import java.util.Random;
/**
 * Class that contains static methods and constants to exercise Java
 * number types and functions from the Math class.
 * 
 * @author Scott Russell
 * @version 9/25/2007
 */
public class Newton
{
    //the number of bits per byte
    public static final short BITS_PER_BYTE = 8;
    
    public static final double EARTH_GRAVITY = 9.8;
    /**
     * A method to compute the logarithm base 2 of the specified number. 
     * @param value a float to compute the log of
     * @return the log base 2 as a float
     */
    public static double log2(double value)
    {
        return Math.log(value)/Math.log(2);
    }
    
    /**
     * Calculates the time needed to travel a given distance in meeters at a constant
     * rate of acceleration in meters/second squared from an initial velocity in meters/second.
     * @param accel
     * @param initVelocity
     * @param distance
     * @return time in seconds
     */
    public static double travelTime(double accel, double initVelocity, double distance)
    {
        //equation we are applying quadratic formula to is accel*time^2+initVelocity*time-distance
        double root = Math.sqrt(initVelocity*initVelocity + 4*accel*distance);
        return (-initVelocity + root)/(2*accel);
    }
    /**
     * Calculates the distance traveled at a constant acceleration.
     * @param accel the constant rate of acceleration in meters/second squared
     * @param velocity the initial velocity in meters/second
     * @param time the time in seconds
     */
    public static double distanceTraveled(double accel, double initVelocity, double time)
    {
        return (accel*time+initVelocity)*time;   
    }
    
    public static int base2To10(String binaryNumber)
    {
        //variable to store the partial result as we compute it
        int result = 0;
        
        //variable to store the exponent used to compute the magnitude of each digit
        int exponent = 0;
        
        // variable to store the magnitude of each digit
        int magnitude =0;
        
        // variable to hold a single digit of the given binary number 
        int digit = 0;
        
        
        //read the binaray number from left to right
        for (int pos = 0; pos < binaryNumber.length(); pos++)
        {
            //for each digit get the digit at the specified position and convert to an integer
            digit=Integer.parseInt(binaryNumber.substring(pos,pos+1));
            
            //compute the value of the exponent based on the digit's position
            exponent = binaryNumber.length() - 1 - pos;
            
            //compute the magnitude as a power of 2 to the computed exponent
            magnitude = (int) Math.pow(2,exponent);
            
            //add this digits contribution to the running total
            result = result + digit*magnitude;
        }
        
        //return the final total result
        return result;
    }
    //the method that will test our work
    public static void main(String[] args)
    {
     System.out.println("The largest and smallest numbers in the int class are " +
        Integer.MAX_VALUE + " and " + Integer.MIN_VALUE +".");
     
     long intValues = (long) Integer.MAX_VALUE - (long) Integer.MIN_VALUE + 1;
     
     System.out.println("This means there are " + 
        intValues + " different values");

     short bitsStored =  (short) log2(intValues);
     System.out.println("The int class uses " + bitsStored + " bits or " + bitsStored/BITS_PER_BYTE +
        " bytes to store each value.");
    
    //test the method with a fixed value    
    String testSequence = "10011";
    System.out.println("Binary string " + testSequence + " is " + base2To10(testSequence) +"?");
    
    //generate a random binary string to test with
    //a constant in the method to determine how long to make the string
    final int NUM_DIGITS=8;
    
    //create random number generator
    Random randNumGen = new Random();
    
    String randSequence = new String();
    
    //generate some random digits
    for (int pos=0; pos < NUM_DIGITS; pos++)
    {
        randSequence = randSequence + String.valueOf(randNumGen.nextInt(2));
    }

    //test the method on the random sequence
    System.out.println("Binary string " + randSequence + " is " + base2To10(randSequence) +"?");
}

}