Left factorials: Difference between revisions
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{{
[[Category:Mathematics]]
<!-- Left Factorial !-->
'''Left factorials''', <big><big>!n</big></big>, may refer to either ''subfactorials'' or to ''factorial sums'';
<br>the same notation can be confusingly seen being used for the two different definitions.
Sometimes, ''subfactorials'' (also known as ''derangements'') may use any of the notations:
:::::::* <big><big> <b> <span style="font-family:serif">!''n''`</span> </b> </big></big>
:::::::* <big><big> <b> <span style="font-family:serif">!''n''</span> </b> </big></big>
:::::::* <big><big> <b> <span style="font-family:serif">''n''¡</span> </b> </big></big>
(It may not be visually obvious, but the last example uses an upside-down exclamation mark.)
This Rosetta Code task will be using this formula (''factorial sums'') for '''left factorial''':
<big><big>
::::: <math> !n = \sum_{k=0}^{n-1} k! </math>
</big></big>
:::: where
<big><big>
::::: <math>!0 = 0</math>
</big></big>
;Task
Display the left factorials for:
* zero through ten (inclusive)
* 20 through 110 (inclusive) by tens
<br>
Display the length (in decimal digits) of the left factorials for:
* 1,000
;Also see:
* The
* The MathWorld entry:
* The MathWorld entry: [http://mathworld.wolfram.com/FactorialSums.html factorial sums]
* The MathWorld entry: [http://mathworld.wolfram.com/Subfactorial.html subfactorial]
;Related task:
* [http://rosettacode.org/wiki/Permutations/Derangements permutations/derangements (subfactorials)]
<br><br>
=={{header|11l}}==
{{trans|D}}
<syntaxhighlight lang="11l">F left_fact(n)
BigInt result = 0
BigInt factorial = 1
L(i) 1 .. n
result += factorial
factorial *= i
R result
print(‘First 11 left factorials:’)
print((0..10).map(i -> left_fact(i)))
print("\n20 through 110 (inclusive) by tens:")
L(i) (20..110).step(10)
print(left_fact(i))
print("\nDigits in 1,000 through 10,000 by thousands:")
print((1000..10000).step(1000).map(i -> String(left_fact(i)).len))</syntaxhighlight>
{{out}}
<pre>
First 11 left factorials:
[0, 1, 2, 4, 10, 34, 154, 874, 5914, 46234, 409114]
20 through 110 (inclusive) by tens:
128425485935180314
9157958657951075573395300940314
20935051082417771847631371547939998232420940314
620960027832821612639424806694551108812720525606160920420940314
141074930726669571000530822087000522211656242116439949000980378746128920420940314
173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
Digits in 1,000 through 10,000 by thousands:
[2565, 5733, 9128, 12670, 16322, 20062, 23875, 27749, 31678, 35656]
</pre>
=={{header|ALGOL 68}}==
Uses the Algol 68G LONG LONG INT type which has programmer definable precision.
{{works with|ALGOL 68G|Any - tested with release 2.8.3.win32}}
<syntaxhighlight lang="algol68"># set the precision of LONG LONG INT - large enough for !n up to ! 10 000 #
PR precision 36000 PR
# stores left factorials in an array #
# we calculate the left factorials, storing their values in the "values" array #
# if step is <= 1, we store we store every left factorial, otherwise we store !x when x MOD step = 0 #
# note this means values[ 0 ] is always !0 #
PROC get left factorials = ( REF[]LONG LONG INT values, INT step )VOID:
BEGIN
INT store position := LWB values;
INT max values := UPB values;
LONG LONG INT result := 0;
LONG LONG INT factorial k := 1;
FOR k FROM 0
WHILE
IF IF step <= 1 THEN TRUE ELSE k MOD step = 0 FI THEN
values[ store position ] := result;
store position +:= 1
FI;
store position <= max values
DO
result +:= factorial k;
factorial k *:= ( k + 1 )
OD
END # get left factorials # ;
# returns the number of digits in n #
OP DIGITCOUNT = ( LONG LONG INT n )INT:
BEGIN
INT result := 1;
LONG LONG INT v := ABS n;
WHILE v > 100 000 000 DO
result +:= 8;
v OVERAB 100 000 000
OD;
WHILE v > 10 DO
result +:= 1;
v OVERAB 10
OD;
result
END # DIGITCOUNT # ;
BEGIN
print( ( "!n for n = 0(1)10", newline ) );
[ 0 : 10 ]LONG LONG INT v;
get left factorials( v, 1 );
FOR i FROM 0 TO UPB v DO
print( ( whole( v[ i ], 0 ), newline ) )
OD
END;
BEGIN
print( ( "!n for n = 20(10)110", newline ) );
[ 0 : 11 ]LONG LONG INT v;
get left factorials( v, 10 );
FOR i FROM 2 TO UPB v DO
print( ( whole( v[ i ], 0 ), newline ) )
OD
END;
BEGIN
print( ( "digit counts of !n for n = 1000(1000)10 000", newline ) );
[ 0 : 10 ]LONG LONG INT v;
get left factorials( v, 1 000 );
FOR i FROM 1 TO UPB v DO
print( ( whole( DIGITCOUNT v[ i ], 0 ), newline ) )
OD
END
</syntaxhighlight>
{{out}}
<pre>
!n for n = 0(1)10
0
1
2
4
10
34
154
874
5914
46234
409114
!n for n = 20(10)110
128425485935180314
9157958657951075573395300940314
20935051082417771847631371547939998232420940314
620960027832821612639424806694551108812720525606160920420940314
141074930726669571000530822087000522211656242116439949000980378746128920420940314
173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
digit counts of !n for n = 1000(1000)10 000
2565
5733
9128
12670
16322
20062
23875
27749
31678
35656
</pre>
=={{header|Arturo}}==
<syntaxhighlight lang="arturo">lfactorial: function [n][
if zero? n -> return 0
fold 0..dec n [x y] -> x + factorial y
]
print "First eleven:"
0..10 | map => lfactorial
| print
print "\n20th through 110th by tens:"
r: range.step: 10 20 110
r | map => lfactorial
| loop => print
print "\nDigits in 1,000th through 10,000th by thousands:"
r: range.step: 1000 1000 10000
r | map'x -> size ~"|lfactorial x|"
| print</syntaxhighlight>
{{out}}
<pre>First eleven:
0 1 2 4 10 34 154 874 5914 46234 409114
20th through 110th by tens:
128425485935180314
9157958657951075573395300940314
20935051082417771847631371547939998232420940314
620960027832821612639424806694551108812720525606160920420940314
141074930726669571000530822087000522211656242116439949000980378746128920420940314
173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
Digits in 1,000th through 10,000th by thousands:
2565 5733 9128 12670 16322 20062 23875 27749 31678 35656</pre>
=={{header|AWK}}==
Old posix AWK doesn't support computing with large numbers. However modern gawk can use GMP if the flag -M is used.
<syntaxhighlight lang="awk">
#!/usr/bin/gawk -Mf
function left_factorial(num) {
result=0
adder=1
if (num==0) return(0)
for (k = 1; k <=num; k++) {
result = result + adder
adder = adder * k
}
return(result)
}
BEGIN {
for (i = 0; i <= 10; i++) {
print "!" i " = " left_factorial(i)
}
for (i = 20; i<= 110; i+=10) {
print "!" i " = " left_factorial(i)
}
for (i = 1000; i<= 10000; i+=1000) {
print "!" i " has " length(left_factorial(i)) " digits"
}
}
</syntaxhighlight>
{{out}}
<pre>
!0 = 0
!1 = 1
!2 = 2
!3 = 4
!4 = 10
!5 = 34
!6 = 154
!7 = 874
!8 = 5914
!9 = 46234
!10 = 409114
!20 = 128425485935180314
!30 = 9157958657951075573395300940314
!40 = 20935051082417771847631371547939998232420940314
!50 = 620960027832821612639424806694551108812720525606160920420940314
!60 = 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70 = 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80 = 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90 = 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100 = 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!110 = 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
!1000 has 2565 digits
!2000 has 5733 digits
!3000 has 9128 digits
!4000 has 12670 digits
!5000 has 16322 digits
!6000 has 20062 digits
!7000 has 23875 digits
!8000 has 27749 digits
!9000 has 31678 digits
!10000 has 35656 digits
</pre>
=={{header|BBC BASIC}}==
{{works with|BBC BASIC for Windows}}
Use the 'Mapm' library.
<syntaxhighlight lang="bbcbasic"> INSTALL @lib$+"BB4WMAPMLIB" : PROCMAPM_Init : MAPM_Dec%=200
Result$="0" : A$="1"
FOR I%=0 TO 10000
IF I% Result$=FNMAPM_Add(Result$,A$) : A$=FNMAPM_Multiply(A$,STR$I%)
IF I% < 111 IF I% MOD 10 = 0 OR I% < 11 PRINT "!";I% " = " FNMAPM_FormatDec(Result$,0)
IF I% > 999 IF I% MOD 1000 = 0 PRINT "!";I% " has " LENFNMAPM_FormatDec(Result$,0) " digits"
NEXT
END</syntaxhighlight>
{{out}}
<pre>
!0 = 0
!1 = 1
!2 = 2
!3 = 4
!4 = 10
!5 = 34
!6 = 154
!7 = 874
!8 = 5914
!9 = 46234
!10 = 409114
!20 = 128425485935180314
!30 = 9157958657951075573395300940314
!40 = 20935051082417771847631371547939998232420940314
!50 = 620960027832821612639424806694551108812720525606160920420940314
!60 = 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70 = 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80 = 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90 = 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100 = 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!110 = 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
!1000 has 2565 digits
!2000 has 5733 digits
!3000 has 9128 digits
!4000 has 12670 digits
!5000 has 16322 digits
!6000 has 20062 digits
!7000 has 23875 digits
!8000 has 27749 digits
!9000 has 31678 digits
!10000 has 35656 digits</pre>
=={{header|Bracmat}}==
{{trans|D}}
<syntaxhighlight lang="bracmat">( ( leftFact
= result factorial i
. 0:?result
& 1:?factorial
& 0:?i
& whl
' ( !i+1:~>!arg:?i
& !factorial+!result:?result
& !factorial*!i:?factorial
)
& !result
)
& ( iterate
= from to step c fun
. !arg:(?from.?to.?step.?fun)
& !from+-1*!step:?from
& !step:?c
& whl
' ( !step+!from:~>!to:?from
& !fun$(leftFact$!from)
)
&
)
& out$"First 11 left factorials:"
& iterate$(0.10.1.out)
& out$"
20 through 110 (inclusive) by tens:"
& iterate$(20.110.10.out)
& out$"
Digits in 1,000 through 10,000 by thousands:"
& iterate
$ ( 1000
. 10000
. 1000
. (=L.@(!arg:? [?L)&out$!L)
)
)</syntaxhighlight>
{{out}}
<pre>First 11 left factorials:
0
1
2
4
10
34
154
874
5914
46234
409114
20 through 110 (inclusive) by tens:
128425485935180314
9157958657951075573395300940314
20935051082417771847631371547939998232420940314
620960027832821612639424806694551108812720525606160920420940314
141074930726669571000530822087000522211656242116439949000980378746128920420940314
173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
Digits in 1,000 through 10,000 by thousands:
2565
5733
9128
12670
16322
20062
23875
27749
31678
35656</pre>
=={{header|C}}==
{{libheader|GMP}}
<syntaxhighlight lang="c">
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <gmp.h>
void mpz_left_fac_ui(mpz_t rop, unsigned long op)
{
mpz_t t1;
mpz_init_set_ui(t1, 1);
mpz_set_ui(rop, 0);
size_t i;
for (i = 1; i <= op; ++i) {
mpz_add(rop, rop, t1);
mpz_mul_ui(t1, t1, i);
}
mpz_clear(t1);
}
size_t mpz_digitcount(mpz_t op)
{
/* mpz_sizeinbase can not be trusted to give accurate base 10 length */
char *t = mpz_get_str(NULL, 10, op);
size_t ret = strlen(t);
free(t);
return ret;
}
int main(void)
{
mpz_t t;
mpz_init(t);
size_t i;
for (i = 0; i <= 110; ++i) {
if (i <= 10 || i % 10 == 0) {
mpz_left_fac_ui(t, i);
gmp_printf("!%u = %Zd\n", i, t);
}
}
for (i = 1000; i <= 10000; i += 1000) {
mpz_left_fac_ui(t, i);
printf("!%u has %u digits\n", i, mpz_digitcount(t));
}
mpz_clear(t);
return 0;
}
</syntaxhighlight>
{{out}}
<pre>
!0 = 0
!1 = 1
!2 = 2
!3 = 4
!4 = 10
!5 = 34
!6 = 154
!7 = 874
!8 = 5914
!9 = 46234
!10 = 409114
!20 = 128425485935180314
!30 = 9157958657951075573395300940314
!40 = 20935051082417771847631371547939998232420940314
!50 = 620960027832821612639424806694551108812720525606160920420940314
!60 = 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70 = 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80 = 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90 = 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100 = 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!110 = 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
!1000 has 2565 digits
!2000 has 5733 digits
!3000 has 9128 digits
!4000 has 12670 digits
!5000 has 16322 digits
!6000 has 20062 digits
!7000 has 23875 digits
!8000 has 27749 digits
!9000 has 31678 digits
!10000 has 35656 digits
</pre>
=={{header|C sharp|C#}}==
<syntaxhighlight lang="csharp">
using System;
using System.Numerics;
namespace LeftFactorial
{
class Program
{
static void Main(string[] args)
{
for (int i = 0; i <= 10; i++)
{
Console.WriteLine(string.Format("!{0} = {1}", i, LeftFactorial(i)));
}
for (int j = 20; j <= 110; j += 10)
{
Console.WriteLine(string.Format("!{0} = {1}", j, LeftFactorial(j)));
}
for (int k = 1000; k <= 10000; k += 1000)
{
Console.WriteLine(string.Format("!{0} has {1} digits", k, LeftFactorial(k).ToString().Length));
}
Console.ReadKey();
}
private static BigInteger Factorial(int number)
{
BigInteger accumulator = 1;
for (int factor = 1; factor <= number; factor++)
{
accumulator *= factor;
}
return accumulator;
}
private static BigInteger LeftFactorial(int n)
{
BigInteger result = 0;
for (int i = 0; i < n; i++)
{
result += Factorial(i);
}
return result;
}
}
}
</syntaxhighlight>
{{out}}
<pre>
!0 = 0
!1 = 1
!2 = 2
!3 = 4
!4 = 10
!5 = 34
!6 = 154
!7 = 874
!8 = 5914
!9 = 46234
!10 = 409114
!20 = 128425485935180314
!30 = 9157958657951075573395300940314
!40 = 20935051082417771847631371547939998232420940314
!50 = 620960027832821612639424806694551108812720525606160920420940314
!60 = 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70 = 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80 = 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90 = 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100 = 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!110 = 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
!1000 has 2565 digits
!2000 has 5733 digits
!3000 has 9128 digits
!4000 has 12670 digits
!5000 has 16322 digits
!6000 has 20062 digits
!7000 has 23875 digits
!8000 has 27749 digits
!9000 has 31678 digits
!10000 has 35656 digits
</pre>
Faster Implementation
<syntaxhighlight lang="csharp">
using System;
using System.Numerics;
namespace LeftFactorial
{
class Program
{
static void Main(string[] args)
{
for (int i = 0; i <= 10; i++)
{
Console.WriteLine(string.Format("!{0} : {1}", i, LeftFactorial(i)));
}
for (int j = 20; j <= 110; j += 10)
{
Console.WriteLine(string.Format("!{0} : {1}", j, LeftFactorial(j)));
}
for (int k = 1000; k <= 10000; k += 1000)
{
Console.WriteLine(string.Format("!{0} : has {1} digits", k, LeftFactorial(k).ToString().Length));
}
Console.ReadKey();
}
private static BigInteger LeftFactorial(int n)
{
BigInteger result = 0;
BigInteger subResult = 1;
for (int i = 0; i < n; i++)
{
if (i == 0)
{
subResult = 1;
}
else
{
subResult *= i;
}
result += subResult;
}
return result;
}
}
}
</syntaxhighlight>
=={{header|C++}}==
<syntaxhighlight lang="cpp">
#include <vector>
#include <string>
#include <algorithm>
#include <iostream>
#include <sstream>
using namespace std;
#if 1 // optimized for 64-bit architecture
typedef unsigned long usingle;
typedef unsigned long long udouble;
const int word_len = 32;
#else // optimized for 32-bit architecture
typedef unsigned short usingle;
typedef unsigned long udouble;
const int word_len = 16;
#endif
class bignum {
private:
// rep_.size() == 0 if and only if the value is zero.
