mailiverse/gwt/jre/java/math/Conversion.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 {@link BigInteger} base conversion from/to any
 * integer represented in a {@link java.lang.String} Object.
 */
class Conversion {

  /**
   * bigRadices values are precomputed maximal powers of radices (integer
   * numbers from 2 to 36) that fit into unsigned int (32 bits). bigRadices[0] =
   * 2 ^ 31, bigRadices[8] = 10 ^ 9, etc.
   */

  static final int bigRadices[] = {
      -2147483648, 1162261467, 1073741824, 1220703125, 362797056, 1977326743,
      1073741824, 387420489, 1000000000, 214358881, 429981696, 815730721,
      1475789056, 170859375, 268435456, 410338673, 612220032, 893871739,
      1280000000, 1801088541, 113379904, 148035889, 191102976, 244140625,
      308915776, 387420489, 481890304, 594823321, 729000000, 887503681,
      1073741824, 1291467969, 1544804416, 1838265625, 60466176};

  /**
   * Holds the maximal exponent for each radix, so that
   * radix<sup>digitFitInInt[radix]</sup> fit in an {@code int} (32 bits).
   */
  static final int[] digitFitInInt = {
      -1, -1, 31, 19, 15, 13, 11, 11, 10, 9, 9, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7,
      7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5};

  /**
   * @see BigInteger#toString(int)
   * @param val
   * @param radix
   * @return
   */
  static String bigInteger2String(BigInteger val, int radix) {
    int sign = val.sign;
    int numberLength = val.numberLength;
    int digits[] = val.digits;

    if (sign == 0) {
      return "0"; //$NON-NLS-1$
    }
    if (numberLength == 1) {
      int highDigit = digits[numberLength - 1];
      long v = highDigit & 0xFFFFFFFFL;
      if (sign < 0) {
        v = -v;
      }
      return Long.toString(v, radix);
    }
    if ((radix == 10) || (radix < Character.MIN_RADIX)
        || (radix > Character.MAX_RADIX)) {
      return val.toString();
    }
    double bitsForRadixDigit;
    bitsForRadixDigit = Math.log(radix) / Math.log(2);
    int resLengthInChars = (int) (val.abs().bitLength() / bitsForRadixDigit + ((sign < 0)
        ? 1 : 0)) + 1;

    char result[] = new char[resLengthInChars];
    int currentChar = resLengthInChars;
    int resDigit;
    if (radix != 16) {
      int temp[] = new int[numberLength];
      System.arraycopy(digits, 0, temp, 0, numberLength);
      int tempLen = numberLength;
      int charsPerInt = digitFitInInt[radix];
      int i;
      // get the maximal power of radix that fits in int
      int bigRadix = bigRadices[radix - 2];
      while (true) {
        // divide the array of digits by bigRadix and convert remainders
        // to characters collecting them in the char array
        resDigit = Division.divideArrayByInt(temp, temp, tempLen, bigRadix);
        int previous = currentChar;
        do {
          result[--currentChar] = Character.forDigit(resDigit % radix, radix);
        } while (((resDigit /= radix) != 0) && (currentChar != 0));
        int delta = charsPerInt - previous + currentChar;
        for (i = 0; i < delta && currentChar > 0; i++) {
          result[--currentChar] = '0';
        }
        for (i = tempLen - 1; (i > 0) && (temp[i] == 0); i--) {
          // empty
        }
        tempLen = i + 1;
        if ((tempLen == 1) && (temp[0] == 0)) { // the quotient is 0
          break;
        }
      }
    } else {
      // radix == 16
      for (int i = 0; i < numberLength; i++) {
        for (int j = 0; (j < 8) && (currentChar > 0); j++) {
          resDigit = digits[i] >> (j << 2) & 0xf;
          result[--currentChar] = Character.forDigit(resDigit, 16);
        }
      }
    }
    while (result[currentChar] == '0') {
      currentChar++;
    }
    if (sign == -1) {
      result[--currentChar] = '-';
    }
    return new String(result, currentChar, resLengthInChars - currentChar);
  }

