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458 lines
14 KiB
Java
458 lines
14 KiB
Java
/*
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* Copyright 2009 Google Inc.
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*
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* Licensed under the Apache License, Version 2.0 (the "License"); you may not
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* use this file except in compliance with the License. You may obtain a copy of
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* the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
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* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
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* License for the specific language governing permissions and limitations under
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* the License.
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*/
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/*
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* Licensed to the Apache Software Foundation (ASF) under one or more
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* contributor license agreements. See the NOTICE file distributed with this
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* work for additional information regarding copyright ownership. The ASF
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* licenses this file to You under the Apache License, Version 2.0 (the
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* "License"); you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
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* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
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* License for the specific language governing permissions and limitations under
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* the License.
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*
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* INCLUDES MODIFICATIONS BY RICHARD ZSCHECH AS WELL AS GOOGLE.
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*/
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package java.math;
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/**
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* Static library that provides the basic arithmetic mutable operations for
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* {@link BigInteger}. The operations provided are listed below. <ul
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* type="circle"> <li>Addition.</li> <li>Subtraction.</li> <li>Comparison.</li>
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* </ul> In addition to this, some <i><b>Inplace</b></i> (mutable) methods are
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* provided.
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*/
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class Elementary {
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/**
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* @see BigInteger#add(BigInteger) .
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* @param op1
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* @param op2
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* @return
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*/
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static BigInteger add(BigInteger op1, BigInteger op2) {
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int resDigits[];
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int resSign;
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int op1Sign = op1.sign;
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int op2Sign = op2.sign;
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if (op1Sign == 0) {
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return op2;
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}
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if (op2Sign == 0) {
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return op1;
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}
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int op1Len = op1.numberLength;
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int op2Len = op2.numberLength;
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if (op1Len + op2Len == 2) {
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long a = (op1.digits[0] & 0xFFFFFFFFL);
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long b = (op2.digits[0] & 0xFFFFFFFFL);
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long res;
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int valueLo;
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int valueHi;
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if (op1Sign == op2Sign) {
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res = a + b;
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valueLo = (int) res;
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valueHi = (int) (res >>> 32);
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return ((valueHi == 0) ? new BigInteger(op1Sign, valueLo)
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: new BigInteger(op1Sign, 2, new int[] {valueLo, valueHi}));
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}
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return BigInteger.valueOf((op1Sign < 0) ? (b - a) : (a - b));
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} else if (op1Sign == op2Sign) {
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resSign = op1Sign;
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// an augend should not be shorter than addend
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resDigits = (op1Len >= op2Len) ? add(op1.digits, op1Len, op2.digits,
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op2Len) : add(op2.digits, op2Len, op1.digits, op1Len);
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} else { // signs are different
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int cmp = ((op1Len != op2Len) ? ((op1Len > op2Len) ? 1 : -1)
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: compareArrays(op1.digits, op2.digits, op1Len));
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if (cmp == BigInteger.EQUALS) {
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return BigInteger.ZERO;
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}
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// a minuend should not be shorter than subtrahend
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if (cmp == BigInteger.GREATER) {
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resSign = op1Sign;
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resDigits = subtract(op1.digits, op1Len, op2.digits, op2Len);
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} else {
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resSign = op2Sign;
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resDigits = subtract(op2.digits, op2Len, op1.digits, op1Len);
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}
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}
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BigInteger res = new BigInteger(resSign, resDigits.length, resDigits);
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res.cutOffLeadingZeroes();
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return res;
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}
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/**
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* Compares two arrays. All elements are treated as unsigned integers. The
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* magnitude is the bit chain of elements in big-endian order.
