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

/**
 * Raise a BigInteger to a long power.
 * @param k number to raise
 * @param e exponent (must be positive or null)
 * @return k<sup>e</sup>
 * @exception IllegalArgumentException if e is negative
 */
public static BigInteger pow(final BigInteger k, long e)
    throws IllegalArgumentException {

    if (e < 0) {
        throw MathRuntimeException.createIllegalArgumentException(
            "cannot raise an integral value to a negative power ({0}^{1})",
            k, e);
    }

    BigInteger result = BigInteger.ONE;
    BigInteger k2p    = k;
    while (e != 0) {
        if ((e & 0x1) != 0) {
            result = result.multiply(k2p);
        }
        k2p = k2p.multiply(k2p);
        e = e >> 1;
    }

    return result;

}
 

/**
 * Computes the integer x that is expressed through the given primes and the
 * congruences with the chinese remainder theorem (CRT).
 * 
 * @param congruences
 *            the congruences c_i
 * @param primes
 *            the primes p_i
 * @return an integer x for that x % p_i == c_i
 */
private static BigInteger chineseRemainder(Vector congruences, Vector primes)
{
    BigInteger retval = ZERO;
    BigInteger all = ONE;
    for (int i = 0; i < primes.size(); i++)
    {
        all = all.multiply((BigInteger)primes.elementAt(i));
    }
    for (int i = 0; i < primes.size(); i++)
    {
        BigInteger a = (BigInteger)primes.elementAt(i);
        BigInteger b = all.divide(a);
        BigInteger b_ = b.modInverse(a);
        BigInteger tmp = b.multiply(b_);
        tmp = tmp.multiply((BigInteger)congruences.elementAt(i));
        retval = retval.add(tmp);
    }

    return retval.mod(all);
}
 

/**
 * Multiply two negative numbers of the same length
 */
public void testCase1() {
    byte aBytes[] = {1, 2, 3, 4, 5, 6, 7, 1, 2, 3};
    byte bBytes[] = {10, 20, 30, 40, 50, 60, 70, 10, 20, 30};
    int aSign = -1;
    int bSign = -1;        
    byte rBytes[] = {10, 40, 100, -55, 96, 51, 76, 40, -45, 85, 105, 4, 28, -86, -117, -52, 100, 120, 90};
    BigInteger aNumber = new BigInteger(aSign, aBytes);
    BigInteger bNumber = new BigInteger(bSign, bBytes);
    BigInteger result = aNumber.multiply(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", 1, result.signum());
}
 

/**
 * Raise a BigInteger to a long power.
 * @param k number to raise
 * @param e exponent (must be positive or null)
 * @return k<sup>e</sup>
 * @exception IllegalArgumentException if e is negative
 */
public static BigInteger pow(final BigInteger k, long e)
    throws IllegalArgumentException {

    if (e < 0) {
        throw MathRuntimeException.createIllegalArgumentException(
            "cannot raise an integral value to a negative power ({0}^{1})",
            k, e);
    }

    BigInteger result = BigInteger.ONE;
    BigInteger k2p    = k;
    while (e != 0) {
        if ((e & 0x1) != 0) {
            result = result.multiply(k2p);
        }
        k2p = k2p.multiply(k2p);
        e = e >> 1;
    }

    return result;

}
 

/**
 * Raise a BigInteger to a long power.
 *
 * @param k Number to raise.
 * @param e Exponent (must be positive or zero).
 * @return k<sup>e</sup>
 * @throws NotPositiveException if {@code e < 0}.
 */
public static BigInteger pow(final BigInteger k, long e) {
    if (e < 0) {
        throw new NotPositiveException(LocalizedFormats.EXPONENT, e);
    }

    BigInteger result = BigInteger.ONE;
    BigInteger k2p    = k;
    while (e != 0) {
        if ((e & 0x1) != 0) {
            result = result.multiply(k2p);
        }
        k2p = k2p.multiply(k2p);
        e = e >> 1;
    }

    return result;

}
 

@Test
public void testMultiplyExactLong() {
    long[] specialValues = new long[] {
        Long.MIN_VALUE, Long.MIN_VALUE + 1, Long.MIN_VALUE + 2,
        Long.MAX_VALUE, Long.MAX_VALUE - 1, Long.MAX_VALUE - 2,
        -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
        -1 - (Long.MIN_VALUE / 2), 0 - (Long.MIN_VALUE / 2), 1 - (Long.MIN_VALUE / 2),
        -1 + (Long.MAX_VALUE / 2), 0 + (Long.MAX_VALUE / 2), 1 + (Long.MAX_VALUE / 2),
    };
    for (long a : specialValues) {
        for (long b : specialValues) {
            BigInteger bdA   = BigInteger.valueOf(a);
            BigInteger bdB   = BigInteger.valueOf(b);
            BigInteger bdMul = bdA.multiply(bdB);
            if (bdMul.compareTo(BigInteger.valueOf(Long.MIN_VALUE)) < 0 ||
                    bdMul.compareTo(BigInteger.valueOf(Long.MAX_VALUE)) > 0) {
                try {
                    FastMath.multiplyExact(a, b);
                    Assert.fail("an exception should have been thrown " + a + b);
                } catch (MathArithmeticException mae) {
                    // expected
                }
            } else {
                Assert.assertEquals(bdMul, BigInteger.valueOf(FastMath.multiplyExact(a, b)));
            }
        }
    }
}
 

