The Java Specialists' Newsletter
Issue 20120120524
Category:
Concurrency
Java version: Java 7 Fork/Join With Fibonacci and Karatsubaby Dr. Heinz M. KabutzAbstract: The new Java 7 Fork/Join Framework allows us to define our algorithms using recursion and then to easily parallelize them. In this newsletter we describe how that works using a fast Fibonacci algorithm that uses the sum of the squares rather than brute force. We also present a faster algorithm for multiplying two large BigInteger numbers, using the Fork/Join Framework and the Karatsuba algorithm.
Welcome to the 201st issue of The Java(tm) Specialists' Newsletter sent to you from the
Island of Crete. Kirk Pepperdine is running his Java Performance Tuning
Course at our conference room this
week. Helene had the brilliant idea that they should shift
their day by a few hours today. So instead of starting sharp
at 9am, we went to a secret beach
for a swim and then began with the lessons at
11:30am. Kirk will catch up with the material tonight. I
think we will do this on all our Cretan courses in future.
A quick jump in our freshwater pool was a perfect way to get
me inspired to write this newsletter (You might enjoy this
short
video my son and his buddy made of our pool  a friend
gave us some old playground slides that we have hooked up to
our pool pump to make a lovely water slide  the video might
be blocked in your region due to the sound track.)
So, now that you're completely annoyed with my introduction
and are sitting there behind your desk fuming with envy,
there are two opportunities that you could take advantage of
to visit our beautiful island :) First off, I am running my
Java Specialist
Master Course here in 11 days time, from the 47
June 2012. It is the perfect course for a Java programmer
who has used Java for at least 2 years and who would like to
grow in their knowledge of Java. Moneyback guarantee if you
are not fully satisfied! Flights to Greece are cheap this
year and Crete is perfectly safe. Secondly, we are running
our second Java
Specialist Symposium from the 1013 September
2012. We doubled the attendance fees from last year ($0) and will
keep on doing that every year for as long as we do the
symposium. Space is limited though, firstcomefirstserved.
One last interesting bit of news from Crete, before we start
with the newsletter. One of the main tourist areas,
Platanias, is also a breeding ground for the loggerhead
turtle, called CarettaCaretta. Why they allowed hotels and
beach umbrellas in that area boggles the mind. Last month,
I took some friends out for a drive in my boat and almost
ran over a turtle that was swimming in the middle of the sea.
It was the first time I saw one of these critters in the wild
and it was a completely amazing experience watching and
filming it. My son was kind enough to turn our recordings
into a short
documentary about the CarettaCaretta. Some viewers
in Canada had errors when they tried to play it. If that
happens, please just try again. I think you will enjoy
seeing the turtle as much as I did.
Join us on Crete (or via webinar) for advanced Core Java Courses:Concurrency Specialists Course 14 April 2014 and
Java Specialists Master Course 2023 May 2014.
Fork/Join With Fibonacci
Figuring out new language features can be daunting. The
JavaDocs are not always that helpful. Here is an example
shown in the RecursiveTask
JavaDocs to demonstrate how the fork/join framework
should be used:
class Fibonacci extends RecursiveTask<Integer> {
final int n;
Fibonacci(int n) { this.n = n; }
Integer compute() {
if (n <= 1)
return n;
Fibonacci f1 = new Fibonacci(n  1);
f1.fork();
Fibonacci f2 = new Fibonacci(n  2);
return f2.compute() + f1.join();
}
}
What is wrong with this example? A minor issue is that it
contains a fairly basic Java syntax error. The compute()
method is implementing a protected abstract method defined
in the RecursiveTask class. In the example, the method is
package access. It should either be protected or public.
We can widen the access to an overridden method, but we
cannot narrow it. Stylistically also, the field "n"
should be private.
However, the syntax error will be semiautomatically repaired
by any decent IDE. The real problem is one of computational
complexity. The algorithm for Fibonacci presented here is
exponential. Solving f(n+1) requires approximately twice as
many steps as f(n). Thus if we manage to solve f(n) with
a single core within some time, then with a 1024 processor
machine, we will only be able to solve the f(n+10) in the
same amount of time.