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*
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* @param a the first array
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* @param b the second array
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* @param size the size of arrays
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* @return 1 if a > b, -1 if a < b, 0 if a == b
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*/
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static int compareArrays(final int[] a, final int[] b, final int size) {
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int i;
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for (i = size - 1; (i >= 0) && (a[i] == b[i]); i--) {
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// empty
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}
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return ((i < 0) ? BigInteger.EQUALS
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: (a[i] & 0xFFFFFFFFL) < (b[i] & 0xFFFFFFFFL) ? BigInteger.LESS
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: BigInteger.GREATER);
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}
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/**
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* Same as @link #inplaceAdd(BigInteger, BigInteger), but without the
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* restriction of non-positive values.
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*
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* @param op1 any number
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* @param op2 any number
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*/
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static void completeInPlaceAdd(BigInteger op1, BigInteger op2) {
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if (op1.sign == 0) {
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System.arraycopy(op2.digits, 0, op1.digits, 0, op2.numberLength);
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} else if (op2.sign == 0) {
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return;
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} else if (op1.sign == op2.sign) {
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add(op1.digits, op1.digits, op1.numberLength, op2.digits,
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op2.numberLength);
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} else {
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int sign = unsignedArraysCompare(op1.digits, op2.digits,
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op1.numberLength, op2.numberLength);
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if (sign > 0) {
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subtract(op1.digits, op1.digits, op1.numberLength, op2.digits,
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op2.numberLength);
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} else {
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inverseSubtract(op1.digits, op1.digits, op1.numberLength, op2.digits,
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op2.numberLength);
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op1.sign = -op1.sign;
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}
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}
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op1.numberLength = Math.max(op1.numberLength, op2.numberLength) + 1;
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op1.cutOffLeadingZeroes();
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op1.unCache();
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}
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/**
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* Same as @link #inplaceSubtract(BigInteger, BigInteger), but without the
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* restriction of non-positive values.
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*
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* @param op1 should have enough space to save the result
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* @param op2
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*/
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static void completeInPlaceSubtract(BigInteger op1, BigInteger op2) {
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int resultSign = op1.compareTo(op2);
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if (op1.sign == 0) {
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System.arraycopy(op2.digits, 0, op1.digits, 0, op2.numberLength);
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op1.sign = -op2.sign;
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} else if (op1.sign != op2.sign) {
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add(op1.digits, op1.digits, op1.numberLength, op2.digits,
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op2.numberLength);
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op1.sign = resultSign;
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} else {
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int sign = unsignedArraysCompare(op1.digits, op2.digits,
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op1.numberLength, op2.numberLength);
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if (sign > 0) {
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subtract(op1.digits, op1.digits, op1.numberLength, op2.digits,
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op2.numberLength); // op1 = op1 - op2
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// op1.sign remains equal
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} else {
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inverseSubtract(op1.digits, op1.digits, op1.numberLength, op2.digits,
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op2.numberLength); // op1 = op2 - op1
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op1.sign = -op1.sign;
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}
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}
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op1.numberLength = Math.max(op1.numberLength, op2.numberLength) + 1;
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op1.cutOffLeadingZeroes();
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op1.unCache();
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}
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/**
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* Performs {@code op1 += op2}. {@code op1} must have enough place to store
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* the result (i.e. {@code op1.bitLength() >= op2.bitLength()}). Both should
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* be positive (i.e. {@code op1 >= op2}).
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*
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* @param op1 the input minuend, and the output result.
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* @param op2 the addend
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*/
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static void inplaceAdd(BigInteger op1, BigInteger op2) {
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// PRE: op1 >= op2 > 0
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add(op1.digits, op1.digits, op1.numberLength, op2.digits, op2.numberLength);
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op1.numberLength = Math.min(
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Math.max(op1.numberLength, op2.numberLength) + 1, op1.digits.length);
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op1.cutOffLeadingZeroes();
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op1.unCache();
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}
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/**
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* Performs: {@code op1 += addend}. The number must to have place to hold a
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* possible carry.
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*/
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static void inplaceAdd(BigInteger op1, final int addend) {
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int carry = inplaceAdd(op1.digits, op1.numberLength, addend);
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if (carry == 1) {
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op1.digits[op1.numberLength] = 1;
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op1.numberLength++;
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}
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op1.unCache();
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}
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/**
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* Adds an integer value to the array of integers remembering carry.
