So I decided to add a one screen fixed point facility to ciforth,
waiting for ages in the projecteuler directory.
I invented a high order process to calculate pi, an opportunity
to demonstrates what you can do with fixed point.
----------------------------------------8< -------------
( *s /s fix-scale -fixedpoint- )
WANT ALIAS
8 CELLS 4 - CONSTANT fix-scale \ n represents n.2^-scale.
1 fix-scale LSHIFT CONSTANT 1/1
1 fix-scale 1- LSHIFT CONSTANT 1/2
\ As */ * / but scaled.
: */s >R M* R> FM/MOD NIP ;
: *s 1/1 */s ; : /s 1/1 SWAP */s ;
\ Most other operators remain the same:
'+ ALIAS +s '- ALIAS -s '*/ ALIAS */s
\ For a RATIO (n/d) return an equivalent scaled NUMBER.
'/s ALIAS rat>s \ By accident.
\ Print a scaled double number with n digits.
: D.s >R 1/1 FM/MOD 0 <# #S #> TYPE &. EMIT
R> 0 DO BASE @ 1/1 */MOD &0 + EMIT LOOP DROP SPACE ;
: U.s 0 SWAP D.s ;
----------------------------------------8< -------------
Actual and tested code. You must add a blank to each ' and define
constants for &. and &0 for it to be ISO.
fix-scale is such that the range is (-8,+8) , but can be changed.

The idea is that cos(pi/2) should be zero.
cos() is calculated by a power series:
1.x^1/1 - 3.x^3/3! + 5.x^5/5! ...
"
AMDX86 ciforth 5.4.0

ciforth lab $Revision: 5.171 $ (c) Albert van der Horst
...
S[ 1 ] OK INCLUDE calcpi.frt
*/s : ISN'T UNIQUE

S[ ] OK 1 DEBUG ! \ Showing terms in calculating cos

S[ ] OK 3 2 rat>s \ calculate cos pi for 1.5

S[ 1729382256910270464 ] OK cos
1 1.12500000000000000000
3 0.21093750000000000000
5 0.01582031249999999843
7 0.00063563755580356949
9 0.00001589093889508771
11 0.00000027086827661827
13 0.00000000334864627606
15 0.00000000003139355702
17 0.00000000000023083444
19 0.00000000000000136609
21 0.00000000000000000520

S[ 81554440978406003 ] OK s.
0.07073720166770290900 \ Is nearly a zero.
S[ ] OK 0 debug !

S[ ] OK \ for third order convergence the precision triples

S[ ] OK third-order
\ the cos is the correction
0.07073720166770290900
0.00005912512715926503
0.00000000000003444466
0.00000000000000000086
0.00000000000000000000
pi=~3.14159265358979323916

S[ ] OK \ for fifth order convergence the zeroes multiply by 5.

S[ ] OK fifth-order
\ cos correction
0.07073720166770290900 0.07079619356654995136
0.00000013322834667081 0.00000013322834667081
-0.00000000000000000346 -0.00000000000000000346
0.00000000000000000086 0.00000000000000000086
0.00000000000000000000 0.00000000000000000000
pi=~3.14159265358979323916

916 864 - .
52 OK

S[ ] OK \ The precision and steps are actually the same for both.
"

The actual code follows.
We take advantage that:
1. the derivative is known to be a sine : dx -dx^3/6
2. second order and fourth order terms are missing.

=========================================================
\ For reference
\ 3.1415926535 8979323846 2643383279
INCLUDE fix.blk
VARIABLE DEBUG 0 DEBUG !
: s. DUP 0< IF &- EMIT THEN ABS 20 U.s ;
\ For x calculate the cosine .
VARIABLE x^2
VARIABLE sum

: cos DUP *s x^2 !
1/1 sum !
1/1 1000 1 DO
I / I 1+ / x^2 @ *s
sum @ I 1- 4 MOD IF OVER + ELSE OVER - THEN sum !
DUP 0= IF DROP LEAVE THEN
DEBUG @ IF I . DUP s. CR THEN
2 +LOOP sum @ ;

\ Third-order order convergence.
: third-order
3 2 rat>s DUP cos DUP s. CR
+ DUP cos DUP s. CR
+ DUP cos DUP s. CR
+ DUP cos DUP s. CR
+ DUP cos DUP s. CR
DROP 2 * "pi=~" TYPE s. CR
;

\ For x return x+3.x^3
: correction DUP DUP DUP *s *s 6 / + ;

\ Fifth order convergence.
: fifth-order
3 2 rat>s DUP cos DUP s. correction DUP s. CR
+ DUP cos DUP s. correction DUP s. CR
+ DUP cos DUP s. correction DUP s. CR
+ DUP cos DUP s. correction DUP s. CR
+ DUP cos DUP s. correction DUP s. CR
DROP 2 * "pi=~" TYPE s. CR
; ==============================================================

For the smart people:
- why is there a plus not a minus in the fifth order correction?
- make a double precision version where the effect is more
visible.

Enjoy

Groetjes Albert
--
Don't praise the day before the evening. One swallow doesn't make spring.
You must not say "hey" before you have crossed the bridge. Don't sell the
hide of the bear until you shot it. Better one bird in the hand than ten in
the air. First gain is a cat spinning. - the Wise from Antrim -

On Sunday, September 3, 2023 at 11:10:04 AM UTC+2, none albert wrote:
> So I decided to add a one screen fixed point facility to ciforth,
> waiting for ages in the projecteuler directory.
> I invented a high order process to calculate pi, an opportunity
> to demonstrates what you can do with fixed point.

