| /* |
| * Copyright (c) 1996, 2007, Oracle and/or its affiliates. All rights reserved. |
| * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
| * |
| * This code is free software; you can redistribute it and/or modify it |
| * under the terms of the GNU General Public License version 2 only, as |
| * published by the Free Software Foundation. Oracle designates this |
| * particular file as subject to the "Classpath" exception as provided |
| * by Oracle in the LICENSE file that accompanied this code. |
| * |
| * This code 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 |
| * version 2 for more details (a copy is included in the LICENSE file that |
| * accompanied this code). |
| * |
| * You should have received a copy of the GNU General Public License version |
| * 2 along with this work; if not, write to the Free Software Foundation, |
| * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
| * |
| * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
| * or visit www.oracle.com if you need additional information or have any |
| * questions. |
| */ |
| |
| /* |
| * Portions Copyright (c) 1995 Colin Plumb. All rights reserved. |
| */ |
| |
| package java.math; |
| |
| import java.util.Random; |
| import java.io.*; |
| |
| /** |
| * Immutable arbitrary-precision integers. All operations behave as if |
| * BigIntegers were represented in two's-complement notation (like Java's |
| * primitive integer types). BigInteger provides analogues to all of Java's |
| * primitive integer operators, and all relevant methods from java.lang.Math. |
| * Additionally, BigInteger provides operations for modular arithmetic, GCD |
| * calculation, primality testing, prime generation, bit manipulation, |
| * and a few other miscellaneous operations. |
| * |
| * <p>Semantics of arithmetic operations exactly mimic those of Java's integer |
| * arithmetic operators, as defined in <i>The Java Language Specification</i>. |
| * For example, division by zero throws an {@code ArithmeticException}, and |
| * division of a negative by a positive yields a negative (or zero) remainder. |
| * All of the details in the Spec concerning overflow are ignored, as |
| * BigIntegers are made as large as necessary to accommodate the results of an |
| * operation. |
| * |
| * <p>Semantics of shift operations extend those of Java's shift operators |
| * to allow for negative shift distances. A right-shift with a negative |
| * shift distance results in a left shift, and vice-versa. The unsigned |
| * right shift operator ({@code >>>}) is omitted, as this operation makes |
| * little sense in combination with the "infinite word size" abstraction |
| * provided by this class. |
| * |
| * <p>Semantics of bitwise logical operations exactly mimic those of Java's |
| * bitwise integer operators. The binary operators ({@code and}, |
| * {@code or}, {@code xor}) implicitly perform sign extension on the shorter |
| * of the two operands prior to performing the operation. |
| * |
| * <p>Comparison operations perform signed integer comparisons, analogous to |
| * those performed by Java's relational and equality operators. |
| * |
| * <p>Modular arithmetic operations are provided to compute residues, perform |
| * exponentiation, and compute multiplicative inverses. These methods always |
| * return a non-negative result, between {@code 0} and {@code (modulus - 1)}, |
| * inclusive. |
| * |
| * <p>Bit operations operate on a single bit of the two's-complement |
| * representation of their operand. If necessary, the operand is sign- |
| * extended so that it contains the designated bit. None of the single-bit |
| * operations can produce a BigInteger with a different sign from the |
| * BigInteger being operated on, as they affect only a single bit, and the |
| * "infinite word size" abstraction provided by this class ensures that there |
| * are infinitely many "virtual sign bits" preceding each BigInteger. |
| * |
| * <p>For the sake of brevity and clarity, pseudo-code is used throughout the |
| * descriptions of BigInteger methods. The pseudo-code expression |
| * {@code (i + j)} is shorthand for "a BigInteger whose value is |
| * that of the BigInteger {@code i} plus that of the BigInteger {@code j}." |
| * The pseudo-code expression {@code (i == j)} is shorthand for |
| * "{@code true} if and only if the BigInteger {@code i} represents the same |
| * value as the BigInteger {@code j}." Other pseudo-code expressions are |
| * interpreted similarly. |
| * |
| * <p>All methods and constructors in this class throw |
| * {@code NullPointerException} when passed |
| * a null object reference for any input parameter. |
| * |
| * @see BigDecimal |
| * @author Josh Bloch |
| * @author Michael McCloskey |
| * @since JDK1.1 |
| */ |
| |
| public class BigInteger extends Number implements Comparable<BigInteger> { |
| /** |
| * The signum of this BigInteger: -1 for negative, 0 for zero, or |
| * 1 for positive. Note that the BigInteger zero <i>must</i> have |
| * a signum of 0. This is necessary to ensures that there is exactly one |
| * representation for each BigInteger value. |
| * |
| * @serial |
| */ |
| final int signum; |
| |
| /** |
| * The magnitude of this BigInteger, in <i>big-endian</i> order: the |
| * zeroth element of this array is the most-significant int of the |
| * magnitude. The magnitude must be "minimal" in that the most-significant |
| * int ({@code mag[0]}) must be non-zero. This is necessary to |
| * ensure that there is exactly one representation for each BigInteger |
| * value. Note that this implies that the BigInteger zero has a |
| * zero-length mag array. |
| */ |
| final int[] mag; |
| |
| // These "redundant fields" are initialized with recognizable nonsense |
| // values, and cached the first time they are needed (or never, if they |
| // aren't needed). |
| |
| /** |
| * One plus the bitCount of this BigInteger. Zeros means unitialized. |
| * |
| * @serial |
| * @see #bitCount |
| * @deprecated Deprecated since logical value is offset from stored |
| * value and correction factor is applied in accessor method. |
| */ |
| @Deprecated |
| private int bitCount; |
| |
| /** |
| * One plus the bitLength of this BigInteger. Zeros means unitialized. |
| * (either value is acceptable). |
| * |
| * @serial |
| * @see #bitLength() |
| * @deprecated Deprecated since logical value is offset from stored |
| * value and correction factor is applied in accessor method. |
| */ |
| @Deprecated |
| private int bitLength; |
| |
| /** |
| * Two plus the lowest set bit of this BigInteger, as returned by |
| * getLowestSetBit(). |
| * |
| * @serial |
| * @see #getLowestSetBit |
| * @deprecated Deprecated since logical value is offset from stored |
| * value and correction factor is applied in accessor method. |
| */ |
| @Deprecated |
| private int lowestSetBit; |
| |
| /** |
| * Two plus the index of the lowest-order int in the magnitude of this |
| * BigInteger that contains a nonzero int, or -2 (either value is acceptable). |
| * The least significant int has int-number 0, the next int in order of |
| * increasing significance has int-number 1, and so forth. |
| * @deprecated Deprecated since logical value is offset from stored |
| * value and correction factor is applied in accessor method. |
| */ |
| @Deprecated |
| private int firstNonzeroIntNum; |
| |
| /** |
| * This mask is used to obtain the value of an int as if it were unsigned. |
| */ |
| final static long LONG_MASK = 0xffffffffL; |
| |
| //Constructors |
| |
| /** |
| * Translates a byte array containing the two's-complement binary |
| * representation of a BigInteger into a BigInteger. The input array is |
| * assumed to be in <i>big-endian</i> byte-order: the most significant |
| * byte is in the zeroth element. |
| * |
| * @param val big-endian two's-complement binary representation of |
| * BigInteger. |
| * @throws NumberFormatException {@code val} is zero bytes long. |
| */ |
| public BigInteger(byte[] val) { |
