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/* java.math.BigDecimal -- Arbitrary precision decimals.
   Copyright (C) 1999, 2000, 2001, 2003, 2005, 2006 Free Software Foundation, Inc.

This file is part of GNU Classpath.

GNU Classpath is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2, or (at your option)
any later version.
 
GNU Classpath is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
General Public License for more details.

You should have received a copy of the GNU General Public License
along with GNU Classpath; see the file COPYING.  If not, write to the
Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301 USA.

Linking this library statically or dynamically with other modules is
making a combined work based on this library.  Thus, the terms and
conditions of the GNU General Public License cover the whole
combination.

As a special exception, the copyright holders of this library give you
permission to link this library with independent modules to produce an
executable, regardless of the license terms of these independent
modules, and to copy and distribute the resulting executable under
terms of your choice, provided that you also meet, for each linked
independent module, the terms and conditions of the license of that
module.  An independent module is a module which is not derived from
or based on this library.  If you modify this library, you may extend
this exception to your version of the library, but you are not
obligated to do so.  If you do not wish to do so, delete this
exception statement from your version. */

package java.math;

public class BigDecimal extends Number implements Comparable<BigDecimal>
{
  private BigInteger intVal;
  private int scale;
  private int precision = 0;
  private static final long serialVersionUID = 6108874887143696463L;

  /**
   * The constant zero as a BigDecimal with scale zero.
   * @since 1.5
   */
  public static final BigDecimal ZERO = 
    new BigDecimal (BigInteger.ZERO, 0);

  /**
   * The constant one as a BigDecimal with scale zero.
   * @since 1.5
   */
  public static final BigDecimal ONE = 
    new BigDecimal (BigInteger.ONE, 0);

  /**
   * The constant ten as a BigDecimal with scale zero.
   * @since 1.5
   */
  public static final BigDecimal TEN = 
    new BigDecimal (BigInteger.TEN, 0);

  public static final int ROUND_UP = 0;
  public static final int ROUND_DOWN = 1;
  public static final int ROUND_CEILING = 2;
  public static final int ROUND_FLOOR = 3;
  public static final int ROUND_HALF_UP = 4;
  public static final int ROUND_HALF_DOWN = 5;
  public static final int ROUND_HALF_EVEN = 6;
  public static final int ROUND_UNNECESSARY = 7;

  /**
   * Constructs a new BigDecimal whose unscaled value is val and whose
   * scale is zero.
   * @param val the value of the new BigDecimal
   * @since 1.5
   */
  public BigDecimal (int val)
  {
    this.intVal = BigInteger.valueOf(val);
    this.scale = 0;
  }
  
  /**
   * Constructs a BigDecimal using the BigDecimal(int) constructor and then
   * rounds according to the MathContext.
   * @param val the value for the initial (unrounded) BigDecimal
   * @param mc the MathContext specifying the rounding
   * @throws ArithmeticException if the result is inexact but the rounding type
   * is RoundingMode.UNNECESSARY
   * @since 1.5
   */
  public BigDecimal (int val, MathContext mc)
  {
    this (val);
    if (mc.getPrecision() != 0)
      {
        BigDecimal result = this.round(mc);
        this.intVal = result.intVal;
        this.scale = result.scale;
        this.precision = result.precision;
      }    
  }
  
  /**
   * Constructs a new BigDecimal whose unscaled value is val and whose
   * scale is zero.
   * @param val the value of the new BigDecimal
   */
  public BigDecimal (long val)
  {
    this.intVal = BigInteger.valueOf(val);
    this.scale = 0;
  }
  
  /**
   * Constructs a BigDecimal from the long in the same way as BigDecimal(long)
   * and then rounds according to the MathContext.
   * @param val the long from which we create the initial BigDecimal
   * @param mc the MathContext that specifies the rounding behaviour
   * @throws ArithmeticException if the result is inexact but the rounding type
   * is RoundingMode.UNNECESSARY
   * @since 1.5
   */
  public BigDecimal (long val, MathContext mc)
  {
    this(val);
    if (mc.getPrecision() != 0)
      {
        BigDecimal result = this.round(mc);
        this.intVal = result.intVal;
        this.scale = result.scale;
        this.precision = result.precision;
      }    
  }
  
