Java Code Examples for java.math.BigInteger#divide()

public CombinationGenerator (int n, int r) {
  if (r > n) {
    throw new IllegalArgumentException ();
  }
  if (n < 1) {
    throw new IllegalArgumentException ();
  }
  this.n = n;
  this.r = r;
  a = new int[r];
  BigInteger nFact = getFactorial (n);
  BigInteger rFact = getFactorial (r);
  BigInteger nminusrFact = getFactorial (n - r);
  total = nFact.divide (rFact.multiply (nminusrFact));
  reset ();
}
 

/**
 * Converts a byte array produced by {@link #encodeMod3Tight(int[])} back to an <code>int</code> array.
 *
 * @param b a byte array
 * @param N number of coefficients
 * @return the decoded array
 */
public static int[] decodeMod3Tight(byte[] b, int N)
{
    BigInteger sum = new BigInteger(1, b);
    int[] coeffs = new int[N];
    for (int i = 0; i < N; i++)
    {
        coeffs[i] = sum.mod(BigInteger.valueOf(3)).intValue() - 1;
        if (coeffs[i] > 1)
        {
            coeffs[i] -= 3;
        }
        sum = sum.divide(BigInteger.valueOf(3));
    }
    return coeffs;
}
 

/**
 * Divide zero by a negative number.
 */
public void testCase11() {
    byte aBytes[] = {0};
    byte bBytes[] = {15, 48, -29, 7, 98, -1, 39, -128};
    int aSign = 0;
    int bSign = -1;        
    byte rBytes[] = {0};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.divide(bNumber);
    byte resBytes[] = new byte[rBytes.length];
    resBytes = result.toByteArray();
    for(int i = 0; i < resBytes.length; i++) {
        assertTrue(resBytes[i] == rBytes[i]);
    }
    assertEquals("incorrect sign", 0, result.signum());
}
 

/**
 * Formats a {@link BigFraction} object to produce a string.  The BigFraction
 * is output in proper format.
 *
 * @param fraction the object to format.
 * @param toAppendTo where the text is to be appended
 * @param pos On input: an alignment field, if desired. On output: the
 *            offsets of the alignment field
 * @return the value passed in as toAppendTo.
 */
@Override
public StringBuffer format(final BigFraction fraction,
                           final StringBuffer toAppendTo, final FieldPosition pos) {
    
    pos.setBeginIndex(0);
    pos.setEndIndex(0);

    BigInteger num = fraction.getNumerator();
    BigInteger den = fraction.getDenominator();
    BigInteger whole = num.divide(den);
    num = num.remainder(den);
    
    if (!BigInteger.ZERO.equals(whole)) {
        getWholeFormat().format(whole, toAppendTo, pos);
        toAppendTo.append(' ');
        if (num.compareTo(BigInteger.ZERO) < 0) {
            num = num.negate();
        }
    }
    getNumeratorFormat().format(num, toAppendTo, pos);
    toAppendTo.append(" / ");
    getDenominatorFormat().format(den, toAppendTo, pos);
    
    return toAppendTo;
}
 

@Override
public byte[][] split(int n) {
  Preconditions.checkArgument(lastRowInt.compareTo(firstRowInt) > 0,
      "last row (%s) is configured less than first row (%s)", lastRow,
      firstRow);
  // +1 to range because the last row is inclusive
  BigInteger range = lastRowInt.subtract(firstRowInt).add(BigInteger.ONE);
  Preconditions.checkState(range.compareTo(BigInteger.valueOf(n)) >= 0,
      "split granularity (%s) is greater than the range (%s)", n, range);

  BigInteger[] splits = new BigInteger[n - 1];
  BigInteger sizeOfEachSplit = range.divide(BigInteger.valueOf(n));
  for (int i = 1; i < n; i++) {
    // NOTE: this means the last region gets all the slop.
    // This is not a big deal if we're assuming n << MAXHEX
    splits[i - 1] = firstRowInt.add(sizeOfEachSplit.multiply(BigInteger
        .valueOf(i)));
  }
  return convertToBytes(splits);
}
 

/**
 * factory method for creating a Point from 3 BigIntegers
 */
public static Point get_instance(BigInteger p_x, BigInteger p_y,
        BigInteger p_z)
{
    if (p_z.signum() < 0)
    {
        // the dominator z of a RationalPoint is expected to be positive
        p_x = p_x.negate();
        p_y = p_y.negate();
        p_z = p_z.negate();
        