| if (val.length == 0) |
| throw new NumberFormatException("Zero length BigInteger"); |
| |
| if (val[0] < 0) { |
| mag = makePositive(val); |
| signum = -1; |
| } else { |
| mag = stripLeadingZeroBytes(val); |
| signum = (mag.length == 0 ? 0 : 1); |
| } |
| } |
| |
| /** |
| * This private constructor translates an int array containing the |
| * two's-complement binary representation of a BigInteger into a |
| * BigInteger. The input array is assumed to be in <i>big-endian</i> |
| * int-order: the most significant int is in the zeroth element. |
| */ |
| private BigInteger(int[] val) { |
| if (val.length == 0) |
| throw new NumberFormatException("Zero length BigInteger"); |
| |
| if (val[0] < 0) { |
| mag = makePositive(val); |
| signum = -1; |
| } else { |
| mag = trustedStripLeadingZeroInts(val); |
| signum = (mag.length == 0 ? 0 : 1); |
| } |
| } |
| |
| /** |
| * Translates the sign-magnitude representation of a BigInteger into a |
| * BigInteger. The sign is represented as an integer signum value: -1 for |
| * negative, 0 for zero, or 1 for positive. The magnitude is a byte array |
| * in <i>big-endian</i> byte-order: the most significant byte is in the |
| * zeroth element. A zero-length magnitude array is permissible, and will |
| * result in a BigInteger value of 0, whether signum is -1, 0 or 1. |
| * |
| * @param signum signum of the number (-1 for negative, 0 for zero, 1 |
| * for positive). |
| * @param magnitude big-endian binary representation of the magnitude of |
| * the number. |
| * @throws NumberFormatException {@code signum} is not one of the three |
| * legal values (-1, 0, and 1), or {@code signum} is 0 and |
| * {@code magnitude} contains one or more non-zero bytes. |
| */ |
| public BigInteger(int signum, byte[] magnitude) { |
| this.mag = stripLeadingZeroBytes(magnitude); |
| |
| if (signum < -1 || signum > 1) |
| throw(new NumberFormatException("Invalid signum value")); |
| |
| if (this.mag.length==0) { |
| this.signum = 0; |
| } else { |
| if (signum == 0) |
| throw(new NumberFormatException("signum-magnitude mismatch")); |
| this.signum = signum; |
| } |
| } |
| |
| /** |
| * A constructor for internal use that translates the sign-magnitude |
| * representation of a BigInteger into a BigInteger. It checks the |
| * arguments and copies the magnitude so this constructor would be |
| * safe for external use. |
| */ |
| private BigInteger(int signum, int[] magnitude) { |
| this.mag = stripLeadingZeroInts(magnitude); |
| |
| if (signum < -1 || signum > 1) |
| throw(new NumberFormatException("Invalid signum value")); |
| |
| if (this.mag.length==0) { |
| this.signum = 0; |
| } else { |
| if (signum == 0) |
| throw(new NumberFormatException("signum-magnitude mismatch")); |
| this.signum = signum; |
| } |
| } |
| |
| /** |
| * Translates the String representation of a BigInteger in the |
| * specified radix into a BigInteger. The String representation |
| * consists of an optional minus or plus sign followed by a |
| * sequence of one or more digits in the specified radix. The |
| * character-to-digit mapping is provided by {@code |
| * Character.digit}. The String may not contain any extraneous |
| * characters (whitespace, for example). |
| * |
| * @param val String representation of BigInteger. |
| * @param radix radix to be used in interpreting {@code val}. |
| * @throws NumberFormatException {@code val} is not a valid representation |
| * of a BigInteger in the specified radix, or {@code radix} is |
| * outside the range from {@link Character#MIN_RADIX} to |
| * {@link Character#MAX_RADIX}, inclusive. |
| * @see Character#digit |
| */ |
| public BigInteger(String val, int radix) { |
| int cursor = 0, numDigits; |
| final int len = val.length(); |
| |
| if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX) |
| throw new NumberFormatException("Radix out of range"); |
| if (len == 0) |
| throw new NumberFormatException("Zero length BigInteger"); |
| |
| // Check for at most one leading sign |
| int sign = 1; |
| int index1 = val.lastIndexOf('-'); |
| int index2 = val.lastIndexOf('+'); |
| if ((index1 + index2) <= -1) { |
| // No leading sign character or at most one leading sign character |
| if (index1 == 0 || index2 == 0) { |
| cursor = 1; |
| if (len == 1) |
| throw new NumberFormatException("Zero length BigInteger"); |
| } |
| if (index1 == 0) |
| sign = -1; |
| } else |
| throw new NumberFormatException("Illegal embedded sign character"); |
| |
| // Skip leading zeros and compute number of digits in magnitude |
| while (cursor < len && |
| Character.digit(val.charAt(cursor), radix) == 0) |
| cursor++; |
| if (cursor == len) { |
| signum = 0; |
| mag = ZERO.mag; |
| return; |
| } |
| |
| numDigits = len - cursor; |
| signum = sign; |
| |
| // Pre-allocate array of expected size. May be too large but can |
| // never be too small. Typically exact. |
| int numBits = (int)(((numDigits * bitsPerDigit[radix]) >>> 10) + 1); |
| int numWords = (numBits + 31) >>> 5; |
| int[] magnitude = new int[numWords]; |
| |
| // Process first (potentially short) digit group |
| int firstGroupLen = numDigits % digitsPerInt[radix]; |
| if (firstGroupLen == 0) |
| firstGroupLen = digitsPerInt[radix]; |
| String group = val.substring(cursor, cursor += firstGroupLen); |
| magnitude[numWords - 1] = Integer.parseInt(group, radix); |
| if (magnitude[numWords - 1] < 0) |
| throw new NumberFormatException("Illegal digit"); |
| |
| // Process remaining digit groups |
| int superRadix = intRadix[radix]; |
| int groupVal = 0; |
| while (cursor < len) { |
| group = val.substring(cursor, cursor += digitsPerInt[radix]); |
| groupVal = Integer.parseInt(group, radix); |
| if (groupVal < 0) |
| throw new NumberFormatException("Illegal digit"); |
| destructiveMulAdd(magnitude, superRadix, groupVal); |
| } |
| // Required for cases where the array was overallocated. |
| mag = trustedStripLeadingZeroInts(magnitude); |
| } |
| |
| // Constructs a new BigInteger using a char array with radix=10 |
| BigInteger(char[] val) { |
| int cursor = 0, numDigits; |
| int len = val.length; |
| |
| // Check for leading minus sign |
| int sign = 1; |
| if (val[0] == '-') { |
| if (len == 1) |
| throw new NumberFormatException("Zero length BigInteger"); |
| sign = -1; |
| cursor = 1; |
| } else if (val[0] == '+') { |
| if (len == 1) |
| throw new NumberFormatException("Zero length BigInteger"); |
| cursor = 1; |
| } |
| |
| // Skip leading zeros and compute number of digits in magnitude |
| while (cursor < len && Character.digit(val[cursor], 10) == 0) |
| cursor++; |
| if (cursor == len) { |
| signum = 0; |
| mag = ZERO.mag; |
| return; |
| } |
| |
| numDigits = len - cursor; |
| signum = sign; |
| |
| // Pre-allocate array of expected size |
| int numWords; |
| if (len < 10) { |
| numWords = 1; |
| } else { |
| int numBits = (int)(((numDigits * bitsPerDigit[10]) >>> 10) + 1); |
| numWords = (numBits + 31) >>> 5; |
| } |
| int[] magnitude = new int[numWords]; |
| |
| // Process first (potentially short) digit group |
| int firstGroupLen = numDigits % digitsPerInt[10]; |
| if (firstGroupLen == 0) |
| firstGroupLen = digitsPerInt[10]; |
| magnitude[numWords - 1] = parseInt(val, cursor, cursor += firstGroupLen); |
| |
| // Process remaining digit groups |
| while (cursor < len) { |
| int groupVal = parseInt(val, cursor, cursor += digitsPerInt[10]); |
| destructiveMulAdd(magnitude, intRadix[10], groupVal); |
| } |
| mag = trustedStripLeadingZeroInts(magnitude); |
| } |
| |
| // Create an integer with the digits between the two indexes |
| // Assumes start < end. The result may be negative, but it |
| // is to be treated as an unsigned value. |
| private int parseInt(char[] source, int start, int end) { |
| int result = Character.digit(source[start++], 10); |
| if (result == -1) |
| throw new NumberFormatException(new String(source)); |
| |
| for (int index = start; index<end; index++) { |
| int nextVal = Character.digit(source[index], 10); |
| if (nextVal == -1) |