  /**
   * Constructs a BigDecimal whose value is given by num rounded according to 
   * mc.  Since num is already a BigInteger, the rounding refers only to the 
   * precision setting in mc, if mc.getPrecision() returns an int lower than
   * the number of digits in num, then rounding is necessary.
   * @param num the unscaledValue, before rounding
   * @param mc the MathContext that specifies the precision
   * @throws ArithmeticException if the result is inexact but the rounding type
   * is RoundingMode.UNNECESSARY
   * * @since 1.5
   */
  public BigDecimal (BigInteger num, MathContext mc)
  {
    this (num, 0);
    if (mc.getPrecision() != 0)
      {
        BigDecimal result = this.round(mc);
        this.intVal = result.intVal;
        this.scale = result.scale;
        this.precision = result.precision;
      }
  }
  
  /**
   * Constructs a BigDecimal from the String val according to the same
   * rules as the BigDecimal(String) constructor and then rounds 
   * according to the MathContext mc.
   * @param val the String from which we construct the initial BigDecimal
   * @param mc the MathContext that specifies the rounding
   * @throws ArithmeticException if the result is inexact but the rounding type
   * is RoundingMode.UNNECESSARY   
   * @since 1.5
   */
  public BigDecimal (String val, MathContext mc)
  {
    this (val);
    if (mc.getPrecision() != 0)
      {
        BigDecimal result = this.round(mc);
        this.intVal = result.intVal;
        this.scale = result.scale;
        this.precision = result.precision;
      }
  }
  
  /**
   * Constructs a BigDecimal whose unscaled value is num and whose
   * scale is zero.
   * @param num the value of the new BigDecimal
   */
  public BigDecimal (BigInteger num) 
  {
    this (num, 0);
  }

  /**
   * Constructs a BigDecimal whose unscaled value is num and whose
   * scale is scale.
   * @param num
   * @param scale
   */
  public BigDecimal (BigInteger num, int scale)
  {
    this.intVal = num;
    this.scale = scale;
  }
  
  /**
   * Constructs a BigDecimal using the BigDecimal(BigInteger, int) 
   * constructor and then rounds according to the MathContext.
   * @param num the unscaled value of the unrounded BigDecimal
   * @param scale the scale of the unrounded BigDecimal
   * @param mc the MathContext specifying the rounding
   * @throws ArithmeticException if the result is inexact but the rounding type
   * is RoundingMode.UNNECESSARY
   * @since 1.5
   */
  public BigDecimal (BigInteger num, int scale, MathContext mc)
  {
    this (num, scale);
    if (mc.getPrecision() != 0)
      {
        BigDecimal result = this.round(mc);
        this.intVal = result.intVal;
        this.scale = result.scale;
        this.precision = result.precision;
      }
  }

  /**
   * Constructs a BigDecimal in the same way as BigDecimal(double) and then
   * rounds according to the MathContext.
   * @param num the double from which the initial BigDecimal is created
   * @param mc the MathContext that specifies the rounding behaviour
   * @throws ArithmeticException if the result is inexact but the rounding type
   * is RoundingMode.UNNECESSARY 
   * @since 1.5
   */
  public BigDecimal (double num, MathContext mc)
  {
    this (num);
    if (mc.getPrecision() != 0)
      {
        BigDecimal result = this.round(mc);
        this.intVal = result.intVal;
        this.scale = result.scale;
        this.precision = result.precision;
      }
  }
  
  public BigDecimal (double num) throws NumberFormatException 
  {
    if (Double.isInfinite (num) || Double.isNaN (num))
      throw new NumberFormatException ("invalid argument: " + num);
    // Note we can't convert NUM to a String and then use the
    // String-based constructor.  The BigDecimal documentation makes
    // it clear that the two constructors work differently.

    final int mantissaBits = 52;
    final int exponentBits = 11;
    final long mantMask = (1L << mantissaBits) - 1;
    final long expMask = (1L << exponentBits) - 1;

    long bits = Double.doubleToLongBits (num);
    long mantissa = bits & mantMask;
    long exponent = (bits >>> mantissaBits) & expMask;
    boolean denormal = exponent == 0;

    // Correct the exponent for the bias.
    exponent -= denormal ? 1022 : 1023;

    // Now correct the exponent to account for the bits to the right
    // of the decimal.
    exponent -= mantissaBits;
    // Ordinary numbers have an implied leading `1' bit.
    if (! denormal)
      mantissa |= (1L << mantissaBits);

