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/*
 * Copyright 2009 Google Inc.
 * 
 * Licensed under the Apache License, Version 2.0 (the "License"); you may not
 * use this file except in compliance with the License. You may obtain a copy of
 * the License at
 * 
 * http://www.apache.org/licenses/LICENSE-2.0
 * 
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
 * License for the specific language governing permissions and limitations under
 * the License.
 */

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements. See the NOTICE file distributed with this
 * work for additional information regarding copyright ownership. The ASF
 * licenses this file to You under the Apache License, Version 2.0 (the
 * "License"); you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 * 
 * http://www.apache.org/licenses/LICENSE-2.0
 * 
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
 * License for the specific language governing permissions and limitations under
 * the License.
 * 
 * INCLUDES MODIFICATIONS BY RICHARD ZSCHECH AS WELL AS GOOGLE.
 */
package java.math;

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




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