| throw new NumberFormatException(new String(source)); |
| result = 10*result + nextVal; |
| } |
| |
| return result; |
| } |
| |
| // bitsPerDigit in the given radix times 1024 |
| // Rounded up to avoid underallocation. |
| private static long bitsPerDigit[] = { 0, 0, |
| 1024, 1624, 2048, 2378, 2648, 2875, 3072, 3247, 3402, 3543, 3672, |
| 3790, 3899, 4001, 4096, 4186, 4271, 4350, 4426, 4498, 4567, 4633, |
| 4696, 4756, 4814, 4870, 4923, 4975, 5025, 5074, 5120, 5166, 5210, |
| 5253, 5295}; |
| |
| // Multiply x array times word y in place, and add word z |
| private static void destructiveMulAdd(int[] x, int y, int z) { |
| // Perform the multiplication word by word |
| long ylong = y & LONG_MASK; |
| long zlong = z & LONG_MASK; |
| int len = x.length; |
| |
| long product = 0; |
| long carry = 0; |
| for (int i = len-1; i >= 0; i--) { |
| product = ylong * (x[i] & LONG_MASK) + carry; |
| x[i] = (int)product; |
| carry = product >>> 32; |
| } |
| |
| // Perform the addition |
| long sum = (x[len-1] & LONG_MASK) + zlong; |
| x[len-1] = (int)sum; |
| carry = sum >>> 32; |
| for (int i = len-2; i >= 0; i--) { |
| sum = (x[i] & LONG_MASK) + carry; |
| x[i] = (int)sum; |
| carry = sum >>> 32; |
| } |
| } |
| |
| /** |
| * Translates the decimal String representation of a BigInteger into a |
| * BigInteger. The String representation consists of an optional minus |
| * sign followed by a sequence of one or more decimal digits. The |
| * character-to-digit mapping is provided by {@code Character.digit}. |
| * The String may not contain any extraneous characters (whitespace, for |
| * example). |
| * |
| * @param val decimal String representation of BigInteger. |
| * @throws NumberFormatException {@code val} is not a valid representation |
| * of a BigInteger. |
| * @see Character#digit |
| */ |
| public BigInteger(String val) { |
| this(val, 10); |
| } |
| |
| /** |
| * Constructs a randomly generated BigInteger, uniformly distributed over |
| * the range 0 to (2<sup>{@code numBits}</sup> - 1), inclusive. |
| * The uniformity of the distribution assumes that a fair source of random |
| * bits is provided in {@code rnd}. Note that this constructor always |
| * constructs a non-negative BigInteger. |
| * |
| * @param numBits maximum bitLength of the new BigInteger. |
| * @param rnd source of randomness to be used in computing the new |
| * BigInteger. |
| * @throws IllegalArgumentException {@code numBits} is negative. |
| * @see #bitLength() |
| */ |
| public BigInteger(int numBits, Random rnd) { |
| this(1, randomBits(numBits, rnd)); |
| } |
| |
| private static byte[] randomBits(int numBits, Random rnd) { |
| if (numBits < 0) |
| throw new IllegalArgumentException("numBits must be non-negative"); |
| int numBytes = (int)(((long)numBits+7)/8); // avoid overflow |
| byte[] randomBits = new byte[numBytes]; |
| |
| // Generate random bytes and mask out any excess bits |
| if (numBytes > 0) { |
| rnd.nextBytes(randomBits); |
| int excessBits = 8*numBytes - numBits; |
| randomBits[0] &= (1 << (8-excessBits)) - 1; |
| } |
| return randomBits; |
| } |
| |
| /** |
| * Constructs a randomly generated positive BigInteger that is probably |
| * prime, with the specified bitLength. |
| * |
| * <p>It is recommended that the {@link #probablePrime probablePrime} |
| * method be used in preference to this constructor unless there |
| * is a compelling need to specify a certainty. |
| * |
| * @param bitLength bitLength of the returned BigInteger. |
| * @param certainty a measure of the uncertainty that the caller is |
| * willing to tolerate. The probability that the new BigInteger |
| * represents a prime number will exceed |
| * (1 - 1/2<sup>{@code certainty}</sup>). The execution time of |
| * this constructor is proportional to the value of this parameter. |
| * @param rnd source of random bits used to select candidates to be |
| * tested for primality. |
| * @throws ArithmeticException {@code bitLength < 2}. |
| * @see #bitLength() |
| */ |
| public BigInteger(int bitLength, int certainty, Random rnd) { |
| BigInteger prime; |
| |
| if (bitLength < 2) |
| throw new ArithmeticException("bitLength < 2"); |
| // The cutoff of 95 was chosen empirically for best performance |
| prime = (bitLength < 95 ? smallPrime(bitLength, certainty, rnd) |
| : largePrime(bitLength, certainty, rnd)); |
| signum = 1; |
| mag = prime.mag; |
| } |
| |
| // Minimum size in bits that the requested prime number has |
| // before we use the large prime number generating algorithms |
| private static final int SMALL_PRIME_THRESHOLD = 95; |
| |
| // Certainty required to meet the spec of probablePrime |
| private static final int DEFAULT_PRIME_CERTAINTY = 100; |
| |
| /** |
| * Returns a positive BigInteger that is probably prime, with the |
| * specified bitLength. The probability that a BigInteger returned |
| * by this method is composite does not exceed 2<sup>-100</sup>. |
| * |
| * @param bitLength bitLength of the returned BigInteger. |
| * @param rnd source of random bits used to select candidates to be |
| * tested for primality. |
| * @return a BigInteger of {@code bitLength} bits that is probably prime |
| * @throws ArithmeticException {@code bitLength < 2}. |
| * @see #bitLength() |
| * @since 1.4 |
| */ |
| public static BigInteger probablePrime(int bitLength, Random rnd) { |
| if (bitLength < 2) |
| throw new ArithmeticException("bitLength < 2"); |
| |
| // The cutoff of 95 was chosen empirically for best performance |
| return (bitLength < SMALL_PRIME_THRESHOLD ? |
| smallPrime(bitLength, DEFAULT_PRIME_CERTAINTY, rnd) : |
| largePrime(bitLength, DEFAULT_PRIME_CERTAINTY, rnd)); |
| } |
| |
| /** |
| * Find a random number of the specified bitLength that is probably prime. |
| * This method is used for smaller primes, its performance degrades on |
| * larger bitlengths. |
| * |
| * This method assumes bitLength > 1. |
| */ |
| private static BigInteger smallPrime(int bitLength, int certainty, Random rnd) { |
| int magLen = (bitLength + 31) >>> 5; |
| int temp[] = new int[magLen]; |
| int highBit = 1 << ((bitLength+31) & 0x1f); // High bit of high int |
| int highMask = (highBit << 1) - 1; // Bits to keep in high int |
| |
| while(true) { |
| // Construct a candidate |
| for (int i=0; i<magLen; i++) |
| temp[i] = rnd.nextInt(); |
| temp[0] = (temp[0] & highMask) | highBit; // Ensure exact length |
| if (bitLength > 2) |
| temp[magLen-1] |= 1; // Make odd if bitlen > 2 |
| |
| BigInteger p = new BigInteger(temp, 1); |
| |
| // Do cheap "pre-test" if applicable |
| if (bitLength > 6) { |
| long r = p.remainder(SMALL_PRIME_PRODUCT).longValue(); |
| if ((r%3==0) || (r%5==0) || (r%7==0) || (r%11==0) || |
| (r%13==0) || (r%17==0) || (r%19==0) || (r%23==0) || |
| (r%29==0) || (r%31==0) || (r%37==0) || (r%41==0)) |
| continue; // Candidate is composite; try another |
| } |
| |
| // All candidates of bitLength 2 and 3 are prime by this point |
| if (bitLength < 4) |
| return p; |
| |
| // Do expensive test if we survive pre-test (or it's inapplicable) |
| if (p.primeToCertainty(certainty, rnd)) |
| return p; |
| } |
| } |
| |
| private static final BigInteger SMALL_PRIME_PRODUCT |
| = valueOf(3L*5*7*11*13*17*19*23*29*31*37*41); |
| |
| /** |
| * Find a random number of the specified bitLength that is probably prime. |
| * This method is more appropriate for larger bitlengths since it uses |
| * a sieve to eliminate most composites before using a more expensive |
| * test. |
| */ |
| private static BigInteger largePrime(int bitLength, int certainty, Random rnd) { |
| BigInteger p; |
| p = new BigInteger(bitLength, rnd).setBit(bitLength-1); |
| p.mag[p.mag.length-1] &= 0xfffffffe; |
| |
| // Use a sieve length likely to contain the next prime number |
| int searchLen = (bitLength / 20) * 64; |
| BitSieve searchSieve = new BitSieve(p, searchLen); |
| BigInteger candidate = searchSieve.retrieve(p, certainty, rnd); |
| |
| while ((candidate == null) || (candidate.bitLength() != bitLength)) { |