// Otherwise, the word rep_[0] keeps the least significant bits.
vector<usingle> rep_;
public:
explicit bignum(usingle n = 0) { if (n > 0) rep_.push_back(n); }
bool equals(usingle n) const {
if (n == 0) return rep_.empty();
if (rep_.size() > 1) return false;
return rep_[0] == n;
}
bignum add(usingle addend) const {
bignum result(0);
udouble sum = addend;
for (size_t i = 0; i < rep_.size(); ++i) {
sum += rep_[i];
result.rep_.push_back(sum & (((udouble)1 << word_len) - 1));
sum >>= word_len;
}
if (sum > 0) result.rep_.push_back((usingle)sum);
return result;
}
bignum add(const bignum& addend) const {
bignum result(0);
udouble sum = 0;
size_t sz1 = rep_.size();
size_t sz2 = addend.rep_.size();
for (size_t i = 0; i < max(sz1, sz2); ++i) {
if (i < sz1) sum += rep_[i];
if (i < sz2) sum += addend.rep_[i];
result.rep_.push_back(sum & (((udouble)1 << word_len) - 1));
sum >>= word_len;
}
if (sum > 0) result.rep_.push_back((usingle)sum);
return result;
}
bignum multiply(usingle factor) const {
bignum result(0);
udouble product = 0;
for (size_t i = 0; i < rep_.size(); ++i) {
product += (udouble)rep_[i] * factor;
result.rep_.push_back(product & (((udouble)1 << word_len) - 1));
product >>= word_len;
}
if (product > 0)
result.rep_.push_back((usingle)product);
return result;
}
void divide(usingle divisor, bignum& quotient, usingle& remainder) const {
quotient.rep_.resize(0);
udouble dividend = 0;
remainder = 0;
for (size_t i = rep_.size(); i > 0; --i) {
dividend = ((udouble)remainder << word_len) + rep_[i - 1];
usingle quo = (usingle)(dividend / divisor);
remainder = (usingle)(dividend % divisor);
if (quo > 0 || i < rep_.size())
quotient.rep_.push_back(quo);
}
reverse(quotient.rep_.begin(), quotient.rep_.end());
}
};
ostream& operator<<(ostream& os, const bignum& x);
ostream& operator<<(ostream& os, const bignum& x) {
string rep;
bignum dividend = x;
bignum quotient;
usingle remainder;
while (true) {
dividend.divide(10, quotient, remainder);
rep += (char)('0' + remainder);
if (quotient.equals(0)) break;
dividend = quotient;
}
reverse(rep.begin(), rep.end());
os << rep;
return os;
}
bignum lfact(usingle n);
bignum lfact(usingle n) {
bignum result(0);
bignum f(1);
for (usingle k = 1; k <= n; ++k) {
result = result.add(f);
f = f.multiply(k);
}
return result;
}
int main() {
for (usingle i = 0; i <= 10; ++i) {
cout << "!" << i << " = " << lfact(i) << endl;
}
for (usingle i = 20; i <= 110; i += 10) {
cout << "!" << i << " = " << lfact(i) << endl;
}
for (usingle i = 1000; i <= 10000; i += 1000) {
stringstream ss;
ss << lfact(i);
cout << "!" << i << " has " << ss.str().size()
<< " digits." << endl;
}
}
</syntaxhighlight>
{{out}}
<pre>
!0 = 0
!1 = 1
!2 = 2
!3 = 4
!4 = 10
!5 = 34
!6 = 154
!7 = 874
!8 = 5914
!9 = 46234
!10 = 409114
!20 = 128425485935180314
!30 = 9157958657951075573395300940314
!40 = 20935051082417771847631371547939998232420940314
!50 = 620960027832821612639424806694551108812720525606160920420940314
!60 = 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70 = 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80 = 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90 = 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100 = 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!110 = 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
!1000 has 2565 digits.
!2000 has 5733 digits.
!3000 has 9128 digits.
!4000 has 12670 digits.
!5000 has 16322 digits.
!6000 has 20062 digits.
!7000 has 23875 digits.
!8000 has 27749 digits.
!9000 has 31678 digits.
!10000 has 35656 digits.
</pre>
===Faster alternative===
{{libheader|GMP}}
<syntaxhighlight lang="cpp">#include <iostream>
#include <gmpxx.h>
template <typename integer>
class left_factorial_generator {
public:
integer next() {
integer result = next_;
next_ += factorial_;
factorial_ *= n_++;
return result;
}
private:
unsigned int n_ = 1;
integer factorial_ = 1;
integer next_ = 0;
};
int main() {
left_factorial_generator<mpz_class> lf;
int i = 0;
std::cout << "Left factorials 0 through 10:\n";
for (; i <= 10; ++i)
std::cout << "!" << i << " = " << lf.next() << '\n';
std::cout << "Left factorials 20 through 110, by tens:\n";
for (; i <= 110; ++i) {
auto n = lf.next();
if (i % 10 == 0)
std::cout << "!" << i << " = " << n << '\n';
}
std::cout << "Lengths of left factorials 1000 through 10000, by thousands:\n";
for (; i <= 10000; ++i) {
auto n = lf.next();
if (i % 1000 == 0)
std::cout << "length of !" << i << " = " << n.get_str().size() << '\n';
}
return 0;
}</syntaxhighlight>
{{out}}
<pre>
Left factorials 0 through 10:
!0 = 0
!1 = 1
!2 = 2
!3 = 4
!4 = 10
!5 = 34
!6 = 154
!7 = 874
!8 = 5914
!9 = 46234
!10 = 409114
Left factorials 20 through 110, by tens:
!20 = 128425485935180314
!30 = 9157958657951075573395300940314
!40 = 20935051082417771847631371547939998232420940314
!50 = 620960027832821612639424806694551108812720525606160920420940314
!60 = 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70 = 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80 = 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90 = 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100 = 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!110 = 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
Lengths of left factorials 1000 through 10000, by thousands:
length of !1000 = 2565
length of !2000 = 5733
length of !3000 = 9128
length of !4000 = 12670
length of !5000 = 16322
length of !6000 = 20062
length of !7000 = 23875
length of !8000 = 27749
length of !9000 = 31678
length of !10000 = 35656
</pre>
=={{header|Clojure}}==
<syntaxhighlight lang="lisp">(ns left-factorial
(:gen-class))
(defn left-factorial [n]
" Compute by updating the state [fact summ] for each k, where k equals 1 to n
Update is next state is [k*fact (summ+k)"
(second
(reduce (fn [[fact summ] k]
[(*' fact k) (+ summ fact)])
[1 0] (range 1 (inc n)))))
(doseq [n (range 11)]
(println (format "!%-3d = %5d" n (left-factorial n))))
(doseq [n (range 20 111 10)]
(println (format "!%-3d = %5d" n (biginteger (left-factorial n)))))
(doseq [n (range 1000 10001 1000)]
(println (format "!%-5d has %5d digits" n (count (str (biginteger (left-factorial n)))))))
</syntaxhighlight>
{{Output}}
<pre>
!0 = 0
!1 = 1
!2 = 2
!3 = 4
!4 = 10
!5 = 34
!6 = 154
!7 = 874
!8 = 5914
!9 = 46234
!10 = 409114
!20 = 128425485935180314
!30 = 9157958657951075573395300940314
!40 = 20935051082417771847631371547939998232420940314
!50 = 620960027832821612639424806694551108812720525606160920420940314
!60 = 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70 = 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80 = 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90 = 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100 = 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!110 = 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
!1000 has 2565 digits
!2000 has 5733 digits
!3000 has 9128 digits
!4000 has 12670 digits
!5000 has 16322 digits
!6000 has 20062 digits
!7000 has 23875 digits
!8000 has 27749 digits
!9000 has 31678 digits
!10000 has 35656 digits
</pre>
=={{header|Common Lisp}}==
<syntaxhighlight lang="lisp">
(defun fact (n)
(reduce #'* (loop for i from 1 to n collect i)))
(defun left-fac (n)
(reduce #'+ (loop for i below n collect (fact i))))
(format t "0 -> 10~&")
(format t "~a~&" (loop for i upto 10 collect (left-fac i)))
(format t "20 -> 110 by 10~&")
(format t "~{~a~&~}" (loop for i from 20 upto 110 by 10 collect (left-fac i)))
(format t "1000 -> 10000 by 1000~&")
(format t "~{~a digits~&~}" (loop for i from 1000 upto 10000 by 1000 collect (length (format nil "~a" (left-fac i)))))
</syntaxhighlight>
{{out}}
<pre>
0 -> 10
(0 1 2 4 10 34 154 874 5914 46234 409114)
20 -> 110 by 10
128425485935180314
9157958657951075573395300940314
20935051082417771847631371547939998232420940314
620960027832821612639424806694551108812720525606160920420940314
141074930726669571000530822087000522211656242116439949000980378746128920420940314
173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
1000 -> 10000 by 1000
2565 digits
5733 digits
9128 digits
12670 digits
16322 digits
20062 digits
23875 digits
27749 digits
31678 digits
35656 digits
</pre>
=={{header|D}}==
<
BigInt leftFact(in uint n) pure nothrow /*
BigInt result = 0, factorial = 1;
foreach (immutable i; 1 .. n + 1) {
Line 36 ⟶ 1,017:
iota(20, 111, 10).map!leftFact);
writefln("\nDigits in 1,000 through 10,000 by thousands:\n%s",
iota(
}</
{{out}}
<pre>First 11 left factorials:
Line 57 ⟶ 1,038:
[2565, 5733, 9128, 12670, 16322, 20062, 23875, 27749, 31678, 35656]</pre>
=={{header|
We use the 'bigint' library and memoization : (remember 'function).
