Supercomputing in Plain English The Tyranny of the Storage Hierarchy Henry Neeman, Director OU Supercomputing Center for Education & Research Blue Waters

Supercomputingin Plain English The Tyranny ofthe Storage HierarchyHenry Neeman, DirectorOU Supercomputing Center for Education & ResearchBlue Waters Undergraduate Petascale Education ProgramMay 29 June 10 2011

Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011

OutlineWhat is the storage hierarchy?RegistersCacheMain Memory (RAM)The Relationship Between RAM and CacheThe Importance of Being LocalHard DiskVirtual Memory*Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011


The Storage HierarchyRegistersCache memoryMain memory (RAM)Hard diskRemovable media (CD, DVD etc)InternetSupercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Fast, expensive, fewSlow, cheap, a lot


A LaptopIntel Core2 Duo SU9600 1.6 GHz w/3 MB L2 Cache4 GB 1066 MHz DDR3 SDRAM256 GB SSD Hard DriveDVD+RW/CD-RW Drive (8x)1 Gbps Ethernet AdapterSupercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Dell Latitude Z600[4]


Storage Speed, Size, CostSupercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011** MFLOP/s: millions of floating point operations per second** 16 64-bit general purpose registers, 8 80-bit floating point registers, 16 128-bit floating point vector registers

LaptopRegisters(Intel Core2 Duo1.6 GHz)CacheMemory(L2)MainMemory(1066MHz DDR3 SDRAM)Hard Drive(SSD)Ethernet(1000 Mbps)DVD+R(16x)Phone Modem(56 Kbps)Speed(MB/sec)[peak]314,573[6](12,800 MFLOP/s*)27,276 [7]4500 [7]250 [9]12522 [10]0.007Size(MB)464 bytes**[11]34096256,000unlimitedunlimitedunlimitedCost($/MB)$285 [13]$0.03 [12]$0.002 [12]chargedper month(typically)$0.00005 [12]charged per month (typically)


Registers[25]


What Are Registers?Registers are memory-like locations inside the Central Processing Unit that hold data that are being used right now in operations.Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Arithmetic/Logic UnitControl UnitRegistersFetch Next InstructionAddSubMultDivAndOrNotIntegerFloating PointFetch DataStore DataIncrement Instruction PtrExecute InstructionCPUSupercomputing in Plain English: Storage HierarchyTue Feb 15 2011


How Registers Are UsedEvery arithmetic or logical operation has one or more operands and one result.Operands are contained in source registers.A black box of circuits performs the operation.The result goes into a destination register.Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Example:addend in R0augend in R1ADDsum in R25712Register RiRegister RjRegister RkoperandoperandresultOperation circuitrySupercomputing in Plain English: Storage HierarchyTue Feb 15 2011


How Many Registers?Typically, a CPU has less than 8 KB (8192 bytes) of registers, usually split into registers for holding integer values and registers for holding floating point (real) values, plus a few special purpose registers.Examples:IBM POWER7 (found in IBM p-Series supercomputers): 226 64-bit integer registers and 348 128-bit merged vector/scalar registers (7376 bytes) [28]Intel Core2 Duo: 16 64-bit general purpose registers, 8 80-bit floating point registers, 16 128-bit floating point vector registers (464 bytes) [11]Intel Itanium2: 128 64-bit integer registers, 128 82-bit floating point registers (2304 bytes) [23]Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


Cache[4]


What is Cache?A special kind of memory where data reside that are about to be used or have just been used.Very fast => very expensive => very small (typically 100 to 10,000 times as expensive as RAM per byte)Data in cache can be loaded into or stored from registers at speeds comparable to the speed of performing computations.Data that are not in cache (but that are in Main Memory) take much longer to load or store.Cache is near the CPU: either inside the CPU or on the motherboard that the CPU sits on.Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


From Cache to the CPUSupercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Typically, data move between cache and the CPU at speeds relatively near to that of the CPU performing calculations.CPUCache27 GB/sec (6x RAM)[7]307 GB/sec[7]


Multiple Levels of CacheMost contemporary CPUs have more than one level of cache. For example:Intel Pentium4 EM64T (Yonah) [??]Level 1 caches: 32 KB instruction, 32 KB dataLevel 2 cache: 2048 KB unified (instruction+data)IBM POWER7 [28]Level 1 cache: 32 KB instruction, 32 KB data per coreLevel 2 cache: 256 KB unified per coreLevel 3 cache: 4096 KB unified per coreSupercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


Why Multiple Levels of Cache?The lower the level of cache:the faster the cache can transfer data to the CPU;the smaller that level of cache is (faster => more expensive => smaller).Example: IBM POWER7 latency to the CPU [28]L1 cache: 1 cycle = 0.29 ns for 3.5 GHzL2 cache: 8.5 cycles = 2.43 ns for 3.5 GHz (average)L3 cache: 23.5 cycles = 5.53 ns for 3.5 GHz (local to core)RAM: 346 cycles = 98.86 ns for 3.5 GHz (1066 MHz RAM)Example: Intel Itanium2 latency to the CPU [19]L1 cache: 1 cycle = 1.0 ns for 1.0 GHzL2 cache: 5 cycles = 5.0 ns for 1.0 GHzL3 cache: 12-15 cycles = 12 15 ns for 1.0 GHzExample: Intel Pentium4 (Yonah)L1 cache: 3 cycles = 1.64 ns for a 1.83 GHz CPU = 12 calculationsL2 cache: 14 cycles = 7.65 ns for a 1.83 GHz CPU = 56 calculationsRAM: 48 cycles = 26.2 ns for a 1.83 GHz CPU = 192 calculations Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


Cache & RAM LatenciesSupercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Better[26]Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


MemLat

3

3.04

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3.02

3

3

3

3

3

3

3

3.02

3

3

3

3

3

3

3

3.02

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3.02

3

3

3

3

3.03

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3.02

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3.6

6.8

9.77

12.75

14.14

14.15

14.15

14.14

14.14

14.18

14.15

14.14

14.15

14.15

14.14

14.18

14.16

14.16

14.14

14.19

14.14

14.14

14.13

14.14

14.14

14.13

14.17

14.15

14.14

14.16

14.14

14.16

14.15

14.16

14.14

14.16

14.14

14.18

14.14

14.16

14.16

14.14

14.15

14.14

14.22

14.16

14.14

14.17

14.14

14.14

14.14

14.17

14.15

14.14

14.16

14.17

14.14

14.14

14.14

14.14

14.14

14.17

14.18

14.16

14.15

14.16

14.15

14.14

14.14

14.16

14.14

14.19

14.15

14.16

14.13

14.14

14.15

14.14

14.16

14.18

14.16

14.14

14.14

14.15

14.14

14.17

14.17

14.17

14.16

14.15

14.2

14.19

14.19

14.21

14.25

14.23

14.26

14.26

14.24

14.25

14.26

14.24

14.27

14.25

14.27

14.26

14.41

14.24

14.28

14.29

14.26

14.28

14.25

14.34

14.3

14.51

14.31

14.37

14.28

14.38

14.54

14.44

14.43

15.08

14.51

14.69

15.33

14.95

16.21

16.72

16.65

18.42

19.44

20.33

26.06

31.63

37.64

42.81

44.53

45.52

45.24

45.73

46.74

46.48

46.53

46.75

46.49

46.62

46.89

47.01

46.86

46.93

47.05

46.89

47.3

47.1

46.94

46.81

47.23

46.9

47.31

47.52

47.12

47.63

46.96

47.11

47.25

47.11

47.36

47.81

47.54

47.12

47.38

47.24

47.39

47.55

47.35

47.4

47.24

47.19

47.51

47.52

47.53

47.29

47.64

48.85

47.66

3 cycles

14 cycles

47 cycles

Memory Latency

Array Size (bytes)

Latency (clock cycles)

Cache & RAM Latency: Intel T2400 (1.83 GHz)

