Power Test on Resolve C++

ultrAslan · #1 29-May-2009, 23:32

Hi All,

I have an assignment due to tomorrow but I can't figure it out. Could anyone help me about that..

Method

Implementation 1 - Adding Power as a global operation

Examine the file Power_Test.cpp, which is a simple test driver for global_procedure Power specified below. (Note that, 0^0 = 1.)

CPP / C++ / C Code:

global_procedure Power (
        alters Natural_Number_1_C& n,
        preserves Integer p
    );
/*!
    requires
        p >= 0
    ensures
        n = #n ^ (p)
!*/

Write a body for the Power operation which uses the "obvious" algorithm -- repeated multiplication by the original n. This body goes into Power_Test.cpp.

Test the above implementation, revising as necessary until you're convinced that this implementation of Power works. For implementation 1, the grader will look at the source code and output of Power_Test.
Implementation 2 - Making Power an extension

Examine the file Power_1_Test.cpp, which is the same simple test driver as above but this time for Power being the extension in abstract_instance class Natural_Power, which is in the file AI/Natural/Power.h in your lab07 directory.

Write a body for the Power operation in the file CI/Natural/Power_1.h in your lab07 directory. DO NOT write the body in the test driver. Use the "obvious" algorithm (repeated multiplication). This should be very straightforward, it is almost a cut and paste from implementation 1!

Test Natural_Power_1::Power using Power_1_Test.cpp as the test driver. Revise the operation body for Power until you're convinced that it works. The grader will look at the source code of Power_1.h and the output for Power_1_Test to grade this part.
Implementation 3 - Making Power more efficient

Copy Power_1_Test.cpp to Power_2_Test.cpp, and make the new test driver use a new implementation of Power simply by replacing ALL occurrences of Power_1, in Power_2_Test.cpp, with Power_2.

Provide a new body for the Power operation in the file CI/Natural/Power_2.h in your lab07 directory. This time use the more efficient and non-obvious "fast powering" method discussed in class.

Test Natural_Power_2::Power using Power_2_Test.cpp as the test driver and revising the operation body as necessary until you're convinced that this implementation of Power also works. The grader will look at the source code of Power_2.h and the output for Power_2_Test to grade implementation 3.

That's the assignment.

Mexican Bob · #2 30-May-2009, 05:51

I don't know if this is what you're looking for, but it may help you get started:

CPP / C++ / C Code:

#include <iostream>

using namespace std;

void pow(long& number, const int exp)
{
    int result = number;
    if(exp > 0)
    {
	for(int i = 1; i < exp; i++)
	{
	    result *= number;
	}
	number = result;
    }
    else if(exp == 0)
    {
	number = 1;
    }
}

int main()
{
    cout << "Enter an integer: ";
    long number;
    cin >> number;
    cout << "Enter an exponent: ";
    int exp;
    cin >> exp;
    cout << number << " ^ " << exp << " = ";
    pow(number, exp);
    cout << number << endl;

    return 0;
}

Output:

Code:

bash-3.2$ ./pow
Enter an integer: 2
Enter an exponent: 28
2 ^ 28 = 268435456
bash-3.2$ ./pow
Enter an integer: 2
Enter an exponent: 29
2 ^ 29 = 536870912
bash-3.2$ ./pow 
Enter an integer: 2
Enter an exponent: 30
2 ^ 30 = 1073741824
bash-3.2$ ./pow
bash-3.2$ ./pow
Enter an integer: 2
Enter an exponent: 0
2 ^ 0 = 1
bash-3.2$ ./pow
Enter an integer: 3
Enter an exponent: 2
3 ^ 2 = 9
bash-3.2$ ./pow
Enter an integer: 3
Enter an exponent: 3
3 ^ 3 = 27
bash-3.2$ ./pow
Enter an integer: 3
Enter an exponent: 4
3 ^ 4 = 81
bash-3.2$ ./pow
Enter an integer: -12
Enter an exponent: 2
-12 ^ 2 = 144
bash-3.2$ ./pow
Enter an integer: -12
Enter an exponent: 3
-12 ^ 3 = -1728
bash-3.2$ ./pow
Enter an integer: 39
Enter an exponent: 4
39 ^ 4 = 2313441

It doesn't gracefully handle storage overflow, so there is still much more to do to make it "worthy."

MxB

ultrAslan · #3 30-May-2009, 08:40

What about recursion? Could you give me an example of that too?

davekw7x · #4 30-May-2009, 23:55

Quote:

Originally Posted by ultrAslan

What about recursion? Could you give me an example of that too?

CPP / C++ / C Code:

//
// An example of a recursive "fast power" function that uses
// squaring.
// 
// Reference: [url]http://www.cse.iitd.ernet.in/~suban/CSL102/lecture/node21.html[/url]
// Exercise 3.6
//
// davekw7x
//
#include <iostream>

using namespace std; 

double fast_power(double x, int n);

int main()
{
    double x, y;
    int n;

    cout << fixed;
    cout << "Enter x and n (n must be greater than or equal to zero): ";
    while ((cin >> x >> n) && (n >= 0)) {
        y = fast_power(x, n);
        cout << x << " to the power " << n << " = " << y << endl << endl;
        cout << "Enter x and n (n must be greater than or equal to zero): ";
    }
    cout << "Goodbye for now." << endl;
    return 0;
}

inline double square(double x)
{
    return x * x;
}

inline bool odd(int n)
{
    return ((n % 2) == 1);
}

//
// Fast power by squaring
//
double fast_power(double x, int n)
{
    if (n == 0) {
        return 1;
    }
    return (odd(n) ? x*square(fast_power(x, n / 2)) : square(fast_power(x, n / 2)));

}

A run:

Code:

Enter x and n (n must be greater than or equal to zero): 1.1 2
1.100000 to the power 2 = 1.210000

Enter x and n (n must be greater than or equal to zero): 2 31
2.000000 to the power 31 = 2147483648.000000

Enter x and n (n must be greater than or equal to zero): 1.99999999 31
2.000000 to the power 31 = 2147483315.140062

Enter x and n (n must be greater than or equal to zero): 0 0
0.000000 to the power 0 = 1.000000

Enter x and n (n must be greater than or equal to zero): 0 1
0.000000 to the power 1 = 0.000000

Enter x and n (n must be greater than or equal to zero): 1 0
1.000000 to the power 0 = 1.000000

Enter x and n (n must be greater than or equal to zero): Hasta la vista, Baby!
Goodbye for now.

Regards,

Dave

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Power Test on Resolve C++

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