The idea of using Fibonacci as an example is not bad, but the
choice of an exponential algorithm was unfortunate. I tried
to produce a fast Java implementation of the famous function.
Exactly three months ago I posted a challenge on java.net to
try to find Fibonacci of one billion. Alexey
Solodovnikov managed to solve the problem in 36 seconds using
gcc 4.5.2 + gmp with a 3 GHz single core machine. His Java
version took about 2.5 hours. Rexy Young solved it using
Dijkstra's famous sum of squares algorithm (more later) in
55 minutes. The code I will present in this newsletter
solved the problem without any 3rd party libraries in 34
minutes in Java on my 8core server.
Something else I have done is start uploading the code from
my newsletters onto GitHub. You can grab it from
git://github.com/kabutz/javaspecialists.git if you like and
then build it with Maven. It will still be changing a lot
until I have decided how to arrange the various packages. I
also still have to pull the source code from over 200 Java
newsletters into my project tree. This will take a while,
but I think it's good that my friend Alvaro pushed me into
this direction. Thanks Alvaro! The license will probably be
Apache 2.0, unless there are any compelling reasons why that
won't do.
The first class we have is Fibonacci. It contains caching
behaviour enabled by default, since a lot of Fibonacci
algorithms do much better with it turned on. You might
notice that the calculate() and doActualCalculate() methods
both declare that they throw the InterruptedException. We
can use interrupts to cancel long calculations.
import java.math.*;
public abstract class Fibonacci {
private final FibonacciCache cache;
protected Fibonacci(FibonacciCache cache) {
this.cache = cache;
}
public Fibonacci() {
this(null);
}
public BigInteger calculate(int n)
throws InterruptedException {
if (cache == null) return doActualCalculate(n);
BigInteger result = cache.get(n);
if (result == null) {
cache.put(n, result = doActualCalculate(n));
}
return result;
}
protected abstract BigInteger doActualCalculate(int n)
throws InterruptedException;
}
Here is an implementation that uses the caching feature of
the Fibonacci class. The algorithm is recursive, but thanks
to the cache, we can do all the calculations in linear time.
However, the BigInteger.add() method is also linear, which
means that overall, this function ends up being quadratic.
This means that if we double the size of n, it will take four
times as long to solve. In addition, because it is still
recursive in nature, the stack depth is a limiting factor in
which numbers we can calculate.
import java.math.*;
public class FibonacciRecursive extends Fibonacci {
public BigInteger doActualCalculate(int n)
throws InterruptedException {
if (Thread.interrupted()) throw new InterruptedException();
if (n < 0) throw new IllegalArgumentException();
if (n == 0) return BigInteger.ZERO;
if (n == 1) return BigInteger.ONE;
return calculate(n  1).add(calculate(n  2));
}
}
At this point, we should probably show the special
FibonacciCache class. It contains the optimization that if
we request "n" and the cache does not contain that, we see
whether "n1" and "n2" are contained. If they are, then we
can use those to quickly calculate the Fibonacci value for
"n". Similarly, we can look for "n+1" and "n+2" or "n+1" and
"n1" to find "n" quickly.
One of the things that kept on happening was that several
threads would request the same number at the same time.
Since neither of them found it, they would both go and work
out the value. This wasted a lot of computing power. Thus,
before we return "null" from this cache, we reserve the right
to calculate the number by adding the value of "n" into the
cacheReservation set. If another thread now tries to
calculate the same fibonacci number, it is suspended until
the first thread finds the answer. The speedup with this
optimization was quite dramatic, but required that the number
or threads in the ForkJoinPool exceeded the number of cores.