<syntaxhighlight lang="lisp">
(lib 'bigint)
(define (!n n)
(if (zero? n) 0
(+ (!n (1- n)) (factorial (1- n)))))
(remember '!n)
</syntaxhighlight>
Output:
<syntaxhighlight lang="lisp">
(for ((n 11)) (printf "!n(%d) = %d" n (!n n)))
(for ((n (in-range 20 120 10))) (printf "!n(%d) = %d" n (!n n)))
!n(0) = 0
!n(1) = 1
!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
!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
; Compute !n : 5 seconds
(for ((n (in-range 1000 10001 500))) (!n n) (writeln n))
; Display results : 12 seconds
(for ((n (in-range 1000 10001 1000))) (printf "Digits of !n(%d) = %d" n (number-length (!n n))))
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
</syntaxhighlight>
=={{header|Elixir}}==
<syntaxhighlight lang="elixir">defmodule LeftFactorial do
def calc(0), do: 0
def calc(n) do
{result, _factorial} = Enum.reduce(1..n, {0, 1}, fn i,{res, fact} ->
{res + fact, fact * i}
end)
result
end
end
Enum.each(0..10, fn i ->
IO.puts "!#{i} = #{LeftFactorial.calc(i)}"
end)
Enum.each(Enum.take_every(20..110, 10), fn i ->
IO.puts "!#{i} = #{LeftFactorial.calc(i)}"
end)
Enum.each(Enum.take_every(1000..10000, 1000), fn i ->
digits = LeftFactorial.calc(i) |> to_char_list |> length
IO.puts "!#{i} has #{digits} digits"
end)</syntaxhighlight>
{{out}}
<pre>
!0 = 0
!1 = 1
!2 = 2
!3 = 4
!4 = 10
!5 = 34
!6 = 154
!7 = 874
!8 = 5914
!9 = 46234
!10 = 409114
!20 = 128425485935180314
!30 = 9157958657951075573395300940314
!40 = 20935051082417771847631371547939998232420940314
!50 = 620960027832821612639424806694551108812720525606160920420940314
!60 = 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70 = 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80 = 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90 = 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100 = 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!110 = 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
!1000 has 2565 digits
!2000 has 5733 digits
!3000 has 9128 digits
!4000 has 12670 digits
!5000 has 16322 digits
!6000 has 20062 digits
!7000 has 23875 digits
!8000 has 27749 digits
!9000 has 31678 digits
!10000 has 35656 digits
</pre>
=={{header|F_Sharp|F#}}==
===The Functıon===
<syntaxhighlight lang="fsharp">
// Generate Sequence of Left Factorials: Nigel Galloway, March 5th., 2019.
let LF=Seq.unfold(fun (Σ,n,g)->Some(Σ,(Σ+n,n*g,g+1I))) (0I,1I,1I)
</syntaxhighlight>
===The Tasks===
;Display LF 0..10
<syntaxhighlight lang="fsharp">
LF |> Seq.take 11|>Seq.iter(printfn "%A")
</syntaxhighlight>
{{out}}
<pre>
0
1
2
4
10
34
154
874
5914
46234
409114
</pre>
;Display LF 20..110 in steps of 10
<syntaxhighlight lang="fsharp">
LF |> Seq.skip 20 |> Seq.take 91 |> Seq.iteri(fun n g->if n%10=0 then printfn "%A" g)
</syntaxhighlight>
{{out}}
<pre>
128425485935180314
9157958657951075573395300940314
20935051082417771847631371547939998232420940314
620960027832821612639424806694551108812720525606160920420940314
141074930726669571000530822087000522211656242116439949000980378746128920420940314
173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
</pre>
;Display the length (in decimal digits) of LF 1000 .. 10000 in steps of 1000
<syntaxhighlight lang="fsharp">
LF |> Seq.skip 1000 |> Seq.take 9001 |> Seq.iteri(fun n g->if n%1000=0 then printfn "%d" (string g).Length)
</syntaxhighlight>
{{out}}
<pre>
2565
5733
9128
12670
16322
20062
23875
27749
31678
35656
</pre>
=={{header|Factor}}==
{{works with|Factor|0.98}}
<syntaxhighlight lang="text">USING: formatting fry io kernel math math.factorials
math.functions math.parser math.ranges sequences ;
IN: rosetta-code.left-factorials
: left-factorial ( n -- m ) <iota> [ n! ] map-sum ;
: print-left-factorials ( seq quot -- )
'[
dup left-factorial @
[ number>string "!" prepend ] dip
"%6s %-6d\n" printf
] each nl ; inline
: digit-count ( n -- count ) log10 >integer 1 + ;
: part1 ( -- ) 11 <iota> [ ] print-left-factorials ;
: part2 ( -- ) 20 110 10 <range> [ ] print-left-factorials ;
: part3 ( -- )
"Number of digits for" print
1,000 10,000 1,000 <range>
[ digit-count ] print-left-factorials ;
: main ( -- ) part1 part2 part3 ;
MAIN: main</syntaxhighlight>
{{out}}
<pre>
!0 0
!1 1
!2 2
!3 4
!4 10
!5 34
!6 154
!7 874
!8 5914
!9 46234
!10 409114
!20 128425485935180314
!30 9157958657951075573395300940314
!40 20935051082417771847631371547939998232420940314
!50 620960027832821612639424806694551108812720525606160920420940314
!60 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!110 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
Number of digits for
!1000 2565
!2000 5733
!3000 9128
!4000 12670
!5000 16322
!6000 20062
!7000 23875
!8000 27749
!9000 31678
!10000 35656
</pre>
=={{header|Forth}}==
{{works with|Gforth 0.7.3}}
This solution inspired by the Fortran one.
<syntaxhighlight lang="forth">36000 CONSTANT #DIGITS \ Enough for !10000
CREATE S #DIGITS ALLOT S #DIGITS ERASE VARIABLE S#
CREATE F #DIGITS ALLOT F #DIGITS ERASE VARIABLE F#
1 F C! 1 F# ! \ F = 1 = 0!
\ "Bignums": represented by two cells on the stack:
\ 1) An address pointing to the least-significant unit
\ 2) An integer size representing the number of character-size units
: mod/ /mod swap ;
: B+ ( addr u addr' u' -- u'') \ Add the second "bignum" into the first
over + >R -rot over + >R ( addr' addr R:end' R:end)
swap >R 0 over R> ( addr 0 addr addr' R:end' R:end)
\ 0: Assume second has equal or more digits, as in our problem
BEGIN over R@ < WHILE \ 1: add all digits from S
dup >R C@ swap dup >R C@ ( addr c a a' R:end' R:end R:addr'* R:addr*)
+ + 10 mod/ R@ C! R> 1+ R> 1+
REPEAT R> drop ( addr c addr* addr'* R:end')
BEGIN dup R@ < WHILE \ 2: add any remaining digits from F
dup >R C@ swap >R ( addr c a' R:end' R:addr'* R:addr*)
+ 10 mod/ R@ C! R> 1+ R> 1+
REPEAT R> drop drop ( addr c addr*)
BEGIN over WHILE \ 3: add any carry digits
>R 10 mod/ ( addr m d R:addr*) R@ C! R> 1+
REPEAT rot - nip ; \ calculate travel distance, discard 0 carry
: B* ( addr u u' -- u'') \ Multiply "bignum" inplace by U'
0 2swap over >R dup >R bounds ( u' 0 addr+u addr R:addr R:u)
DO ( u' c) over I C@ * + 10 mod/ I C! LOOP
nip R> BEGIN ( c u) over WHILE \ insert carry, may have multiple digits
>R 10 mod/ R@ swap R> R@ + ( m u d addr+u R:addr) C! 1+
REPEAT nip R> ( u'' addr) drop ;
: .B ( addr u) over + BEGIN 1- \ print bignum
dup C@ [char] 0 + EMIT over over >=
UNTIL drop drop ;
: .!n 0 <# #s [char] ! hold #> 6 over - spaces type space ;
: REPORT ( n)
dup 10 <= over dup 20 111 within swap 10 mod 0= and or
IF .!n [char] = emit space S S# @ .B cr
ELSE dup 1000 mod 0=
IF .!n ." has " S# @ . ." digits" cr
ELSE drop THEN
THEN ;
: GO 0 REPORT
1 BEGIN dup 10000 <=
WHILE
S S# @ F F# @ B+ S# !
dup REPORT
dup F F# @ rot B* F# !
1+ REPEAT drop ;</syntaxhighlight>
{{out}}
<pre>$ gforth left-factorials.fs -e 'GO bye'
!0 = 0
!1 = 1
!2 = 2
!3 = 4
!4 = 10
!5 = 34
!6 = 154
!7 = 874
!8 = 5914
!9 = 46234
!10 = 409114
!20 = 128425485935180314
!30 = 9157958657951075573395300940314
!40 = 20935051082417771847631371547939998232420940314
!50 = 620960027832821612639424806694551108812720525606160920420940314
!60 = 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70 = 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80 = 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90 = 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100 = 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!110 = 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
!1000 has 2565 digits
!2000 has 5733 digits
!3000 has 9128 digits
!4000 has 12670 digits
!5000 has 16322 digits
!6000 has 20062 digits
!7000 has 23875 digits
!8000 has 27749 digits
!9000 has 31678 digits
!10000 has 35656 digits</pre>
=={{header|Fortran}}==
First, to see how far INTEGER*8 arithmetic can reach. This is the largest size likely available, even though the syntax could easily allow INTEGER*2400 or the like. The F90 MODULE protocol is used simply to avoid the tedium of declaring the type of the function FACT(n) in all routines invoking it, though at the cost of typing out the required blather. Otherwise, this would be acceptable to older Fortran compilers, except for the appending of name information on END statements.
The function names are used as ordinary variables within the function while building the result; earlier compilers often did not allow such usage or produced incorrect code in certain cases. Ordinary integer variables are used since it is obvious that their range will not be exercised before the function result overflows, even with sixty-four bit integers for them. With two's complement arithmetic, negative numbers can appear in spite of the mathematics involved only being able to generate positive numbers, but this relies on the "sign bit" happening to become set and cannot be regarded as a definite check. Only a proper test such as the IF OVERFLOW found in First Fortran (1958) will do, but the modernisers have long abandoned this detail.
Because this calculation won't get far, no attempt is made to save intermediate results (such as the factorial numbers) nor develop the results progressively even though they are to be produced in sequence. Each result is computed from the start, as per the specified formulae.
For output, to have the exclamation mark precede the number without a gap, format sequence <code>"!",I0</code> will do, the <code>I0</code> format code being standardised in F90. However, this produces varying-length digit sequences, which will mean that the following output changes position likewise. Rather than use say <code>I20</code> for the result and have a wide gap, code <code>I0</code> will do, and to start each such number in the same place, the code <code>T6</code> will start it in column six, far enough along not to clash with the first number on the line, given that it will not be large. <syntaxhighlight lang="fortran"> MODULE LAIROTCAF !Calculates "left factorials".
CONTAINS !The usual suspects.
INTEGER*8 FUNCTION FACT(N) !Factorial, the ordinary.
INTEGER N !The number won't ever get far.
INTEGER I !The stepper.
FACT = 1 !Here we go.
DO I = 2,N !Does nothing for N < 2.
FACT = FACT*I !Perhaps this overflows.
IF (FACT.LE.0) STOP "Factorial: Overflow!" !Two's complement arithmetic.
END DO !No longer any IF OVERFLOW tests.
END FUNCTION FACT !Simple enough.
INTEGER*8 FUNCTION LFACT(N) !Left factorial.
INTEGER N !This number won't get far either.
INTEGER K !A stepper.
LFACT = 0 !Here we go.
DO K = 0,N - 1 !Apply the definition.
LFACT = LFACT + FACT(K) !Perhaps this overflows.
IF (LFACT.LE.0) STOP "Lfact: Overflow!" !Unreliable test.
END DO !On to the next step in the summation.
END FUNCTION LFACT !No attempts at saving effort.
END MODULE LAIROTCAF !Just the minimum.
PROGRAM POKE
USE LAIROTCAF
INTEGER I
WRITE (6,*) "Left factorials, from 0 to 10..."
DO I = 0,10
WRITE (6,1) I,LFACT(I)
1 FORMAT ("!",I0,T6,I0)
END DO
WRITE (6,*) "Left factorials, from 20 to 110 by tens..."
DO I = 20,110,10
WRITE (6,1) I,LFACT(I)
END DO
END</syntaxhighlight>
Output:
<pre>
Left factorials, from 0 to 10...
!0 0
!1 1
!2 2
!3 4
!4 10
!5 34
!6 154
!7 874
!8 5914
!9 46234
!10 409114
Left factorials, from 20 to 110 by tens...
!20 128425485935180314
Factorial: Overflow!
</pre>
Obviously, one could proceed using the services of some collection of "bignum" routines, and then the code would merely depict their uses for this problem. Since the task is to produce consecutive values, all that need be done is to maintain a S value holding the accumulated sum, and a F value for the successive factorials to be added into S. The only difficulty is to arrange the proper phasing of the starting values so that the calculation will work. Since only one multiply and one addition is needed per step, explicit code might as well be used, as follows: <syntaxhighlight lang="fortran">Calculates "left factorials", in sequence, and shows some.
INTEGER ENUFF,BASE !Some parameters.
PARAMETER (BASE = 10, ENUFF = 40000) !This should do.
INTEGER LF,F(ENUFF),LS,S(ENUFF) !Big numbers in digits F(1:LF), S(1:LS)
INTEGER N !A stepper.
INTEGER L !Locates digits.
INTEGER C !A carry for arithmetic.
INTEGER MSG !I/O unit number.
MSG = 6 !Standard output.
LF = 1; F(1) = 1 !Set F = 1 = 0!
LS = 1; S(1) = 0 !Set S = 0 = !0
WRITE (MSG,1) 0,0 !Pre-emptive first result.
1 FORMAT ("!",I0,T6,666I1) !This will do for reasonable sizes.
10 DO N = 1,10000 !Step away.
Commence the addition of F to S.
20 C = 0 !Clear the carry.
DO L = 1,MIN(LF,LS) !First, both S and F have low-order digits.
C = S(L) + F(L) + C !So, a three-part addition.
S(L) = MOD(C,BASE) !Place the digit.
C = C/BASE !Carry to the next digit up.
END DO !Ends with L and C important.
Careful. L fingers the next digit up, and C is to carry in to that digit.
IF (LF.GT.LS) THEN !Has F more digits than S?
DO L = L,LF !Yes. Continue adding, with leading zero digits from S.
C = F(L) + C !Thus.
LS = LS + 1 !Another digit for S.
S(LS) = MOD(C,BASE) !Place.
C = C/BASE !Carry to the next digit up.
END DO !Continue to the end of F.
END IF !Either way, F has been added in.
Continue carrying, with C for digit L.
DO WHILE(C .GT. 0) !Extend the carry into S.
IF (L.LE.LS) THEN !If F had fewer digits than S,
C = C + S(L) !S digits await.
ELSE !Otherwise,
LS = LS + 1 !Extend S.
END IF !C is ready.
S(L) = MOD(C,BASE) !Place it.
C = C/BASE !The carry for the next digit up.
L = L + 1 !Locate it.
END DO !Perhaps a multi-digit carry.
Contemplate what to do with the current S.
IF (N.LE.10) THEN !First selection: !N for 0 to 10.
WRITE (MSG,1) N,S(LS:1:-1) !Show the value. Digits from the high-order end down.
ELSE IF (20.LE.N .AND. N.LE.110) THEN !Second selection: for 20 to 110,
IF (MOD(N,10).EQ.0) WRITE (MSG,1) N,S(LS:1:-1) !Show only every tenth.
ELSE !Third selection
IF (MOD(N,1000).EQ.0) WRITE (MSG,21) N,LS !Show only the number of digits.
21 FORMAT ("!",I0," has ",I0," digits.") !Which is why BASE is only 10.
END IF !So much for the selection of output.
Calculate the next factorial, ready for the next one up.
C = 0 !Start a multiply.