| p = p.add(BigInteger.valueOf(2*searchLen)); |
| if (p.bitLength() != bitLength) |
| p = new BigInteger(bitLength, rnd).setBit(bitLength-1); |
| p.mag[p.mag.length-1] &= 0xfffffffe; |
| searchSieve = new BitSieve(p, searchLen); |
| candidate = searchSieve.retrieve(p, certainty, rnd); |
| } |
| return candidate; |
| } |
| |
| /** |
| * Returns the first integer greater than this {@code BigInteger} that |
| * is probably prime. The probability that the number returned by this |
| * method is composite does not exceed 2<sup>-100</sup>. This method will |
| * never skip over a prime when searching: if it returns {@code p}, there |
| * is no prime {@code q} such that {@code this < q < p}. |
| * |
| * @return the first integer greater than this {@code BigInteger} that |
| * is probably prime. |
| * @throws ArithmeticException {@code this < 0}. |
| * @since 1.5 |
| */ |
| public BigInteger nextProbablePrime() { |
| if (this.signum < 0) |
| throw new ArithmeticException("start < 0: " + this); |
| |
| // Handle trivial cases |
| if ((this.signum == 0) || this.equals(ONE)) |
| return TWO; |
| |
| BigInteger result = this.add(ONE); |
| |
| // Fastpath for small numbers |
| if (result.bitLength() < SMALL_PRIME_THRESHOLD) { |
| |
| // Ensure an odd number |
| if (!result.testBit(0)) |
| result = result.add(ONE); |
| |
| while(true) { |
| // Do cheap "pre-test" if applicable |
| if (result.bitLength() > 6) { |
| long r = result.remainder(SMALL_PRIME_PRODUCT).longValue(); |
| if ((r%3==0) || (r%5==0) || (r%7==0) || (r%11==0) || |
| (r%13==0) || (r%17==0) || (r%19==0) || (r%23==0) || |
| (r%29==0) || (r%31==0) || (r%37==0) || (r%41==0)) { |
| result = result.add(TWO); |
| continue; // Candidate is composite; try another |
| } |
| } |
| |
| // All candidates of bitLength 2 and 3 are prime by this point |
| if (result.bitLength() < 4) |
| return result; |
| |
| // The expensive test |
| if (result.primeToCertainty(DEFAULT_PRIME_CERTAINTY, null)) |
| return result; |
| |
| result = result.add(TWO); |
| } |
| } |
| |
| // Start at previous even number |
| if (result.testBit(0)) |
| result = result.subtract(ONE); |
| |
| // Looking for the next large prime |
| int searchLen = (result.bitLength() / 20) * 64; |
| |
| while(true) { |
| BitSieve searchSieve = new BitSieve(result, searchLen); |
| BigInteger candidate = searchSieve.retrieve(result, |
| DEFAULT_PRIME_CERTAINTY, null); |
| if (candidate != null) |
| return candidate; |
| result = result.add(BigInteger.valueOf(2 * searchLen)); |
| } |
| } |
| |
| /** |
| * Returns {@code true} if this BigInteger is probably prime, |
| * {@code false} if it's definitely composite. |
| * |
| * This method assumes bitLength > 2. |
| * |
| * @param certainty a measure of the uncertainty that the caller is |
| * willing to tolerate: if the call returns {@code true} |
| * the probability that this BigInteger is prime exceeds |
| * {@code (1 - 1/2<sup>certainty</sup>)}. The execution time of |
| * this method is proportional to the value of this parameter. |
| * @return {@code true} if this BigInteger is probably prime, |
| * {@code false} if it's definitely composite. |
| */ |
| boolean primeToCertainty(int certainty, Random random) { |
| int rounds = 0; |
| int n = (Math.min(certainty, Integer.MAX_VALUE-1)+1)/2; |
| |
| // The relationship between the certainty and the number of rounds |
| // we perform is given in the draft standard ANSI X9.80, "PRIME |
| // NUMBER GENERATION, PRIMALITY TESTING, AND PRIMALITY CERTIFICATES". |
| int sizeInBits = this.bitLength(); |
| if (sizeInBits < 100) { |
| rounds = 50; |
| rounds = n < rounds ? n : rounds; |
| return passesMillerRabin(rounds, random); |
| } |
| |
| if (sizeInBits < 256) { |
| rounds = 27; |
| } else if (sizeInBits < 512) { |
| rounds = 15; |
| } else if (sizeInBits < 768) { |
| rounds = 8; |
| } else if (sizeInBits < 1024) { |
| rounds = 4; |
| } else { |
| rounds = 2; |
| } |
| rounds = n < rounds ? n : rounds; |
| |
| return passesMillerRabin(rounds, random) && passesLucasLehmer(); |
| } |
| |
| /** |
| * Returns true iff this BigInteger is a Lucas-Lehmer probable prime. |
| * |
| * The following assumptions are made: |
| * This BigInteger is a positive, odd number. |
| */ |
| private boolean passesLucasLehmer() { |
| BigInteger thisPlusOne = this.add(ONE); |
| |
| // Step 1 |
| int d = 5; |
| while (jacobiSymbol(d, this) != -1) { |
| // 5, -7, 9, -11, ... |
| d = (d<0) ? Math.abs(d)+2 : -(d+2); |
| } |
| |
| // Step 2 |
| BigInteger u = lucasLehmerSequence(d, thisPlusOne, this); |
| |
| // Step 3 |
| return u.mod(this).equals(ZERO); |
| } |
| |
| /** |
| * Computes Jacobi(p,n). |
| * Assumes n positive, odd, n>=3. |
| */ |
| private static int jacobiSymbol(int p, BigInteger n) { |
| if (p == 0) |
| return 0; |
| |
| // Algorithm and comments adapted from Colin Plumb's C library. |
| int j = 1; |
| int u = n.mag[n.mag.length-1]; |
| |
| // Make p positive |
| if (p < 0) { |
| p = -p; |
| int n8 = u & 7; |
| if ((n8 == 3) || (n8 == 7)) |
| j = -j; // 3 (011) or 7 (111) mod 8 |
| } |
| |
| // Get rid of factors of 2 in p |
| while ((p & 3) == 0) |
| p >>= 2; |
| if ((p & 1) == 0) { |
| p >>= 1; |
| if (((u ^ (u>>1)) & 2) != 0) |
| j = -j; // 3 (011) or 5 (101) mod 8 |
| } |
| if (p == 1) |
| return j; |
| // Then, apply quadratic reciprocity |
| if ((p & u & 2) != 0) // p = u = 3 (mod 4)? |
| j = -j; |
| // And reduce u mod p |
| u = n.mod(BigInteger.valueOf(p)).intValue(); |
| |
| // Now compute Jacobi(u,p), u < p |
| while (u != 0) { |
| while ((u & 3) == 0) |
| u >>= 2; |
| if ((u & 1) == 0) { |
| u >>= 1; |
| if (((p ^ (p>>1)) & 2) != 0) |
| j = -j; // 3 (011) or 5 (101) mod 8 |
| } |
| if (u == 1) |
| return j; |
| // Now both u and p are odd, so use quadratic reciprocity |
| assert (u < p); |
| int t = u; u = p; p = t; |
| if ((u & p & 2) != 0) // u = p = 3 (mod 4)? |
| j = -j; |
| // Now u >= p, so it can be reduced |
| u %= p; |
| } |
| return 0; |
| } |
| |
| private static BigInteger lucasLehmerSequence(int z, BigInteger k, BigInteger n) { |
| BigInteger d = BigInteger.valueOf(z); |
| BigInteger u = ONE; BigInteger u2; |
| BigInteger v = ONE; BigInteger v2; |
| |
| for (int i=k.bitLength()-2; i>=0; i--) { |
| u2 = u.multiply(v).mod(n); |
| |
| v2 = v.square().add(d.multiply(u.square())).mod(n); |
| if (v2.testBit(0)) |
| v2 = v2.subtract(n); |
| |
| v2 = v2.shiftRight(1); |
| |
| u = u2; v = v2; |
| if (k.testBit(i)) { |
| u2 = u.add(v).mod(n); |
| if (u2.testBit(0)) |
| u2 = u2.subtract(n); |
| |
| u2 = u2.shiftRight(1); |
| v2 = v.add(d.multiply(u)).mod(n); |
| if (v2.testBit(0)) |
| v2 = v2.subtract(n); |
| v2 = v2.shiftRight(1); |
| |
| u = u2; v = v2; |
| } |
| } |
| return u; |
| } |
| |
| private static volatile Random staticRandom; |
| |
| private static Random getSecureRandom() { |
| if (staticRandom == null) { |
| staticRandom = new java.security.SecureRandom(); |
| } |
| return staticRandom; |
| } |
| |
| /** |
| * Returns true iff this BigInteger passes the specified number of |
| * Miller-Rabin tests. This test is taken from the DSA spec (NIST FIPS |
| * 186-2). |
| * |
| * The following assumptions are made: |
| * This BigInteger is a positive, odd number greater than 2. |
| * iterations<=50. |
| */ |
| private boolean passesMillerRabin(int iterations, Random rnd) { |
| // Find a and m such that m is odd and this == 1 + 2**a * m |
| BigInteger thisMinusOne = this.subtract(ONE); |
| BigInteger m = thisMinusOne; |
| int a = m.getLowestSetBit(); |
| m = m.shiftRight(a); |
| |
| // Do the tests |
| if (rnd == null) { |
| rnd = getSecureRandom(); |
| } |
| for (int i=0; i<iterations; i++) { |
| // Generate a uniform random on (1, this) |
| BigInteger b; |
| do { |
| b = new BigInteger(this.bitLength(), rnd); |
| } while (b.compareTo(ONE) <= 0 || b.compareTo(this) >= 0); |
| |
| int j = 0; |
| BigInteger z = b.modPow(m, this); |
| while(!((j==0 && z.equals(ONE)) || z.equals(thisMinusOne))) { |
| if (j>0 && z.equals(ONE) || ++j==a) |
| return false; |
| z = z.modPow(TWO, this); |
