The following C function evaluates the polynomial of degree n at point x P(x) = ao a1 x + a2 x² + …+ an x" double directPoly(double a[], double x, long n) long i; double result a[0]; double xPower = x; %3D for (i { result += a[i]*xPower; = 1; i <= n; i++) xPower *= x; return result; 1. For a given degree n, what is the number of multiplications needed to evaluate the polynomial at a point x? 2. Write a C program that calls the above function, and use the vector "a[i] P(x) at x = 0.6 for n ranging from 1 to 1000. 3. Time the execution of the function directPoly as number of clock cycles using the clock() function for each value of n, and plot the execution times as function of n. Put the resulting plot in the form RunTime = C n + K? What are the values of Cand K? 4. Use k x 1 and k x k loop unrolling with k = 2, 4, within directPoly and plot the execution times as function of n. Put them in the form Cn + K. Compare with the plot obtained in the previous question. What can we conclude from the comparisons? = i" to evaluate
The following C function evaluates the polynomial of degree n at point x P(x) = ao a1 x + a2 x² + …+ an x" double directPoly(double a[], double x, long n) long i; double result a[0]; double xPower = x; %3D for (i { result += a[i]*xPower; = 1; i <= n; i++) xPower *= x; return result; 1. For a given degree n, what is the number of multiplications needed to evaluate the polynomial at a point x? 2. Write a C program that calls the above function, and use the vector "a[i] P(x) at x = 0.6 for n ranging from 1 to 1000. 3. Time the execution of the function directPoly as number of clock cycles using the clock() function for each value of n, and plot the execution times as function of n. Put the resulting plot in the form RunTime = C n + K? What are the values of Cand K? 4. Use k x 1 and k x k loop unrolling with k = 2, 4, within directPoly and plot the execution times as function of n. Put them in the form Cn + K. Compare with the plot obtained in the previous question. What can we conclude from the comparisons? = i" to evaluate
Computer Networking: A Top-Down Approach (7th Edition)
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please help me its c
![The following C function evaluates the polynomial of degreen at point x
P(x) = ao + a1 x + a2 x² + ……+ an x"
double directPoly(double a[], double x, long n)
{
long i;
double result =
a[0];
double xPower = x;
for (i
{
result += a[i]*xPower;
1; i <= n; i++)
ХРower *3 X;
return result;
1. For a given degree n, what is the number of multiplications needed to evaluate the polynomial
at a point x?
2. Write a C program that calls the above function, and use the vector "a[i]
P(x) at x = 0.6 for n ranging from 1 to 1000.
3. Time the execution of the function directPoly as number of clock cycles using the clock()
function for each value of n, and plot the execution times as function of n. Put the resulting plot
in the form RunTime = Cn + K? What are the values of C and K?
4. Use k x 1 and k x k loop unrolling with k = 2, 4, within directPoly and plot the execution times as
function of n. Put them in the form Cn+ K. Compare with the plot obtained in the previous
question. What can we conclude from the comparisons?
= i" to evaluate](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd44fa7f7-aa0f-4d28-9368-561deeaf6767%2F64fbea95-7caf-4d59-a320-4f20a0058af1%2F2l83oad_processed.png&w=3840&q=75)
Transcribed Image Text:The following C function evaluates the polynomial of degreen at point x
P(x) = ao + a1 x + a2 x² + ……+ an x"
double directPoly(double a[], double x, long n)
{
long i;
double result =
a[0];
double xPower = x;
for (i
{
result += a[i]*xPower;
1; i <= n; i++)
ХРower *3 X;
return result;
1. For a given degree n, what is the number of multiplications needed to evaluate the polynomial
at a point x?
2. Write a C program that calls the above function, and use the vector "a[i]
P(x) at x = 0.6 for n ranging from 1 to 1000.
3. Time the execution of the function directPoly as number of clock cycles using the clock()
function for each value of n, and plot the execution times as function of n. Put the resulting plot
in the form RunTime = Cn + K? What are the values of C and K?
4. Use k x 1 and k x k loop unrolling with k = 2, 4, within directPoly and plot the execution times as
function of n. Put them in the form Cn+ K. Compare with the plot obtained in the previous
question. What can we conclude from the comparisons?
= i" to evaluate
![Another C function that evaluate the polynomial of degreen at point x
P(x) = ao + a, x + a2 x? +
... + an x't
is given below and is based on the observation that
Р(x) — ао + х (а1 + x (аz +....+ x(аn-1+ an х) ...))
This polynomial evaluation method is known as the Horner method.
double HornerPoly(double a[], double x, long n)
{
long i;
double result = a[n];
for (i = n
1; і >-
0; i--)
result =
a[i] + result*x;
return result;
1. Repeat Questions 1 through 4 of Problem 4 for the HornerPoly function.
2. Compare the runtime performances of directPoly and HornerPoly for both the original loop
versions and the loop unrolling versions. What can we conclude from this comparsion.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd44fa7f7-aa0f-4d28-9368-561deeaf6767%2F64fbea95-7caf-4d59-a320-4f20a0058af1%2Fc17n4uj_processed.png&w=3840&q=75)
Transcribed Image Text:Another C function that evaluate the polynomial of degreen at point x
P(x) = ao + a, x + a2 x? +
... + an x't
is given below and is based on the observation that
Р(x) — ао + х (а1 + x (аz +....+ x(аn-1+ an х) ...))
This polynomial evaluation method is known as the Horner method.
double HornerPoly(double a[], double x, long n)
{
long i;
double result = a[n];
for (i = n
1; і >-
0; i--)
result =
a[i] + result*x;
return result;
1. Repeat Questions 1 through 4 of Problem 4 for the HornerPoly function.
2. Compare the runtime performances of directPoly and HornerPoly for both the original loop
versions and the loop unrolling versions. What can we conclude from this comparsion.
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