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The DSI utilities are a mishmash of classes accumulated during the last twenty years in projects developed at the DSI (Dipartimento di Scienze dell'Informazione, i.e., Information Sciences Department), now DI (Dipartimento di Informatica, i.e., Informatics Department), of the Universita` degli Studi di Milano.
package it.unimi.dsi.test;
/*
* Copyright (C) 2014-2020 Sebastiano Vigna
*
* This program is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License as published by the Free
* Software Foundation; either version 3 of the License, or (at your option)
* any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, see x2i (0 ≤ {@code i} ≤ {@link #BITS}).
* @see #newMatrix(int)
*/
public static long[][][] quad(long[][] x) {
final long[][][] result = new long[BITS + 1][][];
result[0] = x;
//ProgressLogger progressLogger = new ProgressLogger(LOGGER, "quadratures");
//progressLogger.expectedUpdates = 4095;
//progressLogger.displayLocalSpeed = true;
//progressLogger.start("Starting quadratures...");
for(int i = 1; i <= BITS; i++) {
result[i] = multiply(result[i - 1], result[i - 1]);
//progressLogger.update();
}
//progressLogger.done();
return result;
}
/** Returns the identity matrix in compact representation.
*
* @return a compact representation of the identity.
* @see #newMatrix(int)
*/
public static long[][] identity() {
final long[][] m = newMatrix(BITS);
for(int i = 64; i-- != 0;) m[i][0] = 1L << i;
for(int i = 64; i-- != 0;) m[BITS - 64 + i][BITS / 64 - 1] = 1L << i;
return m;
}
/** Checks whether a specified matrix in compact representation is the identity.
*
* @return true if {@code m} is the identity matrix.
* @see #newMatrix(int)
*/
public static boolean isIdentity(final long[][] m) {
for(int r = 64; r-- != 0;) if (m[r][0] != 1L << r) return false;
for(int cw = 1; cw < BITS / 64; cw++)
for(int r = 64; r-- != 0;) if (m[r][cw] != 0) return false;
for(int r = 64; r < BITS - 64; r++) if (m[r][0] != 0) return false;
for(int r = 64; r-- != 0;) if (m[BITS - 64 + r][BITS / 64 - 1] != 1L << r) return false;
for(int cw = 0; cw < BITS / 64 - 1; cw++)
for(int r = 64; r-- != 0;) if (m[BITS - 64 + r][cw] != 0) return false;
return true;
}
/** Computes the power of a matrix to a given exponent, given the quadratures of the matrix.
*
* @param q the quadratures of some matrix as returned by {@link #quad(long[][])}.
* @param e an exponent smaller than or equal to 2{@link #BITS}.
* @return the matrix whose array of quadratures is {@code q} raised to exponent {@code e}.
* @see #newMatrix(int)
*/
public static long[][] mPow(long[][][] q, BigInteger e) {
long[][] r = identity();
for(int i = 0; ! e.equals(BigInteger.ZERO); i++) {
if (e.testBit(0)) r = multiply(r, q[i]);
e = e.shiftRight(1);
}
return r;
}
/** Checks whether a specified matrix in compact representation has full period.
*
* @param m a matrix in compact representation.
* @return true of {@code m} has full period (i.e., 2{@link #BITS} − 1).
* @see #newMatrix(int)
*/
public static boolean isFull(long[][] m) {
final long[][][] q = quad(m);
if (! Arrays.deepEquals(m, q[BITS])) {
System.err.println("Does not give the identity");;
return false;
}
for(int i = 0; i < numCofactors; i++) {
if (isIdentity(mPow(q, cofactor[i]))){
System.err.println("Gives the identity on cofactor " + cofactor[i]);
return false;
}
}
return true;
}
/** Creates a matrix in compact form representing a xorshift generator as suggested by Marsaglia
* in “Xorshift RNGs”,
* Journal of Statistical Software, 8:1−6, 2003.
*
* @param a the first shift parameter.
* @param b the second shift parameter.
* @param c the third shift parameter.
* @param bits the number of bits in a row.
* @return a matrix representing a xorshift generator with specified parameters and number of bits.
* @see #newMatrix(int)
*/
public static long[][] makeABCMatrix(final int a, final int b , final int c, final int bits) {
final long[][] m = XorShift.newMatrix(bits);
final long[] top = multiply(left[a], right[b]);
for(int i = 64; i-- != 0;) m[i][bits / 64 - 1] = top[i];
for(int i = 64; i-- != 0;) m[bits - 64 + i][bits / 64 - 1] = right[c][i];
for(int i = 64; i-- != 0;) m[bits - 64 + i][bits / 64 - 2] = 1L << i;
for(int i = 64; i-- != 0;) m[64 + i][0] = 1L << i;
return m;
}
public final static class Compute implements Runnable {
final int a, b, c;
public Compute(int a, int b, int c) {
this.a = a;
this.b = b;
this.c = c;
}
@Override
public void run() {
final long[][] m = makeABCMatrix(a, b, c, BITS);
System.out.println(a + " " + b + " " + c + " " + isFull(m));
}
}
public static void main(final String arg[]) {
if (arg.length > 0) throw new IllegalArgumentException("This command takes no arguments (BITS=" + BITS + ")");
final ExecutorService exec = Executors.newFixedThreadPool(Runtime.getRuntime().availableProcessors());
for(int a = 1; a < 64; a++) {
for(int b = 1; b <= 64 - a; b++) {
// Only pairs a+b<=64 such that a and b are coprime.
if (BigInteger.valueOf(a).gcd(BigInteger.valueOf(b)).intValue() != 1) continue;
for(int c = 1; c < 64; c++) exec.execute(new Compute(a, b, c));
}
}
exec.shutdown();
}
}