/**
 * A000197 or what I call the "inverse hyperfactorial" is the product
 * 1^n*2^(n-1)*..*(n-1)^2*n^1 = 1!*2!*3!*...(n-1)!*n!.
 * @param n
 * @return the "inverse hyperfactorial" of n aka 1!*2!*3!*...(n-1)!*n!
 */
public static BigInteger inverse(int n) {
	BigInteger result = I_1;
	BigInteger kFactorial = I_1;
	for (int k=2; k<=n; k++) {
		kFactorial = kFactorial.multiply(BigInteger.valueOf(k));
		result = result.multiply(kFactorial);
	}
	return result;
}
 

private BigInteger generateV(BigInteger y, BigInteger p,
         BigInteger q, BigInteger g, BigInteger w, BigInteger r)
         throws SignatureException {

    byte[] s2;
    try {
        s2 = md.digest();
    } catch (RuntimeException re) {
        // Only for RawDSA due to its 20-byte length restriction
        throw new SignatureException(re.getMessage());
    }
    // get the leftmost min(N, outLen) bits of the digest value
    int nBytes = q.bitLength()/8;
    if (nBytes < s2.length) {
        s2 = Arrays.copyOfRange(s2, 0, nBytes);
    }
    BigInteger z = new BigInteger(1, s2);

    BigInteger u1 = z.multiply(w).mod(q);
    BigInteger u2 = (r.multiply(w)).mod(q);

    BigInteger t1 = g.modPow(u1,p);
    BigInteger t2 = y.modPow(u2,p);
    BigInteger t3 = t1.multiply(t2);
    BigInteger t5 = t3.mod(p);
    return t5.mod(q);
}
 

public BigInteger calcNumSequences() {
	BigInteger numSequences = BigInteger.ZERO;
	for (SimpleConfSpace.Position pos : positions) {
		BigInteger numResTypes = BigInteger.valueOf(pos.resFlex.resTypes.size());
		if (MathTools.isZero(numSequences)) {
			numSequences = numResTypes;
		} else {
			numSequences = numSequences.multiply(numResTypes);
		}
	}
	return numSequences;
}
 

@Test
public void testMultiplyExactInt() {
    int[] specialValues = new int[] {
        Integer.MIN_VALUE, Integer.MIN_VALUE + 1, Integer.MIN_VALUE + 2,
        Integer.MAX_VALUE, Integer.MAX_VALUE - 1, Integer.MAX_VALUE - 2,
        -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
        -1 - (Integer.MIN_VALUE / 2), 0 - (Integer.MIN_VALUE / 2), 1 - (Integer.MIN_VALUE / 2),
        -1 + (Integer.MAX_VALUE / 2), 0 + (Integer.MAX_VALUE / 2), 1 + (Integer.MAX_VALUE / 2),
    };
    for (int a : specialValues) {
        for (int b : specialValues) {
            BigInteger bdA   = BigInteger.valueOf(a);
            BigInteger bdB   = BigInteger.valueOf(b);
            BigInteger bdMul = bdA.multiply(bdB);
            if (bdMul.compareTo(BigInteger.valueOf(Integer.MIN_VALUE)) < 0 ||
                bdMul.compareTo(BigInteger.valueOf(Integer.MAX_VALUE)) > 0) {
                try {
                    FastMath.multiplyExact(a, b);
                    fail("an exception should have been thrown " + a + b);
                } catch (MathRuntimeException mae) {
                    // expected
                }
            } else {
                assertEquals(bdMul, BigInteger.valueOf(FastMath.multiplyExact(a, b)));
            }
        }
    }
}
 

public SimpleToken(@Required String name, @Required String symbol, @Required BigInteger initialAmount, @Required int decimals) {
    this.name = name;
    this.symbol = symbol;
    this.decimals = decimals;
    totalSupply = initialAmount.multiply(BigInteger.TEN.pow(decimals));;
    balances.put(Msg.sender(), totalSupply);
    emit(new TransferEvent(null, Msg.sender(), totalSupply));
}
 

private BigInteger generateV(BigInteger y, BigInteger p,
         BigInteger q, BigInteger g, BigInteger w, BigInteger r)
         throws SignatureException {

    byte[] s2;
    try {
        s2 = md.digest();
    } catch (RuntimeException re) {
        // Only for RawDSA due to its 20-byte length restriction
        throw new SignatureException(re.getMessage());
    }
    // get the leftmost min(N, outLen) bits of the digest value
    int nBytes = q.bitLength()/8;
    if (nBytes < s2.length) {
        s2 = Arrays.copyOfRange(s2, 0, nBytes);
    }
    BigInteger z = new BigInteger(1, s2);

