-
Supercomputingin Plain English The Tyranny ofthe Storage
HierarchyPRESENTERNAMEPRESENTERTITLEPRESENTERDEPARTMENTPRESENTERINSTITUTIONDAY
MONTH DATE YEARYour Logo Here
Slides by Henry Neeman, University of Oklahoma
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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 INSTITUTION, DAY MONTH DATE YEAR
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
The Storage HierarchyRegistersCache memoryMain memory (RAM)Hard
diskRemovable media (CD, DVD etc)InternetSupercomputing in Plain
English: Storage Hierarchy INSTITUTION, DAY MONTH DATE YEAR*Fast,
expensive, fewSlow, cheap, a lot
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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
INSTITUTION, DAY MONTH DATE YEAR*Dell Latitude Z600[4]
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
Storage Speed, Size, CostSupercomputing in Plain English:
Storage Hierarchy INSTITUTION, DAY MONTH DATE YEAR** 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)
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
-
Registers[25]
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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 INSTITUTION, DAY MONTH DATE YEAR*Arithmetic/Logic
UnitControl UnitRegistersFetch Next
InstructionAddSubMultDivAndOrNotIntegerFloating PointFetch
DataStore DataIncrement Instruction PtrExecute
InstructionCPUSupercomputing in Plain English: Storage HierarchyTue
Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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 INSTITUTION, DAY MONTH DATE
YEAR*Example:addend in R0augend in R1ADDsum in R25712Register
RiRegister RjRegister RkoperandoperandresultOperation
circuitrySupercomputing in Plain English: Storage HierarchyTue Feb
15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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 INSTITUTION,
DAY MONTH DATE YEAR*Supercomputing in Plain English: Storage
HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
-
Cache[4]
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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 INSTITUTION,
DAY MONTH DATE YEAR*Supercomputing in Plain English: Storage
HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
From Cache to the CPUSupercomputing in Plain English: Storage
Hierarchy INSTITUTION, DAY MONTH DATE YEAR*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]
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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 INSTITUTION, DAY MONTH DATE
YEAR*Supercomputing in Plain English: Storage HierarchyTue Feb 15
2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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 INSTITUTION, DAY
MONTH DATE YEAR*Supercomputing in Plain English: Storage
HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
Cache & RAM LatenciesSupercomputing in Plain English:
Storage Hierarchy INSTITUTION, DAY MONTH DATE
YEAR*Better[26]Supercomputing in Plain English: Storage
HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
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
L2 Cache Line Size128 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
==================================
Size(bytes)Latency(cycles)Latency(ns)
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
================================
Size(bytes)Latency(cycles)Latency(ns)
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
=======================================
Size(bytes)Latency(cycles)Latency(ns)
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]
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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 INSTITUTION,
DAY MONTH DATE YEAR*Supercomputing in Plain English: Storage
HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
What Main Memory Looks LikeSupercomputing in Plain English:
Storage Hierarchy INSTITUTION, DAY MONTH DATE
YEAR*012345678910536,870,911You can think of main memory as a big
long 1D array of bytes.
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
-
The Relationship BetweenMain Memory & Cache
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
RAM is SlowSupercomputing in Plain English: Storage Hierarchy
INSTITUTION, DAY MONTH DATE YEAR*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.
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
Why Have Cache?Supercomputing in Plain English: Storage
Hierarchy INSTITUTION, DAY MONTH DATE YEAR*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]
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
Cache & RAM BandwidthsSupercomputing in Plain English:
Storage Hierarchy INSTITUTION, DAY MONTH DATE
YEAR*Better[26]Supercomputing in Plain English: Storage
HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
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
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522247853.258255.26
542727848.058246.77
563207838.118250.94
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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
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880647853.538243.88
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1044487865.088261.5
1085447865.778247.68
1126407858.748247.77
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1208327863.588238.6
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1996807867.898243.68
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2211847867.298224.45
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2355207866.978248.44
2437127857.758256.1
2519047864.658246.46
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2775047868.738256.85
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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
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6584327774.668060.33
6799367752.698101
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7710727772.358068.58
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8212487763.728074.29
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9605127768.828096.28
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10895367760.128078.07
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13987847515.067858
14428167624.127895.5
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15360007636.537945.8
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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
L1 Cache Line Size64 bytes
L2 Cache Line Size128 bytes
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
===========================
Size(bytes)Bandwidth(bytes/cycle)Bandwidth(MB/s)
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
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31313920.941723.53
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76656640.761386.02
79052800.771407.95
81530880.761398.48
MAXIMAL WRITE BANDWIDTH
10247.7714210.38
MEMORY COPY BANDWIDTH TEST
==========================
Size(bytes)Bandwidth(bytes/cycle)Bandwidth(MB/s)
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30726.1811309.64
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51206.2511429.84
61446.3511607.8
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92166.3111531.02
102406.3611622.61
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7475202.965412.62
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8212482.815132.24
8478722.845188.02
8744962.734989.11
9021442.745004.81
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9605122.474511.26
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10895361.522771.07
11243521.332424.51
11601921.182149.8
11970561.12009.58
12349441.031874.84
12738561.041896.16
13137921.011847.3
13557760.991815.14
13987840.951733.94
14428160.921690.97
14888960.911662.4
15360000.891631.91
15841280.871592.98
16343040.861576.36
16855040.851555.82
17387520.841535.8
17940480.821501.29
18503680.811484.7
19087360.81459.02
19691520.791442.87
20316160.791444.34
20951040.781422.38
21606400.771404.3
22282240.761390.2
22978560.751379.78
23705600.741360.23
24453120.741358.37
25221120.731336.56
26009600.731332.53
26828800.721309.32
27668480.711306.57
28538880.71287.96
29440000.711294.49
30361600.71274.23
31313920.691265.65
32296960.691258.17
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
Your Logo Here
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 INSTITUTION, DAY MONTH DATE YEAR*Supercomputing in Plain
English: Storage HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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 INSTITUTION, DAY MONTH DATE YEAR*Supercomputing in Plain
English: Storage HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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 INSTITUTION,
DAY MONTH DATE YEAR*Supercomputing in Plain English: Storage
HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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 INSTITUTION, DAY MONTH DATE
YEAR*Supercomputing in Plain English: Storage HierarchyTue Feb 15
2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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 INSTITUTION, DAY MONTH DATE YEAR*Supercomputing in Plain
English: Storage HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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
INSTITUTION, DAY MONTH DATE YEAR*Supercomputing in Plain English:
Storage HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
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Direct Mapped Cache IllustrationSupercomputing in Plain English:
Storage Hierarchy INSTITUTION, DAY MONTH DATE YEAR*Must go
intocache address11100101Main Memory Address0100101011100101Notice
that 11100101 is the low 8 bits of 0100101011100101.
