Re: My prime counting function

From:
rossum <rossum48@coldmail.com>
Newsgroups:
comp.lang.java.programmer
Date:
Mon, 04 Aug 2008 20:29:38 +0100
Message-ID:
<d5le9450h0j2fduo4lllgbrd3b9kaddl7j@4ax.com>
On Sun, 3 Aug 2008 21:43:24 -0700 (PDT), Andrew Thompson
<andrewthommo@gmail.com> wrote:

No, it's just I don't care, not until you post an
SSCCE (written in Java, to bring this rot 'on-topic').

I am not James, but I did write a prime counting program based on his
ideas. Not quite an SSCCE as it uses a couple of functions from my
own maths library.

rossum

//----- Start Code ------

import mjrutilities.Maths;
// This provides two/three functions:
// long iSqrt(long num)
// int iSqrt(int num)
// which both return the int (long) square root of
// the given number.
// and
// int nthPrime(int n)
// which returns the nth prime number.

import java.util.HashMap;
import java.util.Map;

/**
 * <p>Title: PrimeCount</p>
 *
 * <p>Description: gives an exact count of the primes less than or
equal to a given number:<br>
 *
 * pi(1) = 0<br>
 * pi(2) = 1<br>
 * pi(10 = 4<br>
 * pi(100) = 25<br>
 * pi(1000) = 168</p>
 *
 * Comments from original version:
 *
 * -----------------------------------------
 *
 * Written by James S. Harris. Copyright (c) 2002-2003. All rights
reserved.
 *
 * My suggestion is to write your own version modifying this one.
 * Commercial use is not permitted without my written permission.
 *
 * Proper attribution might get me some credit for having found the
prime counting function
 * So play with this and share, and *please* mention where you got
it from.
 *
 * -----------------------------------------
 *
 * @author Martin Ross, based on JSH
 * @version 1.0
 * @date August 2007
 */
public class PrimeCount {
    private PrimeCount() { }

    /**
     * Calculates pi(limit) [the number of primes up to limit] for
     * a long value of limit.
     *
     * @param limit how far to count primes.
     * @return the number of primes up to limit.
     */
    public static long pi(long limit) {
        long retVal = 0L;
        if (limit < Integer.MAX_VALUE) {
            retVal = pi((int)limit);
        } else {
            // Have to do it the hard way
            if (limit % 2 == 1) { ++limit; } // Evens only
            long limRoot = Maths.iSqrt(limit);
            long level = Math.min(limRoot, pi(limRoot));
            retVal = P(limit, level);
        } // end if
        return retVal;
    } // end pi(long)

    /**
     * Calculates pi(limit) [the number of primes up to limit] for
     * an int value of limit.
     *
     * @param limit how far to count primes.
     * @return the number of primes up to limit.
     */
    public static int pi(int limit) {
        if (limit < 2) { return 0; }
        if (limit == 2) { return 1; }

        // Use even limit - halves data storage.
        if (limit % 2 == 1) { ++limit; }
        int retVal = 0;
        if (limit < 17) {
            switch (limit) {
                case 4:
                    retVal = 2;
                    break;
                case 6:
                    retVal = 3;
                    break;
                case 8: case 10:
                    retVal = 4;
                    break;
                case 12:
                    retVal = 5;
                    break;
                case 14: case 16:
                    retVal = 6;
                    break;
                default:
                    throw new IllegalStateException("PrimeCount.pi
invalid internal value of limit parameter.");
            } // end switch
        } else if (limit < KNOWN_SIZE &&
knownCounts.containsKey(limit)) {
            // We have seen this number before
            retVal = knownCounts.get(limit);
        } else {
            // Have to do it the hard way
            if (limit % 2 == 1) { ++limit; }
            int limRoot = Maths.iSqrt(limit);
            int level = Math.min(limRoot, pi(limRoot));
            retVal = P(limit, level);

            if (limit < KNOWN_SIZE) { knownCounts.put(limit, retVal);
}
        } // end if
        return retVal;
    } // end pi(int)

    /**
     * this is the inner recursive function - int version.
     */
    private static int P(int x, int n) {
        // Adjust n
        if (needToCheck(x, n)) {
            n = Math.min(n, pi(Maths.iSqrt(x)));
        } // end if

        // P(x, n) = x - 1 - sum for i=1 to n of {P([x/p_i],i-1) -
        // (i-1)}
        // I have adjusted for j = 0 to n-1. MJR
        int sum = 0;
        for (int j = 0; j < n; ++j) {
            sum += P(x / Maths.nthPrime(j + 1), j) - j;
        } // end for

        return x - 1 - sum;
    } // end P(int, int)

    /**
     * this is the inner recursive function - long version.
     */
    private static long P(long x, long n) {
        if (x < Integer.MAX_VALUE && n < Integer.MAX_VALUE) {
            return P((int)x, (int)n);
        } // end if

        // Adjust n
        if (needToCheck(x, n)) {
            n = Math.min(n, pi(Maths.iSqrt(x)));
        } // end if

        // P(x, n) = x - 1 - sum for i=1 to n of {P([x/p_i],i-1) -
        // (i-1)}
        // I have adjusted for j = 0 to n-1. MJR
        long sum = 0;
        if (n > Integer.MAX_VALUE) {
            throw new IndexOutOfBoundsException("PrimeCount.P n too
large for integer counter.");
        } // end if
        for (int j = 0; j < n; ++j) {
            sum += P(x / Maths.nthPrime(j + 1), j) - j;
        } // end for

        return x - 1 - sum;
    } // end P(long, long)

    /**
     * Determines if we need to compare n and pi(iSqrt(x))
     * May avoid some additional recursion.
     */
    private static boolean needToCheck(long x, long n) {
        switch ((int)n) {
            case 8: return x <= 361;
            case 7: return x <= 289;
            case 6: return x <= 169;
            case 5: return x <= 121;
            case 4: return x <= 49;
            case 3: return x <= 25;
            case 2: return x <= 9;
            case 1: return x <= 4;
            default: return true;
        } // end switch
    } // end needToCheck()

    // Keep small values - uses lazy evaluation.
    private final static int KNOWN_SIZE = 1000;
    private static Map<Integer, Integer> knownCounts = new
HashMap<Integer, Integer>(KNOWN_SIZE / 2);

    /**
     * code to test prime counting.
     *
     * @param args not used.
     */
    public static void main(String[] args) {
        for (int i = 0; i < 1001; i += 50) {
            System.out.println("pi(" + i + ") = " + PrimeCount.pi(i));
        } // end for
        System.out.println();

        long target = 1;
        for (int j = 1; j < 11; ++j) {
            target *= 10L;
            System.out.println("pi(10^" + j + ") = " +
PrimeCount.pi(target));
        } // end for
        System.out.println("Complete.");

    } // end main()

} // end class PrimeCount

//----- End Code ------

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