  static long divideLongByBillion(long a) {
    long quot;
    long rem;

    if (a >= 0) {
      long bLong = 1000000000L;
      quot = (a / bLong);
      rem = (a % bLong);
    } else {
      /*
       * Make the dividend positive shifting it right by 1 bit then get the
       * quotient an remainder and correct them properly
       */
      long aPos = a >>> 1;
      long bPos = 1000000000L >>> 1;
      quot = aPos / bPos;
      rem = aPos % bPos;
      // double the remainder and add 1 if 'a' is odd
      rem = (rem << 1) + (a & 1);
    }
    return ((rem << 32) | (quot & 0xFFFFFFFFL));
  }

  /**
   * Builds the correspondent {@code String} representation of {@code val} being
   * scaled by {@code scale}.
   *
   * @see BigInteger#toString()
   * @see BigDecimal#toString()
   */
  static String toDecimalScaledString(BigInteger val, int scale) {
    int sign = val.sign;
    int numberLength = val.numberLength;
    int digits[] = val.digits;
    int resLengthInChars;
    int currentChar;
    char result[];

    if (sign == 0) {
      switch (scale) {
        case 0:
          return "0"; //$NON-NLS-1$
        case 1:
          return "0.0"; //$NON-NLS-1$
        case 2:
          return "0.00"; //$NON-NLS-1$
        case 3:
          return "0.000"; //$NON-NLS-1$
        case 4:
          return "0.0000"; //$NON-NLS-1$
        case 5:
          return "0.00000"; //$NON-NLS-1$
        case 6:
          return "0.000000"; //$NON-NLS-1$
        default:
          StringBuilder result1 = new StringBuilder();
          if (scale < 0) {
            result1.append("0E+"); //$NON-NLS-1$
          } else {
            result1.append("0E"); //$NON-NLS-1$
          }
          result1.append(-scale);
          return result1.toString();
      }
    }
    // one 32-bit unsigned value may contains 10 decimal digits
    resLengthInChars = numberLength * 10 + 1 + 7;
    // Explanation why +1+7:
    // +1 - one char for sign if needed.
    // +7 - For "special case 2" (see below) we have 7 free chars for
    // inserting necessary scaled digits.
    result = new char[resLengthInChars + 1];
    // allocated [resLengthInChars+1] characters.
    // a free latest character may be used for "special case 1" (see
    // below)
    currentChar = resLengthInChars;
    if (numberLength == 1) {
      int highDigit = digits[0];
      if (highDigit < 0) {
        long v = highDigit & 0xFFFFFFFFL;
        do {
          long prev = v;
          v /= 10;
          result[--currentChar] = (char) (0x0030 + ((int) (prev - v * 10)));
        } while (v != 0);
      } else {
        int v = highDigit;
        do {
          int prev = v;
          v /= 10;
          result[--currentChar] = (char) (0x0030 + (prev - v * 10));
        } while (v != 0);
      }
    } else {
      int temp[] = new int[numberLength];
      int tempLen = numberLength;
      System.arraycopy(digits, 0, temp, 0, tempLen);
      BIG_LOOP : while (true) {
        // divide the array of digits by bigRadix and convert
        // remainders
        // to characters collecting them in the char array
        long result11 = 0;
        for (int i1 = tempLen - 1; i1 >= 0; i1--) {
          long temp1 = (result11 << 32) + (temp[i1] & 0xFFFFFFFFL);
          long res = divideLongByBillion(temp1);
          temp[i1] = (int) res;
          result11 = (int) (res >> 32);
        }
        int resDigit = (int) result11;
        int previous = currentChar;
        do {
          result[--currentChar] = (char) (0x0030 + (resDigit % 10));
        } while (((resDigit /= 10) != 0) && (currentChar != 0));
        int delta = 9 - previous + currentChar;
        for (int i = 0; (i < delta) && (currentChar > 0); i++) {
          result[--currentChar] = '0';
        }
        int j = tempLen - 1;
        for (; temp[j] == 0; j--) {
          if (j == 0) { // means temp[0] == 0
            break BIG_LOOP;
          }
        }
        tempLen = j + 1;
      }
      while (result[currentChar] == '0') {
        currentChar++;
      }
    }
    boolean negNumber = (sign < 0);
    int exponent = resLengthInChars - currentChar - scale - 1;
    if (scale == 0) {
      if (negNumber) {
        result[--currentChar] = '-';
      }
      return new String(result, currentChar, resLengthInChars - currentChar);
    }
    if ((scale > 0) && (exponent >= -6)) {
      if (exponent >= 0) {
        // special case 1
        int insertPoint = currentChar + exponent;
        for (int j = resLengthInChars - 1; j >= insertPoint; j--) {
          result[j + 1] = result[j];
        }
        result[++insertPoint] = '.';
        if (negNumber) {
          result[--currentChar] = '-';
        }
        return new String(result, currentChar, resLengthInChars - currentChar
            + 1);
      }
      // special case 2
      for (int j = 2; j < -exponent + 1; j++) {
        result[--currentChar] = '0';
      }
      result[--currentChar] = '.';
      result[--currentChar] = '0';
      if (negNumber) {
        result[--currentChar] = '-';
      }
      return new String(result, currentChar, resLengthInChars - currentChar);
    }
    int startPoint = currentChar + 1;
    int endPoint = resLengthInChars;
    StringBuilder result1 = new StringBuilder(16 + endPoint - startPoint);
    if (negNumber) {
      result1.append('-');
    }
    if (endPoint - startPoint >= 1) {
      result1.append(result[currentChar]);
      result1.append('.');
      result1.append(result, currentChar + 1, resLengthInChars - currentChar
          - 1);
    } else {
      result1.append(result, currentChar, resLengthInChars - currentChar);
    }
    result1.append('E');
    if (exponent > 0) {
      result1.append('+');
    }
    result1.append(Integer.toString(exponent));
    return result1.toString();
  }