    // Shave off factors of 10.
    while (exponent < 0 && (mantissa & 1) == 0)
      {
	++exponent;
	mantissa >>= 1;
      }

    intVal = BigInteger.valueOf (bits < 0 ? - mantissa : mantissa);
    if (exponent < 0)
      {
	// We have MANTISSA * 2 ^ (EXPONENT).
	// Since (1/2)^N == 5^N * 10^-N we can easily convert this
	// into a power of 10.
	scale = (int) (- exponent);
	BigInteger mult = BigInteger.valueOf (5).pow (scale);
	intVal = intVal.multiply (mult);
      }
    else
      {
	intVal = intVal.shiftLeft ((int) exponent);
	scale = 0;
      }
  }

  /**
   * Constructs a BigDecimal from the char subarray and rounding 
   * according to the MathContext.
   * @param in the char array
   * @param offset the start of the subarray
   * @param len the length of the subarray
   * @param mc the MathContext for rounding
   * @throws NumberFormatException if the char subarray is not a valid 
   * BigDecimal representation
   * @throws ArithmeticException if the result is inexact but the rounding 
   * mode is RoundingMode.UNNECESSARY
   * @since 1.5
   */
  public BigDecimal(char[] in, int offset, int len, MathContext mc)
  {
    this(in, offset, len);
    // If mc has precision other than zero then we must round.
    if (mc.getPrecision() != 0)
      {
        BigDecimal temp = this.round(mc);
        this.intVal = temp.intVal;
        this.scale = temp.scale;
        this.precision = temp.precision;
      }
  }
  
  /**
   * Constructs a BigDecimal from the char array and rounding according
   * to the MathContext. 
   * @param in the char array
   * @param mc the MathContext
   * @throws NumberFormatException if <code>in</code> is not a valid BigDecimal
   * representation
   * @throws ArithmeticException if the result is inexact but the rounding mode
   * is RoundingMode.UNNECESSARY
   * @since 1.5
   */
  public BigDecimal(char[] in, MathContext mc)
  {
    this(in, 0, in.length);
    // If mc has precision other than zero then we must round.
    if (mc.getPrecision() != 0)
      {
        BigDecimal temp = this.round(mc);
        this.intVal = temp.intVal;
        this.scale = temp.scale;
        this.precision = temp.precision;
      } 
  }
  
  /**
   * Constructs a BigDecimal from the given char array, accepting the same
   * sequence of characters as the BigDecimal(String) constructor.
   * @param in the char array
   * @throws NumberFormatException if <code>in</code> is not a valid BigDecimal
   * representation
   * @since 1.5
   */
  public BigDecimal(char[] in)
  {
    this(in, 0, in.length);
  }
  
  /**
   * Constructs a BigDecimal from a char subarray, accepting the same sequence
   * of characters as the BigDecimal(String) constructor.  
   * @param in the char array
   * @param offset the start of the subarray
   * @param len the length of the subarray
   * @throws NumberFormatException if <code>in</code> is not a valid
   * BigDecimal representation.
   * @since 1.5
   */
  public BigDecimal(char[] in, int offset, int len)
  {
    //  start is the index into the char array where the significand starts
    int start = offset;
    //  end is one greater than the index of the last character used
    int end = offset + len;
    //  point is the index into the char array where the exponent starts
    //  (or, if there is no exponent, this is equal to end)
    int point = offset;
    //  dot is the index into the char array where the decimal point is 
    //  found, or -1 if there is no decimal point
    int dot = -1;
    
    //  The following examples show what these variables mean.  Note that
    //  point and dot don't yet have the correct values, they will be 
    //  properly assigned in a loop later on in this method.
    //
    //  Example 1
    //
    //         +  1  0  2  .  4  6  9
    //  __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
    //
    //  offset = 2, len = 8, start = 3, dot = 6, point = end = 10
    //
    //  Example 2
    //
    //         +  2  3  4  .  6  1  3  E  -  1
    //  __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
    //
    //  offset = 2, len = 11, start = 3, dot = 6, point = 10, end = 13
    //
    //  Example 3
    //
    //         -  1  2  3  4  5  e  7  
    //  __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
    //
    //  offset = 2, len = 8, start = 3, dot = -1, point = 8, end = 10 
    
    //  Determine the sign of the number.
    boolean negative = false;
    if (in[offset] == '+')
      {
        ++start;
        ++point;
      }
    else if (in[offset] == '-')
      {
        ++start;
        ++point;
        negative = true;
      }

