Amdahl's Law. Execution time new = ((1 f) + f/s) Execution time. S. Then:
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1 Amdahl's Law Useful for evaluating the impact of a change. (A general observation.) Insight: Improving a feature cannot improve performance beyond the use of the feature Suppose we introduce a particular enhancement that improves fraction f of execution time by factor S. Then: Execution time new = ((1 f) + f/s) Execution time
2 Example Task: complete EE/CS 314 project Walk to lab: 15 minutes Work in lab: 600 minutes Food: 45 minutes Walk home: 10 minutes Total time = 670 minutes. Skip meals! And sleep in the lab! :-) 10.4% improvement Observation: doesn't help with the time spent working.
3 Other Performance Metrics Commonly used: MIPS (Millions of instructions per second) MIPS = Instruction count Execution time 10 6 Problems with MIPS as a metric: Instructions with different capabilities? Programs with different instruction mixes? Might not predict which machine is faster!
4 MIPS As A Performance Metric Consider an optimized and unoptimized version of a program: Memory ALU Branch Total Instrs. Instrs. Instrs. Instrs. Unopt 200 M 150 M 50 M 400 M Optimized 100 M 100 M 50 M 250 M Memory ALU Branch CPI cycles (2x) cycles (1x) cycles (3x) Unopt 400 M 150 M 150 M 1.75 Optimized 200 M 100 M 150 M 1.8
5 MIPS As A Performance Metric Assume a 750MHz Clock: MIPS (Unopt): 750/1.75 = MIPS (opt): 750/1.8 = Execution time: Unopt: CP I IC 1/CR = /750 = 0.93 secs Opt: CP I IC 1/CR = /750 = 0.6 secs MIPS doesn't predict which program is faster! (why?)
6 What Is "Typical"? Source of serious debate Instruction mix can signi cantly impact performance Benchmarks for performance Started with simple toy programs (quicksort, sieve, etc) Moved to synthetic benchmarks (dhrystone, whetstone) Kernels (time critical parts of real programs) Today: SPEC (collection of standard programs)
7 Summarizing Performance Given the execution time of a number of programs, can we come up with one gure of merit? Arithmetic mean: Average time = 1 n n i=1 Execution time i Assumes each benchmark is equally important; long-running benchmarks dominate. If we know workload, we can weight execution times: Weighted average time = n i=1 W i Execution time i n i=1 W i
8 Normalized Performance Pick weights to be 1/(time on a reference machine) What if we attempt a summary using normalized performance? Consider two machines A and B: P1 P2 Relative to A Relative to B secs secs P1 P2 AM P1 P2 AM A B Total execution time on A: 60 secs Total execution time on B: 101 secs If equal runs of programs P1 and P2, A is 1.7 times faster than B.
9 Geometric Mean Can be used to combine relative measures. Geometric Mean = n n R i i=1 P1 P2 Relative to A Relative to B secs secs P1 P2 GM P1 P2 GM A B Some unfortunate properties: does not track execution time! all improvements are equal
10 Harmonic Mean Used to average rates like MIPS or MFLOPS. Harmonic Mean = n n i=1 (1/R i ) Another way to look at it: 1 Harmonic Mean = n i=1 (1/R i ) n i.e. convert rate to time/task, average, convert back to rate. Also can be weighted like arithmetic mean.
11 Performance Estimation Time is the measure of performance! Recall how we derived the CPU performance equation. Typically, tradeoff between performance and cost. cost: parts, labor for assembly, etc. New metric: power. portable devices want to extend battery life
12 Power Where does power dissipation come from? Underlying implementation: transistor networks We can approximate these as RC circuits Power dissipated: CV 2, C capacitance, V voltage. (Resistors are dissipative) Power dissipated when the voltage on a wire changes. (Quick recap: I = V R e t/rc, E = CV 2 ) time 1/V, energy V 2 power V 3
13 Power Total power: Alpha 21164: 50W Alpha 21264: 72W 550 MHz Pentium III: 30.8W 300 MHz Mobile Pentium II: 9W 160 MHz StrongARM: 0.5W Sources of power consumption: Inputs to combinational logic, Šip-Šops Signals within combinational logic Clock keeps changing!
14 Power Minimize power consumption: Avoid spurious changes of signal values Turn off clock when part of the circuit not in use clock gating Modes of operation: turn off large parts of the chip Slow down clock in idle mode Reduce voltage in idle mode Only activate part of circuit used for computation? Eliminate clocks?
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