CS352: Computer Architecture Spring 2000 Homework 1

## General Instructions

This homework covers material covered in Chapters 1, 2 and 3 of the textbook. Please present your solutions clearly. Be very precise in your answers and clearly indicate how you have derived your answers.

Homework due on: Tuesday, February 22, 2000 (in class)

## Questions

1.
Chapter 1: Exercise 1.45 from textbook. (10 points)
2.
Chapter 2:
(a)
Exercises 2.18 (10 points), 2.19 (5 points), 2.20 (10 points), 2.21 (5 points), 2.22 (5 points), 2.23 (10 points), 2.24 (10 points), 2.26 (5 points), 2.27 (5 points), 2.28 (15 points), and 2.29 (15 points) from the textbook.
(b)
In this exercise, assume that we are considering enhancing a machine by adding a vector mode to it. When a computation is run in the vector mode, it is 20 times faster than the normal mode of execution. We call the percentage of time that could be spent using vector mode the percentage of vectorization. (25 points),

• What percentage of vectorization is needed to achieve a speedup of 2 for a program?
• What percentage of vectorization is needed to achieve one-half the maximum speedup attainable from using the vector mode?
• Suppose you have measured the percentage of vectorization of programs to be 70%. The hardware design group says that they can double the speed of the vector rate with a significant additional engineering investment. You wonder whether the compiler crew could increase the use of vector mode as another approach to increasing performance. How much increase in the percentage of vectorization (relative to the current value) would you need to obtain the same performance gain as the hardware improvement? Which investment would you recommend?

3.
Chapter 3: Exercises 3.12 (5 points), 3.13 (10 points), 3.14 (10 points), 3.16 (15 points), 3.17 (20 points), and 3.18 (10 points) from the textbook.