  /* can process only 32-bit numbers */
  static String toDecimalScaledString(long value, int scale) {
    int resLengthInChars;
    int currentChar;
    char result[];
    boolean negNumber = value < 0;
    if (negNumber) {
      value = -value;
    }
    if (value == 0) {
      switch (scale) {
        case 0:
          return "0"; //$NON-NLS-1$
        case 1:
          return "0.0"; //$NON-NLS-1$
        case 2:
          return "0.00"; //$NON-NLS-1$
        case 3:
          return "0.000"; //$NON-NLS-1$
        case 4:
          return "0.0000"; //$NON-NLS-1$
        case 5:
          return "0.00000"; //$NON-NLS-1$
        case 6:
          return "0.000000"; //$NON-NLS-1$
        default:
          StringBuilder result1 = new StringBuilder();
          if (scale < 0) {
            result1.append("0E+"); //$NON-NLS-1$
          } else {
            result1.append("0E"); //$NON-NLS-1$
          }
          result1.append((scale == Integer.MIN_VALUE)
              ? "2147483648" : Integer.toString(-scale)); //$NON-NLS-1$
          return result1.toString();
      }
    }
    // one 32-bit unsigned value may contains 10 decimal digits
    resLengthInChars = 18;
    // Explanation why +1+7:
    // +1 - one char for sign if needed.
    // +7 - For "special case 2" (see below) we have 7 free chars for
    // inserting necessary scaled digits.
    result = new char[resLengthInChars + 1];
    // Allocated [resLengthInChars+1] characters.
    // a free latest character may be used for "special case 1" (see below)
    currentChar = resLengthInChars;
    long v = value;
    do {
      long prev = v;
      v /= 10;
      result[--currentChar] = (char) (0x0030 + (prev - v * 10));
    } while (v != 0);