Sheet1

10243

10883.04

11523

12163

12803

13443

14083

14723

15363

16003

16643

17283

17923

18563

19203

19843

20483

21123

22403.02

23683

24963

26243

27523

28803

30083

31363

32643.02

33923

35203

36483

37763

39043

40323

41603

43523.02

45443

47363

49283

51203

53123

55043

56963

58883

60803

62723

65283

67843

70403

72963

75523

78083.02

80643

83203

86403

89603

92803.03

96003

99203

102403

105603

109443

113283

117123

120963

124803

129283

133763

138243

142723

147203

152323

157443

162563

167683

173443

179203

184963

191363.02

197763

204163

210563

217603

224643

231683

239363

247043

255363

263683

272003

280963

289923

299523

309123

319363

329603.6

340486.8

351369.77

3628812.75

3744014.14

3865614.15

3987214.15

4115214.14

4249614.14

4384014.18

4524814.15

4672014.14

4819214.15

4972814.15

5132814.14

5299214.18

5465614.16

5638414.16

5817614.14

6003214.19

6195214.14

6393614.14

6598414.13

6809614.14

7027214.14

7251214.13

7481614.17

7718414.15

7961614.14

8211214.16

8473614.14

8742414.16

9017614.15

9305614.16

9600014.14

9900814.16

10214414.14

10534414.18

10867214.14

11212814.16

11564814.16

11929614.14

12307214.15

12697614.14

13094414.22

13504014.16

13926414.14

14361614.17

14816014.14

15283214.14

15763214.14

16256014.17

16768014.15

17292814.14

17836814.16

18400014.17

18976014.14

19571214.14

20185614.14

20819214.14

21472014.14

22144014.17

22841614.18

23558414.16

24300814.15

25062414.16

25849614.15

26662414.14

27500814.14

28364814.16

29254414.14

30169614.19

31116814.15

32089614.16

33094414.13

34131214.14

35200014.15

36300814.14

37440014.16

38611214.18

39820814.16

41068814.14

42355214.14

43680014.15

45049614.14

46457614.17

47910414.17

49408014.17

50956814.16

52550414.15

54195214.2

55891214.19

57638414.19

59443214.21

61305614.25

63225614.23

65203214.26

67244814.26

69350414.24

71520014.25

73760014.26

76070414.24

78451214.27

80908814.25

83443214.27

86054414.26

88748814.41

91526414.24

94387214.28

97337614.29

100384014.26

103526414.28

106764814.25

110105614.34

113548814.3

117100814.51

120761614.31

124537614.37

128435214.28

132454414.38

136595214.54

140864014.44

145267214.43

149811215.08

154496014.51

159328014.69

164307215.33

169446414.95

174745616.21

180211216.72

185843216.65

191654418.42

197644819.44

203827220.33

210201626.06

216774431.63

223552037.64

230540842.81

237747244.53

245177645.52

252844845.24

260748845.73

268902446.74

277305646.48

285977646.53

294918446.75

304140846.49

313651246.62

323456046.89

333568047.01

343993646.86

354745646.93

365836847.05

377273646.89

389068847.3

401228847.1

413772846.94

426707246.81

440044847.23

453798446.9

467980847.31

482611247.52

497696047.12

513254447.63

529299246.96

545843247.11

562905647.25

580499247.11

598643247.36

617356847.81

636652847.54

656550447.12

677068847.38

698227247.24

720051247.39

742553647.55

765760047.35

789696047.4

814374447.24

839827247.19

866073647.51

893139247.52

921056047.53

949843247.29

979526447.64

1010137648.85

1041708847.66

rmma_intelt2400_memfwdlat_20070

RIGHTMARK MEMORY ANALYZER V3.72 TEST RESULTS

============================================

CPU ModelGenuine Intel(R) Core(TM) Duo (Yonah) 1828.7 MHz

L1 Cache Line Size64 bytes


Test TypeD-Cache Latency

Test StatusCompleted successfully

Selected Tests120

Set Size134217728 bytes

Memory Allocation1

Thread Lock0

Min Block Size1024 bytes

Max Block Size10485760 bytes

Stride Size64 bytes

Segments Count1

NOP Count0

Measurement Mode0

NOP Latency0

D-CACHE FORWARD READ LATENCY TEST

=================================

Size(bytes)Latency(cycles)Latency(ns)

