252 lines
13 KiB
Java
252 lines
13 KiB
Java
/*
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* Copyright (c) 2018, Oracle and/or its affiliates. All rights reserved.
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* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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*
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* This code is free software; you can redistribute it and/or modify it
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* under the terms of the GNU General Public License version 2 only, as
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* published by the Free Software Foundation. Oracle designates this
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* particular file as subject to the "Classpath" exception as provided
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* by Oracle in the LICENSE file that accompanied this code.
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*
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* This code is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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* version 2 for more details (a copy is included in the LICENSE file that
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* accompanied this code).
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*
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* You should have received a copy of the GNU General Public License version
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* 2 along with this work; if not, write to the Free Software Foundation,
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* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
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*
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* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
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* or visit www.oracle.com if you need additional information or have any
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* questions.
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*/
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package sun.security.util.math.intpoly;
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import java.math.BigInteger;
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/**
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* An IntegerFieldModuloP designed for use with the Curve448.
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* The representation uses 16 signed long values.
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*/
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public class IntegerPolynomial448 extends IntegerPolynomial {
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private static final int POWER = 448;
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private static final int NUM_LIMBS = 16;
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private static final int BITS_PER_LIMB = 28;
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public static final BigInteger MODULUS
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= TWO.pow(POWER).subtract(TWO.pow(POWER / 2))
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.subtract(BigInteger.valueOf(1));
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public IntegerPolynomial448() {
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super(BITS_PER_LIMB, NUM_LIMBS, 1, MODULUS);
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}
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private void modReduceIn(long[] limbs, int index, long x) {
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limbs[index - NUM_LIMBS] += x;
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limbs[index - NUM_LIMBS / 2] += x;
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}
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@Override
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protected void finalCarryReduceLast(long[] limbs) {
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long carry = limbs[numLimbs - 1] >> bitsPerLimb;
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limbs[numLimbs - 1] -= carry << bitsPerLimb;
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modReduceIn(limbs, numLimbs, carry);
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}
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@Override
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protected void reduce(long[] a) {
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// carry(14, 2)
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long carry14 = carryValue(a[14]);
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a[14] -= (carry14 << BITS_PER_LIMB);
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a[15] += carry14;
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long carry15 = carryValue(a[15]);
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a[15] -= (carry15 << BITS_PER_LIMB);
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// reduce(0, 1)
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a[0] += carry15;
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a[8] += carry15;
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// carry(0, 15)
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carry(a, 0, 15);
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}
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@Override
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protected void mult(long[] a, long[] b, long[] r) {
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// Use grade-school multiplication into primitives to avoid the