:--)

With a little help of our friends (Wil Baden, mpfr authors), you
could have done:

NEEDS -xopg

..ARBITRARY.P ( default 4096 byte variables )

0-VALUE GVAL a 0-VALUE GVAL b 0-VALUE GVAL c
0-VALUE GVAL disc

: quadraticroot ( F: a b c -- y1 y2 )
TO c TO b TO a
LET disc=SQRT(b*b-4*a*c):
LET ((-b+disc)/(2*a),(-b-disc)/(2*a)):
;

FORTH> CR LET. MAX(quadraticroot(1,-1,-1)): ( golden ratio)
1.6180339887498948482045868343656381177203 ok
( OEIS: 1, 6, 1, 8, 0, 3, 3, 9, 8, 8, 7, 4, 9, 8, 9, 4, 8, 4, 8, 2, 0, 4, 5, 8, 6,
8, 3, 4, 3, 6, 5, 6, 3, 8, 1, 1, 7, 7, 2, 0, 3, ^^ 0, 9, 1, 7, 9, 8, 0, 5, 7, 6, 2, 8,
6, 2, 1, 3, 5, 4, 4, 8, 6, 2, 2, 7, 0, 5, 2, 6, 0, 4, 6, 2, 8, 1, 8, 9, 0, 2, 4, 4,
9, 7, 0, 7, 2, 0, 7, 2, 0, 4, 1, 8, 9, 3, 9, 1, 1, 3, 7, 4, 8, 4, 7, 5
Wolfram: can't be copied because of HTML tricks )

I'm currently using xopg in my iSPICE simulator. One day, there
may be an arbitrary-precision SPICE, but for now speed is
more interesting.

-marcel

Marcel Hendrix schrieb am Sonntag, 3. September 2023 um 12:36:11 UTC+2:
> On Sunday, September 3, 2023 at 11:10:04 AM UTC+2, none albert wrote:
> > So I decided to add a one screen fixed point facility to ciforth,
> > waiting for ages in the projecteuler directory.
> > I invented a high order process to calculate pi, an opportunity
> > to demonstrates what you can do with fixed point.
> :--)

\ Calculation of digits of pi without floating-point
\ The algorithm calculate one digit at the time
\ Michel Jean, April 2020

1001 constant nbr-digits \ number of digit - add one, the last digit is not printed
variable pos \ position in the array
variable ret \ carry (retenue in french ;-) )
nbr-digits 10 * 3 / constant nbr-cells \ initialisation on the number of cells
variable arr-cells nbr-cells cells allot

: initialisation ( -- ) \ initialisation of the array
nbr-cells 0 do
2 arr-cells i cells + !
loop ;

: algo-base ( -- )
pos @ 1 = if
1 cells arr-cells + @ 10 * ret @ +
dup
10 mod arr-cells 1 cells + !
10 / ret !
else
pos @ cells arr-cells + @ 10 * ret @ +
2 pos @ * 1 -
2dup
mod arr-cells pos @ cells + !
/ pos @ 1 - * ret !
then ;

: release-stack \ hold the last digit and release other digits of the stack
depth 1 > if depth 1- roll . recurse else then ;

: release-stack+1 \ hold the last digit and release other digits of the stack + 1 modulo 10
depth 1 > if
depth 1- roll 1+ 10 mod .
recurse else then ;

: set-predigit ( -- n )
ret @ dup 9 < if release-stack else
dup 10 = if release-stack+1 drop 0 else
then then ;

: 1digit ( -- ) \ calculate 1 digit at the time
1 nbr-cells do
i pos ! algo-base -1 +loop set-predigit ;

: run ( -- )
0 ret ! initialisation
nbr-digits 50 / 0 do
50 0 do 1digit loop \ 50 digits by line
cr loop
drop ; \ drop the last digit (value not safe)

cr run

On 3/09/2023 11:00 pm, minforth wrote:
> Marcel Hendrix schrieb am Sonntag, 3. September 2023 um 12:36:11 UTC+2:
>> On Sunday, September 3, 2023 at 11:10:04 AM UTC+2, none albert wrote:
>>> So I decided to add a one screen fixed point facility to ciforth,
>>> waiting for ages in the projecteuler directory.
>>> I invented a high order process to calculate pi, an opportunity
>>> to demonstrates what you can do with fixed point.
>> :--)
>
> \ Calculation of digits of pi without floating-point
> \ The algorithm calculate one digit at the time
> \ Michel Jean, April 2020

Fails after 263 digits on a 16-bit forth. Single precision math only
takes one so far.

