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https://github.com/moparisthebest/mailiverse
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927 lines
28 KiB
Java
927 lines
28 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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* The library implements some logical operations over {@code BigInteger}. The
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* operations provided are listed below. <ul type="circle"> <li>not</li> <li>and
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* </li> <li>andNot</li> <li>or</li> <li>xor</li> </ul>
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*/
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class Logical {
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/**
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* @see BigInteger#and(BigInteger)
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* @param val
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* @param that
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* @return
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*/
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static BigInteger and(BigInteger val, BigInteger that) {
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if (that.sign == 0 || val.sign == 0) {
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return BigInteger.ZERO;
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}
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if (that.equals(BigInteger.MINUS_ONE)) {
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return val;
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}
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if (val.equals(BigInteger.MINUS_ONE)) {
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return that;
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}
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if (val.sign > 0) {
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if (that.sign > 0) {
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return andPositive(val, that);
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} else {
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return andDiffSigns(val, that);
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}
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} else {
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if (that.sign > 0) {
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return andDiffSigns(that, val);
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} else if (val.numberLength > that.numberLength) {
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return andNegative(val, that);
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} else {
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return andNegative(that, val);
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}
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}
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}
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/**
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* Return sign = positive.magnitude & magnitude = -negative.magnitude.
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* @param positive
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* @param negative
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* @return
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*/
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static BigInteger andDiffSigns(BigInteger positive, BigInteger negative) {
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// PRE: positive is positive and negative is negative
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int iPos = positive.getFirstNonzeroDigit();
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int iNeg = negative.getFirstNonzeroDigit();
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// Look if the trailing zeros of the negative will "blank" all
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// the positive digits
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if (iNeg >= positive.numberLength) {
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return BigInteger.ZERO;
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}
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int resLength = positive.numberLength;
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int resDigits[] = new int[resLength];
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// Must start from max(iPos, iNeg)
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int i = Math.max(iPos, iNeg);
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if (i == iNeg) {
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resDigits[i] = -negative.digits[i] & positive.digits[i];
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i++;
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}
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int limit = Math.min(negative.numberLength, positive.numberLength);
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for (; i < limit; i++) {
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resDigits[i] = ~negative.digits[i] & positive.digits[i];
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}
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// if the negative was shorter must copy the remaining digits
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// from positive
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if (i >= negative.numberLength) {
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for (; i < positive.numberLength; i++) {
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resDigits[i] = positive.digits[i];
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}
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} // else positive ended and must "copy" virtual 0's, do nothing then
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BigInteger result = new BigInteger(1, resLength, resDigits);
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result.cutOffLeadingZeroes();
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return result;
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}
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/**
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* Return sign = -1, magnitude = -(-longer.magnitude & -shorter.magnitude).
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* @param longer
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* @param shorter
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* @return
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*/
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static BigInteger andNegative(BigInteger longer, BigInteger shorter) {
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// PRE: longer and shorter are negative
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// PRE: longer has at least as many digits as shorter
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int iLonger = longer.getFirstNonzeroDigit();
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int iShorter = shorter.getFirstNonzeroDigit();
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// Does shorter matter?
