/*
* 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.
*/
package java.math;
import java.io.IOException;
import java.io.ObjectInputStream;
import java.io.ObjectOutputStream;
import java.io.Serializable;
import java.util.Random;
/**
* An immutable arbitrary-precision signed integer.
*
* <h3>Fast Cryptography</h3>
* This implementation is efficient for operations traditionally used in
* cryptography, such as the generation of large prime numbers and computation
* of the modular inverse.
*
* <h3>Slow Two's Complement Bitwise Operations</h3>
* This API includes operations for bitwise operations in two's complement
* representation. Two's complement is not the internal representation used by
* this implementation, so such methods may be inefficient. Use {@link
* java.util.BitSet} for high-performance bitwise operations on
* arbitrarily-large sequences of bits.
*/
public class BigInteger extends Number
implements Comparable<BigInteger>, Serializable {
/** This is the serialVersionUID used by the sun implementation. */
private static final long serialVersionUID = -8287574255936472291L;
private transient BigInt bigInt;
private transient boolean nativeIsValid = false;
private transient boolean javaIsValid = false;
/** The magnitude of this in the little-endian representation. */
transient int[] digits;
/**
* The length of this in measured in ints. Can be less than
* digits.length().
*/
transient int numberLength;
/** The sign of this. */
transient int sign;
/** The {@code BigInteger} constant 0. */
public static final BigInteger ZERO = new BigInteger(0, 0);
/** The {@code BigInteger} constant 1. */
public static final BigInteger ONE = new BigInteger(1, 1);
/** The {@code BigInteger} constant 10. */
public static final BigInteger TEN = new BigInteger(1, 10);
/** The {@code BigInteger} constant -1. */
static final BigInteger MINUS_ONE = new BigInteger(-1, 1);
/** All the {@code BigInteger} numbers in the range [0,10] are cached. */
static final BigInteger[] SMALL_VALUES = { ZERO, ONE, new BigInteger(1, 2),
new BigInteger(1, 3), new BigInteger(1, 4), new BigInteger(1, 5),
new BigInteger(1, 6), new BigInteger(1, 7), new BigInteger(1, 8),
new BigInteger(1, 9), TEN };
private transient int firstNonzeroDigit = -2;
/** sign field, used for serialization. */
private int signum;
/** absolute value field, used for serialization */
private byte[] magnitude;
/** Cache for the hash code. */
private transient int hashCode = 0;
BigInteger(BigInt bigInt) {
if (bigInt == null || bigInt.getNativeBIGNUM() == 0) {
throw new AssertionError();
}
setBigInt(bigInt);
}
BigInteger(int sign, long value) {
BigInt bigInt = new BigInt();
bigInt.putULongInt(value, (sign < 0));
setBigInt(bigInt);
}
/**
* Constructs a number without creating new space. This construct should be
* used only if the three fields of representation are known.
*
* @param sign the sign of the number.
* @param numberLength the length of the internal array.
* @param digits a reference of some array created before.
*/
BigInteger(int sign, int numberLength, int[] digits) {
setJavaRepresentation(sign, numberLength, digits);
}
/**
* Constructs a random non-negative {@code BigInteger} instance in the range
* {@code [0, pow(2, numBits)-1]}.
*
* @param numBits maximum length of the new {@code BigInteger} in bits.
* @param random is the random number generator to be used.
* @throws IllegalArgumentException if {@code numBits} < 0.
*/
public BigInteger(int numBits, Random random) {
if (numBits < 0) {
throw new IllegalArgumentException("numBits < 0: " + numBits);
}
if (numBits == 0) {
setJavaRepresentation(0, 1, new int[] { 0 });
} else {
int sign = 1;
int numberLength = (numBits + 31) >> 5;
int[] digits = new int[numberLength];
for (int i = 0; i < numberLength; i++) {
digits[i] = random.nextInt();
}
// Clear any extra bits.
digits[numberLength - 1] >>>= (-numBits) & 31;
setJavaRepresentation(sign, numberLength, digits);
}
javaIsValid = true;
}
/**
* Constructs a random {@code BigInteger} instance in the range {@code [0,
* pow(2, bitLength)-1]} which is probably prime. The probability that the
* returned {@code BigInteger} is prime is greater than
* {@code 1 - 1/2<sup>certainty</sup>)}.
*
* <p><b>Note:</b> the {@code Random} argument is ignored if
* {@code bitLength >= 16}, where this implementation will use OpenSSL's
* {@code BN_generate_prime_ex} as a source of cryptographically strong pseudo-random numbers.
*
* @param bitLength length of the new {@code BigInteger} in bits.
* @param certainty tolerated primality uncertainty.
* @throws ArithmeticException if {@code bitLength < 2}.
