Getting Real, Getting Dirty (without getting real dirty)

Getting Real, Getting Dirty(without getting real dirty)Ron K. CytronJoint work with Krishna Kavi University of Alabama at HuntsvilleApril 2001Dante Cannarozzi, Sharath Cholleti, Morgan Deters, Steve DonahueMark Franklin, Matt Hampton, Michael Henrichs, Nicholas Leidenfrost, Jonathan Nye, Michael Plezbert, Conrad WarmboldCenter for Distributed Object ComputingDepartment of Computer ScienceWashington UniversityFunded by the National Science Foundation under grant 0081214Funded by DARPA under contract F33615-00-C-1697

OutlineMotivationAllocationCollectionConclusion

Traditional architecture and object-oriented programsCaches are still biased toward Fortran-like behaviorCPU is still responsible for storage managementObject-management activity invalidates cachesGC disruptiveCompaction

An OO-biased design using IRAMs(with Krishna Kavi)CPU and cache stay the same, off-the-shelfMemory system redesigned to support OO programsCPU + cacheMMMML2 cacheLogicIRAM

IRAM interfaceMMMMLogicIRAMmallocaddrStable address for an object allows better cache behaviorObject can be relocated within IRAM, but its address to the CPU is constant

IRAM interfaceMMMMLogicIRAMputfield/getfieldvalueObject referencingtracked inside IRAM-supports garbage collection

IRAM interfaceMMMMLogicIRAMgccompactprefetchGoal: relegate storage-management functions to IRAM

Macro accessesMMMMLogicIRAMp.getLeft().getNext()*(*(p+12)+32)Observe: code sequences contain common gestures (superoperators)

Gesture abstractionMMMMLogicIRAMp.getLeft().getNext()*(*(p+12)+32)M143(x): *(*(x+12)+32)Goal: decrease traffic between CPU and storage

Gesture applicationMMMMLogicIRAMMacro 143 (p)M143(x): *(*(x+12)+32)p.getLeft().getNext()

Gesture applicationMMMMLogicIRAMMacro 143 (p)M143(x): *(*(x+12)+32)p.getLeft().getNext()p.getLeft().getNext()

Automatic prefetchingGoal: decrease traffic between CPU and storageMMMMLogicIRAMCPU + cacheL2 cacheFetch pp

p.getLeft().getNext()Automatic prefetchingGoal: decrease traffic between CPU and storageMMMMLogicIRAMCPU + cacheL2 cacheFetch pp

ChallengesAlgorithmicBounded-time methods for allocation and collectionGood average performance as wellArchitecturalLean interface between the CPU and IRAMEfficient realization

Storage Allocation (Real Time)Not necessarily fastNecessarily predictableAble to satisfy any reasonable requestDeveloper should know maxlive characteristics of the applicationThis is true for non-embedded systems as well

How much storage?curlivethe number of objects live at a point in timecurspacethe number of bytes live at a point in timeHandlesObject Space

Objects concurrently live

How much object space?

Storage AllocationFree ListLinked list of free blocksSearch for desired fitWorst case O(n) for n blocks in the list

Worst-case free-list behaviorThe longer the free-list, the more pronounced the effectNo a priori bound on how much worse the list-based scheme could getAverage performance similar

Chart1

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Worst

Avg

Number of objects allocated

Slowdown of List-Based Allocator

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3000 objects size 1000 and 2000#Objects1803000

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180 objects size 32K

Worst2nd3rdavg

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Speedup of Buddy over List

Sheet3

Knuths Buddy SystemFree-list segregated by sizeAll requests rounded up to a power of 2

Knuths Buddy System (1)2561286432168421Begin with one large blockSuppose we want a block of size 16

Knuths Buddy System (2)Begin with one large blockRecursively subdivide2561286432168421

Knuths Buddy System (3)2561286432168421Begin with one large blockRecursively subdivide

Knuths Buddy System (4)2561286432168421Begin with one large blockRecursively subdivide

Knuths Buddy System (5)2561286432168421Begin with one large blockYield 2 blocks size 16

Knuths Buddy System (6)One of those blocks can be given to the program2561286432168421Begin with one large blockYield: 2 blocks size 16

Worst-case free-list behaviorThe longer the free-list, the more pronounced the effectNo a priori bound on how much worse the list-based scheme could getAverage performance similar

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Worst

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Spec Benchmark Results

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Buddy SystemIf a block can be found, it can be found in log(N), where N is the size of the heapThe application cannot make that worse

DefragmentationTo keep up with the diversity of requested block sizes, an allocator may have to reorganize smaller blocks into larger ones

DefragmentationFree ListFree-list permutes adjacent blocksStorage becomes fragmented, with many small blocks and no large onesBlocks in memory Free list

DefragmentationFree ListFree-list permutes adjacent blocksTwo issues:Blocks in memory Free listJoin adjacent blocks

DefragmentationFree ListFree-list permutes adjacent blocksTwo issues:Blocks in memory Free list

Reorganize holes (move live storage)Join adjacent blocks

DefragmentationFree ListFree-list permutes adjacent blocksTwo issues:Blocks in memory Free list

Reorganize holes

Organization by address can help [Kavi]Join adjacent blocks

Buddiesjoining adjacent blocksThe blocks resulting from subdivision are viewed as buddiesTheir address differs by exactly one bitThe address of a block of size 2 differs with its buddys address at bit n01n

Knuths Buddy System (6)2561286432168421

Knuths Buddy System (5)2561286432168421When a block becomes free, it tries to rejoin its buddyA bit in its buddy tells whether the buddy is freeIf so, they glue together and make a block twice as big

Two problemsOscillationBuddy looks like it may split, glue, split, glueisnt this wasted effort?FragmentationWhat happens when Buddy cant glue but has space it would like to combine?

2561286432168421Buddyoscillation

Problem is lack of hysteresisSome programs allocate objects which are almost immediately deallocated.Continuous, incremental approaches to garbage collection only make this worse!Oscillation is expensive: blocks are glued only to be quickly subdivided again

Estranged Buddy SystemVariant of Knuths ideaWhen deallocated, blocks are not eager to rejoin their buddiesEvidence of value [Kaufman, TOPLAS 84]Slight improvement on spec benchmarksAlgorithmic improvement over Kaufman

Buddy-Busy and Buddy-Free2Blocks whose buddies are busyBlocks whose buddies are freek

Estranged BuddyAllocationAllocation heuristicBuddy-busyBuddy-freeGlue one level below, buddy-freeSearch up (Knuth)Glue below

How well does Estranged Buddy do?(contrived example)

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Estranged Buddy on Spec

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Speedup of Estranged Buddy over Knuth

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Estranged Buddy over Buddy

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Recall: two problemsOscillationBuddy looks like it may split, glue, split, glueisnt this wasted effort?Typically not, but can beFragmentationWhat happens when Buddy cant glue but has space it would like to combine?

Buddy SystemFragmentationInternal fragmentation from rounding-up of requests to powers of twoNot really a concern these daysAssume a program can run in maxlive bytesHow much storage needed so Buddy never has to defragment?What is a good algorithm for Buddy defragmentation?