import java.math.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.concurrent.locks.*;
class FibonacciCache {
private final ConcurrentMap<Integer, BigInteger> cache =
new ConcurrentHashMap<>();
private final Lock lock = new ReentrantLock();
private final Condition solutionArrived = lock.newCondition();
private final Set<Integer> cacheReservation = new HashSet<>();
public BigInteger get(int n) throws InterruptedException {
lock.lock();
try {
while (cacheReservation.contains(n)) {
// we now want to wait until the answer is in the cache
solutionArrived.await();
}
BigInteger result = cache.get(n);
if (result != null) {
return result;
}
BigInteger nMinusOne = cache.get(n  1);
BigInteger nMinusTwo = cache.get(n  2);
if (nMinusOne != null && nMinusTwo != null) {
result = nMinusOne.add(nMinusTwo);
put(n, result);
return result;
}
BigInteger nPlusOne = cache.get(n + 1);
BigInteger nPlusTwo = cache.get(n + 2);
if (nPlusOne != null && nPlusTwo != null) {
result = nPlusTwo.subtract(nPlusOne);
put(n, result);
return result;
}
if (nPlusOne != null && nMinusOne != null) {
result = nPlusOne.subtract(nMinusOne);
put(n, result);
return result;
}
cacheReservation.add(n);
return null;
} finally {
lock.unlock();
}
}
public void put(int n, BigInteger value) {
lock.lock();
try {
solutionArrived.signalAll();
cacheReservation.remove(n);
cache.putIfAbsent(n, value);
} finally {
lock.unlock();
}
}
}
Some of the algorithms do not need caching. For example, if
we solve the problem with iteration, then we will never try
to find the same Fibonacci number more than once. Our
NonCachingFibonacci abstract base class redefines the
calculate() method as abstract and stops us from overriding
doActualCalculate():
import java.math.*;
public abstract class NonCachingFibonacci extends Fibonacci {
protected NonCachingFibonacci() {
super(null);
}
public final BigInteger doActualCalculate(int n)
throws InterruptedException {
throw new UnsupportedOperationException();
}
public abstract BigInteger calculate(int n)
throws InterruptedException;
}
The first example that uses the NonCachingFibonacci is the
iterative solution. If we ran this with "long" values, it
would be very fast. However, we are slowed down by the
BigInteger method being linear, which again makes this
function quadratic, similar to the FibonacciRecursive class
shown earlier. Since it is not recursive, this function
does not run out of stack space as would happen with
FibonacciRecursive.
import java.math.*;
public class FibonacciIterative extends NonCachingFibonacci {
public BigInteger calculate(int n)
throws InterruptedException {
if (n < 0) throw new IllegalArgumentException();
BigInteger n0 = BigInteger.ZERO;
BigInteger n1 = BigInteger.ONE;
for (int i = 0; i < n; i++) {
if (Thread.interrupted()) throw new InterruptedException();
BigInteger temp = n1;
n1 = n1.add(n0);
n0 = temp;
}
return n0;
}
}
The classical Fibonacci algorithm as described in the
RecursiveTask JavaDocs is exponential. The only way of
making it a bit performant is to cache the previous values.
In this version we do not cache, making it incredibly
slow. We can thus only calculate for very small values of n.
import java.math.*;
public class FibonacciRecursiveNonCaching
extends NonCachingFibonacci {
public BigInteger calculate(int n)
throws InterruptedException {
if (Thread.interrupted()) throw new InterruptedException();
if (n < 0) throw new IllegalArgumentException();
if (n == 0) return BigInteger.ZERO;
if (n == 1) return BigInteger.ONE;
return calculate(n  1).add(calculate(n  2));
}
}
We have shown simple iterative and recursive solutions.
However, there is also a formula that we can use to
calculate a specific Fibonacci number, without having to go
back and calculate the previous numbers. This formula
depends on the square root of 5. With "long" and "double",
we can work out an accurate value of Fibonacci up to n=71.
Let phi = (1 + root5) / 2 and psi = (1  root5) / 2 .