DO L = 1,LF !Step up the digits to produce N! in F.
C = F(L)*N + C !A digit.
F(L) = MOD(C,BASE) !Place.
C = C/BASE !Extract the carry.
END DO !On to the next digit.
DO WHILE(C .GT. 0) !While any carry remains,
LF = LF + 1 !Add another digit to F.
IF (LF.GT.ENUFF) STOP "F overflow!" !Perhaps not.
F(LF) = MOD(C,BASE) !The digit.
C = C/BASE !Carry to the next digit up.
END DO !If there is one, as when N > BASE.
END DO !On to the next result.
END !Ends with a new factorial that won't be used.</syntaxhighlight>
Output: achieved in a few seconds. A larger BASE would give a faster calculation, but would complicate the digit count.
<pre>
!0 0
!1 1
!2 2
!3 4
!4 10
!5 34
!6 154
!7 874
!8 5914
!9 46234
!10 409114
!20 128425485935180314
!30 9157958657951075573395300940314
!40 20935051082417771847631371547939998232420940314
!50 620960027832821612639424806694551108812720525606160920420940314
!60 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!110 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
!1000 has 2565 digits.
!2000 has 5733 digits.
!3000 has 9128 digits.
!4000 has 12670 digits.
!5000 has 16322 digits.
!6000 has 20062 digits.
!7000 has 23875 digits.
!8000 has 27749 digits.
!9000 has 31678 digits.
!10000 has 35656 digits.
</pre>
=={{header|FreeBASIC}}==
{{trans|C}}
{{libheader|GMP}}
<syntaxhighlight lang="freebasic">' FB 1.05.0 Win64
#include "gmp.bi"
Sub leftFactorial(rop As __mpz_struct, op As ULong)
Dim As __mpz_struct t1
mpz_init_set_ui(@t1, 1)
mpz_set_ui(@rop, 0)
For i As ULong = 1 To op
mpz_add(@rop, @rop, @t1)
mpz_mul_ui(@t1, @t1, i)
Next
mpz_clear(@t1)
End Sub
Function digitCount(op As __mpz_struct) As ULong
Dim As ZString Ptr t = mpz_get_str(0, 10, @op)
Dim As ULong ret = Len(*t)
Deallocate(t)
Return ret
End Function
Dim As __mpz_struct t
mpz_init(@t)
For i As ULong = 0 To 110
If i <= 10 OrElse i Mod 10 = 0 Then
leftFactorial(t, i)
gmp_printf(!"!%u = %Zd\n", i, @t)
End If
Next
Print
For i As ULong = 1000 To 10000 Step 1000
leftFactorial(t, i)
Print "!"; Str(i); " has "; digitCount(t); " digits"
Next
mpz_clear(@t)
Print
Print "Press any key to quit"
Sleep</syntaxhighlight>
{{out}}
<pre>
!0 = 0
!1 = 1
!2 = 2
!3 = 4
!4 = 10
!5 = 34
!6 = 154
!7 = 874
!8 = 5914
!9 = 46234
!10 = 409114
!20 = 128425485935180314
!30 = 9157958657951075573395300940314
!40 = 20935051082417771847631371547939998232420940314
!50 = 620960027832821612639424806694551108812720525606160920420940314
!60 = 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70 = 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80 = 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90 = 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100 = 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!110 = 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
!1000 has 2565 digits
!2000 has 5733 digits
!3000 has 9128 digits
!4000 has 12670 digits
!5000 has 16322 digits
!6000 has 20062 digits
!7000 has 23875 digits
!8000 has 27749 digits
!9000 has 31678 digits
!10000 has 35656 digits
</pre>
=={{header|Fōrmulæ}}==
{{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}}==
Frink contains efficient algorithms for calculating and caching factorials and this program will work for arbitrarily-large numbers.
<syntaxhighlight lang="frink">leftFactorial[n] :=
{
sum = 0
for k = 0 to n-1
sum = sum + k!
return sum
}
println["Zero through ten"]
for n = 0 to 10
println["$n\t" + leftFactorial[n]]
println["\n20 through 110"]
for n = 20 to 110 step 10
println["$n\t" + leftFactorial[n]]
println["\nlength of 1000 through 10000"]
for n = 1000 to 10000 step 1000
println["$n has " + length[toString[leftFactorial[n]]] + " digits"]</syntaxhighlight>
{{out}}
<pre>
Zero through ten
0 0
1 1
2 2
3 4
4 10
5 34
6 154
7 874
8 5914
9 46234
10 409114
20 through 110
20 128425485935180314
30 9157958657951075573395300940314
40 20935051082417771847631371547939998232420940314
50 620960027832821612639424806694551108812720525606160920420940314
60 141074930726669571000530822087000522211656242116439949000980378746128920420940314
70 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
80 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
90 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
100 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
110 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
length of 1000 through 10000
1000 has 2565 digits
2000 has 5733 digits
3000 has 9128 digits
4000 has 12670 digits
5000 has 16322 digits
6000 has 20062 digits
7000 has 23875 digits
8000 has 27749 digits
9000 has 31678 digits
10000 has 35656 digits
</pre>
=={{header|Go}}==
<syntaxhighlight lang="go">package main
import (
"fmt"
"math/big"
)
func main() {
fmt.Print("!0 through !10: 0")
one := big.NewInt(1)
n := big.NewInt(1)
f := big.NewInt(1)
l := big.NewInt(1)
next := func() { f.Mul(f, n); l.Add(l, f); n.Add(n, one) }
for ; ; next() {
fmt.Print(" ", l)
if n.Int64() == 10 {
break
}
}
fmt.Println()
for {
for i := 0; i < 10; i++ {
next()
}
fmt.Printf("!%d: %d\n", n, l)
if n.Int64() == 110 {
break
}
}
fmt.Println("Lengths of !1000 through !10000 by thousands:")
for i := 110; i < 1000; i++ {
next()
}
for {
fmt.Print(" ", len(l.String()))
if n.Int64() == 10000 {
break
}
for i := 0; i < 1000; i++ {
next()
}
}
fmt.Println()
}</syntaxhighlight>
{{out}}
<pre>
!0 through !10: 0 1 2 4 10 34 154 874 5914 46234 409114
!20: 128425485935180314
!30: 9157958657951075573395300940314
!40: 20935051082417771847631371547939998232420940314
!50: 620960027832821612639424806694551108812720525606160920420940314
!60: 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70: 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80: 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90: 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100: 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!110: 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
Lengths of !1000 through !10000 by thousands:
2565 5733 9128 12670 16322 20062 23875 27749 31678 35656
</pre>
=={{header|Haskell}}==
<syntaxhighlight lang="haskell">leftFact :: [Integer]
leftFact = scanl (+) 0 fact
fact :: [Integer]
fact = scanl (*) 1 [1 ..]
main :: IO ()
main =
mapM_
putStrLn
[ "0 ~ 10:"
, show $ (leftFact !!) <$> [0 .. 10]
, ""
, "20 ~ 110 by tens:"
, unlines $ show . (leftFact !!) <$> [20,30 .. 110]
, ""
, "length of 1,000 ~ 10,000 by thousands:"
, show $ length . show . (leftFact !!) <$> [1000,2000 .. 10000]
, ""
]</syntaxhighlight>
{{Out}}
<pre>0 ~ 10:
[0,1,2,4,10,34,154,874,5914,46234,409114]
20 ~ 110 by tens:
128425485935180314
9157958657951075573395300940314
20935051082417771847631371547939998232420940314
620960027832821612639424806694551108812720525606160920420940314
141074930726669571000530822087000522211656242116439949000980378746128920420940314
173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
length of 1,000 ~ 10,000 by thousands:
[2565,5733,9128,12670,16322,20062,23875,27749,31678,35656]</pre>
=={{header|Icon}} and {{header|Unicon}}==
{{trans|D}}
The following works in both languages:
<syntaxhighlight lang="text">procedure main()
every writes(lfact(0 | !10)," ")
write()
write()
every write(lfact(20 to 110 by 10))
write()
every writes(*lfact(1000 to 10000 by 1000)," ")
write()
end
procedure lfact(n)
r := 0
f := 1
every (i := !n, r +:= .f, f *:= .i)
return r
end</syntaxhighlight>
{{out}}
<pre>
->lfact
0 1 2 4 10 34 154 874 5914 46234 409114
128425485935180314
9157958657951075573395300940314
20935051082417771847631371547939998232420940314
620960027832821612639424806694551108812720525606160920420940314
141074930726669571000530822087000522211656242116439949000980378746128920420940314
173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
2565 5733 9128 12670 16322 20062 23875 27749 31678 35656
->
</pre>
Line 77 ⟶ 1,851:
This could be made more efficient (in terms of machine time), is there a practical application for this? The more efficient machine approach would require a more specialized interface or memory dedicated to caching.
<
Task examples:
<
0 0
1 1
Line 114 ⟶ 1,888:
8000 27749
9000 31678
10000 35656</
=={{header|
<syntaxhighlight lang="java">import java.math.BigInteger;
public class LeftFac{
public static BigInteger factorial(BigInteger n){
BigInteger ans = BigInteger.ONE;
for(BigInteger x = BigInteger.ONE; x.compareTo(n) <= 0; x = x.add(BigInteger.ONE)){
ans = ans.multiply(x);
}
return ans;
}
public static BigInteger leftFact(BigInteger n){
BigInteger ans = BigInteger.ZERO;
for(BigInteger k = BigInteger.ZERO; k.compareTo(n.subtract(BigInteger.ONE)) <= 0; k = k.add(BigInteger.ONE)){
ans = ans.add(factorial(k));
}
return ans;
}
public static void main(String[] args){
for(int i = 0; i <= 10; i++){
System.out.println("!" + i + " = " + leftFact(BigInteger.valueOf(i)));
}
for(int i = 20; i <= 110; i += 10){
System.out.println("!" + i + " = " + leftFact(BigInteger.valueOf(i)));
}
for(int i = 1000; i <= 10000; i += 1000){
System.out.println("!" + i + " has " + leftFact(BigInteger.valueOf(i)).toString().length() + " digits");
}
}
}</syntaxhighlight>
{{out}}
<pre>!0 = 0
!1 = 1
!2 = 2
!3 = 4
!4 = 10
!5 = 34
!6 = 154
!7 = 874
!8 = 5914
!9 = 46234
!10 = 409114
!20 = 128425485935180314
!30 = 9157958657951075573395300940314
!40 = 20935051082417771847631371547939998232420940314
!50 = 620960027832821612639424806694551108812720525606160920420940314
!60 = 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70 = 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80 = 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90 = 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100 = 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!110 = 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
!1000 has 2565 digits
!2000 has 5733 digits
!3000 has 9128 digits
!4000 has 12670 digits
!5000 has 16322 digits
!6000 has 20062 digits
!7000 has 23875 digits
!8000 has 27749 digits
!9000 has 31678 digits
!10000 has 35656 digits</pre>
=={{header|
jq currently only has builtin support for IEEE 64-bit numbers, so in this section we will first present the algorithm using the builtin arithmetic
operators and then adapt it for use with the BigInt library at https://gist.github.com/pkoppstein/d06a123f30c033195841
'''Using builtin arithmetic''':
<syntaxhighlight lang="jq">def left_factorial:
reduce range(1; .+1) as $i
# state: [i!, !i]
([1,0]; .[1] += .[0] | .[0] *= $i)
| .[1];</syntaxhighlight>
'''Using BigInt.jq''':
The BigInt library can be used with jq 1.4, but we will take this opportunity to showcase jq 1.5's support for importing such libraries as modules.
If your jq does not have support for modules, add the BigInt.jq file, remove the 'import' statement and strip off the "BigInt::" prefix.
To compute the lengths of the decimal representation without having to recompute !n,
we also define left_factorial_lengths(gap) to emit [n, ( !n|length) ] when n % gap == 0.
<syntaxhighlight lang="jq">import "BigInt" as BigInt;
# integer input
def long_left_factorial:
reduce range(1; .+1) as $i
# state: [i!, !i]
( ["1", "0"];
.[1] = BigInt::long_add(.[0]; .[1])
| .[0] = BigInt::long_multiply(.[0]; $i | tostring) )
| .[1];
# input and gap should be integers
def long_left_factorial_lengths(gap):
reduce range(1; .+1) as $i
# state: [i!, !i, gap]
(["1", "0", []];
.[1] = BigInt::long_add(.[0]; .[1])
| .[0] = BigInt::long_multiply(.[0]; $i|tostring)
| (.[1] | tostring | length) as $lf
| if $i % gap == 0 then .[2] += [[$i, $lf]] else . end)
| .[2];</syntaxhighlight>
'''The specific tasks''':
<syntaxhighlight lang="sh">((range(0;11), (range(2; 12) * 10)) | "\(.): \(long_left_factorial)"),
(10000 | long_left_factorial_lengths(1000) | .[] | "\(.[0]): length is \(.[1])")</syntaxhighlight>
{{out}}
(scrollable)
<div style="overflow:scroll; height:200px;">
<syntaxhighlight lang="sh">$ jq -r -n -L . -f Long_left_factorial.jq
0: 0
1: 1
2: 2
3: 4
4: 10
5: 34
6: 154
7: 874
8: 5914
9: 46234
10: 409114
20: 128425485935180314
30: 9157958657951075573395300940314
40: 20935051082417771847631371547939998232420940314
50: 620960027832821612639424806694551108812720525606160920420940314
60: 141074930726669571000530822087000522211656242116439949000980378746128920420940314
70: 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
80: 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
90: 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
100: 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
110: 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
1000: length is 2565
2000: length is 5733
3000: length is 9128
4000: length is 12670
5000: length is 16322
6000: length is 20062
7000: length is 23875
8000: length is 27749
9000: length is 31678
10000: length is 35656</syntaxhighlight>
</div>
=={{header|Julia}}==
{{works with|Julia|0.6}}
<syntaxhighlight lang="julia">leftfactorial(n::Integer) = n ≤ 0 ? zero(n) : sum(factorial, 0:n-1)
@show leftfactorial.(0:10)
@show ndigits.(leftfactorial.(big.(1000:1000:10_000)))</syntaxhighlight>
{{out}}
<pre>leftfactorial.(0:10) = [0, 1, 2, 4, 10, 34, 154, 874, 5914, 46234, 409114]
ndigits.(leftfactorial.(big.(1000:1000:10000))) = [2565, 5733, 9128, 12670, 16322, 20062, 23875, 27749, 31678, 35656]</pre>
=={{header|Kotlin}}==
<syntaxhighlight lang="scala">// version 1.0.6
import java.math.BigInteger
fun leftFactorial(n: Int): BigInteger {
if (n == 0) return BigInteger.ZERO
var fact = BigInteger.ONE
var sum = fact
for (i in 1 until n) {
fact *= BigInteger.valueOf(i.toLong())
sum += fact
}
return sum
}
fun main(args: Array<String>) {
for (i in 0..110)
if (i <= 10 || (i % 10) == 0)
println("!${i.toString().padEnd(3)} = ${leftFactorial(i)}")
println("\nLength of the following left factorials:")
for (i in 1000..10000 step 1000)
println("!${i.toString().padEnd(5)} has ${leftFactorial(i).toString().length} digits")
}</syntaxhighlight>
{{out}}
<pre>
!0 = 0
!1 = 1
!2 = 2
!3 = 4
!4 = 10
!5 = 34
!6 = 154
!7 = 874
!8 = 5914
!9 = 46234
!10 = 409114
!20 = 128425485935180314
Line 156 ⟶ 2,097:
!80 = 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90 = 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100
!110
Length of the following left factorials:
!