In article <2265ddd9-d878-4644-a122-38c8447304f7n@googlegroups.com>,
Marcel Hendrix <mhx@iae.nl> wrote:
>On Sunday, September 3, 2023 at 11:10:04 AM UTC+2, none albert wrote:
>> So I decided to add a one screen fixed point facility to ciforth,
>> waiting for ages in the projecteuler directory.
>> I invented a high order process to calculate pi, an opportunity
>> to demonstrates what you can do with fixed point.
>
>:--)
>
>With a little help of our friends (Wil Baden, mpfr authors), you
>could have done:
>
>NEEDS -xopg
>
>.ARBITRARY.P ( default 4096 byte variables )
>
>0-VALUE GVAL a 0-VALUE GVAL b 0-VALUE GVAL c
>0-VALUE GVAL disc
>
>: quadraticroot ( F: a b c -- y1 y2 )
> TO c TO b TO a
> LET disc=SQRT(b*b-4*a*c):
> LET ((-b+disc)/(2*a),(-b-disc)/(2*a)):
>;
>
>FORTH> CR LET. MAX(quadraticroot(1,-1,-1)): ( golden ratio)
> 1.6180339887498948482045868343656381177203 ok
>( OEIS: 1, 6, 1, 8, 0, 3, 3, 9, 8, 8, 7, 4, 9, 8, 9, 4, 8, 4, 8, 2, 0, 4, 5, 8, 6,
>8, 3, 4, 3, 6, 5, 6, 3, 8, 1, 1, 7, 7, 2, 0, 3, ^^ 0, 9, 1, 7, 9, 8, 0, 5, 7, 6, 2, 8,
>6, 2, 1, 3, 5, 4, 4, 8, 6, 2, 2, 7, 0, 5, 2, 6, 0, 4, 6, 2, 8, 1, 8, 9, 0, 2, 4, 4,
>9, 7, 0, 7, 2, 0, 7, 2, 0, 4, 1, 8, 9, 3, 9, 1, 1, 3, 7, 4, 8, 4, 7, 5
>Wolfram: can't be copied because of HTML tricks )
>
>I'm currently using xopg in my iSPICE simulator. One day, there
>may be an arbitrary-precision SPICE, but for now speed is
>more interesting.

Thank you for drawing attention that I can do nice things with a
one screen facility, while others need big packages. ;-)

>
>-marcel
--
Don't praise the day before the evening. One swallow doesn't make spring.
You must not say "hey" before you have crossed the bridge. Don't sell the
hide of the bear until you shot it. Better one bird in the hand than ten in
the air. First gain is a cat spinning. - the Wise from Antrim -

On Sunday, September 3, 2023 at 3:31:49 PM UTC-4, none albert wrote:

> Thank you for drawing attention that I can do nice things with a
> one screen facility, while others need big packages. ;-)
>

I am seeing a t-shirt or a bumper sticker that says:

"Forth programmers do it with smaller packages"

:-)))))))))))

In article <ud23be$u4ff$1@dont-email.me>, dxforth <dxforth@gmail.com> wrote:
>On 3/09/2023 11:00 pm, minforth wrote:
>> Marcel Hendrix schrieb am Sonntag, 3. September 2023 um 12:36:11 UTC+2:
>>> On Sunday, September 3, 2023 at 11:10:04 AM UTC+2, none albert wrote:
>>>> So I decided to add a one screen fixed point facility to ciforth,
>>>> waiting for ages in the projecteuler directory.
>>>> I invented a high order process to calculate pi, an opportunity
>>>> to demonstrates what you can do with fixed point.
>>> :--)
>>
>> \ Calculation of digits of pi without floating-point
>> \ The algorithm calculate one digit at the time
>> \ Michel Jean, April 2020
>
>Fails after 263 digits on a 16-bit forth. Single precision math only
>takes one so far.
>
Happily chugging along with 10,000 digits in my 64 bits Forth,
in one minute 17 seconds.
The lines contain 50 digits, on average only.

Groetjes Albert
--
Don't praise the day before the evening. One swallow doesn't make spring.
You must not say "hey" before you have crossed the bridge. Don't sell the
hide of the bear until you shot it. Better one bird in the hand than ten in
the air. First gain is a cat spinning. - the Wise from Antrim -

In article <2265ddd9-d878-4644-a122-38c8447304f7n@googlegroups.com>,
Marcel Hendrix <mhx@iae.nl> wrote:
>On Sunday, September 3, 2023 at 11:10:04 AM UTC+2, none albert wrote:
>> So I decided to add a one screen fixed point facility to ciforth,
>> waiting for ages in the projecteuler directory.
>> I invented a high order process to calculate pi, an opportunity
>> to demonstrates what you can do with fixed point.
>
>:--)
>
>With a little help of our friends (Wil Baden, mpfr authors), you
>could have done:
>
>NEEDS -xopg
>
>.ARBITRARY.P ( default 4096 byte variables )
>
>0-VALUE GVAL a 0-VALUE GVAL b 0-VALUE GVAL c
>0-VALUE GVAL disc
>
>: quadraticroot ( F: a b c -- y1 y2 )
> TO c TO b TO a
> LET disc=SQRT(b*b-4*a*c):
> LET ((-b+disc)/(2*a),(-b-disc)/(2*a)):
>;
>
>FORTH> CR LET. MAX(quadraticroot(1,-1,-1)): ( golden ratio)
> 1.6180339887498948482045868343656381177203 ok
<SNIP>
Challenge accepted.
Adding a square root on top of the one screen:
--------------------8<----------------------------------

INCLUDE fix.blk
: s. DUP 0< IF &- EMIT THEN ABS 20 U.s ;

\ For DOUBLE return FLOOR of its square root
\ If the double is interpreted as a scaled number, so must floor.
: DSQRT 2DUP OR 0= IF DROP EXIT THEN
DUP IF MAX-INT ELSE 1000 THEN >R
BEGIN 2DUP R@ SM/REM R@ + 1 RSHIFT DUP R@ < WHILE RDROP >R DROP REPEAT
2DROP 2DROP R> ;

: SQRTs 1/1 M* DSQRT ;

: golden-ratio 5 1 rat>s SQRTs 1/1 +s 1/1 2 * /s s. ;

golden-ratio
\ 1.61803398874989484788
--------------------8<----------------------------------

