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https://issues.apache.org/jira/browse/RNG-50?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=16565206#comment-16565206
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Alex D Herbert edited comment on RNG-50 at 8/1/18 12:37 PM:
------------------------------------------------------------
{quote}However what to do with your use-case (large mean single use)?
{quote}
We know that when the mean is between 40 and 80 then the {{log(n!)}} is used
approximately 0.7 to 0.3% of the time within the algorithm loop. When the mean
is higher this usage within the algorithm drops off.
The log gamma function used to compute {{log(n!)}} uses some double
computations in a loop of size 15 and then 2 {{Math.log}} calls. A cache of
just the {{log(n!)}} values is unlikely to make much of a speed difference
inside the loop as there a fair few other things happening including Gaussian
and Exponential sampling using the RNG. (But of course a JMH benchmark would
avoid presumptions.)
However it will also be used once per sample at the value of {{(int)mean}} at
the initialisation of the algorithm.
The other pre-computed values for the Poisson sample use 2 {{Math.exp}}, 2
{{Math.log}} calls and 2 {{Math.sqrt}} calls. All of these values are based
purely on the integer value of the mean.
So there may be some value in passing in a cache of not only {{log(n!)}} but
also the entire initialisation state of the LargeMeanPoissonSampler if the
range of the mean is known.
The cache could perform lazy initialisation something like:
{code:java}
package org.apache.commons.rng.sampling.distribution;
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 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 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[index];
if (value == null) {
// Compute and store for reuse
value = computeState(lambda);
values[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}
This was a simple example using {{double[]}} but the state could be wrapped as
an immutable object.
The LargeMeanPoissonSampler would then have to do this for initialisation:
{code:java}
lambda = Math.floor(mean);
initialise(cache.getState((int) lambda);
{code}
was (Author: alexherbert):
{quote}However what to do with your use-case (large mean single use)?
{quote}
We know that when the mean is between 40 and 80 then the {{log(n!)}} is used
approximately 0.7 to 0.3% of the time within the algorithm loop. When the mean
is higher this usage within the algorithm drops off.
The log gamma function used to compute {{log(n!)}} uses some double
computations in a loop of size 15 and then 2 {{Math.log}} calls. A cache of
just the {{log(n!)}} values is unlikely to make much of a speed difference
inside the loop as there a fair few other things happening including Gaussian
and Exponential sampling using the RNG. (But of course a JMH benchmark would
avoid presumptions.)
However it will also be used once per sample at the value of {{(int)mean}} at
the initialisation of the algorithm.
The other pre-computed values for the Poisson sample use 2 {{Math.exp}}, 2
{{Math.log}} calls and 2 {{Math.sqrt}} calls. All of these values are based
purely on the integer value of the mean.
So there may be some value in passing in a cache of not only {{log(n!)}} but
also the entire initialisation state of the LargeMeanPoissonSampler if the
range of the mean is known.
The cache could perform lazy initialisation something like:
{code:java}
package org.apache.commons.rng.sampling.distribution;
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 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 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[index];
if (value == null) {
// Compute and store for reuse
value = computeState(lambda);
values[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}
This was a simple example using {{double[]}} but the state could be wrapped as
an immutable object.
The LargeMeanPoissonSampler would then have to do this for initialisation:
{code:java}
lambda = Math.floor(mean);
initialise(cache.getState((int) lambda);
{code}
> 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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