    }
    if ((p_x.mod(p_z)).signum() == 0 && (p_x.mod(p_z)).signum() == 0)
    {
        // p_x and p_y can be divided by p_z
        p_x = p_x.divide(p_z);
        p_y = p_y.divide(p_z);
        p_z = BigInteger.ONE;
    }
    if (p_z.equals(BigInteger.ONE))
    {
        if ( (p_x.abs()).compareTo(Limits.CRIT_INT_BIG) <= 0 &&
                (p_y.abs()).compareTo(Limits.CRIT_INT_BIG) <= 0 )
        {
            // the Point fits into an IntPoint
            return new IntPoint(p_x.intValue(), p_y.intValue());
        }
    }
    return new RationalPoint(p_x, p_y, p_z);
}
 

public Rational(BigInteger numerator, BigInteger denominator) {
    if (denominator.equals(BigInteger.ZERO)) {
      throw new IllegalArgumentException("Denominator must != 0");
    } else if (denominator.compareTo(BigInteger.ZERO) < 0) {
      denominator = denominator.multiply(BI_M1);
      numerator = numerator.multiply(BI_M1);
    }
//    BigInteger negative = numerator.signum() < 0 ? minusOne : BigInteger.ONE;
//    numerator = numerator.multiply(negative);
    BigInteger gcd = numerator.gcd(denominator);
    this.numerator = numerator.divide(gcd);
    this.denominator = denominator.divide(gcd);
  }
 

/**
 * Create a {@link BigFraction} given the numerator and denominator as
 * {@code BigInteger}. The {@link BigFraction} is reduced to lowest terms.
 *
 * @param num the numerator, must not be {@code null}.
 * @param den the denominator, must not be {@code null}.
 * @throws ZeroException if the denominator is zero.
 * @throws NullArgumentException if either of the arguments is null
 */
public BigFraction(BigInteger num, BigInteger den) {
    MathUtils.checkNotNull(num, LocalizedFormats.NUMERATOR);
    MathUtils.checkNotNull(den, LocalizedFormats.DENOMINATOR);
    if (BigInteger.ZERO.equals(den)) {
        throw new ZeroException(LocalizedFormats.ZERO_DENOMINATOR);
    }
    if (BigInteger.ZERO.equals(num)) {
        numerator   = BigInteger.ZERO;
        denominator = BigInteger.ONE;
    } else {

        // reduce numerator and denominator by greatest common denominator
        final BigInteger gcd = num.gcd(den);
        if (BigInteger.ONE.compareTo(gcd) < 0) {
            num = num.divide(gcd);
            den = den.divide(gcd);
        }

        // move sign to numerator
        if (BigInteger.ZERO.compareTo(den) > 0) {
            num = num.negate();
            den = den.negate();
        }

        // store the values in the final fields
        numerator   = num;
        denominator = den;

    }
}
 

public static void divideAndRemainder(int order) {
    int failCount1 = 0;

    for (int i=0; i<SIZE; i++) {
        BigInteger x = fetchNumber(order).abs();
        while(x.compareTo(BigInteger.valueOf(3L)) != 1)
            x = fetchNumber(order).abs();
        BigInteger z = x.divide(BigInteger.valueOf(2L));
        BigInteger y[] = x.divideAndRemainder(x);
        if (!y[0].equals(BigInteger.ONE)) {
            failCount1++;
            System.err.println("fail1 x :"+x);
            System.err.println("      y :"+y);
        }
        else if (!y[1].equals(BigInteger.ZERO)) {
            failCount1++;
            System.err.println("fail2 x :"+x);
            System.err.println("      y :"+y);
        }

        y = x.divideAndRemainder(z);
        if (!y[0].equals(BigInteger.valueOf(2))) {
            failCount1++;
            System.err.println("fail3 x :"+x);
            System.err.println("      y :"+y);
        }
    }
    report("divideAndRemainder for " + order + " bits", failCount1);
}
 

public static void main (String [] args) throws Exception {
	BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	int T=Integer.parseInt(br.readLine());
	for (int t=1;t<=T;t++) {
		//Worse swap count = summation of arithmetic progression = [n(n-1)]/2
		//Average swap = worst swap / 2
		BigInteger bi=new BigInteger(br.readLine());
		BigInteger bi2=bi.subtract(BigInteger.ONE);
		
		BigInteger up=bi.multiply(bi2);
		BigInteger btm=new BigInteger("4");
		BigInteger gcd=up.gcd(btm);
		
		up=up.divide(gcd);
		btm=btm.divide(gcd);
		
