(42S) Big Factorial

[Thomas Klemm]

This program allows to calculate all digits of \(n!\):

Code:

00 { 61-Byte Prgm }
01▸LBL "BIG!"
02 STO 01
03 RCL "1"
04▸LBL 00
05 RCL× 01
06 ENTER
07 RCL÷ 00
08 IP
09 STO "."
10 RCL× 00
11 -
12 INDEX "."
13 J+
14 ENTER
15 DIM?
16 RCL- ST Y
17 GETM
18 STO "."
19 DIM?
20 RCL+ ST Y
21 DIM "."
22 R↓
23 R↓
24 RCL+ "."
25 DSE 01
26 GTO 00
27 END

Question

Is there a better way to shift the elements of an array to the left?

Initialisation

We create an array 1 of length 10 and use 10 digits in each element.

1 ENTER 10 NEWMAT
EDIT
←
1
EXIT
STO "1"

E 10 STO 00

Example

69
XEQ "BIG!"

[ 1×10 Matrix ]

171'122'452
4'281'413'113
7'246'833'888
1'272'839'092
2'705'448'935
2'036'939'364
8'040'923'257
2'797'541'406
4'742'400'000
0

Compare this to:

69! = 171122452'4281413113'7246833888'1272839092'2705448935'2036939364'8040923257'2797​541406'4742400000'0000000000

Here we use 10 digits for each element of the array.
For higher values of \(n\) this needs to be reduced accordingly.
The result of multiplying by \(n\) must fit into the 12 digits provided by the HP-42S.

Using Free42 with its 34 decimal digits allows to calculate \(1000!\) without further adjustments.
You just have to create the array 1 as a [ 1×257 Matrix ].