    BigInteger u1 = z.multiply(w).mod(q);
    BigInteger u2 = (r.multiply(w)).mod(q);

    BigInteger t1 = g.modPow(u1,p);
    BigInteger t2 = y.modPow(u2,p);
    BigInteger t3 = t1.multiply(t2);
    BigInteger t5 = t3.mod(p);
    return t5.mod(q);
}
 

@Test
public void testDoubleValueForLargeNumeratorAndDenominator() {
    final BigInteger pow400 = BigInteger.TEN.pow(400);
    final BigInteger pow401 = BigInteger.TEN.pow(401);
    final BigInteger two = new BigInteger("2");
    final BigFraction large = new BigFraction(pow401.add(BigInteger.ONE),
                                              pow400.multiply(two));

    Assert.assertEquals(5, large.doubleValue(), 1e-15);
}
 

public void testNanoTime() throws Exception {
    String name = "name";
    DiagnosticCommand arg = new DiagnosticCommand(name,
            "desc", DiagnosticArgumentType.NANOTIME,
            false, "0");
    DiagnosticCommand[] args = {arg};

    BigInteger bi = new BigInteger("7");
    //These should work
    parse(name, bi.toString(), name + "=7ns", args);

    bi = bi.multiply(BigInteger.valueOf(1000));
    parse(name, bi.toString(), name + "=7us", args);

    bi = bi.multiply(BigInteger.valueOf(1000));
    parse(name, bi.toString(), name + "=7ms", args);

    bi = bi.multiply(BigInteger.valueOf(1000));
    parse(name, bi.toString(), name + "=7s", args);

    bi = bi.multiply(BigInteger.valueOf(60));
    parse(name, bi.toString() , name + "=7m", args);

    bi = bi.multiply(BigInteger.valueOf(60));
    parse(name, bi.toString() , name + "=7h", args);

    bi = bi.multiply(BigInteger.valueOf(24));
    parse(name, bi.toString() , name + "=7d", args);

    parse(name, "0", name + "=0", args);

    shouldFail(name + "=7xs", args);
    shouldFail(name + "=7mms", args);
    shouldFail(name + "=7f", args);
    //Currently, only value 0 is allowed without unit
    shouldFail(name + "=7", args);
}
 

private static void testMultiply() {
    System.out.println("Testing BigInteger.multiply");
    int py = 2000;
    int px = Integer.MAX_VALUE - py;
    BigInteger x = BigInteger.ONE.shiftLeft(px);
    BigInteger y = BigInteger.ONE.shiftLeft(py);
    try {
        BigInteger actual = x.multiply(y);
        throw new RuntimeException("(1 << " + px + " ) * (1 << " + py + ").bitLength()=" + actual.bitLength());
    } catch (ArithmeticException e) {
        // expected
    }
}
 

/**
 * Simple series expansion for exp(x).
 * The convergence criterion works only for |x|<=1, so it should not be called directly, only via one of the reduction formulas.
 */
private static BigDecimal expSeriesExpansion(BigDecimal x, Scale outScale) {
    // get demanded precision and compute the series limit for it:
	// for large arguments, the series doesn't converge so quickly,
	// we have to add extra precision...
	int xMag = Magnitude.of(x);
	if (xMag < 0) xMag = 0; // do not reduce precision if magnitude is < 0
	Scale errorScale = outScale.add(xMag);
       BigDecimal maxErr = errorScale.getErrorBound();
       if (DEBUG) LOG.debug("outScale=" + outScale + ", errorScale=" + errorScale + ", maxErr=" + maxErr);
    
    // calculate series expansion:
       BigDecimal r = F_1;
    BigDecimal xpow = F_1;
    BigInteger iFac = I_1;
    int i=1;
    BigDecimal elem;
    Scale internalScale = errorScale.add(1);
    do {
        xpow = internalScale.applyTo(xpow.multiply(x)); // x^i
        iFac = iFac.multiply(BigInteger.valueOf(i)); // i!
        if (DEBUG) LOG.debug("i=" + i + ", iFac=" + iFac);
        elem = BigDecimalMath.divide(xpow, iFac, internalScale);
        r = r.add(elem);
        if (DEBUG) LOG.debug("exp(" + x + ")[" + i + "] = " + r);
        i++;
    // stop if the error is smaller than allowed:
    } while (elem.abs().compareTo(maxErr) > 0);
    
    if (DEBUG) LOG.debug("exp(" + x + ") = " + r);
    return outScale.applyTo(r);
}
 

public static BigInteger new_multiply(BigInteger op1, BigInteger op2) {
  return op1.multiply(op2);
}
 

