Computer Systems: A Programmer's Perspective (3rd Edition)
3rd Edition
ISBN: 9780134092669
Author: Bryant, Randal E. Bryant, David R. O'Hallaron, David R., Randal E.; O'Hallaron, Bryant/O'hallaron
Publisher: PEARSON
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Textbook Question
Chapter 5.7, Problem 5.5PP
Practice Problem 5.5 (solution page 575)
Suppose we wish to write a function to evaluate I polynomial where a polynomial of degree n is defined to have a set of coefficients a0, a1 a2 ….an. For a value x. we evaluate the polynomial by computing
(5.2) a() + a1x + a2x2 + + anxn (5.2)
This evaluation can be implemented by the following function, having as arguments an array of coefficients a, a value x, and the polynomial degree degree (the value n in Equation 5.2). In this function, we compute both the successive terms of the equation and the successive powers of x within a single loop:
- A. For degree n, how many additions and how many multiplications does this code perform?
- B. On our reference machine, with arithmetic operations having the latencies shown in Figure 5.12, we measure the CPE for this function to be 5.00. Explain how this CPE arises based on the data dependencies formed between iterations due to the operations implementing lines 7-8 of the function.
Figure 5.12 Latency, issue time, and capacity characteristics of reference machine operations. Latency indicates the total number of clock cycles required to perform the actual operations, while issue time indicates the minimum number of cycles between two independent operations. The capacity indicates how many of these operations can be issued simultaneously. The times for division depend on the data values.
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ENGINEERING • COMPUTER-ENGINEERING
2 - calculate the first four iterations for the
approximate value of the root of the function
f(x) = x*log(x) - 1 using the method below:
a) Bissection Method. Use as interval for the
root the values [2,3].
(c) A palindromic number is a number that is the same if read forwards or
backwards: 12321 and 641146 are examples. It is possible to represent a
number using an array of digits (numbers 0- 9), for example: [1,9,5, 2] could
represent 1952.
i. Using an appropriate iteration construct, write an algorithm as a procedure
that decides if an input array A[1..n] of digits is a palindromic number.
Example 7: Code the below problem using C++
Sample Input:
1.
4
1234
Sample Output:
16
Ayush has an array a of n integers. He wants to collapse the entire array into a
single element. To do this, he can perform the operation described below any
number of times. Each operation grants some points, and Ayush's total score will
be the sum of the points granted over all operations he performs.
Let aſi..j] denote the subarray of a starting at index i and ending at j. Define
min; j to be the minimum value in a[i..j].
In one operation he can do the following:
• Select any subarray a[i. j] of a of size at least 2 and replace this subarray by
a single element equal to the sum of elements of the subarray.
The number of points granted by such an operation, which will be added to his
total score, is (j – i+1) · min;j.
For example, consider an array a = [2, 3, 5]. If he selects the subarray a[1..2],
his total score increases by 2 · 2 = 4 points. Now a = [5, 5].
Ayush performs operations until only a…
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