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if (iLonger >= shorter.numberLength) {
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return longer;
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}
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int resLength;
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int resDigits[];
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int i = Math.max(iShorter, iLonger);
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int digit;
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if (iShorter > iLonger) {
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digit = -shorter.digits[i] & ~longer.digits[i];
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} else if (iShorter < iLonger) {
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digit = ~shorter.digits[i] & -longer.digits[i];
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} else {
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digit = -shorter.digits[i] & -longer.digits[i];
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}
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if (digit == 0) {
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for (i++; i < shorter.numberLength
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&& (digit = ~(longer.digits[i] | shorter.digits[i])) == 0; i++) {
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// digit
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}
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// = ~longer.digits[i] & ~shorter.digits[i]
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if (digit == 0) {
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// shorter has only the remaining virtual sign bits
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for (; i < longer.numberLength && (digit = ~longer.digits[i]) == 0; i++) {
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// empty
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}
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if (digit == 0) {
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resLength = longer.numberLength + 1;
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resDigits = new int[resLength];
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resDigits[resLength - 1] = 1;
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BigInteger result = new BigInteger(-1, resLength, resDigits);
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return result;
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}
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}
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}
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resLength = longer.numberLength;
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resDigits = new int[resLength];
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resDigits[i] = -digit;
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for (i++; i < shorter.numberLength; i++) {
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// resDigits[i] = ~(~longer.digits[i] & ~shorter.digits[i];)
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resDigits[i] = longer.digits[i] | shorter.digits[i];
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}
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// shorter has only the remaining virtual sign bits
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for (; i < longer.numberLength; i++) {
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resDigits[i] = longer.digits[i];
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}
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BigInteger result = new BigInteger(-1, resLength, resDigits);
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return result;
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}
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/**
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* @see BigInteger#andNot(BigInteger)
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* @param val
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* @param that
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* @return
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*/
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static BigInteger andNot(BigInteger val, BigInteger that) {
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if (that.sign == 0) {
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return val;
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}
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if (val.sign == 0) {
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return BigInteger.ZERO;
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}
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if (val.equals(BigInteger.MINUS_ONE)) {
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return that.not();
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}
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if (that.equals(BigInteger.MINUS_ONE)) {
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return BigInteger.ZERO;
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}
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// if val == that, return 0
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if (val.sign > 0) {
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if (that.sign > 0) {
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return andNotPositive(val, that);
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} else {
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return andNotPositiveNegative(val, that);
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}
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} else {
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if (that.sign > 0) {
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return andNotNegativePositive(val, that);
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} else {
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return andNotNegative(val, that);
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}
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}
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}
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/**
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* Return sign = 1, magnitude = -val.magnitude & ~(-that.magnitude).
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* @param val
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* @param that
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* @return
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*/
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static BigInteger andNotNegative(BigInteger val, BigInteger that) {
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// PRE: val < 0 && that < 0
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int iVal = val.getFirstNonzeroDigit();
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int iThat = that.getFirstNonzeroDigit();
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if (iVal >= that.numberLength) {
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return BigInteger.ZERO;
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}
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int resLength = that.numberLength;
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int resDigits[] = new int[resLength];
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int limit;
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int i = iVal;
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if (iVal < iThat) {
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// resDigits[i] = -val.digits[i] & -1;
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resDigits[i] = -val.digits[i];
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limit = Math.min(val.numberLength, iThat);
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for (i++; i < limit; i++) {
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// resDigits[i] = ~val.digits[i] & -1;
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resDigits[i] = ~val.digits[i];
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}
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if (i == val.numberLength) {
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for (; i < iThat; i++) {
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// resDigits[i] = -1 & -1;
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resDigits[i] = -1;
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}
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// resDigits[i] = -1 & ~-that.digits[i];
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resDigits[i] = that.digits[i] - 1;
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} else {
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// resDigits[i] = ~val.digits[i] & ~-that.digits[i];
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resDigits[i] = ~val.digits[i] & (that.digits[i] - 1);
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}
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} else if (iThat < iVal) {
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// resDigits[i] = -val.digits[i] & ~~that.digits[i];
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resDigits[i] = -val.digits[i] & that.digits[i];
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} else {
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// resDigits[i] = -val.digits[i] & ~-that.digits[i];
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resDigits[i] = -val.digits[i] & (that.digits[i] - 1);
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}
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limit = Math.min(val.numberLength, that.numberLength);
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for (i++; i < limit; i++) {
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// resDigits[i] = ~val.digits[i] & ~~that.digits[i];
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resDigits[i] = ~val.digits[i] & that.digits[i];
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}
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for (; i < that.numberLength; i++) {
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// resDigits[i] = -1 & ~~that.digits[i];
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resDigits[i] = that.digits[i];
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}
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BigInteger result = new BigInteger(1, resLength, resDigits);
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result.cutOffLeadingZeroes();
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return result;
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}
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/**
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* Return sign = -1, magnitude = -(-negative.magnitude & ~positive.magnitude).
