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380 lines
12 KiB
Java
380 lines
12 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 all the <b>bit level</b> operations for
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* {@link BigInteger}. The operations are: <ul type="circle"> <li>Left Shifting</li>
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* <li>Right Shifting</li> <li>Bit clearing</li> <li>Bit setting</li> <li>Bit
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* counting</li> <li>Bit testing</li> <li>Getting of the lowest bit set</li>
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* </ul> All operations are provided in immutable way, and some in both mutable
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* and immutable.
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*/
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class BitLevel {
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/**
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* @see BigInteger#bitCount()
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* @param val
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* @return
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*/
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static int bitCount(BigInteger val) {
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int bCount = 0;
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if (val.sign == 0) {
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return 0;
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}
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int i = val.getFirstNonzeroDigit();
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if (val.sign > 0) {
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for (; i < val.numberLength; i++) {
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bCount += Integer.bitCount(val.digits[i]);
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}
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} else {
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// (sign < 0)
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// this digit absorbs the carry
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bCount += Integer.bitCount(-val.digits[i]);
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for (i++; i < val.numberLength; i++) {
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bCount += Integer.bitCount(~val.digits[i]);
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}
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// We take the complement sum:
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bCount = (val.numberLength << 5) - bCount;
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}
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return bCount;
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}
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/**
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* @see BigInteger#bitLength()
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* @param val
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* @return
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*/
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static int bitLength(BigInteger val) {
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if (val.sign == 0) {
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return 0;
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}
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int bLength = (val.numberLength << 5);
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int highDigit = val.digits[val.numberLength - 1];
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if (val.sign < 0) {
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int i = val.getFirstNonzeroDigit();
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// We reduce the problem to the positive case.
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if (i == val.numberLength - 1) {
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// ~~ is to handle int overflow
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highDigit = ~~(highDigit - 1);
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}
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}
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// Subtracting all sign bits
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bLength -= Integer.numberOfLeadingZeros(highDigit);
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return bLength;
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}
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/**
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* Performs a flipBit on the BigInteger, returning a BigInteger with the the
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* specified bit flipped.
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*
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* @param val BigInteger to operate on
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* @param n the bit to flip
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*/
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static BigInteger flipBit(BigInteger val, int n) {
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int resSign = (val.sign == 0) ? 1 : val.sign;
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int intCount = n >> 5;
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int bitN = n & 31;
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int resLength = Math.max(intCount + 1, val.numberLength) + 1;
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int resDigits[] = new int[resLength];
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int i;
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int bitNumber = 1 << bitN;
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System.arraycopy(val.digits, 0, resDigits, 0, val.numberLength);
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if (val.sign < 0) {
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if (intCount >= val.numberLength) {
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resDigits[intCount] = bitNumber;
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} else {
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// val.sign<0 y intCount < val.numberLength
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int firstNonZeroDigit = val.getFirstNonzeroDigit();
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if (intCount > firstNonZeroDigit) {
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resDigits[intCount] ^= bitNumber;
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} else if (intCount < firstNonZeroDigit) {
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resDigits[intCount] = -bitNumber;
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for (i = intCount + 1; i < firstNonZeroDigit; i++) {
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resDigits[i] = -1;
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}
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resDigits[i] = resDigits[i]--;
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} else {
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i = intCount;
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resDigits[i] = -((-resDigits[intCount]) ^ bitNumber);
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if (resDigits[i] == 0) {
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for (i++; resDigits[i] == -1; i++) {
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resDigits[i] = 0;
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}
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resDigits[i]++;
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}
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}
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}
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} else {
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// case where val is positive
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resDigits[intCount] ^= bitNumber;
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}
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BigInteger result = new BigInteger(resSign, 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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* Performs {@code val <<= count}.
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*/
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// val should have enough place (and one digit more)
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static void inplaceShiftLeft(BigInteger val, int count) {
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int intCount = count >> 5; // count of integers
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val.numberLength += intCount
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+ (Integer.numberOfLeadingZeros(val.digits[val.numberLength - 1])
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- (count & 31) >= 0 ? 0 : 1);
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shiftLeft(val.digits, val.digits, intCount, count & 31);
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val.cutOffLeadingZeroes();
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val.unCache();
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}
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/**
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* Performs {@code val >>= count} where {@code val} is a positive number.
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*/
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static void inplaceShiftRight(BigInteger val, int count) {
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int sign = val.signum();
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if (count == 0 || val.signum() == 0) {
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return;
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}
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int intCount = count >> 5; // count of integers
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val.numberLength -= intCount;
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if (!shiftRight(val.digits, val.numberLength, val.digits, intCount,
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count & 31)
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&& sign < 0) {
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// remainder not zero: add one to the result
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int i;
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for (i = 0; (i < val.numberLength) && (val.digits[i] == -1); i++) {
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val.digits[i] = 0;
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}
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if (i == val.numberLength) {
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val.numberLength++;
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}
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val.digits[i]++;
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}
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val.cutOffLeadingZeroes();
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val.unCache();
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}
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/**
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* Check if there are 1s in the lowest bits of this BigInteger.
