Zack Lane ReCAP Coordinator July 31, 2012 ReCAP Columbia University.
Recap
description
Transcript of Recap
1
RecapRecap
2
Amdahl’s Law• Performance impact of optimizing part of a program:
• Let an optimization speedup f fraction of time by a factor of s:
– New Time = OldTime x [(1-f) x 1 + f x (1/s)]
– Speedup =
• s > 1.0 for speedup, f <= 1.0 as it is a fraction
NewTime
OldTimeSpeedup
sf
fsf
fOldTime
OldTime
1
1
])1[(
3
Amdahl’s Law
Old Time New Time
= s
4
Example 1
Which change is more effective on a certain Processor: speeding up 10-fold the floating point square root operation only, which takes up 20% of execution time, or speeding up 2-fold all floating point operations, which take up 50% of total execution time? (Assume that the cost of accomplishing either change is the same, and thetwo changes are mutually exclusive.)
Which change is more effective on a certain Processor: speeding up 10-fold the floating point square root operation only, which takes up 20% of execution time, or speeding up 2-fold all floating point operations, which take up 50% of total execution time? (Assume that the cost of accomplishing either change is the same, and thetwo changes are mutually exclusive.)
SPEEDUPSQ = 1/((1-0.2) + (0.2/10)) = 1.22, or 22%
SPEEDUPFP = 1/((1-0.5) + (0.5/2)) = 1.33, or 33%
5
Example
SPEEDUPSQ = 1/((1-0.2) + (0.2/10)) = 1.22, or 22%
SPEEDUPFP = 1/((1-0.5) + (0.5/2)) = 1.33, or 33%
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Sqrt (b) Sqrt (a) FP (b) FP (a)
6
Amdahl’s Law
Law of Diminishing Returns: The Performance Enhancement Possible Is Limited By the Amount That the Improved Feature Is Used.
7
Example
• A server spends 50% of CPU time on I/O and 50% on computation. What is the speedup if we replace the CPU with one that is 8 times faster?
enhancementspeedup overall
enhancement
enhancement
enhanc sement peedup overall
2n1n
0.5 n 11 0.5n
n 8 n 1.77
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
1 3 5 7 9 11 13 15 17 19 21 23 25 27
Enhancement Factor
Sp
eed
up
8
• Suppose a program takes 1 unit of time to execute serially
• A fraction of the program, s, is inherently serial (unparallelizable)
• For example, consider a program that, when executing on one core processor, spends 20% of its time in a non-parallelizable region. How much faster will this program run on a 4-processor system?
• What is the maximum speedup from parallelization? 5
Multi-Core (parallelism) and Amdah’s law
New Execution Time
=1-s
+ sP
New Execution Time =.8T
+ .2T = 0.4T4
Speedup =1T/0.4T = 2.5