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From "Alex D Herbert (JIRA)" <j...@apache.org>
Subject [jira] [Comment Edited] (RNG-50) PoissonSampler single use speed improvements
Date Wed, 01 Aug 2018 14:38:00 GMT

    [ https://issues.apache.org/jira/browse/RNG-50?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=16565413#comment-16565413
] 

Alex D Herbert edited comment on RNG-50 at 8/1/18 2:38 PM:
-----------------------------------------------------------

Sorry about the link. I've updated it.
{quote}If so, LargeMeanPoissonSamplerCache should be thread-safe
{quote}
I don't think this pattern requires thread safety.

The lazy initialisation is such that all that is shared across all the threads is the fixed
length array of cached states. If the state is null then the state is computed and put into
the array. The method always keeps a reference to the computed state so it has a guaranteed
return value.

If multiple threads each try and access the same null state then they will all compute it.
Then each thread will put it into the array, replacing a value that may have been computed
by another thread. However this will just be a duplication with the same underlying values.

If the write to the array is done via the local memory cache then no other threads running
using different local cache will see it. However it will eventually be synchronised back to
main memory and then out to any other CPU cache memory.

So you may get some duplication of computation across threads. But avoid any synchronisation
issues.

The alternative is to go for synchronisation when the state is null. This should be done using
a synchronisation on the level of the index that is missing. So allowing other threads to
synchronise and update a different missing value. This could use {{java.util.concurrent.atomic.AtomicReferenceArray<E>}}.
{code:java}
package org.apache.commons.rng.sampling.distribution;

import java.util.concurrent.atomic.AtomicReferenceArray;

import org.apache.commons.rng.sampling.distribution.InternalUtils.FactorialLog;

/**
 * Compute initialisation state for the LargeMeanPoissonSampler caching values
 * in a set range.
 */
public class LargeMeanPoissonSamplerCache {

    /** Class to compute {@code log(n!)}. This has no cached values. */
    private static final InternalUtils.FactorialLog NO_CACHE_FACTORIAL_LOG;

    static {
        NO_CACHE_FACTORIAL_LOG = FactorialLog.create();
    }

    /** The minimum N covered by the cache. */
    private final int minN;
    /** The maximum N covered by the cache. */
    private final int maxN;
    /** The cache of states between {@link minN} and {@link maxN}. */
    private final AtomicReferenceArray<double[]> values;

    /**
     * @param minN The minimum N covered by the cache.
     * @param maxN The maximum N covered by the cache.
     * @throws IllegalArgumentException if {@code mean <= 0}.
     */
    public LargeMeanPoissonSamplerCache(int minN, int maxN) {
        if (minN < 0) {
            throw new IllegalArgumentException(
                    "MinN: " + minN + " <= " + 0);
        }
        if (maxN <= minN) {
            throw new IllegalArgumentException(
                    "MaxN: " + maxN + " <= " + minN);
        }
        this.minN = minN;
        this.maxN = maxN;
        values = new AtomicReferenceArray<double[]>(maxN - minN + 1);
    }

    /**
     * Get the initialisation state of the LargeMeanPoissonSampler.
     *
     * @param lambda The integer value of the Poisson mean
     *               ({@code Math.floor(mean)}).
     * @return the initialisation state
     */
    double[] getState(int lambda) {
        if (lambda < minN || lambda > maxN)
            return computeState(lambda);
        final int index = lambda - minN;
        double[] value = values.get(index);
        if (value == null) {
            // Compute and store for reuse
            value = computeState(lambda);
            values.lazySet(index, value);
            // or
            values.compareAndSet(index, null, value);
        }
        return value;
    }