| } |
| } |
| return true; |
| } |
| |
| /** |
| * This internal constructor differs from its public cousin |
| * with the arguments reversed in two ways: it assumes that its |
| * arguments are correct, and it doesn't copy the magnitude array. |
| */ |
| BigInteger(int[] magnitude, int signum) { |
| this.signum = (magnitude.length==0 ? 0 : signum); |
| this.mag = magnitude; |
| } |
| |
| /** |
| * This private constructor is for internal use and assumes that its |
| * arguments are correct. |
| */ |
| private BigInteger(byte[] magnitude, int signum) { |
| this.signum = (magnitude.length==0 ? 0 : signum); |
| this.mag = stripLeadingZeroBytes(magnitude); |
| } |
| |
| //Static Factory Methods |
| |
| /** |
| * Returns a BigInteger whose value is equal to that of the |
| * specified {@code long}. This "static factory method" is |
| * provided in preference to a ({@code long}) constructor |
| * because it allows for reuse of frequently used BigIntegers. |
| * |
| * @param val value of the BigInteger to return. |
| * @return a BigInteger with the specified value. |
| */ |
| public static BigInteger valueOf(long val) { |
| // If -MAX_CONSTANT < val < MAX_CONSTANT, return stashed constant |
| if (val == 0) |
| return ZERO; |
| if (val > 0 && val <= MAX_CONSTANT) |
| return posConst[(int) val]; |
| else if (val < 0 && val >= -MAX_CONSTANT) |
| return negConst[(int) -val]; |
| |
| return new BigInteger(val); |
| } |
| |
| /** |
| * Constructs a BigInteger with the specified value, which may not be zero. |
| */ |
| private BigInteger(long val) { |
| if (val < 0) { |
| val = -val; |
| signum = -1; |
| } else { |
| signum = 1; |
| } |
| |
| int highWord = (int)(val >>> 32); |
| if (highWord==0) { |
| mag = new int[1]; |
| mag[0] = (int)val; |
| } else { |
| mag = new int[2]; |
| mag[0] = highWord; |
| mag[1] = (int)val; |
| } |
| } |
| |
| /** |
| * Returns a BigInteger with the given two's complement representation. |
| * Assumes that the input array will not be modified (the returned |
| * BigInteger will reference the input array if feasible). |
| */ |
| private static BigInteger valueOf(int val[]) { |
| return (val[0]>0 ? new BigInteger(val, 1) : new BigInteger(val)); |
| } |
| |
| // Constants |
| |
| /** |
| * Initialize static constant array when class is loaded. |
| */ |
| private final static int MAX_CONSTANT = 16; |
| private static BigInteger posConst[] = new BigInteger[MAX_CONSTANT+1]; |
| private static BigInteger negConst[] = new BigInteger[MAX_CONSTANT+1]; |
| static { |
| for (int i = 1; i <= MAX_CONSTANT; i++) { |
| int[] magnitude = new int[1]; |
| magnitude[0] = i; |
| posConst[i] = new BigInteger(magnitude, 1); |
| negConst[i] = new BigInteger(magnitude, -1); |
| } |
| } |
| |
| /** |
| * The BigInteger constant zero. |
| * |
| * @since 1.2 |
| */ |
| public static final BigInteger ZERO = new BigInteger(new int[0], 0); |
| |
| /** |
| * The BigInteger constant one. |
| * |
| * @since 1.2 |
| */ |
| public static final BigInteger ONE = valueOf(1); |
| |
| /** |
| * The BigInteger constant two. (Not exported.) |
| */ |
| private static final BigInteger TWO = valueOf(2); |
| |
| /** |
| * The BigInteger constant ten. |
| * |
| * @since 1.5 |
| */ |
| public static final BigInteger TEN = valueOf(10); |
| |
| // Arithmetic Operations |
| |
| /** |
| * Returns a BigInteger whose value is {@code (this + val)}. |
| * |
| * @param val value to be added to this BigInteger. |
| * @return {@code this + val} |
| */ |
| public BigInteger add(BigInteger val) { |
| if (val.signum == 0) |
| return this; |
| if (signum == 0) |
| return val; |
| if (val.signum == signum) |
| return new BigInteger(add(mag, val.mag), signum); |
| |
| int cmp = compareMagnitude(val); |
| if (cmp == 0) |
| return ZERO; |
| int[] resultMag = (cmp > 0 ? subtract(mag, val.mag) |
| : subtract(val.mag, mag)); |
| resultMag = trustedStripLeadingZeroInts(resultMag); |
| |
| return new BigInteger(resultMag, cmp == signum ? 1 : -1); |
| } |
| |
| /** |
| * Adds the contents of the int arrays x and y. This method allocates |
| * a new int array to hold the answer and returns a reference to that |
| * array. |
| */ |
| private static int[] add(int[] x, int[] y) { |
| // If x is shorter, swap the two arrays |
| if (x.length < y.length) { |
| int[] tmp = x; |
| x = y; |
| y = tmp; |
| } |
| |
| int xIndex = x.length; |
| int yIndex = y.length; |
| int result[] = new int[xIndex]; |
| long sum = 0; |
| |
| // Add common parts of both numbers |
| while(yIndex > 0) { |
| sum = (x[--xIndex] & LONG_MASK) + |
| (y[--yIndex] & LONG_MASK) + (sum >>> 32); |
| result[xIndex] = (int)sum; |
| } |
| |
| // Copy remainder of longer number while carry propagation is required |
| boolean carry = (sum >>> 32 != 0); |
| while (xIndex > 0 && carry) |
| carry = ((result[--xIndex] = x[xIndex] + 1) == 0); |
| |
| // Copy remainder of longer number |
| while (xIndex > 0) |
| result[--xIndex] = x[xIndex]; |
| |
| // Grow result if necessary |
| if (carry) { |
| int bigger[] = new int[result.length + 1]; |
| System.arraycopy(result, 0, bigger, 1, result.length); |
| bigger[0] = 0x01; |
| return bigger; |
| } |
| return result; |
| } |
| |
| /** |
| * Returns a BigInteger whose value is {@code (this - val)}. |
| * |
| * @param val value to be subtracted from this BigInteger. |
| * @return {@code this - val} |
| */ |
| public BigInteger subtract(BigInteger val) { |
| if (val.signum == 0) |
| return this; |
| if (signum == 0) |
| return val.negate(); |
| if (val.signum != signum) |
| return new BigInteger(add(mag, val.mag), signum); |
| |
| int cmp = compareMagnitude(val); |
| if (cmp == 0) |
| return ZERO; |
| int[] resultMag = (cmp > 0 ? subtract(mag, val.mag) |
| : subtract(val.mag, mag)); |
| resultMag = trustedStripLeadingZeroInts(resultMag); |
| return new BigInteger(resultMag, cmp == signum ? 1 : -1); |
| } |
| |
| /** |
| * Subtracts the contents of the second int arrays (little) from the |
| * first (big). The first int array (big) must represent a larger number |
| * than the second. This method allocates the space necessary to hold the |
| * answer. |
| */ |
| private static int[] subtract(int[] big, int[] little) { |
| int bigIndex = big.length; |
| int result[] = new int[bigIndex]; |
| int littleIndex = little.length; |
| long difference = 0; |
| |
| // Subtract common parts of both numbers |
| while(littleIndex > 0) { |
| difference = (big[--bigIndex] & LONG_MASK) - |
| (little[--littleIndex] & LONG_MASK) + |
| (difference >> 32); |
| result[bigIndex] = (int)difference; |
| } |
| |
| // Subtract remainder of longer number while borrow propagates |
| boolean borrow = (difference >> 32 != 0); |
| while (bigIndex > 0 && borrow) |
| borrow = ((result[--bigIndex] = big[bigIndex] - 1) == -1); |
| |
| // Copy remainder of longer number |
| while (bigIndex > 0) |
| result[--bigIndex] = big[bigIndex]; |
| |
| return result; |
| } |
| |
| /** |
| * Returns a BigInteger whose value is {@code (this * val)}. |
| * |
| * @param val value to be multiplied by this BigInteger. |
| * @return {@code this * val} |
| */ |
| public BigInteger multiply(BigInteger val) { |
| if (val.signum == 0 || signum == 0) |
| return ZERO; |
| |
| int[] result = multiplyToLen(mag, mag.length, |
| val.mag, val.mag.length, null); |
| result = trustedStripLeadingZeroInts(result); |
| return new BigInteger(result, signum == val.signum ? 1 : -1); |
| } |
| |
| /** |
| * Package private methods used by BigDecimal code to multiply a BigInteger |
| * with a long. Assumes v is not equal to INFLATED. |
| */ |
| BigInteger multiply(long v) { |
| if (v == 0 || signum == 0) |
| return ZERO; |
| if (v == BigDecimal.INFLATED) |
| return multiply(BigInteger.valueOf(v)); |
| int rsign = (v > 0 ? signum : -signum); |
| if (v < 0) |
| v = -v; |
| long dh = v >>> 32; // higher order bits |
| long dl = v & LONG_MASK; // lower order bits |
| |
| int xlen = mag.length; |
| int[] value = mag; |
| int[] rmag = (dh == 0L) ? (new int[xlen + 1]) : (new int[xlen + 2]); |