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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 INSTITUTION, DAY MONTH DATE YEAR*Supercomputing
in Plain English: Storage HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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 INSTITUTION, DAY MONTH DATE
YEAR*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
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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 INSTITUTION, DAY MONTH DATE YEAR*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
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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 INSTITUTION, DAY MONTH DATE YEAR*Supercomputing
in Plain English: Storage HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
Fully Associative IllustrationSupercomputing in Plain English:
Storage Hierarchy INSTITUTION, DAY MONTH DATE YEAR*Could go intoany
cache lineMain Memory Address0100101011100101
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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 INSTITUTION, DAY MONTH DATE YEAR*Supercomputing
in Plain English: Storage HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
2-Way Set Associative IllustrationSupercomputing in Plain
English: Storage Hierarchy INSTITUTION, DAY MONTH DATE YEAR*Could
go into cache address11100101Main Memory
Address0100101011100101Could go intocache address01100101OR
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR*Supercomputing in Plain English: Storage
HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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 INSTITUTION, DAY MONTH DATE YEAR*Supercomputing
in Plain English: Storage HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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 INSTITUTION, DAY MONTH DATE YEAR*Supercomputing
in Plain English: Storage HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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
INSTITUTION, DAY MONTH DATE YEAR*Supercomputing in Plain English:
Storage HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
Cache Store ExamplesCore 2 Duo [26]L1 cache: write-backPentium D
[26]L1 cache: write-throughSupercomputing in Plain English: Storage
Hierarchy INSTITUTION, DAY MONTH DATE YEAR*Supercomputing in Plain
English: Storage HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
-
The Importance of Being Local[15]
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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 INSTITUTION, DAY MONTH DATE YEAR*Supercomputing
in Plain English: Storage HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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
INSTITUTION, DAY MONTH DATE YEAR*Supercomputing in Plain English:
Storage HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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 INSTITUTION, DAY MONTH DATE
YEAR*Supercomputing in Plain English: Storage HierarchyTue Feb 15
2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
Data Locality Is Empirical: CData locality has been observed
empirically in many, many programs.Supercomputing in Plain English:
Storage Hierarchy INSTITUTION, DAY MONTH DATE YEAR*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
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
Data Locality Is Empirical: F90Data locality has been observed
empirically in many, many programs.Supercomputing in Plain English:
Storage Hierarchy INSTITUTION, DAY MONTH DATE YEAR*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
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
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No Locality Example: CIn principle, you could write a program
that exhibited absolutely no data locality at all:Supercomputing in
Plain English: Storage Hierarchy INSTITUTION, DAY MONTH DATE
YEAR*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
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
No Locality Example: F90In principle, you could write a program
that exhibited absolutely no data locality at all:Supercomputing in
Plain English: Storage Hierarchy INSTITUTION, DAY MONTH DATE
YEAR*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
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
Permuted vs. OrderedSupercomputing in Plain English: Storage
Hierarchy INSTITUTION, DAY MONTH DATE YEAR*In a simple array fill,
locality provides a factor of 8 to 20 speedup over a randomly
ordered fill on a Pentium4.
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
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
Your Logo Here
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
INSTITUTION, DAY MONTH DATE YEAR*Supercomputing in Plain English:
Storage HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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
INSTITUTION, DAY MONTH DATE YEAR*The definition of A = B C isfor r
{1, nr}, c {1, nc}.Supercomputing in Plain English: Storage
HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR*Supercomputing in Plain English: Storage
HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
Your Logo Here
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 INSTITUTION, DAY MONTH DATE
YEAR*Supercomputing in Plain English: Storage HierarchyTue Feb 15
2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
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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
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR*Supercomputing in Plain English: Storage
HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
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Matrix Multiply BehaviorSupercomputing in Plain English: Storage
Hierarchy INSTITUTION, DAY MONTH DATE YEAR*If the matrix is big,
then each sweep of a row will clobber nearby values in cache.
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
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Performance of Matrix MultiplySupercomputing in Plain English:
Storage Hierarchy INSTITUTION, DAY MONTH DATE YEAR*
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
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
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TilingSupercomputing in Plain English: Storage Hierarchy
INSTITUTION, DAY MONTH DATE YEAR*
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
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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 INSTITUTION,
DAY MONTH DATE YEAR*Supercomputing in Plain English: Storage
HierarchyTue Feb 15 2011
Supercomputing in Plain English: Storage Hierarchy INSTITUTION,
DAY MONTH DATE YEAR
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Tiling Code: F90SUBROUTINE mat