line = line exponentialfactorial(n) |
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the inverse factorial of 6 is: 3 |
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end |
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the inverse factorial of 24 is: 4 |
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say line |
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the inverse factorial of 120 is: 5 |
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the inverse factorial of 720 is: 6 |
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say "exponential factorial 5: ", |
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length(format(exponentialfactorial(5), , , 0)) "digits" |
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the inverse factorial of 40320 is: 8 |
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the inverse factorial of 362880 is: 9 |
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line = "inverse factorials: " |
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numbers = "1 2 6 24 120 720 5040 40320 362880 3628800 119" |
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the inverse factorial of 119 is: undefined |
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do i = 1 to words(numbers) |
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line = line inversefactorial(word(numbers,i)) |
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end |
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say line |
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return |
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superfactorial: procedure |
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parse arg n |
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sf = 1 |
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f = 1 |
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do k = 1 to n |
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f = f * k |
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sf = sf * f |
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end |
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return sf |
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hyperfactorial: procedure |
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parse arg n |
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hf = 1 |
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do k = 1 to n |
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hf = hf * k ** k |
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end |
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return hf |
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alternatingfactorial: procedure |
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parse arg n |
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af = 0 |
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f = 1 |
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do i = 1 to n |
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f = f * i |
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af = af + (-1) ** (n - i) * f |
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end |
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return af |
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exponentialfactorial: procedure |
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parse arg n |
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ef = 1 |
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do i = 1 to n |
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ef = i ** ef |
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end |
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return ef |
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inversefactorial: procedure |
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parse arg f |
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n = 1 |
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do i = 2 while n < f |
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n = n * i |
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end |
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if n = f then |
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if i > 2 then |
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return i - 1 |
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else |
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return 0 |
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else |
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return "undefined" |
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</syntaxhighlight> |
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{{out}} |
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<pre> |
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superfactorials 0-9: 1 1 2 12 288 34560 24883200 125411328000 5056584744960000 1834933472251084800000 |
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hyperfactorials 0-9: 1 1 4 108 27648 86400000 4031078400000 3319766398771200000 55696437941726556979200000 21577941222941856209168026828800000 |
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alternating factorials 0-9: 0 1 1 5 19 101 619 4421 35899 326981 |
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exponential factorials 0-4: 1 1 2 9 262144 |
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exponential factorial 5: 183231 digits |
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inverse factorials: 0 2 3 4 5 6 7 8 9 10 undefined |
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</pre> |
</pre> |
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