| long carry = 0; |
| int rstart = rmag.length - 1; |
| for (int i = xlen - 1; i >= 0; i--) { |
| long product = (value[i] & LONG_MASK) * dl + carry; |
| rmag[rstart--] = (int)product; |
| carry = product >>> 32; |
| } |
| rmag[rstart] = (int)carry; |
| if (dh != 0L) { |
| carry = 0; |
| rstart = rmag.length - 2; |
| for (int i = xlen - 1; i >= 0; i--) { |
| long product = (value[i] & LONG_MASK) * dh + |
| (rmag[rstart] & LONG_MASK) + carry; |
| rmag[rstart--] = (int)product; |
| carry = product >>> 32; |
| } |
| rmag[0] = (int)carry; |
| } |
| if (carry == 0L) |
| rmag = java.util.Arrays.copyOfRange(rmag, 1, rmag.length); |
| return new BigInteger(rmag, rsign); |
| } |
| |
| /** |
| * Multiplies int arrays x and y to the specified lengths and places |
| * the result into z. There will be no leading zeros in the resultant array. |
| */ |
| private int[] multiplyToLen(int[] x, int xlen, int[] y, int ylen, int[] z) { |
| int xstart = xlen - 1; |
| int ystart = ylen - 1; |
| |
| if (z == null || z.length < (xlen+ ylen)) |
| z = new int[xlen+ylen]; |
| |
| long carry = 0; |
| for (int j=ystart, k=ystart+1+xstart; j>=0; j--, k--) { |
| long product = (y[j] & LONG_MASK) * |
| (x[xstart] & LONG_MASK) + carry; |
| z[k] = (int)product; |
| carry = product >>> 32; |
| } |
| z[xstart] = (int)carry; |
| |
| for (int i = xstart-1; i >= 0; i--) { |
| carry = 0; |
| for (int j=ystart, k=ystart+1+i; j>=0; j--, k--) { |
| long product = (y[j] & LONG_MASK) * |
| (x[i] & LONG_MASK) + |
| (z[k] & LONG_MASK) + carry; |
| z[k] = (int)product; |
| carry = product >>> 32; |
| } |
| z[i] = (int)carry; |
| } |
| return z; |
| } |
| |
| /** |
| * Returns a BigInteger whose value is {@code (this<sup>2</sup>)}. |
| * |
| * @return {@code this<sup>2</sup>} |
| */ |
| private BigInteger square() { |
| if (signum == 0) |
| return ZERO; |
| int[] z = squareToLen(mag, mag.length, null); |
| return new BigInteger(trustedStripLeadingZeroInts(z), 1); |
| } |
| |
| /** |
| * Squares the contents of the int array x. The result is placed into the |
| * int array z. The contents of x are not changed. |
| */ |
| private static final int[] squareToLen(int[] x, int len, int[] z) { |
| /* |
| * The algorithm used here is adapted from Colin Plumb's C library. |
| * Technique: Consider the partial products in the multiplication |
| * of "abcde" by itself: |
| * |
| * a b c d e |
| * * a b c d e |
| * ================== |
| * ae be ce de ee |
| * ad bd cd dd de |
| * ac bc cc cd ce |
| * ab bb bc bd be |
| * aa ab ac ad ae |
| * |
| * Note that everything above the main diagonal: |
| * ae be ce de = (abcd) * e |
| * ad bd cd = (abc) * d |
| * ac bc = (ab) * c |
| * ab = (a) * b |
| * |
| * is a copy of everything below the main diagonal: |
| * de |
| * cd ce |
| * bc bd be |
| * ab ac ad ae |
| * |
| * Thus, the sum is 2 * (off the diagonal) + diagonal. |
| * |
| * This is accumulated beginning with the diagonal (which |
| * consist of the squares of the digits of the input), which is then |
| * divided by two, the off-diagonal added, and multiplied by two |
| * again. The low bit is simply a copy of the low bit of the |
| * input, so it doesn't need special care. |
| */ |
| int zlen = len << 1; |
| if (z == null || z.length < zlen) |
| z = new int[zlen]; |
| |
| // Store the squares, right shifted one bit (i.e., divided by 2) |
| int lastProductLowWord = 0; |
| for (int j=0, i=0; j<len; j++) { |
| long piece = (x[j] & LONG_MASK); |
| long product = piece * piece; |
| z[i++] = (lastProductLowWord << 31) | (int)(product >>> 33); |
| z[i++] = (int)(product >>> 1); |
| lastProductLowWord = (int)product; |
| } |
| |
| // Add in off-diagonal sums |
| for (int i=len, offset=1; i>0; i--, offset+=2) { |
| int t = x[i-1]; |
| t = mulAdd(z, x, offset, i-1, t); |
| addOne(z, offset-1, i, t); |
| } |
| |
| // Shift back up and set low bit |
| primitiveLeftShift(z, zlen, 1); |
| z[zlen-1] |= x[len-1] & 1; |
| |
| return z; |
| } |
| |
| /** |
| * Returns a BigInteger whose value is {@code (this / val)}. |
| * |
| * @param val value by which this BigInteger is to be divided. |
| * @return {@code this / val} |
| * @throws ArithmeticException if {@code val} is zero. |
| */ |
| public BigInteger divide(BigInteger val) { |
| MutableBigInteger q = new MutableBigInteger(), |
| a = new MutableBigInteger(this.mag), |
| b = new MutableBigInteger(val.mag); |
| |
| a.divide(b, q); |
| return q.toBigInteger(this.signum == val.signum ? 1 : -1); |
| } |
| |
| /** |
| * Returns an array of two BigIntegers containing {@code (this / val)} |
| * followed by {@code (this % val)}. |
| * |
| * @param val value by which this BigInteger is to be divided, and the |
| * remainder computed. |
| * @return an array of two BigIntegers: the quotient {@code (this / val)} |
| * is the initial element, and the remainder {@code (this % val)} |
| * is the final element. |
| * @throws ArithmeticException if {@code val} is zero. |
| */ |
| public BigInteger[] divideAndRemainder(BigInteger val) { |
| BigInteger[] result = new BigInteger[2]; |
| MutableBigInteger q = new MutableBigInteger(), |
| a = new MutableBigInteger(this.mag), |
| b = new MutableBigInteger(val.mag); |
| MutableBigInteger r = a.divide(b, q); |
| result[0] = q.toBigInteger(this.signum == val.signum ? 1 : -1); |
| result[1] = r.toBigInteger(this.signum); |
| return result; |
| } |
| |
| /** |
| * Returns a BigInteger whose value is {@code (this % val)}. |
| * |
| * @param val value by which this BigInteger is to be divided, and the |
| * remainder computed. |
| * @return {@code this % val} |
| * @throws ArithmeticException if {@code val} is zero. |
| */ |
| public BigInteger remainder(BigInteger val) { |
| MutableBigInteger q = new MutableBigInteger(), |
| a = new MutableBigInteger(this.mag), |
| b = new MutableBigInteger(val.mag); |
| |
| return a.divide(b, q).toBigInteger(this.signum); |
| } |
| |
| /** |
| * Returns a BigInteger whose value is <tt>(this<sup>exponent</sup>)</tt>. |
| * Note that {@code exponent} is an integer rather than a BigInteger. |
| * |
| * @param exponent exponent to which this BigInteger is to be raised. |
| * @return <tt>this<sup>exponent</sup></tt> |
| * @throws ArithmeticException {@code exponent} is negative. (This would |
| * cause the operation to yield a non-integer value.) |
| */ |
| public BigInteger pow(int exponent) { |
| if (exponent < 0) |
| throw new ArithmeticException("Negative exponent"); |
| if (signum==0) |
| return (exponent==0 ? ONE : this); |
| |
| // Perform exponentiation using repeated squaring trick |
| int newSign = (signum<0 && (exponent&1)==1 ? -1 : 1); |
| int[] baseToPow2 = this.mag; |
| int[] result = {1}; |
| |
| while (exponent != 0) { |
| if ((exponent & 1)==1) { |
| result = multiplyToLen(result, result.length, |
| baseToPow2, baseToPow2.length, null); |
| result = trustedStripLeadingZeroInts(result); |
| } |
| if ((exponent >>>= 1) != 0) { |
| baseToPow2 = squareToLen(baseToPow2, baseToPow2.length, null); |
| baseToPow2 = trustedStripLeadingZeroInts(baseToPow2); |
| } |
| } |
| return new BigInteger(result, newSign); |
| } |
| |
| /** |
| * Returns a BigInteger whose value is the greatest common divisor of |
| * {@code abs(this)} and {@code abs(val)}. Returns 0 if |
| * {@code this==0 && val==0}. |
| * |
| * @param val value with which the GCD is to be computed. |
| * @return {@code GCD(abs(this), abs(val))} |
| */ |
| public BigInteger gcd(BigInteger val) { |
| if (val.signum == 0) |
| return this.abs(); |
| else if (this.signum == 0) |
| return val.abs(); |
| |
| MutableBigInteger a = new MutableBigInteger(this); |
| MutableBigInteger b = new MutableBigInteger(val); |
| |
| MutableBigInteger result = a.hybridGCD(b); |
| |
| return result.toBigInteger(1); |
| } |
| |
| /** |
| * Package private method to return bit length for an integer. |
| */ |
| static int bitLengthForInt(int n) { |
| return 32 - Integer.numberOfLeadingZeros(n); |
| } |
| |
| /** |
| * Left shift int array a up to len by n bits. Returns the array that |