		StringBuilder sb=new StringBuilder();
		sb.append("Case ");
		sb.append(t);
		sb.append(": ");
		sb.append(up.toString());
		if (!btm.equals(BigInteger.ONE)) {
			sb.append('/');
			sb.append(btm.toString());
		}
		System.out.println(sb.toString());
	}
}
 

public BigInteger calcDifficultyAlt(
        BigInteger currentTimestamp, BigInteger parentTimestamp, BigInteger parentDifficulty) {
    BigInteger diffBase = parentDifficulty.divide(this.constants.getDifficultyBoundDivisor());
    BigInteger diffMultiplier =
            max(
                    BigInteger.ONE.subtract(
                            currentTimestamp.subtract(parentTimestamp).divide(BigInteger.TEN)),
                    LOWER_BOUND);
    return parentDifficulty.add(diffBase.multiply(diffMultiplier));
}
 

public BigInteger calcDifficulty(BlockHeader curBlock, BlockHeader parent) {
    BigInteger pd = parent.getDifficultyBI();
    BigInteger quotient = pd.divide(this.constants.getDifficultyBoundDivisor());

    BigInteger sign = getCalcDifficultyMultiplier(curBlock, parent);

    BigInteger fromParent = pd.add(quotient.multiply(sign));
    BigInteger difficulty = max(this.constants.getMinimumMiningDifficulty(), fromParent);

    return difficulty;
}
 

public long getLong() throws StandardException
{
	if (isNull())
		return 0L;
	
	BigInteger bi = new BigInteger(data2c);
	
	// If at any time we see that the value to be scaled down
	// is within the range for a long, then we are guaranteed
	// that the scaled down value is within the range for long.
	boolean rangeOk = false;
	if ((bi.compareTo(BigIntegerDecimal.MAXLONG_PLUS_ONE) < 0)
		&& (bi.compareTo(BigIntegerDecimal.MINLONG_MINUS_ONE) > 0))
		rangeOk = true;
		
	for (int i = 0; i < sqlScale; i++)
	{
		bi = bi.divide(BigIntegerDecimal.TEN);
		if (rangeOk)
			continue;
		
		if ((bi.compareTo(BigIntegerDecimal.MAXLONG_PLUS_ONE) < 0)
				&& (bi.compareTo(BigIntegerDecimal.MINLONG_MINUS_ONE) > 0))
				rangeOk = true;
		}
	
	// TODO Range checking
	if (!rangeOk)
		throw StandardException.newException(SQLState.LANG_OUTSIDE_RANGE_FOR_DATATYPE, "BIGINT");
	
	return bi.longValue();
}
 

/**
 * Iterate over keys within the passed inclusive range.
 */
public static Iterable<byte[]> iterateOnSplits(
    final byte[] a, final byte[]b, final int num)
{  
  byte [] aPadded;
  byte [] bPadded;
  if (a.length < b.length) {
    aPadded = padTail(a, b.length - a.length);
    bPadded = b;
  } else if (b.length < a.length) {
    aPadded = a;
    bPadded = padTail(b, a.length - b.length);
  } else {
    aPadded = a;
    bPadded = b;
  }
  if (compareTo(aPadded,bPadded) >= 0) {
    throw new IllegalArgumentException("b <= a");
  }
  if (num <= 0) {
    throw new IllegalArgumentException("num cannot be < 0");
  }
  byte [] prependHeader = {1, 0};
  final BigInteger startBI = new BigInteger(add(prependHeader, aPadded));
  final BigInteger stopBI = new BigInteger(add(prependHeader, bPadded));
  final BigInteger diffBI = stopBI.subtract(startBI);
  final BigInteger splitsBI = BigInteger.valueOf(num + 1);
  if(diffBI.compareTo(splitsBI) < 0) {
    return null;
  }
  final BigInteger intervalBI;
  try {
    intervalBI = diffBI.divide(splitsBI);
  } catch(Exception e) {
    LOG.error("Exception caught during division", e);
    return null;
  }

  final Iterator<byte[]> iterator = new Iterator<byte[]>() {
    private int i = -1;
    
    @Override
    public boolean hasNext() {
      return i < num+1;
    }

    @Override
    public byte[] next() {
      i++;
      if (i == 0) return a;
      if (i == num + 1) return b;
      
      BigInteger curBI = startBI.add(intervalBI.multiply(BigInteger.valueOf(i)));
      byte [] padded = curBI.toByteArray();
      if (padded[1] == 0)
        padded = tail(padded, padded.length - 2);
      else
        padded = tail(padded, padded.length - 1);
      return padded;
    }

    @Override
    public void remove() {
      throw new UnsupportedOperationException();
    }
    