Fibonacci(n) = (phi^n  psi^n) / (phi  psi) , where "^" means
"to the power of". Or we could simply say
Fibonacci(n) = (phi^n  psi^n) / root5 .
import java.math.*;
public class FibonacciFormulaLong extends NonCachingFibonacci {
private static final double root5 = Math.sqrt(5);
private static final double PHI = (1 + root5) / 2;
private static final double PSI = (1  root5) / 2;
private static final int MAXIMUM_PRECISE_NUMBER = 71;
public BigInteger calculate(int n)
throws InterruptedException {
if (Thread.interrupted()) throw new InterruptedException();
if (n < 0) throw new IllegalArgumentException();
if (n > MAXIMUM_PRECISE_NUMBER)
throw new IllegalArgumentException(
"Precision loss after " + MAXIMUM_PRECISE_NUMBER);
return new BigInteger(Long.toString(fibWithFormula(n)));
}
private static long fibWithFormula(int n) {
return (long)((Math.pow(PHI, n)  Math.pow(PSI, n)) / root5);
}
}
If we want to be able to work out Fibonacci(1000) with this
formula, we are forced to use BigDecimal. Unfortunately it
is a rather slow class. I used a value of root5 that would
give me an accurate Fibonacci number up to n=1000. The more
accurate we make root5, the slower this algorithm takes. The
biggest time sink is the call to divide(root5) at the end of
the calculation.
import java.math.*;
public class FibonacciFormulaBigInteger extends NonCachingFibonacci {
private static final BigDecimal root5 = new BigDecimal(
"2.23606797749978969640917366873127623544061835961152572" +
"4270897245410520925637804899414414408378782274969508176" +
"1507737835042532677244470738635863601215334527088667781" +
"7319187916581127664532263985658053576135041753378");
private static final BigDecimal PHI = root5.add(
new BigDecimal(1)).divide(new BigDecimal(2));
private static final BigDecimal PSI = root5.subtract(
new BigDecimal(1)).divide(new BigDecimal(2));
private static final int MAXIMUM_PRECISE_NUMBER = 1000;
public BigInteger calculate(int n) throws InterruptedException {
if (Thread.interrupted()) throw new InterruptedException();
if (n < 0) throw new IllegalArgumentException();
if (n > MAXIMUM_PRECISE_NUMBER)
throw new IllegalArgumentException(
"Precision loss after " + MAXIMUM_PRECISE_NUMBER);
BigDecimal phiToTheN = PHI.pow(n);
if (Thread.interrupted()) throw new InterruptedException();
BigDecimal psiToTheN = PSI.pow(n);
if (Thread.interrupted()) throw new InterruptedException();
BigDecimal phiMinusPsi = phiToTheN.subtract(psiToTheN);
BigDecimal result = phiMinusPsi.divide(
root5, 0, RoundingMode.UP);
return result.toBigInteger();
}
}
So far, the best we have achieved is a linear algorithm, but
with the addition of linear BigInteger.add(), we ended up
with quadratic performance. Can we do better?
One of the algorithms that is popular is Dijkstra's sum of
the squares is also mentioned on R.Knott's
website.
My implementation goes like this: if n is odd, then
f(2n1) = f(n1)^2 + f(n)^2 ; otherwise
f(2n) = (2 * f(n1) + f(n)) * f(n) .
import java.math.*;
public class FibonacciRecursiveDijkstra extends Fibonacci {
public BigInteger doActualCalculate(int n)
throws InterruptedException {
if (Thread.interrupted()) throw new InterruptedException();
if (n == 0) return BigInteger.ZERO;
if (n == 1) return BigInteger.ONE;
if (n % 2 == 1) {
// f(2n1) = f(n1)^2 + f(n)^2
int left = (n + 1) / 2;
int right = (n + 1) / 2  1;
return square(calculate(left)).add(square(calculate(right)));
} else {
// f(2n) = (2 * f(n1) + f(n)) * f(n)
int n_ = n / 2;
BigInteger fn = calculate(n_);
BigInteger fn_1 = calculate(n_  1);
return (fn_1.add(fn_1).add(fn)).multiply(fn);
}
}
protected BigInteger multiply(BigInteger bi0, BigInteger bi1) {
return bi0.multiply(bi1);
}
protected BigInteger square(BigInteger num) {
return multiply(num, num);
}
}
The algorithm now is logarithmic, meaning that we can solve
Fibonacci(1000) with about 10 calculations. I expected this
to be really fast and to outperform all the other algorithms.