Buddy Configurations8421

Buddy Configurations

Heap Full

Buddy cant allocate size-2 block

How Big a Heap for Non-Blocking Buddy (M = maxlive)?Easy bound: M log MBetter bound: M k, where k is the number of distinct sizes to be allocatedSounds like a good bound, but it isntDefragmentation may be necessary2561286432168421M bytes each level

Managing object relocationEvery object has a stable handle, whose address does not changeEvery handle points to its objects current locationAll references to objects are indirect, through a handle

Buddy DefragmentationWhen stuck at level kNo blocks free above level kNo glueable blocks free below level kAssume maxlive still sufficesExample: k=6, size 64 not available2561286432168421

Defragmentation Algorithm326416

Defragmentation Algorithm326416swap

Defragmentation Algorithm326416glue

Defragmentation Algorithm326416

Defragmentation AlgorithmRecursively visit below to develop two buddies that can be gluedAnalogous to the recursive allocation algorithmStill, choices to be made.studies underway

Need 4 bytesMove 3 bytes?Move 1 byte?

Recall: two problemsOscillationBuddy looks like it may split, glue, split, glueisnt this wasted effort?Typically not, but can beFragmentationWhat happens when Buddy cant glue but has space it would like to combine?New algorithm to defragment BuddySelective approachshould beat ListOptimizations needed

Towards an IRAM implementationVHDL of Buddy System completeDRAM clocked at 150 MHz10 cycles per DRAM accessNeed 7 accesses per level to split blocksFor 16Mbyte heap24 levels1680 cycles worst case: 11us168x slower than a readCan we do better?

Two tricksFind a suitable free-block quicklyReturn its address quickly

Finding a suitable free blockNo space at 16, but 16 points to the level above it that has a block to offer

Finding a suitable free blockEvery level points to the level above it that has a block to offerPointers are maintained using Tarjans path-compressionLocating pointers are not stored in DRAM2561286432168421

Alternative free-block finderPath-compression may be too complex for hardwareInstead, track the largest available free block

Alternative free-block finderPath-compression may be too complex for hardwareInstead, track the largest available free blockTends to break up large blocks and favor formation of small ones2561286432168421

Fast return for mallocWant 16 bytesZip to the 64 displayWLOG we return the first part of that block immediately to the requestor643216

Want 16 bytesZip to the 64 displayWLOG we return the first part of that block immediately to the requestorAdjustment to the structures happens in parallel with the return643216Fast return for malloc

Improved IRAM allocator~10 cycles fast return~1000 cycles to recover, worst caseIs this good enough?Compare software implementation~1000 cycles worst case~600 cycles average on spec benchmarksHardware can be much fasterDepends on recover time

Do programs allow us to recover?Run of jackJVM instructions between requests 56% of requests separated by at least 100 JVM instructionsAssume 10x expansion, JVM to native codeFor the 56%, we return in 10 cyclesCode motion might improve others

MinMedianMax3181174053

Garbage CollectionWhile allocators are needed for most modern languages, garbage collection is not universally acceptedGenerational and incremental approaches help most applicationsEmbedded and real-time need assurances of bounded behavior

Why not garbage collect?Some programmers want ultimate control over storageReal-Time applications need bounded-time overheadRT Java spec relegates allocation and collection to user controlIsnt this a step back from Java?

Marking Phasethe problemTo discover the dead objects, we use calculatus eliminatusFind live objectsAll others are dead

Marking Phasethe problemTo discover the dead objects, weFind live objects

stackheapPointers from the stack to the heap make objects live

Marking Phasethe problemTo discover the dead objects, weFind live objects

Pointers from the stack to the heap make objects liveThese objects make other objects live

Marking Phasethe problemTo discover the dead objects, weFind live objectsSweep all others away as dead

stackheap

Marking Phasethe problemTo discover the dead objects, weFind live objectsSweep all others away as deadPerhaps compact the heap

stackheap

Problems with mark phaseTakes an unbounded amount of timeCan limit it using generational collection but then its not clear what will get collectedWe seek an approach that spends a constant amount of time per program operation and collects objects continuously

Two ApproachesVariation on reference countingContaminated garbage collection [PLDI00]

Reference CountingAn integer is associated with every object, summingStack referencesHeap referencesObjects with reference count of zero are deadstackheap1221110000

Problems with Reference CountingStandard problem is that objects in cyclesstackheap1211110000

Standard problem is that objects in cycles (and those touched by such objects) cannot be collectedstackheap1211110000Problems with Reference Counting

Standard problem is that objects in cycles (and those touched by such objects) cannot be collectedContaminated gc will collect such objectsOverhead of counting can be highUntyped stack complicates thingsstackheap1211110000Problems with Reference Counting

The Untyped StackThe stack is a collection of untyped cellsIn JVM, safety is verified at class-load timeNo need to tag stack locations with what they containLeads to imprecision in all gc methodsstackheapHeapAddress?

IdeaWhen a stack frame pops, all of its cells are deadDont worry about tracking cell pointersInstead, associate an object with the last stack frame that can reference the object

Reference Counting Approachs is zero or one, indicating none or at least one stack reference to the objecth precisely reflects the number of heap references to the objectIf s+h=0 object is deadsh

Our treatment of stack activityObject is associated with the last-to-be-popped frame that can reference the objectstack

Our treatment of stack activityObject is associated with the last-to-be-popped frame that can reference the objectWhen that frame popsIf object is returned, the receiving frame owns the objectstack

Our treatment of stack activityObject is associated with the last-to-be-popped frame that can reference the objectWhen that frame popsOtherwise the object is deadstack

Our reference-counting implementationThe objects associated with the frame are linked togetherstackheap01201frame1

Our reference-counting implementationThe objects associated with the frame are linked togetherWhen a stack frame pops, all of its cells no longer can point at anything

stackheap01201frame1

Our reference-counting implementationThe objects associated with the frame are linked togetherWhen a stack frame pops, all of its cells no longer can point at anythingThis object is unlinked, but still thought to be live


Our reference-counting implementationThe objects associated with the frame are linked togetherWhen a stack frame pops, all of its cells no longer can point at anythingThis object is dead and is collected


Our reference-counting implementationThe objects associated with the frame are linked togetherWhen a stack frame pops, all of its cells no longer can point at anythingThis object is also dead

stackheap0201frame1

Our reference-counting implementationThe objects associated with the frame are linked togetherWhen a stack frame pops, all of its cells no longer can point at anythingThis object is still live

stackheap101frame1

Our reference-counting implementationThe objects associated with the frame are linked togetherWhen a stack frame pops, all of its cells no longer can point at anythingNow the frame is gone

stackheap101frame1

Our reference-counting implementationThe objects associated with the frame are linked togetherWhen a stack frame pops, all of its cells no longer can point at anythingThis object was linked to its frame all along

stackheap101frame1

Our reference-counting implementationThe objects associated with the frame are linked togetherWhen a stack frame pops, all of its cells no longer can point at anythingThis object was linked to its frame all alongWhen heap count becomes zero, the object is scheduled for deletion in that frame

stackheap101frame0

Our reference-counting implementationThe objects associated with the frame are linked togetherWhen a stack frame pops, all of its cells no longer can point at anythingThis object was linked to its frame all alongWhen heap count becomes zero, the object is scheduled for deletion in that frameWhen frame pops, all are dead

stackheap101frame0


stackheap001frame0


stackheap000frame0

Reference CountingPredictable, constant overhead for each JVM instructionputfield decreases count at old pointed-to object, increases count at new pointed-to objectareturn associates object with stack frame if not already associated belowHow well does it do? We shall see!

