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FORTH for the SHARP PC-E500 (S)
06-21-2022, 02:16 AM
Post: #70
RE: FORTH for the SHARP PC-E500 (S)
Compute digits of pi.
The following Forth500 program is based on the C code to compute the digits of pi by Dik T. Winter, CWI Amsterdam. It computes up to 9864 digits of pi, but is memory-restricted to about 6000 digits max:
Code:
.( Loading BIG-PI...)

ANEW _BIG_PI_

DECIMAL

0 VALUE b       0 VALUE c
0 VALUE e       0 VALUE g
0. 2VALUE d     

\ array f located at HERE + 40 bytes (hold area)
: f!    CELLS HERE + 40 + ! ;
: f@    CELLS HERE + 40 + @ ;

: big-pi    ( +n -- )
  DUP 4 < ABORT" too small"
  \ c=7*n/2; c-=c%14
  7 UM* D2/ D>S DUP 14 MOD - TO c
  \ check for sufficient space to store array f
  c UNUSED 40 - 1 RSHIFT U> ABORT" out of memory"
  \ f[0...c-1]=2000
  c 0 DO 2000 I f! LOOP
  \ e=0
  0 TO e
  CR
  BEGIN
    \ d=0; g=2*c-1; b=c
    0. TO d
    c 2* 1- TO g
    c TO b
    BEGIN
      \ d+=f[b]*10000; f[b]=d%g; d/=g; g-=2; b--
      b f@ 10000 UM* +TO d
      d g 0 D/MOD
      TO d
      D>S b f!
      -2 +TO g
      -1 +TO b
    b WHILE
      \ d*=b
      d b UMD* TO d
    REPEAT
    \ printf("%.4u",e+d/10000); e=d%10000
    d 10000 SM/REM
    e + 0 <# # # # # #> TYPE
    TO e
    \ c-=14
    -14 +TO c
  c 0= UNTIL
;

A screenful with the first 152 digits of pi (this takes one minute to compute):
Code:
152 big-pi
3141592653589793238462643383279502884197
1693993751058209749445923078164062862089
9862803482534211706798214808651328230664
70938446095505822317253594081284 OK[0]

A C program for the PC-G850(V)(S):
Code:
1 unsigned long a=10000,d;
2 unsigned b,c,e,*f,g;
3 main(){
4  printf("digits?");scanf("%u",&c);
5  c=7*c/2;c-=c%14;f=malloc(4*c+4);
6  for(;b-c;)f[b++]=a/5;
7  for(;d=0,g=c*2;c-=14,printf("%.4lu",e+d/a),e=d%a)
8   for(b=c;d+=f[b]*a,f[b]=d%--g,d/=g--,--b;d*=b);
9 }

The PC-G850VS calculates the first 152 digits of pi in 1 minute and 15 seconds.

This slightly modified version in C with 64 bit integers correctly computes up to 54935 digits of pi:
Code:
uint64_t a=10000,b,c,d,e,*f,g;
main(){printf("digits?");scanf("%llu",&c);c*=3.5;c-=c%14;f=malloc(sizeof(*f)*(c+1));
for(;b-c;)f[b++]=a/5;for(;d=0,g=c*2;c-=14,printf("%.4llu",e+d/a),e=d%a)
for(b=c;d+=f[b]*a,f[b]=d%--g,d/=g--,--b;d*=b);}

The 54936th digit is off by one, followed by 10000 instead of 0000:

362524395716152714669005814610000
___________________________^x____
where a 7 should appear in place of the 6, falling the 1 to carry over to the 6. When pushing for 100000 digits this happens a few more times. I reckon the algorithm can be fixed to perform the carry. But this algorithm is quite slow for long digit sequences. There are also better algorithms, e.g. BBP, Chudnovsky.

- Rob

"I count on old friends" -- HP 71B,Prime|Ti VOY200,Nspire CXII CAS|Casio fx-CG50...|Sharp PC-G850,E500,2500,1500,14xx,13xx,12xx...
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FORTH for the SHARP PC-E500 (S) - Helix - 09-06-2021, 11:41 PM
RE: FORTH for the SHARP PC-E500 (S) - robve - 06-21-2022 02:16 AM



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