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* @param negative
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* @param positive
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* @return
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*/
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static BigInteger andNotNegativePositive(BigInteger negative,
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BigInteger positive) {
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// PRE: negative < 0 && positive > 0
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int resLength;
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int resDigits[];
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int limit;
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int digit;
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int iNeg = negative.getFirstNonzeroDigit();
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int iPos = positive.getFirstNonzeroDigit();
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if (iNeg >= positive.numberLength) {
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return negative;
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}
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resLength = Math.max(negative.numberLength, positive.numberLength);
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int i = iNeg;
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if (iPos > iNeg) {
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resDigits = new int[resLength];
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limit = Math.min(negative.numberLength, iPos);
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for (; i < limit; i++) {
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// 1st case: resDigits [i] = -(-negative.digits[i] & (~0))
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// otherwise: resDigits[i] = ~(~negative.digits[i] & ~0) ;
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resDigits[i] = negative.digits[i];
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}
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if (i == negative.numberLength) {
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for (i = iPos; i < positive.numberLength; i++) {
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// resDigits[i] = ~(~positive.digits[i] & -1);
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resDigits[i] = positive.digits[i];
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}
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}
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} else {
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digit = -negative.digits[i] & ~positive.digits[i];
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if (digit == 0) {
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limit = Math.min(positive.numberLength, negative.numberLength);
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for (i++; i < limit
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&& (digit = ~(negative.digits[i] | positive.digits[i])) == 0; i++) {
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// digit
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}
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// = ~negative.digits[i] & ~positive.digits[i]
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if (digit == 0) {
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// the shorter has only the remaining virtual sign bits
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for (; i < positive.numberLength
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&& (digit = ~positive.digits[i]) == 0; i++) {
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// digit = -1 & ~positive.digits[i]
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}
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for (; i < negative.numberLength
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&& (digit = ~negative.digits[i]) == 0; i++) {
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// empty
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}
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// digit = ~negative.digits[i] & ~0
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if (digit == 0) {
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resLength++;
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resDigits = new int[resLength];
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resDigits[resLength - 1] = 1;
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BigInteger result = new BigInteger(-1, resLength, resDigits);
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return result;
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}
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}
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}
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resDigits = new int[resLength];
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resDigits[i] = -digit;
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i++;
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}
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limit = Math.min(positive.numberLength, negative.numberLength);
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for (; i < limit; i++) {
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// resDigits[i] = ~(~negative.digits[i] & ~positive.digits[i]);
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resDigits[i] = negative.digits[i] | positive.digits[i];
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}
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// Actually one of the next two cycles will be executed
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for (; i < negative.numberLength; i++) {
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resDigits[i] = negative.digits[i];
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}
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for (; i < positive.numberLength; i++) {
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resDigits[i] = positive.digits[i];
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}
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BigInteger result = new BigInteger(-1, resLength, resDigits);
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return result;
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}
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/**
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* Return sign = 1, magnitude = val.magnitude & ~that.magnitude.
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* @param val
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* @param that
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* @return
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*/
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static BigInteger andNotPositive(BigInteger val, BigInteger that) {
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// PRE: both arguments are positive
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int resDigits[] = new int[val.numberLength];
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int limit = Math.min(val.numberLength, that.numberLength);
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int i;
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for (i = val.getFirstNonzeroDigit(); i < limit; i++) {
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resDigits[i] = val.digits[i] & ~that.digits[i];
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}
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for (; i < val.numberLength; i++) {
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resDigits[i] = val.digits[i];
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}
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BigInteger result = new BigInteger(1, val.numberLength, resDigits);
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result.cutOffLeadingZeroes();
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return result;
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}
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/**
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* Return sign = 1, magnitude = positive.magnitude & ~(-negative.magnitude).