102431.64

10883.041.66

115231.64

121631.64

128031.64

134431.64

140831.64

147231.64

153631.64

160031.64

166431.64

172831.64

179231.64

185631.64

192031.64

198431.64

204831.64

211231.64

22403.021.65

236831.64

249631.64

262431.64

275231.64

288031.64

300831.64

313631.64

32643.021.65

339231.64

352031.64

364831.64

377631.64

390431.64

403231.64

416031.64

43523.021.65

454431.64

473631.64

492831.64

512031.64

531231.64

550431.64

569631.64

588831.64

608031.64

627231.64

652831.64

678431.64

704031.64

729631.64

755231.64

78083.021.65

806431.64

832031.64

864031.64

896031.64

92803.031.65

960031.64

992031.64

1024031.64

1056031.64

1094431.64

1132831.64

1171231.64

1209631.64

1248031.64

1292831.64

1337631.64

1382431.64

1427231.64

1472031.64

1523231.64

1574431.64

1625631.64

1676831.64

1734431.64

1792031.64

1849631.64

191363.021.65

1977631.64

2041631.64

2105631.64

2176031.64

2246431.64

2316831.64

2393631.64

2470431.64

2553631.64

2636831.64

2720031.64

2809631.64

2899231.64

2995231.64

3091231.64

3193631.64

329603.61.97

340486.83.72

351369.775.34

3628812.756.97

3744014.147.73

3865614.157.74

3987214.157.74

4115214.147.73

4249614.147.73

4384014.187.76

4524814.157.74

4672014.147.73

4819214.157.74

4972814.157.74

5132814.147.73

5299214.187.76

5465614.167.75

5638414.167.74

5817614.147.73

6003214.197.76

6195214.147.73

6393614.147.73

6598414.137.73

6809614.147.73

7027214.147.73

7251214.137.73

7481614.177.75

7718414.157.74

7961614.147.73

8211214.167.74

8473614.147.73

8742414.167.74

9017614.157.74

9305614.167.74

9600014.147.73

9900814.167.74

10214414.147.73

10534414.187.76

10867214.147.73

11212814.167.75

11564814.167.75

11929614.147.73

12307214.157.74

12697614.147.73

13094414.227.77

13504014.167.74

13926414.147.73

14361614.177.75

14816014.147.73

15283214.147.73

15763214.147.73

16256014.177.75

16768014.157.74

17292814.147.73

17836814.167.74

18400014.177.75

18976014.147.73

19571214.147.73

20185614.147.73

20819214.147.73

21472014.147.73

22144014.177.75

22841614.187.75

23558414.167.74

24300814.157.74

25062414.167.74

25849614.157.74

26662414.147.73

27500814.147.73

28364814.167.74

29254414.147.73

30169614.197.76

31116814.157.74

32089614.167.74

33094414.137.73

34131214.147.73

35200014.157.74

36300814.147.73

37440014.167.74

38611214.187.76

39820814.167.74

41068814.147.73

42355214.147.73

43680014.157.74

45049614.147.73

46457614.177.75

47910414.177.75

49408014.177.75

50956814.167.75

52550414.157.74

54195214.27.76

55891214.197.76

57638414.197.76

59443214.217.77

61305614.257.79

63225614.237.78

65203214.267.8

67244814.267.8

69350414.247.79

71520014.257.79

73760014.267.8

76070414.247.79

78451214.277.81

80908814.257.79

83443214.277.8

86054414.267.8

88748814.417.88

91526414.247.79

94387214.287.81

97337614.297.82

100384014.267.8

103526414.287.81

106764814.257.79

110105614.347.84

113548814.37.82

117100814.517.93

120761614.317.82

124537614.377.86

128435214.287.81

132454414.387.87

136595214.547.95

140864014.447.89

145267214.437.89

149811215.088.25

154496014.517.94

159328014.698.03

164307215.338.38

169446414.958.18

174745616.218.86

180211216.729.14

185843216.659.1

191654418.4210.07

197644819.4410.63

203827220.3311.12

210201626.0614.25

216774431.6317.3

223552037.6420.58

230540842.8123.41

237747244.5324.35

245177645.5224.89

252844845.2424.74

260748845.7325.01

268902446.7425.56

277305646.4825.42

285977646.5325.45

294918446.7525.56

304140846.4925.42

313651246.6225.49

323456046.8925.64

333568047.0125.71

343993646.8625.62

354745646.9325.66

365836847.0525.73

377273646.8925.64

389068847.325.86

401228847.125.75

413772846.9425.67

426707246.8125.6

440044847.2325.83

453798446.925.64

467980847.3125.87

482611247.5225.99

497696047.1225.77

513254447.6326.05

529299246.9625.68

545843247.1125.76

562905647.2525.84

580499247.1125.76

598643247.3625.9

617356847.8126.14

636652847.5426

656550447.1225.77

677068847.3825.91

698227247.2425.83

720051247.3925.91

742553647.5526

765760047.3525.89

789696047.425.92

814374447.2425.83

839827247.1925.81

866073647.5125.98

893139247.5225.98

921056047.5325.99

949843247.2925.86

979526447.6426.05

1010137648.8526.71

1041708847.6626.06

D-CACHE BACKWARD READ LATENCY TEST

==================================


102431.64

10883.021.65

115231.64

121631.64

128031.64

134431.64

140831.64

147231.64

153631.64

160031.64

166431.64

172831.64

179231.64

185631.64

192031.64

198431.64

204831.64

211231.64

224031.64

236831.64

249631.64

262431.64

275231.64

288031.64

300831.64

313631.64

326431.64

339231.64

352031.64

364831.64

377631.64

390431.64

403231.64

416031.64

435231.64

454431.64

473631.64

492831.64

512031.64

531231.64

550431.64

569631.64

588831.64

608031.64

627231.64

652831.64

678431.64

704031.64

729631.64

755231.64

780831.64

806431.64

832031.64

864031.64

896031.64

928031.64

960031.64

992031.64

1024031.64

1056031.64

1094431.64

1132831.64

1171231.64

1209631.64

1248031.64

1292831.64

1337631.64

1382431.64

1427231.64

1472031.64

1523231.64

1574431.64

1625631.64

1676831.64

1734431.64

1792031.64

1849631.64

1913631.64

1977631.64

2041631.64

2105631.64

2176031.64

2246431.64

2316831.64

2393631.64

2470431.64

2553631.64

2636831.64

2720031.64

2809631.64

2899231.64

2995231.64

3091231.64

3193631.64

329603.61.97

340486.813.72

351369.745.33

3628812.756.97

3744014.137.73

3865614.197.76

3987214.167.74

4115214.147.73

4249614.147.73

4384014.147.73

4524814.167.74

4672014.157.74

4819214.167.74

4972814.157.74

5132814.147.73

5299214.167.74

5465614.147.73

5638414.137.73

5817614.147.73

6003214.157.74

6195214.167.74

6393614.187.75

6598414.147.73

6809614.137.73

7027214.157.74

7251214.147.73

7481614.167.74

7718414.167.75

7961614.157.74

8211214.147.73

8473614.147.73

8742414.167.74

9017614.147.73

9305614.137.73

9600014.147.73

9900814.147.73

10214414.157.74

10534414.197.76

10867214.137.73

11212814.157.74

11564814.157.74

11929614.137.73

12307214.167.74

12697614.147.73

13094414.157.74

13504014.27.77

13926414.157.74

14361614.167.75

14816014.147.73

15283214.137.73

15763214.147.73

16256014.157.74

16768014.157.74

17292814.167.74

17836814.147.73

18400014.147.73

18976014.157.74

19571214.187.75

20185614.157.74

20819214.147.73

21472014.167.74

22144014.167.74

22841614.167.74

23558414.147.73

24300814.147.73

25062414.137.73

25849614.197.76

26662414.167.74

27500814.147.73

28364814.157.74

29254414.167.74

30169614.167.74

31116814.157.74

32089614.177.75

33094414.177.75

34131214.157.74

35200014.147.73

36300814.187.75

37440014.157.74

38611214.157.74

39820814.147.73

41068814.187.76

42355214.177.75

43680014.147.73

45049614.147.73

46457614.147.73

47910414.147.73

49408014.157.74

50956814.157.74

52550414.167.74

54195214.197.76

55891214.187.76

57638414.217.77

59443214.37.82

61305614.327.83

63225614.277.8

65203214.287.81

67244814.297.81

69350414.337.84

71520014.257.79

73760014.617.99

76070414.337.84

78451214.387.86

80908814.337.84

83443214.357.85

86054414.437.89

88748814.367.85

91526414.267.8

94387214.397.87

97337614.287.81

100384014.317.82

103526414.387.87

106764814.347.84

110105614.437.89

113548814.417.88

117100814.517.93

120761614.347.84

124537614.47.87

128435214.397.87

132454414.517.94

136595214.357.85

140864014.668.02

145267215.348.39

149811214.778.08

154496016.59.02

159328015.198.31

164307215.788.63

169446415.278.35

174745615.28.31

180211215.788.63

185843217.589.61

191654418.5510.14

197644820.0510.97

203827221.611.81

210201626.2514.36

216774432.2617.64

223552039.621.65

230540842.9623.49

237747245.6224.95

245177645.9725.14

252844846.6125.49

260748846.8225.6

268902446.1825.25

277305647.2125.82

285977646.8725.63

294918446.9525.67

304140847.9326.21

313651247.2425.83

323456046.6425.5

333568047.2325.82

343993647.3425.89

354745646.9725.68

365836847.2825.86

377273647.4425.94

389068847.6426.05

401228846.9825.69

413772847.5225.99

426707247.4225.93

440044847.3725.9

453798447.4925.97

467980847.7126.09

482611247.9926.24

497696047.6726.07

513254447.425.92

529299247.6626.06

545843247.8526.17

562905647.6826.08

58049924826.25

598643247.4925.97

617356847.726.08

636652847.6326.05

656550448.0726.29

677068847.4925.97

698227247.7126.09

720051248.2626.39

742553647.3425.89

765760047.2825.86

789696047.6426.05

814374447.8826.18

839827248.0526.28

866073647.7926.13

893139247.8526.17

921056047.626.03

949843247.4125.92

979526447.8626.17

1010137648.8926.73

1041708847.4625.95

D-CACHE RANDOM READ LATENCY TEST

================================


10243.031.65

108831.64

115231.64

121631.64

128031.64

13443.031.65

140831.64

147231.64

153631.64

160031.64

166431.64

172831.64

179231.64

185631.64

192031.64

19843.011.65

204831.64

211231.64

224031.64

236831.64

249631.64

26243.031.65

275231.64

288031.64

300831.64

31363.021.65

326431.64

339231.64

352031.64

364831.64

37763.021.65

390431.64

403231.64

416031.64

435231.64

45443.031.65

473631.64

492831.64

512031.64

531231.64

55043.021.65

569631.64