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*
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* @return a possible generated carry (0 or 1)
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*/
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static int inplaceAdd(int a[], final int aSize, final int addend) {
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long carry = addend & 0xFFFFFFFFL;
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for (int i = 0; (carry != 0) && (i < aSize); i++) {
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carry += a[i] & 0xFFFFFFFFL;
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a[i] = (int) carry;
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carry >>= 32;
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}
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return (int) carry;
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}
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/**
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* Performs {@code op1 -= op2}. {@code op1} must have enough place to store
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* the result (i.e. {@code op1.bitLength() >= op2.bitLength()}). Both should
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* be positive (what implies that {@code op1 >= op2}).
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*
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* @param op1 the input minuend, and the output result.
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* @param op2 the subtrahend
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*/
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static void inplaceSubtract(BigInteger op1, BigInteger op2) {
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// PRE: op1 >= op2 > 0
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subtract(op1.digits, op1.digits, op1.numberLength, op2.digits,
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op2.numberLength);
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op1.cutOffLeadingZeroes();
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op1.unCache();
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}
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/**
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* @see BigInteger#subtract(BigInteger) .
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* @param op1
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* @param op2
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* @return
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*/
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static BigInteger subtract(BigInteger op1, BigInteger op2) {
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int resSign;
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int resDigits[];
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int op1Sign = op1.sign;
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int op2Sign = op2.sign;
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if (op2Sign == 0) {
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return op1;
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}
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if (op1Sign == 0) {
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return op2.negate();
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}
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int op1Len = op1.numberLength;
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int op2Len = op2.numberLength;
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if (op1Len + op2Len == 2) {
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long a = (op1.digits[0] & 0xFFFFFFFFL);
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long b = (op2.digits[0] & 0xFFFFFFFFL);
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if (op1Sign < 0) {
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a = -a;
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}
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if (op2Sign < 0) {
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b = -b;
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}
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return BigInteger.valueOf(a - b);
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}
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int cmp = ((op1Len != op2Len) ? ((op1Len > op2Len) ? 1 : -1)
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: Elementary.compareArrays(op1.digits, op2.digits, op1Len));
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if (cmp == BigInteger.LESS) {
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resSign = -op2Sign;
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resDigits = (op1Sign == op2Sign) ? subtract(op2.digits, op2Len,
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op1.digits, op1Len) : add(op2.digits, op2Len, op1.digits, op1Len);
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} else {
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resSign = op1Sign;
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if (op1Sign == op2Sign) {
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if (cmp == BigInteger.EQUALS) {
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return BigInteger.ZERO;
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}
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resDigits = subtract(op1.digits, op1Len, op2.digits, op2Len);
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} else {
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resDigits = add(op1.digits, op1Len, op2.digits, op2Len);
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}
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}
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BigInteger res = new BigInteger(resSign, resDigits.length, resDigits);
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res.cutOffLeadingZeroes();
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return res;
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}
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/**
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* Addss the value represented by {@code b} to the value represented by
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* {@code a}. It is assumed the magnitude of a is not less than the magnitude
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* of b.
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*
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* @return {@code a + b}
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*/
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private static int[] add(int a[], int aSize, int b[], int bSize) {
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// PRE: a[] >= b[]
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int res[] = new int[aSize + 1];
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add(res, a, aSize, b, bSize);
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return res;
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}
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/**
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* Performs {@code res = a + b}.
