1 Hyperbolic Geometry The fact that an essay on geometry such as ...

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1 Hyperbolic Geometry The fact that an essay on geometry such as this must include an additional qualifier signifying what kind of geometry is to be discussed is a relatively new requirement. From around 300 B.C. until the early 19th century, 'geometry' meant Euclidean geometry, for there were no competing systems to rival the intrinsic truth of Euclid's geometry put forth in his Elements. But a particularly troublesome piece of the Euclidean puzzle began to lead thinkers down new avenues of geometrical description.

angle measure of a straight line
euclid
parallel postulate
pq
euclidean geometry
parallel lines
right angles
side
angle
line

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ECSE425Lecture20:
CacheBasics
H&PAppendixC
©2011Gross,Hayward,Arbel,Vu,Meyer
Textbookﬁgures©2007ElsevierScienceLastTime
•  IntroducPontoMemoryHierarchy
•  Whatarecaches?
•  Whycache?
•  FourQuesPons
– Q1:Blockplacement
©2011Gross,Hayward,Arbel,Vu,Meyer;
ECSE425,Fall2011,Lecture20 2©2007ElsevierScienceToday
•  TwoQuesPons:
– Q1:Blockplacement
– Q2:BlockidenPﬁca on
©2011Gross,Hayward,Arbel,Vu,Meyer;
ECSE425,Fall2011,Lecture20 3©2007ElsevierScienceFourMemoryHierarchyQuesPons
MainmemoryisdividedintoblockseachconsisPng
ofseveraldataelements(e.g.bytes)
1.  Blockplacement
– Wherecanablockbeplacedintheupperlevel?
2.  BlockidenPﬁca on
– Howisablockfoundifitisintheupperlevel?
3.  Blockreplacement
– Whichblockshouldbereplacedonamiss?
4.  Writestrategy
– Whathappensonawrite?
©2011Gross,Haward,Arbel,Vu,Meyer;
ECSE425,Fall2011,Lecture19 4©2007ElsevierScienceQ1:BlockPlacement
•  Fullyassocia ve
– Ablockcanappearanywhereinthecache
– Slowandcomplex,butthebesthitrate
•  Directmappedcache
– Eachblockcanonlyappearinoneplaceinthecache
•  Blockaddressmod#blocksincache
– Fastandsimple,butmoremisses
•  Setassocia vecachesstrikeabalance
©2011Gross,Haward,Arbel,Vu,Meyer;
ECSE425,Fall2011,Lecture19 5©2007ElsevierScienceSetAssocia veCaches
•  Ablockcanbeplacedinasetofplacesinthe
cache(calledways)
•  First,mapablockontoaset
– Blockaddressmod#setsincache
•  Theblockcanbeplacedanywhereinthatset
– nblocksinaset=>n-waysetassocia ve
©2011Gross,Haward,Arbel,Vu,Meyer;
ECSE425,Fall2011,Lecture19 6©2007ElsevierScienceBlockPlacement
C
f
M
©2011Gross,Haward,Arbel,Vu,Meyer;
ECSE425,Fall2011,Lecture19 7©2007ElsevierScienceGeneralizedAssocia vity
•  Ingeneral,mblocksincache,nblocksinaset,s
setsincache
– m=s*n
•  n-waysetassocia ve=> n>1ands>1
– fullyassocia ve=> n=mands=1(m-ways.a.)
– directmapped=>n=1ands=m(1-ways.a.)
•  Mapping:setnumberiscalled“index”
•  index=block#mods
©2011Gross,Haward,Arbel,Vu,Meyer;
ECSE425,Fall2011,Lecture19 8©2007ElsevierScienceRealCaches
•  Mostprocessorcachestodayare
– Directmapped,orn-waysetassocia ve, n≤8
•  Full-associa vity reservedforsmall,specialized
memories
– E.g.,Transla onLook-asideBuﬀer(TLB)
©2011Gross,Haward,Arbel,Vu,Meyer;
ECSE425,Fall2011,Lecture19 9©2007ElsevierScienceQ2:BlockIdenPﬁca on
•  Cachesholdasubsetofblocksinmainmemory
– Manyblocksmaptooneorafewentriesincache
– Howisablockfoundifitisinthecache?
•  Dividethememoryaddressintoﬁelds
•  Blockaddress(higher-orderbits)
– Indicatestheblocknumberinmemorywewillaccess
•  Blockoﬀset(lower-orderbits)
– Indicatesthedatawithinablockwewanttoretrieve
©2011Gross,Hayward,Arbel,Vu,Meyer;
ECSE425,Fall2011,Lecture20 10©2007ElsevierScience