Contaminated Garbage CollectionNeed to collect objects involved in reference cycles without resorting to marking live objectsIdeaAssociate each object with a stack frame such that when that frame returns, the object is known to be deadLike escape analysis, but dynamic

Contaminated garbage collectionInitially each object is associated with the frame in which it is instantiatedstackACBDE

Contaminated garbage collectionInitially each object is associated with the frame in which it is instantiatedWhen B references A, A becomes as live as BstackACBDE

Contaminated garbage collectionInitially each object is associated with the frame in which it is instantiatedNow A, B, and C are as live as CstackACBDE

Contaminated garbage collectionInitially each object is associated with the frame in which it is instantiatedEven though D is less live than C, it gets contaminatedShould something reference D later, all will be affectedstackACBDE

Contaminated garbage collectionInitially each object is associated with the frame in which it is instantiatedStatic finger of lifeNow all objects appear to live foreverstackACBDE

Contaminated garbage collectionInitially each object is associated with the frame in which it is instantiatedStatic finger of lifeNow all objects appear to live foreverEven if E points away!stackACBDE

Contaminated garbage collectionEvery object is a member of an equilive setAll objects in a set are scheduled for deallocation at the same timeSets are maintained using Tarjans disjoint union/find algorithmNearly constant amount of overhead per operation

Contaminated GCEach equilive set is associated with a framestack

Contaminated GCEach equilive set is associated with a frameSuppose an object in one set references an object in another set (in either direction)stack

Contaminated GCEach equilive set is associated with a frameSuppose an object in one set references an object in another set (in either direction)Contamination!The sets are unionedstack

Contaminated GCEach equilive set is associated with a frameWhen a frame pops, objects associated with it are deadstack

Summary of methodsReference countingCant handle cyclesHandles pointing at and then awayContaminated GCTolerates cyclesCant track pointing and then pointing awayBoth techniques:Incur cost at putfield, areturn(Nearly) constant overhead per operation

Implementation detailsSUN JDK 1.1 interpreter versionMany subtle places where references are generated: String.intern(), ldc instruction, class loader, JNIEach gc method took about 3 months to implementCan run either method or both in concertFairly optimized, more is possible

Spec benchmark effectiveness

Size1R

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None

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Dante

Both

Nick

None

Size 10 Relative

Size10A

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Dante

Both

Nick

None

size 10 Absolute

Size1A

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CGC

Both

RefCount

None

Size 1 Absolute

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Spec benchmark effectiveness