* @see <a href="http://www.openssl.org/docs/crypto/BN_rand.html">
* Specification of random generator used from OpenSSL library</a>
*/
public BigInteger(int bitLength, int certainty, Random random) {
if (bitLength < 2) {
throw new ArithmeticException("bitLength < 2: " + bitLength);
}
if (bitLength < 16) {
// We have to generate short primes ourselves, because OpenSSL bottoms out at 16 bits.
int candidate;
do {
candidate = random.nextInt() & ((1 << bitLength) - 1);
candidate |= (1 << (bitLength - 1)); // Set top bit.
if (bitLength > 2) {
candidate |= 1; // Any prime longer than 2 bits must have the bottom bit set.
}
} while (!isSmallPrime(candidate));
BigInt prime = new BigInt();
prime.putULongInt(candidate, false);
setBigInt(prime);
} else {
// We need a loop here to work around an OpenSSL bug; http://b/8588028.
do {
setBigInt(BigInt.generatePrimeDefault(bitLength));
} while (bitLength() != bitLength);
}
}
private static boolean isSmallPrime(int x) {
if (x == 2) {
return true;
}
if ((x % 2) == 0) {
return false;
}
final int max = (int) Math.sqrt(x);
for (int i = 3; i <= max; i += 2) {
if ((x % i) == 0) {
return false;
}
}
return true;
}
/**
* Constructs a new {@code BigInteger} by parsing {@code value}. The string
* representation consists of an optional plus or minus sign followed by a
* non-empty sequence of decimal digits. Digits are interpreted as if by
* {@code Character.digit(char,10)}.
*
* @param value string representation of the new {@code BigInteger}.
* @throws NullPointerException if {@code value == null}.
* @throws NumberFormatException if {@code value} is not a valid
* representation of a {@code BigInteger}.
*/
public BigInteger(String value) {
BigInt bigInt = new BigInt();
bigInt.putDecString(value);
setBigInt(bigInt);
}
/**
* Constructs a new {@code BigInteger} instance by parsing {@code value}.
* The string representation consists of an optional plus or minus sign
* followed by a non-empty sequence of digits in the specified radix. Digits
* are interpreted as if by {@code Character.digit(char, radix)}.
*
* @param value string representation of the new {@code BigInteger}.
* @param radix the base to be used for the conversion.
* @throws NullPointerException if {@code value == null}.
* @throws NumberFormatException if {@code value} is not a valid
* representation of a {@code BigInteger} or if {@code radix <
* Character.MIN_RADIX} or {@code radix > Character.MAX_RADIX}.
*/
public BigInteger(String value, int radix) {
if (value == null) {
throw new NullPointerException("value == null");
}
if (radix == 10) {
BigInt bigInt = new BigInt();
bigInt.putDecString(value);
setBigInt(bigInt);
} else if (radix == 16) {
BigInt bigInt = new BigInt();
bigInt.putHexString(value);
setBigInt(bigInt);
} else {
if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX) {
throw new NumberFormatException("Invalid radix: " + radix);
}
if (value.isEmpty()) {
throw new NumberFormatException("value.isEmpty()");
}
BigInteger.parseFromString(this, value, radix);
}
}
/**
* Constructs a new {@code BigInteger} instance with the given sign and
* magnitude.
*
* @param signum sign of the new {@code BigInteger} (-1 for negative, 0 for
* zero, 1 for positive).
* @param magnitude magnitude of the new {@code BigInteger} with the most
* significant byte first.
* @throws NullPointerException if {@code magnitude == null}.
* @throws NumberFormatException if the sign is not one of -1, 0, 1 or if
* the sign is zero and the magnitude contains non-zero entries.
*/
public BigInteger(int signum, byte[] magnitude) {
if (magnitude == null) {
throw new NullPointerException("magnitude == null");
}
if (signum < -1 || signum > 1) {
throw new NumberFormatException("Invalid signum: " + signum);
}
if (signum == 0) {
for (byte element : magnitude) {
if (element != 0) {
throw new NumberFormatException("signum-magnitude mismatch");
}
}
}
BigInt bigInt = new BigInt();
bigInt.putBigEndian(magnitude, signum < 0);
setBigInt(bigInt);
}
/**
* Constructs a new {@code BigInteger} from the given two's complement
* representation. The most significant byte is the entry at index 0. The
* most significant bit of this entry determines the sign of the new {@code
* BigInteger} instance. The array must be nonempty.
*
* @param value two's complement representation of the new {@code
* BigInteger}.
* @throws NullPointerException if {@code value == null}.
* @throws NumberFormatException if the length of {@code value} is zero.
*/
public BigInteger(byte[] value) {
if (value.length == 0) {
throw new NumberFormatException("value.length == 0");
}
BigInt bigInt = new BigInt();
bigInt.putBigEndianTwosComplement(value);
setBigInt(bigInt);
}
/**
* Returns the internal native representation of this big integer, computing
* it if necessary.