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*
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* @param numberOfBits the number of the lowest bits to check
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* @return false if all bits are 0s, true otherwise
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*/
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static boolean nonZeroDroppedBits(int numberOfBits, int digits[]) {
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int intCount = numberOfBits >> 5;
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int bitCount = numberOfBits & 31;
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int i;
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for (i = 0; (i < intCount) && (digits[i] == 0); i++) {
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}
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return ((i != intCount) || (digits[i] << (32 - bitCount) != 0));
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}
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/**
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* @see BigInteger#shiftLeft(int)
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* @param source
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* @param count
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* @return
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*/
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static BigInteger shiftLeft(BigInteger source, int count) {
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int intCount = count >> 5;
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count &= 31; // %= 32
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int resLength = source.numberLength + intCount + ((count == 0) ? 0 : 1);
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int resDigits[] = new int[resLength];
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shiftLeft(resDigits, source.digits, intCount, count);
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BigInteger result = new BigInteger(source.sign, 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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* Abstractly shifts left an array of integers in little endian (i.e.,
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* shift it right). Total shift distance in bits is intCount * 32 + count
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*
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* @param result the destination array
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* @param source the source array
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* @param intCount the shift distance in integers
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* @param count an additional shift distance in bits
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*/
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static void shiftLeft(int result[], int source[], int intCount, int count) {
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if (count == 0) {
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System.arraycopy(source, 0, result, intCount, result.length - intCount);
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} else {
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int rightShiftCount = 32 - count;
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result[result.length - 1] = 0;
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for (int i = result.length - 1; i > intCount; i--) {
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result[i] |= source[i - intCount - 1] >>> rightShiftCount;
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result[i - 1] = source[i - intCount - 1] << count;
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}
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}
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for (int i = 0; i < intCount; i++) {
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result[i] = 0;
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}
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}
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static BigInteger shiftLeftOneBit(BigInteger source) {
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int srcLen = source.numberLength;
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int resLen = srcLen + 1;
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int resDigits[] = new int[resLen];
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shiftLeftOneBit(resDigits, source.digits, srcLen);
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BigInteger result = new BigInteger(source.sign, resLen, 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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* Shifts the source digits left one bit, creating a value whose magnitude is
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* doubled.
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*
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* @param result an array of digits that will hold the computed result when
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* this method returns. The size of this array is {@code srcLen + 1},
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* and the format is the same as {@link BigInteger#digits}.
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* @param source the array of digits to shift left, in the same format as
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* {@link BigInteger#digits}.
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* @param srcLen the length of {@code source}; may be less than {@code
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* source.length}
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*/
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static void shiftLeftOneBit(int result[], int source[], int srcLen) {
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int carry = 0;
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for (int i = 0; i < srcLen; i++) {
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int val = source[i];
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result[i] = (val << 1) | carry;
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carry = val >>> 31;
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}
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if (carry != 0) {
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result[srcLen] = carry;
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}
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}
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/**
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* @see BigInteger#shiftRight(int)
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* @param source
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* @param count
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* @return
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*/
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static BigInteger shiftRight(BigInteger source, int count) {
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int intCount = count >> 5; // count of integers
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count &= 31; // count of remaining bits
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if (intCount >= source.numberLength) {
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return ((source.sign < 0) ? BigInteger.MINUS_ONE : BigInteger.ZERO);
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}
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int i;
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int resLength = source.numberLength - intCount;
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int resDigits[] = new int[resLength + 1];
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shiftRight(resDigits, resLength, source.digits, intCount, count);
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if (source.sign < 0) {
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// Checking if the dropped bits are zeros (the remainder equals to
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// 0)
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for (i = 0; (i < intCount) && (source.digits[i] == 0); i++) {
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}
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// If the remainder is not zero, add 1 to the result
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if ((i < intCount)
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|| ((count > 0) && ((source.digits[i] << (32 - count)) != 0))) {
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for (i = 0; (i < resLength) && (resDigits[i] == -1); i++) {
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resDigits[i] = 0;
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}
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if (i == resLength) {
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resLength++;
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}
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resDigits[i]++;
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}
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}
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BigInteger result = new BigInteger(source.sign, 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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* Shifts right an array of integers. Total shift distance in bits is intCount
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* * 32 + count.
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*
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* @param result the destination array
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* @param resultLen the destination array's length
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* @param source the source array
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* @param intCount the number of elements to be shifted
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* @param count the number of bits to be shifted
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* @return dropped bit's are all zero (i.e. remaider is zero)
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*/
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static boolean shiftRight(int result[], int resultLen, int source[],
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int intCount, int count) {
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int i;
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boolean allZero = true;
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for (i = 0; i < intCount; i++) {
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allZero &= source[i] == 0;
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}
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if (count == 0) {
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System.arraycopy(source, intCount, result, 0, resultLen);
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i = resultLen;
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} else {
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int leftShiftCount = 32 - count;
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allZero &= (source[i] << leftShiftCount) == 0;
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for (i = 0; i < resultLen - 1; i++) {
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result[i] = (source[i + intCount] >>> count)
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| (source[i + intCount + 1] << leftShiftCount);
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}
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result[i] = (source[i + intCount] >>> count);
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i++;
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}
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return allZero;
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}
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/**
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* Performs a fast bit testing for positive numbers. The bit to to be tested
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* must be in the range {@code [0, val.bitLength()-1]}
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*/
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static boolean testBit(BigInteger val, int n) {
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// PRE: 0 <= n < val.bitLength()
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return ((val.digits[n >> 5] & (1 << (n & 31))) != 0);
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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 BitLevel() {
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}
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}
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