CPSC 330 - Spring 2008 Homework 6 Due on Friday, April 25 [Revised 4/22 with added examples] Example: Consider enhancing a scalar machine by providing a vector mode, which is 4 times faster than the normal mode of operation. (a) If the percentage of vectorization is 25%, what is the overall speedup? 1 1 1 speedup = ----------------- = ---------- = ----- = 16/13 = 1.23 (1-1/4) + (1/4)/4 3/4 + 1/16 13/16 (b) What percent of vectorization is needed to achieve an overall speedup of 2? 1 2 = ------------- => (1-f) + (f/4) = 1/2 (1-f) + (f/4) => 4-4f+f = 2 => -3f = -2 => f = 2/3 so % vectorization needed is 67% 1. Consider an enhancement to a computer system that provides an eight times speedup when in use. What is the overall speedup if the enhancement can only be used for one half of a program's normal execution time? Show the result as a fraction. 2. What fraction of normal execution time must the 8x enhancement be used to achieve an overall speedup of 4? Show the result as a fraction. Example: Consider a program that executes 100 million instructions in 5 seconds. What is the MIPS rating for this program? 100*10^6 insts MIPS = -------------- = 20 MIPS 5 secs * 10^6 Consider a processor with a CPI value of 10 cycles/inst. and a clock frequency of 200 MHz. What is the MIPS rating for this processor? 200 M cycles/sec MIPS = --------------------- = 20 MIPS 10 cycles/inst * 10^6 3. A program executes 10 billion instructions on a processor with an avg. CPI of 2.0 and a clock frequency of 4 GHz. What is the MIPS value? a) show the calculation by first determining exection time, then dividing number of instructions by execution time b) show the calculation by the MIPS formula that does not include the instruction count.