(16C) e to 400 decimal places
02-06-2015, 02:12 AM (This post was last modified: 06-15-2017 01:18 PM by Gene.)
Post: #1
 Rick314 Junior Member Posts: 15 Joined: Oct 2014
(16C) e to 400 decimal places
See the attached scans of handwritten pages I wrote in 1982 to approximate e (2.71828...) to 400+ decimal places on an HP-16C. It takes about 3.5 hours to run, plus the time to enter the 2 program halves and see the results 8 digits at a time. The results are that the fractional portion of e truncated to 404 digits is:
Code:
71828182 84590452 35360287 47135266 24977572 47093699 95957496 69676277 24076630 35354759 45713821 78525166 42742746 63919320 03059921 81741359 66290435 72900334 29526059 56307381 32328627 94349076 32338298 80753195 25101901 15738341 87930702 15408914 99348841 67509244 76146066 80822648 00168477 41185374 23454424 37107539 07774499 20695517 02761838 60626133 13845830 00752044 93382656 02976067 37113200 70932870 91274437 47047230 69697720 93101416 9283

Attached File(s) Thumbnail(s)

02-07-2015, 07:20 AM
Post: #2
 Dieter Senior Member Posts: 1,780 Joined: Dec 2013
RE: (HP-16C) e to 400 decimal places
(02-06-2015 02:12 AM)Rick314 Wrote:  See the attached scans of handwritten pages I wrote in 1982 to approximate e (2.71828...) to 400+ decimal places on an HP-16C.

Wow, what a coincidence: at the same time I wrote the same e program using the same method on my 41C. Or maybe... it's not quite that coincidental, because those were the days when things like these were done on programmable calculators. My math teacher had a similar program for his TI59 and 700 or 800 digits, while I could finally come up with more than 2200. ;-)

Dieter
02-11-2015, 01:11 AM
Post: #3
 Rick314 Junior Member Posts: 15 Joined: Oct 2014
RE: (HP-16C) e to 400 decimal places
(02-07-2015 07:20 AM)Dieter Wrote:  My math teacher had a similar program for his TI59 and 700 or 800 digits, while I could finally come up with more than 2200.

Hello Dieter. Your comment prompted me to resurrect my 1992 Turbo Pascal 6.0 program that approximates e to 1,000,010 decimal places (E1MEG_P.TXT, attached). Key routines were coded in 80386 assembly language, and there are 4 algorithm enhancements explained in the header that I claim as my own. I've looked into it and think it is the fastest algorithm published. In 1992 it took 6.85 hours running on a 25 MHz 80386 PC. I just re-ran it on my 2004 Windows XP 1.3 GHz Pentium 4 PC, the latest I have that still runs 80386 assembly code, and it took 2 minutes 45 seconds. That's interesting: 150x faster due just to 12 years of hardware improvements. Now we are 11 more years into the future... The first and last page of output are also attached (E1MEG_R.TXT).

Attached File(s)
02-11-2015, 09:11 AM
Post: #4
 Thomas Klemm Senior Member Posts: 953 Joined: Dec 2013
RE: (HP-16C) e to 400 decimal places
Is the spigot algorithm used?

Cheers
Thomas

Cf. The calculation of e to many significant digits by A. H. J. Sale
02-11-2015, 02:33 PM
Post: #5
 Frido Bohn Junior Member Posts: 31 Joined: Jan 2015
RE: (HP-16C) e to 400 decimal places
Quote:... resurrect my 1992 Turbo Pascal 6.0 program that approximates e to 1,000,010 decimal places (E1MEG_P.TXT, attached).

Wow! This is a very fine example how programs should be written. Very structured and full of explanatory comments. This yields a lot of motivation to dive deeper into this matter. Thanks for sharing!

Any idea how to translate that 386-assembler code into something digestible for the Core-iN generation?

Cheers
Frido
02-12-2015, 12:51 PM (This post was last modified: 02-12-2015 12:54 PM by Dieter.)
Post: #6
 Dieter Senior Member Posts: 1,780 Joined: Dec 2013
RE: (HP-16C) e to 400 decimal places
(02-11-2015 01:11 AM)Rick314 Wrote:  Hello Dieter. Your comment prompted me to resurrect my 1992 Turbo Pascal 6.0 program that approximates e to 1,000,010 decimal places (E1MEG_P.TXT, attached). Key routines were coded in 80386 assembly language,

Unbelievable – that's exactly what I did in 1995! I also used Turbo Pascal 6.0 and the main calculation loop was coded in 386 assembly. Since the Pascal compiler did not support 386 instructions I used Borland's TASM for this task. However, the algorithm was the same as the one used on the '41C. ;-)

Dieter
02-12-2015, 12:56 PM
Post: #7
 Dieter Senior Member Posts: 1,780 Joined: Dec 2013
RE: (HP-16C) e to 400 decimal places
(02-11-2015 02:33 PM)Frido Bohn Wrote:  Any idea how to translate that 386-assembler code into something digestible for the Core-iN generation?