  };
  
  return new Iterable<byte[]>() {
    @Override
    public Iterator<byte[]> iterator() {
      return iterator;
    }
  };
}
 

private StringBuffer format(BigInteger number, StringBuffer result,
        FieldDelegate delegate, boolean formatLong) {

    boolean isNegative = number.signum() == -1;
    if (isNegative) {
        number = number.negate();
    }

    int compactDataIndex = selectCompactPattern(number);
    if (compactDataIndex != -1) {
        Number divisor = divisors.get(compactDataIndex);
        int iPart = getIntegerPart(number.doubleValue(), divisor.doubleValue());
        String prefix = getAffix(false, true, isNegative, compactDataIndex, iPart);
        String suffix = getAffix(false, false, isNegative, compactDataIndex, iPart);
        if (!prefix.isEmpty() || !suffix.isEmpty()) {
            appendPrefix(result, prefix, delegate);
            if (number.mod(new BigInteger(divisor.toString()))
                    .compareTo(BigInteger.ZERO) == 0) {
                number = number.divide(new BigInteger(divisor.toString()));

                decimalFormat.setDigitList(number, isNegative, 0);
                decimalFormat.subformatNumber(result, delegate,
                        isNegative, true, getMaximumIntegerDigits(),
                        getMinimumIntegerDigits(), getMaximumFractionDigits(),
                        getMinimumFractionDigits());
            } else {
                // To avoid truncation of fractional part store the value in
                // BigDecimal and follow BigDecimal path instead of
                // BigInteger path
                BigDecimal nDecimal = new BigDecimal(number)
                        .divide(new BigDecimal(divisor.toString()), getRoundingMode());
                decimalFormat.setDigitList(nDecimal, isNegative, getMaximumFractionDigits());
                decimalFormat.subformatNumber(result, delegate,
                        isNegative, false, getMaximumIntegerDigits(),
                        getMinimumIntegerDigits(), getMaximumFractionDigits(),
                        getMinimumFractionDigits());
            }
            appendSuffix(result, suffix, delegate);
        } else {
            number = isNegative ? number.negate() : number;
            defaultDecimalFormat.format(number, result, delegate, formatLong);
        }
    } else {
        number = isNegative ? number.negate() : number;
        defaultDecimalFormat.format(number, result, delegate, formatLong);
    }
    return result;
}
 

public BigRational expandTo(BigInteger newDenominator) {
	BigInteger multiplier = newDenominator.divide(this.den);
	return new BigRational(this.num.multiply(multiplier), this.den.multiply(multiplier));
}
 

@Override
public TypedValue getValueInternal(ExpressionState state) throws EvaluationException {
	Object leftOperand = getLeftOperand().getValueInternal(state).getValue();
	Object rightOperand = getRightOperand().getValueInternal(state).getValue();

	if (leftOperand instanceof Number && rightOperand instanceof Number) {
		Number leftNumber = (Number) leftOperand;
		Number rightNumber = (Number) rightOperand;

		if (leftNumber instanceof BigDecimal || rightNumber instanceof BigDecimal) {
			BigDecimal leftBigDecimal = NumberUtils.convertNumberToTargetClass(leftNumber, BigDecimal.class);
			BigDecimal rightBigDecimal = NumberUtils.convertNumberToTargetClass(rightNumber, BigDecimal.class);
			int scale = Math.max(leftBigDecimal.scale(), rightBigDecimal.scale());
			return new TypedValue(leftBigDecimal.divide(rightBigDecimal, scale, RoundingMode.HALF_EVEN));
		}
		else if (leftNumber instanceof Double || rightNumber instanceof Double) {
			this.exitTypeDescriptor = "D";
			return new TypedValue(leftNumber.doubleValue() / rightNumber.doubleValue());
		}
		else if (leftNumber instanceof Float || rightNumber instanceof Float) {
			this.exitTypeDescriptor = "F";
			return new TypedValue(leftNumber.floatValue() / rightNumber.floatValue());
		}
		else if (leftNumber instanceof BigInteger || rightNumber instanceof BigInteger) {
			BigInteger leftBigInteger = NumberUtils.convertNumberToTargetClass(leftNumber, BigInteger.class);
			BigInteger rightBigInteger = NumberUtils.convertNumberToTargetClass(rightNumber, BigInteger.class);
			return new TypedValue(leftBigInteger.divide(rightBigInteger));
		}
		else if (leftNumber instanceof Long || rightNumber instanceof Long) {
			this.exitTypeDescriptor = "J";
			return new TypedValue(leftNumber.longValue() / rightNumber.longValue());
		}
		else if (CodeFlow.isIntegerForNumericOp(leftNumber) || CodeFlow.isIntegerForNumericOp(rightNumber)) {
			this.exitTypeDescriptor = "I";
			return new TypedValue(leftNumber.intValue() / rightNumber.intValue());
		}
		else {
			// Unknown Number subtypes -> best guess is double division
			return new TypedValue(leftNumber.doubleValue() / rightNumber.doubleValue());
		}
	}