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* @param positive
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* @param negative
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* @return
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*/
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static BigInteger andNotPositiveNegative(BigInteger positive,
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BigInteger negative) {
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// PRE: positive > 0 && negative < 0
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int iNeg = negative.getFirstNonzeroDigit();
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int iPos = positive.getFirstNonzeroDigit();
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if (iNeg >= positive.numberLength) {
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return positive;
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}
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int resLength = Math.min(positive.numberLength, negative.numberLength);
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int resDigits[] = new int[resLength];
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// Always start from first non zero of positive
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int i = iPos;
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for (; i < iNeg; i++) {
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// resDigits[i] = positive.digits[i] & -1 (~0)
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resDigits[i] = positive.digits[i];
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}
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if (i == iNeg) {
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resDigits[i] = positive.digits[i] & (negative.digits[i] - 1);
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i++;
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}
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for (; i < resLength; i++) {
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// resDigits[i] = positive.digits[i] & ~(~negative.digits[i]);
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resDigits[i] = positive.digits[i] & negative.digits[i];
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}
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BigInteger result = new BigInteger(1, resLength, resDigits);
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result.cutOffLeadingZeroes();
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return result;
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}
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/**
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* Return sign = 1, magnitude = val.magnitude & that.magnitude.
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* @param val
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* @param that
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* @return
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*/
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static BigInteger andPositive(BigInteger val, BigInteger that) {
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// PRE: both arguments are positive
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int resLength = Math.min(val.numberLength, that.numberLength);
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int i = Math.max(val.getFirstNonzeroDigit(), that.getFirstNonzeroDigit());
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if (i >= resLength) {
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return BigInteger.ZERO;
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}
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int resDigits[] = new int[resLength];
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for (; i < resLength; i++) {
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resDigits[i] = val.digits[i] & that.digits[i];
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}
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BigInteger result = new BigInteger(1, resLength, resDigits);
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result.cutOffLeadingZeroes();
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return result;
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}
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/**
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* @see BigInteger#not()
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* @param val
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* @return
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*/
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static BigInteger not(BigInteger val) {
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if (val.sign == 0) {
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return BigInteger.MINUS_ONE;
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}
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if (val.equals(BigInteger.MINUS_ONE)) {
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return BigInteger.ZERO;
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}
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int resDigits[] = new int[val.numberLength + 1];
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int i;
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if (val.sign > 0) {
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// ~val = -val + 1
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if (val.digits[val.numberLength - 1] != -1) {
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for (i = 0; val.digits[i] == -1; i++) {
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// empty
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}
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} else {
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for (i = 0; (i < val.numberLength) && (val.digits[i] == -1); i++) {
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// empty
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}
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if (i == val.numberLength) {
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resDigits[i] = 1;
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return new BigInteger(-val.sign, i + 1, resDigits);
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}
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}
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// Here a carry 1 was generated
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} else {
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// (val.sign < 0)
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// ~val = -val - 1
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for (i = 0; val.digits[i] == 0; i++) {
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resDigits[i] = -1;
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}
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// Here a borrow -1 was generated
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}
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// Now, the carry/borrow can be absorbed
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resDigits[i] = val.digits[i] + val.sign;
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|
// Copying the remaining unchanged digit
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for (i++; i < val.numberLength; i++) {
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resDigits[i] = val.digits[i];
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}
|
|
return new BigInteger(-val.sign, i, resDigits);
|
|
}
|
|
|
|
/**
|
|
* @see BigInteger#or(BigInteger).