I'm not sure if I get you right, but of course even the latest Intel processors still support the commands of their earliest ancestors like the 8088, 80286 and 80386.

Dieter
02-12-2015, 06:22 PM
Post: #8
 rprosperi Senior Member Posts: 2,381 Joined: Dec 2013
RE: (HP-16C) e to 400 decimal places
(02-12-2015 12:56 PM)Dieter Wrote:
(02-11-2015 02:33 PM)Frido Bohn Wrote:  Any idea how to translate that 386-assembler code into something digestible for the Core-iN generation?

I'm not sure if I get you right, but of course even the latest Intel processors still support the commands of their earliest ancestors like the 8088, 80286 and 80386.

Dieter

The 386 in-line stuff back then probably ran in real mode, which won't work under Windows, etc. today.

--Bob Prosperi
02-12-2015, 06:22 PM
Post: #9
 Frido Bohn Junior Member Posts: 31 Joined: Jan 2015
RE: (HP-16C) e to 400 decimal places
Hi Dieter,

I tripped over Rick's statement,
(02-11-2015 01:11 AM)Rick314 Wrote:  I just re-ran it on my 2004 Windows XP 1.3 GHz Pentium 4 PC, the latest I have that still runs 80386 assembly code,...
and interpreted that Pentiums would be able to manage assembler code while later processors would not. However, I may be wrong and Rick didn't have any newer Intel processor at hands.

Cheers
Frido
02-12-2015, 06:53 PM
Post: #10
 Thomas Klemm Senior Member Posts: 953 Joined: Dec 2013
RE: (HP-16C) e to 400 decimal places
(02-11-2015 02:33 PM)Frido Bohn Wrote:  Wow! This is a very fine example how programs should be written.

Here's a very fine example how programs should not be written:
Code:
a[87700],b,c=87700,d,e=1e4,f=1e5,h; main(){for(;b=c--,b>84700;h=printf("%05d",e+d/f),e=d%=f) for(;--b;d+=f*(h?a[b]:e),a[b]=d%b,d/=b);}

It calculates e to 15000 places in ~ 4.7 seconds on a Dell Precision T5400.

Cf. Arndt • Haenel, $$\pi$$ - Unleashed
6.4 Spigot algorithm for e
p.85

A similar program (roemer) was a winning entry at the 6th International Obfuscated C Code Contest (1989):
Code:
                                                                         char                                                             _3141592654[3141           ],__3141[3141];_314159[31415],_3141[31415];main(){register char*       _3_141,*_3_1415, *_3__1415; register int _314,_31415,__31415,*_31,     _3_14159,__3_1415;*_3141592654=__31415=2,_3141592654[0][_3141592654    -1]=1[__3141]=5;__3_1415=1;do{_3_14159=_314=0,__31415++;for( _31415   =0;_31415<(3,14-4)*__31415;_31415++)_31415[_3141]=_314159[_31415]= - 1;_3141[*_314159=_3_14159]=_314;_3_141=_3141592654+__3_1415;_3_1415= __3_1415    +__3141;for                 (_31415 = 3141-            __3_1415  ;                  _31415;_31415--            ,_3_141 ++,                  _3_1415++){_314            +=_314<<2 ;                  _314<<=1;_314+=           *_3_1415;_31                   =_314159+_314;           if(!(*_31+1)                   )* _31 =_314 /           __31415,_314                   [_3141]=_314 %           __31415 ;* (                   _3__1415=_3_141          )+= *_3_1415                     = *_31;while(*          _3__1415 >=                      31415/3141 ) *          _3__1415+= -                     10,(*--_3__1415         )++;_314=_314                     [_3141]; if ( !         _3_14159 && *                     _3_1415)_3_14159         =1,__3_1415 =                     3141-_31415;}if(         _314+(__31415                      >>1)>=__31415 )         while ( ++ *                       _3_141==3141/314        )*_3_141--=0                        ;}while(_3_14159        ) ; { char *                        __3_14= "3.1415";        write((3,1),                        (--*__3_14,__3_14        ),(_3_14159                          ++,++_3_14159))+       3.1415926; }                          for ( _31415 = 1;      _31415<3141-                           1;_31415++)write(     31415% 314-(                            3,14),_3141592654[   _31415    ] +                            "0123456789","314"   [ 3]+1)-_314;                            puts((*_3141592654=0 ,_3141592654))                              ;_314= *"3.141592";}

Cheers
Thomas
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