>
>-marcel

Groetjes Albert
--
Don't praise the day before the evening. One swallow doesn't make spring.
You must not say "hey" before you have crossed the bridge. Don't sell the
hide of the bear until you shot it. Better one bird in the hand than ten in
the air. First gain is a cat spinning. - the Wise from Antrim -

On Monday, September 4, 2023 at 11:30:29 AM UTC+2, none albert wrote:
> In article <2265ddd9-d878-4644...@googlegroups.com>,
> Marcel Hendrix <m...@iae.nl> wrote:
[..]
> Challenge accepted.
> Adding a square root on top of the one screen:
[..]
> : golden-ratio 5 1 rat>s SQRTs 1/1 +s 1/1 2 * /s s. ;
>
> golden-ratio
> \ 1.61803398874989484788

Are the last 4 digits accurate?

avh: 1.61803398874989484788
mpc: 1.6180339887498948482045868343656381177203

-marcel

On Monday, September 4, 2023 at 11:25:46 AM UTC+2, none albert wrote:
[..]
> Happily chugging along with 10,000 digits in my 64 bits Forth,
> in one minute 17 seconds.
> The lines contain 50 digits, on average only.

Here it needs 2.23 seconds (I/O time about 200ms).

FORTH> RUN
3141592653589793238462643383279502884197169399375
10582097494459230781640628620899862803482534211706
79821480865132823066470938446095505822317253594081
2848111745028410270193852110555964462294895493038
19644288109756659334461284756482337867831652712019
091456485669234603486104543266482133936072602491412
73724587006606315588174881520920962829254091715364
3678925903600113305305488204665213841469519415116
094330572703657595919530921861173819326117931051185
48074462379962749567351885752724891227938183011949
1298336733624406566430860213949463952247371907021
798609437027705392171762931767523846748184676694051
32000568127145263560827785771342757789609173637178
72146844090122495343014654958537105079227968925892
35420199561121290219608640344181598136297747713099
60518707211349999998372978049951059731732816096318
59502445945534690830264252230825334468503526193118
81710100031378387528865875332083814206171776691473
03598253490428755468731159562863882353787593751957
78185778053217122680661300192787661119590921642019
89380952572010654858632788659361533818279682303019
52035301852968995773622599413891249721775283479131
51557485724245415069595082953311686172785588907509
83817546374649393192550604009277016711390098488240
12858361603563707660104710181942955596198946767837
44944825537977472684710404753464620804668425906949
12933136770289891521047521620569660240580381501935
11253382430035587640247496473263914199272604269922
79678235478163600934172164121992458631503028618297
45557067498385054945885869269956909272107975093029
55321165344987202755960236480665499119881834797753
56636980742654252786255181841757467289097777279380
00816470600161452491921732172147723501414419735685
48161361157352552133475741849468438523323907394143
33454776241686251898356948556209921922218427255025
42568876717904946016534668049886272327917860857843
83827967976681454100953883786360950680064225125205
11739298489608412848862694560424196528502221066118
63067442786220391949450471237137869609563643719172
87467764657573962413890865832645995813390478027590
09946576407895126946839835259570982582262052248940
77267194782684826014769909026401363944374553050682
03496252451749399651431429809190659250937221696461
51570985838741059788595977297549893016175392846813
82686838689427741559918559252459539594310499725246
80845987273644695848653836736222626099124608051243
8843904512441365497627807977156914359977001296160
894416948685558484063534220722258284886481584560285
0601684273945226746767889525213852254995466672782
398645659611635488623057745649803559363456817432411
25150760694794510965960940252288797108931456691368
67228748940560101503308617928680920874760917824938
58900971490967598526136554978189312978482168299894
87226588048575640142704775551323796414515237462343
64542858444795265867821051141354735739523113427166
10213596953623144295248493718711014576540359027993
44037420073105785390621983874478084784896833214457
13868751943506430218453191048481005370614680674919
2781911979399520614196634287544406437451237181921
799983910159195618146751426912397489409071864942319
6156794520809514655022523160388193014209376213785
595663893778708303906979207734672218256259966150142
15030680384477345492026054146659252014974428507325
18666002132434088190710486331734649651453905796268
56100550810665879699816357473638405257145910289706
41401109712062804390397595156771577004203378699360
07230558763176359421873125147120532928191826186125
86732157919841484882916447060957527069572209175671
1672291098169091528017350671274858322287183520935
396572512108357915136988209144421006751033467110314
12671113699086585163983150197016515116851714376576
18351556508849099898599823873455283316355076479185
35893226185489632132933089857064204675259070915481
41654985946163718027098199430992448895757128289059
23233260972997120844335732654893823911932597463667
30583604142813883032038249037589852437441702913276
56180937734440307074692112019130203303801976211011
00449293215160842444859637669838952286847831235526
58213144957685726243344189303968642624341077322697
8028073189154411010446823252716201052652272111660
396665573092547110557853763466820653109896526918620
56476931257058635662018558100729360659876486117910
45334885034611365768675324944166803962657978771855
60845529654126654085306143444318586769751456614068
00700237877659134401712749470420562230538994561314
07112700040785473326993908145466464588079727082668
30634328587856983052358089330657574067954571637752
54202114955761581400250126228594130216471550979259
23099079654737612551765675135751782966645477917450
11299614890304639947132962107340437518957359614589