    /**
     * compute the initialisation state of the LargeMeanPoissonSampler.
     *
     * @param lambda The integer value of the Poisson mean
     *               ({@code Math.floor(mean)}).
     * @return the initialisation state
     */
    private final static double[] computeState(int lambda) {
        final double logLambda = Math.log(lambda);
        final double logLambdaFactorial = 
                NO_CACHE_FACTORIAL_LOG.value(lambda);
        final double delta = Math.sqrt(lambda * 
                Math.log(32 * lambda / Math.PI + 1));
        final double halfDelta = delta / 2;
        final double twolpd = 2 * lambda + delta;
        final double c1 = 1 / (8 * lambda);
        final double a1 = Math.sqrt(Math.PI * twolpd) * Math.exp(c1);
        final double a2 = (twolpd / delta) * 
                Math.exp(-delta * (1 + delta) / twolpd);
        final double aSum = a1 + a2 + 1;
        final double p1 = a1 / aSum;
        final double p2 = a2 / aSum;
        return new double[] { logLambda, logLambdaFactorial, delta, 
                halfDelta, twolpd, p1, p2, c1 };
    }
}
{code}
I've never bothered to do this as the suggested pattern (leave the JVM to sort out main memory
synchronisation) has always worked for me. I've used this on machines running 16-cores and
obtained the same results as a single core.

I could have an investigation by adding an extension to the benchmark I currently have.


was (Author: alexherbert):
Sorry about the link. I've updated it.
{quote}If so, LargeMeanPoissonSamplerCache should be thread-safe
{quote}
I don't think this pattern requires thread safety.

The lazy initialisation is such that all that is shared across all the threads is the fixed
length array of cached states. If the state is null then the state is computed and put into
the array. The method always keeps a reference to the computed state so it has a guaranteed
return value.

If multiple threads each try and access the same null state then they will all compute it.
Then each thread will put it into the array, replacing a value that may have been computed
by another thread. However this will just be a duplication with the same underlying values.

If the write to the array is done via the local memory cache then no other threads running
using different local cache will see it. However it will eventually be synchronised back to
main memory and then out to any other CPU cache memory.

So you may get some duplication of computation across threads. But avoid any synchronisation
issues.

The alternative is to go for synchronisation when the state is null. This should be done using
a synchronisation on the level of the index that is missing. So allowing other threads to
synchronise and update a different missing value. This could use {{java.util.concurrent.atomic.AtomicReferenceArray<E>}}.
{code:java}
package org.apache.commons.rng.sampling.distribution;

import java.util.concurrent.atomic.AtomicReferenceArray;

import org.apache.commons.rng.sampling.distribution.InternalUtils.FactorialLog;

/**
 * Compute initialisation state for the LargeMeanPoissonSampler caching values
 * in a set range.
 */
public class LargeMeanPoissonSamplerCache {

    /** Class to compute {@code log(n!)}. This has no cached values. */
    private static final InternalUtils.FactorialLog NO_CACHE_FACTORIAL_LOG;

    static {
        NO_CACHE_FACTORIAL_LOG = FactorialLog.create();
    }

    /** The minimum N covered by the cache. */
    private final int minN;
    /** The maximum N covered by the cache. */
    private final int maxN;
    /** The cache of initialisation states between {@link minN} and {@link maxN}. */
    private final AtomicReferenceArray<double[]> values;

    /**
     * @param minN The minimum N covered by the cache.
     * @param maxN The maximum N covered by the cache.
     * @throws IllegalArgumentException if {@code mean <= 0}.
     */
    public LargeMeanPoissonSamplerCache(int minN, int maxN) {
        if (minN < 0) {
            throw new IllegalArgumentException("MinN: " + minN + " <= " + 0);
        }
        if (maxN <= minN) {
            throw new IllegalArgumentException("MaxN: " + maxN + " <= " + minN);
        }
        this.minN = minN;
        this.maxN = maxN;
        values = new AtomicReferenceArray<double[]>(maxN - minN + 1);
    }

    /**
     * Get the initialisation state of the LargeMeanPoissonSampler.
     *
     * @param lambda The integer value of the Poisson mean ({@code Math.floor(mean)}).
     * @return the initialisation state
     */
    double[] getState(int lambda) {
        if (lambda < minN || lambda > maxN)
            return computeState(lambda);
        final int index = lambda - minN;
        double[] value = values.get(index);
        if (value == null) {
            // Compute and store for reuse
            value = computeState(lambda);
            values.compareAndSet(index, null, value);
            // or values.lazySet(index, value);
        }
        return value;
    }
    