|
|
* @param val
|
|
* @param that
|
|
* @return
|
|
*/
|
|
static BigInteger or(BigInteger val, BigInteger that) {
|
|
if (that.equals(BigInteger.MINUS_ONE) || val.equals(BigInteger.MINUS_ONE)) {
|
|
return BigInteger.MINUS_ONE;
|
|
}
|
|
if (that.sign == 0) {
|
|
return val;
|
|
}
|
|
if (val.sign == 0) {
|
|
return that;
|
|
}
|
|
|
|
if (val.sign > 0) {
|
|
if (that.sign > 0) {
|
|
if (val.numberLength > that.numberLength) {
|
|
return orPositive(val, that);
|
|
} else {
|
|
return orPositive(that, val);
|
|
}
|
|
} else {
|
|
return orDiffSigns(val, that);
|
|
}
|
|
} else {
|
|
if (that.sign > 0) {
|
|
return orDiffSigns(that, val);
|
|
} else if (that.getFirstNonzeroDigit() > val.getFirstNonzeroDigit()) {
|
|
return orNegative(that, val);
|
|
} else {
|
|
return orNegative(val, that);
|
|
}
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Return sign = -1, magnitude = -(positive.magnitude | -negative.magnitude).
|
|
* @param positive
|
|
* @param negative
|
|
* @return
|
|
*/
|
|
static BigInteger orDiffSigns(BigInteger positive, BigInteger negative) {
|
|
// Jumping over the least significant zero bits
|
|
int iNeg = negative.getFirstNonzeroDigit();
|
|
int iPos = positive.getFirstNonzeroDigit();
|
|
int i;
|
|
int limit;
|
|
|
|
// Look if the trailing zeros of the positive will "copy" all
|
|
// the negative digits
|
|
if (iPos >= negative.numberLength) {
|
|
return negative;
|
|
}
|
|
int resLength = negative.numberLength;
|
|
int resDigits[] = new int[resLength];
|
|
|
|
if (iNeg < iPos) {
|
|
// We know for sure that this will
|
|
// be the first non zero digit in the result
|
|
for (i = iNeg; i < iPos; i++) {
|
|
resDigits[i] = negative.digits[i];
|
|
}
|
|
} else if (iPos < iNeg) {
|
|
i = iPos;
|
|
resDigits[i] = -positive.digits[i];
|
|
limit = Math.min(positive.numberLength, iNeg);
|
|
for (i++; i < limit; i++) {
|
|
resDigits[i] = ~positive.digits[i];
|
|
}
|
|
if (i != positive.numberLength) {
|
|
resDigits[i] = ~(-negative.digits[i] | positive.digits[i]);
|
|
} else {
|
|
for (; i < iNeg; i++) {
|
|
resDigits[i] = -1;
|
|
}
|
|
// resDigits[i] = ~(-negative.digits[i] | 0);
|
|
resDigits[i] = negative.digits[i] - 1;
|
|
}
|
|
i++;
|
|
} else {
|
|
// iNeg == iPos
|
|
// Applying two complement to negative and to result
|
|
i = iPos;
|
|
resDigits[i] = -(-negative.digits[i] | positive.digits[i]);
|
|
i++;
|
|
}
|
|
limit = Math.min(negative.numberLength, positive.numberLength);
|
|
for (; i < limit; i++) {
|
|
// Applying two complement to negative and to result
|
|
// resDigits[i] = ~(~negative.digits[i] | positive.digits[i] );
|
|
resDigits[i] = negative.digits[i] & ~positive.digits[i];
|
|
}
|
|
for (; i < negative.numberLength; i++) {
|
|
resDigits[i] = negative.digits[i];
|
|
}
|
|
|
|
BigInteger result = new BigInteger(-1, resLength, resDigits);
|
|
result.cutOffLeadingZeroes();
|
|
return result;
|
|
}
|
|
|
|
/**
|
|
* Return sign = -1, magnitude = -(-val.magnitude | -that.magnitude).