588831.64

608031.64

627231.64

65283.021.65

678431.64

704031.64

729631.64

755231.64

78083.021.65

806431.64

832031.64

864031.64

896031.64

928031.64

960031.64

992031.64

1024031.64

105603.021.65

1094431.64

1132831.64

1171231.64

1209631.64

1248031.64

1292831.64

1337631.64

1382431.64

1427231.64

147203.031.65

1523231.64

1574431.64

1625631.64

1676831.64

173443.031.66

1792031.64

1849631.64

1913631.64

197763.021.65

2041631.64

2105631.64

2176031.64

2246431.64

2316831.64

239363.021.65

2470431.64

2553631.64

2636831.64

272003.031.66

2809631.64

2899231.64

2995231.64

3091231.64

319363.031.66

329603.61.97

340486.653.64

351369.575.24

3628812.556.86

3744013.987.65

3865614.017.66

3987214.157.74

4115214.177.75

4249614.217.77

4384014.147.73

4524814.167.74

4672014.147.73

4819214.157.74

4972814.147.73

5132814.147.73

5299214.177.75

5465614.157.74

5638414.187.75

5817614.157.74

6003214.137.73

6195214.167.74

6393614.157.74

6598414.137.73

6809614.187.75

7027214.177.75

7251214.167.74

7481614.177.75

7718414.167.74

7961614.167.74

8211214.167.74

8473614.157.74

8742414.147.73

9017614.167.74

9305614.147.73

9600014.137.73

9900814.167.75

10214414.157.74

10534414.137.73

10867214.157.74

11212814.157.74

11564814.137.73

11929614.147.73

12307214.147.73

12697614.147.73

13094414.187.75

13504014.147.73

13926414.147.73

14361614.167.74

14816014.167.74

15283214.147.73

15763214.157.74

16256014.147.73

16768014.147.73

17292814.157.74

17836814.157.74

18400014.137.73

18976014.167.74

19571214.167.74

20185614.147.73

20819214.147.73

21472014.157.74

22144014.157.74

22841614.167.75

23558414.157.74

24300814.157.74

25062414.137.73

25849614.147.73

26662414.157.73

27500814.147.73

28364814.177.75

29254414.187.76

30169614.147.73

31116814.167.75

32089614.167.74

33094414.167.74

34131214.167.75

35200014.167.74

36300814.157.74

37440014.187.75

38611214.157.74

39820814.147.73

41068814.157.74

42355214.147.73

43680014.177.75

45049614.157.74

46457614.177.75

47910414.267.8

49408014.167.74

50956814.157.74

52550414.197.76

54195214.367.85

55891214.487.92

57638414.67.98

59443214.748.06

61305614.868.12

63225615.038.22

65203215.18.25

67244815.218.32

69350415.278.35

71520015.378.4

73760015.488.46

76070415.648.55

78451215.698.58

80908815.778.62

83443215.958.72

86054415.958.72

88748816.048.77

91526416.18.81

94387216.258.88

97337616.318.92

100384016.378.95

103526416.519.03

106764816.839.21

110105616.659.1

113548816.889.23

117100816.799.18

120761616.849.21

124537616.959.27

1284352179.3

132454417.159.38

136595217.319.47

140864017.49.52

145267217.549.59

149811217.439.53

154496017.69.62

159328018.4110.07

164307219.0810.44

169446418.3510.03

174745619.0710.43

180211219.9110.89

185843221.9812.02

191654423.4112.8

197644836.4619.93

203827242.323.13

210201649.3426.98

216774475.0541.04

223552094.0151.41

2305408101.1755.32

2377472108.3159.23

2451776111.6261.04

2528448114.4262.57

2607488116.7263.83

2689024116.0363.45

2773056116.7363.83

2859776117.3464.16

2949184118.0364.54

3041408120.8266.07

3136512121.8866.65

3234560124.1767.9

3335680127.0569.47

3439936127.3669.64

3547456129.8771.02

3658368131.2571.77

3772736136.5474.67

3890688135.9674.35

4012288140.1476.63

413772814177.1

4267072142.6778.01

4400448145.4779.55

4537984146.5480.13

4679808149.4881.74

4826112151.6682.93

4976960151.682.9

5132544155.9185.26

5292992156.2785.45

5458432157.4286.08

5629056158.6586.76

5804992159.0386.96

5986432161.0788.08

6173568162.0688.62

6366528163.589.4

6565504165.1490.3

6770688167.2891.47

6982272167.9991.86

7200512169.9592.93

7425536170.8993.45

7657600171.9894.04

7896960173.1394.67

8143744174.5195.43

8398272175.3895.9

8660736176.1496.32

8931392177.4697.04

9210560178.8697.81

9498432179.698.21

9795264180.4198.65

10101376179.5398.17

10417088180.2598.56

D-CACHE PSEUDO-RANDOM READ LATENCY TEST

=======================================


10243.021.65

108831.64

115231.64

121631.64

12803.031.65

134431.64

140831.64

147231.64

153631.64

16003.031.65

166431.64

172831.64

179231.64

18563.031.65

192031.64

198431.64

204831.64

211231.64

224031.64

236831.64

249631.64

262431.64

27523.031.65

288031.64

300831.64

313631.64

32643.021.65

339231.64

352031.64

364831.64

377631.64

39043.031.66

403231.64

416031.64

435231.64

454431.64

473631.64

492831.64

512031.64

53123.031.66

550431.64

569631.64

588831.64

60803.021.65

627231.64

652831.64

678431.64

70403.021.65

729631.64

755231.64

780831.64

806431.64

83203.021.65

864031.64

896031.64

928031.64

96003.031.65

992031.64

1024031.64

1056031.64

109443.021.65

1132831.64

1171231.64

1209631.64

1248031.64

1292831.64

1337631.64

1382431.64

1427231.64

1472031.64

1523231.64

1574431.64

1625631.64

167683.031.65

1734431.64

1792031.64

1849631.64

1913631.64

1977631.64

2041631.64

2105631.64

217603.031.66

2246431.64

2316831.64

2393631.64

2470431.64

255363.031.66

2636831.64

2720031.64

2809631.64

289923.021.65

2995231.64

3091231.64

3193631.64

329603.611.97

340486.83.72

351369.85.36

3628812.756.97

3744014.167.74

3865614.187.75

3987214.177.75

4115214.167.74

4249614.157.74

4384014.157.74

4524814.167.74

4672014.157.74

4819214.147.73

4972814.157.74

5132814.147.73

5299214.177.75

5465614.197.76

5638414.197.76

5817614.157.74

6003214.177.75

6195214.167.74

6393614.167.75

6598414.187.75

6809614.167.74

7027214.167.74

7251214.217.77

7481614.157.74

7718414.187.75

7961614.217.77

8211214.187.75

8473614.197.76

8742414.217.77

9017614.137.73

9305614.177.75

9600014.167.74

9900814.197.76

10214414.147.73

10534414.157.74

10867214.167.74

11212814.217.77

11564814.167.74

11929614.167.75

12307214.157.74

12697614.167.74

13094414.167.75

13504014.157.74

13926414.187.75

14361614.177.75

14816014.167.74

15283214.177.75

15763214.217.77

16256014.187.75

16768014.197.76

17292814.177.75

17836814.187.75

18400014.27.77

18976014.187.76

19571214.187.75

20185614.157.74

20819214.187.76

21472014.167.74

22144014.177.75

22841614.177.75

23558414.197.76

24300814.187.76

25062414.167.74

25849614.187.75

26662414.177.75

27500814.197.76

28364814.167.75

29254414.217.77

30169614.187.75

31116814.177.75

32089614.187.76

33094414.187.75

34131214.157.74

35200014.197.76

36300814.177.75

37440014.177.75

38611214.177.75

39820814.167.75

41068814.27.77

42355214.177.75

43680014.187.76

45049614.187.76

46457614.167.74

47910414.167.74

49408014.187.75

50956814.157.74

52550414.177.75

54195214.187.76

55891214.237.78

57638414.227.78

59443214.237.78

61305614.267.8

63225614.277.8

65203214.297.82

67244814.297.82

69350414.267.8

71520014.277.8

73760014.337.84

76070414.317.83

78451214.357.84

80908814.297.81

83443214.297.81

86054414.337.84

88748814.297.81

91526414.277.81

94387214.277.8

97337614.437.89

100384014.317.82

103526414.277.8

106764814.277.8

110105614.347.84

113548814.337.83

117100814.327.83

120761614.437.89

124537614.347.84

128435214.37.82

132454414.357.85

136595214.698.03

140864014.397.87

145267214.387.86

149811214.638

154496014.597.98

159328014.78.04

164307214.968.18

169446415.238.33

174745615.218.31

180211216.058.78

185843218.219.96

191654419.4610.64

197644823.3612.77

203827229.7916.29

210201633.9618.57

216774461.8633.82

223552077.5542.41

230540889.1448.74

237747294.651.73

245177694.9251.9

252844895.4952.21

260748896.8252.95

268902497.5753.36

277305697.4453.28

285977698.153.65

294918498.2353.71

304140898.2653.73

313651298.3953.8

323456098.6753.95

333568099.254.25

343993699.1454.21

354745698.9354.1

365836899.1854.23

377273699.2954.3

389068899.8654.6

401228899.4154.36

413772899.3154.31

426707299.7254.53

440044899.6854.51

453798499.3654.33

467980899.1454.21

482611299.5554.44

497696099.6754.5

513254499.3154.31

529299299.2154.25

545843299.4854.4

5629056100.1254.75

580499299.4354.37

598643299.854.58

617356899.4354.37

636652899.5154.42

656550499.3954.35

677068899.6754.5

698227299.4954.4

720051299.254.25

742553699.9854.67

765760099.3854.34

789696099.8654.61

814374499.8254.59

839827299.5854.45

8660736100.2454.82

8931392100.2954.84

9210560100.1554.76

9498432100.0254.69

979526499.8754.61

10101376100.4554.93

10417088100.1654.77

Main Memory[13]


What is Main Memory?Where data reside for a program that is currently runningSometimes called RAM (Random Access Memory): you can load from or store into any main memory location at any timeSometimes called core (from magnetic cores that some memories used, many years ago)Much slower => much cheaper => much bigger

Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


What Main Memory Looks LikeSupercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*012345678910536,870,911You can think of main memory as a big long 1D array of bytes.


The Relationship BetweenMain Memory & Cache


RAM is SlowSupercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*CPU307 GB/sec[6]4.4 GB/sec[7] (1.4%)BottleneckThe speed of data transferbetween Main Memory and theCPU is much slower than thespeed of calculating, so the CPUspends most of its time waitingfor data to come in or go out.