    //  Check each character looking for the decimal point and the 
    //  start of the exponent.
    while (point < end)
      {
        char c = in[point];
        if (c == '.')
          {
            // If dot != -1 then we've seen more than one decimal point.
            if (dot != -1)
              throw new NumberFormatException("multiple `.'s in number");
            dot = point;
          }
        // Break when we reach the start of the exponent.
        else if (c == 'e' || c == 'E')
          break;
        // Throw an exception if the character was not a decimal or an 
        // exponent and is not a digit.
        else if (!Character.isDigit(c))
          throw new NumberFormatException("unrecognized character at " + point
                                          + ": " + c);
        ++point;
      }

    // val is a StringBuilder from which we'll create a BigInteger
    // which will be the unscaled value for this BigDecimal
    StringBuilder val = new StringBuilder(point - start - 1);
    if (dot != -1)
      {
        // If there was a decimal we must combine the two parts that 
        // contain only digits and we must set the scale properly.
        val.append(in, start, dot - start);
        val.append(in, dot + 1, point - dot - 1);
        scale = point - 1 - dot;
      }
    else
      {
        // If there was no decimal then the unscaled value is just the number
        // formed from all the digits and the scale is zero.
        val.append(in, start, point - start);
        scale = 0;
      }
    if (val.length() == 0)
      throw new NumberFormatException("no digits seen");

    // Prepend a negative sign if necessary.
    if (negative)
      val.insert(0, '-');
    intVal = new BigInteger(val.toString());

    // Now parse exponent.
    // If point < end that means we broke out of the previous loop when we
    // saw an 'e' or an 'E'.
    if (point < end)
      {
        point++;
        // Ignore a '+' sign.
        if (in[point] == '+')
          point++;

        // Throw an exception if there were no digits found after the 'e'
        // or 'E'.
        if (point >= end)
          throw new NumberFormatException("no exponent following e or E");

        try
          {
            // Adjust the scale according to the exponent.  
            // Remember that the value of a BigDecimal is
            // unscaledValue x Math.pow(10, -scale)
            scale -= Integer.parseInt(new String(in, point, end - point));
          }
        catch (NumberFormatException ex)
          {
            throw new NumberFormatException("malformed exponent");
          }
      }
  }
  
  public BigDecimal (String num) throws NumberFormatException 
  {
    int len = num.length();
    int start = 0, point = 0;
    int dot = -1;
    boolean negative = false;
    if (num.charAt(0) == '+')
      {
	++start;
	++point;
      }
    else if (num.charAt(0) == '-')
      {
	++start;
	++point;
	negative = true;
      }

    while (point < len)
      {
	char c = num.charAt (point);
	if (c == '.')
	  {
	    if (dot >= 0)
	      throw new NumberFormatException ("multiple `.'s in number");
	    dot = point;
	  }
	else if (c == 'e' || c == 'E')
	  break;
	else if (Character.digit (c, 10) < 0)
	  throw new NumberFormatException ("unrecognized character: " + c);
	++point;
      }

    String val;
    if (dot >= 0)
      {
	val = num.substring (start, dot) + num.substring (dot + 1, point);
	scale = point - 1 - dot;
      }
    else
      {
	val = num.substring (start, point);
	scale = 0;
      }
    if (val.length () == 0)
      throw new NumberFormatException ("no digits seen");

    if (negative)
      val = "-" + val;
    intVal = new BigInteger (val);

    // Now parse exponent.
    if (point < len)
      {
        point++;
        if (num.charAt(point) == '+')
          point++;

        if (point >= len )
          throw new NumberFormatException ("no exponent following e or E");
	
        try 
	  {	    
        scale -= Integer.parseInt (num.substring (point));
	  }
        catch (NumberFormatException ex) 
	  {
	    throw new NumberFormatException ("malformed exponent");
	  }
      }
  }

  public static BigDecimal valueOf (long val) 
  {
    return valueOf (val, 0);
  }

  public static BigDecimal valueOf (long val, int scale) 
    throws NumberFormatException 
  {
    if ((scale == 0) && ((int)val == val))
      switch ((int) val)
	{
	case 0:
	  return ZERO;
	case 1:
	  return ONE;
	}