0193897131117904297828564750320319869151402870808
599048010941214722131794764777262241425485454033215
71853061422881375850430633217518297986622371721591
60771669254748738986654949450114654062843366393790
03976926567214638530673609657120918076383271664162
7488880078692560290228472104031721186082041900042
296617119637792133757511495950156604963186294726547
36425230817703675159067350235072835405670403867435
13622224771589150495309844489333096340878076932599
39780541934144737744184263129860809988868741326047
21569516239658645730216315981931951673538129741677
29478672422924654366800980676928238280689964004824
35403701416314965897940924323789690706977942236250
82216889573837986230015937764716512289357860158816
17557829735233446042815126272037343146531977774160
31990665541876397929334419521541341899485444734567
38316249934191318148092777710386387734317720754565
45322077709212019051660962804909263601975988281613
32316663652861932668633606273567630354477628035045
07772355471058595487027908143562401451718062464362
67945612753181340783303362542327839449753824372058
35311477119926063813346776879695970309833913077109
87040859133746414428227726346594704745878477872019
27715280731767907707157213444730605700733492436931
13835049316312840425121925651798069411352801314701
30478164378851852909285452011658393419656213491434
15956258658655705526904965209858033850722426482939
72858478316305777756068887644624824685792603953527
73480304802900587607582510474709164396136267604492
56274204208320856611906254543372131535958450687724
60290161876679524061634252257719542916299193064553
77991403734043287526288896399587947572917464263574
55254079091451357111369410911939325191076020825202
61879853188770584297259167781314969900901921169717
37278476847268608490033770242429165130050051683233
64350389517029893922334517220138128069650117844087
45196012122859937162313017114448464090389064495444
00619869075485160263275052983491874078668088183385
10228334508504860825039302133219715518430635455007
66828294930413776552793975175461395398468339363830
47461199665385815384205685338621867252334028308711
23282789212507712629463229563989898935821167456270
10218356462201349671518819097303811980049734072396
10368540664319395097901906996395524530054505806855
01956730229219139339185680344903982059551002263535
36192041994745538593810234395544959778377902374216
17271117236434354394782218185286240851400666044332
5888569867054315470696574745855033232334210730154
594051655379068662733379958511562578432298827372319
89875714159578111963583300594087306812160287649628
67446047746491599505497374256269010490377819868359
38146574126804925648798556145372347867330390468838
34363465537949864192705638729317487233208376011230
29911367938627089438799362016295154133714248928307
22012690147546684765357616477379467520049075715552
78196536213239264061601363581559074220202031872776
05277219005561484255518792530343513984425322341576
23361064250639049750086562710953591946589751413103
48227693062474353632569160781547818115284366795706
11086153315044521274739245449454236828860613408414
86377670096120715124914043027253860764823634143346
23518975766452164137679690314950191085759844239198
62916421939949072362346468441173940326591840443780
51333894525742399508296591228508555821572503107125
70126683024029295252201187267675622041542051618416
34847565169998116141010029960783869092916030288400
26910414079288621507842451670908700069928212066041
83718065355672525325675328612910424877618258297651
57959847035622262934860034158722980534989650226291
74878820273420922224533985626476691490556284250391
27577102840279980663658254889264880254566101729670
26640765590429099456815065265305371829412703369313
78517860904070866711496558343434769338578171138645
5873678123014587687126603489139095620099393610310
291616152881384379099042317473363948045759314931405
29763475748119356709110137751721008031559024853090
66920376719220332290943346768514221447737939375170
34436619910403375111735471918550464490263655128162
28824462575916333039107225383742182140883508657391
77150968288747826569959957449066175834413752239709
68340800535598491754173818839994469748676265516582
7658483588453142775687900290951702835297163445621
296404352311760066510124120065975585127617858382920
41974844236080071930457618932349229279650198751872
12726750798125547095890455635792122103334669749923
56302549478024901141952123828153091140790738602515
22742995818072471625916685451333123948049470791191
53267343028244186041426363954800044800267049624820
17928964766975831832713142517029692348896276684403
23260927524960357996469256504936818360900323809293
45958897069536534940603402166544375589004563288225
05452556405644824651518754711962184439658253375438
8569094113031509526179378002974120766514793942590
298969594699556576121865619673378623625612521632086
28692221032748892186543648022967807057656151446320
46927906821207388377814233562823608963208068222468
01224826117718589638140918390367367222088832151375
56003727983940041529700287830766709444745601345564
17254370906979396122571429894671543578468788614445
81231459357198492252847160504922124247014121478057
34551050080190869960330276347870810817545011930714
12233908663938339529425786905076431006383519834389
34159613185434754649556978103829309716465143840700
70736041123735998434522516105070270562352660127648
48308407611830130527932054274628654036036745328651
05706587488225698157936789766974220575059683440869
73502014102067235850200724522563265134105592401902
74216248439140359989535394590944070469120914093870
01264560016237428802109276457931065792295524988727
58461012648369998922569596881592056001016552563756
2.489 seconds elapsed. ok

