Practice Problem 5.6 (solution page 575)
Let us continue exploring ways to evaluate polynomials, as described in Practice Problem 5 5. We can reduce the number of multiplications in evaluating a polynomial by applying Horner’s method, named after British mathematician William G. Horner (1786-1837). The idea is to repeatedly factor out the powers of x to get the following evaluation:
a0+x(a1+x(a2+···x(an-1+xan)···)) (5.3)
Using Horner's method, we can implement polynomial evaluation using the following code:
- A. For degree n, how many additions and how many multiplications does this code perform?
- B. On our reference machine, with the arithmetic operations having the latencies shown in Figure 5.12, we measure the CPE for this function to be 8.00. Explain how this CPE arises based on the data dependencies formed between iterations due to the operations implementing line 7 of the function.
- C. Explain how the function shown in Practice Problem 5.5 can run faster, even though it requires more operations.
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
EBK COMPUTER SYSTEMS
Additional Engineering Textbook Solutions
C Programming Language
Starting Out With Visual Basic (7th Edition)
Starting Out with Java: From Control Structures through Data Structures (4th Edition) (What's New in Computer Science)
Java How To Program (Early Objects)
Objects First with Java: A Practical Introduction Using BlueJ (6th Edition)
C++ How to Program (10th Edition)
- Computer Networking: A Top-Down Approach (7th Edi...Computer EngineeringISBN:9780133594140Author:James Kurose, Keith RossPublisher:PEARSONComputer Organization and Design MIPS Edition, Fi...Computer EngineeringISBN:9780124077263Author:David A. Patterson, John L. HennessyPublisher:Elsevier ScienceNetwork+ Guide to Networks (MindTap Course List)Computer EngineeringISBN:9781337569330Author:Jill West, Tamara Dean, Jean AndrewsPublisher:Cengage Learning
- Concepts of Database ManagementComputer EngineeringISBN:9781337093422Author:Joy L. Starks, Philip J. Pratt, Mary Z. LastPublisher:Cengage LearningPrelude to ProgrammingComputer EngineeringISBN:9780133750423Author:VENIT, StewartPublisher:Pearson EducationSc Business Data Communications and Networking, T...Computer EngineeringISBN:9781119368830Author:FITZGERALDPublisher:WILEY