*/
BigInt getBigInt() {
if (nativeIsValid) {
return bigInt;
}
synchronized (this) {
if (nativeIsValid) {
return bigInt;
}
BigInt bigInt = new BigInt();
bigInt.putLittleEndianInts(digits, (sign < 0));
setBigInt(bigInt);
return bigInt;
}
}
private void setBigInt(BigInt bigInt) {
this.bigInt = bigInt;
this.nativeIsValid = true;
}
private void setJavaRepresentation(int sign, int numberLength, int[] digits) {
// decrement numberLength to drop leading zeroes...
while (numberLength > 0 && digits[--numberLength] == 0) {
;
}
// ... and then increment it back because we always drop one too many
if (digits[numberLength++] == 0) {
sign = 0;
}
this.sign = sign;
this.digits = digits;
this.numberLength = numberLength;
this.javaIsValid = true;
}
void prepareJavaRepresentation() {
if (javaIsValid) {
return;
}
synchronized (this) {
if (javaIsValid) {
return;
}
int sign = bigInt.sign();
int[] digits = (sign != 0) ? bigInt.littleEndianIntsMagnitude() : new int[] { 0 };
setJavaRepresentation(sign, digits.length, digits);
}
}
/** Returns a {@code BigInteger} whose value is equal to {@code value}. */
public static BigInteger valueOf(long value) {
if (value < 0) {
if (value != -1) {
return new BigInteger(-1, -value);
}
return MINUS_ONE;
} else if (value < SMALL_VALUES.length) {
return SMALL_VALUES[(int) value];
} else {// (value > 10)
return new BigInteger(1, value);
}
}
/**
* Returns the two's complement representation of this {@code BigInteger} in
* a byte array.
*/
public byte[] toByteArray() {
return twosComplement();
}
/**
* Returns a {@code BigInteger} whose value is the absolute value of {@code
* this}.
*/
public BigInteger abs() {
BigInt bigInt = getBigInt();
if (bigInt.sign() >= 0) {
return this;
}
BigInt a = bigInt.copy();
a.setSign(1);
return new BigInteger(a);
}
/**
* Returns a {@code BigInteger} whose value is the {@code -this}.
*/
public BigInteger negate() {
BigInt bigInt = getBigInt();
int sign = bigInt.sign();
if (sign == 0) {
return this;
}
BigInt a = bigInt.copy();
a.setSign(-sign);
return new BigInteger(a);
}
/**
* Returns a {@code BigInteger} whose value is {@code this + value}.
*/
public BigInteger add(BigInteger value) {
BigInt lhs = getBigInt();
BigInt rhs = value.getBigInt();
if (rhs.sign() == 0) {
return this;
}
if (lhs.sign() == 0) {
return value;
}
return new BigInteger(BigInt.addition(lhs, rhs));
}
/**
* Returns a {@code BigInteger} whose value is {@code this - value}.
*/
public BigInteger subtract(BigInteger value) {
BigInt lhs = getBigInt();
BigInt rhs = value.getBigInt();
if (rhs.sign() == 0) {
return this;
}
return new BigInteger(BigInt.subtraction(lhs, rhs));
}
/**
* Returns the sign of this {@code BigInteger}.
*
* @return {@code -1} if {@code this < 0}, {@code 0} if {@code this == 0},
* {@code 1} if {@code this > 0}.
*/
public int signum() {
if (javaIsValid) {
return sign;
}
return getBigInt().sign();
}
/**
* Returns a {@code BigInteger} whose value is {@code this >> n}. For
* negative arguments, the result is also negative. The shift distance may
* be negative which means that {@code this} is shifted left.
*
* <p><b>Implementation Note:</b> Usage of this method on negative values is
* not recommended as the current implementation is not efficient.
*
* @param n shift distance
* @return {@code this >> n} if {@code n >= 0}; {@code this << (-n)}
* otherwise
*/
public BigInteger shiftRight(int n) {
return shiftLeft(-n);
}
/**
* Returns a {@code BigInteger} whose value is {@code this << n}. The
* result is equivalent to {@code this * pow(2, n)} if n >= 0. The shift
* distance may be negative which means that {@code this} is shifted right.
* The result then corresponds to {@code floor(this / pow(2, -n))}.
*
* <p><b>Implementation Note:</b> Usage of this method on negative values is
* not recommended as the current implementation is not efficient.
*
* @param n shift distance.
* @return {@code this << n} if {@code n >= 0}; {@code this >> (-n)}.
* otherwise
*/
public BigInteger shiftLeft(int n) {
if (n == 0) {
return this;
}
int sign = signum();
if (sign == 0) {
return this;
}
if ((sign > 0) || (n >= 0)) {
return new BigInteger(BigInt.shift(getBigInt(), n));
} else {
// Negative numbers faking 2's complement:
// Not worth optimizing this:
// Sticking to Harmony Java implementation.
return BitLevel.shiftRight(this, -n);
}
}
BigInteger shiftLeftOneBit() {
return (signum() == 0) ? this : BitLevel.shiftLeftOneBit(this);
}
/**
* Returns the length of the value's two's complement representation without
* leading zeros for positive numbers / without leading ones for negative
* values.
