CodeMocha » Code

Bit Operations

Chet — Sat, 04 Jul 2009 18:31:41 +0000

For CS351, Intro to Systems, we had to do several operations using bit operators only. These took awhile, but are pretty cool to show off. We were graded by how few operations we used to return the right values for the generated test cases, including some difficult boundary ones.

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//NOR operation using only ~ and &

int bitNor(int x, int y) {

    return (~x)&(~y);

}

The XOR operation is equivalent to the (x NAND y) AND (x OR y).

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//XOR operation using only ~ and &

int bitXor(int x, int y) {

    return (~(x&y))&(~((~x)&(~y)));

}

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//Return true if x is not equal to y not using comparison operators.

int isNotEqual(int x, int y) {

    return !!(x^y);

}

There are two types of shifts, arithmetic and logical. Left shifts are the same in both types, but right shifts are different. Logical shifts insert zeroes to fill in the empty spaces to keep the logic of the bits, but arithmetic shifts fill in the value of the sign bit to preserve the sign of the operand in twos-complement integers.

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int rightLogicalShift(int x, int n) {

    int allOnes = ~0;

    int y = ~((allOnes) << (32 + (~n + 1)));

    return ((x >> n) & y);

}

Euclidean Algorithm

Chet — Sat, 04 Jul 2009 03:46:41 +0000

One of my favorite algorithms is the simple, elegant Euclidean algorithm for finding the greatest common denominator of two numbers. In ML or another functional language it really is beautiful:

1 2	fun gcd(a, 0) = a \| gcd(a, b) = gcd(b, a mod b);

Of course, the same can be done in Java iteratively:

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public int gcd(int a, int b){

    int c;

    while (b>0){

        c = a;

        a = b;

        b = c%b;

    }

    return a;

}

Or recursively:

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public int gcd(int a, int b){

    if(b==0){

        return a;

    }else{

        return gcd(b, a%b);

    }

}

Recursive Fibonacci

Chet — Sat, 04 Jul 2009 03:40:28 +0000

Here are two recursive fibonacci functions in ML I did for CS243. Can you tell which one is more efficient?

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fun fibonacci(n) = 

  let

      fun fib((a, b), i)=  

    if i=0 then b

        else fib((b, a + b), i-1);

           in

  fib((0, 1), n)

  end;

fun fibonacci(0) = 1

  | fibonacci(1) = 1

  | fibonacci(n) = fibonacci(n-1) + fibonacci(n-2);

Circle Calculator

Chet — Sat, 04 Jul 2009 03:26:57 +0000

For my first code post I thought it might be appropriate to put the first code from the first lab of my first computer science class at Wheaton.

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import java.util.Scanner;

public class Circle {

     public static void main(String[] args) {

        Scanner keyboard = new Scanner(System.in);  // input from keyboard

        System.out.print("Please enter the radius-->");

        double radius = keyboard.nextDouble();   // radius to work with

        double diameter = radius*2;

        System.out.println("The diameter is " + diameter);

        double circumference = Math.PI*2*radius;

        System.out.println("The circumference is " + circumference);

        double area = Math.PI * Math.pow(radius, 2);

        System.out.println("The area is " + area);

        double volume = (4.0 / 3.0) * Math.PI * Math.pow(radius, 3);

        System.out.println("The volume of a sphere is " + volume);

        double surfaceArea = Math.PI * 4 *  Math.pow(radius, 2);

        System.out.println("The surface area of a sphere is " + surfaceArea);

     }

}