mailiverse/gwt/jre/java/math/BitLevel.java

/*
 * 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 <b>bit level</b> operations for
 * {@link BigInteger}. The operations are: <ul type="circle"> <li>Left Shifting</li>
 * <li>Right Shifting</li> <li>Bit clearing</li> <li>Bit setting</li> <li>Bit
 * counting</li> <li>Bit testing</li> <li>Getting of the lowest bit set</li>
 * </ul> 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() {
  }
}