*
* <p>The two's complement representation of {@code this} will be at least
* {@code bitLength() + 1} bits long.
*
* <p>The value will fit into an {@code int} if {@code bitLength() < 32} or
* into a {@code long} if {@code bitLength() < 64}.
*
* @return the length of the minimal two's complement representation for
* {@code this} without the sign bit.
*/
public int bitLength() {
// Optimization to avoid unnecessary duplicate representation:
if (!nativeIsValid && javaIsValid) {
return BitLevel.bitLength(this);
}
return getBigInt().bitLength();
}
/**
* Tests whether the bit at position n in {@code this} is set. The result is
* equivalent to {@code this & pow(2, n) != 0}.
*
* <p><b>Implementation Note:</b> Usage of this method is not recommended as
* the current implementation is not efficient.
*
* @param n position where the bit in {@code this} has to be inspected.
* @throws ArithmeticException if {@code n < 0}.
*/
public boolean testBit(int n) {
if (n < 0) {
throw new ArithmeticException("n < 0: " + n);
}
int sign = signum();
if (sign > 0 && nativeIsValid && !javaIsValid) {
return getBigInt().isBitSet(n);
} else {
// Negative numbers faking 2's complement:
// Not worth optimizing this:
// Sticking to Harmony Java implementation.
prepareJavaRepresentation();
if (n == 0) {
return ((digits[0] & 1) != 0);
}
int intCount = n >> 5;
if (intCount >= numberLength) {
return (sign < 0);
}
int digit = digits[intCount];
n = (1 << (n & 31)); // int with 1 set to the needed position
if (sign < 0) {
int firstNonZeroDigit = getFirstNonzeroDigit();
if (intCount < firstNonZeroDigit) {
return false;
} else if (firstNonZeroDigit == intCount) {
digit = -digit;
} else {
digit = ~digit;
}
}
return ((digit & n) != 0);
}
}
/**
* Returns a {@code BigInteger} which has the same binary representation
* as {@code this} but with the bit at position n set. The result is
* equivalent to {@code this | pow(2, n)}.
*
* <p><b>Implementation Note:</b> Usage of this method is not recommended as
* the current implementation is not efficient.
*
* @param n position where the bit in {@code this} has to be set.
* @throws ArithmeticException if {@code n < 0}.
*/
public BigInteger setBit(int n) {
prepareJavaRepresentation();
if (!testBit(n)) {
return BitLevel.flipBit(this, n);
} else {
return this;
}
}
/**
* Returns a {@code BigInteger} which has the same binary representation
* as {@code this} but with the bit at position n cleared. The result is
* equivalent to {@code this & ~pow(2, n)}.
*
* <p><b>Implementation Note:</b> Usage of this method is not recommended as
* the current implementation is not efficient.
*
* @param n position where the bit in {@code this} has to be cleared.
* @throws ArithmeticException if {@code n < 0}.
*/
public BigInteger clearBit(int n) {
prepareJavaRepresentation();
if (testBit(n)) {
return BitLevel.flipBit(this, n);
} else {
return this;
}
}
/**
* Returns a {@code BigInteger} which has the same binary representation
* as {@code this} but with the bit at position n flipped. The result is
* equivalent to {@code this ^ pow(2, n)}.
*
* <p><b>Implementation Note:</b> Usage of this method is not recommended as
* the current implementation is not efficient.
*
* @param n position where the bit in {@code this} has to be flipped.
* @throws ArithmeticException if {@code n < 0}.
*/
public BigInteger flipBit(int n) {
prepareJavaRepresentation();
if (n < 0) {
throw new ArithmeticException("n < 0: " + n);
}
return BitLevel.flipBit(this, n);
}
/**
* Returns the position of the lowest set bit in the two's complement
* representation of this {@code BigInteger}. If all bits are zero (this==0)
* then -1 is returned as result.
*
* <p><b>Implementation Note:</b> Usage of this method is not recommended as
* the current implementation is not efficient.
*/
public int getLowestSetBit() {
prepareJavaRepresentation();
if (sign == 0) {
return -1;
}
// (sign != 0) implies that exists some non zero digit
int i = getFirstNonzeroDigit();
return ((i << 5) + Integer.numberOfTrailingZeros(digits[i]));
}
/**
* Returns the number of bits in the two's complement representation of
* {@code this} which differ from the sign bit. If {@code this} is negative,
* the result is equivalent to the number of bits set in the two's
* complement representation of {@code -this - 1}.
*
* <p>Use {@code bitLength(0)} to find the length of the binary value in
* bits.