|
|
* @param val
|
|
* @param that
|
|
* @return
|
|
*/
|
|
static BigInteger orNegative(BigInteger val, BigInteger that) {
|
|
// PRE: val and that are negative;
|
|
// PRE: val has at least as many trailing zeros digits as that
|
|
int iThat = that.getFirstNonzeroDigit();
|
|
int iVal = val.getFirstNonzeroDigit();
|
|
int i;
|
|
|
|
if (iVal >= that.numberLength) {
|
|
return that;
|
|
} else if (iThat >= val.numberLength) {
|
|
return val;
|
|
}
|
|
|
|
int resLength = Math.min(val.numberLength, that.numberLength);
|
|
int resDigits[] = new int[resLength];
|
|
|
|
// Looking for the first non-zero digit of the result
|
|
if (iThat == iVal) {
|
|
resDigits[iVal] = -(-val.digits[iVal] | -that.digits[iVal]);
|
|
i = iVal;
|
|
} else {
|
|
for (i = iThat; i < iVal; i++) {
|
|
resDigits[i] = that.digits[i];
|
|
}
|
|
resDigits[i] = that.digits[i] & (val.digits[i] - 1);
|
|
}
|
|
|
|
for (i++; i < resLength; i++) {
|
|
resDigits[i] = val.digits[i] & that.digits[i];
|
|
}
|
|
|
|
BigInteger result = new BigInteger(-1, resLength, resDigits);
|
|
result.cutOffLeadingZeroes();
|
|
return result;
|
|
}
|
|
|
|
/**
|
|
* Return sign = 1, magnitude = longer.magnitude | shorter.magnitude.
|
|
* @param longer
|
|
* @param shorter
|
|
* @return
|
|
*/
|
|
static BigInteger orPositive(BigInteger longer, BigInteger shorter) {
|
|
// PRE: longer and shorter are positive;
|
|
// PRE: longer has at least as many digits as shorter
|
|
int resLength = longer.numberLength;
|
|
int resDigits[] = new int[resLength];
|
|
|
|
int i = Math.min(longer.getFirstNonzeroDigit(),
|
|
shorter.getFirstNonzeroDigit());
|
|
for (i = 0; i < shorter.numberLength; i++) {
|
|
resDigits[i] = longer.digits[i] | shorter.digits[i];
|
|
}
|
|
for (; i < resLength; i++) {
|
|
resDigits[i] = longer.digits[i];
|
|
}
|
|
|
|
BigInteger result = new BigInteger(1, resLength, resDigits);
|
|
return result;
|
|
}
|
|
|
|
/**
|
|
* @see BigInteger#xor(BigInteger)
|
|
* @param val
|
|
* @param that
|
|
* @return
|
|
*/
|
|
static BigInteger xor(BigInteger val, BigInteger that) {
|
|
if (that.sign == 0) {
|
|
return val;
|
|
}
|
|
if (val.sign == 0) {
|
|
return that;
|
|
}
|
|
if (that.equals(BigInteger.MINUS_ONE)) {
|
|
return val.not();
|
|
}
|
|
if (val.equals(BigInteger.MINUS_ONE)) {
|
|
return that.not();
|
|
}
|
|
|
|
if (val.sign > 0) {
|
|
if (that.sign > 0) {
|
|
if (val.numberLength > that.numberLength) {
|
|
return xorPositive(val, that);
|
|
} else {
|
|
return xorPositive(that, val);
|
|
}
|
|
} else {
|
|
return xorDiffSigns(val, that);
|
|
}
|
|
} else {
|
|
if (that.sign > 0) {
|
|
return xorDiffSigns(that, val);
|
|
} else if (that.getFirstNonzeroDigit() > val.getFirstNonzeroDigit()) {
|
|
return xorNegative(that, val);
|
|
} else {
|
|
return xorNegative(val, that);
|
|
}
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Return sign = 1, magnitude = -(positive.magnitude ^ -negative.magnitude).
