1 COMP 206: Computer Architecture and Implementation Montek Singh Mon., Sep 5, 2005 Lecture 2

2Outline  Quantitative Principles of Computer Design Amdahl’s law (make the common case fast) Amdahl’s law (make the common case fast)  Performance Metrics MIPS, FLOPS, and all that… MIPS, FLOPS, and all that…  Examples

3 Quantitative Principles of Computer Design Execution time Response time Latency Execution time Response time Latency Performance Rate of producing results Throughput Bandwidth Performance Rate of producing results Throughput Bandwidth

4Comparison “Y is n times larger than X” “Y is n% larger than X”

5 “Validity of the single processor approach to achieving large scale computing capabilities”, G. M. Amdahl, AFIPS Conference Proceedings, pp , April 1967 Amdahl’s Law (1967)  Historical context Amdahl was demonstrating “the continued validity of the single processor approach and of the weaknesses of the multiple processor approach” Amdahl was demonstrating “the continued validity of the single processor approach and of the weaknesses of the multiple processor approach” Paper contains no mathematical formulation, just arguments and simulation Paper contains no mathematical formulation, just arguments and simulation  “The nature of this overhead appears to be sequential so that it is unlikely to be amenable to parallel processing techniques.”  “A fairly obvious conclusion which can be drawn at this point is that the effort expended on achieving high parallel performance rates is wasted unless it is accompanied by achievements in sequential processing rates of very nearly the same magnitude.”  Nevertheless, it is of widespread applicability in all kinds of situations

6 Amdahl’s Law Fraction of results generated at this rate Average execution rate (performance) Weighted harmonic mean Note: Not “fraction of time spent working at this rate” Note: Not “fraction of time spent working at this rate” “Bottleneckology: Evaluating Supercomputers”, Jack Worlton, COMPCOM 85, pp

7 Example of Amdahl’s Law 30% of results are generated at the rate of 1 MFLOPS, 20% at 10 MFLOPS, 50% at 100 MFLOPS. What is the average performance? What is the bottleneck? 30% of results are generated at the rate of 1 MFLOPS, 20% at 10 MFLOPS, 50% at 100 MFLOPS. What is the average performance? What is the bottleneck? Bottleneck: the rate that consumes most of the time

8 Amdahl’s Law (HP3 book, pp ) Fraction enhanced Speedup enhanced Speedup overall Speedup enhanced Fraction enhanced

9 Implications of Amdahl’s Law  The performance improvements provided by a feature are limited by how often that feature is used  As stated, Amdahl’s Law is valid only if the system always works with exactly one of the rates If a non-blocking cache is used, or there is overlap between CPU and I/O operations, Amdahl’s Law as given here is not applicable If a non-blocking cache is used, or there is overlap between CPU and I/O operations, Amdahl’s Law as given here is not applicable  Bottleneck is the most promising target for improvements “Make the common case fast” “Make the common case fast” Infrequent events, even if they consume a lot of time, will make little difference to performance Infrequent events, even if they consume a lot of time, will make little difference to performance  Typical use: Change only one parameter of system, and compute effect of this change The same program, with the same input data, should run on the machine in both cases The same program, with the same input data, should run on the machine in both cases

10 “Make The Common Case Fast”  All instructions require an instruction fetch, only a fraction require a data fetch/store Optimize instruction access over data access Optimize instruction access over data access  Programs exhibit locality Spatial Locality Spatial Locality  items with addresses near one another tend to be referenced close together in time Temporal Locality Temporal Locality  recently accessed items are likely to be accessed in the near future  Access to small memories is faster Provide a storage hierarchy such that the most frequent accesses are to the smallest (closest) memories. Provide a storage hierarchy such that the most frequent accesses are to the smallest (closest) memories. Reg's Cache Memory Disk / Tape

11 “Make The Common Case Fast” (2)  What is the common case? The rate at which the system spends most of its time The rate at which the system spends most of its time The “bottleneck” The “bottleneck”  What does this statement mean precisely? Make the common case faster, rather than making some other case faster Make the common case faster, rather than making some other case faster Make the common case faster by a certain amount, rather than making some other case faster by the same amount Make the common case faster by a certain amount, rather than making some other case faster by the same amount  Absolute amount?  Relative amount?  This principle is merely an informal statement of a frequently correct consequence of Amdahl’s Law

12 “Make The Common Case Fast” (3a) A machine produces 20% and 80% of its results at the rates of 1 and 3 MFLOPS, respectively. What is more advantageous: to improve the 1 MFLOPS rate, or to improve the 3 MFLOPS rate? A machine produces 20% and 80% of its results at the rates of 1 and 3 MFLOPS, respectively. What is more advantageous: to improve the 1 MFLOPS rate, or to improve the 3 MFLOPS rate? Generalize problem: Assume rates are x and y MFLOPS At ( x,y ) = (1,3), this indicates that it is better to improve x, the 1 MFLOPS rate, which is not the common case. So, the 3 MFLOPS rate is the common case in this example.

13 “Make The Common Case Fast” (3b) Let’s say that we want to make the same relative change to one or the other rate, rather than the same absolute change. At ( x,y ) = (1,3), this indicates that it is better to improve y, the 3 MFLOPS rate, which is the common case. If there are two different execution rates, making the common case faster by the same relative amount is always more advantageous than the alternative. However, this does not necessarily hold if we make absolute changes of the same magnitude. For three or more rates, further analysis is needed.

14 Basics of Performance

15 Details of CPI

16MIPS  Machines with different instruction sets?  Programs with different instruction mixes? Dynamic frequency of instructions Dynamic frequency of instructions  Uncorrelated with performance Marketing metric Marketing metric  “Meaningless Indicator of Processor Speed”

17MFLOP/s  Popular in supercomputing community  Often not where time is spent  Not all FP operations are equal “Normalized” MFLOP/s “Normalized” MFLOP/s  Can magnify performance differences A better algorithm (e.g., with better data reuse) can run faster even with higher FLOP count A better algorithm (e.g., with better data reuse) can run faster even with higher FLOP count DGEQRF vs. DGEQR2 in LAPACK DGEQRF vs. DGEQR2 in LAPACK

18 Aspects of CPU Performance