After all, the iterative and simple recursive solutions both
are quadratic. However, it turns out that the bottleneck in
the above code is the BigInteger.multiply() method, which is
quadratic. So we now have O(n^2 * log n) performance. Good
enough to find Fibonacci for a thousand but not for a
billion.
After some research, I stumbled across the algorithm by Karatsuba.
Instead of quadratic performance, it can achieve 3n^1.585
performance. There are other algorithms one can use as your
numbers get larger, but I tried to build this solver without
using thirdparty libraries. Examples of thirdparty
libraries are JScience's
LargeInteger, which internally uses
Karatsuba and also a parallel version. However, I really
wanted a solution that could cooperate with an existing
ForkJoinPool rather than start new threads. Another option
would be to simply use a
Java wrapper to GMP,
which should give us the same speed as a C wrapper to GMP,
since all we are doing is delegate the Fibonacci function to
GMP.
For large numbers, Karatsuba's multiplication algorithm, is a
lot faster than ordinary BigInteger multiply. We give two
implementations, the BasicKaratsuba for singlethreaded
calculations and the ParallelKaratsuba that utilizes the
Fork/Join Framework. Another place that mentions Karatsuba
is in Sedgewick and Wayne's book Introduction to Programming in Java: An
Interdisciplinary Approach.
import java.math.*;
public interface Karatsuba {
BigInteger multiply(BigInteger x, BigInteger y);
}
Our Karatsuba calculations use some utility functions for
adding and splitting BigIntegers.
import java.math.*;
class BigIntegerUtils {
public static BigInteger add(BigInteger... ints) {
BigInteger sum = ints[0];
for (int i = 1; i < ints.length; i++) {
sum = sum.add(ints[i]);
}
return sum;
}
public static BigInteger[] split(BigInteger x, int m) {
BigInteger left = x.shiftRight(m);
BigInteger right = x.subtract(left.shiftLeft(m));
return new BigInteger[]{left, right};
}
}
The BasicKaratsuba contains a threshold value. If either of
the numbers being multiplied is less than the threshold, then
we use the standard BigInteger.multiply().
import java.math.*;
import static eu.javaspecialists.tjsn.math.numbers.BigIntegerUtils.*;
public class BasicKaratsuba implements Karatsuba {
public static final String THRESHOLD_PROPERTY_NAME =
"eu.javaspecialists.tjsn.math.numbers.BasicKaratsubaThreshold";
private static final int THRESHOLD = Integer.getInteger(
THRESHOLD_PROPERTY_NAME, 1000);
public BigInteger multiply(BigInteger x, BigInteger y) {
int m = java.lang.Math.min(x.bitLength(), y.bitLength())/2;
if (m <= THRESHOLD)
return x.multiply(y);
// x = x1 * 2^m + x0
// y = y1 * 2^m + y0
BigInteger[] xs = BigIntegerUtils.split(x, m);
BigInteger[] ys = BigIntegerUtils.split(y, m);
// xy = (x1*2^m + x0)(y1*2^m + y0) = z2*2^2m + z1*2^m + z0
// where:
// z2 = x1 * y1
// z0 = x0 * y0
// z1 = x1 * y0 + x0 * y1 = (x1 + x0)(y1 + y0)  z2  z0
BigInteger z2 = multiply(xs[0], ys[0]);
BigInteger z0 = multiply(xs[1], ys[1]);
BigInteger z1 = multiply(add(xs), add(ys)).
subtract(z2).subtract(z0);
// result = z2 * 2^2m + z1 * 2^m + z0
return z2.shiftLeft(2 * m).add(z1.shiftLeft(m)).add(z0);
}
}
The ParallelKaratsuba is almost identical to the
BasicKaratsuba, except that it distributes the individual
tasks to the ForkJoinPool. We can thus utilize the available
hardware to multiply the numbers faster. Note how similar it
looks to the sequential version in BasicKaratsuba. As long
as your algorithm is recursive, it is very easy to employ the
Fork/Join framework to speed up your work.
