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README

README
	for progs/core2papers/many_digits
$Id: README,v 1.6 2010/06/25 10:15:49 exact Exp $
============================================================

Jan 2010:
	The following are CORE 2 library's performance on
	some problems from the "Many Digits" friendly competition (2005).

	Our results are for Problems C01-C010 competition.
		The original competition asks for 10^n (n=2,3,4,...) digits
		of output depending on the problem.   
	Below, we show our results to 100 digits only.
		We check our results with the output from Maple 11.
		In most cases, we agree with Maple 11 up to the last digit
		(this ought to be the case).  But in Problem C04, we differ
		in the last 3 digits.  So one of us must be wrong...
	SUMMARY:
	  Since Core is leveraged on MPFR for most of these problems, our performance
		cannot beat MPFR.  However, the MPFR team uses hand-coded precision,
		Core has automated all these computations.
	  Core cannot do C08 because of memory overflow.
	  Core cannot do C06 and C09 because we have not
		yet implemented inverse elementary functions,
		and elementary hyperbolic functions. 

============================================================
Problem C01 : compute sin(tan(cos(1))) to 100 digits.

CORE 2 = 0.5645109298619598058276864064502964857764866158258856955552147245934844803576138875921296745208522198
MAPLE =  0.5645109298619598058276864064502964857764866158258856955552147245934844803576138875921296745208522198
it took 0 mseconds.
============================================================
Problem C02 : compute sqrt(e()/pi()) to 100 digits.

CORE 2 = 0.9301913671026328586681246236333315560297109207042887264450006489855422345460234483872155723942699766
MAPLE =  0.9301913671026328586681246236333315560297109207042887264450006489855422345460234483872155723942699765
it took 0 mseconds.
============================================================
Problem C03 : compute sin((e+1)^3) to 100 digits.

CORE 2 = 0.9094952410572662471855472194521742688939652422138080108799599078079083693175099387713504636663839043
MAPLE =  0.9094952410572662471855472194521742688939652422138080108799599078079083693175099387713504636663838965
it took 0 mseconds.
============================================================
Problem C04 : compute exp(pi*sqrt(2011)) to 100 digits.

CORE 2 = 15287325030838530726060718956632626460288135250495712354991535.08911292681099318912549002226654964403
MAPLE =  15287325030838530726060718956632626460288135250495712354991535.08911292681099318912549002226654964319 
it took 0 mseconds.
============================================================
Problem C05 : compute exp(exp(exp(1/2))) to 100 digits.

CORE 2 = 181.3313036085456935150575745126539838088636924785147592794392700131812592190818654155341658216570329
MAPLE =  181.3313036085456935150575745126539838088636924785147592794392700131812592190818654155341658216570329
it took 1 mseconds.
============================================================
Problem C06 : compute atanh(1 - atanh(1 - atanh(1 - atanh(1/Pi)))) to 100 digits.

CORE 2 = "atanh" not implemented yet

MAPLE = 
============================================================
Problem C07 : compute pi^1000 to 100 digits.

CORE 2 = 1.412123544515764812310439732881587635475963461582062574048346324112952884474452775306450654297508705e+497
MAPLE  = 1.412123544515764812310439732881587635475963461582062574048346324112952884474452775306450654297508713e+497
it took 1 mseconds.
============================================================
Problem C08 : compute sin(6^(6^6)) to 100 digits.

CORE 2 = out of memory
MAPLE =  −.9243782759082769071599129104213945374204053566344957618861208133051072506448921516566917643513054166
============================================================
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