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*/
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private static void add(int res[], int a[], int aSize, int b[], int bSize) {
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// PRE: a.length < max(aSize, bSize)
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int i;
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long carry = (a[0] & 0xFFFFFFFFL) + (b[0] & 0xFFFFFFFFL);
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res[0] = (int) carry;
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carry >>= 32;
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if (aSize >= bSize) {
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for (i = 1; i < bSize; i++) {
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carry += (a[i] & 0xFFFFFFFFL) + (b[i] & 0xFFFFFFFFL);
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res[i] = (int) carry;
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carry >>= 32;
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}
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for (; i < aSize; i++) {
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carry += a[i] & 0xFFFFFFFFL;
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res[i] = (int) carry;
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carry >>= 32;
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}
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} else {
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for (i = 1; i < aSize; i++) {
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carry += (a[i] & 0xFFFFFFFFL) + (b[i] & 0xFFFFFFFFL);
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res[i] = (int) carry;
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carry >>= 32;
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}
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for (; i < bSize; i++) {
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carry += b[i] & 0xFFFFFFFFL;
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res[i] = (int) carry;
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carry >>= 32;
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}
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}
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if (carry != 0) {
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res[i] = (int) carry;
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}
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}
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/**
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* Performs {@code res = b - a}.
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*/
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private static void inverseSubtract(int res[], int a[], int aSize, int b[],
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int bSize) {
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int i;
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long borrow = 0;
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if (aSize < bSize) {
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for (i = 0; i < aSize; i++) {
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borrow += (b[i] & 0xFFFFFFFFL) - (a[i] & 0xFFFFFFFFL);
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res[i] = (int) borrow;
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borrow >>= 32; // -1 or 0
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}
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for (; i < bSize; i++) {
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borrow += b[i] & 0xFFFFFFFFL;
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res[i] = (int) borrow;
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borrow >>= 32; // -1 or 0
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}
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} else {
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for (i = 0; i < bSize; i++) {
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borrow += (b[i] & 0xFFFFFFFFL) - (a[i] & 0xFFFFFFFFL);
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res[i] = (int) borrow;
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borrow >>= 32; // -1 or 0
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}
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for (; i < aSize; i++) {
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borrow -= a[i] & 0xFFFFFFFFL;
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res[i] = (int) borrow;
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borrow >>= 32; // -1 or 0
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}
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}
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}
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/**
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* Subtracts the value represented by {@code b} from the value represented by
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* {@code a}. It is assumed the magnitude of a is not less than the magnitude
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* of b.
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*
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* @return {@code a - b}
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*/
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private static int[] subtract(int a[], int aSize, int b[], int bSize) {
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// PRE: a[] >= b[]
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int res[] = new int[aSize];
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subtract(res, a, aSize, b, bSize);
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return res;
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}
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/**
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* Performs {@code res = a - b}. It is assumed the magnitude of a is not less
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* than the magnitude of b.
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*/
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private static void subtract(int res[], int a[], int aSize, int b[], int bSize) {
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// PRE: a[] >= b[]
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int i;
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long borrow = 0;
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for (i = 0; i < bSize; i++) {
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borrow += (a[i] & 0xFFFFFFFFL) - (b[i] & 0xFFFFFFFFL);
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res[i] = (int) borrow;
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borrow >>= 32; // -1 or 0
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}
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for (; i < aSize; i++) {
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borrow += a[i] & 0xFFFFFFFFL;
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res[i] = (int) borrow;
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borrow >>= 32; // -1 or 0
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}
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}
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/**
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* Compares two arrays, representing unsigned integer in little-endian order.
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* Returns +1,0,-1 if a is - respective - greater, equal or lesser then b
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*/
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private static int unsignedArraysCompare(int[] a, int[] b, int aSize,
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int bSize) {
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if (aSize > bSize) {
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return 1;
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} else if (aSize < bSize) {
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return -1;
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} else {
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int i;
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for (i = aSize - 1; i >= 0 && a[i] == b[i]; i--) {
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// empty
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}
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return i < 0 ? BigInteger.EQUALS
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: ((a[i] & 0xFFFFFFFFL) < (b[i] & 0xFFFFFFFFL) ? BigInteger.LESS
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: BigInteger.GREATER);
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}
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}
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/**
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* Just to denote that this class can't be instantiated.
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*/
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private Elementary() {
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}
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}
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