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// temporary array allocation. This is equivalent to the following
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// code:
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// long[] c = new long[2 * NUM_LIMBS - 1];
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// for(int i = 0; i < NUM_LIMBS; i++) {
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// for(int j - 0; j < NUM_LIMBS; j++) {
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// c[i + j] += a[i] * b[j]
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// }
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// }
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long c0 = (a[0] * b[0]);
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long c1 = (a[0] * b[1]) + (a[1] * b[0]);
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long c2 = (a[0] * b[2]) + (a[1] * b[1]) + (a[2] * b[0]);
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long c3 = (a[0] * b[3]) + (a[1] * b[2]) + (a[2] * b[1]) + (a[3] * b[0]);
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long c4 = (a[0] * b[4]) + (a[1] * b[3]) + (a[2] * b[2]) + (a[3] * b[1]) + (a[4] * b[0]);
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long c5 = (a[0] * b[5]) + (a[1] * b[4]) + (a[2] * b[3]) + (a[3] * b[2]) + (a[4] * b[1]) + (a[5] * b[0]);
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long c6 = (a[0] * b[6]) + (a[1] * b[5]) + (a[2] * b[4]) + (a[3] * b[3]) + (a[4] * b[2]) + (a[5] * b[1]) + (a[6] * b[0]);
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long c7 = (a[0] * b[7]) + (a[1] * b[6]) + (a[2] * b[5]) + (a[3] * b[4]) + (a[4] * b[3]) + (a[5] * b[2]) + (a[6] * b[1]) + (a[7] * b[0]);
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long c8 = (a[0] * b[8]) + (a[1] * b[7]) + (a[2] * b[6]) + (a[3] * b[5]) + (a[4] * b[4]) + (a[5] * b[3]) + (a[6] * b[2]) + (a[7] * b[1]) + (a[8] * b[0]);
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long c9 = (a[0] * b[9]) + (a[1] * b[8]) + (a[2] * b[7]) + (a[3] * b[6]) + (a[4] * b[5]) + (a[5] * b[4]) + (a[6] * b[3]) + (a[7] * b[2]) + (a[8] * b[1]) + (a[9] * b[0]);
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long c10 = (a[0] * b[10]) + (a[1] * b[9]) + (a[2] * b[8]) + (a[3] * b[7]) + (a[4] * b[6]) + (a[5] * b[5]) + (a[6] * b[4]) + (a[7] * b[3]) + (a[8] * b[2]) + (a[9] * b[1]) + (a[10] * b[0]);
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long c11 = (a[0] * b[11]) + (a[1] * b[10]) + (a[2] * b[9]) + (a[3] * b[8]) + (a[4] * b[7]) + (a[5] * b[6]) + (a[6] * b[5]) + (a[7] * b[4]) + (a[8] * b[3]) + (a[9] * b[2]) + (a[10] * b[1]) + (a[11] * b[0]);
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long c12 = (a[0] * b[12]) + (a[1] * b[11]) + (a[2] * b[10]) + (a[3] * b[9]) + (a[4] * b[8]) + (a[5] * b[7]) + (a[6] * b[6]) + (a[7] * b[5]) + (a[8] * b[4]) + (a[9] * b[3]) + (a[10] * b[2]) + (a[11] * b[1]) + (a[12] * b[0]);
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long c13 = (a[0] * b[13]) + (a[1] * b[12]) + (a[2] * b[11]) + (a[3] * b[10]) + (a[4] * b[9]) + (a[5] * b[8]) + (a[6] * b[7]) + (a[7] * b[6]) + (a[8] * b[5]) + (a[9] * b[4]) + (a[10] * b[3]) + (a[11] * b[2]) + (a[12] * b[1]) + (a[13] * b[0]);
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long c14 = (a[0] * b[14]) + (a[1] * b[13]) + (a[2] * b[12]) + (a[3] * b[11]) + (a[4] * b[10]) + (a[5] * b[9]) + (a[6] * b[8]) + (a[7] * b[7]) + (a[8] * b[6]) + (a[9] * b[5]) + (a[10] * b[4]) + (a[11] * b[3]) + (a[12] * b[2]) + (a[13] * b[1]) + (a[14] * b[0]);
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long c15 = (a[0] * b[15]) + (a[1] * b[14]) + (a[2] * b[13]) + (a[3] * b[12]) + (a[4] * b[11]) + (a[5] * b[10]) + (a[6] * b[9]) + (a[7] * b[8]) + (a[8] * b[7]) + (a[9] * b[6]) + (a[10] * b[5]) + (a[11] * b[4]) + (a[12] * b[3]) + (a[13] * b[2]) + (a[14] * b[1]) + (a[15] * b[0]);
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long c16 = (a[1] * b[15]) + (a[2] * b[14]) + (a[3] * b[13]) + (a[4] * b[12]) + (a[5] * b[11]) + (a[6] * b[10]) + (a[7] * b[9]) + (a[8] * b[8]) + (a[9] * b[7]) + (a[10] * b[6]) + (a[11] * b[5]) + (a[12] * b[4]) + (a[13] * b[3]) + (a[14] * b[2]) + (a[15] * b[1]);
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long c17 = (a[2] * b[15]) + (a[3] * b[14]) + (a[4] * b[13]) + (a[5] * b[12]) + (a[6] * b[11]) + (a[7] * b[10]) + (a[8] * b[9]) + (a[9] * b[8]) + (a[10] * b[7]) + (a[11] * b[6]) + (a[12] * b[5]) + (a[13] * b[4]) + (a[14] * b[3]) + (a[15] * b[2]);
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long c18 = (a[3] * b[15]) + (a[4] * b[14]) + (a[5] * b[13]) + (a[6] * b[12]) + (a[7] * b[11]) + (a[8] * b[10]) + (a[9] * b[9]) + (a[10] * b[8]) + (a[11] * b[7]) + (a[12] * b[6]) + (a[13] * b[5]) + (a[14] * b[4]) + (a[15] * b[3]);
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long c19 = (a[4] * b[15]) + (a[5] * b[14]) + (a[6] * b[13]) + (a[7] * b[12]) + (a[8] * b[11]) + (a[9] * b[10]) + (a[10] * b[9]) + (a[11] * b[8]) + (a[12] * b[7]) + (a[13] * b[6]) + (a[14] * b[5]) + (a[15] * b[4]);
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long c20 = (a[5] * b[15]) + (a[6] * b[14]) + (a[7] * b[13]) + (a[8] * b[12]) + (a[9] * b[11]) + (a[10] * b[10]) + (a[11] * b[9]) + (a[12] * b[8]) + (a[13] * b[7]) + (a[14] * b[6]) + (a[15] * b[5]);
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long c21 = (a[6] * b[15]) + (a[7] * b[14]) + (a[8] * b[13]) + (a[9] * b[12]) + (a[10] * b[11]) + (a[11] * b[10]) + (a[12] * b[9]) + (a[13] * b[8]) + (a[14] * b[7]) + (a[15] * b[6]);
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long c22 = (a[7] * b[15]) + (a[8] * b[14]) + (a[9] * b[13]) + (a[10] * b[12]) + (a[11] * b[11]) + (a[12] * b[10]) + (a[13] * b[9]) + (a[14] * b[8]) + (a[15] * b[7]);
