2 Question 1 – 4.7Suppose you wish to run a program P with 7.5 * 109 instructions on a 5GHz machine with a CPI of 0.8.What is the expected CPU time?When you run P, it takes 3 seconds of wall clock time to complete. What is the percentage of the CPU time P received?
3 Question 1 The expected CPU time CPU Time = IC * CPI * Clock cycle time= 7.5 * 109 * 0.8 * 1/5*109= 1.2secondsThe percentage of the CPU time P1.2seconds/3 seconds = 40%
4 Question 2 – 4.11Consider program P, which runs on a 1 GHz machine M in 10 seconds. An optimization is made to P, replacing all instances of multiplying a value by 4 (mult X,X,4) with two instructions that set x to x + x twice(add X,X;add X,X). Call this new optimized program P’. The CPI of a multiply instruction is 4, and the CPI of an add is 1. After recompiling, the program now runs in 9 seconds on machine M. How many multiplies were replaced by the new compiler?
5 Question 2The number of multiplies that were replaced the by new compilerLet Number of multiplies replaced in new compiler = XNumber of cycles executed in the old compiler = 4XNumber of cycles executed in new compiler = 2XTotal number of cycles difference 4X-2X = 2XTotal number of cycles difference between P and P’ = 1010 – 9*109 = 1092X = 109 => X = 5* 108
6 Question 3 – 4.45Assume that multiply instructions take 12 cycles and account for 15% of the instructions in a typical program, an the other 85% of the instructions require an average of 4 cycles for each instruction. What percentage of time does the CPU spend doing multiplication?
7 Question 3 CPU Time for multiply instructions CPU Time = IC * CPI * Clock cycle time= IC*0.15 * 12 * CC= 1.8*IC*CCCPU Time for all instructions= (IC*0.15*12 + IC*0.85*4)*CC= 5.2*IC*CCPercentage of time CPU spend doing multiplication1.8*IC*CC/5.2*IC*CC = 34.6%
8 Question 4 – 4.46Your hardware engineering team has indicated that it would be possible to reduce the number of cycles required for multiplication to 8 in Exercise 4.45, but this will require a 20% increase in the cycle time. Nothing else will be affected by the change. Should they proceed with the modification?
9 Question 4 CPU Time for original hardware CPU Time = IC * CPI * Clock cycle time= (IC*0.15*12 + IC*0.85*4)*CC= 5.2*IC*CCCPU Time for new hardware= (IC*0.15*8 + IC*0.85*4)*1.2CC= 5.52*IC*CCComparing original and new hardwarePerformancenew/Performanceorg = 5.2*IC*CC/5.52*IC*CC= 0.942Modification should not be made because it reduces performance