	return state.operate(Operation.DIVIDE, leftOperand, rightOperand);
}
 

public SimpleBigDecimal divide(SimpleBigDecimal b)
{
    checkScale(b);
    BigInteger dividend = bigInt.shiftLeft(scale);
    return new SimpleBigDecimal(dividend.divide(b.bigInt), scale);
}
 

static Object bigIntegerBinaryOperation(BigInteger lhs, BigInteger rhs, int kind)
{

    switch(kind)
    {
        // arithmetic
        case PLUS:
            return lhs.add(rhs);

        case MINUS:
            return lhs.subtract(rhs);

        case STAR:
            return lhs.multiply(rhs);

        case SLASH:
            return lhs.divide(rhs);

        case MOD:
        case MODX:
            return lhs.mod(rhs);

        case POWER:
        case POWERX:
            return lhs.pow(rhs.intValue());

        // bitwise
        case LSHIFT:
        case LSHIFTX:
            return lhs.shiftLeft(rhs.intValue());

        case RSIGNEDSHIFT:
        case RSIGNEDSHIFTX:
            return lhs.shiftRight(rhs.intValue());

        case RUNSIGNEDSHIFT:
        case RUNSIGNEDSHIFTX:
            if ( lhs.signum() >= 0 )
                return lhs.shiftRight(rhs.intValue());
            BigInteger opener = BigInteger.ONE.shiftLeft(lhs.toString(2).length() + 1);
            BigInteger opened = lhs.subtract(opener);
            BigInteger mask = opener.subtract(BigInteger.ONE).shiftRight(rhs.intValue() + 1);
            return opened.shiftRight(rhs.intValue()).and(mask);


        case BIT_AND:
        case BIT_ANDX:
            return lhs.and(rhs);

        case BIT_OR:
        case BIT_ORX:
            return lhs.or(rhs);

        case XOR:
        case XORX:
            return lhs.xor(rhs);

    }
    throw new InterpreterError(
            "Unimplemented binary integer operator");
}
 

/**
 * Iterate over keys within the passed range.
 */
public static Iterable<byte[]> iterateOnSplits(final byte[] a, final byte[] b, boolean inclusive, final int num) {
    byte[] aPadded;
    byte[] bPadded;
    if (a.length < b.length) {
        aPadded = padTail(a, b.length - a.length);
        bPadded = b;
    } else if (b.length < a.length) {
        aPadded = a;
        bPadded = padTail(b, a.length - b.length);
    } else {
        aPadded = a;
        bPadded = b;
    }
    if (compareTo(aPadded, bPadded) >= 0) {
        throw new IllegalArgumentException("b <= a");
    }
    if (num <= 0) {
        throw new IllegalArgumentException("num cannot be <= 0");
    }
    byte[] prependHeader = { 1, 0 };
    final BigInteger startBI = new BigInteger(add(prependHeader, aPadded));
    final BigInteger stopBI = new BigInteger(add(prependHeader, bPadded));
    BigInteger diffBI = stopBI.subtract(startBI);
    if (inclusive) {
        diffBI = diffBI.add(BigInteger.ONE);
    }
    final BigInteger splitsBI = BigInteger.valueOf(num + 1L);
    if (diffBI.compareTo(splitsBI) < 0) {
        return null;
    }
    final BigInteger intervalBI;
    try {
        intervalBI = diffBI.divide(splitsBI);
    } catch (Exception e) {
        LOG.error("Exception caught during division", e);
        return null;
    }

    final Iterator<byte[]> iterator = new Iterator<byte[]>() {
        private int i = -1;

        @Override
        public boolean hasNext() {
            return i < num + 1;
        }

        @Override
        public byte[] next() {
            i++;
            if (i == 0)
                return a;
            if (i == num + 1)
                return b;

            BigInteger curBI = startBI.add(intervalBI.multiply(BigInteger.valueOf(i)));
            byte[] padded = curBI.toByteArray();
            if (padded[1] == 0)
                padded = tail(padded, padded.length - 2);
            else
                padded = tail(padded, padded.length - 1);
            return padded;
        }

        @Override
        public void remove() {
            throw new UnsupportedOperationException();
        }

    };

    return () -> iterator;
}