    long exponent = (long) resLengthInChars - (long) currentChar - scale - 1L;
    if (scale == 0) {
      if (negNumber) {
        result[--currentChar] = '-';
      }
      return new String(result, currentChar, resLengthInChars - currentChar);
    }
    if (scale > 0 && exponent >= -6) {
      if (exponent >= 0) {
        // special case 1
        int insertPoint = currentChar + (int) exponent;
        for (int j = resLengthInChars - 1; j >= insertPoint; j--) {
          result[j + 1] = result[j];
        }
        result[++insertPoint] = '.';
        if (negNumber) {
          result[--currentChar] = '-';
        }
        return new String(result, currentChar, resLengthInChars - currentChar
            + 1);
      }
      // special case 2
      for (int j = 2; j < -exponent + 1; j++) {
        result[--currentChar] = '0';
      }
      result[--currentChar] = '.';
      result[--currentChar] = '0';
      if (negNumber) {
        result[--currentChar] = '-';
      }
      return new String(result, currentChar, resLengthInChars - currentChar);
    }
    int startPoint = currentChar + 1;
    int endPoint = resLengthInChars;
    StringBuilder result1 = new StringBuilder(16 + endPoint - startPoint);
    if (negNumber) {
      result1.append('-');
    }
    if (endPoint - startPoint >= 1) {
      result1.append(result[currentChar]);
      result1.append('.');
      result1.append(result, currentChar + 1, resLengthInChars - currentChar
          - 1);
    } else {
      result1.append(result, currentChar, resLengthInChars - currentChar);
    }
    result1.append('E');
    if (exponent > 0) {
      result1.append('+');
    }
    result1.append(Long.toString(exponent));
    return result1.toString();
  }

  /**
   * Just to denote that this class can't be instantiated.
   */
  private Conversion() {
  }

//   /**
//    * @see BigInteger#doubleValue()
//    */
  // static double bigInteger2Double(BigInteger val) {
  // // val.bitLength() < 64
  // if ((val.numberLength < 2)
  // || ((val.numberLength == 2) && (val.digits[1] > 0))) {
  // return val.longValue();
  // }
  // // val.bitLength() >= 33 * 32 > 1024
  // if (val.numberLength > 32) {
  // return ((val.sign > 0) ? Double.POSITIVE_INFINITY
  // : Double.NEGATIVE_INFINITY);
  // }
  // int bitLen = val.abs().bitLength();
  // long exponent = bitLen - 1;
  // int delta = bitLen - 54;
  // // We need 54 top bits from this, the 53th bit is always 1 in lVal.
  // long lVal = val.abs().shiftRight(delta).longValue();
  // /*
  // * Take 53 bits from lVal to mantissa. The least significant bit is
  // * needed for rounding.
  // */
  // long mantissa = lVal & 0x1FFFFFFFFFFFFFL;
  // if (exponent == 1023) {
  // if (mantissa == 0X1FFFFFFFFFFFFFL) {
  // return ((val.sign > 0) ? Double.POSITIVE_INFINITY
  // : Double.NEGATIVE_INFINITY);
  // }
  // if (mantissa == 0x1FFFFFFFFFFFFEL) {
  // return ((val.sign > 0) ? Double.MAX_VALUE : -Double.MAX_VALUE);
  // }
  // }
  // // Round the mantissa
  // if (((mantissa & 1) == 1)
  // && (((mantissa & 2) == 2) || BitLevel.nonZeroDroppedBits(delta,
  // val.digits))) {
  // mantissa += 2;
  // }
  // mantissa >>= 1; // drop the rounding bit
  // long resSign = (val.sign < 0) ? 0x8000000000000000L : 0;
  // exponent = ((1023 + exponent) << 52) & 0x7FF0000000000000L;
  // long result = resSign | exponent | mantissa;
  // return Double.longBitsToDouble(result);
  // }
}