|
|
* @param positive
|
|
* @param negative
|
|
* @return
|
|
*/
|
|
static BigInteger xorDiffSigns(BigInteger positive, BigInteger negative) {
|
|
int resLength = Math.max(negative.numberLength, positive.numberLength);
|
|
int resDigits[];
|
|
int iNeg = negative.getFirstNonzeroDigit();
|
|
int iPos = positive.getFirstNonzeroDigit();
|
|
int i;
|
|
int limit;
|
|
|
|
// The first
|
|
if (iNeg < iPos) {
|
|
resDigits = new int[resLength];
|
|
i = iNeg;
|
|
// resDigits[i] = -(-negative.digits[i]);
|
|
resDigits[i] = negative.digits[i];
|
|
limit = Math.min(negative.numberLength, iPos);
|
|
// Skip the positive digits while they are zeros
|
|
for (i++; i < limit; i++) {
|
|
// resDigits[i] = ~(~negative.digits[i]);
|
|
resDigits[i] = negative.digits[i];
|
|
}
|
|
// if the negative has no more elements, must fill the
|
|
// result with the remaining digits of the positive
|
|
if (i == negative.numberLength) {
|
|
for (; i < positive.numberLength; i++) {
|
|
// resDigits[i] = ~(positive.digits[i] ^ -1) -> ~(~positive.digits[i])
|
|
resDigits[i] = positive.digits[i];
|
|
}
|
|
}
|
|
} else if (iPos < iNeg) {
|
|
resDigits = new int[resLength];
|
|
i = iPos;
|
|
// Applying two complement to the first non-zero digit of the result
|
|
resDigits[i] = -positive.digits[i];
|
|
limit = Math.min(positive.numberLength, iNeg);
|
|
for (i++; i < limit; i++) {
|
|
// Continue applying two complement the result
|
|
resDigits[i] = ~positive.digits[i];
|
|
}
|
|
// When the first non-zero digit of the negative is reached, must apply
|
|
// two complement (arithmetic negation) to it, and then operate
|
|
if (i == iNeg) {
|
|
resDigits[i] = ~(positive.digits[i] ^ -negative.digits[i]);
|
|
i++;
|
|
} else {
|
|
// if the positive has no more elements must fill the remaining digits
|
|
// with
|
|
// the negative ones
|
|
for (; i < iNeg; i++) {
|
|
// resDigits[i] = ~(0 ^ 0)
|
|
resDigits[i] = -1;
|
|
}
|
|
for (; i < negative.numberLength; i++) {
|
|
// resDigits[i] = ~(~negative.digits[i] ^ 0)
|
|
resDigits[i] = negative.digits[i];
|
|
}
|
|
}
|
|
} else {
|
|
int digit;
|
|
// The first non-zero digit of the positive and negative are the same
|
|
i = iNeg;
|
|
digit = positive.digits[i] ^ -negative.digits[i];
|
|
if (digit == 0) {
|
|
limit = Math.min(positive.numberLength, negative.numberLength);
|
|
for (i++; i < limit
|
|
&& (digit = positive.digits[i] ^ ~negative.digits[i]) == 0; i++) {
|
|
// empty
|
|
}
|
|
if (digit == 0) {
|
|
// shorter has only the remaining virtual sign bits
|
|
for (; i < positive.numberLength
|
|
&& (digit = ~positive.digits[i]) == 0; i++) {
|
|
// empty
|
|
}
|
|
for (; i < negative.numberLength
|
|
&& (digit = ~negative.digits[i]) == 0; i++) {
|
|
// empty
|
|
}
|
|
if (digit == 0) {
|
|
resLength = resLength + 1;
|
|
resDigits = new int[resLength];
|
|
resDigits[resLength - 1] = 1;
|
|
|
|
BigInteger result = new BigInteger(-1, resLength, resDigits);
|
|
return result;
|
|
}
|
|
}
|
|
}
|
|
resDigits = new int[resLength];
|
|
resDigits[i] = -digit;
|
|
i++;
|
|
}
|
|
|
|
limit = Math.min(negative.numberLength, positive.numberLength);
|
|
for (; i < limit; i++) {
|
|
resDigits[i] = ~(~negative.digits[i] ^ positive.digits[i]);
|
|
}
|
|
for (; i < positive.numberLength; i++) {
|
|
// resDigits[i] = ~(positive.digits[i] ^ -1)
|
|
resDigits[i] = positive.digits[i];
|
|
}
|
|
for (; i < negative.numberLength; i++) {
|
|
// resDigits[i] = ~(0 ^ ~negative.digits[i])
|
|
resDigits[i] = negative.digits[i];
|
|
}
|
|
|
|
BigInteger result = new BigInteger(-1, resLength, resDigits);
|
|
result.cutOffLeadingZeroes();
|
|
return result;
|
|
}
|
|
|
|
/**
|
|
* Return sign = 0, magnitude = -val.magnitude ^ -that.magnitude.