Why Have Cache?Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*CPUCache is much closer to the speedof the CPU, so the CPU doesnthave to wait nearly as long forstuff thats already in cache:it can do moreoperations per second!4.4 GB/sec[7] (1%)27 GB/sec (9%)[7]


Cache & RAM BandwidthsSupercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Better[26]Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


Cache & RAM Bandwidth

14247.1814210.38

14386.7714180.11

14435.2214165.56

14457.6514182.99

14466.7114185.19

14476.2814174.7

14485.114198.12

14498.3414169.3

14483.5114182.34

14498.0114181.44

14498.7414202.71

14508.1114139.8

14507.5814181.87

14513.114194.58

14500.0414158.15

14513.5114186.06

14516.7714194.11

14513.8114155.92

14509.3614188.26

14516.2714178.59

14518.3114180.03

14508.4714184.54

14511.1814191.08

14519.2214189.59

14515.1614190.39

14509.7714188.29

14507.1114183.02

14515.5914192.23

14508.5314186.89

14518.0514168.5

14203.114024.38

14196.0914044.27

11519.7211755.13

8650.69079.46

7843.678249.91

7844.668255.21

7848.98237.1

7856.328259.32

7841.438262.92

7856.788259.96

7847.188246.82

7853.258255.26

7848.058246.77

7838.118250.94

7853.978243.19

7853.788261.14

7849.578248.73

7854.248260.4

7853.68231.9

7847.248253.33

7857.718177.5

7861.58247.45

7857.648257.7

7860.948253.15

7837.248255.14

7853.538243.88

7850.788254.16

7860.198240.45

7862.658235.63

7860.98257.26

7865.088261.5

7865.778247.68

7858.748247.77

7857.178205.32

7863.588238.6

7861.458249.15

7863.958235.33

7865.718255.3

7855.078243.98

7868.618258.39

7853.498236.09

7860.658210.25

7859.688254

7867.578253.59

7867.228259.73

7851.688246.81

7866.578256.6

7861.838241.05

7836.388247.16

7867.898243.68

7867.728261.13

7865.678240.21

7867.298224.45

7860.898257.53

7866.978248.44

7857.758256.1

7864.658246.46

7866.928256.44

7864.358240.2

7868.738256.85

7857.198257.51

7850.648260.73

7865.468251.95

7858.488259.42

7860.478259.32

7864.988261.1

7872.738245.37

7867.558259.95

7861.678224.83

7857.068237.93

7860.468199.36

7849.258257.12

7870.998189.58

7865.28215.24

7862.68237.23

7852.58248.6

7852.088245.84

7866.578258.02

7856.98250.85

7853.578230.01

7840.18190.94

7820.758177.06

7806.388128.59

7777.878140.93

7779.198088.6

7778.958101.97

7774.668060.33

7752.698101

7770.038094.78

7776.568053.9

7758.878101.12

7772.358068.58

7772.168095.8

7763.728074.29

7773.928083.87

7777.268070.48

7771.848099.73

7719.598075.81

7768.828096.28

7775.098056.91

7771.168086.48

7755.968096.3

7760.128078.07

7759.88068.23

7631.788054.83

7618.28047.63

7732.027956.87

7655.858042.72

7725.87996.28

7714.618056.72

7515.067858

7624.127895.5

7637.937741.66

7636.537945.8

7341.237853.66

7515.287781.19

7237.047747.09

7461.547250.46

7256.97378.14

6696.777106.15

6737.496343.97

6547.116249.16

5991.115018.53

5836.484482.27

4959.793418.65

4657.392772.85

4336.382547.29

3988.922312.31

40162166.92

3931.62095.44

3810.271995.24

3820.211954.69

3848.281899.1

3799.91840.8

3772.091796.24

3765.111742.41

3750.181723.53

3743.71703.83

3682.081668.98

3664.431642.6

3704.841618.6

3619.751592.33

3603.381585.18

3629.121563.99

3661.951535.88

3667.141531.17

3665.121524.09

3658.151495.36

3603.331507.28

3649.911488.69

3607.021469.99

3496.531455.48

3640.171464.54

3644.711452.88

3596.211437.13

3635.891446.52

3537.251427.81

3623.651422.92

3597.521420.96

3601.781442.96

3568.331423.41

3584.591443.29

3608.711427.09

3626.661400.76

3584.251398.39

3566.341386.02

3616.271407.95

3500.151398.48

32 KB (L1 cache size)

2 MB (L2 cache size)

7.7 GB/sec

14.2 GB/sec

3.5 GB/sec

1.4 GB/sec

Read BW

Write BW

Array Size (bytes)

Bandwidth (MB/sec)

Cache & RAM Bandwidth: Intel T2400 (1.83 GHz)