| * results from the shift since space may have to be reallocated. |
| */ |
| private static int[] leftShift(int[] a, int len, int n) { |
| int nInts = n >>> 5; |
| int nBits = n&0x1F; |
| int bitsInHighWord = bitLengthForInt(a[0]); |
| |
| // If shift can be done without recopy, do so |
| if (n <= (32-bitsInHighWord)) { |
| primitiveLeftShift(a, len, nBits); |
| return a; |
| } else { // Array must be resized |
| if (nBits <= (32-bitsInHighWord)) { |
| int result[] = new int[nInts+len]; |
| for (int i=0; i<len; i++) |
| result[i] = a[i]; |
| primitiveLeftShift(result, result.length, nBits); |
| return result; |
| } else { |
| int result[] = new int[nInts+len+1]; |
| for (int i=0; i<len; i++) |
| result[i] = a[i]; |
| primitiveRightShift(result, result.length, 32 - nBits); |
| return result; |
| } |
| } |
| } |
| |
| // shifts a up to len right n bits assumes no leading zeros, 0<n<32 |
| static void primitiveRightShift(int[] a, int len, int n) { |
| int n2 = 32 - n; |
| for (int i=len-1, c=a[i]; i>0; i--) { |
| int b = c; |
| c = a[i-1]; |
| a[i] = (c << n2) | (b >>> n); |
| } |
| a[0] >>>= n; |
| } |
| |
| // shifts a up to len left n bits assumes no leading zeros, 0<=n<32 |
| static void primitiveLeftShift(int[] a, int len, int n) { |
| if (len == 0 || n == 0) |
| return; |
| |
| int n2 = 32 - n; |
| for (int i=0, c=a[i], m=i+len-1; i<m; i++) { |
| int b = c; |
| c = a[i+1]; |
| a[i] = (b << n) | (c >>> n2); |
| } |
| a[len-1] <<= n; |
| } |
| |
| /** |
| * Calculate bitlength of contents of the first len elements an int array, |
| * assuming there are no leading zero ints. |
| */ |
| private static int bitLength(int[] val, int len) { |
| if (len == 0) |
| return 0; |
| return ((len - 1) << 5) + bitLengthForInt(val[0]); |
| } |
| |
| /** |
| * Returns a BigInteger whose value is the absolute value of this |
| * BigInteger. |
| * |
| * @return {@code abs(this)} |
| */ |
| public BigInteger abs() { |
| return (signum >= 0 ? this : this.negate()); |
| } |
| |
| /** |
| * Returns a BigInteger whose value is {@code (-this)}. |
| * |
| * @return {@code -this} |
| */ |
| public BigInteger negate() { |
| return new BigInteger(this.mag, -this.signum); |
| } |
| |
| /** |
| * Returns the signum function of this BigInteger. |
| * |
| * @return -1, 0 or 1 as the value of this BigInteger is negative, zero or |
| * positive. |
| */ |
| public int signum() { |
| return this.signum; |
| } |
| |
| // Modular Arithmetic Operations |
| |
| /** |
| * Returns a BigInteger whose value is {@code (this mod m}). This method |
| * differs from {@code remainder} in that it always returns a |
| * <i>non-negative</i> BigInteger. |
| * |
| * @param m the modulus. |
| * @return {@code this mod m} |
| * @throws ArithmeticException {@code m} ≤ 0 |
| * @see #remainder |
| */ |
| public BigInteger mod(BigInteger m) { |
| if (m.signum <= 0) |
| throw new ArithmeticException("BigInteger: modulus not positive"); |
| |
| BigInteger result = this.remainder(m); |
| return (result.signum >= 0 ? result : result.add(m)); |
| } |
| |
| /** |
| * Returns a BigInteger whose value is |
| * <tt>(this<sup>exponent</sup> mod m)</tt>. (Unlike {@code pow}, this |
| * method permits negative exponents.) |
| * |
| * @param exponent the exponent. |
| * @param m the modulus. |
| * @return <tt>this<sup>exponent</sup> mod m</tt> |
| * @throws ArithmeticException {@code m} ≤ 0 or the exponent is |
| * negative and this BigInteger is not <i>relatively |
| * prime</i> to {@code m}. |
| * @see #modInverse |
| */ |
| public BigInteger modPow(BigInteger exponent, BigInteger m) { |
| if (m.signum <= 0) |
| throw new ArithmeticException("BigInteger: modulus not positive"); |
| |
| // Trivial cases |
| if (exponent.signum == 0) |
| return (m.equals(ONE) ? ZERO : ONE); |
| |
| if (this.equals(ONE)) |
| return (m.equals(ONE) ? ZERO : ONE); |
| |
| if (this.equals(ZERO) && exponent.signum >= 0) |
| return ZERO; |
| |
| if (this.equals(negConst[1]) && (!exponent.testBit(0))) |
| return (m.equals(ONE) ? ZERO : ONE); |
| |
| boolean invertResult; |
| if ((invertResult = (exponent.signum < 0))) |
| exponent = exponent.negate(); |
| |
| BigInteger base = (this.signum < 0 || this.compareTo(m) >= 0 |
| ? this.mod(m) : this); |
| BigInteger result; |
| if (m.testBit(0)) { // odd modulus |
| result = base.oddModPow(exponent, m); |
| } else { |
| /* |
| * Even modulus. Tear it into an "odd part" (m1) and power of two |
| * (m2), exponentiate mod m1, manually exponentiate mod m2, and |
| * use Chinese Remainder Theorem to combine results. |
| */ |
| |
| // Tear m apart into odd part (m1) and power of 2 (m2) |
| int p = m.getLowestSetBit(); // Max pow of 2 that divides m |
| |
| BigInteger m1 = m.shiftRight(p); // m/2**p |
| BigInteger m2 = ONE.shiftLeft(p); // 2**p |
| |
| // Calculate new base from m1 |
| BigInteger base2 = (this.signum < 0 || this.compareTo(m1) >= 0 |
| ? this.mod(m1) : this); |
| |
| // Caculate (base ** exponent) mod m1. |
| BigInteger a1 = (m1.equals(ONE) ? ZERO : |
| base2.oddModPow(exponent, m1)); |
| |
| // Calculate (this ** exponent) mod m2 |
| BigInteger a2 = base.modPow2(exponent, p); |
| |
| // Combine results using Chinese Remainder Theorem |
| BigInteger y1 = m2.modInverse(m1); |
| BigInteger y2 = m1.modInverse(m2); |
| |
| result = a1.multiply(m2).multiply(y1).add |
| (a2.multiply(m1).multiply(y2)).mod(m); |
| } |
| |
| return (invertResult ? result.modInverse(m) : result); |
| } |
| |
| static int[] bnExpModThreshTable = {7, 25, 81, 241, 673, 1793, |
| Integer.MAX_VALUE}; // Sentinel |
| |
| /** |
| * Returns a BigInteger whose value is x to the power of y mod z. |
| * Assumes: z is odd && x < z. |
| */ |
| private BigInteger oddModPow(BigInteger y, BigInteger z) { |
| /* |
| * The algorithm is adapted from Colin Plumb's C library. |
| * |
| * The window algorithm: |
| * The idea is to keep a running product of b1 = n^(high-order bits of exp) |
| * and then keep appending exponent bits to it. The following patterns |
| * apply to a 3-bit window (k = 3): |
| * To append 0: square |
| * To append 1: square, multiply by n^1 |
| * To append 10: square, multiply by n^1, square |
| * To append 11: square, square, multiply by n^3 |
| * To append 100: square, multiply by n^1, square, square |
| * To append 101: square, square, square, multiply by n^5 |
| * To append 110: square, square, multiply by n^3, square |
| * To append 111: square, square, square, multiply by n^7 |
| * |
| * Since each pattern involves only one multiply, the longer the pattern |
| * the better, except that a 0 (no multiplies) can be appended directly. |
| * We precompute a table of odd powers of n, up to 2^k, and can then |
| * multiply k bits of exponent at a time. Actually, assuming random |
| * exponents, there is on average one zero bit between needs to |
| * multiply (1/2 of the time there's none, 1/4 of the time there's 1, |
| * 1/8 of the time, there's 2, 1/32 of the time, there's 3, etc.), so |
| * you have to do one multiply per k+1 bits of exponent. |
| * |
| * The loop walks down the exponent, squaring the result buffer as |
| * it goes. There is a wbits+1 bit lookahead buffer, buf, that is |
| * filled with the upcoming exponent bits. (What is read after the |
| * end of the exponent is unimportant, but it is filled with zero here.) |
| * When the most-significant bit of this buffer becomes set, i.e. |
| * (buf & tblmask) != 0, we have to decide what pattern to multiply |
| * by, and when to do it. We decide, remember to do it in future |
| * after a suitable number of squarings have passed (e.g. a pattern |
| * of "100" in the buffer requires that we multiply by n^1 immediately; |
| * a pattern of "110" calls for multiplying by n^3 after one more |
| * squaring), clear the buffer, and continue. |
| * |
| * When we start, there is one more optimization: the result buffer |
| * is implcitly one, so squaring it or multiplying by it can be |
| * optimized away. Further, if we start with a pattern like "100" |