    return new BigDecimal (BigInteger.valueOf (val), scale);
  }

  public BigDecimal add (BigDecimal val) 
  {
    // For addition, need to line up decimals.  Note that the movePointRight
    // method cannot be used for this as it might return a BigDecimal with
    // scale == 0 instead of the scale we need.
    BigInteger op1 = intVal;
    BigInteger op2 = val.intVal;
    if (scale < val.scale)
      op1 = op1.multiply (BigInteger.TEN.pow (val.scale - scale));
    else if (scale > val.scale)
      op2 = op2.multiply (BigInteger.TEN.pow (scale - val.scale));

    return new BigDecimal (op1.add (op2), Math.max (scale, val.scale));
  }
  
  /**
   * Returns a BigDecimal whose value is found first by calling the 
   * method add(val) and then by rounding according to the MathContext mc.
   * @param val the augend
   * @param mc the MathContext for rounding
   * @throws ArithmeticException if the value is inexact but the rounding is
   * RoundingMode.UNNECESSARY
   * @return <code>this</code> + <code>val</code>, rounded if need be
   * @since 1.5
   */
  public BigDecimal add (BigDecimal val, MathContext mc)
  {
    return add(val).round(mc);
  }

  public BigDecimal subtract (BigDecimal val) 
  {
    return this.add(val.negate());
  }

  /**
   * Returns a BigDecimal whose value is found first by calling the 
   * method subtract(val) and then by rounding according to the MathContext mc.
   * @param val the subtrahend
   * @param mc the MathContext for rounding
   * @throws ArithmeticException if the value is inexact but the rounding is
   * RoundingMode.UNNECESSARY
   * @return <code>this</code> - <code>val</code>, rounded if need be
   * @since 1.5
   */
  public BigDecimal subtract (BigDecimal val, MathContext mc)
  {
    return subtract(val).round(mc);
  }

  public BigDecimal multiply (BigDecimal val) 
  {
    return new BigDecimal (intVal.multiply (val.intVal), scale + val.scale);
  }
  
  /**
   * Returns a BigDecimal whose value is (this x val) before it is rounded
   * according to the MathContext mc. 
   * @param val the multiplicand
   * @param mc the MathContext for rounding
   * @return a new BigDecimal with value approximately (this x val)
   * @throws ArithmeticException if the value is inexact but the rounding mode
   * is RoundingMode.UNNECESSARY
   * @since 1.5
   */
  public BigDecimal multiply (BigDecimal val, MathContext mc)
  {
    return multiply(val).round(mc);
  }

  public BigDecimal divide (BigDecimal val, int roundingMode) 
    throws ArithmeticException, IllegalArgumentException 
  {
    return divide (val, scale, roundingMode);
  }
  
  /**
   * Returns a BigDecimal whose value is (this / val), with the specified scale
   * and rounding according to the RoundingMode 
   * @param val the divisor
   * @param scale the scale of the BigDecimal returned
   * @param roundingMode the rounding mode to use
   * @return a BigDecimal whose value is approximately (this / val)
   * @throws ArithmeticException if divisor is zero or the rounding mode is
   * UNNECESSARY but the specified scale cannot represent the value exactly
   * @since 1.5
   */
  public BigDecimal divide(BigDecimal val, 
                           int scale, RoundingMode roundingMode)
  {
    return divide (val, scale, roundingMode.ordinal());
  }

  /**
   * Returns a BigDecimal whose value is (this / val) rounded according to the
   * RoundingMode
   * @param val the divisor
   * @param roundingMode the rounding mode to use
   * @return a BigDecimal whose value is approximately (this / val)
   * @throws ArithmeticException if divisor is zero or the rounding mode is
   * UNNECESSARY but the specified scale cannot represent the value exactly
   */
  public BigDecimal divide (BigDecimal val, RoundingMode roundingMode)
  {
    return divide (val, scale, roundingMode.ordinal());
  }
  
  public BigDecimal divide(BigDecimal val, int newScale, int roundingMode)
    throws ArithmeticException, IllegalArgumentException 
  {
    if (roundingMode < 0 || roundingMode > 7)
      throw 
	new IllegalArgumentException("illegal rounding mode: " + roundingMode);

    if (intVal.signum () == 0)	// handle special case of 0.0/0.0
      return newScale == 0 ? ZERO : new BigDecimal (ZERO.intVal, newScale);
    