Sheet1

102414247.1814210.38

204814386.7714180.11

307214435.2214165.56

409614457.6514182.99

512014466.7114185.19

614414476.2814174.7

716814485.114198.12

819214498.3414169.3

921614483.5114182.34

1024014498.0114181.44

1126414498.7414202.71

1228814508.1114139.8

1331214507.5814181.87

1433614513.114194.58

1536014500.0414158.15

1638414513.5114186.06

1740814516.7714194.11

1843214513.8114155.92

1945614509.3614188.26

2048014516.2714178.59

2150414518.3114180.03

2252814508.4714184.54

2355214511.1814191.08

2457614519.2214189.59

2560014515.1614190.39

2662414509.7714188.29

2764814507.1114183.02

2867214515.5914192.23

2969614508.5314186.89

3072014518.0514168.5

3174414203.114024.38

3276814196.0914044.27

3379211519.7211755.13

358408650.69079.46

378887843.678249.91

399367844.668255.21

419847848.98237.1

440327856.328259.32

460807841.438262.92

481287856.788259.96

501767847.188246.82

522247853.258255.26

542727848.058246.77

563207838.118250.94

583687853.978243.19

604167853.788261.14

624647849.578248.73

645127854.248260.4

665607853.68231.9

696327847.248253.33

727047857.718177.5

757767861.58247.45

788487857.648257.7

819207860.948253.15

849927837.248255.14

880647853.538243.88

911367850.788254.16

942087860.198240.45

972807862.658235.63

1003527860.98257.26

1044487865.088261.5

1085447865.778247.68

1126407858.748247.77

1167367857.178205.32

1208327863.588238.6

1249287861.458249.15

1290247863.958235.33

1331207865.718255.3

1382407855.078243.98

1433607868.618258.39

1484807853.498236.09

1536007860.658210.25

1587207859.688254

1638407867.578253.59

1689607867.228259.73

1751047851.688246.81

1812487866.578256.6

1873927861.838241.05

1935367836.388247.16

1996807867.898243.68

2068487867.728261.13

2140167865.678240.21

2211847867.298224.45

2283527860.898257.53

2355207866.978248.44

2437127857.758256.1

2519047864.658246.46

2600967866.928256.44

2682887864.358240.2

2775047868.738256.85

2867207857.198257.51

2959367850.648260.73

3061767865.468251.95

3164167858.488259.42

3266567860.478259.32

3368967864.988261.1

3481607872.738245.37

3594247867.558259.95

3706887861.678224.83

3829767857.068237.93

3952647860.468199.36

4085767849.258257.12

4218887870.998189.58

4352007865.28215.24

4495367862.68237.23

4638727852.58248.6

4792327852.088245.84

4945927866.578258.02

5109767856.98250.85

5273607853.578230.01

5447687840.18190.94

5621767820.758177.06

5806087806.388128.59

5990407777.878140.93

6184967779.198088.6

6379527778.958101.97

6584327774.668060.33

6799367752.698101

7014407770.038094.78

7239687776.568053.9

7475207758.878101.12

7710727772.358068.58

7956487772.168095.8

8212487763.728074.29

8478727773.928083.87

8744967777.268070.48

9021447771.848099.73

9308167719.598075.81

9605127768.828096.28

9912327775.098056.91

10229767771.168086.48

10557447755.968096.3

10895367760.128078.07

11243527759.88068.23

11601927631.788054.83

11970567618.28047.63

12349447732.027956.87

12738567655.858042.72

13137927725.87996.28

13557767714.618056.72

13987847515.067858

14428167624.127895.5

14888967637.937741.66

15360007636.537945.8

15841287341.237853.66

16343047515.287781.19

16855047237.047747.09

17387527461.547250.46

17940487256.97378.14

18503686696.777106.15

19087366737.496343.97

19691526547.116249.16

20316165991.115018.53

20951045836.484482.27

21606404959.793418.65

22282244657.392772.85

22978564336.382547.29

23705603988.922312.31

244531240162166.92

25221123931.62095.44

26009603810.271995.24

26828803820.211954.69

27668483848.281899.1

28538883799.91840.8

29440003772.091796.24

30361603765.111742.41

31313923750.181723.53

32296963743.71703.83

33310723682.081668.98

34355203664.431642.6

35430403704.841618.6

36546563619.751592.33

37693443603.381585.18

38881283629.121563.99

40099843661.951535.88

41359363667.141531.17

42659843665.121524.09

44001283658.151495.36

45383683603.331507.28

46807043649.911488.69

48271363607.021469.99

49786883496.531455.48

51343363640.171464.54

52951043644.711452.88

54609923596.211437.13

56320003635.891446.52

58081283537.251427.81

59904003623.651422.92

61777923597.521420.96

63713283601.781442.96

65710083568.331423.41

67768323584.591443.29

69888003608.711427.09

72079363626.661400.76

74332163584.251398.39

76656643566.341386.02

79052803616.271407.95

81530883500.151398.48

rmma_intelt2400_membw_20070904

RIGHTMARK MEMORY ANALYZER V3.72 TEST RESULTS

============================================

CPU ModelGenuine Intel(R) Core(TM) Duo (Yonah) 1828.7 MHz



Test TypeMemory Bandwidth

Test StatusCompleted successfully

Selected Tests7

Set Size134217728 bytes

Memory Allocation1

Thread Lock0

Min Block Size1024 bytes

Max Block Size8388608 bytes

CPU Register Usage0

Read Prefetch Type0

Prefetch Distance0 bytes

Block Prefetch Size1024 bytes

Stride Size64 bytes

Non-Temporal Store0

Copy-to-Self Mode0

MEMORY READ BANDWIDTH TEST

==========================

Size(bytes)Bandwidth(bytes/cycle)Bandwidth(MB/s)