*
* <p><b>Implementation Note:</b> Usage of this method is not recommended as
* the current implementation is not efficient.
*/
public int bitCount() {
prepareJavaRepresentation();
return BitLevel.bitCount(this);
}
/**
* Returns a {@code BigInteger} whose value is {@code ~this}. The result
* of this operation is {@code -this-1}.
*
* <p><b>Implementation Note:</b> Usage of this method is not recommended as
* the current implementation is not efficient.
*/
public BigInteger not() {
this.prepareJavaRepresentation();
return Logical.not(this);
}
/**
* Returns a {@code BigInteger} whose value is {@code this & value}.
*
* <p><b>Implementation Note:</b> Usage of this method is not recommended
* as the current implementation is not efficient.
*
* @param value value to be and'ed with {@code this}.
* @throws NullPointerException if {@code value == null}.
*/
public BigInteger and(BigInteger value) {
this.prepareJavaRepresentation();
value.prepareJavaRepresentation();
return Logical.and(this, value);
}
/**
* Returns a {@code BigInteger} whose value is {@code this | value}.
*
* <p><b>Implementation Note:</b> Usage of this method is not recommended as
* the current implementation is not efficient.
*
* @param value value to be or'ed with {@code this}.
* @throws NullPointerException if {@code value == null}.
*/
public BigInteger or(BigInteger value) {
this.prepareJavaRepresentation();
value.prepareJavaRepresentation();
return Logical.or(this, value);
}
/**
* Returns a {@code BigInteger} whose value is {@code this ^ value}.
*
* <p><b>Implementation Note:</b> Usage of this method is not recommended as
* the current implementation is not efficient.
*
* @param value value to be xor'ed with {@code this}
* @throws NullPointerException if {@code value == null}
*/
public BigInteger xor(BigInteger value) {
this.prepareJavaRepresentation();
value.prepareJavaRepresentation();
return Logical.xor(this, value);
}
/**
* Returns a {@code BigInteger} whose value is {@code this & ~value}.
* Evaluating {@code x.andNot(value)} returns the same result as {@code
* x.and(value.not())}.
*
* <p><b>Implementation Note:</b> Usage of this method is not recommended
* as the current implementation is not efficient.
*
* @param value value to be not'ed and then and'ed with {@code this}.
* @throws NullPointerException if {@code value == null}.
*/
public BigInteger andNot(BigInteger value) {
this.prepareJavaRepresentation();
value.prepareJavaRepresentation();
return Logical.andNot(this, value);
}
/**
* Returns this {@code BigInteger} as an int value. If {@code this} is too
* big to be represented as an int, then {@code this % (1 << 32)} is
* returned.
*/
@Override
public int intValue() {
if (nativeIsValid && bigInt.twosCompFitsIntoBytes(4)) {
return (int) bigInt.longInt();
}
this.prepareJavaRepresentation();
return (sign * digits[0]);
}
/**
* Returns this {@code BigInteger} as a long value. If {@code this} is too
* big to be represented as a long, then {@code this % pow(2, 64)} is
* returned.
*/
@Override
public long longValue() {
if (nativeIsValid && bigInt.twosCompFitsIntoBytes(8)) {
return bigInt.longInt();
}
prepareJavaRepresentation();
long value = numberLength > 1
? ((long) digits[1]) << 32 | digits[0] & 0xFFFFFFFFL
: digits[0] & 0xFFFFFFFFL;
return sign * value;
}
/**
* Returns this {@code BigInteger} as a float. If {@code this} is too big to
* be represented as a float, then {@code Float.POSITIVE_INFINITY} or
* {@code Float.NEGATIVE_INFINITY} is returned. Note that not all integers
* in the range {@code [-Float.MAX_VALUE, Float.MAX_VALUE]} can be exactly
* represented as a float.
*/
@Override
public float floatValue() {
return (float) doubleValue();
}
/**
* Returns this {@code BigInteger} as a double. If {@code this} is too big
* to be represented as a double, then {@code Double.POSITIVE_INFINITY} or
* {@code Double.NEGATIVE_INFINITY} is returned. Note that not all integers
* in the range {@code [-Double.MAX_VALUE, Double.MAX_VALUE]} can be exactly
* represented as a double.
*/
@Override
public double doubleValue() {
return Conversion.bigInteger2Double(this);
}
/**
* Compares this {@code BigInteger} with {@code value}. Returns {@code -1}
* if {@code this < value}, {@code 0} if {@code this == value} and {@code 1}
* if {@code this > value}, .
*
* @param value value to be compared with {@code this}.
* @throws NullPointerException if {@code value == null}.
*/
public int compareTo(BigInteger value) {
return BigInt.cmp(getBigInt(), value.getBigInt());
}
/**
* Returns the minimum of this {@code BigInteger} and {@code value}.
*
* @param value value to be used to compute the minimum with {@code this}.