Marcel Hendrix schrieb am Montag, 4. September 2023 um 19:14:06 UTC+2:
> On Monday, September 4, 2023 at 11:25:46 AM UTC+2, none albert wrote:
> [..]
> > Happily chugging along with 10,000 digits in my 64 bits Forth,
> > in one minute 17 seconds.
> > The lines contain 50 digits, on average only.
> Here it needs 2.23 seconds (I/O time about 200ms).
>
> FORTH> RUN
> 3141592653589793238462643383279502884197169399375
> 10582097494459230781640628620899862803482534211706
> 79821480865132823066470938446095505822317253594081
> 2848111745028410270193852110555964462294895493038
> 19644288109756659334461284756482337867831652712019
> 091456485669234603486104543266482133936072602491412
> 73724587006606315588174881520920962829254091715364
> 3678925903600113305305488204665213841469519415116
> 094330572703657595919530921861173819326117931051185
> 48074462379962749567351885752724891227938183011949
> 1298336733624406566430860213949463952247371907021
> 798609437027705392171762931767523846748184676694051
> 32000568127145263560827785771342757789609173637178
> 72146844090122495343014654958537105079227968925892
> 35420199561121290219608640344181598136297747713099
> 60518707211349999998372978049951059731732816096318
> 59502445945534690830264252230825334468503526193118
> 81710100031378387528865875332083814206171776691473
> 03598253490428755468731159562863882353787593751957
> 78185778053217122680661300192787661119590921642019
> 89380952572010654858632788659361533818279682303019
> 52035301852968995773622599413891249721775283479131
> 51557485724245415069595082953311686172785588907509
> 83817546374649393192550604009277016711390098488240
> 12858361603563707660104710181942955596198946767837
> 44944825537977472684710404753464620804668425906949
> 12933136770289891521047521620569660240580381501935
> 11253382430035587640247496473263914199272604269922
> 79678235478163600934172164121992458631503028618297
> 45557067498385054945885869269956909272107975093029
> 55321165344987202755960236480665499119881834797753
> 56636980742654252786255181841757467289097777279380
> 00816470600161452491921732172147723501414419735685
> 48161361157352552133475741849468438523323907394143
> 33454776241686251898356948556209921922218427255025
> 42568876717904946016534668049886272327917860857843
> 83827967976681454100953883786360950680064225125205
> 11739298489608412848862694560424196528502221066118
> 63067442786220391949450471237137869609563643719172
> 87467764657573962413890865832645995813390478027590
> 09946576407895126946839835259570982582262052248940
> 77267194782684826014769909026401363944374553050682
> 03496252451749399651431429809190659250937221696461
> 51570985838741059788595977297549893016175392846813
> 82686838689427741559918559252459539594310499725246
> 80845987273644695848653836736222626099124608051243
> 8843904512441365497627807977156914359977001296160
> 894416948685558484063534220722258284886481584560285
> 0601684273945226746767889525213852254995466672782
> 398645659611635488623057745649803559363456817432411
> 25150760694794510965960940252288797108931456691368
> 67228748940560101503308617928680920874760917824938
> 58900971490967598526136554978189312978482168299894
> 87226588048575640142704775551323796414515237462343
> 64542858444795265867821051141354735739523113427166
> 10213596953623144295248493718711014576540359027993
> 44037420073105785390621983874478084784896833214457
> 13868751943506430218453191048481005370614680674919
> 2781911979399520614196634287544406437451237181921
> 799983910159195618146751426912397489409071864942319
> 6156794520809514655022523160388193014209376213785
> 595663893778708303906979207734672218256259966150142
> 15030680384477345492026054146659252014974428507325
> 18666002132434088190710486331734649651453905796268
> 56100550810665879699816357473638405257145910289706
> 41401109712062804390397595156771577004203378699360
> 07230558763176359421873125147120532928191826186125
> 86732157919841484882916447060957527069572209175671
> 1672291098169091528017350671274858322287183520935
> 396572512108357915136988209144421006751033467110314
> 12671113699086585163983150197016515116851714376576
> 18351556508849099898599823873455283316355076479185
> 35893226185489632132933089857064204675259070915481
> 41654985946163718027098199430992448895757128289059
> 23233260972997120844335732654893823911932597463667
> 30583604142813883032038249037589852437441702913276
> 56180937734440307074692112019130203303801976211011
> 00449293215160842444859637669838952286847831235526
> 58213144957685726243344189303968642624341077322697
> 8028073189154411010446823252716201052652272111660
> 396665573092547110557853763466820653109896526918620
> 56476931257058635662018558100729360659876486117910
> 45334885034611365768675324944166803962657978771855
> 60845529654126654085306143444318586769751456614068
> 00700237877659134401712749470420562230538994561314
> 07112700040785473326993908145466464588079727082668
> 30634328587856983052358089330657574067954571637752
> 54202114955761581400250126228594130216471550979259
> 23099079654737612551765675135751782966645477917450
> 11299614890304639947132962107340437518957359614589
> 0193897131117904297828564750320319869151402870808
> 599048010941214722131794764777262241425485454033215
> 71853061422881375850430633217518297986622371721591
> 60771669254748738986654949450114654062843366393790
> 03976926567214638530673609657120918076383271664162
> 7488880078692560290228472104031721186082041900042
> 296617119637792133757511495950156604963186294726547