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long c23 = (a[8] * b[15]) + (a[9] * b[14]) + (a[10] * b[13]) + (a[11] * b[12]) + (a[12] * b[11]) + (a[13] * b[10]) + (a[14] * b[9]) + (a[15] * b[8]);
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long c24 = (a[9] * b[15]) + (a[10] * b[14]) + (a[11] * b[13]) + (a[12] * b[12]) + (a[13] * b[11]) + (a[14] * b[10]) + (a[15] * b[9]);
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long c25 = (a[10] * b[15]) + (a[11] * b[14]) + (a[12] * b[13]) + (a[13] * b[12]) + (a[14] * b[11]) + (a[15] * b[10]);
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long c26 = (a[11] * b[15]) + (a[12] * b[14]) + (a[13] * b[13]) + (a[14] * b[12]) + (a[15] * b[11]);
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long c27 = (a[12] * b[15]) + (a[13] * b[14]) + (a[14] * b[13]) + (a[15] * b[12]);
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long c28 = (a[13] * b[15]) + (a[14] * b[14]) + (a[15] * b[13]);
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long c29 = (a[14] * b[15]) + (a[15] * b[14]);
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long c30 = (a[15] * b[15]);
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carryReduce(r, c0, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12,
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c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25,
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c26, c27, c28, c29, c30);
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}
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private void carryReduce(long[] r, long c0, long c1, long c2, long c3,
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long c4, long c5, long c6, long c7, long c8,
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long c9, long c10, long c11, long c12, long c13,
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long c14, long c15, long c16, long c17, long c18,
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long c19, long c20, long c21, long c22, long c23,
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long c24, long c25, long c26, long c27, long c28,
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long c29, long c30) {
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// reduce(8, 7)
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c8 += c24;
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c16 += c24;
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c9 += c25;
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c17 += c25;
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c10 += c26;
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c18 += c26;
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c11 += c27;
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c19 += c27;
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c12 += c28;
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c20 += c28;
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c13 += c29;
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c21 += c29;
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c14 += c30;
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c22 += c30;
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// reduce(4, 4)
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r[4] = c4 + c20;
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r[12] = c12 + c20;
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r[5] = c5 + c21;
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r[13] = c13 + c21;
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r[6] = c6 + c22;
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c14 += c22;
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r[7] = c7 + c23;
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c15 += c23;
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//carry(14, 2)
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long carry14 = carryValue(c14);
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r[14] = c14 - (carry14 << BITS_PER_LIMB);
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c15 += carry14;
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long carry15 = carryValue(c15);
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r[15] = c15 - (carry15 << BITS_PER_LIMB);
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c16 += carry15;
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// reduce(0, 4)
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r[0] = c0 + c16;
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r[8] = c8 + c16;
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r[1] = c1 + c17;
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r[9] = c9 + c17;
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r[2] = c2 + c18;
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r[10] = c10 + c18;
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r[3] = c3 + c19;
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r[11] = c11 + c19;
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// carry(0, 15)
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carry(r, 0, 15);
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}
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@Override
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protected void square(long[] a, long[] r) {
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// Use grade-school multiplication with a simple squaring optimization.
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// Multiply into primitives to avoid the temporary array allocation.
