Re: Ile zajmie komputerowi mnożenie liczb rzędu 2^128

eGospodarka.pl › Grupy › pl.comp.programming › Ile zajmie komputerowi mnożenie liczb rzędu 2^128 › Re: Ile zajmie komputerowi mnożenie liczb rzędu 2^128

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From: Piotr Chamera <p...@p...onet.pl>
Newsgroups: pl.comp.programming
Subject: Re: Ile zajmie komputerowi mnożenie liczb rzędu 2^128
Date: Wed, 4 Dec 2019 13:25:13 +0100
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[ ukryj nagłówki ]
W dniu 2019-12-04 o 12:43, o...@g...com pisze:
>>> Naprawdę będzie całkowita? Tak z ciekawości sprawdziłem dla 2^64
>>>
>>> 2^64 -5= 18446744073709551611 * 2,5= 46116860184273879027,5 +2,5=
46116860184273879030 /2
>>> =23058430092136939515 * 2,5 =57646075230342348787,5 +2,5 = 57646075230342348790
/2 =
>>> 28823037615171174395 *2,5= 72057594037927935993,75 + 2,5 ...
>>
>> Coś mi się źle wymnożyło :)
>
> Chyba tak. Kilka pierwszych wyrazów:
>
> 850705917302346158658436518579420528630
>
> 425352958651173079329218259289710264315
>
> 1063382396627932698323045648224275660790
>
> 531691198313966349161522824112137830395
>
> 1329227995784915872903807060280344575990
>
> 664613997892457936451903530140172287995
>
> 1661534994731144841129758825350430719990
>
> 830767497365572420564879412675215359995
>
> 2076918743413931051412198531688038399990
>
> 1038459371706965525706099265844019199995
>

Jeśli się gdzieś nie pomyliłem, to komplet wyników
pośrednich (po mnożeniu, dodawaniu i dzieleniu) to:

340282366920938463463374607431768211451
425352958651173079329218259289710264315
531691198313966349161522824112137830395
664613997892457936451903530140172287995
830767497365572420564879412675215359995
1038459371706965525706099265844019199995
1298074214633706907132624082305023999995
1622592768292133633915780102881279999995
2028240960365167042394725128601599999995
2535301200456458802993406410751999999995
3169126500570573503741758013439999999995
3961408125713216879677197516799999999995
4951760157141521099596496895999999999995
6189700196426901374495621119999999999995
7737125245533626718119526399999999999995
9671406556917033397649407999999999999995
12089258196146291747061759999999999999995
15111572745182864683827199999999999999995
18889465931478580854783999999999999999995
23611832414348226068479999999999999999995
29514790517935282585599999999999999999995
36893488147419103231999999999999999999995
46116860184273879039999999999999999999995
57646075230342348799999999999999999999995
72057594037927935999999999999999999999995
90071992547409919999999999999999999999995
112589990684262399999999999999999999999995
140737488355327999999999999999999999999995
175921860444159999999999999999999999999995
219902325555199999999999999999999999999995
274877906943999999999999999999999999999995
343597383679999999999999999999999999999995
429496729599999999999999999999999999999995
536870911999999999999999999999999999999995
671088639999999999999999999999999999999995
838860799999999999999999999999999999999995
1048575999999999999999999999999999999999995
1310719999999999999999999999999999999999995
1638399999999999999999999999999999999999995
2047999999999999999999999999999999999999995
2559999999999999999999999999999999999999995
3199999999999999999999999999999999999999995
3999999999999999999999999999999999999999995
4999999999999999999999999999999999999999995
6249999999999999999999999999999999999999995
7812499999999999999999999999999999999999995
9765624999999999999999999999999999999999995
12207031249999999999999999999999999999999995
15258789062499999999999999999999999999999995
19073486328124999999999999999999999999999995
23841857910156249999999999999999999999999995
29802322387695312499999999999999999999999995
37252902984619140624999999999999999999999995
46566128730773925781249999999999999999999995
58207660913467407226562499999999999999999995
72759576141834259033203124999999999999999995
90949470177292823791503906249999999999999995
113686837721616029739379882812499999999999995
142108547152020037174224853515624999999999995
177635683940025046467781066894531249999999995
222044604925031308084726333618164062499999995
277555756156289135105907917022705078124999995
346944695195361418882384896278381347656249995
433680868994201773602981120347976684570312495
542101086242752217003726400434970855712890620

ale dalsze iteracje już są ułamkowe.

dla 2^64 całkowite są tylko do 32 iteracji:

18446744073709551611
23058430092136939515
28823037615171174395
36028797018963967995
45035996273704959995
56294995342131199995
70368744177663999995
87960930222079999995
109951162777599999995
137438953471999999995
171798691839999999995
214748364799999999995
268435455999999999995
335544319999999999995
419430399999999999995
524287999999999999995
655359999999999999995
819199999999999999995
1023999999999999999995
1279999999999999999995
1599999999999999999995
1999999999999999999995
2499999999999999999995
3124999999999999999995
3906249999999999999995
4882812499999999999995
6103515624999999999995
7629394531249999999995
9536743164062499999995
11920928955078124999995
14901161193847656249995
18626451492309570312495
23283064365386962890620
116415321826934814453105/4
582076609134674072265545/16
2910383045673370361327805/64
14551915228366851806639345/256
72759576141834259033198005/1024
363797880709171295165995145/4096
1818989403545856475829996205/16384
9094947017729282379150062945/65536
45474735088646411895750642405/262144
227373675443232059478754522745/1048576
1136868377216160297393777856605/4194304
5684341886080801486968910254545/16777216
28421709430404007434844635158805/67108864
142108547152020037174223511338345/268435456
710542735760100185871118898869005/1073741824
3552713678800500929355599863054145/4294967296
17763568394002504646778020790107205/17179869184
88817841970012523233890189849881945/68719476736
444089209850062616169451292846793405/274877906944
2220446049250313080847257838623501745/1099511627776
11102230246251565404236294690675647605/4398046511104
55511151231257827021181495443610793545/1759218604441
6
277555756156289135105907565178984189805/703687441776
64
1387778780781445675529538177738641837345/28147497671
0656
6938893903907228377647692296068092740005/11258999068
42624
34694469519536141888238467109839997913145/4503599627
370496
173472347597680709441192358067198126418205/180143985
09481984
867361737988403547205961880407983179500945/720575940
37927936
4336808689942017736029809762327886087144405/28823037
6151711744
21684043449710088680149050252791311194280745/1152921
504606846976
108420217248550443400745257028564079005638605/461168
6018427387904
542101086242752217003726308201250487165132545/184467
44073709551616