Homework 8 Solutions - Computer Architecture and Design | ELEC 5200, Assignments of Computer Architecture and Organization

Download Homework 8 Solutions - Computer Architecture and Design | ELEC 5200 and more Assignments Computer Architecture and Organization in PDF only on Docsity! ELEC 5200-001/6200-001 Computer Architecture and Design Fall 2008 Homework 8 Solution Assigned 11/21/08, due 12/1/08 Problem 1: The SPEC ratio of a target computer for a SPEC benchmark program is the performance of the target computer divided by the performance of Sun Ultra 5_10 processor running at 300MHz; performance is defined as the reciprocal of the run time. Suppose a low voltage cool-core processor has following run times for the SPECINT2000 benchmarks: No. Program Function CPU s Cool-core Sun Ultra 5_10 1 gzip Data compression 20 1400 2 vpr FPGA place and route 40 1400 3 gcc Gnu C compiler 22 1100 4 mcf Combinatorial optimization 18 1800 5 crafty Chess player 10 1000 6 parser Word processor 12 1800 7 eon Computer visualization 26 1300 8 perlbmk Perl application 18 1800 9 gap Group theory 22 1100 10 vortex Object-oriented database 38 1900 11 bzip2 Data compression 10 1500 12 twolf VLSI place and route 60 3000 Compute the summary SPECINT2000 performance rating for the cool-core processor. Solution: Following table shows the SPEC ratios for 12 programs: No. Program Function Run time CPU s SPEC ratio Cool-core Sun Ultra 5_10 1 gzip Data compression 20 1400 70 2 vpr FPGA place and route 40 1400 35 3 gcc Gnu C compiler 22 1100 50 4 mcf Combinatorial optimization 18 1800 100 5 crafty Chess player 10 1000 100 6 parser Word processor 12 1800 150 7 eon Computer visualization 26 1300 50 8 perlbmk Perl application 18 1800 100 9 gap Group theory 22 1100 50 10 vortex Object-oriented database 38 1900 50 11 bzip2 Data compression 10 1500 150 12 twolf VLSI place and route 60 3000 50 Taking the geometric mean of 12 SPEC ratios, we get a SPECINT2000 rating of 71.5. Problem 2: Following run times are recorded for two programs when run on Computers A and B: Computing system Run time (seconds) Program 1 Program 2 Computer A 1.0 100.0 Computer B 4.0 20.0 Evaluate the performance using arithmetic mean and geometric mean formulas for: (a) Computer A, normalized with respect to Computer B, and (b) Computer B, normalized with respect to Computer A. Which formula gives consistent result if we were to select the higher performance computer? Solution: System and reference Performance ratio Mean performance Program 1 Program 2 Arithmetic mean Geometric mean (a) Computer A, w.r.t. B 4.0 0.2 2.100 0.894 (b) Computer B, w.r.t. A 0.25 5.0 2.625 1.118 Using the arithmetic mean, we cannot determine which computer is faster. Each looks faster than the other. However, the geometric mean consistently shows computer B with higher performance. Problem 3: Consider a parallel processing scenario where a computing task of duration T is divided into n equal parts and all parts are executed simultaneously on n similar performance processors. However, now each processor has to communicate with n – 1 processors and that adds a communication overhead fraction β(n – 1) to its processing time. Show that such parallel processing corresponds to Amdahl’s law in which the fraction that cannot be speeded up is βn. Further show that for very small values of the inter-processor communication factor β, the maximum speedup ≈ n/2. What is the maximum speedup for β = 0.01? Solution: For parallel processing, we obtain T 1 Speedup =  =  (1) (T/n) + Tβ(n – 1) (1/n) + β(n – 1)