|
|
* @param val
|
|
* @param that
|
|
* @return
|
|
*/
|
|
static BigInteger xorNegative(BigInteger val, BigInteger that) {
|
|
// PRE: val and that are negative
|
|
// PRE: val has at least as many trailing zero digits as that
|
|
int resLength = Math.max(val.numberLength, that.numberLength);
|
|
int resDigits[] = new int[resLength];
|
|
int iVal = val.getFirstNonzeroDigit();
|
|
int iThat = that.getFirstNonzeroDigit();
|
|
int i = iThat;
|
|
int limit;
|
|
|
|
if (iVal == iThat) {
|
|
resDigits[i] = -val.digits[i] ^ -that.digits[i];
|
|
} else {
|
|
resDigits[i] = -that.digits[i];
|
|
limit = Math.min(that.numberLength, iVal);
|
|
for (i++; i < limit; i++) {
|
|
resDigits[i] = ~that.digits[i];
|
|
}
|
|
// Remains digits in that?
|
|
if (i == that.numberLength) {
|
|
// Jumping over the remaining zero to the first non one
|
|
for (; i < iVal; i++) {
|
|
// resDigits[i] = 0 ^ -1;
|
|
resDigits[i] = -1;
|
|
}
|
|
// resDigits[i] = -val.digits[i] ^ -1;
|
|
resDigits[i] = val.digits[i] - 1;
|
|
} else {
|
|
resDigits[i] = -val.digits[i] ^ ~that.digits[i];
|
|
}
|
|
}
|
|
|
|
limit = Math.min(val.numberLength, that.numberLength);
|
|
// Perform ^ between that al val until that ends
|
|
for (i++; i < limit; i++) {
|
|
// resDigits[i] = ~val.digits[i] ^ ~that.digits[i];
|
|
resDigits[i] = val.digits[i] ^ that.digits[i];
|
|
}
|
|
// Perform ^ between val digits and -1 until val ends
|
|
for (; i < val.numberLength; i++) {
|
|
// resDigits[i] = ~val.digits[i] ^ -1 ;
|
|
resDigits[i] = val.digits[i];
|
|
}
|
|
for (; i < that.numberLength; i++) {
|
|
// resDigits[i] = -1 ^ ~that.digits[i] ;
|
|
resDigits[i] = that.digits[i];
|
|
}
|
|
|
|
BigInteger result = new BigInteger(1, resLength, resDigits);
|
|
result.cutOffLeadingZeroes();
|
|
return result;
|
|
}
|
|
|
|
/**
|
|
* Return sign = 0, magnitude = longer.magnitude | shorter.magnitude.
|
|
*
|
|
* @param longer
|
|
* @param shorter
|
|
* @return
|
|
*/
|
|
static BigInteger xorPositive(BigInteger longer, BigInteger shorter) {
|
|
// PRE: longer and shorter are positive;
|
|
// PRE: longer has at least as many digits as shorter
|
|
int resLength = longer.numberLength;
|
|
int resDigits[] = new int[resLength];
|
|
int i = Math.min(longer.getFirstNonzeroDigit(),
|
|
shorter.getFirstNonzeroDigit());
|
|
for (; i < shorter.numberLength; i++) {
|
|
resDigits[i] = longer.digits[i] ^ shorter.digits[i];
|
|
}
|
|
for (; i < longer.numberLength; i++) {
|
|
resDigits[i] = longer.digits[i];
|
|
}
|
|
|
|
BigInteger result = new BigInteger(1, resLength, resDigits);
|
|
result.cutOffLeadingZeroes();
|
|
return result;
|
|
}
|
|
|
|
/**
|
|
* Just to denote that this class can't be instantiated.
|
|
*/
|
|
private Logical() {
|
|
}
|
|
}
|