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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 .
*
*/
import java.math.BigInteger;
public class XorShiftPoly {
private XorShiftPoly() {}
/** The number of bits of state of the generator. */
public static int bits;
/** The period of the generator (2{@link #bits} − 1). */
public static BigInteger twoToBitsMinus1;
/** Factors of the Fermat “primes” up to the eleventh (22048 + 1). */
public static final BigInteger[] factor = {
new BigInteger("3"),
new BigInteger("5"),
new BigInteger("17"),
new BigInteger("257"),
new BigInteger("65537"),
new BigInteger("641"),
new BigInteger("6700417"),
new BigInteger("274177"),
new BigInteger("67280421310721"),
new BigInteger("59649589127497217"),
new BigInteger("5704689200685129054721"),
new BigInteger("1238926361552897"),
new BigInteger("93461639715357977769163558199606896584051237541638188580280321"),
new BigInteger("2424833"),
new BigInteger("7455602825647884208337395736200454918783366342657"),
new BigInteger("741640062627530801524787141901937474059940781097519023905821316144415759504705008092818711693940737"),
new BigInteger("45592577"),
new BigInteger("6487031809"),
new BigInteger("4659775785220018543264560743076778192897"),
new BigInteger("130439874405488189727484768796509903946608530841611892186895295776832416251471863574140227977573104895898783928842923844831149032913798729088601617946094119449010595906710130531906171018354491609619193912488538116080712299672322806217820753127014424577"),
new BigInteger("319489"),
new BigInteger("974849"),
new BigInteger("167988556341760475137"),
new BigInteger("3560841906445833920513"),
new BigInteger("173462447179147555430258970864309778377421844723664084649347019061363579192879108857591038330408837177983810868451546421940712978306134189864280826014542758708589243873685563973118948869399158545506611147420216132557017260564139394366945793220968665108959685482705388072645828554151936401912464931182546092879815733057795573358504982279280090942872567591518912118622751714319229788100979251036035496917279912663527358783236647193154777091427745377038294584918917590325110939381322486044298573971650711059244462177542540706913047034664643603491382441723306598834177")
};
/** An array of cofactors. Entry 0 ≤ {@code i} < {@link #numCofactors} contains {@link #twoToBitsMinus1} divided by {@link #factor factor[i]}. Note that some
* entries can be {@code null} if {@link #bits} is less then 4096. */
public static final BigInteger[] cofactor = new BigInteger[factor.length];
/** The actual number of valid entries in {@link #cofactor}. */
public static int numCofactors;
/** Computes the power to a given exponent, given the quadratures.
*
* @param e an exponent smaller than or equal to 2{@link #bits}.
*/
public static void mPow(BigInteger e) {
System.out.println("p := 1;");
for(int i = 0; ! e.equals(BigInteger.ZERO); i++) {
if (e.testBit(0)) System.out.println("p := *p * q[" + i + "];");
e = e.shiftRight(1);
}
}
public static void main(final String arg[]) {
bits = Integer.parseInt(arg[0]);
if (bits > 4096 || bits != Integer.highestOneBit(bits)) {
System.err.println("The number of bits must be a power of two smaller than or equal to 4096");
System.exit(1);
}
BigInteger result = BigInteger.ONE;
twoToBitsMinus1 = BigInteger.valueOf(2).pow(bits).subtract(BigInteger.ONE);
int n;
// Initialize cofactors.
for(n = 0; n < factor.length; n++) {
cofactor[n] = twoToBitsMinus1.divide(factor[n]);
result = result.multiply(factor[n]);
if (twoToBitsMinus1.equals(result)) break;
}
numCofactors = n + 1;
// Safety check (you know, those numbers are LONG).
if (! twoToBitsMinus1.equals(result)) throw new AssertionError();
System.out.println("Array q[" + (bits + 1) + "];");
// Quadratures
System.out.println("q[0] := x;");
for(int i1 = 1; i1 <= bits; i1++) System.out.println("q[" + i1 + "] := q[" + (i1 - 1) + "] * q[" + (i1 - 1) + "];");
System.out.println("!!('Check: ', if q[" + bits + "] = x then 1 else 0; &q fi);");
// Exponentiation to cofactors
for(int i = 0; i < numCofactors; i++) {
mPow(cofactor[i]);
System.out.println("!!('Result: ', if p = 1 then 0; &q else 1 fi);");
}
}
}