* @throws NullPointerException if {@code value == null}.
*/
public BigInteger min(BigInteger value) {
return this.compareTo(value) == -1 ? this : value;
}
/**
* Returns the maximum of this {@code BigInteger} and {@code value}.
*
* @param value value to be used to compute the maximum with {@code this}
* @throws NullPointerException if {@code value == null}
*/
public BigInteger max(BigInteger value) {
return this.compareTo(value) == 1 ? this : value;
}
@Override
public int hashCode() {
if (hashCode != 0) {
return hashCode;
}
prepareJavaRepresentation();
for (int i = 0; i < numberLength; ++i) {
hashCode = hashCode * 33 + digits[i];
}
hashCode = hashCode * sign;
return hashCode;
}
@Override
public boolean equals(Object x) {
if (this == x) {
return true;
}
if (x instanceof BigInteger) {
return this.compareTo((BigInteger) x) == 0;
}
return false;
}
/**
* Returns a string representation of this {@code BigInteger} in decimal
* form.
*/
@Override
public String toString() {
return getBigInt().decString();
}
/**
* Returns a string containing a string representation of this {@code
* BigInteger} with base radix. If {@code radix < Character.MIN_RADIX} or
* {@code radix > Character.MAX_RADIX} then a decimal representation is
* returned. The characters of the string representation are generated with
* method {@code Character.forDigit}.
*
* @param radix base to be used for the string representation.
*/
public String toString(int radix) {
if (radix == 10) {
return getBigInt().decString();
} else {
prepareJavaRepresentation();
return Conversion.bigInteger2String(this, radix);
}
}
/**
* Returns a {@code BigInteger} whose value is greatest common divisor
* of {@code this} and {@code value}. If {@code this == 0} and {@code
* value == 0} then zero is returned, otherwise the result is positive.
*
* @param value value with which the greatest common divisor is computed.
* @throws NullPointerException if {@code value == null}.
*/
public BigInteger gcd(BigInteger value) {
return new BigInteger(BigInt.gcd(getBigInt(), value.getBigInt()));
}
/**
* Returns a {@code BigInteger} whose value is {@code this * value}.
*
* @throws NullPointerException if {@code value == null}.
*/
public BigInteger multiply(BigInteger value) {
return new BigInteger(BigInt.product(getBigInt(), value.getBigInt()));
}
/**
* Returns a {@code BigInteger} whose value is {@code pow(this, exp)}.
*
* @throws ArithmeticException if {@code exp < 0}.
*/
public BigInteger pow(int exp) {
if (exp < 0) {
throw new ArithmeticException("exp < 0: " + exp);
}
return new BigInteger(BigInt.exp(getBigInt(), exp));
}
/**
* Returns a two element {@code BigInteger} array containing
* {@code this / divisor} at index 0 and {@code this % divisor} at index 1.
*
* @param divisor value by which {@code this} is divided.
* @throws NullPointerException if {@code divisor == null}.
* @throws ArithmeticException if {@code divisor == 0}.
* @see #divide
* @see #remainder
*/
public BigInteger[] divideAndRemainder(BigInteger divisor) {
BigInt divisorBigInt = divisor.getBigInt();
BigInt quotient = new BigInt();
BigInt remainder = new BigInt();
BigInt.division(getBigInt(), divisorBigInt, quotient, remainder);
return new BigInteger[] {new BigInteger(quotient), new BigInteger(remainder) };
}
/**
* Returns a {@code BigInteger} whose value is {@code this / divisor}.
*
* @param divisor value by which {@code this} is divided.
* @return {@code this / divisor}.
* @throws NullPointerException if {@code divisor == null}.
* @throws ArithmeticException if {@code divisor == 0}.
*/
public BigInteger divide(BigInteger divisor) {
BigInt quotient = new BigInt();
BigInt.division(getBigInt(), divisor.getBigInt(), quotient, null);
return new BigInteger(quotient);
}
/**
* Returns a {@code BigInteger} whose value is {@code this % divisor}.
* Regarding signs this methods has the same behavior as the % operator on
* ints: the sign of the remainder is the same as the sign of this.
*
* @param divisor value by which {@code this} is divided.
* @throws NullPointerException if {@code divisor == null}.
* @throws ArithmeticException if {@code divisor == 0}.
*/
public BigInteger remainder(BigInteger divisor) {
BigInt remainder = new BigInt();
BigInt.division(getBigInt(), divisor.getBigInt(), null, remainder);
return new BigInteger(remainder);
}
/**
* Returns a {@code BigInteger} whose value is {@code 1/this mod m}. The
* modulus {@code m} must be positive. The result is guaranteed to be in the
* interval {@code [0, m)} (0 inclusive, m exclusive). If {@code this} is
* not relatively prime to m, then an exception is thrown.
*
* @param m the modulus.