Size1R

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Dante

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Nick

None

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None

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CGC

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None

size 10 Absolute

Size1A

20688454391

019604170949431

151948120604564444

033233314434

07767125717103

0717496812

151948119674564430

03668152272920935

100899484490256765

CGC

Both

RefCount

None

Size 1 Absolute

Sheet1



jess01960417094943146129jess0.42498211540.79555160530.7955516053


db0332333144348088db0.41085558850.45178041540.4517804154

javac0776712571710326127javac0.29727867720.34538982660.3453898266


mtrt151948119674564430276108mtrt0.98375273440.43363466470.9839555536

jack03668152272920935410479jack0.89362671420.94899860890.9489986089

checkit100899484490256765120723checkit0.86920470830.86039114340.9439626252



jess0262206401116418106649jess0.24585321940.8460557530.846055753


db011842413194430124173db0.95370169040.96432396740.9643239674

javac80041355372194945613211103javac0.67995717730.74601497850.7839301194


mtrt3038964905181264434798974mtrt0.99429268040.61409257370.9944503826

jack07333985603224353813783jack0.90122059570.97007433190.9700743319

checkit100899484490256765120723checkit0.86920470830.86039114340.9439626252

Sheet2

Sheet3

Exactness of Equilive Sets

Distance to die in frames

Chart4

6152

3679

6709

503

62

18

2481

jess

Size1R

20688454391

019604170949431

151948120604564444

033233314434

07767125717103

0717496812

151948119674564430

03668152272920935

100899484490256765

CGC

Both

RefCount

None

Size 1

Size 10R

60744634399

0262206401116418

1519484025641104444

011842413194430

80041355372194945613

0774628291

3038964905181264434

07333985603224353

100899484490256765

CGC

Both

RefCount

None

Size 10 Relative

Size10A

60744634399

0262206401116418

1519484025641104444

011842413194430

80041355372194945613

0774628291

3038964905181264434

07333985603224353

100899484490256765

CGC

Both

RefCount

None

size 10 Absolute

Size1A

20688454391

019604170949431

151948120604564444

033233314434

07767125717103

0717496812

151948119674564430

03668152272920935

100899484490256765

CGC

Both

RefCount

None

Size 1 Absolute

Sheet1



jess01960417094943146129jess0.42498211540.79555160530.7955516053


db0332333144348088db0.41085558850.45178041540.4517804154

javac0776712571710326127javac0.29727867720.34538982660.3453898266


mtrt151948119674564430276108mtrt0.98375273440.43363466470.9839555536

jack03668152272920935410479jack0.89362671420.94899860890.9489986089

checkit100899484490256765120723checkit0.86920470830.86039114340.9439626252



jess0262206401116418106649jess0.24585321940.8460557530.846055753


db011842413194430124173db0.95370169040.96432396740.9643239674

javac80041355372194945613211103javac0.67995717730.74601497850.7839301194


mtrt3038964905181264434798974mtrt0.99429268040.61409257370.9944503826

jack07333985603224353813783jack0.90122059570.97007433190.9700743319

checkit100899484490256765120723checkit0.86920470830.86039114340.9439626252

Size of equilive sets

Benchmark123456--10>10

compress206110327212


jess33801829315819681031


raytrace40516949115031835342782


db8191383214213


javac3413640340176142722


mpegaudio214108398211


mtrt40323936614761799242782


jack1360018546313517471930271

Distance to die

Benchmark012345>5

compress17419315884642511

Benchmark012345>5

jess61523679670950362182481

Benchmark012345>5

raytrace3580623823290711387611449638315144

Benchmark012345>5

db66762012076037222129

Benchmark012345>5

javac36021954134022140688157

Benchmark012345>5

mpegaudio18120417374561811

Benchmark012345>5

mtrt35581237592900313685112606287152047

Benchmark012345>5

jack799726307119495252117172215

Sheet1

jess

Sheet2

Sheet3

Chart5

35806

23823

29071

13876

11449

6383

15144

raytrace

Size1R

20688454391

019604170949431

151948120604564444

033233314434

07767125717103

0717496812

151948119674564430

03668152272920935

100899484490256765

CGC

Both

RefCount

None

Size 1

Size 10R

60744634399

0262206401116418

1519484025641104444

011842413194430

80041355372194945613

0774628291

3038964905181264434

07333985603224353

100899484490256765

CGC

Both

RefCount

None

Size 10 Relative

Size10A

60744634399

0262206401116418

1519484025641104444

011842413194430

80041355372194945613

0774628291

3038964905181264434

07333985603224353

100899484490256765

CGC

Both

RefCount

None

size 10 Absolute

Size1A

20688454391

019604170949431

151948120604564444

033233314434

07767125717103

0717496812

151948119674564430

03668152272920935

100899484490256765

CGC

Both

RefCount

None

Size 1 Absolute

Sheet1



jess01960417094943146129jess0.42498211540.79555160530.7955516053


db0332333144348088db0.41085558850.45178041540.4517804154

javac0776712571710326127javac0.29727867720.34538982660.3453898266


mtrt151948119674564430276108mtrt0.98375273440.43363466470.9839555536

jack03668152272920935410479jack0.89362671420.94899860890.9489986089

checkit100899484490256765120723checkit0.86920470830.86039114340.9439626252



jess0262206401116418106649jess0.24585321940.8460557530.846055753


db011842413194430124173db0.95370169040.96432396740.9643239674

javac80041355372194945613211103javac0.67995717730.74601497850.7839301194


mtrt3038964905181264434798974mtrt0.99429268040.61409257370.9944503826

jack07333985603224353813783jack0.90122059570.97007433190.9700743319

checkit100899484490256765120723checkit0.86920470830.86039114340.9439626252





jess33801829315819681031


raytrace40516949115031835342782


db8191383214213


javac3413640340176142722




mtrt40323936614761799242782


jack1360018546313517471930271

Distance to die

Benchmark012345>5

compress17419315884642511

Benchmark012345>5

jess61523679670950362182481

Benchmark012345>5

raytrace3580623823290711387611449638315144

Benchmark012345>5

db66762012076037222129

Benchmark012345>5

javac36021954134022140688157

Benchmark012345>5

mpegaudio18120417374561811

Benchmark012345>5

mtrt35581237592900313685112606287152047

Benchmark012345>5

jack799726307119495252117172215

Sheet1

raytrace

Sheet2

Sheet3

Chart6

667

620

1207

603

72

22

129

db

Size1R

20688454391

019604170949431

151948120604564444

033233314434

07767125717103

0717496812

151948119674564430

03668152272920935

100899484490256765

CGC

Both

RefCount

None

Size 1

Size 10R

60744634399

0262206401116418

1519484025641104444

011842413194430

80041355372194945613

0774628291

3038964905181264434

07333985603224353

100899484490256765

CGC

Both

RefCount

None

Size 10 Relative

Size10A

60744634399

0262206401116418

1519484025641104444

011842413194430

80041355372194945613

0774628291

3038964905181264434

07333985603224353

100899484490256765

CGC

Both

RefCount

None

size 10 Absolute

Size1A

20688454391

019604170949431

151948120604564444

033233314434

07767125717103

0717496812

151948119674564430

03668152272920935

100899484490256765

CGC

Both

RefCount

None

