Bernoulli Numbers

[Dieter]

(12-18-2013 12:52 AM)Namir Wrote:  Bernoulli Numbers using Series Approximations

Hi Namir,

I think the RCL 00 in your line 31 should read RCL 01, right?

Then I tried my own implementation of this algorithm. I changed the way the tolerance is handled. If the user does not enter one, the current value in R01 is used. If this value is >=1 or <0, the tolerance defaults to 1E-5. Also the number of iterations is calculated beforehand so that the loop requires no tests and a simple DSE counter will do.

The following version uses only R00 - R02, and even R02 may be replaced with a stack register if the calculation of the factor starting at line 25 is placed behind the loop. Also no flags are required.

Code:


01 LBL"BN"
02 RCL 01
03 "TOL=?"
04 PROMPT
05 FRC
06 LASTX
07 X=Y?   ' tolerance >=1
08 X<=0?  ' or =< 0 ?
09 1E-5   ' set default tolerance
10 STO 01
11 "N=?"
12 PROMPT
13 STO 00
14 1
15 RCL 00
16 X=Y?
17 -,5
18 X<0?
19 RTN
20 2
21 MOD
22 -
23 X=0?
24 RTN
25 RCL 00
26 FACT
27 PI
28 ST+ X
29 RCL 00
30 Y^X
31 /
32 ST+ X
33 RCL 01
34 RCL 00
35 1/X
36 CHS
37 Y^X
38 INT
39 STO 02   ' set number of iterations
40 CLX
41 ISG 02
42 LBL 01
43 RCL 02
44 RCL 00
45 CHS
46 Y^X
47 +
48 DSE 02
49 GTO 01
50 *
51 RCL 00
52 -4
53 MOD
54 SIGN
55 *
56 CHS
57 END

What do you think? Any errors or things to change?

Dieter