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/*
* Copyright 2011 Phil Burk, Mobileer Inc
*
* Licensed 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 com.softsynth.math;
import java.util.ArrayList;
/**
* Tool for factoring primes and prime ratios. This class contains a static array of primes
* generated using the Sieve of Eratosthenes.
*
* @author Phil Burk (C) 2011 Mobileer Inc
*/
public class PrimeFactors {
private static final int SIEVE_SIZE = 1000;
private static int[] primes;
private final int[] factors;
static {
// Use Sieve of Eratosthenes to fill Prime table
boolean[] sieve = new boolean[SIEVE_SIZE];
ArrayList<Integer> primeList = new ArrayList<Integer>();
int i = 2;
while (i < (SIEVE_SIZE / 2)) {
if (!sieve[i]) {
primeList.add(i);
int multiple = 2 * i;
while (multiple < SIEVE_SIZE) {
sieve[multiple] = true;
multiple += i;
}
}
i += 1;
}
primes = primeListToArray(primeList);
}
private static int[] primeListToArray(ArrayList<Integer> primeList) {
int[] primes = new int[primeList.size()];
for (int i = 0; i < primes.length; i++) {
primes[i] = primeList.get(i);
}
return primes;
}
public PrimeFactors(int[] factors) {
this.factors = factors;
}
public PrimeFactors(int numerator, int denominator) {
int[] topFactors = factor(numerator);
int[] bottomFactors = factor(denominator);
factors = subtract(topFactors, bottomFactors);
}
public PrimeFactors subtract(PrimeFactors pf) {
return new PrimeFactors(subtract(factors, pf.factors));
}
public PrimeFactors add(PrimeFactors pf) {
return new PrimeFactors(add(factors, pf.factors));
}
public static int[] subtract(int[] factorsA, int[] factorsB) {
int max;
int min;
if (factorsA.length > factorsB.length) {
max = factorsA.length;
min = factorsB.length;
} else {
min = factorsA.length;
max = factorsB.length;
}
ArrayList<Integer> primeList = new ArrayList<Integer>();
int i;
for (i = 0; i < min; i++) {
primeList.add(factorsA[i] - factorsB[i]);
}
if (factorsA.length > factorsB.length) {
for (; i < max; i++) {
primeList.add(factorsA[i]);
}
} else {
for (; i < max; i++) {
primeList.add(0 - factorsB[i]);
}
}
trimPrimeList(primeList);
return primeListToArray(primeList);
}
public static int[] add(int[] factorsA, int[] factorsB) {
int max;
int min;
if (factorsA.length > factorsB.length) {
max = factorsA.length;
min = factorsB.length;
} else {
min = factorsA.length;
max = factorsB.length;
}
ArrayList<Integer> primeList = new ArrayList<Integer>();
int i;
for (i = 0; i < min; i++) {
primeList.add(factorsA[i] + factorsB[i]);
}
if (factorsA.length > factorsB.length) {
for (; i < max; i++) {
primeList.add(factorsA[i]);
}
} else if (factorsB.length > factorsA.length) {
for (; i < max; i++) {
primeList.add(factorsB[i]);
}
}
trimPrimeList(primeList);
return primeListToArray(primeList);
}
private static void trimPrimeList(ArrayList<Integer> primeList) {
int i;
// trim zero factors off end.
for (i = primeList.size() - 1; i >= 0; i--) {
if (primeList.get(i) == 0) {
primeList.remove(i);
} else {
break;
}
}
}
public static int[] factor(int n) {
ArrayList<Integer> primeList = new ArrayList<Integer>();
int i = 0;
int p = primes[i];
int exponent = 0;
while (n > 1) {
// does the prime number divide evenly into n?
int d = n / p;
int m = d * p;
if (m == n) {
n = d;
exponent += 1;
} else {
primeList.add(exponent);
exponent = 0;
i += 1;
p = primes[i];
}
}
if (exponent > 0) {
primeList.add(exponent);
}
return primeListToArray(primeList);
}
/**
* Get prime from table.
*
*
* @param n Warning: Do not exceed getPrimeCount()-1.
* @return Nth prime number, the 0th prime is 2
*/
public static int getPrime(int n) {
return primes[n];
}
/**
* @return the number of primes stored in the table
*/
public static int getPrimeCount() {
return primes.length;
}
public JustRatio getJustRatio() {
long n = 1;
long d = 1;
for (int i = 0; i < factors.length; i++) {
int exponent = factors[i];
int p = primes[i];
if (exponent > 0) {
for (int k = 0; k < exponent; k++) {
n = n * p;
}
} else if (exponent < 0) {
exponent = 0 - exponent;
for (int k = 0; k < exponent; k++) {
d = d * p;
}
}
}
return new JustRatio(n, d);
}
public int[] getFactors() {
return factors.clone();
}
@Override
public String toString() {
StringBuffer buffer = new StringBuffer();
printFactors(buffer, 1);
buffer.append("/");
printFactors(buffer, -1);
return buffer.toString();
}
private void printFactors(StringBuffer buffer, int sign) {
boolean gotSome = false;
for (int i = 0; i < factors.length; i++) {
int pf = factors[i] * sign;
if (pf > 0) {
if (gotSome)
buffer.append('*');
int prime = primes[i];
if (pf == 1) {
buffer.append("" + prime);
} else if (pf == 2) {
buffer.append(prime + "*" + prime);
} else if (pf > 2) {
buffer.append("(" + prime + "^" + pf + ")");
}
gotSome = true;
}
}
if (!gotSome) {
buffer.append("1");
}
}
}
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