> 36425230817703675159067350235072835405670403867435
> 13622224771589150495309844489333096340878076932599
> 39780541934144737744184263129860809988868741326047
> 21569516239658645730216315981931951673538129741677
> 29478672422924654366800980676928238280689964004824
> 35403701416314965897940924323789690706977942236250
> 82216889573837986230015937764716512289357860158816
> 17557829735233446042815126272037343146531977774160
> 31990665541876397929334419521541341899485444734567
> 38316249934191318148092777710386387734317720754565
> 45322077709212019051660962804909263601975988281613
> 32316663652861932668633606273567630354477628035045
> 07772355471058595487027908143562401451718062464362
> 67945612753181340783303362542327839449753824372058
> 35311477119926063813346776879695970309833913077109
> 87040859133746414428227726346594704745878477872019
> 27715280731767907707157213444730605700733492436931
> 13835049316312840425121925651798069411352801314701
> 30478164378851852909285452011658393419656213491434
> 15956258658655705526904965209858033850722426482939
> 72858478316305777756068887644624824685792603953527
> 73480304802900587607582510474709164396136267604492
> 56274204208320856611906254543372131535958450687724
> 60290161876679524061634252257719542916299193064553
> 77991403734043287526288896399587947572917464263574
> 55254079091451357111369410911939325191076020825202
> 61879853188770584297259167781314969900901921169717
> 37278476847268608490033770242429165130050051683233
> 64350389517029893922334517220138128069650117844087
> 45196012122859937162313017114448464090389064495444
> 00619869075485160263275052983491874078668088183385
> 10228334508504860825039302133219715518430635455007
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> 47461199665385815384205685338621867252334028308711
> 23282789212507712629463229563989898935821167456270
> 10218356462201349671518819097303811980049734072396
> 10368540664319395097901906996395524530054505806855
> 01956730229219139339185680344903982059551002263535
> 36192041994745538593810234395544959778377902374216
> 17271117236434354394782218185286240851400666044332
> 5888569867054315470696574745855033232334210730154
> 594051655379068662733379958511562578432298827372319
> 89875714159578111963583300594087306812160287649628
> 67446047746491599505497374256269010490377819868359
> 38146574126804925648798556145372347867330390468838
> 34363465537949864192705638729317487233208376011230
> 29911367938627089438799362016295154133714248928307
> 22012690147546684765357616477379467520049075715552
> 78196536213239264061601363581559074220202031872776
> 05277219005561484255518792530343513984425322341576
> 23361064250639049750086562710953591946589751413103
> 48227693062474353632569160781547818115284366795706
> 11086153315044521274739245449454236828860613408414
> 86377670096120715124914043027253860764823634143346
> 23518975766452164137679690314950191085759844239198
> 62916421939949072362346468441173940326591840443780
> 51333894525742399508296591228508555821572503107125
> 70126683024029295252201187267675622041542051618416
> 34847565169998116141010029960783869092916030288400
> 26910414079288621507842451670908700069928212066041
> 83718065355672525325675328612910424877618258297651
> 57959847035622262934860034158722980534989650226291
> 74878820273420922224533985626476691490556284250391
> 27577102840279980663658254889264880254566101729670
> 26640765590429099456815065265305371829412703369313
> 78517860904070866711496558343434769338578171138645
> 5873678123014587687126603489139095620099393610310
> 291616152881384379099042317473363948045759314931405
> 29763475748119356709110137751721008031559024853090
> 66920376719220332290943346768514221447737939375170
> 34436619910403375111735471918550464490263655128162
> 28824462575916333039107225383742182140883508657391
> 77150968288747826569959957449066175834413752239709
> 68340800535598491754173818839994469748676265516582
> 7658483588453142775687900290951702835297163445621
> 296404352311760066510124120065975585127617858382920
> 41974844236080071930457618932349229279650198751872
> 12726750798125547095890455635792122103334669749923
> 56302549478024901141952123828153091140790738602515
> 22742995818072471625916685451333123948049470791191
> 53267343028244186041426363954800044800267049624820
> 17928964766975831832713142517029692348896276684403
> 23260927524960357996469256504936818360900323809293
> 45958897069536534940603402166544375589004563288225
> 05452556405644824651518754711962184439658253375438
> 8569094113031509526179378002974120766514793942590
> 298969594699556576121865619673378623625612521632086
> 28692221032748892186543648022967807057656151446320
> 46927906821207388377814233562823608963208068222468
> 01224826117718589638140918390367367222088832151375
> 56003727983940041529700287830766709444745601345564
> 17254370906979396122571429894671543578468788614445
> 81231459357198492252847160504922124247014121478057
> 34551050080190869960330276347870810817545011930714
> 12233908663938339529425786905076431006383519834389
> 34159613185434754649556978103829309716465143840700
> 70736041123735998434522516105070270562352660127648
> 48308407611830130527932054274628654036036745328651
> 05706587488225698157936789766974220575059683440869
> 73502014102067235850200724522563265134105592401902
> 74216248439140359989535394590944070469120914093870
> 01264560016237428802109276457931065792295524988727
> 58461012648369998922569596881592056001016552563756
> 2.489 seconds elapsed. ok
>
> No idea if it's correct :--)