import java.math.*;
import java.util.concurrent.*;
import static eu.javaspecialists.tjsn.math.numbers.BigIntegerUtils.*;
public class ParallelKaratsuba implements Karatsuba {
public static final String THRESHOLD_PROPERTY_NAME =
"eu.javaspecialists.tjsn.math.numbers.ParallelKaratsubaThreshold";
private static final int THRESHOLD = Integer.getInteger(
THRESHOLD_PROPERTY_NAME, 1000);
private final ForkJoinPool pool;
public ParallelKaratsuba(ForkJoinPool pool) {
this.pool = pool;
}
public BigInteger multiply(BigInteger x, BigInteger y) {
return pool.invoke(new KaratsubaTask(x, y));
}
private static class KaratsubaTask
extends RecursiveTask<BigInteger> {
private final BigInteger x, y;
public KaratsubaTask(BigInteger x, BigInteger y) {
this.x = x;
this.y = y;
}
protected BigInteger compute() {
int m = (Math.min(x.bitLength(), y.bitLength()) / 2);
if (m <= THRESHOLD) {
return x.multiply(y);
}
BigInteger[] xs = split(x, m);
BigInteger[] ys = split(y, m);
KaratsubaTask z2task = new KaratsubaTask(xs[0], ys[0]);
KaratsubaTask z0task = new KaratsubaTask(xs[1], ys[1]);
KaratsubaTask z1task = new KaratsubaTask(add(xs), add(ys));
z0task.fork();
z2task.fork();
BigInteger z0, z2;
BigInteger z1 = z1task.invoke().subtract(
z2 = z2task.join()).subtract(z0 = z0task.join());
return z2.shiftLeft(2*m).add(z1.shiftLeft(m)).add(z0);
}
}
}
Karatsuba makes a big difference in the performance,
especially if we are able to utilize the available cores.
We can do the same thing with Dijkstra's Fibonacci algorithm
where we distribute the various Fibonacci calculations to
the various cores. However, the biggest speedup is probably
from the Karatsuba multiply, since that is where most of the
time is spent. Our parallel solution uses its own internal
FibonaccciCache.
import java.math.*;
import java.util.concurrent.*;
public class FibonacciRecursiveParallelDijkstraKaratsuba
extends NonCachingFibonacci {
public static final String SEQUENTIAL_THRESHOLD_PROPERTY_NAME =
"eu.javaspecialists.tjsn.math.fibonacci.SequentialThreshold";
private final static int SEQUENTIAL_THRESHOLD =
Integer.getInteger(SEQUENTIAL_THRESHOLD_PROPERTY_NAME, 10000);
private final FibonacciCache cache = new FibonacciCache();
private final Fibonacci sequential =
new FibonacciRecursiveDijkstraKaratsuba();
private final ForkJoinPool pool;
private final Karatsuba karatsuba;
public FibonacciRecursiveParallelDijkstraKaratsuba(
ForkJoinPool pool) {
this.pool = pool;
karatsuba = new ParallelKaratsuba(pool);
}
public BigInteger calculate(int n) throws InterruptedException {
if (Thread.interrupted()) throw new InterruptedException();
BigInteger result = pool.invoke(new FibonacciTask(n));
if (result == null) throw new InterruptedException();
return result;
}
private class FibonacciTask extends RecursiveTask<BigInteger> {
private final int n;
private FibonacciTask(int n) {
this.n = n;
}
protected BigInteger compute() {
try {
BigInteger result = cache.get(n);
if (result != null) {
return result;
}
if (n < SEQUENTIAL_THRESHOLD) {
result = sequential.calculate(n);
} else {
if (n % 2 == 1) {
// f(2n1) = f(n1)^2 + f(n)^2
int left = (n + 1) / 2;
int right = (n + 1) / 2  1;
FibonacciTask f0 = new FibonacciTask(left);
FibonacciTask f1 = new FibonacciTask(right);
f1.fork();
BigInteger bi0 = f0.invoke();
BigInteger bi1 = f1.join();
if (isCancelled()) return null;