Size 1 Absolute

Sheet1



jess01960417094943146129jess0.42498211540.79555160530.7955516053


db0332333144348088db0.41085558850.45178041540.4517804154

javac0776712571710326127javac0.29727867720.34538982660.3453898266


mtrt151948119674564430276108mtrt0.98375273440.43363466470.9839555536

jack03668152272920935410479jack0.89362671420.94899860890.9489986089

checkit100899484490256765120723checkit0.86920470830.86039114340.9439626252



jess0262206401116418106649jess0.24585321940.8460557530.846055753


db011842413194430124173db0.95370169040.96432396740.9643239674

javac80041355372194945613211103javac0.67995717730.74601497850.7839301194


mtrt3038964905181264434798974mtrt0.99429268040.61409257370.9944503826

jack07333985603224353813783jack0.90122059570.97007433190.9700743319

checkit100899484490256765120723checkit0.86920470830.86039114340.9439626252





jess33801829315819681031


raytrace40516949115031835342782


db8191383214213


javac3413640340176142722




mtrt40323936614761799242782


jack1360018546313517471930271

Distance to die

Benchmark012345>5

compress17419315884642511

Benchmark012345>5

jess61523679670950362182481

Benchmark012345>5

raytrace3580623823290711387611449638315144

Benchmark012345>5

db66762012076037222129

Benchmark012345>5

javac36021954134022140688157

Benchmark012345>5

mpegaudio18120417374561811

Benchmark012345>5

mtrt35581237592900313685112606287152047

Benchmark012345>5

jack799726307119495252117172215

Sheet1

db

Sheet2

Sheet3

Chart7

3602

1954

1340

221

406

88

157

javac

Size1R

20688454391

019604170949431

151948120604564444

033233314434

07767125717103

0717496812

151948119674564430

03668152272920935

100899484490256765

CGC

Both

RefCount

None

Size 1

Size 10R

60744634399

0262206401116418

1519484025641104444

011842413194430

80041355372194945613

0774628291

3038964905181264434

07333985603224353

100899484490256765

CGC

Both

RefCount

None

Size 10 Relative

Size10A

60744634399

0262206401116418

1519484025641104444

011842413194430

80041355372194945613

0774628291

3038964905181264434

07333985603224353

100899484490256765

CGC

Both

RefCount

None

size 10 Absolute

Size1A

20688454391

019604170949431

151948120604564444

033233314434

07767125717103

0717496812

151948119674564430

03668152272920935

100899484490256765

CGC

Both

RefCount

None

Size 1 Absolute

Sheet1



jess01960417094943146129jess0.42498211540.79555160530.7955516053


db0332333144348088db0.41085558850.45178041540.4517804154

javac0776712571710326127javac0.29727867720.34538982660.3453898266


mtrt151948119674564430276108mtrt0.98375273440.43363466470.9839555536

jack03668152272920935410479jack0.89362671420.94899860890.9489986089

checkit100899484490256765120723checkit0.86920470830.86039114340.9439626252



jess0262206401116418106649jess0.24585321940.8460557530.846055753


db011842413194430124173db0.95370169040.96432396740.9643239674

javac80041355372194945613211103javac0.67995717730.74601497850.7839301194


mtrt3038964905181264434798974mtrt0.99429268040.61409257370.9944503826

jack07333985603224353813783jack0.90122059570.97007433190.9700743319

checkit100899484490256765120723checkit0.86920470830.86039114340.9439626252





jess33801829315819681031


raytrace40516949115031835342782


db8191383214213


javac3413640340176142722




mtrt40323936614761799242782


jack1360018546313517471930271

Distance to die

Benchmark012345>5

compress17419315884642511

Benchmark012345>5

jess61523679670950362182481

Benchmark012345>5

raytrace3580623823290711387611449638315144

Benchmark012345>5

db66762012076037222129

Benchmark012345>5

javac36021954134022140688157

Benchmark012345>5

mpegaudio18120417374561811

Benchmark012345>5

mtrt35581237592900313685112606287152047

Benchmark012345>5

jack799726307119495252117172215

Sheet1

javac

Sheet2

Sheet3

Chart8

181

204

173

74

56

18

11

mpegaudio

Size1R

20688454391

019604170949431

151948120604564444

033233314434

07767125717103

0717496812

151948119674564430

03668152272920935

100899484490256765

CGC

Both

RefCount

None

Size 1

Size 10R

60744634399

0262206401116418

1519484025641104444

011842413194430

80041355372194945613

0774628291

3038964905181264434

07333985603224353

100899484490256765

CGC

Both

RefCount

None

Size 10 Relative

Size10A

60744634399

0262206401116418

1519484025641104444

011842413194430

80041355372194945613

0774628291

3038964905181264434

07333985603224353

100899484490256765

CGC

Both

RefCount

None

size 10 Absolute

Size1A

20688454391

019604170949431

151948120604564444

033233314434

07767125717103

0717496812

151948119674564430

03668152272920935

100899484490256765

CGC

Both

RefCount

None

Size 1 Absolute

Sheet1



jess01960417094943146129jess0.42498211540.79555160530.7955516053


db0332333144348088db0.41085558850.45178041540.4517804154

javac0776712571710326127javac0.29727867720.34538982660.3453898266


mtrt151948119674564430276108mtrt0.98375273440.43363466470.9839555536

jack03668152272920935410479jack0.89362671420.94899860890.9489986089

checkit100899484490256765120723checkit0.86920470830.86039114340.9439626252



jess0262206401116418106649jess0.24585321940.8460557530.846055753


db011842413194430124173db0.95370169040.96432396740.9643239674

javac80041355372194945613211103javac0.67995717730.74601497850.7839301194


mtrt3038964905181264434798974mtrt0.99429268040.61409257370.9944503826

jack07333985603224353813783jack0.90122059570.97007433190.9700743319

checkit100899484490256765120723checkit0.86920470830.86039114340.9439626252





jess33801829315819681031


raytrace40516949115031835342782


db8191383214213


javac3413640340176142722




mtrt40323936614761799242782


jack1360018546313517471930271

Distance to die

Benchmark012345>5

compress17419315884642511

Benchmark012345>5

jess61523679670950362182481

Benchmark012345>5

raytrace3580623823290711387611449638315144

Benchmark012345>5

db66762012076037222129

Benchmark012345>5

javac36021954134022140688157

Benchmark012345>5

mpegaudio18120417374561811

Benchmark012345>5

mtrt35581237592900313685112606287152047

Benchmark012345>5

jack799726307119495252117172215

Sheet1

mpegaudio

Sheet2

Sheet3

Chart9

7997

263071

19495

2521

1717

22

15

jack

Size1R

20688454391

019604170949431

151948120604564444

033233314434

07767125717103

0717496812

151948119674564430

03668152272920935

100899484490256765

CGC

Both

RefCount

None

Size 1

Size 10R

60744634399

0262206401116418

1519484025641104444

011842413194430

80041355372194945613

0774628291

3038964905181264434

07333985603224353

100899484490256765

CGC

Both

RefCount

None

Size 10 Relative

Size10A

60744634399

0262206401116418

1519484025641104444

011842413194430

80041355372194945613

0774628291

3038964905181264434

07333985603224353

100899484490256765

CGC

Both

RefCount

None

size 10 Absolute

Size1A

20688454391

019604170949431

151948120604564444

033233314434

07767125717103

0717496812

151948119674564430

03668152272920935

100899484490256765

CGC

Both

RefCount

None

Size 1 Absolute

Sheet1