* @throws NullPointerException if {@code m == null}
* @throws ArithmeticException if {@code m < 0 or} if {@code this} is not
* relatively prime to {@code m}
*/
public BigInteger modInverse(BigInteger m) {
if (m.signum() <= 0) {
throw new ArithmeticException("modulus not positive");
}
return new BigInteger(BigInt.modInverse(getBigInt(), m.getBigInt()));
}
/**
* Returns a {@code BigInteger} whose value is {@code
* pow(this, exponent) mod modulus}. The modulus must be positive. The
* result is guaranteed to be in the interval {@code [0, modulus)}.
* If the exponent is negative, then
* {@code pow(this.modInverse(modulus), -exponent) mod modulus} is computed.
* The inverse of this only exists if {@code this} is relatively prime to the modulus,
* otherwise an exception is thrown.
*
* @throws NullPointerException if {@code modulus == null} or {@code exponent == null}.
* @throws ArithmeticException if {@code modulus < 0} or if {@code exponent < 0} and
* not relatively prime to {@code modulus}.
*/
public BigInteger modPow(BigInteger exponent, BigInteger modulus) {
if (modulus.signum() <= 0) {
throw new ArithmeticException("modulus.signum() <= 0");
}
int exponentSignum = exponent.signum();
if (exponentSignum == 0) { // OpenSSL gets this case wrong; http://b/8574367.
return ONE.mod(modulus);
}
BigInteger base = exponentSignum < 0 ? modInverse(modulus) : this;
return new BigInteger(BigInt.modExp(base.getBigInt(), exponent.getBigInt(), modulus.getBigInt()));
}
/**
* Returns a {@code BigInteger} whose value is {@code this mod m}. The
* modulus {@code m} must be positive. The result is guaranteed to be in the
* interval {@code [0, m)} (0 inclusive, m exclusive). The behavior of this
* function is not equivalent to the behavior of the % operator defined for
* the built-in {@code int}'s.
*
* @param m the modulus.
* @return {@code this mod m}.
* @throws NullPointerException if {@code m == null}.
* @throws ArithmeticException if {@code m < 0}.
*/
public BigInteger mod(BigInteger m) {
if (m.signum() <= 0) {
throw new ArithmeticException("m.signum() <= 0");
}
return new BigInteger(BigInt.modulus(getBigInt(), m.getBigInt()));
}
/**
* Tests whether this {@code BigInteger} is probably prime. If {@code true}
* is returned, then this is prime with a probability greater than
* {@code 1 - 1/2<sup>certainty</sup>)}. If {@code false} is returned, then this
* is definitely composite. If the argument {@code certainty} <= 0, then
* this method returns true.
*
* @param certainty tolerated primality uncertainty.
* @return {@code true}, if {@code this} is probably prime, {@code false}
* otherwise.
*/
public boolean isProbablePrime(int certainty) {
if (certainty <= 0) {
return true;
}
return getBigInt().isPrime(certainty);
}
/**
* Returns the smallest integer x > {@code this} which is probably prime as
* a {@code BigInteger} instance. The probability that the returned {@code
* BigInteger} is prime is greater than {@code 1 - 1/2<sup>100</sup>}.
*
* @return smallest integer > {@code this} which is probably prime.
* @throws ArithmeticException if {@code this < 0}.
*/
public BigInteger nextProbablePrime() {
if (sign < 0) {
throw new ArithmeticException("sign < 0");
}
return Primality.nextProbablePrime(this);
}
/**
* Returns a random positive {@code BigInteger} instance in the range {@code
* [0, pow(2, bitLength)-1]} which is probably prime. The probability that
* the returned {@code BigInteger} is prime is greater than {@code 1 - 1/2<sup>100</sup>)}.
*
* @param bitLength length of the new {@code BigInteger} in bits.
* @return probably prime random {@code BigInteger} instance.
* @throws IllegalArgumentException if {@code bitLength < 2}.
*/
public static BigInteger probablePrime(int bitLength, Random random) {
return new BigInteger(bitLength, 100, random);
}
/* Private Methods */
/**
* Returns the two's complement representation of this BigInteger in a byte
* array.