result = square(bi1).add(square(bi0));
} else {
// f(2n) = (2 * f(n1) + f(n)) * f(n)
int n_ = n / 2;
FibonacciTask f0 = new FibonacciTask(n_);
FibonacciTask f1 = new FibonacciTask(n_  1);
f1.fork();
BigInteger bi0 = f0.invoke();
BigInteger bi1 = f1.join();
if (isCancelled()) return null;
result = karatsuba.multiply(
bi1.add(bi1).add(bi0), bi0);
}
}
cache.put(n, result);
return result;
} catch (InterruptedException e) {
cancel(true);
return null;
}
}
private BigInteger square(BigInteger num) {
return karatsuba.multiply(num, num);
}
}
}
The FibonacciGenerator uses the given Fibonacci function to
work out the result as a BigDecimal. However, the conversion
of BigDecimal to a String is again, you guessed it,
quadratic. Instead, what we do is print out the first and
last 10 bytes and an Adler32 checksum.
import java.math.*;
import java.util.zip.*;
public class FibonacciGenerator {
private final Fibonacci fib;
public FibonacciGenerator(Fibonacci fib) {
this.fib = fib;
}
public void findFib(int n) throws InterruptedException {
System.out.printf("Searching for Fibonacci(%,d)%n", n);
long time = System.currentTimeMillis();
BigInteger num = fib.calculate(n);
time = System.currentTimeMillis()  time;
printProof(num);
System.out.printf(" Time to calculate %d ms%n%n", time);
}
private void printProof(BigInteger num) {
System.out.printf(" Number of bits: %d%n", num.bitLength());
byte[] numHex = num.toByteArray();
System.out.print(" First 10 bytes: ");
for (int i = 0; i < 10; i++) {
System.out.printf(" %02x", numHex[i]);
}
System.out.println();
System.out.print(" Last 10 bytes: ");
for (int i = numHex.length  10; i < numHex.length; i++) {
System.out.printf(" %02x", numHex[i]);
}
System.out.println();
Checksum ck = new Adler32();
ck.update(numHex, 0, numHex.length);
System.out.printf(" Adler32 Checksum: 0x%016x%n",
ck.getValue());
}
}
The FibonacciGeneratorExample finds Fibonacci of one billion
in about 34 minutes on my 8core server.
import java.util.concurrent.*;
public class FibonacciGeneratorExample {
private static ForkJoinPool pool = new ForkJoinPool(
Runtime.getRuntime().availableProcessors() * 4);
public static void main(String[] args)
throws InterruptedException {
int[] ns;
if (args.length != 0) {
ns = new int[args.length];
for (int i = 0; i < ns.length; i++) {
ns[i] = Integer.parseInt(args[i]);
}
} else {
ns = new int[]{
1_000_000,
10_000_000,
100_000_000, // takes a bit long
1_000_000_000, // takes a bit long
};
}
test(new FibonacciRecursiveParallelDijkstraKaratsuba(pool), ns);
}
private static void test(Fibonacci fib, int... ns)
throws InterruptedException {
for (int n : ns) {
FibonacciGenerator fibgen = new FibonacciGenerator(fib);
fibgen.findFib(n);
System.out.println(pool);
}
}
}
I would love to hear if you can come up with an algorithm in
Java to solve Fibonacci one billion faster on my hardware
than my 34.58 minutes. Fastest solution gets a whopping
34.58% discount on the Java Symposium entrance
fees! The rules are: you need to write the code
yourself, but you can use existing algorithms.
Kind regards
Heinz
P.S. Did you know that the Fibonacci series occurs in nature?
For example, the shells of a turtle are arranged according to
the series. That's something to think about as you watch
this big fellow swimming around the Gulf of Chania.
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