    // Ensure that pow gets a non-negative value.
    BigInteger valIntVal = val.intVal;
    int power = newScale - (scale - val.scale);
    if (power < 0)
      {
	// Effectively increase the scale of val to avoid an
	// ArithmeticException for a negative power.
        valIntVal = valIntVal.multiply (BigInteger.TEN.pow (-power));
	power = 0;
      }

    BigInteger dividend = intVal.multiply (BigInteger.TEN.pow (power));
    
    BigInteger parts[] = dividend.divideAndRemainder (valIntVal);

    BigInteger unrounded = parts[0];
    if (parts[1].signum () == 0) // no remainder, no rounding necessary
      return new BigDecimal (unrounded, newScale);

    if (roundingMode == ROUND_UNNECESSARY)
      throw new ArithmeticException ("Rounding necessary");

    int sign = intVal.signum () * valIntVal.signum ();

    if (roundingMode == ROUND_CEILING)
      roundingMode = (sign > 0) ? ROUND_UP : ROUND_DOWN;
    else if (roundingMode == ROUND_FLOOR)
      roundingMode = (sign < 0) ? ROUND_UP : ROUND_DOWN;
    else
      {
	// half is -1 if remainder*2 < positive intValue (*power), 0 if equal,
	// 1 if >. This implies that the remainder to round is less than,
	// equal to, or greater than half way to the next digit.
	BigInteger posRemainder
	  = parts[1].signum () < 0 ? parts[1].negate() : parts[1];
	valIntVal = valIntVal.signum () < 0 ? valIntVal.negate () : valIntVal;
	int half = posRemainder.shiftLeft(1).compareTo(valIntVal);

	switch(roundingMode)
	  {
	  case ROUND_HALF_UP:
	    roundingMode = (half < 0) ? ROUND_DOWN : ROUND_UP;
	    break;
	  case ROUND_HALF_DOWN:
	    roundingMode = (half > 0) ? ROUND_UP : ROUND_DOWN;
	    break;
	  case ROUND_HALF_EVEN:
	    if (half < 0)
	      roundingMode = ROUND_DOWN;
	    else if (half > 0)
	      roundingMode = ROUND_UP;
	    else if (unrounded.testBit(0)) // odd, then ROUND_HALF_UP
	      roundingMode = ROUND_UP;
	    else                           // even, ROUND_HALF_DOWN
	      roundingMode = ROUND_DOWN;
	    break;
	  }
      }

    if (roundingMode == ROUND_UP)
      unrounded = unrounded.add (BigInteger.valueOf (sign > 0 ? 1 : -1));

    // roundingMode == ROUND_DOWN
    return new BigDecimal (unrounded, newScale);
  }
  
  /**
   * Performs division, if the resulting quotient requires rounding
   * (has a nonterminating decimal expansion), 
   * an ArithmeticException is thrown. 
   * #see divide(BigDecimal, int, int)
   * @since 1.5
   */
  public BigDecimal divide(BigDecimal divisor)
    throws ArithmeticException, IllegalArgumentException 
  {
    return divide(divisor, scale, ROUND_UNNECESSARY);
  }

  /**
   * Returns a BigDecimal whose value is the remainder in the quotient
   * this / val.  This is obtained by 
   * subtract(divideToIntegralValue(val).multiply(val)).  
   * @param val the divisor
   * @return a BigDecimal whose value is the remainder
   * @throws ArithmeticException if val == 0
   * @since 1.5
   */
  public BigDecimal remainder(BigDecimal val)
  {
    return subtract(divideToIntegralValue(val).multiply(val));
  }

  /**
   * Returns a BigDecimal array, the first element of which is the integer part
   * of this / val, and the second element of which is the remainder of 
   * that quotient.
   * @param val the divisor
   * @return the above described BigDecimal array
   * @throws ArithmeticException if val == 0
   * @since 1.5
   */
  public BigDecimal[] divideAndRemainder(BigDecimal val)
  {
    BigDecimal[] result = new BigDecimal[2];
    result[0] = divideToIntegralValue(val);
    result[1] = subtract(result[0].multiply(val));
    return result;
  }
  
  /**
   * Returns a BigDecimal whose value is the integer part of the quotient 
   * this / val.  The preferred scale is this.scale - val.scale.
   * @param val the divisor
   * @return a BigDecimal whose value is the integer part of this / val.
   * @throws ArithmeticException if val == 0
   * @since 1.5
   */
  public BigDecimal divideToIntegralValue(BigDecimal val)
  {