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Left factorials: Difference between revisions
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!10000 has 35656 digits
</pre>
=={{header|Lambdatalk}}==
<lang scheme>
2.1) defining !n
{def MEM {A.new 1}}
{def MEM.get {lambda {:n} {A.get :n {MEM}}}}
{def MEM.set! {lambda {:n :val} {A.get :n {A.set! :n :val {MEM}}}}}
{def MEM.undef? {lambda {:n} {W.equal? {A.get :n {MEM}} undefined} }}
{def !n
{def n!
{lambda {:n}
{if {MEM.undef? :n}
then {MEM.set! :n {long_mult :n {MEM.get {- :n 1}}}}
else {MEM.get :n} }} }
{lambda {:n}
{S.reduce long_add 1 {S.map n! {S.serie 1 {- :n 1}}}}}}
2.2) the task
A) computing !n from 2 to 10 takes about 4ms
{S.map {lambda {:n} {br}!n(:n) = {!n :n}}
{S.serie 2 10}}
->
!n(2) = 2
!n(3) = 4
!n(4) = 10
!n(5) = 34
!n(6) = 154
!n(7) = 874
!n(8) = 5914
!n(9) = 46234
!n(10) = 409114
B) computing !n from 20 to 110 with step 10 takes about 25ms
{S.map {lambda {:n} {br}!n(:n) = {!n :n}}
{S.serie 20 110 10}}
->
!n(20) = 128425485935180314
!n(30) = 9157958657951075573395300940314
!n(40) = 20935051082417771847631371547939998232420940314
!n(50) = 620960027832821612639424806694551108812720525606160920420940314
!n(60) = 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!n(70) = 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!n(80) = 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!n(90) = 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!n(100) = 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!n(110) = 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
C) computing !n from 1000 to 1000 with step 1000 takes about 87 seconds
1) compute n! from 1 to 10000 and store in MEM // about 86 seconds
{def foo {!n 10000}} -> foo
2) take 10 values from MEM // about 1ms
{S.map {lambda {:n}
{br}Digits of !n(:n) = {W.length {A.get {- :n 1} {MEM}}}}
{S.serie 1000 10000 1000}}
->
Digits of !n(1000) = 2565
Digits of !n(2000) = 5733
Digits of !n(3000) = 9128
Digits of !n(4000) = 12670
Digits of !n(5000) = 16322
Digits of !n(6000) = 20062
Digits of !n(7000) = 23875
Digits of !n(8000) = 27749
Digits of !n(9000) = 31678
Digits of !n(10000) = 35656
</lang>
=={{header|Lua}}==
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