jess01960417094943146129jess0.42498211540.79555160530.7955516053


db0332333144348088db0.41085558850.45178041540.4517804154

javac0776712571710326127javac0.29727867720.34538982660.3453898266


mtrt151948119674564430276108mtrt0.98375273440.43363466470.9839555536

jack03668152272920935410479jack0.89362671420.94899860890.9489986089

checkit100899484490256765120723checkit0.86920470830.86039114340.9439626252



jess0262206401116418106649jess0.24585321940.8460557530.846055753


db011842413194430124173db0.95370169040.96432396740.9643239674

javac80041355372194945613211103javac0.67995717730.74601497850.7839301194


mtrt3038964905181264434798974mtrt0.99429268040.61409257370.9944503826

jack07333985603224353813783jack0.90122059570.97007433190.9700743319

checkit100899484490256765120723checkit0.86920470830.86039114340.9439626252





jess33801829315819681031


raytrace40516949115031835342782


db8191383214213


javac3413640340176142722




mtrt40323936614761799242782


jack1360018546313517471930271

Distance to die

Benchmark012345>5

compress17419315884642511

Benchmark012345>5

jess61523679670950362182481

Benchmark012345>5

raytrace3580623823290711387611449638315144

Benchmark012345>5

db66762012076037222129

Benchmark012345>5

javac36021954134022140688157

Benchmark012345>5

mpegaudio18120417374561811

Benchmark012345>5

mtrt35581237592900313685112606287152047

Benchmark012345>5

jack799726307119495252117172215

Sheet1

jack

Sheet2

Sheet3

Speed of CGC

Chart12

0.991.05

11.24

11.2

11.14

11.17

0.991.04

0.981.2

11.1

over JDK big heap

over JDK same heap

Size1R

20688454391

019604170949431

151948120604564444

033233314434

07767125717103

0717496812

151948119674564430

03668152272920935

100899484490256765

CGC

Both

RefCount

None

Size 1

Size 10R

60744634399

0262206401116418

1519484025641104444

011842413194430

80041355372194945613

0774628291

3038964905181264434

07333985603224353

100899484490256765

CGC

Both

RefCount

None

Size 10 Relative

Size10A

60744634399

0262206401116418

1519484025641104444

011842413194430

80041355372194945613

0774628291

3038964905181264434

07333985603224353

100899484490256765

CGC

Both

RefCount

None

size 10 Absolute

Size1A

20688454391

019604170949431

151948120604564444

033233314434

07767125717103

0717496812

151948119674564430

03668152272920935

100899484490256765

CGC

Both

RefCount

None

Size 1 Absolute

Sheet1



jess01960417094943146129jess0.42498211540.79555160530.7955516053


db0332333144348088db0.41085558850.45178041540.4517804154

javac0776712571710326127javac0.29727867720.34538982660.3453898266


mtrt151948119674564430276108mtrt0.98375273440.43363466470.9839555536

jack03668152272920935410479jack0.89362671420.94899860890.9489986089

checkit100899484490256765120723checkit0.86920470830.86039114340.9439626252



jess0262206401116418106649jess0.24585321940.8460557530.846055753


db011842413194430124173db0.95370169040.96432396740.9643239674

javac80041355372194945613211103javac0.67995717730.74601497850.7839301194


mtrt3038964905181264434798974mtrt0.99429268040.61409257370.9944503826

jack07333985603224353813783jack0.90122059570.97007433190.9700743319

checkit100899484490256765120723checkit0.86920470830.86039114340.9439626252





jess33801829315819681031


raytrace40516949115031835342782


db8191383214213


javac3413640340176142722




mtrt40323936614761799242782


jack1360018546313517471930271

Distance to die

Benchmark012345>5

compress17419315884642511

Benchmark012345>5

jess61523679670950362182481

Benchmark012345>5

raytrace3580623823290711387611449638315144

Benchmark012345>5

db66762012076037222129

Benchmark012345>5

javac36021954134022140688157

Benchmark012345>5

mpegaudio18120417374561811

Benchmark012345>5

mtrt35581237592900313685112606287152047

Benchmark012345>5

jack799726307119495252117172215

Benchmarkover JDK big heapover JDK same heap

compress0.991.05

jess11.24

raytrace11.2

db11.14

javac11.17

mpegaudio0.991.04

mtrt0.981.2

jack11.1

Sheet1

00

00

00

00

00

00

00

00

over JDK big heap

over JDK same heap

Sheet2

Sheet3

Speedups of Mark-Free Approaches

Chart1

1.08587519711.05

1.08712328771.24

1.03173100871.2

1.0466379311.14

1.12153846151.17

1.02357534551.04

1.05431407481.2

1.04654699291.1

RefCount

CGC

Sheet1

size 1myjavavanjavadanjava-fh on ->myjavapaperscaleBenchmarkRefCountCGC

_201_compress416.29694.63413.16399.511.05433.818compress1.091.05

_202_jess8.2612.97.048.031.248.7296jess1.091.24

_205_raytrace42.41507.06 (pl)34.5240.151.241.424raytrace1.031.2

_209_db2.313.12.132.321.142.4282db1.051.14

_213_javac5.127.444.865.071.175.6862javac1.121.17

_222_mpegaudio45.5666.5144.8745.591.0446.6648mpegaudio1.021.04

_227_mtrt42.18printlist39.291.241.424mtrt1.051.2

_228_jack89.18139.3383.2187.461.191.531jack1.051.1

size 10

_201_compress537.12786.59460.9477.96

_202_jess72.11167.8563.2165.75

_205_raytrace110.97639.7899.34105.26

_209_db64.5146.9944.0158.73

_213_javac46.671.8837.3938.04

_222_mpegaudio529.37655.21459.8461.21

_227_mtrt146.891139.49125.01144.44

_228_jack196.02285.62164.33173.69

size 100

_201_compress5009.45208.18

_202_jessBombBomb

_205_raytraceBomb

_209_dbBomb

Sheet1

00

00

00

00

00

00

00

00

RefCount

CGC

Sheet2

Sheet3

Future PlansVHDL simulation of more efficient buddy allocatorVHDL simulation of garbage collection methodsBetter buddy defragmentationExperiment with informed allocationComparison/integration with other IRAM-based methods (with Krishna Kavi)

Informed Storage ManagementEvidence that programs allocate many objects of the same size

Benchmark jack20% fragmentation

Chart2

20.4308333079

19.4737394356

0

21.2995305716

0

0

0

21.6032066074

0

0

0

0

0

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0

13.7349212677

0

0

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0

0

0

0

0

0

9.3837042925

0

0

0

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0

0

0

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0

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0

8.6969675262

0

0

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0

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0

0

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0

0

0

0

0

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0

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0

8.5849625007

0

0

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0

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0

0

0

0

0

0

0

0

0

0

0

0

0

0

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0

0

0

0

0

0

7.7879025594

0

0

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0

0

0

0

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0

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0

0

0

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0

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0

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0

0

0

0

0

0

0

0

0

5.672425342

0

0

0

0

3

0

0

2.3219280949

1.5849625007

Buddy block-size (log)

Number of requests (log)