@Callable
public static byte[] multiply(byte[] val) {
    BigInteger testValue = new BigInteger(val);
    BigInteger result = testValue.multiply(testValue);
    return result.toByteArray();
}
 

public static RsaSharing generateSharing(final int keySizeBits, final int numServers, final int threshold) throws InvalidKeySpecException, NoSuchAlgorithmException {

		final int primeLength = (keySizeBits / 2);
		
		System.out.print("  Generating p...");
		final BigInteger p = Primes.generateSafePrime(primeLength);
		final BigInteger pPrime = Primes.getSophieGermainPrime(p);
		System.out.println(" done.");

		System.out.print("  Generating q...");
		final BigInteger q = Primes.generateSafePrime(primeLength);
		final BigInteger qPrime = Primes.getSophieGermainPrime(q);
		System.out.println(" done.");

		System.out.print("  Computing moduli...");
		final BigInteger m = pPrime.multiply(qPrime);
		final BigInteger n = p.multiply(q);
		System.out.println(" done.");

		// Public exponent (e must be greater than numServers)
		final BigInteger e = BigInteger.valueOf(65537);
		if (e.longValue() <= numServers) {
			throw new IllegalArgumentException("e must be greater than the number of servers!");
		}

		// Create standard RSA Public key pair
		System.out.print("  Creating RSA keypair...");
		final RSAPublicKeySpec publicKeySpec = new RSAPublicKeySpec(n, e);
		final KeyFactory keyFactory = KeyFactory.getInstance("RSA");
		final RSAPublicKey publicKey = (RSAPublicKey) keyFactory.generatePublic(publicKeySpec);

		// Create standard RSA Private key
		final BigInteger totient = p.subtract(BigInteger.ONE).multiply(q.subtract(BigInteger.ONE));
		final BigInteger realD = Exponentiation.modInverse(e, totient);
		final RSAPrivateKeySpec privateKeySpec = new RSAPrivateKeySpec(n, realD);
		final RSAPrivateKey privateKey = (RSAPrivateKey) keyFactory.generatePrivate(privateKeySpec);
		System.out.println(" done.");

		// Create secret shares of "d"
		System.out.print("  Generating secret shares...");
		final BigInteger d = Exponentiation.modInverse(e, m);

		// Generate random polynomial coefficients for secret sharing of d
		final BigInteger[] coefficients = RandomNumberGenerator.generateRandomArray(threshold, m);

		// Set the secret as the first coefficient
		coefficients[0] = d;

		// Evaluate the polynomial from 1 to numSevers (must not evaluate at zero!)
		final ShamirShare[] shares = new ShamirShare[numServers];
		for (int i = 0; i < numServers; i++) {
			BigInteger xCoord = BigInteger.valueOf(i + 1);
			shares[i] = Polynomials.evaluatePolynomial(coefficients, xCoord, m);
		}
		System.out.println(" done.");

		// Generate public and private verification keys
		System.out.print("  Creating public and private verification keys...");

		// Generate public verification key v as a random square modulo n
		final BigInteger sqrtV = RandomNumberGenerator.generateRandomInteger(n);
		final BigInteger v = sqrtV.modPow(ThresholdSignatures.TWO, n);

		// Generate private verification keys as v^share mod n
		final BigInteger[] verificationKeys = new BigInteger[shares.length];
		for (int i = 0; i < shares.length; i++) {
			verificationKeys[i] = v.modPow(shares[i].getY(), n);
		}
		System.out.println(" done.");

		return new RsaSharing(numServers, threshold, publicKey, privateKey, shares, v, verificationKeys);
	}
 

/**
 * Implements the {@code multiply} operator directly here for certain types
 * of supported operands and otherwise delegates to any registered overloader
 * for types not supported here.
 * <p>Supported operand types:
 * <ul>
 * <li>numbers
 * <li>String and int ('abc' * 2 == 'abcabc')
 * </ul>
 */
@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);
			return new TypedValue(leftBigDecimal.multiply(rightBigDecimal));
		}
		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.multiply(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 multiplication
			return new TypedValue(leftNumber.doubleValue() * rightNumber.doubleValue());
		}
	}

	if (leftOperand instanceof String && rightOperand instanceof Integer) {
		int repeats = (Integer) rightOperand;
		StringBuilder result = new StringBuilder();
		for (int i = 0; i < repeats; i++) {
			result.append(leftOperand);
		}
		return new TypedValue(result.toString());
	}

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