3rd Edition

ISBN: 8220101459107

Author: O'HALLARON

Publisher: YUZU

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Chapter 5.7, Problem 5.6PP

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(a_n-₁+xa_n)···)) (5.3)

Chapter 5.7, Problem 5.6PP, Practice Problem 5.6 (solution page 575) Let us continue exploring ways to evaluate polynomials, as

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.

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Chapter 5.7, Problem 5.5PP

Chapter 5.8, Problem 5.7PP

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Chapter 5 Solutions

EBK COMPUTER SYSTEMS

Ch. 5.1 - Prob. 5.1PP Ch. 5.2 - Prob. 5.2PP Ch. 5.4 - Prob. 5.3PP Ch. 5.6 - Prob. 5.4PP Ch. 5.7 - Practice Problem 5.5 (solution page 575) Suppose...Ch. 5.7 - Practice Problem 5.6 (solution page 575) Let us...Ch. 5.8 - Prob. 5.7PP Ch. 5.9 - Prob. 5.8PP Ch. 5.11 - Prob. 5.9PP Ch. 5.12 - Prob. 5.10PP

Ch. 5.12 - Prob. 5.11PP Ch. 5.12 - Prob. 5.12PP Ch. 5 - Prob. 5.13HW Ch. 5 - Write a version of the inner product procedure...Ch. 5 - Write a version of the inner product procedure...Ch. 5 - Prob. 5.16HW Ch. 5 - Prob. 5.17HW Ch. 5 - Prob. 5.18HW Ch. 5 - Prob. 5.19HW

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