!
!
!
!
!
!
!
!9000 has 31678 digits
!10000 has 35656 digits
</pre>
=={{header|Lambdatalk}}==
The code can be tested in this wiki page: http://lambdaway.free.fr/lambdawalks/?view=left_factorial
<syntaxhighlight lang="scheme">
'''1) defining !n'''
{def !n // the main function's name
{def !n.mem {A.new 0 1 2}} // initializing a global array
// memorizing the computed values of !n
{def !n.set // computing and storing the values
{lambda {:n}
{A.set! :n // assign at n
{long_mult :n {A.get {- :n 1} {!n.mem}} } // product of n and computed value at n-1
{!n.mem}}}} // in the global array
{def !n.get // getting a value
{lambda {:n}
{A.get :n {if {W.equal? {A.get :n {!n.mem}} undefined} // if it doesn't exist
then {!n.set :n} // then compute it
else {!n.mem}}}}} // else get it from the global array
{lambda {:n} // the main function's body
{if {< :n 2} // if n=0 and n=1
then :n // then return 0 or 1
else {S.reduce long_add // apply add_long to
1 {S.map !n.get {S.serie 1 {- :n 1}}}}}}} // the sequence of computed values
'''2) the task'''
A) computing !n from 2 to 10 takes about 4ms
{S.map {lambda {:n} {br}!n(:n) = {!n :n}}
{S.serie 0 10}}
->
!n(0) = 0
!n(1) = 1
!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
</syntaxhighlight>
=={{header|Lua}}==
Takes about five seconds...
<syntaxhighlight lang="lua">-- Lua bindings for GNU bc
require("bc")
-- Return table of factorials from 0 to n
function facsUpTo (n)
local f, fList = bc.number(1), {}
fList[0] = 1
for i = 1, n do
f = bc.mul(f, i)
fList[i] = f
end
return fList
end
-- Return left factorial of n
function leftFac (n)
local sum = bc.number(0)
for k = 0, n - 1 do sum = bc.add(sum, facList[k]) end
return bc.tostring(sum)
end
-- Main procedure
facList = facsUpTo(10000)
for i = 0, 10 do print("!" .. i .. " = " .. leftFac(i)) end
for i = 20, 110, 10 do print("!" .. i .. " = " .. leftFac(i)) end
for i = 1000, 10000, 1000 do
print("!" .. i .. " contains " .. #leftFac(i) .. " digits")
end</syntaxhighlight>
{{out}}
<pre>!0 = 0
!1 = 1
!2 = 2
!3 = 4
!4 = 10
!5 = 34
!6 = 154
!7 = 874
!8 = 5914
!9 = 46234
!10 = 409114
!20 = 128425485935180314
!30 = 9157958657951075573395300940314
!40 = 20935051082417771847631371547939998232420940314
!50 = 620960027832821612639424806694551108812720525606160920420940314
!60 = 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70 = 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80 = 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90 = 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100 = 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!110 = 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
!1000 contains 2565 digits
!2000 contains 5733 digits
!3000 contains 9128 digits
!4000 contains 12670 digits
!5000 contains 16322 digits
!6000 contains 20062 digits
!7000 contains 23875 digits
!8000 contains 27749 digits
!9000 contains 31678 digits
!10000 contains 35656 digits</pre>
=={{header|Maple}}==
<syntaxhighlight lang="maple">left_factorial := n -> add(k!, k = 1 .. n - 1);
seq(left_factorial(i), i = 1 .. 10);
seq(left_factorial(i), i = 20 .. 110, 10);
seq(length(left_factorial(i)), i = 1000 .. 10000, 1000);</syntaxhighlight>
{{out}}
<pre>0, 1, 3, 9, 33, 153, 873, 5913, 46233, 409113
128425485935180313, 9157958657951075573395300940313, 20935051082417771847631371547939998232420940313, 620960027832821612639424806694551108812720525606160920420940313, 141074930726669571000530822087000522211656242116439949000980378746128920420940313, 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940313, 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940313, 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940313, 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940313, 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940313
2565, 5733, 9128, 12670, 16322, 20062, 23875, 27749, 31678, 35656</pre>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">left[n_] := left[n] = Sum[k!, {k, 0, n - 1}]
Print["left factorials 0 through 10:"]
Print[left /@ Range[0, 10] // TableForm]
Print["left factorials 20 through 110, by tens:"]
Print[left /@ Range[20, 110, 10] // TableForm]
Print["Digits in left factorials 1,000 through 10,000, by thousands:"]
Print[Length[IntegerDigits[left[#]]] & /@ Range[1000, 10000, 1000] // TableForm]</syntaxhighlight>
{{out}}
<pre>left factorials 0 through 10:
0
1
2
4
10
34
154
874
5914
46234
409114
left factorials 20 through 110, by tens:
128425485935180314
9157958657951075573395300940314
20935051082417771847631371547939998232420940314
620960027832821612639424806694551108812720525606160920420940314
141074930726669571000530822087000522211656242116439949000980378746128920420940314
173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
Digits in left factorials 1,000 through 10,000, by thousands:
2565
5733
9128
12670
16322
20062
23875
27749
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}}==
{{trans|Python}}
<syntaxhighlight lang="nim">import iterutils, bigints
proc lfact: iterator: BigInt =
result = iterator: BigInt =
yield 0.initBigInt
var
fact = 1.initBigInt
sum = 0.initBigInt
n = 1.initBigInt
while true:
sum += fact
fact *= n
n += 1
yield sum
echo "first 11:\n "
for i in lfact().slice(last = 10):
echo " ", i
echo "20 through 110 (inclusive) by tens:"
for i in lfact().slice(20, 110, 10):
echo " ", i
echo "Digits in 1,000 through 10,000 (inclusive) by thousands:"
for i in lfact().slice(1_000, 10_000, 1_000):
echo " ", ($i).len</syntaxhighlight>
{{out}}
<pre>first 11:
0
1
2
4
10
34
154
874
5914
46234
409114
20 through 110 (inclusive) by tens:
128425485935180314
9157958657951075573395300940314
20935051082417771847631371547939998232420940314
620960027832821612639424806694551108812720525606160920420940314
141074930726669571000530822087000522211656242116439949000980378746128920420940314
173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
Digits in 1,000 through 10,000 (inclusive) by thousands:
2565
5733
9128
12670
16322
20062
23875
27749
31678
35656</pre>
=={{header|Oforth}}==
<syntaxhighlight lang="oforth">: leftFact | i | 0 1 rot loop: i [ tuck + swap i * ] drop ;</syntaxhighlight>
{{out}}
<pre>
>seqFrom(0, 10) map(#leftFact) println
[0, 1, 2, 4, 10, 34, 154, 874, 5914, 46234, 409114]
</pre>
<pre>
>seqFrom(2, 11) apply(#[ 10 * leftFact println ])
128425485935180314
9157958657951075573395300940314
20935051082417771847631371547939998232420940314
620960027832821612639424806694551108812720525606160920420940314
141074930726669571000530822087000522211656242116439949000980378746128920420940314
173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
</pre>
<pre>
>seq(10) map(#[ 1000 * leftFact asString size ]) println
[2565, 5733, 9128, 12670, 16322, 20062, 23875, 27749, 31678, 35656]
</pre>
=={{header|PARI/GP}}==
<syntaxhighlight lang="parigp">lf(n)=sum(k=0,n-1,k!);
apply(lf, [0..10])
apply(lf, 10*[2..11])
forstep(n=1000,1e4,1000,print1(#digits(lf(n))", "))</syntaxhighlight>
{{out}}
<pre>%1 = [0, 1, 2, 4, 10, 34, 154, 874, 5914, 46234, 409114]
%2 = [128425485935180314, 9157958657951075573395300940314, 20935051082417771847631371547939998232420940314, 620960027832821612639424806694551108812720525606160920420940314, 141074930726669571000530822087000522211656242116439949000980378746128920420940314, 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314, 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314, 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314, 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314, 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314]
2565, 5733, 9128, 12670, 16322, 20062, 23875, 27749, 31678, 35656, </pre>
=={{header|Perl}}==
By caching the last used factorial and left factorial values, I avoid needless recomputation. By only retaining the most recently used values, instead of all past values, I avoid the need to store twenty thousand enormous numbers.
If performance is a concern, this will run over 100x faster by replacing the line "use bigint" with "use Math::GMP qw/:constant/" (after installing that module).
<syntaxhighlight lang="perl">#!perl
use 5.010;
use strict;
use warnings;
use bigint;
sub leftfact {
my ($n) = @_;
state $cached = 0;
state $factorial = 1;
state $leftfact = 0;
if( $n < $cached ) {
($cached, $factorial, $leftfact) = (0, 1, 0);
}
while( $n > $cached ) {
$leftfact += $factorial;
$factorial *= ++$cached;
}
return $leftfact;
}
printf "!%d = %s\n", $_, leftfact($_) for 0 .. 10, map $_*10, 2..11;
printf "!%d has %d digits.\n", $_, length leftfact($_) for map $_*1000, 1..10;
</syntaxhighlight>
Since I copied the printf format strings from the Raku implementation,
the output from the code above is identical to the output of the Raku code.
=={{header|Phix}}==
{{trans|Lua}}
{{libheader|Phix/mpfr}}
<!--<syntaxhighlight lang="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>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">lf_list</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">init</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">mpz</span> <span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">lf_list</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpz_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">lf_list</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">f</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">lf</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">bool</span> <span style="color: #000000;">len</span><span style="color: #0000FF;">=</span><span style="color: #004600;">false</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- Returns left factorial of n, or it's length, as a string</span>
<span style="color: #004080;">mpz</span> <span style="color: #000000;">sumf</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span> <span style="color: #7060A8;">mpz_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sumf</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sumf</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lf_list</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">len</span><span style="color: #0000FF;">?</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">mpz_sizeinbase</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sumf</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">))</span>
<span style="color: #0000FF;">:</span><span style="color: #7060A8;">shorten</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sumf</span><span style="color: #0000FF;">)))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #000080;font-style:italic;">-- Main procedure</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
<span style="color: #000000;">init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">10000</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">10</span> <span style="color: #008080;">do</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;">"!%d = %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)})</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">20</span> <span style="color: #008080;">to</span> <span style="color: #000000;">110</span> <span style="color: #008080;">by</span> <span style="color: #000000;">10</span> <span style="color: #008080;">do</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;">"!%d = %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)})</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1000</span> <span style="color: #008080;">to</span> <span style="color: #000000;">10000</span> <span style="color: #008080;">by</span> <span style="color: #000000;">1000</span> <span style="color: #008080;">do</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;">"!%d contains %s digits\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)})</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</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;">"complete (%3.2fs)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">})</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
!0 = 0
!1 = 1
!2 = 2
!3 = 4
!4 = 10
!5 = 34
!6 = 154
!7 = 874
!8 = 5914
!9 = 46234
!10 = 409114
!20 = 128425485935180314
!30 = 9157958657951075573395300940314
!40 = 20935051082417771847631371547939998232420940314
!50 = 62096002783282161263...25606160920420940314 (63 digits)
!60 = 14107493072666957100...78746128920420940314 (81 digits)
!70 = 17363951180298752669...09216528920420940314 (99 digits)
!80 = 90608958798769534653...22336528920420940314 (117 digits)
!90 = 16695570072624210767...42336528920420940314 (137 digits)
!100 = 94278623976582657916...42336528920420940314 (156 digits)
!110 = 14572298106158529700...42336528920420940314 (177 digits)
!1000 contains 2565 digits
!2000 contains 5733 digits
!3000 contains 9128 digits
!4000 contains 12670 digits
!5000 contains 16322 digits
!6000 contains 20062 digits
!7000 contains 23875 digits
!8000 contains 27749 digits
!9000 contains 31678 digits
!10000 contains 35656 digits
complete (0.45s)
</pre>
=={{header|PicoLisp}}==
<syntaxhighlight lang="picolisp">(de n! (N)
(cache '(NIL) N
(if (> 2 N) 1
(* N (n! (dec N))))))
(de !n (Num)
(if (= Num 0) 1
(sum n! (range 0 (dec Num)))))
(de pril (List) (mapcar 'println List))
(prinl "0-10")
(pril (mapcar '!n (range 0 10)))
(prinl "20 - 110")
(pril (mapcar '!n (range 20 110 10)))
(prinl "length of 1000 - 10000")
(pril (mapcar 'length (mapcar '!n (range 1000 10000 1000))))
</syntaxhighlight>
{{out}}
<syntaxhighlight lang="text">0-10
1
1
2
4
10
34
154
874
5914
46234
409114
20 - 110
128425485935180314
9157958657951075573395300940314
20935051082417771847631371547939998232420940314
620960027832821612639424806694551108812720525606160920420940314
141074930726669571000530822087000522211656242116439949000980378746128920420940314
173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
1000 - 10000
2565
5733
9128
12670
16322
20062
23875
27749
31678
35656
</syntaxhighlight>
=={{header|PL/I}}==
In PL/I the biggest integer type is <tt>'''fixed decimal(31)'''</tt> i.e. 31 digits.