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// This is equivalent to the following code:
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// long[] c = new long[2 * NUM_LIMBS - 1];
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// for(int i = 0; i < NUM_LIMBS; i++) {
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// c[2 * i] = a[i] * a[i];
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// for(int j = i + 1; j < NUM_LIMBS; j++) {
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// c[i + j] += 2 * a[i] * a[j]
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// }
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// }
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long c0 = a[0] * a[0];
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long c1 = 2 * a[0] * a[1];
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long c2 = a[1] * a[1] + 2 * a[0] * a[2];
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long c3 = 2 * (a[0] * a[3] + a[1] * a[2]);
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long c4 = a[2] * a[2] + 2 * (a[0] * a[4] + a[1] * a[3]);
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long c5 = 2 * (a[0] * a[5] + a[1] * a[4] + a[2] * a[3]);
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long c6 = a[3] * a[3] + 2 * (a[0] * a[6] + a[1] * a[5] + a[2] * a[4]);
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long c7 = 2 * (a[0] * a[7] + a[1] * a[6] + a[2] * a[5] + a[3] * a[4]);
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long c8 = a[4] * a[4] + 2 * (a[0] * a[8] + a[1] * a[7] + a[2] * a[6] + a[3] * a[5]);
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long c9 = 2 * (a[0] * a[9] + a[1] * a[8] + a[2] * a[7] + a[3] * a[6] + a[4] * a[5]);
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long c10 = a[5] * a[5] + 2 * (a[0] * a[10] + a[1] * a[9] + a[2] * a[8] + a[3] * a[7] + a[4] * a[6]);
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long c11 = 2 * (a[0] * a[11] + a[1] * a[10] + a[2] * a[9] + a[3] * a[8] + a[4] * a[7] + a[5] * a[6]);
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long c12 = a[6] * a[6] + 2 * (a[0] * a[12] + a[1] * a[11] + a[2] * a[10] + a[3] * a[9] + a[4] * a[8] + a[5] * a[7]);
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long c13 = 2 * (a[0] * a[13] + a[1] * a[12] + a[2] * a[11] + a[3] * a[10] + a[4] * a[9] + a[5] * a[8] + a[6] * a[7]);
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long c14 = a[7] * a[7] + 2 * (a[0] * a[14] + a[1] * a[13] + a[2] * a[12] + a[3] * a[11] + a[4] * a[10] + a[5] * a[9] + a[6] * a[8]);
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long c15 = 2 * (a[0] * a[15] + a[1] * a[14] + a[2] * a[13] + a[3] * a[12] + a[4] * a[11] + a[5] * a[10] + a[6] * a[9] + a[7] * a[8]);
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long c16 = a[8] * a[8] + 2 * (a[1] * a[15] + a[2] * a[14] + a[3] * a[13] + a[4] * a[12] + a[5] * a[11] + a[6] * a[10] + a[7] * a[9]);
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long c17 = 2 * (a[2] * a[15] + a[3] * a[14] + a[4] * a[13] + a[5] * a[12] + a[6] * a[11] + a[7] * a[10] + a[8] * a[9]);
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long c18 = a[9] * a[9] + 2 * (a[3] * a[15] + a[4] * a[14] + a[5] * a[13] + a[6] * a[12] + a[7] * a[11] + a[8] * a[10]);
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long c19 = 2 * (a[4] * a[15] + a[5] * a[14] + a[6] * a[13] + a[7] * a[12] + a[8] * a[11] + a[9] * a[10]);
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long c20 = a[10] * a[10] + 2 * (a[5] * a[15] + a[6] * a[14] + a[7] * a[13] + a[8] * a[12] + a[9] * a[11]);
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long c21 = 2 * (a[6] * a[15] + a[7] * a[14] + a[8] * a[13] + a[9] * a[12] + a[10] * a[11]);
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long c22 = a[11] * a[11] + 2 * (a[7] * a[15] + a[8] * a[14] + a[9] * a[13] + a[10] * a[12]);
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long c23 = 2 * (a[8] * a[15] + a[9] * a[14] + a[10] * a[13] + a[11] * a[12]);
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long c24 = a[12] * a[12] + 2 * (a[9] * a[15] + a[10] * a[14] + a[11] * a[13]);
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long c25 = 2 * (a[10] * a[15] + a[11] * a[14] + a[12] * a[13]);
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long c26 = a[13] * a[13] + 2 * (a[11] * a[15] + a[12] * a[14]);
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long c27 = 2 * (a[12] * a[15] + a[13] * a[14]);
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long c28 = a[14] * a[14] + 2 * a[13] * a[15];
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long c29 = 2 * a[14] * a[15];
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long c30 = a[15] * a[15];
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carryReduce(r, c0, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12,
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c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25,
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c26, c27, c28, c29, c30);
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}
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}
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