On 5/09/2023 3:14 am, Marcel Hendrix wrote:
> [..]
> 58461012648369998922569596881592056001016552563756
> 2.489 seconds elapsed. ok
>
> No idea if it's correct :--)

After only 1000 digits? One would hope so. Otherwise what would
be the value of having a 64-bit cpu? Using mixed-math on a 16-bit
machine it's possible to generate around 45,000 digits accurately
using Machin's formula before arithmetic overflow. So the question
isn't whether 1000 digits is accurate but rather, when does it fails
and what was the cause.

On Tuesday, September 5, 2023 at 1:27:17 AM UTC+2, dxforth wrote:
> On 5/09/2023 3:14 am, Marcel Hendrix wrote:
> > [..]
> > 58461012648369998922569596881592056001016552563756
> > 2.489 seconds elapsed. ok
> >
> > No idea if it's correct :--)
> After only 1000 digits? One would hope so. Otherwise what would
> be the value of having a 64-bit cpu? Using mixed-math on a 16-bit
> machine it's possible to generate around 45,000 digits accurately
> using Machin's formula before arithmetic overflow. So the question
> isn't whether 1000 digits is accurate but rather, when does it fails
> and what was the cause.

That is what I meant: there could be an implementation problem.
(I'm now certain its correct upto 10,000 digits.)

-marcel

I've just created an app that shows* 45,000 digits of pi in just 0.025s!

8th -ee '"pi_dec_1m.txt" f:slurp 0 45000 b:slice >s . cr'

* you need to have downloaded 'pi_dec_1m.txt' first...

On 05/09/2023 14:51, Marcel Hendrix wrote:
> On Tuesday, September 5, 2023 at 1:27:17 AM UTC+2, dxforth wrote:
>> On 5/09/2023 3:14 am, Marcel Hendrix wrote:
>>> [..]
>>> 58461012648369998922569596881592056001016552563756
>>> 2.489 seconds elapsed. ok
>>>
>>> No idea if it's correct :--)
>> After only 1000 digits? One would hope so. Otherwise what would
>> be the value of having a 64-bit cpu? Using mixed-math on a 16-bit
>> machine it's possible to generate around 45,000 digits accurately
>> using Machin's formula before arithmetic overflow. So the question
>> isn't whether 1000 digits is accurate but rather, when does it fails
>> and what was the cause.
>
> That is what I meant: there could be an implementation problem.
> (I'm now certain its correct upto 10,000 digits.)
>
> -marcel

Ron AARON schrieb am Dienstag, 5. September 2023 um 14:55:11 UTC+2:
> I've just created an app that shows* 45,000 digits of pi in just 0.025s!

Now you should be able to confirm that
.... the millionth digit of pi after the decimal point is a '1' ...
without wrecking your electricity bill ;-)

On 06/09/2023 9:15, minforth wrote:
> Ron AARON schrieb am Dienstag, 5. September 2023 um 14:55:11 UTC+2:
>> I've just created an app that shows* 45,000 digits of pi in just 0.025s!
>
> Now you should be able to confirm that
> ... the millionth digit of pi after the decimal point is a '1' ...
> without wrecking your electricity bill ;-)

Exactly :)

On 6/09/2023 10:35 pm, Ron AARON wrote:
> On 06/09/2023 9:15, minforth wrote:
>> Ron AARON schrieb am Dienstag, 5. September 2023 um 14:55:11 UTC+2:
>>> I've just created an app that shows* 45,000 digits of pi in just 0.025s!
>>
>> Now you should be able to confirm that
>> ... the millionth digit of pi after the decimal point is a '1' ...
>> without wrecking your electricity bill  ;-)
>
> Exactly :)

The computer that calculates PI is not the problem. It's the computer
that is connected to the internet that drains money :)

On Wednesday, September 6, 2023 at 8:35:57 AM UTC-5, dxforth wrote:
> On 6/09/2023 10:35 pm, Ron AARON wrote:
> > On 06/09/2023 9:15, minforth wrote:
> >> Ron AARON schrieb am Dienstag, 5. September 2023 um 14:55:11 UTC+2:
> >>> I've just created an app that shows* 45,000 digits of pi in just 0.025s!
> >>
> >> Now you should be able to confirm that
> >> ... the millionth digit of pi after the decimal point is a '1' ...
> >> without wrecking your electricity bill ;-)
> >
> > Exactly :)T> The computer that calculates PI is not the problem. It's the computer
> that is connected to the internet that drains money :)

There is a town in Texas where a company is bit coin mining. The company consumes more power than all the
homes in the town.
--
me

On Wednesday, September 6, 2023 at 11:14:26 PM UTC+2, S Jack wrote:
> On Wednesday, September 6, 2023 at 8:35:57 AM UTC-5, dxforth wrote:
[..]
> > > Exactly :)T> The computer that calculates PI is not the problem. It's the computer
> > that is connected to the internet that drains money :)
> There is a town in Texas where a company is bit coin mining. The company consumes more power than all the
> homes in the town.

A company? If you go that far, the persons with the spreadsheets will increase
the size of the facility until you consume all the power that is available without
huge price jumps (and maybe even then). The town probably willingly subsidizes
them.

-marcel

Marcel Hendrix schrieb am Donnerstag, 7. September 2023 um 06:50:44 UTC+2:
> On Wednesday, September 6, 2023 at 11:14:26 PM UTC+2, S Jack wrote:
> > On Wednesday, September 6, 2023 at 8:35:57 AM UTC-5, dxforth wrote:
> [..]
> > > > Exactly :)T> The computer that calculates PI is not the problem. It's the computer
> > > that is connected to the internet that drains money :)
> > There is a town in Texas where a company is bit coin mining. The company consumes more power than all the
> > homes in the town.
> A company? If you go that far, the persons with the spreadsheets will increase
> the size of the facility until you consume all the power that is available without
> huge price jumps (and maybe even then). The town probably willingly subsidizes
> them.
I read that the whole Chinese province north of Beijing (called inner Mongolia)
consumed more electricity for bitcoin mining than for anything else (illegal power
theft not counted) during the covid pandemy. Regarding the "conditions" of many
of their coal-fired power plants (I've been there) the CO2 impact is gigantic.

Good that our government is now deindustrializing our country to compensate that.