To the best of my knowledge, no big integers exist.
Results are shown for the first 11 integers, as required;
then for the integers from 20 through 30 only, because factorials for n = 40 and larger are not possible.
<syntaxhighlight lang="pli">lf: procedure (n) returns (fixed decimal (31) );
declare n fixed binary;
declare (s, f) fixed (31);
declare (i, j) fixed;
s = 0;
do i = n-1 to 0 by -1;
f = 1;
do j = i to 1 by -1;
f = f * j;
end;
s = s + f;
end;
return (s);
end lf;
declare n fixed binary;
do n = 0 to 10, 20 to 30;
put skip list ('Left factorial of ' || n || '=' || lf(n) );
end;
end left_factorials;</syntaxhighlight>
{{out}}
<pre>
Left factorial of 0= 0
Left factorial of 1= 1
Left factorial of 2= 2
Left factorial of 3= 4
Left factorial of 4= 10
Left factorial of 5= 34
Left factorial of 6= 154
Left factorial of 7= 874
Left factorial of 8= 5914
Left factorial of 9= 46234
Left factorial of 10= 409114
Left factorial of 20= 128425485935180314
Left factorial of 21= 2561327494111820314
Left factorial of 22= 53652269665821260314
Left factorial of 23= 1177652997443428940314
Left factorial of 24= 27029669736328405580314
Left factorial of 25= 647478071469567844940314
Left factorial of 26= 16158688114800553828940314
Left factorial of 27= 419450149241406189412940314
Left factorial of 28= 11308319599659758350180940314
Left factorial of 29= 316196664211373618851684940314
Left factorial of 30= 9157958657951075573395300940314
</pre>
=={{header|PowerShell}}==
{{works with|PowerShell|4.0}}
<syntaxhighlight lang="powershell">
function left-factorial ([BigInt]$n) {
[BigInt]$k, [BigInt]$fact = ([BigInt]::Zero), ([BigInt]::One)
[BigInt]$lfact = ([BigInt]::Zero)
while($k -lt $n){
if($k -gt ([BigInt]::Zero)) {
$fact = [BigInt]::Multiply($fact, $k)
$lfact = [BigInt]::Add($lfact, $fact)
} else {
$lfact = ([BigInt]::One)
}
$k = [BigInt]::Add($k, [BigInt]::One)
}
$lfact
}
0..9 | foreach{
"!$_ = $(left-factorial $_)"
}
for($i = 10; $i -le 110; $i += 10) {
"!$i = $(left-factorial $i)"
}
for($i = 1000; $i -le 10000; $i += 1000) {
$digits = [BigInt]::Log10($(left-factorial $i))
$digits = [Math]::Floor($digits) + 1
if($digits -gt 1) {"!$i has $digits digits"}
else {"!$i has $digits digit"}
}
</syntaxhighlight>
<b>Output:</b>
<pre>
!0 = 0
!1 = 1
!2 = 2
!3 = 4
!4 = 10
!5 = 34
!6 = 154
!7 = 874
!8 = 5914
!9 = 46234
!10 = 409114
!20 = 128425485935180314
!30 = 9157958657951075573395300940314
!40 = 20935051082417771847631371547939998232420940314
!50 = 620960027832821612639424806694551108812720525606160920420940314
!60 = 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70 = 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80 = 9060895879876953465345168046502906376940248300119563651843276746197520942896963148820085319918409223365289204
20940314
!90 = 1669557007262421076703416768839462336073351516357586413634591033592403996240486951022572307223584266878750799
3136908442336528920420940314
!100 = 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203
520208889371641659121356556442336528920420940314
!110 = 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337
422204397431927131629058103519228197429698252556442336528920420940314
!1000 has 2565 digits
!2000 has 5733 digits
!3000 has 9128 digits
!4000 has 12670 digits
!5000 has 16322 digits
!6000 has 20062 digits
!7000 has 23875 digits
!8000 has 27749 digits
!9000 has 31678 digits
!10000 has 35656 digits
</pre>
=={{header|Prolog}}==
{{works with|SWI Prolog}}
<syntaxhighlight lang="prolog">leftfact(N):-
leftfact(N, 0, 0, 1).
leftfact(N, N, _, _):-
!.
leftfact(N, M, L, F):-
((M =< 10 ; (M =< 110, 0 is M mod 10)) ->
writef("!%w = %w\n", [M, L])
;
(0 is M mod 1000 ->
number_string(L, S),
string_length(S, Len),
writef("length of !%w is %w\n", [M, Len])
;
true)),
L1 is L + F,
M1 is M + 1,
F1 is F * M1,
leftfact(N, M1, L1, F1).
main:-
leftfact(10001).</syntaxhighlight>
{{out}}
<pre>
!0 = 0
!1 = 1
!2 = 2
!3 = 4
!4 = 10
!5 = 34
!6 = 154
!7 = 874
!8 = 5914
!9 = 46234
!10 = 409114
!20 = 128425485935180314
!30 = 9157958657951075573395300940314
!40 = 20935051082417771847631371547939998232420940314
!50 = 620960027832821612639424806694551108812720525606160920420940314
!60 = 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70 = 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80 = 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90 = 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100 = 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!110 = 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
length of !1000 is 2565
length of !2000 is 5733
length of !3000 is 9128
length of !4000 is 12670
length of !5000 is 16322
length of !6000 is 20062
length of !7000 is 23875
length of !8000 is 27749
length of !9000 is 31678
length of !10000 is 35656
</pre>
=={{header|Python}}==
<
def lfact():
Line 184 ⟶ 2,798:
print(lf)
print('Digits in 1,000 through 10,000 (inclusive) by thousands:\n %r'
% [len(str(lf)) for lf in islice(lfact(), 1000, 10001, 1000)] )</
{{out}}
Line 202 ⟶ 2,816:
Digits in 1,000 through 10,000 (inclusive) by thousands:
[2565, 5733, 9128, 12670, 16322, 20062, 23875, 27749, 31678, 35656]</pre>
Or, sidestepping the use of '''while''' and '''yield''', we can directly define left factorials in terms of the '''scanl''' abstraction
(a fold or catamorphism, like functools.reduce, but one which returns the whole accumulation of intermediate values – see, for example, The Algebra of Programming, Bird and de Moor, 1997).
'''scanl''' in turn, has a natural definition in terms of the itertools functions '''accumulate''' and '''chain'''.
{{Trans|Haskell}}
<syntaxhighlight lang="python">'''Left factorials'''
from itertools import (accumulate, chain, count, islice)
from operator import (mul, add)
# leftFact :: [Integer]
def leftFact():
'''Left factorial series defined in terms
of the factorial series.
'''
return accumulate(
chain([0], fact()), add
)
# fact :: [Integer]
def fact():
'''The factorial series.
'''
return accumulate(
chain([1], count(1)), mul
)
# ------------------------- TEST -------------------------
# main :: IO ()
def main():
'''Tests'''
print(
'Terms 0 thru 10 inclusive:\n %r'
% take(11)(leftFact())
)
print('\nTerms 20 thru 110 (inclusive) by tens:')
for x in takeFromThenTo(20)(30)(110)(leftFact()):
print(x)
print(
'\n\nDigit counts for terms 1k through 10k (inclusive) by k:\n %r'
% list(map(
compose(len)(str),
takeFromThenTo(1000)(2000)(10000)(
leftFact()
)
))
)
# ----------------------- GENERIC ------------------------
# compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
def compose(g):
'''Function composition.'''
return lambda f: lambda x: g(f(x))
# scanl :: (b -> a -> b) -> b -> [a] -> [b]
def scanl(f):
'''scanl is like reduce, but defines a succession of
intermediate values, building from the left.
'''
def go(a):
def g(xs):
return accumulate(chain([a], xs), f)
return g
return go
# take :: Int -> [a] -> [a]
# take :: Int -> String -> String
def take(n):
'''The prefix of xs of length n,
or xs itself if n > length xs'''
return lambda xs: (
xs[0:n]
if isinstance(xs, list)
else list(islice(xs, n))
)
# takeFromThenTo :: Int -> Int -> Int -> [a] -> [a]
def takeFromThenTo(a):
'''Values drawn from a series betweens positions a and b
at intervals of size z'''
return lambda b: lambda z: lambda xs: islice(
xs, a, 1 + z, b - a
)
if __name__ == '__main__':
main()</syntaxhighlight>
{{Out}}
<pre>Terms 0 thru 10 inclusive:
[0, 1, 2, 4, 10, 34, 154, 874, 5914, 46234, 409114]
Terms 20 thru 110 (inclusive) by tens:
128425485935180314
9157958657951075573395300940314
20935051082417771847631371547939998232420940314
620960027832821612639424806694551108812720525606160920420940314
141074930726669571000530822087000522211656242116439949000980378746128920420940314
173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
Digit counts for terms 1k through 10k (inclusive) by k:
[2565, 5733, 9128, 12670, 16322, 20062, 23875, 27749, 31678, 35656]</pre>
=={{header|Quackery}}==
<syntaxhighlight lang="quackery"> [ 1 swap times [ i 1+ * ] ] is ! ( n --> n )
[ 0 swap times [ i ! + ] ] is !n ( n --> n )
say "First 11 left factorials:" cr
11 times [ i^ !n echo sp ] cr
cr
say "20 through 110 (inclusive) by tens:" cr
10 times [ i^ 2 + 10 * !n echo cr ]
cr
say "Digits in 1,000 through 10,000 by thousands:" cr
10 times [ i^ 1+ 1000 * !n number$ size echo cr ]
cr</syntaxhighlight>
{{out}}
<pre>First 11 left factorials:
0 1 2 4 10 34 154 874 5914 46234 409114
20 through 110 (inclusive) by tens:
128425485935180314
9157958657951075573395300940314
20935051082417771847631371547939998232420940314
620960027832821612639424806694551108812720525606160920420940314
141074930726669571000530822087000522211656242116439949000980378746128920420940314
173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
Digits in 1,000 through 10,000 by thousands:
2565
5733
9128
12670
16322
20062
23875
27749
31678
35656</pre>
=={{header|R}}==
===Imperative solution===
<syntaxhighlight lang="rsplus">library(gmp)
left_factorial <- function(n) {
if (n == 0) return(0)
result <- as.bigz(0)
adder <- as.bigz(1)
for (k in 1:n) {
result <- result + adder
adder <- adder * k
}
result
}
digit_count <- function(n) {
nchar(as.character(n))
}
for (n in 0:10) {
cat("!",n," = ",sep = "")
cat(as.character(left_factorial(n)))
cat("\n")
}
for (n in seq(20,110,10)) {
cat("!",n," = ",sep = "")
cat(as.character(left_factorial(n)))
cat("\n")
}
for (n in seq(1000,10000,1000)) {
cat("!",n," has ",digit_count(left_factorial(n))," digits\n", sep = "")
}
</syntaxhighlight>
{{out}}
<pre>
!0 = 0
!1 = 1
!2 = 2
!3 = 4
!4 = 10
!5 = 34
!6 = 154
!7 = 874
!8 = 5914
!9 = 46234
!10 = 409114
!20 = 128425485935180314
!30 = 9157958657951075573395300940314
!40 = 20935051082417771847631371547939998232420940314
!50 = 620960027832821612639424806694551108812720525606160920420940314
!60 = 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70 = 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80 = 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90 = 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100 = 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!110 = 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
!1000 has 2565 digits
!2000 has 5733 digits
!3000 has 9128 digits
!4000 has 12670 digits
!5000 has 16322 digits
!6000 has 20062 digits
!7000 has 23875 digits
!8000 has 27749 digits
!9000 has 31678 digits
!10000 has 35656 digits</pre>
===Vectorization solution===
Due to vectorization, these sorts of problems are R's bread and butter. The only challenge comes from making sure that R plays nice with objects from the gmp library.
<syntaxhighlight lang="rsplus">library(gmp)
leftFact <- function(numbs)
{
#As we will never actually use the numeric values of our outputs, we will
#immediately coerce them to characters. For technical reasons to do with
#nchar misbehaving, this also makes task 3 much easier.
#As task 1 will demonstrate, the n=0 special case is covered.
sapply(numbs, function(n) as.character(sum(factorialZ(seq_len(n)-1))))
}
printer <- function(inputs) print(data.frame(Value = leftFact(inputs), row.names = paste0("!", inputs)))
#Task 1
printer(0:10)
#Task 2
printer(seq(20, 110, by = 10))
#Task 3
inputs<-seq(1000, 10000, by = 1000)
print(data.frame(Digits = sapply(leftFact(inputs), nchar), row.names = paste0("!", inputs)))</syntaxhighlight>
{{out}}
<pre>> printer(0:10)
Value
!0 0
!1 1
!2 2
!3 4
!4 10
!5 34
!6 154
!7 874
!8 5914
!9 46234
!10 409114
> printer(seq(20, 110, by = 10))
Value
!20 128425485935180314
!30 9157958657951075573395300940314
!40 20935051082417771847631371547939998232420940314
!50 620960027832821612639424806694551108812720525606160920420940314
!60 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!110 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
> print(data.frame(Digits = sapply(leftFact(inputs), nchar), row.names = paste0("!", inputs)))
Digits
!1000 2565
!2000 5733
!3000 9128
!4000 12670
!5000 16322
!6000 20062
!7000 23875
!8000 27749
!9000 31678
!10000 35656</pre>
=={{header|Racket}}==
<syntaxhighlight lang="racket">#lang racket
(define ! (let ((rv# (make-hash))) (λ (n) (hash-ref! rv# n (λ () (if (= n 0) 1 (* n (! (- n 1)))))))))
(define (!n n)
;; note that in-range n is from 0 to n-1 inclusive
(for/sum ((k (in-range n))) (! k)))
(define (dnl. s) (for-each displayln s))
(dnl
"Display the left factorials for:"
"zero through ten (inclusive)"
(pretty-format (for/list ((i (in-range 0 (add1 10)))) (!n i)))
"20 through 110 (inclusive) by tens"
(pretty-format (for/list ((i (in-range 20 (add1 110) 10))) (!n i)))
"Display the length (in decimal digits) of the left factorials for:"
"1,000, 2,000 through 10,000 (inclusive), by thousands."
