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Re: 2^20991011-1

• To: mathgroup at smc.vnet.net
• Subject: [mg45462] Re: 2^20991011-1
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Fri, 9 Jan 2004 05:20:29 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <bti1no$a7g$1@smc.vnet.net>
• Reply-to: kuska at informatik.uni-leipzig.de
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

perhaps you computer and an english news-group don't like
german comments.

An other point may be, that with a multi precision arithmetic
2^x_Integer is simply a shift left operation and the -1 need
only a simple addition.

There are several public domain/open source implementations
of multi-precission arithmetic namely

http://www.swox.com/gmp/

and you should have
a look at this source code

Regards
  Jens

Friedrich Laher wrote:
> 
> how can mathematica do that that fast ( 100 seconds on 2.4GHz Athalon )
> while the following needs almost 100 minutes
> #include<stdio.h>
> /*
> Zahl = 2^20 996 011 -  1 get decimal representation,
> but
> base 10^9 Zahl, 9 dec. digits codes binary in 32Bit.
> 
> 20 996 011*DekadischerLog(2) = 6 320 429, 100 ...
> Zahl
> has 6 320 431 dec. digits, so needs 702 271 unsigned long's ( of 32 bit ).
> 
> 20 996 011 bit's are 656 125 *32 + 11, 2^11-1 = 2074
> ---------------------
> 1 Stunde 38 Min. 3 Sek
> --------------------
> */
> unsigned long Zahl[702271], *DezZeiger;
> int main()
> {
> asm("
> #                       INITIALISIERUNG
> 
>         PUSHL %ebx
>         MOVD %esp,%mm3; LEA Zahl+4*702271,%esp
> 
>         MOVL  $656125,%ecx
>         MOVD    %ecx,%mm2; MOVL $1,%eax; MOVD %eax,%mm1
> 
>         CLC;CMC;  CLD
> 
>         LEA Zahl,%edi; MOVD %edi,%mm0
> 
>         MOV $2047,%edx; MOVL $1000000000,%ebx
> InitLoop:
>         SBB %eax,%eax; DIV %ebx; STOSL; LOOP InitLoop; JMP DezStore
> 
> #       HAUPTSCHLEIFE
> DivLoop:
>         LODSL; DIVL %ebx
> unShortened:
>         STOSL; LOOP DivLoop
> DezStore:
>         PUSHL %edx
>         MOVD  %mm2,%ecx; TESTL %ecx,%ecx; JE endCalc
> 
>         MOVD %mm0,%esi; MOVL %esi,%edi
> 
>         LODSL; SUBL %edx,%edx; DIVL %ebx
> 
>         TESTL %eax,%eax
>         JNE unShortened; PSUBD %mm1,%mm2; LOOP DivLoop; JMP DezStore
> endCalc:
>         MOVL %esp, DezZeiger; MOVD %mm3,%esp
>         POPL %ebx
> ");
> for(;DezZeiger != Zahl+702271;++DezZeiger)printf("%09u ",*DezZeiger);
> 
> printf("\n");
> }