10247.7914247.18

20487.8714386.77

30727.8914435.22

40967.9114457.65

51207.9114466.71

61447.9214476.28

71687.9214485.1

81927.9314498.34

92167.9214483.51

102407.9314498.01

112647.9314498.74

122887.9314508.11

133127.9314507.58

143367.9414513.1

153607.9314500.04

163847.9414513.51

174087.9414516.77

184327.9414513.81

194567.9314509.36

204807.9414516.27

215047.9414518.31

225287.9314508.47

235527.9414511.18

245767.9414519.22

256007.9414515.16

266247.9314509.77

276487.9314507.11

286727.9414515.59

296967.9314508.53

307207.9414518.05

317447.7714203.1

327687.7614196.09

337926.311519.72

358404.738650.6

378884.297843.67

399364.297844.66

419844.297848.9

440324.37856.32

460804.297841.43

481284.37856.78

501764.297847.18

522244.297853.25

542724.297848.05

563204.297838.11

583684.297853.97

604164.297853.78

624644.297849.57

645124.297854.24

665604.297853.6

696324.297847.24

727044.37857.71

757764.37861.5

788484.37857.64

819204.37860.94

849924.297837.24

880644.297853.53

911364.297850.78

942084.37860.19

972804.37862.65

1003524.37860.9

1044484.37865.08

1085444.37865.77

1126404.37858.74

1167364.37857.17

1208324.37863.58

1249284.37861.45

1290244.37863.95

1331204.37865.71

1382404.37855.07

1433604.37868.61

1484804.297853.49

1536004.37860.65

1587204.37859.68

1638404.37867.57

1689604.37867.22

1751044.297851.68

1812484.37866.57

1873924.37861.83

1935364.297836.38

1996804.37867.89

2068484.37867.72

2140164.37865.67

2211844.37867.29

2283524.37860.89

2355204.37866.97

2437124.37857.75

2519044.37864.65

2600964.37866.92

2682884.37864.35

2775044.37868.73

2867204.37857.19

2959364.297850.64

3061764.37865.46

3164164.37858.48

3266564.37860.47

3368964.37864.98

3481604.37872.73

3594244.37867.55

3706884.37861.67

3829764.37857.06

3952644.37860.46

4085764.297849.25

4218884.37870.99

4352004.37865.2

4495364.37862.6

4638724.297852.5

4792324.297852.08

4945924.37866.57

5109764.37856.9

5273604.297853.57

5447684.297840.1

5621764.287820.75

5806084.277806.38

5990404.257777.87

6184964.257779.19

6379524.257778.95

6584324.257774.66

6799364.247752.69

7014404.257770.03

7239684.257776.56

7475204.247758.87

7710724.257772.35

7956484.257772.16

8212484.257763.72

8478724.257773.92

8744964.257777.26

9021444.257771.84

9308164.227719.59

9605124.257768.82

9912324.257775.09

10229764.257771.16

10557444.247755.96

10895364.247760.12

11243524.247759.8

11601924.177631.78

11970564.177618.2

12349444.237732.02

12738564.197655.85

13137924.227725.8

13557764.227714.61

13987844.117515.06

14428164.177624.12

14888964.187637.93

15360004.187636.53

15841284.017341.23

16343044.117515.28

16855043.967237.04

17387524.087461.54

17940483.977256.9

18503683.666696.77

19087363.686737.49

19691523.586547.11

20316163.285991.11

20951043.195836.48

21606402.714959.79

22282242.554657.39

22978562.374336.38

23705602.183988.92

24453122.24016

25221122.153931.6

26009602.083810.27

26828802.093820.21

27668482.13848.28

28538882.083799.9

29440002.063772.09

30361602.063765.11

31313922.053750.18

32296962.053743.7

33310722.013682.08

343552023664.43

35430402.033704.84

36546561.983619.75

37693441.973603.38

38881281.983629.12

400998423661.95

41359362.013667.14

426598423665.12

440012823658.15

45383681.973603.33

468070423649.91

48271361.973607.02

49786881.913496.53

51343361.993640.17

52951041.993644.71

54609921.973596.21

56320001.993635.89

58081281.933537.25

59904001.983623.65

61777921.973597.52

63713281.973601.78

65710081.953568.33

67768321.963584.59

69888001.973608.71

72079361.983626.66

74332161.963584.25

76656641.953566.34

79052801.983616.27

81530881.913500.15

MAXIMAL READ BANDWIDTH

245767.9414519.22

MEMORY WRITE BANDWIDTH TEST

===========================


10247.7714210.38

20487.7514180.11

30727.7514165.56

40967.7614182.99

51207.7614185.19

61447.7514174.7

71687.7614198.12

81927.7514169.3

92167.7614182.34

102407.7514181.44

112647.7714202.71

122887.7314139.8

133127.7514181.87

143367.7614194.58

153607.7414158.15

163847.7614186.06

174087.7614194.11

184327.7414155.92

194567.7614188.26

204807.7514178.59

215047.7514180.03

225287.7614184.54

235527.7614191.08

245767.7614189.59

256007.7614190.39

266247.7614188.29

276487.7614183.02

286727.7614192.23

296967.7614186.89

307207.7514168.5

317447.6714024.38

327687.6814044.27

337926.4311755.13

358404.969079.46

378884.518249.91

399364.518255.21

419844.58237.1

440324.528259.32

460804.528262.92

481284.528259.96

501764.518246.82

522244.518255.26

542724.518246.77

563204.518250.94

583684.518243.19

604164.528261.14

624644.518248.73

645124.528260.4

665604.58231.9

696324.518253.33

727044.478177.5

757764.518247.45

788484.528257.7

819204.518253.15

849924.518255.14

880644.518243.88

911364.518254.16

942084.518240.45

972804.58235.63

1003524.528257.26

1044484.528261.5

1085444.518247.68

1126404.518247.77

1167364.498205.32

1208324.518238.6

1249284.518249.15

1290244.58235.33

1331204.518255.3

1382404.518243.98

1433604.528258.39

1484804.58236.09

1536004.498210.25

1587204.518254

1638404.518253.59

1689604.528259.73

1751044.518246.81

1812484.518256.6

1873924.518241.05

1935364.518247.16

1996804.518243.68

2068484.528261.13

2140164.518240.21

2211844.58224.45

2283524.528257.53

2355204.518248.44

2437124.518256.1

2519044.518246.46

2600964.518256.44

2682884.518240.2

2775044.528256.85

2867204.528257.51

2959364.528260.73

3061764.518251.95

3164164.528259.42

3266564.528259.32

3368964.528261.1

3481604.518245.37

3594244.528259.95

3706884.58224.83

3829764.58237.93

3952644.488199.36

4085764.528257.12

4218884.488189.58

4352004.498215.24

4495364.58237.23

4638724.518248.6

4792324.518245.84

4945924.528258.02

5109764.518250.85

5273604.58230.01

5447684.488190.94

5621764.478177.06

5806084.448128.59

5990404.458140.93

6184964.428088.6

6379524.438101.97

6584324.418060.33

6799364.438101

7014404.438094.78

7239684.48053.9

7475204.438101.12

7710724.418068.58

7956484.438095.8

8212484.428074.29

8478724.428083.87

8744964.418070.48

9021444.438099.73

9308164.428075.81

9605124.438096.28

9912324.418056.91

10229764.428086.48

10557444.438096.3

10895364.428078.07

11243524.418068.23

11601924.48054.83

11970564.48047.63

12349444.357956.87

12738564.48042.72

13137924.377996.28

13557764.418056.72

13987844.37858

14428164.327895.5

14888964.237741.66

15360004.347945.8

15841284.297853.66

16343044.257781.19

16855044.247747.09

17387523.967250.46

17940484.037378.14

18503683.897106.15

19087363.476343.97

19691523.426249.16

20316162.745018.53

20951042.454482.27

21606401.873418.65

22282241.522772.85

22978561.392547.29

23705601.262312.31

24453121.182166.92

25221121.152095.44

26009601.091995.24

26828801.071954.69

27668481.041899.1

28538881.011840.8

29440000.981796.24

30361600.951742.41

31313920.941723.53

32296960.931703.83

33310720.911668.98

34355200.91642.6

35430400.891618.6

36546560.871592.33

37693440.871585.18

38881280.861563.99

40099840.841535.88

41359360.841531.17

42659840.831524.09

44001280.821495.36

45383680.821507.28

46807040.811488.69

48271360.81469.99

49786880.81455.48

51343360.81464.54

52951040.791452.88

54609920.791437.13

56320000.791446.52

58081280.781427.81

59904000.781422.92

61777920.781420.96

63713280.791442.96

65710080.781423.41

67768320.791443.29

69888000.781427.09

72079360.771400.76

74332160.761398.39

76656640.761386.02

79052800.771407.95

81530880.761398.48

MAXIMAL WRITE BANDWIDTH

10247.7714210.38

MEMORY COPY BANDWIDTH TEST

==========================


10245.8210648.75

20486.2511431.17

30726.1811309.64

40966.3311583.39

51206.2511429.84

61446.3511607.8

71686.2911510.59

81926.3411599.43

92166.3111531.02

102406.3611622.61

112646.3211551.17

122886.3411599.04

133126.3211555.78

143366.3511620.62

153606.1711287.61

163846.1211196.41

174083.957228.88

184322.915326.2

194562.955396.99

2048035491.1

215042.965417.67

225282.935357.97

235522.965414.54

2457635491.85

256002.975432.51

266242.945384.95

276482.975435.02

286723.015498.14

296962.975440.47

307202.955403.39

317442.985447.28

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419842.995472.63

440322.995468.92

460802.995463.01

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5017635481.14

5222435484.35

542722.995470.94

5632035484.3

583682.995463.75

6041635485.67

624642.995474.95

6451235489.08

6656035481.57

696323.015505.31

7270435491.62

757762.995472.22

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8192035485.19

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880642.995465.31

911362.995476.62

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14336035494.93

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1638403.015507.81

16896035495.35

1751043.015511.85

1812483.015503.42

1873923.015507.25

1935363.015502.67

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21401635481.46

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2867202.975435.19

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23705600.741360.23

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26009600.731332.53

26828800.721309.32

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28538880.71287.96

29440000.711294.49

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31313920.691265.65

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33310720.681247.35

34355200.681248.1

35430400.671232.97

36546560.671221.7

37693440.671216.35

38881280.661212.83

40099840.661206.05

41359360.651189.26

42659840.651183.24

44001280.641165.64

45383680.651184.89

46807040.641164.57

48271360.651190.02

49786880.631155.19

51343360.641163.24

52951040.641162.7

54609920.641168.97

56320000.651183.23

58081280.631160.75

59904000.631151.1

61777920.631158.05

63713280.641171.36

65710080.641170.73

67768320.631151.42

69888000.641168.89

72079360.631157.37

74332160.641167.04

76656640.641171.26

79052800.631153.88

81530880.641176.82

MAXIMAL COPY BANDWIDTH

102406.3611622.61

Cache Use JargonCache Hit: the data that the CPU needs right now are already in cache.Cache Miss: the data that the CPU needs right now are not currently in cache.If all of your data are small enough to fit in cache, then when you run your program, youll get almost all cache hits (except at the very beginning), which means that your performance could be excellent!Sadly, this rarely happens in real life: most problems of scientific or engineering interest are bigger than just a few MB.Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


Cache LinesA cache line is a small, contiguous region in cache, corresponding to a contiguous region in RAM of the same size, that is loaded all at once.Typical size: 32 to 1024 bytesExamplesCore 2 Duo [26]L1 data cache: 64 bytes per lineL2 cache: 64 bytes per linePOWER7 [28]L1 instruction cache: 128 bytes per lineL1 data cache: 128 bytes per lineL2 cache: 128 bytes per lineL3 cache: 128bytes per line Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


How Cache WorksWhen you request data from a particular address in Main Memory, heres what happens:The hardware checks whether the data for that address is already in cache. If so, it uses it.Otherwise, it loads from Main Memory the entire cache line that contains the address.For example, on a 1.83 GHz Pentium4 Core Duo (Yonah), a cache miss makes the program stall (wait) at least 48 cycles (26.2 nanoseconds) for the next cache line to load time that could have been spent performing up to 192 calculations! [26]Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


If Its in Cache, Its Also in RAMIf a particular memory address is currently in cache, then its also in Main Memory (RAM).That is, all of a programs data are in Main Memory, but some are also in cache.Well revisit this point shortly.Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


Mapping Cache Lines to RAMMain memory typically maps into cache in one of three ways:Direct mapped (occasionally)Fully associative (very rare these days)Set associative (common)DONTPANIC!Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


Direct Mapped CacheDirect Mapped Cache is a scheme in which each location in main memory corresponds to exactly one location in cache (but not the reverse, since cache is much smaller than main memory).Typically, if a cache address is represented by c bits, and a main memory address is represented by m bits, then the cache location associated with main memory address A is MOD(A,2c); that is, the lowest c bits of A.Example: POWER4 L1 instruction cacheSupercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


Direct Mapped Cache IllustrationSupercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Must go intocache address11100101Main Memory Address0100101011100101Notice that 11100101 is the low 8 bits of 0100101011100101.


Jargon: Cache ConflictSuppose that the cache address 11100101 currently contains RAM address 0100101011100101.But, we now need to load RAM address 1100101011100101, which maps to the same cache address as 0100101011100101.This is called a cache conflict : the CPU needs a RAM location that maps to a cache line already in use.In the case of direct mapped cache, every cache conflict leads to the new cache line clobbering the old cache line.This can lead to serious performance problems.Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


Problem with Direct Mapped: F90If you have two arrays that start in the same place relative to cache, then they might clobber each other all the time: no cache hits!Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*REAL,DIMENSION(multiple_of_cache_size) :: a, b, cINTEGER :: index

DO index = 1, multiple_of_cache_size a(index) = b(index) + c(index)END DOIn this example, a(index), b(index) and c(index) all map to the same cache line, so loading c(index) clobbers b(index) no cache reuse!Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


Problem with Direct Mapped: CIf you have two arrays that start in the same place relative to cache, then they might clobber each other all the time: no cache hits!Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*float a[multiple_of_cache_size], b[multiple_of_cache_size, c[multiple_of_cache_size];int index;

for (index = 0; index < multiple_of_cache_size; index++) { a[index] = b[index] + c[index]; }In this example, a[index], b[index] and c[index] all map to the same cache line, so loading c[index] clobbers b[index] no cache reuse!Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


Fully Associative CacheFully Associative Cache can put any line of main memory into any cache line.Typically, the cache management system will put the newly loaded data into the Least Recently Used cache line, though other strategies are possible (e.g., Random, First In First Out, Round Robin, Least Recently Modified).So, this can solve, or at least reduce, the cache conflict problem.But, fully associative cache tends to be expensive, so its pretty rare: you need Ncache. NRAM connections!Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


Fully Associative IllustrationSupercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Could go intoany cache lineMain Memory Address0100101011100101


Set Associative CacheSet Associative Cache is a compromise between direct mapped and fully associative. A line in main memory can map to any of a fixed number of cache lines.For example, 2-way Set Associative Cache can map each main memory line to either of 2 cache lines (e.g., to the Least Recently Used), 3-way maps to any of 3 cache lines, 4-way to 4 lines, and so on.Set Associative cache is cheaper than fully associative you need K . NRAM connections but more robust than direct mapped.Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