*/
private byte[] twosComplement() {
prepareJavaRepresentation();
if (this.sign == 0) {
return new byte[] { 0 };
}
BigInteger temp = this;
int bitLen = bitLength();
int iThis = getFirstNonzeroDigit();
int bytesLen = (bitLen >> 3) + 1;
/* Puts the little-endian int array representing the magnitude
* of this BigInteger into the big-endian byte array. */
byte[] bytes = new byte[bytesLen];
int firstByteNumber = 0;
int highBytes;
int bytesInInteger = 4;
int hB;
if (bytesLen - (numberLength << 2) == 1) {
bytes[0] = (byte) ((sign < 0) ? -1 : 0);
highBytes = 4;
firstByteNumber++;
} else {
hB = bytesLen & 3;
highBytes = (hB == 0) ? 4 : hB;
}
int digitIndex = iThis;
bytesLen -= iThis << 2;
if (sign < 0) {
int digit = -temp.digits[digitIndex];
digitIndex++;
if (digitIndex == numberLength) {
bytesInInteger = highBytes;
}
for (int i = 0; i < bytesInInteger; i++, digit >>= 8) {
bytes[--bytesLen] = (byte) digit;
}
while (bytesLen > firstByteNumber) {
digit = ~temp.digits[digitIndex];
digitIndex++;
if (digitIndex == numberLength) {
bytesInInteger = highBytes;
}
for (int i = 0; i < bytesInInteger; i++, digit >>= 8) {
bytes[--bytesLen] = (byte) digit;
}
}
} else {
while (bytesLen > firstByteNumber) {
int digit = temp.digits[digitIndex];
digitIndex++;
if (digitIndex == numberLength) {
bytesInInteger = highBytes;
}
for (int i = 0; i < bytesInInteger; i++, digit >>= 8) {
bytes[--bytesLen] = (byte) digit;
}
}
}
return bytes;
}
static int multiplyByInt(int[] res, int[] a, int aSize, int factor) {
long carry = 0;
for (int i = 0; i < aSize; i++) {
carry += (a[i] & 0xFFFFFFFFL) * (factor & 0xFFFFFFFFL);
res[i] = (int) carry;
carry >>>= 32;
}
return (int) carry;
}
static int inplaceAdd(int[] a, int aSize, int addend) {
long carry = addend & 0xFFFFFFFFL;
for (int i = 0; (carry != 0) && (i < aSize); i++) {
carry += a[i] & 0xFFFFFFFFL;
a[i] = (int) carry;
carry >>= 32;
}
return (int) carry;
}
/** @see BigInteger#BigInteger(String, int) */
private static void parseFromString(BigInteger bi, String value, int radix) {
int stringLength = value.length();
int endChar = stringLength;
int sign;
int startChar;
if (value.charAt(0) == '-') {
sign = -1;
startChar = 1;
stringLength--;
} else {
sign = 1;
startChar = 0;
}
/*
* We use the following algorithm: split a string into portions of n
* characters and convert each portion to an integer according to the
* radix. Then convert an pow(radix, n) based number to binary using the
* multiplication method. See D. Knuth, The Art of Computer Programming,
* vol. 2.
*/
int charsPerInt = Conversion.digitFitInInt[radix];
int bigRadixDigitsLength = stringLength / charsPerInt;
int topChars = stringLength % charsPerInt;
if (topChars != 0) {
bigRadixDigitsLength++;
}
int[] digits = new int[bigRadixDigitsLength];
// Get the maximal power of radix that fits in int
int bigRadix = Conversion.bigRadices[radix - 2];
// Parse an input string and accumulate the BigInteger's magnitude
int digitIndex = 0; // index of digits array
int substrEnd = startChar + ((topChars == 0) ? charsPerInt : topChars);
for (int substrStart = startChar; substrStart < endChar;
substrStart = substrEnd, substrEnd = substrStart + charsPerInt) {
int bigRadixDigit = Integer.parseInt(value.substring(substrStart, substrEnd), radix);
int newDigit = multiplyByInt(digits, digits, digitIndex, bigRadix);
newDigit += inplaceAdd(digits, digitIndex, bigRadixDigit);
digits[digitIndex++] = newDigit;
}
int numberLength = digitIndex;
bi.setJavaRepresentation(sign, numberLength, digits);
}
int getFirstNonzeroDigit() {
if (firstNonzeroDigit == -2) {
int i;
if (this.sign == 0) {
i = -1;
} else {
for (i = 0; digits[i] == 0; i++) {
;
}
}
firstNonzeroDigit = i;
}
return firstNonzeroDigit;
}
/**
* Returns a copy of the current instance to achieve immutability
*/
BigInteger copy() {
prepareJavaRepresentation();
int[] copyDigits = new int[numberLength];
System.arraycopy(digits, 0, copyDigits, 0, numberLength);
return new BigInteger(sign, numberLength, copyDigits);
}
/**
* Assigns all transient fields upon deserialization of a {@code BigInteger}
* instance.
*/
private void readObject(ObjectInputStream in)
throws IOException, ClassNotFoundException {
in.defaultReadObject();
BigInt bigInt = new BigInt();
bigInt.putBigEndian(magnitude, signum < 0);
setBigInt(bigInt);
}
/**
* Prepares this {@code BigInteger} for serialization, i.e. the
* non-transient fields {@code signum} and {@code magnitude} are assigned.
*/
private void writeObject(ObjectOutputStream out) throws IOException {
BigInt bigInt = getBigInt();
signum = bigInt.sign();
magnitude = bigInt.bigEndianMagnitude();
out.defaultWriteObject();
}
}