1. Recap

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

3. Amdahl’s Law
Old Time
New Time
= s

4. Improving all FP operations
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 the
two 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%
Note that there are three categories of operations here: floating point square root operations, other floating point operations, and non-FP operations. When we change one of these categories, we group the other two categories as the “other case”.
Improving all FP operations
is more effective

5. Improving all FP operations
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%
Note that there are three categories of operations here: floating point square root operations, other floating point operations, and non-FP operations. When we change one of these categories, we group the other two categories as the “other case”.
Improving all FP operations
is more effective

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?

8. Multi-Core (parallelism) and Amdah’s law
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
New Execution Time =
1-s + s P
New Execution Time =
.8T +
.2T
0.4T 4
Speedup =1T/0.4T = 2.5