(pretty-format (for/list ((i (in-range 1000 10001 1000))) (add1 (order-of-magnitude (!n i))))))</syntaxhighlight>
{{out}}
<pre>Display the left factorials for:
zero through ten (inclusive)
'(0 1 2 4 10 34 154 874 5914 46234 409114)
20 through 110 (inclusive) by tens
'(128425485935180314
9157958657951075573395300940314
20935051082417771847631371547939998232420940314
620960027832821612639424806694551108812720525606160920420940314
141074930726669571000530822087000522211656242116439949000980378746128920420940314
173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314)
Display the length (in decimal digits) of the left factorials for:
1,000, 2,000 through 10,000 (inclusive), by thousands.
'(2565 5733 9128 12670 16322 20062 23875 27749 31678 35656)</pre>
=={{header|Raku}}==
(formerly Perl 6)
Implement left factorial as a prefix !. Note that this redefines the core prefix ! (not) function.
<syntaxhighlight lang="raku" line>sub prefix:<!> ($k) { (constant l = 0, |[\+] 1, (|[\*] 1..*))[$k] }
$ = !10000; # Pre-initialize
.say for ( 0 … 10, 20 … 110 ).hyper(:4batch).map: { sprintf "!%d = %s", $_, !$_ };
.say for (1000, 2000 … 10000).hyper(:4batch).map: { sprintf "!%d has %d digits.", $_, chars !$_ };</syntaxhighlight>
{{out}}
<pre>!0 = 0
!1 = 1
!2 = 2
!3 = 4
!4 = 10
!5 = 34
!6 = 154
!7 = 874
!8 = 5914
!9 = 46234
!10 = 409114
!20 = 128425485935180314
!30 = 9157958657951075573395300940314
!40 = 20935051082417771847631371547939998232420940314
!50 = 620960027832821612639424806694551108812720525606160920420940314
!60 = 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70 = 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80 = 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90 = 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100 = 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!110 = 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
!1000 has 2565 digits.
!2000 has 5733 digits.
!3000 has 9128 digits.
!4000 has 12670 digits.
!5000 has 16322 digits.
!6000 has 20062 digits.
!7000 has 23875 digits.
!8000 has 27749 digits.
!9000 has 31678 digits.
!10000 has 35656 digits.</pre>
If you would rather not override prefix ! operator and you can live with just defining lazy lists and indexing into them, this should suffice; (and is in fact very slightly faster than the first example since it avoids routine dispatch overhead):
<syntaxhighlight lang="raku" line>constant leftfact = 0, |[\+] 1, (|[\*] 1..*);
$ = leftfact[10000]; # Pre-initialize
.say for ( 0 … 10, 20 … 110 ).hyper(:4batch).map: { sprintf "!%d = %s", $_, leftfact[$_] };
.say for (1000, 2000 … 10000).hyper(:4batch).map: { sprintf "!%d has %d digits.", $_, chars leftfact[$_] };</syntaxhighlight>
Same output.
=={{header|REXX}}==
Programmer's note: this REXX version automatically adjusts the number of decimal digits (precision) after the factorial is calculated.
This is possible because there will be a number of trailing zeros which allow a floating point number to be converted to an integer.
<syntaxhighlight lang="rexx">/*REXX program computes/display the left factorial (or its dec. width) of N (or a range)*/
parse arg bot
if
if
bot= abs(bot)
w= length(top) /*width of the largest number request. */
do j=bot to
end /*j*/ /* [↑] show either L! or # of digits*/
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
do #=3 to x-1; != ! * # /*compute L! for all numbers ─── ► X.*/
return $ /*return the sum (L!) to the invoker.*/</syntaxhighlight>
{{out|output|text= when using the input of: <tt> 0 10 </tt>}}
<pre>
left ! of 0 ───► 0
Line 240 ⟶ 3,239:
left ! of 10 ───► 409114
</pre>
<pre>
left ! of 20 ───► 128425485935180314
Line 253 ⟶ 3,252:
left ! of 110 ───► 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
</pre>
<pre>
left ! of 1000 ───► 2565 digits
Line 265 ⟶ 3,264:
left ! of 9000 ───► 31678 digits
left ! of 10000 ───► 35656 digits
</pre>
=={{header|Ring}}==
<syntaxhighlight lang="ring">
a = leftFact(0,10,1)
see "" + a + nl
func leftFact f,t,s
see "------ From " + f + " --To -> " + t +" Step " + s + " -------" + nl
for i = f to t step s
leftFact = 1
fct = 1
for j = 1 to i - 1
fct = fct * j
leftFact = leftFact + fct
next
if i >= 1000 see "" + i + " " + len(string(leftFact)) + " digits" + nl
else see "" + i + " " + leftFact + nl ok
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}}==
<
y << lf #yield left_factorial
lf += f
f *= n
end
end</syntaxhighlight>
'''Test:'''
<syntaxhighlight lang="ruby">tens = 20.step(110, 10)
thousands = 1000.step(10_000, 1000)
10001.times do |n|
Line 289 ⟶ 3,337:
puts "!#{n} has #{lf.to_s.size} digits"
end
end</syntaxhighlight>
{{out}}
<pre>!0 = 0
Line 324 ⟶ 3,371:
!10000 has 35656 digits
</pre>
=={{header|Run BASIC}}==
<syntaxhighlight lang="runbasic">a = lftFct(0,10,1)
a = lftFct(20,110,10)
a = lftFct(1000,10000,1000)
function lftFct(f,t,s)
print :print "------ From ";f;" --To-> ";t;" Step ";s;" -------"
for i = f to t step s
lftFct = 1
fct = 1
for j = 1 to i-1
fct = fct * j
lftFct = lftFct + fct
next j
if i >= 1000 then
print i;" ";len(str$(lftFct));" "digits"
else
print i;" ";lftFct
end if
next i
end function</syntaxhighlight>Output:
<pre>------ From 0 --To-> 10 Step 1 -------
0 1
1 1
2 2
3 4
4 10
5 34
6 154
7 874
8 5914
9 46234
10 409114
------ From 20 --To-> 110 Step 10 -------
20 128425485935180314
30 9157958657951075573395300940314
40 20935051082417771847631371547939998232420940314
50 620960027832821612639424806694551108812720525606160920420940314
60 141074930726669571000530822087000522211656242116439949000980378746128920420940314
70 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
80 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
90 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
100 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
110 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
------ From 1000 --To-> 10000 Step 1000 -------
1000 2565 digits
2000 5733 digits
3000 9128 digits
4000 12670 digits
5000 16322 digits
6000 20062 digits
7000 23875 digits
8000 27749 digits
9000 31678 digits
10000 35656 digits</pre>
=={{header|Rust}}==
<syntaxhighlight lang="rust">
#[cfg(target_pointer_width = "64")]
type USingle = u32;
#[cfg(target_pointer_width = "64")]
type UDouble = u64;
#[cfg(target_pointer_width = "64")]
const WORD_LEN: i32 = 32;
#[cfg(not(target_pointer_width = "64"))]
type USingle = u16;
#[cfg(not(target_pointer_width = "64"))]
type UDouble = u32;
#[cfg(not(target_pointer_width = "64"))]
const WORD_LEN: i32 = 16;
use std::cmp;
#[derive(Debug,Clone)]
struct BigNum {
// rep_.size() == 0 if and only if the value is zero.
// Otherwise, the word rep_[0] keeps the least significant bits.
rep_: Vec<USingle>,
}
impl BigNum {
pub fn new(n: USingle) -> BigNum {
let mut result = BigNum { rep_: vec![] };
if n > 0 { result.rep_.push(n); }
result
}
pub fn equals(&self, n: USingle) -> bool {
if n == 0 { return self.rep_.is_empty() }
if self.rep_.len() > 1 { return false }
self.rep_[0] == n
}
pub fn add_big(&self, addend: &BigNum) -> BigNum {
let mut result = BigNum::new(0);
let mut sum = 0 as UDouble;
let sz1 = self.rep_.len();
let sz2 = addend.rep_.len();
for i in 0..cmp::max(sz1, sz2) {
if i < sz1 { sum += self.rep_[i] as UDouble }
if i < sz2 { sum += addend.rep_[i] as UDouble }
result.rep_.push(sum as USingle);
sum >>= WORD_LEN;
}
if sum > 0 { result.rep_.push(sum as USingle) }
result
}
pub fn multiply(&self, factor: USingle) -> BigNum {
let mut result = BigNum::new(0);
let mut product = 0 as UDouble;
for i in 0..self.rep_.len() {
product += self.rep_[i] as UDouble * factor as UDouble;
result.rep_.push(product as USingle);
product >>= WORD_LEN;
}
if product > 0 {
result.rep_.push(product as USingle);
}
result
}
pub fn divide(&self, divisor: USingle, quotient: &mut BigNum,
remainder: &mut USingle) {
quotient.rep_.truncate(0);
let mut dividend: UDouble;
*remainder = 0;
for i in 0..self.rep_.len() {
let j = self.rep_.len() - 1 - i;
dividend = ((*remainder as UDouble) << WORD_LEN)
+ self.rep_[j] as UDouble;
let quo = (dividend / divisor as UDouble) as USingle;
*remainder = (dividend % divisor as UDouble) as USingle;
if quo > 0 || j < self.rep_.len() - 1 {
quotient.rep_.push(quo);
}
}
quotient.rep_.reverse();
}
fn to_string(&self) -> String {
let mut rep = String::new();
let mut dividend = (*self).clone();
let mut remainder = 0 as USingle;
let mut quotient = BigNum::new(0);
loop {
dividend.divide(10, &mut quotient, &mut remainder);
rep.push(('0' as USingle + remainder) as u8 as char);
if quotient.equals(0) { break; }
dividend = quotient.clone();
}
rep.chars().rev().collect::<String>()
}
}
use std::fmt;
impl fmt::Display for BigNum {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
write!(f, "{}", self.to_string())
}
}
fn lfact(n: USingle) -> BigNum {
let mut result = BigNum::new(0);
let mut f = BigNum::new(1);
for k in 1 as USingle..n + 1 {
result = result.add_big(&f);
f = f.multiply(k);
}
result
}
fn main() {
for i in 0..11 {
println!("!{} = {}", i, lfact(i));
}
for i in 2..12 {
let j = i * 10;
println!("!{} = {}", j, lfact(j));
}
for i in 1..11 {
let j = i * 1000;
println!("!{} has {} digits.", j, lfact(j).to_string().len());
}
}
</syntaxhighlight>
{{out}}
<pre>
!0 = 0
!1 = 1
!2 = 2
!3 = 4
!4 = 10
!5 = 34
!6 = 154
!7 = 874
!8 = 5914
!9 = 46234
!10 = 409114
!20 = 128425485935180314
!30 = 9157958657951075573395300940314
!40 = 20935051082417771847631371547939998232420940314
!50 = 620960027832821612639424806694551108812720525606160920420940314
!60 = 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70 = 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80 = 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90 = 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100 = 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!110 = 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
!1000 has 2565 digits.
!2000 has 5733 digits.
!3000 has 9128 digits.
!4000 has 12670 digits.
!5000 has 16322 digits.
!6000 has 20062 digits.
!7000 has 23875 digits.
!8000 has 27749 digits.
!9000 has 31678 digits.
!10000 has 35656 digits.
</pre>
===Faster alternative===
This solution uses the arbitrary precision integers from the rug crate,
which uses GMP under the covers.
<syntaxhighlight lang="rust">// [dependencies]
// rug = "1.9"
fn left_factorials() -> impl std::iter::Iterator<Item = rug::Integer> {
use rug::Integer;
let mut factorial = Integer::from(1);
let mut next = Integer::from(0);
let mut n = 1;
std::iter::from_fn(move || {
let result = next.clone();
next += &factorial;
factorial *= n;
n += 1;
Some(result)
})
}
fn main() {
let mut lf = left_factorials().take(10001).enumerate();
println!("Left factorials 0 through 10:");
for (i, n) in lf.by_ref().take(11) {
println!("!{} = {}", i, n);
}
println!("Left factorials 20 through 110, by tens:");
for (i, n) in lf.by_ref().take(100).skip(9).step_by(10) {
println!("!{} = {}", i, n);
}
println!("Lengths of left factorials 1000 through 10000, by thousands:");
for (i, n) in lf.skip(1000 - 111).step_by(1000) {
println!("length of !{} = {}", i, n.to_string().len());
}
}</syntaxhighlight>
{{out}}
<pre>
Left factorials 0 through 10:
!0 = 0
!1 = 1
!2 = 2
!3 = 4
!4 = 10
!5 = 34
!6 = 154
!7 = 874
!8 = 5914
!9 = 46234
!10 = 409114
Left factorials 20 through 110, by tens:
!20 = 128425485935180314
!30 = 9157958657951075573395300940314
!40 = 20935051082417771847631371547939998232420940314
!50 = 620960027832821612639424806694551108812720525606160920420940314
!60 = 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70 = 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80 = 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90 = 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100 = 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!110 = 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
Lengths of left factorials 1000 through 10000, by thousands:
length of !1000 = 2565
length of !2000 = 5733
length of !3000 = 9128
length of !4000 = 12670
length of !5000 = 16322
length of !6000 = 20062
length of !7000 = 23875
length of !8000 = 27749
length of !9000 = 31678
length of !10000 = 35656
</pre>
=={{header|Scala}}==
<syntaxhighlight lang="scala">object LeftFactorial extends App {
// this part isn't really necessary, it just shows off Scala's ability
// to match the mathematical syntax: !n
implicit class RichInt(n:Int) {
def unary_!() = factorial.take(n).sum
}
val factorial: Stream[BigInt] = 1 #:: factorial.zip(Stream.from(1)).map(n => n._2 * factorial(n._2 - 1))
for (n <- (0 to 10) ++
(20 to 110 by 10);
value = !n) {
println(s"!${n} = ${value}")
}
for (n <- 1000 to 10000 by 1000;
length = (!n).toString.length) {
println(s"length !${n} = ${length}")
}
}
</syntaxhighlight>
{{out}}
<pre>
!0 = 0
!1 = 1
!2 = 2
!3 = 4
!4 = 10
!5 = 34
!6 = 154
!7 = 874
!8 = 5914
!9 = 46234
!10 = 409114
!20 = 128425485935180314
!30 = 9157958657951075573395300940314
!40 = 20935051082417771847631371547939998232420940314
!50 = 620960027832821612639424806694551108812720525606160920420940314
!60 = 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70 = 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80 = 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90 = 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100 = 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!110 = 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
length !1000 = 2565
length !2000 = 5733
length !3000 = 9128
length !4000 = 12670
length !5000 = 16322
length !6000 = 20062
length !7000 = 23875
length !8000 = 27749
length !9000 = 31678
length !10000 = 35656
</pre>
=={{header|Scheme}}==
This version uses the iota method in the standard lists library.
