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Hodnocené. / 5. Na základě hodnocení zákazníků
108 Cray T3E User’s Guide
This equation can be normalized by setting W
1
+ W
p
= 1. Here W
1
= α
(the sequential portion) and W
p
= 1 − α (the parallel portion). Now you
get
S
p
=
1
α + (1 − α)/p
.
For example, if you have a program which contains a 10 % sequential
part the equation reads
S
p
=
1
0.1 + 0.9/p
.
Setting p →∞, you get the maximum speedup, which is 1/0.1 = 10.
Therefore, the sequential part starts to dominate, when you add more
processors.
Efficiency e measures how well the code is parallellized:
e =
S
p
p
.
In the best case the efficiency is 1 and we say that the scalability is linear.
Ambdahls’ law gives a rather pessimistic picture of scalability. In many
cases it is not necessary to keep the model size fixed when doing parallel
computing. This way, the parallel part of the program (1 − α)canbe
increased at the same time you add more processors.
Gustafson’s law specifies a different scalability concept: you do not keep
the model size fixed — instead, you keep the solution time fixed. This
means that you want to solve the largest problem size possible, given a
time limit. A typical case is weather forecasting: you want to get a 24-
hour forecast within one hour, since the value of this forecast decreases
rapidly as time goes by.
Gustafson’s scaling law can be expressed as follows:
S
0
p
=
W
1
+ pW
p
W
1
+ W
p
.
Note that the time on p processors is compared to the time it would take
to compute this task on one processor. By normalizing (W
1
+ W
p
= 1, as
above) you find
S
0
p
= p − α
0
(p − 1).
Suppose that you have 128 processors available. Now,
S
0
128
= 128 − α
0
(128 − 1) = 128 − 127α
0
.
If the sequential part is α
0
= 0.1, you obtain a speedup of 128 − 12.7 =
115.3. If α
0
= 0.05, you get a speedup of about 122. However, note
that the bigger model size might actually not fit in the memory of one
processor, so you most probably are not able to do the comparison runs.
- Cray T3E 1
- User’s Guide 1
- Cray T3E User’s Guide 3 3
- Contents 4
- Contents 5 5
- B Glossary 113 6
- Bibliography 118 6
- Index 120 6
- Introduction 7
- 1.2 Usage policy 8
- 1.3 Overview of the system 9
- 1.4 Programming environment 9
- 10 Cray T3E User’s Guide 10
- Chapter 1. Introduction 11 11
- 12 Cray T3E User’s Guide 12
- Using the Cray T3E at CSC 13
- 2.2 Files 14
- 2.3 Editing files 16
- 2.5 Executing in batch mode 17
- 2.6 More information 18
- The Cray T3E system 20
- 3.2 Distributed memory 21
- 3.3 Processing elements 21
- 3.4 Processor architecture 23
- 3.5 Local memory hierarchy 24
- 26 Cray T3E User’s Guide 26
- Processing Element 27
- I/O Controller 27
- Interconnection 27
- Network 27
- 3.9 File systems 28
- 3.10 Resource monitoring 29
- 30 Cray T3E User’s Guide 30
- 3.11 More information 31
- Program development 32
- 4.3.1 BLAS 34
- 4.3.2 LAPACK 34
- 4.3.3 BLACS 35
- 4.3.4 PBLAS and ScaLAPACK 35
- 4.3.5 Details 35
- 36 Cray T3E User’s Guide 36
- 4.6 More information 38
- Fortran programming 40
- 5.2 Basic usage 41
- 5.4 Compiler options 42
- 5.5 Optimization options 42
- 5.6 Optimizing for cache 44
- 5.7 Compiler directives 45
- 5.8 Fortran 90 modules 48
- 5.9 Source code preprocessing 49
- 5.10 More information 51
- C and C++ programming 52
- 6.2 The C compiler 53
- 6.3 Calling Fortran from C 54
- 6.4 C compiler options 55
- #pragma _CRI symmetric var 59
- #pragma _CRI unroll [n] 59
- 6.6 The C++ compiler 61
- 6.7 More information 61
- Interprocess communication 62
- 7.2.1 Format of the MPI calls 63
- 7.2.2 Some MPI routines 64
- 7.2.3 An example of using MPI 64
- 7.2.5 MPI data types 67
- 7.3.1 Using PVM on the T3E 68
- #include <mpp/shmem.h> 71
- INCLUDE ’mpp/shmem.fh’ 71
- 7.4.2 Data addresses 72
- 7.4.4 Reduction routines 74
- 7.4.6 Example of using SHMEM 76
- 78 Cray T3E User’s Guide 78
- 0:c= 10121416 78
- 1:c= 2468 78
- 80 Cray T3E User’s Guide 80
- Batch queuing system 81
- 82 Cray T3E User’s Guide 82
- # QSUB -l p_mpp_t=7000 82
- 8.3 Status of the NQE job 83
- 84 Cray T3E User’s Guide 84
- 8.4 Deleting an NQE batch job 86
- 8.5 Queues 86
- 8.6 More information 87
- Programming tools 88
- 9.2 Program Browser 89
- 9.3 Debugging programs 92
- 9.3.2 Examining core files 93
- 94 Cray T3E User’s Guide 94
- 9.4.1 MPP Apprentice 95
- 9.4.2 The appview command 98
- 9.4.3 PAT 98
- 9.5.1 The VAMPIRtrace library 100
- 102
- 9.5.3 More information 103
- Miscellaneous notes 104
- 10.1.3 The CPU clock timer 105
- 10.1.4 Example of timing 106
- 108 Cray T3E User’s Guide 108
- 10.4 More information 110
- About CSC 111
- 112 Cray T3E User’s Guide 112
- Glossary 113
- 114 Cray T3E User’s Guide 114
- Appendix B. Glossary 115 115
- Metacomputer Environment 116
- Bibliography 118
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