jack_s100_distributions-srt

Jack

Size(log)Num(log)wasted bytesTotal Buddysingle buddy

81413493320.4308333079011307944813141349320.4308333079320.4308333079

16728081419.47373943560116492961611472808119.4737394356419.4737394356

242518452521.2641058038201476168059046432115251845221.264105803800

3262605515.93399026330200336032005258105721.2995305716521.2995305716

40171744617.38990017284121856109916166411617174417.389900172800

481804104620.78285107642886566411546265664006197584820.914040535400

56854238619.704278550868339045467123264006283008621.432414463300

64355675618.44020004702276320064006318576121.6032066074621.6032066074

7277079.588714635643120985601281177709.588714635600

802888711.4958550269138624369664128007365811.836839359700

885611712.4540421975224440718208128007926913.178197984600

962291711.1617617433733122932481280071156013.496853777400

1041827710.8352609186438482338561280071338713.708545071400

11219377.59245703733088247041280071358013.729195859100

1201073.32192809498012801280071359013.730257835700

1284475.4594316186056321280071363413.7349212677713.7349212677

13649288.9425145053590401259522561184928.942514505300

1441684179240962560085088.988684686800

152381.58496250073127682560085118.997179480900

1685785.83289001425016145922560085689.149747119500

176983.169925001472023042560085779.172427508600

1842084.3219280949144051202560085979.221587121300

200381.58496250071687682560086009.228818690500

2083685.1699250014172892162560086369.312882955300

224180322562560086379.315149562300

2483184.954196310424879362560086689.383704292589.3837042925

26421397.7347096202528241090565121192137.734709620200

27229148010245120092157.748192849600

2801902325125120092167.754887502200

2883795.20945336568288189445120092537.982993574700

29629143210245120092557.994353436900

3284395.42626475477912220165120092988.219168520500

3521901605125120092998.224001674200

3682694.70043971813744133125120093258.344295907900

4083094.90689059563120153605120093558.471675214400

41689376840965120093638.50382573800

4482694.70043971811664133125120093898.60362634500

4882694.7004397181624133125120094158.696967526298.6969675262

520193107.592457037397272197632102411101937.592457037300

52826104.70043971811289626624102400102197.774787059600

56817104.0874628413775217408102400102367.882643049400

57611004481024102400102377.888743248900

60815103.9068905956624015360102400102527.977279923500

64824104.5849625007902424576102400102768.108524456800

68813103.7004397181436813312102400102898.174925682500

69611003281024102400102908.1799090900

72813103.7004397181384813312102400103038.243173983500

76811103.4594316186281611264102400103148.294620748900

80811103.4594316186237611264102400103258.344295907900

81611002081024102400103268.348728154200

82421014002048102400103288.357552004600

83221013842048102400103308.366322214200

84811103.4594316186193611264102400103418.41362792900

88811103.4594316186149611264102400103528.459431618600

92811103.4594316186105611264102400103638.50382573800

96811103.459431618661611264102400103748.546894459900

100810103.321928094916010240102400103848.5849625007108.5849625007

1032106116.7279204546107696217088204811111066.727920454600

104810113.32192809491000020480204800111166.857980995100

10889113.1699250014864018432204800111256.965784284700

11289113.1699250014828018432204800111347.066089190500

115211108962048204800111357.076815597100

11688113704016384204800111437.159871336800

12087112.8073549221588014336204800111507.228818690500

12487112.8073549221560014336204800111577.294620748900

128810113.3219280949760020480204800111677.383704292500

1328411228808192204800111717.417852514900

1368411227208192204800111757.451211111800

1408411225608192204800111797.483815777300

14483111.584962500718006144204800111827.507794640200

14883111.584962500716806144204800111857.531381460500

15283111.584962500715606144204800111887.554588851700

15683111.584962500714406144204800111917.57742882800

16083111.584962500713206144204800111947.599912842200

162411104242048204800111957.607330313700

164011104082048204800111967.614709844100

16483111.584962500712006144204800111997.636624620500

16883111.584962500710806144204800112027.658211482800

17283111.58496250079606144204800112057.679480099500

17683111.58496250078406144204800112087.700439718100

18083111.58496250077206144204800112117.721099188700

184821114004096204800112137.734709620200

188821113204096204800112157.748192849600

192821112404096204800112177.761551232400

196821111604096204800112197.774787059600

2048211104096204800112217.7879025594117.7879025594

2056112020404096409611121000

20882121401681924096001231.584962500700

21282121393681924096001252.321928094900

21682121385681924096001272.807354922100

22082121377681924096001293.169925001400

224821213696819240960012113.459431618600

228821213616819240960012133.700439718100

230411201792409640960012143.807354922100

23282121353681924096001216400

236821213456819240960012184.169925001400

240821213376819240960012204.321928094900

241611201680409640960012214.392317422800

244821213296819240960012234.523561956100

248821213216819240960012254.643856189800

252821213136819240960012274.754887502200

253621213120819240960012294.857980995100

25687122.8073549221106962867240960012365.169925001400

260811201488409640960012375.209453365600

264811201448409640960012385.247927513400

268811201408409640960012395.285402218900

272811201368409640960012405.321928094900

276811201328409640960012415.357552004600

280811201288409640960012425.392317422800

284811201248409640960012435.426264754700

288811201208409640960012445.459431618600

292811201168409640960012455.491853096300

296811201128409640960012465.523561956100

300811201088409640960012475.554588851700

304811201048409640960012485.584962500700

308811201008409640960012495.614709844100

32721120824409640960012505.643856189800

36161120480409640960012515.672425342125.672425342

4104113040888192819211131000

4608113035848192819200132100

51283131.58496250079192245768192001352.321928094900

65361130165681928192001362.584962500700

80722131240163848192001383133

82003141.5849625007245524915216384111431.584962500700

921611407168163841638400144200

10248114061361638416384001452.3219280949142.3219280949

163923151.5849625007491289830432768111531.5849625007151.5849625007

611697763128688881

CompressSize(log)Num(log)

831238.285402218902496811543128.285402218938.2854022189

162817411.45994384840450721611155281711.4599438484411.4599438484

241534510.583082767512272490883211156153410.583082767500

3219657.6147098441062723200156173010.7565563225510.7565563225

408366.3750394313199253126411157836.375039431300

4810666.72792045461696678464001571897.562242424200

5611166.7944158664888710464001573008.228818690500

6411266.80735492210716864001574128.686500527268.6865005272

7212076.9068905956672015360128111581206.906890595600

8018377.5156998383878423424128001583038.243173983500

8815977.3128829553636020352128001584628.851749041400

9610076.6438561898320012800128001585629.134426320200

1045275.700439718112486656128001586149.262094845400

1121874.16992500142882304128001586329.303780748200

120371.584962500724384128001586359.310612781700

128572.32192809490640128001586409.321928094979.3219280949

13610886.75488750221296027648256111591086.754887502200

168281176512256001591106.781359713500

176381.5849625007240768256001591136.820178962400

2001283.58496250076723072256001591256.965784284700

20828196512256001591276.988684686800

2241803225625600159128787

26410496.70043971812579253248512111601046.700439718100

352190160512512001601056.714245517700

416792.80735492216723584512001601126.807354922100

48819024512512001601136.820178962496.8201789624

52054105.75488750222721655296102411161545.754887502200

70411003201024102400161555.781359713500

82421014002048102400161575.832890014200

83221013842048102400161595.8826430494105.8826430494

10322111203240962048111622100

16401110408204820480016231.584962500700

18081110240204820480016242112

20561120204040964096111631000

253621213120819240960016331.584962500700

3272112082440964096001634200

36161120480409640960016352.3219280949122.3219280949

41041130408881928192111641000

65361130165681928192001642100

800825134.64385618984600204800819200164274.7548875022134.7548875022

82003141.58496250072455249152163841116531.5849625007141.5849625007

163923151.58496250074912898304327681116631.5849625007151.5849625007

6554425174.64385618981638200327680013107221167254.6438561898174.6438561898

13800850185.643856189862068001310720026214411168505.6438561898185.6438561898

27600825194.643856189862070001310720052428811169254.6438561898194.6438561898

96256810203.321928094986008010485760104857611170103.3219280949203.3219280949

115712810213.3219280949940024020971520209715211171103.321928094900

128000810213.3219280949817144020971520209715200171204.3219280949214.3219280949

285696810223.32192809491337336041943040419430411172103.321928094900

315392810223.32192809491040376041943040419430400172204.3219280949224.3219280949

1

564666641665656480.3390054593frag

runing sum

raytracesize(log)num(log)diff from before?index0

831223314.9303215420249784812093122314.930321542

16438039418.740699797707008624161121043803918.7406997977

2448352515.5612879452386816154726432112114835215.5612879452

3219627514.2605520523062806432002116797916.0528015189

4010473613.354387142325135267027264112121047313.3543871423

4814067.12928301692240896064002121061313.3735449032

561518610.5679560754121449715264002121213113.5664108612

6424567.93663793901568064002121237613.5952574814

727392712.851749041441395294617612811213739212.8517490414

801202710.23122118075769615385612800213859413.0691140618

8816277.339850002964802073612800213875613.0960562392

968176.339850002925921036812800213883713.1093409688

1045275.70043971811248665612800213888913.1178054117

1121974.2479275134304243212800213890813.1208858428

120371.58496250072438412800213891113.121371626

1284675.52356195610588812800213895713.1287998908

13616487.35755200461968041984256112141647.3575520046

16818088256256002141657.3663222142

176381.5849625007240768256002141687.3923174228

19218064256256002141697.4008794363

2001283.58496250076723072256002141817.4998458871

208381.5849625007144768256002141847.5235619561

22418032256256002141857.5313814605

2648596.4093909361210804352051211215856.4093909361

35219016051251200215866.4262647547

416792.8073549221672358451200215936.5391588111

52025104.64385618981260025600102411216254.6438561898

69611003281024102400216264.7004397181

82421014002048102400216284.8073549221

83221013842048102400216304.9068905956

103221112032409620481121721

16401110408204820480021731.5849625007

205621214080819240961121821

253621213120819240960021842

32721120824409640960021852.3219280949

36161120480409640960021862.5849625007

410411304088819281921121910

653611301656819281920021921

807221312401638481920021942

82003141.58496250072455249152163841122031.5849625007

163923151.58496250074912898304327681122131.5849625007

16000811801021362621442621443122210

1384136119710800.1156233189


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num(log)

Block-size (log)


raytrace

0

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Benchmark raytrace12% fragmentation