iota takes three values, a count, an optional start value (defaults to 0), and an optional step value (defaults to 1)
so (iota 5) produces a list (0 1 2 3 4)
and (iota 5 100 2) produces a list (100 102 104 106 108)
<syntaxhighlight lang="scheme">
(import (scheme base) ;; library imports in R7RS style
(scheme write)
(srfi 1 lists))
(define (factorial n)
(fold * 1 (iota n 1)))
(define (left-factorial n)
(fold + 0 (map factorial (iota n))))
(define (show i r) ; to pretty print the results
(display "!") (display i) (display " ") (display r) (newline))
;; show left factorials for zero through ten (inclusive)
(for-each
(lambda (i) (show i (left-factorial i)))
(iota 11))
;; show left factorials for 20 through 110 (inclusive) by tens
(for-each
(lambda (i) (show i (left-factorial i)))
(iota 10 20 10))
;; number of digits in 1000 through 10000 by thousands:
(for-each
(lambda (i) (show i (string-length (number->string (left-factorial i)))))
(iota 10 1000 1000))
</syntaxhighlight>
=={{header|Seed7}}==
<syntaxhighlight lang="seed7">$ include "seed7_05.s7i";
include "bigint.s7i";
const func bigInteger: leftFact (in integer: n) is func
result
var bigInteger: leftFact is 0_;
local
var bigInteger: factorial is 1_;
var integer: i is 0;
begin
for i range 1 to n do
leftFact +:= factorial;
factorial *:= bigInteger conv i;
end for;
end func;
const proc: main is func
local
var integer: n is 0;
begin
writeln("First 11 left factorials:");
for n range 0 to 10 do
write(" " <& leftFact(n));
end for;
writeln;
writeln("20 through 110 (inclusive) by tens:");
for n range 20 to 110 step 10 do
writeln(leftFact(n));
end for;
writeln;
writeln("Digits in 1,000 through 10,000 by thousands:");
for n range 1000 to 10000 step 1000 do
writeln(length(str(leftFact(n))));
end for;
writeln;
end func;</syntaxhighlight>
{{out}}
<pre>
First 11 left factorials:
0 1 2 4 10 34 154 874 5914 46234 409114
20 through 110 (inclusive) by tens:
128425485935180314
9157958657951075573395300940314
20935051082417771847631371547939998232420940314
620960027832821612639424806694551108812720525606160920420940314
141074930726669571000530822087000522211656242116439949000980378746128920420940314
173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
Digits in 1,000 through 10,000 by thousands:
2565
5733
9128
12670
16322
20062
23875
27749
31678
35656
</pre>
=={{header|Sidef}}==
Built-in:
<syntaxhighlight lang="ruby">say 20.of { .left_factorial }</syntaxhighlight>
Straightforward:
<syntaxhighlight lang="ruby">func left_factorial(n) {
^n -> sum { _! }
}</syntaxhighlight>
Alternatively, using ''Range.reduce()'':
<syntaxhighlight lang="ruby">func left_factorial(n) {
^n -> reduce({ |a,b| a + b! }, 0)
}</syntaxhighlight>
A faster approach:
<syntaxhighlight lang="ruby">func left_factorial(n) {
static cached = 0
static factorial = 1
static leftfact = 0
if (n < cached) {
cached = 0
factorial = 1
leftfact = 0
}
while (n > cached) {
leftfact += factorial
factorial *= ++cached
}
leftfact
}</syntaxhighlight>
Completing the task:
<syntaxhighlight lang="ruby">for n in (0..10, 20..110 `by` 10) {
printf("!%d = %s\n", n, left_factorial(n))
}
for n in (1000..10000 `by` 1000) {
printf("!%d has %d digits.\n", n, left_factorial(n).len)
}</syntaxhighlight>
{{out}}
<pre>!0 = 0
!1 = 1
!2 = 2
!3 = 4
!4 = 10
!5 = 34
!6 = 154
!7 = 874
!8 = 5914
!9 = 46234
!10 = 409114
!20 = 128425485935180314
!30 = 9157958657951075573395300940314
!40 = 20935051082417771847631371547939998232420940314
!50 = 620960027832821612639424806694551108812720525606160920420940314
!60 = 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70 = 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80 = 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90 = 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100 = 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!110 = 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
!1000 has 2565 digits.
!2000 has 5733 digits.
!3000 has 9128 digits.
!4000 has 12670 digits.
!5000 has 16322 digits.
!6000 has 20062 digits.
!7000 has 23875 digits.
!8000 has 27749 digits.
!9000 has 31678 digits.
!10000 has 35656 digits.
</pre>
=={{header|Standard ML}}==
<syntaxhighlight lang="sml">
(* reuse earlier factorial calculations in dfac, apply to listed arguments in cumlfac *)
(* example: left factorial n, is #3 (dfac (0,n-1,1,1) ) *)
(* output list contains (number, factorial, left factorial) *)
(* tested in PolyML *)
val store = ref 0;
val rec dfac = fn
(from,to,acc,cm) => if from = to then (from,acc,cm) else (store:=(from+1)*acc;dfac (from+1,to,!store,!store+cm ) );
val rec cumlfac = fn
(x::y::rm) => x :: cumlfac ( dfac (#1 x, #1 y, #2 x, #3 x) :: rm ) |
rm =>rm ;
val arguments = List.tabulate (10,fn 0=>(0,1,1)|i=>(i,0,0)) @
List.tabulate (10,fn i=> (10*i+19,0,0) ) @
List.tabulate ( 10,fn i=> (1000*i+999,0,0));
val result = (~1,0,0)::(cumlfac arguments);
(* done *)
(* display: *)
List.app (fn triple :int*int*int =>
print(Int.toString (1+ #1 triple ) ^ " : " ^ Int.fmt StringCvt.DEC (#3 triple ) ^" \n" )
) (List.take(result,21) ) ;
List.app (fn triple :int*int*int =>
print( Int.toString (1+ #1 triple ) ^ " : " ^ Int.toString (size(Int.toString (#3 triple ))) ^" \n" ) ) (List.drop(result,21) );
</syntaxhighlight>
{{out}}
<pre>
time poly --script thisscript
0 : 0
1 : 1
2 : 2
3 : 4
4 : 10
5 : 34
6 : 154
7 : 874
8 : 5914
9 : 46234
10 : 409114
20 : 128425485935180314
30 : 9157958657951075573395300940314
40 : 20935051082417771847631371547939998232420940314
50 : 620960027832821612639424806694551108812720525606160920420940314
60 : 141074930726669571000530822087000522211656242116439949000980378746128920420940314
70 : 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
80 : 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
90 : 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
100 : 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
110 : 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
1000 : 2565
2000 : 5733
3000 : 9128
4000 : 12670
5000 : 16322
6000 : 20062
7000 : 23875
8000 : 27749
9000 : 31678
10000 : 35656
(CPU 2.1Ghz:) 0.36 real 0.29 user 0.08 sys
</pre>
=={{header|Swift}}==
{{libheader|AttaSwift BigInt}}
<syntaxhighlight lang="swift">import BigInt
func factorial<T: BinaryInteger>(_ n: T) -> T {
guard n != 0 else {
return 1
}
return stride(from: n, to: 0, by: -1).reduce(1, *)
}
prefix func ! <T: BinaryInteger>(n: T) -> T {
guard n != 0 else {
return 0
}
return stride(from: 0, to: n, by: 1).lazy.map(factorial).reduce(0, +)
}
for i in 0...10 {
print("!\(i) = \(!i)")
}
print()
for i in stride(from: BigInt(20), through: 110, by: 10) {
print("!\(i) = \(!i)")
}
print()
print("!1000 = \((!BigInt(1000)).description.count) digit number")
print()
for i in stride(from: BigInt(2000), through: 10_000, by: 1000) {
print("!\(i) = \((!i).description.count) digit number")
}</syntaxhighlight>
{{out}}
<pre style="overflow: scroll; height: 25em>!0 = 0
!1 = 1
!2 = 2
!3 = 4
!4 = 10
!5 = 34
!6 = 154
!7 = 874
!8 = 5914
!9 = 46234
!10 = 409114
!20 = 128425485935180314
!30 = 9157958657951075573395300940314
!40 = 20935051082417771847631371547939998232420940314
!50 = 620960027832821612639424806694551108812720525606160920420940314
!60 = 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70 = 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80 = 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90 = 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100 = 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!110 = 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
!1000 = 2565 digit number
!2000 = 5733 digit number
!3000 = 9128 digit number
!4000 = 12670 digit number
!5000 = 16322 digit number
!6000 = 20062 digit number
!7000 = 23875 digit number
!8000 = 27749 digit number
!9000 = 31678 digit number
!10000 = 35656 digit number</pre>
=={{header|Tcl}}==
<
set s 0
for {set i [set f 1]} {$i <= $n} {incr i} {
Line 340 ⟶ 4,066:
for {set i 1000} {$i <= 10000} {incr i 1000} {
puts "!$i has [string length [leftfact $i]] digits"
}</
{{out}}
<pre>
Line 374 ⟶ 4,100:
!9000 has 31678 digits
!10000 has 35656 digits
</pre>
=={{header|Wren}}==
{{libheader|Wren-fmt}}
{{libheader|Wren-big}}
<syntaxhighlight lang="wren">import "./fmt" for Fmt
import "./big" for BigInt
var lfacts = List.filled(12, BigInt.zero)
var lfact = BigInt.one
var sum = BigInt.zero
for (i in 1..10) {
sum = sum + lfact
lfacts[i] = sum
lfact = lfact * i
}
System.print("Left factorials from 0 to 10:")
for (i in 0..10) System.write(" %(lfacts[i])")
for (i in 11..110) {
sum = sum + lfact
if (i%10 == 0) lfacts[i/10] = sum
lfact = lfact * i
}
System.print("\n\nLeft factorials from 20 to 110 by tens:")
for (i in 2..11) Fmt.print(" !$-3d -> $s", i * 10, lfacts[i])
for (i in 111..10000) {
sum = sum + lfact
if (i%1000 == 0) lfacts[i/1000] = sum
lfact = lfact * i
}
System.print("\nLengths of left factorals from 1000 to 10000 by thousands:")
for (i in 1..10) Fmt.print(" !$-5d -> $5s", i * 1000, lfacts[i].toString.count)</syntaxhighlight>
{{out}}
<pre>
Left factorials from 0 to 10:
0 1 2 4 10 34 154 874 5914 46234 409114
Left factorials from 20 to 110 by tens:
!20 -> 128425485935180314
!30 -> 9157958657951075573395300940314
!40 -> 20935051082417771847631371547939998232420940314
!50 -> 620960027832821612639424806694551108812720525606160920420940314
!60 -> 141074930726669571000530822087000522211656242116439949000980378746128920420940314
!70 -> 173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
!80 -> 906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
!90 -> 16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
!100 -> 942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
!110 -> 145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
Lengths of left factorals from 1000 to 10000 by thousands:
!1000 -> 2565
!2000 -> 5733
!3000 -> 9128
!4000 -> 12670
!5000 -> 16322
!6000 -> 20062
!7000 -> 23875
!8000 -> 27749
!9000 -> 31678
!10000 -> 35656
</pre>
=={{header|zkl}}==
{{trans|D}}
<syntaxhighlight lang="zkl">var BN=Import("zklBigNum");
fcn leftFact(n){
[1..n].reduce(fcn(p,n,rf){ p+=rf.value; rf.set(rf.value*n); p },
BN(0),Ref(BN(1)));
}</syntaxhighlight>
<syntaxhighlight lang="zkl">println("First 11 left factorials:\n", [0..10].apply(leftFact));
lfs:=[20..111,10].apply(leftFact);
println(("\n20 through 110 (inclusive) by tens:\n" +
"%d\n"*lfs.len()).fmt(lfs.xplode()));
println("Digits in 1,000 through 10,000 by thousands:\n",
[0d1_000..0d10_000, 1000].pump(List,fcn(n){leftFact(n).toString().len()}));</syntaxhighlight>
{{out}}
<pre>
First 11 left factorials:
L(0,1,2,4,10,34,154,874,5914,46234,409114)
20 through 110 (inclusive) by tens:
128425485935180314
9157958657951075573395300940314
20935051082417771847631371547939998232420940314
620960027832821612639424806694551108812720525606160920420940314
141074930726669571000530822087000522211656242116439949000980378746128920420940314
173639511802987526699717162409282876065556519849603157850853034644815111221599509216528920420940314
906089587987695346534516804650290637694024830011956365184327674619752094289696314882008531991840922336528920420940314
16695570072624210767034167688394623360733515163575864136345910335924039962404869510225723072235842668787507993136908442336528920420940314
942786239765826579160595268206839381354754349601050974345395410407078230249590414458830117442618180732911203520208889371641659121356556442336528920420940314
145722981061585297004706728001906071948635199234860720988658042536179281328615541936083296163475394237524337422204397431927131629058103519228197429698252556442336528920420940314
Digits in 1,000 through 10,000 by thousands:
L(2565,5733,9128,12670,16322,20062,23875,27749,31678,35656)
</pre>
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