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MathGroup Archive 2004

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2^20991011-1

  • To: mathgroup at smc.vnet.net
  • Subject: [mg45441] 2^20991011-1
  • From: Friedrich Laher <mathefritz at schmieder-laher.de>
  • Date: Wed, 7 Jan 2004 17:31:05 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

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");
}


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