Chart1

14.930321542

18.7406997977

16.0528015189

13.5952574814

13.1287998908

7.5313814605

6.5391588111

4.9068905956

1.5849625007

2.5849625007

2

1.5849625007

1.5849625007

0




Jack

Size(log)Num(log)wasted bytesTotal Buddysingle buddy

81413493320.43083330790113079448

16728081419.473739435601164929616

242518452521.2641058038201476168059046432

3262605515.93399026330200336032

40171744617.389900172841218561099161664

481804104620.78285107642886566411546265664

56854238619.704278550868339045467123264

64355675618.44020004702276320064

7277079.58871463564312098560128

802888711.4958550269138624369664128

885611712.4540421975224440718208128

962291711.161761743373312293248128

1041827710.835260918643848233856128

11219377.5924570373308824704128

1201073.3219280949801280128

1284475.459431618605632128

13649288.942514505359040125952256

144168417924096256

152381.5849625007312768256

1685785.8328900142501614592256

176983.16992500147202304256

1842084.321928094914405120256

200381.5849625007168768256

2083685.169925001417289216256

22418032256256

2483184.95419631042487936256

26421397.734709620252824109056512

2722914801024512

280190232512512

2883795.2094533656828818944512

2962914321024512

3284395.4262647547791222016512

352190160512512

3682694.7004397181374413312512

4083094.9068905956312015360512

4168937684096512

4482694.7004397181166413312512

4882694.700439718162413312512

520193107.5924570373972721976321024

52826104.700439718112896266241024

56817104.08746284137752174081024

576110044810241024

60815103.90689059566240153601024

64824104.58496250079024245761024

68813103.70043971814368133121024

696110032810241024

72813103.70043971813848133121024

76811103.45943161862816112641024

80811103.45943161862376112641024

816110020810241024

824210140020481024

832210138420481024

84811103.45943161861936112641024

88811103.45943161861496112641024

92811103.45943161861056112641024

96811103.4594316186616112641024

100810103.3219280949160102401024

1032106116.72792045461076962170882048

104810113.321928094910000204802048

10889113.16992500148640184322048

11289113.16992500148280184322048

1152111089620482048

116881137040163842048

12087112.80735492215880143362048

12487112.80735492215600143362048

128810113.32192809497600204802048

13284112288081922048

13684112272081922048

14084112256081922048

14483111.5849625007180061442048

14883111.5849625007168061442048

15283111.5849625007156061442048

15683111.5849625007144061442048

16083111.5849625007132061442048

1624111042420482048

1640111040820482048

16483111.5849625007120061442048

16883111.5849625007108061442048

17283111.584962500796061442048

17683111.584962500784061442048

18083111.584962500772061442048

1848211140040962048

1888211132040962048

1928211124040962048

1968211116040962048

20482111040962048

20561120204040964096

20882121401681924096

21282121393681924096

21682121385681924096

22082121377681924096

22482121369681924096

22882121361681924096

23041120179240964096

23282121353681924096

23682121345681924096

24082121337681924096

24161120168040964096

24482121329681924096

24882121321681924096

25282121313681924096

25362121312081924096

25687122.807354922110696286724096

26081120148840964096

26481120144840964096

26881120140840964096

27281120136840964096

27681120132840964096

28081120128840964096

28481120124840964096

28881120120840964096

29281120116840964096

29681120112840964096

30081120108840964096

30481120104840964096

30881120100840964096

3272112082440964096

3616112048040964096

41041130408881928192

46081130358481928192

51283131.58496250079192245768192

65361130165681928192

80722131240163848192

82003141.5849625007245524915216384

9216114071681638416384

10248114061361638416384

163923151.5849625007491289830432768

611697763128688880.1955124921frag

CompressSize(log)Num(log)

831238.2854022189024968

162817411.459943848404507216

241534510.5830827675122724908832

3219657.61470984410627232

408366.37503943131992531264

4810666.72792045461696678464

5611166.7944158664888710464

6411266.80735492210716864

7212076.9068905956672015360128

8018377.5156998383878423424128

8815977.3128829553636020352128

9610076.6438561898320012800128

1045275.700439718112486656128

1121874.16992500142882304128

120371.584962500724384128

128572.32192809490640128

13610886.75488750221296027648256

168281176512256

176381.5849625007240768256

2001283.58496250076723072256

20828196512256

22418032256256

26410496.70043971812579253248512

352190160512512

416792.80735492216723584512

48819024512512

52054105.754887502227216552961024

704110032010241024

824210140020481024

832210138420481024

10322111203240962048

1640111040820482048

1808111024020482048

20561120204040964096

25362121312081924096

3272112082440964096

3616112048040964096

41041130408881928192

65361130165681928192

800825134.643856189846002048008192

82003141.5849625007245524915216384

163923151.5849625007491289830432768

6554425174.643856189816382003276800131072

13800850185.6438561898620680013107200262144

27600825194.6438561898620700013107200524288

96256810203.3219280949860080104857601048576

115712810213.32192809499400240209715202097152

128000810213.32192809498171440209715202097152

285696810223.321928094913373360419430404194304

315392810223.321928094910403760419430404194304

564666641665656480.3390054593frag

runing sum

raytracesize(log)num(log)diff from before?index0

831223314.9303215420249784812093122314.930321542

16438039418.740699797707008624161121043803918.7406997977

2448352515.5612879452386816154726432112114835215.5612879452

3219627514.2605520523062806432002116797916.0528015189

4010473613.354387142325135267027264112121047313.3543871423

4814067.12928301692240896064002121061313.3735449032

561518610.5679560754121449715264002121213113.5664108612

6424567.93663793901568064002121237613.5952574814

727392712.851749041441395294617612811213739212.8517490414

801202710.23122118075769615385612800213859413.0691140618

8816277.339850002964802073612800213875613.0960562392

968176.339850002925921036812800213883713.1093409688

1045275.70043971811248665612800213888913.1178054117

1121974.2479275134304243212800213890813.1208858428

120371.58496250072438412800213891113.121371626

1284675.52356195610588812800213895713.1287998908

13616487.35755200461968041984256112141647.3575520046

16818088256256002141657.3663222142

176381.5849625007240768256002141687.3923174228

19218064256256002141697.4008794363

2001283.58496250076723072256002141817.4998458871

208381.5849625007144768256002141847.5235619561

22418032256256002141857.5313814605

2648596.4093909361210804352051211215856.4093909361

35219016051251200215866.4262647547

416792.8073549221672358451200215936.5391588111

52025104.64385618981260025600102411216254.6438561898

69611003281024102400216264.7004397181

82421014002048102400216284.8073549221

83221013842048102400216304.9068905956

103221112032409620481121721

16401110408204820480021731.5849625007

205621214080819240961121821

253621213120819240960021842

32721120824409640960021852.3219280949

36161120480409640960021862.5849625007

410411304088819281921121910

653611301656819281920021921

807221312401638481920021942

82003141.58496250072455249152163841122031.5849625007

163923151.58496250074912898304327681122131.5849625007

16000811801021362621442621443122210

1384136119710800.1156233189


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Num(log)

Block size (log)


jack (20% fragmentation)

0

0

0

0

0

0

0

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0

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0

Num(log)

Block size (log)

Number of requests(log)

compress (34% fragmentation)

0

0

0

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num(log)

Documents

Getting Real, Getting Dirty (without getting real dirty)