2-Way Set Associative IllustrationSupercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Could go into cache address11100101Main Memory Address0100101011100101Could go intocache address01100101OR


Cache Associativity ExamplesCore 2 Duo [26]L1 data cache: 8-way set associativeL2 cache: 8-way set associativePOWER4 [12]L1 instruction cache: direct mappedL1 data cache: 2-way set associativeL2 cache: 8-way set associativeL3 cache: 8-way set associativePOWER7 [28]L1 instruction cache: 4-way set associativeL1 data cache: 8-way set associativeL2 cache: 8-way set associativeL3 cache: 8-way set associative



If Its in Cache, Its Also in RAMAs we saw earlier:If a particular memory address is currently in cache, then its also in Main Memory (RAM).That is, all of a programs data are in Main Memory, but some are also in cache.Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


Changing a Value Thats in CacheSuppose that you have in cache a particular line of main memory (RAM).If you dont change the contents of any of that lines bytes while its in cache, then when it gets clobbered by another main memory line coming into cache, theres no loss of information.But, if you change the contents of any byte while its in cache, then you need to store it back out to main memory before clobbering it. Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


Cache Store StrategiesTypically, there are two possible cache store strategies:Write-through: every single time that a value in cache is changed, that value is also stored back into main memory (RAM).Write-back: every single time that a value in cache is changed, the cache line containing that cache location gets marked as dirty. When a cache line gets clobbered, then if it has been marked as dirty, then it is stored back into main memory (RAM). [14] Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


Cache Store ExamplesCore 2 Duo [26]L1 cache: write-backPentium D [26]L1 cache: write-throughSupercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


The Importance of Being Local[15]


More Data Than CacheLets say that you have 1000 times more data than cache. Then wont most of your data be outside the cache?

YES!

Okay, so how does cache help?Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


Improving Your Cache Hit RateMany scientific codes use a lot more data than can fit in cache all at once.Therefore, you need to ensure a high cache hit rate even though youve got much more data than cache.So, how can you improve your cache hit rate?Use the same solution as in Real Estate:Location, Location, Location!Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


Data LocalityData locality is the principle that, if you use data in a particular memory address, then very soon youll use either the same address or a nearby address.Temporal locality: if youre using address A now, then youll probably soon use address A again.Spatial locality: if youre using address A now, then youll probably soon use addresses between A-k and A+k, where k is small.Note that this principle works well for sufficiently small values of soon.Cache is designed to exploit locality, which is why a cache miss causes a whole line to be loaded.Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


Data Locality Is Empirical: CData locality has been observed empirically in many, many programs.Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*void ordered_fill (float* array, int array_length){ /* ordered_fill */ int index;

for (index = 0; index < array_length; index++) { array[index] = index; } /* for index */} /* ordered_fill */

Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


Data Locality Is Empirical: F90Data locality has been observed empirically in many, many programs.Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*SUBROUTINE ordered_fill (array, array_length) IMPLICIT NONE INTEGER,INTENT(IN) :: array_length REAL,DIMENSION(array_length),INTENT(OUT) :: array INTEGER :: index

DO index = 1, array_length array(index) = index END DOEND SUBROUTINE ordered_fill

Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


No Locality Example: CIn principle, you could write a program that exhibited absolutely no data locality at all:Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*void random_fill (float* array, int* random_permutation_index, int array_length){ /* random_fill */ int index;

for (index = 0; index < array_length; index++) { array[random_permutation_index[index]] = index; } /* for index */} /* random_fill */Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


No Locality Example: F90In principle, you could write a program that exhibited absolutely no data locality at all:Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*SUBROUTINE random_fill (array, random_permutation_index, array_length) IMPLICIT NONE INTEGER,INTENT(IN) :: array_length INTEGER,DIMENSION(array_length),INTENT(IN) :: && random_permutation_index REAL,DIMENSION(array_length),INTENT(OUT) :: array INTEGER :: index

DO index = 1, array_length array(random_permutation_index(index)) = index END DOEND SUBROUTINE random_fillSupercomputing in Plain English: Storage HierarchyTue Feb 15 2011


Permuted vs. OrderedSupercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*In a simple array fill, locality provides a factor of 8 to 20 speedup over a randomly ordered fill on a Pentium4.


Permuted vs Ordered

27.251.379997

11.070.76

4.050.36

1.640.18

0.710.09

0.350.04

0.180.02

0.080.01

Random

Ordered

Array size (log2 bytes)

CPU seconds

Sheet1

Sizelog(size)RandomOrdered

1342177282727.251.379997

671088642611.070.76

33554432254.050.36

16777216241.640.18

8388608230.710.09

4194304220.350.04

2097152210.180.02

1048576200.080.01

Sheet2

Sheet3

Exploiting Data LocalityIf you know that your code is capable of operating with a decent amount of data locality, then you can get speedup by focusing your energy on improving the locality of the codes behavior.This will substantially increase your cache reuse.Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


A Sample ApplicationMatrix-Matrix MultiplyLet A, B and C be matrices of sizesnr nc, nr nk and nk nc, respectively:Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*The definition of A = B C isfor r {1, nr}, c {1, nc}.Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


Matrix Multiply w/InitializationSUBROUTINE matrix_matrix_mult_by_init (dst, src1, src2, & & nr, nc, nq) IMPLICIT NONE INTEGER,INTENT(IN) :: nr, nc, nq REAL,DIMENSION(nr,nc),INTENT(OUT) :: dst REAL,DIMENSION(nr,nq),INTENT(IN) :: src1 REAL,DIMENSION(nq,nc),INTENT(IN) :: src2

INTEGER :: r, c, q

DO c = 1, nc DO r = 1, nr dst(r,c) = 0.0 DO q = 1, nq dst(r,c) = dst(r,c) + src1(r,q) * src2(q,c) END DO !! q END DO !! r END DO !! cEND SUBROUTINE matrix_matrix_mult_by_init



Matrix Multiply w/Initializationvoid matrix_matrix_mult_by_init ( float** dst, float** src1, float** src2, int nr, int nc, int nq){ /* matrix_matrix_mult_by_init */ int r, c, q;

for (r = 0; r < nr; r++) { for (c = 0; c < nc; c++) { dst[r][c] = 0.0; for (q = 0; q < nq; q++) { dst[r][c] = dst[r][c] + src1[r][q] * src2[q][c]; } /* for q */ } /* for c */ } /* for r */} /* matrix_matrix_mult_by_init */Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011


Matrix Multiply Via IntrinsicSUBROUTINE matrix_matrix_mult_by_intrinsic ( & & dst, src1, src2, nr, nc, nq) IMPLICIT NONE INTEGER,INTENT(IN) :: nr, nc, nq REAL,DIMENSION(nr,nc),INTENT(OUT) :: dst REAL,DIMENSION(nr,nq),INTENT(IN) :: src1 REAL,DIMENSION(nq,nc),INTENT(IN) :: src2

dst = MATMUL(src1, src2)END SUBROUTINE matrix_matrix_mult_by_intrinsic



Matrix Multiply BehaviorSupercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*If the matrix is big, then each sweep of a row will clobber nearby values in cache.


Performance of Matrix MultiplySupercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*


Chart1

0.020.010.01

0.050.050.03

0.10.110.08

0.380.760.28

1.782.180.58

8.979.592.4

17.920.984.72

72.881.4618.76

156.6161.4437.41

723.9690.98151.55

Naive

Init

Intrinsic

Total Problem Size in bytes (nr*nc+nr*nq+nq*nc)

CPU sec

Matrix-Matrix Multiply

Sheet1

819200.020.010.01

1966080.050.050.03

3276800.10.110.08

7864320.380.760.28

13107201.782.180.58

31457288.979.592.4

524288017.920.984.72

1258291272.881.4618.76

20971520156.6161.4437.41

50331648723.9690.98151.55

Sheet2

Sheet3

TilingSupercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*


TilingTile: a small rectangular subdomain of a problem domain. Sometimes called a block or a chunk.Tiling: breaking the domain into tiles.Tiling strategy: operate on each tile to completion, then move to the next tile.Tile size can be set at runtime, according to whats best for the machine that youre running on.Supercomputing in Plain English: Storage Hierarchy BWUPEP2011, UIUC, May 29 - June 10 2011*Supercomputing in Plain English: Storage HierarchyTue Feb 15 2011

Supe

Documents

Supercomputing in Plain English The Tyranny of the Storage Hierarchy Henry Neeman, Director OU Supercomputing Center for Education & Research Blue Waters