/**
* Licensed to the Apache Software Foundation (ASF) under one
* or more contributor license agreements. See the NOTICE file
* distributed with this work for additional information
* regarding copyright ownership. The ASF licenses this file
* to you under the Apache License, Version 2.0 (the
* "License"); you may not use this file except in compliance
* with the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.hadoop.examples.pi.math;
import java.util.ArrayList;
import java.util.List;
import org.apache.hadoop.examples.pi.Combinable;
import org.apache.hadoop.examples.pi.Container;
import org.apache.hadoop.examples.pi.Util;
/** Represent the summation \sum \frac{2^e \mod n}{n}. */
public class Summation implements Container<Summation>, Combinable<Summation> {
/** Variable n in the summation. */
public final ArithmeticProgression N;
/** Variable e in the summation. */
public final ArithmeticProgression E;
private Double value = null;
/** Constructor */
public Summation(ArithmeticProgression N, ArithmeticProgression E) {
if (N.getSteps() != E.getSteps()) {
throw new IllegalArgumentException("N.getSteps() != E.getSteps(),"
+ "\n N.getSteps()=" + N.getSteps() + ", N=" + N
+ "\n E.getSteps()=" + E.getSteps() + ", E=" + E);
}
this.N = N;
this.E = E;
}
/** Constructor */
Summation(long valueN, long deltaN,
long valueE, long deltaE, long limitE) {
this(valueN, deltaN, valueN - deltaN*((valueE - limitE)/deltaE),
valueE, deltaE, limitE);
}
/** Constructor */
Summation(long valueN, long deltaN, long limitN,
long valueE, long deltaE, long limitE) {
this(new ArithmeticProgression('n', valueN, deltaN, limitN),
new ArithmeticProgression('e', valueE, deltaE, limitE));
}
/** {@inheritDoc} */
@Override
public Summation getElement() {return this;}
/** Return the number of steps of this summation */
long getSteps() {return E.getSteps();}
/** Return the value of this summation */
public Double getValue() {return value;}
/** Set the value of this summation */
public void setValue(double v) {this.value = v;}
/** {@inheritDoc} */
@Override
public String toString() {
return "[" + N + "; " + E + (value == null? "]": "]value=" + Double.doubleToLongBits(value));
}
/** {@inheritDoc} */
@Override
public boolean equals(Object obj) {
if (obj == this)
return true;
if (obj != null && obj instanceof Summation) {
final Summation that = (Summation)obj;
return this.N.equals(that.N) && this.E.equals(that.E);
}
throw new IllegalArgumentException(obj == null? "obj == null":
"obj.getClass()=" + obj.getClass());
}
/** Not supported */
@Override
public int hashCode() {
throw new UnsupportedOperationException();
}
/** Covert a String to a Summation. */
public static Summation valueOf(final String s) {
int i = 1;
int j = s.indexOf("; ", i);
if (j < 0)
throw new IllegalArgumentException("i=" + i + ", j=" + j + " < 0, s=" + s);
final ArithmeticProgression N = ArithmeticProgression.valueOf(s.substring(i, j));
i = j + 2;
j = s.indexOf("]", i);
if (j < 0)
throw new IllegalArgumentException("i=" + i + ", j=" + j + " < 0, s=" + s);
final ArithmeticProgression E = ArithmeticProgression.valueOf(s.substring(i, j));
final Summation sigma = new Summation(N, E);
i = j + 1;
if (s.length() > i) {
final String value = Util.parseStringVariable("value", s.substring(i));
sigma.setValue(value.indexOf('.') < 0?
Double.longBitsToDouble(Long.parseLong(value)):
Double.parseDouble(value));
}
return sigma;
}
/** Compute the value of the summation. */
public double compute() {
if (value == null)
value = N.limit <= MAX_MODULAR? compute_modular(): compute_montgomery();
return value;
}
private static final long MAX_MODULAR = 1L << 32;
/** Compute the value using {@link Modular#mod(long, long)}. */
double compute_modular() {
long e = E.value;
long n = N.value;
double s = 0;
for(; e > E.limit; e += E.delta) {
s = Modular.addMod(s, Modular.mod(e, n)/(double)n);
n += N.delta;
}
return s;
}
final Montgomery montgomery = new Montgomery();
/** Compute the value using {@link Montgomery#mod(long)}. */
double compute_montgomery() {
long e = E.value;
long n = N.value;
double s = 0;
for(; e > E.limit; e += E.delta) {
s = Modular.addMod(s, montgomery.set(n).mod(e)/(double)n);
n += N.delta;
}
return s;
}
/** {@inheritDoc} */
@Override
public int compareTo(Summation that) {
final int de = this.E.compareTo(that.E);
if (de != 0) return de;
return this.N.compareTo(that.N);
}
/** {@inheritDoc} */
@Override
public Summation combine(Summation that) {
if (this.N.delta != that.N.delta || this.E.delta != that.E.delta)
throw new IllegalArgumentException(
"this.N.delta != that.N.delta || this.E.delta != that.E.delta"
+ ",\n this=" + this
+ ",\n that=" + that);
if (this.E.limit == that.E.value && this.N.limit == that.N.value) {
final double v = Modular.addMod(this.value, that.value);
final Summation s = new Summation(
new ArithmeticProgression(N.symbol, N.value, N.delta, that.N.limit),
new ArithmeticProgression(E.symbol, E.value, E.delta, that.E.limit));
s.setValue(v);
return s;
}
return null;
}
/** Find the remaining terms. */
public <T extends Container<Summation>> List<Summation> remainingTerms(List<T> sorted) {
final List<Summation> results = new ArrayList<Summation>();
Summation remaining = this;
if (sorted != null)
for(Container<Summation> c : sorted) {
final Summation sigma = c.getElement();
if (!remaining.contains(sigma))
throw new IllegalArgumentException("!remaining.contains(s),"
+ "\n remaining = " + remaining
+ "\n s = " + sigma
+ "\n this = " + this
+ "\n sorted = " + sorted);
final Summation s = new Summation(sigma.N.limit, N.delta, remaining.N.limit,
sigma.E.limit, E.delta, remaining.E.limit);
if (s.getSteps() > 0)
results.add(s);
remaining = new Summation(remaining.N.value, N.delta, sigma.N.value,
remaining.E.value, E.delta, sigma.E.value);
}
if (remaining.getSteps() > 0)
results.add(remaining);
return results;
}
/** Does this contains that? */
public boolean contains(Summation that) {
return this.N.contains(that.N) && this.E.contains(that.E);
}
/** Partition the summation. */
public Summation[] partition(final int nParts) {
final Summation[] parts = new Summation[nParts];
final long steps = (E.limit - E.value)/E.delta + 1;
long prevN = N.value;
long prevE = E.value;
for(int i = 1; i < parts.length; i++) {
final long k = (i * steps)/parts.length;
final long currN = N.skip(k);
final long currE = E.skip(k);
parts[i - 1] = new Summation(
new ArithmeticProgression(N.symbol, prevN, N.delta, currN),
new ArithmeticProgression(E.symbol, prevE, E.delta, currE));
prevN = currN;
prevE = currE;
}
parts[parts.length - 1] = new Summation(
new ArithmeticProgression(N.symbol, prevN, N.delta, N.limit),
new ArithmeticProgression(E.symbol, prevE, E.delta, E.limit));
return parts;
}
}