Left factorials: Difference between revisions
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{{FormulaeEntry|page=https://formulae.org/?script=examples/Left_factorials}}
'''Solution'''
The following function calculates the left factorial directly by its definition:
[[File:Fōrmulæ - Left factorials 08.png]]
However, the following is much faster:
[[File:Fōrmulæ - Left factorials 01.png]]
'''Test case 1. Showing left factorials from zero to ten'''
[[File:Fōrmulæ - Left factorials 02.png]]
[[File:Fōrmulæ - Left factorials 03.png]]
'''Test case 2. Showing left factorials from 20 to 110, by tens'''
[[File:Fōrmulæ - Left factorials 04.png]]
[[File:Fōrmulæ - Left factorials 05.png|858px]]
'''Test case 3. Showing length of left factorials, from 1,000 to 10,000 by thousands'''
[[File:Fōrmulæ - Left factorials 06.png]]
[[File:Fōrmulæ - Left factorials 07.png]]
=={{header|Frink}}==
Line 2,291 ⟶ 2,319:
31678
35656</pre>
=={{header|Maxima}}==
<syntaxhighlight lang="maxima">
l_factorial(n):=sum(k!,k,0,n-1)$
/* Test cases */
makelist(l_factorial(i),i,0,10);
makelist(l_factorial(i),i,20,110,10);
</syntaxhighlight>
{{out}}
<pre>
[0,1,2,4,10,34,154,874,5914,46234,409114]
[128425485935180314,9157958657951075573395300940314,20935051082417771847631371547939998232420940314,620960027832821612639424806694551108812720525606160920420940314,141074930726669571000530822087000522211656242116439949000980378746128920420940314,173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314,906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314,16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314,942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314,145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314]
</pre>
=={{header|Nim}}==
Line 3,240 ⟶ 3,284:
next
</syntaxhighlight>
=={{header|RPL}}==
For small values of n, the built-in number type can support the job:
≪ '''IF''' DUP '''THEN''' 0 1 ROT 1 - '''FOR''' k k FACT + '''NEXT END''' ≫ ‘<span style="color:blue">LFACT</span>’ STO
≪ { } 0 10 '''FOR''' n n <span style="color:blue">LFACT</span> + '''NEXT''' ≫ EVAL
'''Output:'''
1: { 0 1 2 4 10 34 154 874 5914 46234 409114 }
For 20 through 110 (inclusive) by tens, we need a kind of BigInt library if using a RPL version from the previous century. <code>ADDbig</code> and <code>MULbig</code> are defined at [[Long multiplication#RPL|Long multiplication]].
Calculation is optimized by using the recursive formula: <code>!(n+1) = !n * n + 1</code>
≪ "1" SWAP
'''WHILE''' DUP 1 > '''REPEAT'''
1 - DUP →STR ROT <span style="color:blue">MULbig</span> "1" <span style="color:blue"><span style="color:blue">ADDbig</span></span> SWAP
'''END''' DROP
≫ ‘<span style="color:blue">LFACTbig</span>’ STO
≪ 20 110 '''FOR''' n n <span style="color:blue">LFACTbig</span> 10 '''STEP''' ≫ EVAL
{{out}}
<pre>
10: "128425485935180314"
9: "9157958657951075573395300940314"
8: "20935051082417771847631371547939998232420940314"
7: "620960027832821612639424806694551108812720525606160920420940314"
6: "141074930726669571000530822087000522211656242116439949000980378746128920420940314"
5: "173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314"
4: "906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314"
3: "16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314"
2: "942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314"
1: "145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314"
</pre>
=={{header|Ruby}}==
Line 4,030 ⟶ 4,105:
{{libheader|Wren-fmt}}
{{libheader|Wren-big}}
<syntaxhighlight lang="
import "./big" for BigInt
var lfacts = List.filled(12, BigInt.zero)
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