    /**
     * compute the initialisation state of the LargeMeanPoissonSampler.
     *
     * @param lambda The integer value of the Poisson mean ({@code Math.floor(mean)}).
     * @return the initialisation state
     */
    private final static double[] computeState(int lambda) {
        final double logLambda = Math.log(lambda);
        final double logLambdaFactorial = NO_CACHE_FACTORIAL_LOG.value(lambda);
        final double delta = Math.sqrt(lambda * Math.log(32 * lambda / Math.PI + 1));
        final double halfDelta = delta / 2;
        final double twolpd = 2 * lambda + delta;
        final double c1 = 1 / (8 * lambda);
        final double a1 = Math.sqrt(Math.PI * twolpd) * Math.exp(c1);
        final double a2 = (twolpd / delta) * Math.exp(-delta * (1 + delta) / twolpd);
        final double aSum = a1 + a2 + 1;
        final double p1 = a1 / aSum;
        final double p2 = a2 / aSum;
        return new double[] { logLambda, logLambdaFactorial, delta, 
                halfDelta, twolpd, p1, p2, c1 };
    }
}
{code}
I've never bothered to do this as the suggested pattern (leave the JVM to sort out main memory
synchronisation) has always worked for me. I've used this on machines running 16-cores and
obtained the same results as a single core.

I could have an investigation by adding an extension to the benchmark I currently have.

> PoissonSampler single use speed improvements
> --------------------------------------------
>
>                 Key: RNG-50
>                 URL: https://issues.apache.org/jira/browse/RNG-50
>             Project: Commons RNG
>          Issue Type: Improvement
>    Affects Versions: 1.0
>            Reporter: Alex D Herbert
>            Priority: Minor
>         Attachments: PoissonSamplerTest.java, jmh-result.csv
>
>
> The Sampler architecture of {{org.apache.commons.rng.sampling.distribution}} is nicely
written for fast sampling of small dataset sizes. The constructors for the samplers do not
check the input parameters are valid for the respective distributions (in contrast to the
old {{org.apache.commons.math3.random.distribution}} classes). I assume this is a design choice
for speed. Thus most of the samplers can be used within a loop to sample just one value with
very little overhead.
> The {{PoissonSampler}} precomputes log factorial numbers upon construction if the mean
is above 40. This is done using the {{InternalUtils.FactorialLog}} class. As of version 1.0
this internal class is currently only used in the {{PoissonSampler}}.
> The cache size is limited to 2*PIVOT (where PIVOT=40). But it creates and precomputes
the cache every time a PoissonSampler is constructed if the mean is above the PIVOT value.
> Why not create this once in a static block for the PoissonSampler?
> {code:java}
> /** {@code log(n!)}. */
> private static final FactorialLog factorialLog;
>      
> static 
> {
>     factorialLog = FactorialLog.create().withCache((int) (2 * PoissonSampler.PIVOT));
> }
> {code}
> This will make the construction cost of a new {{PoissonSampler}} negligible. If the table
is computed dynamically as a static construction method then the overhead will be in the first
use. Thus the following call will be much faster:
> {code:java}
> UniformRandomProvider rng = ...;
> int value = new PoissonSampler(rng, 50).sample();
> {code}
> I have tested this modification (see attached file) and the results are:
> {noformat}
> Mean 40  Single construction ( 7330792) vs Loop construction                        
 (24334724)   (3.319522.2x faster)
> Mean 40  Single construction ( 7330792) vs Loop construction with static FactorialLog
( 7990656)   (1.090013.2x faster)
> Mean 50  Single construction ( 6390303) vs Loop construction                        
 (19389026)   (3.034132.2x faster)
> Mean 50  Single construction ( 6390303) vs Loop construction with static FactorialLog
( 6146556)   (0.961857.2x faster)
> Mean 60  Single construction ( 6041165) vs Loop construction                        
 (21337678)   (3.532047.2x faster)
> Mean 60  Single construction ( 6041165) vs Loop construction with static FactorialLog
( 5329129)   (0.882136.2x faster)
> Mean 70  Single construction ( 6064003) vs Loop construction                        
 (23963516)   (3.951765.2x faster)
> Mean 70  Single construction ( 6064003) vs Loop construction with static FactorialLog
( 5306081)   (0.875013.2x faster)
> Mean 80  Single construction ( 6064772) vs Loop construction                        
 (26381365)   (4.349935.2x faster)
> Mean 80  Single construction ( 6064772) vs Loop construction with static FactorialLog
( 6341274)   (1.045591.2x faster)
> {noformat}
> Thus the speed improvements would be approximately 3-4 fold for single use Poisson sampling.



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