| * in the lookahead window, rather than placing n into the buffer |
| * and then starting to square it, we have already computed n^2 |
| * to compute the odd-powers table, so we can place that into |
| * the buffer and save a squaring. |
| * |
| * This means that if you have a k-bit window, to compute n^z, |
| * where z is the high k bits of the exponent, 1/2 of the time |
| * it requires no squarings. 1/4 of the time, it requires 1 |
| * squaring, ... 1/2^(k-1) of the time, it reqires k-2 squarings. |
| * And the remaining 1/2^(k-1) of the time, the top k bits are a |
| * 1 followed by k-1 0 bits, so it again only requires k-2 |
| * squarings, not k-1. The average of these is 1. Add that |
| * to the one squaring we have to do to compute the table, |
| * and you'll see that a k-bit window saves k-2 squarings |
| * as well as reducing the multiplies. (It actually doesn't |
| * hurt in the case k = 1, either.) |
| */ |
| // Special case for exponent of one |
| if (y.equals(ONE)) |
| return this; |
| |
| // Special case for base of zero |
| if (signum==0) |
| return ZERO; |
| |
| int[] base = mag.clone(); |
| int[] exp = y.mag; |
| int[] mod = z.mag; |
| int modLen = mod.length; |
| |
| // Select an appropriate window size |
| int wbits = 0; |
| int ebits = bitLength(exp, exp.length); |
| // if exponent is 65537 (0x10001), use minimum window size |
| if ((ebits != 17) || (exp[0] != 65537)) { |
| while (ebits > bnExpModThreshTable[wbits]) { |
| wbits++; |
| } |
| } |
| |
| // Calculate appropriate table size |
| int tblmask = 1 << wbits; |
| |
| // Allocate table for precomputed odd powers of base in Montgomery form |
| int[][] table = new int[tblmask][]; |
| for (int i=0; i<tblmask; i++) |
| table[i] = new int[modLen]; |
| |
| // Compute the modular inverse |
| int inv = -MutableBigInteger.inverseMod32(mod[modLen-1]); |
| |
| // Convert base to Montgomery form |
| int[] a = leftShift(base, base.length, modLen << 5); |
| |
| MutableBigInteger q = new MutableBigInteger(), |
| a2 = new MutableBigInteger(a), |
| b2 = new MutableBigInteger(mod); |
| |
| MutableBigInteger r= a2.divide(b2, q); |
| table[0] = r.toIntArray(); |
| |
| // Pad table[0] with leading zeros so its length is at least modLen |
| if (table[0].length < modLen) { |
| int offset = modLen - table[0].length; |
| int[] t2 = new int[modLen]; |
| for (int i=0; i<table[0].length; i++) |
| t2[i+offset] = table[0][i]; |
| table[0] = t2; |
| } |
| |
| // Set b to the square of the base |
| int[] b = squareToLen(table[0], modLen, null); |
| b = montReduce(b, mod, modLen, inv); |
| |
| // Set t to high half of b |
| int[] t = new int[modLen]; |
| for(int i=0; i<modLen; i++) |
| t[i] = b[i]; |
| |
| // Fill in the table with odd powers of the base |
| for (int i=1; i<tblmask; i++) { |
| int[] prod = multiplyToLen(t, modLen, table[i-1], modLen, null); |
| table[i] = montReduce(prod, mod, modLen, inv); |
| } |
| |
| // Pre load the window that slides over the exponent |
| int bitpos = 1 << ((ebits-1) & (32-1)); |
| |
| int buf = 0; |
| int elen = exp.length; |
| int eIndex = 0; |
| for (int i = 0; i <= wbits; i++) { |
| buf = (buf << 1) | (((exp[eIndex] & bitpos) != 0)?1:0); |
| bitpos >>>= 1; |
| if (bitpos == 0) { |
| eIndex++; |
| bitpos = 1 << (32-1); |
| elen--; |
| } |
| } |
| |
| int multpos = ebits; |
| |
| // The first iteration, which is hoisted out of the main loop |
| ebits--; |
| boolean isone = true; |
| |
| multpos = ebits - wbits; |
| while ((buf & 1) == 0) { |
| buf >>>= 1; |
| multpos++; |
| } |
| |
| int[] mult = table[buf >>> 1]; |
| |
| buf = 0; |
| if (multpos == ebits) |
| isone = false; |
| |
| // The main loop |
| while(true) { |
| ebits--; |
| // Advance the window |
| buf <<= 1; |
| |
| if (elen != 0) { |
| buf |= ((exp[eIndex] & bitpos) != 0) ? 1 : 0; |
| bitpos >>>= 1; |
| if (bitpos == 0) { |
| eIndex++; |
| bitpos = 1 << (32-1); |
| elen--; |
| } |
| } |
| |
| // Examine the window for pending multiplies |
| if ((buf & tblmask) != 0) { |
| multpos = ebits - wbits; |
| while ((buf & 1) == 0) { |
| buf >>>= 1; |
| multpos++; |
| } |
| mult = table[buf >>> 1]; |
| buf = 0; |
| } |
| |
| // Perform multiply |
| if (ebits == multpos) { |
| if (isone) { |
| b = mult.clone(); |
| isone = false; |
| } else { |
| t = b; |
| a = multiplyToLen(t, modLen, mult, modLen, a); |
| a = montReduce(a, mod, modLen, inv); |
| t = a; a = b; b = t; |
| } |
| } |
| |
| // Check if done |
| if (ebits == 0) |
| break; |
| |
| // Square the input |
| if (!isone) { |
| t = b; |
| a = squareToLen(t, modLen, a); |
| a = montReduce(a, mod, modLen, inv); |
| t = a; a = b; b = t; |
| } |
| } |
| |
| // Convert result out of Montgomery form and return |
| int[] t2 = new int[2*modLen]; |
| for(int i=0; i<modLen; i++) |
| t2[i+modLen] = b[i]; |
| |
| b = montReduce(t2, mod, modLen, inv); |
| |
| t2 = new int[modLen]; |
| for(int i=0; i<modLen; i++) |
| t2[i] = b[i]; |
| |
| return new BigInteger(1, t2); |
| } |
| |
| /** |
| * Montgomery reduce n, modulo mod. This reduces modulo mod and divides |
| * by 2^(32*mlen). Adapted from Colin Plumb's C library. |
| */ |
| private static int[] montReduce(int[] n, int[] mod, int mlen, int inv) { |
| int c=0; |
| int len = mlen; |
| int offset=0; |
| |
| do { |
| int nEnd = n[n.length-1-offset]; |
| int carry = mulAdd(n, mod, offset, mlen, inv * nEnd); |
| c += addOne(n, offset, mlen, carry); |
| offset++; |
| } while(--len > 0); |
| |
| while(c>0) |
| c += subN(n, mod, mlen); |
| |
| while (intArrayCmpToLen(n, mod, mlen) >= 0) |
| subN(n, mod, mlen); |
| |
| return n; |
| } |
| |
| |
| /* |
| * Returns -1, 0 or +1 as big-endian unsigned int array arg1 is less than, |
| * equal to, or greater than arg2 up to length len. |
| */ |
| private static int intArrayCmpToLen(int[] arg1, int[] arg2, int len) { |
| for (int i=0; i<len; i++) { |
| long b1 = arg1[i] & LONG_MASK; |
| long b2 = arg2[i] & LONG_MASK; |
| if (b1 < b2) |
| return -1; |
| if (b1 > b2) |
| return 1; |
| } |
| return 0; |
| } |
| |
| /** |
| * Subtracts two numbers of same length, returning borrow. |
| */ |
| private static int subN(int[] a, int[] b, int len) { |
| long sum = 0; |
| |
| while(--len >= 0) { |
| sum = (a[len] & LONG_MASK) - |
| (b[len] & LONG_MASK) + (sum >> 32); |
| a[len] = (int)sum; |
| } |
| |
| return (int)(sum >> 32); |
| } |
| |
| /** |
| * Multiply an array by one word k and add to result, return the carry |
| */ |
| static int mulAdd(int[] out, int[] in, int offset, int len, int k) { |
| long kLong = k & LONG_MASK; |
| long carry = 0; |
| |
| offset = out.length-offset - 1; |
| for (int j=len-1; j >= 0; j--) { |
| long product = (in[j] & LONG_MASK) * kLong + |
| (out[offset] & LONG_MASK) + carry; |
| out[offset--] = (int)product; |
| carry = product >>> 32; |
| } |
| return (int)carry; |
| } |
| |
| /** |
| * Add one word to the number a mlen words into a. Return the resulting |
| * carry. |
| */ |
| static int addOne(int[] a, int offset, int mlen, int carry) { |
| offset = a.length-1-mlen-offset; |
| long t = (a[offset] & LONG_MASK) + (carry & LONG_MASK); |
| |
| a[offset] = (int)t; |
| if ((t >>> 32) == 0) |
| return 0; |
| while (--mlen >= 0) { |
| if (--offset < 0) { // Carry out of number |
| return 1; |
| } else { |
| a[offset]++; |
| if (a[offset] != 0) |
| return 0; |
| } |
| } |
| return 1; |
| } |
| |
| /** |
| * Returns a BigInteger whose value is (this ** exponent) mod (2**p) |
| */ |
| private BigInteger modPow2(BigInteger exponent, int p) { |
| /* |
| * Perform exponentiation using repeated squaring trick, chopping off |
| * high order bits as indicated by modulus. |
| */ |
| BigInteger result = valueOf(1); |
| BigInteger baseToPow2 = this.mod2(p); |
| int expOffset = 0; |
| |
| int limit = exponent.bitLength(); |
| |
| if (this.testBit(0)) |
| limit = (p-1) < limit ? (p-1) : limit; |
| |
| while (expOffset < limit) { |
| if (exponent.testBit(expOffset)) |
| result = result.multiply(baseToPow2).mod2(p); |
| expOffset++; |
| if (expOffset < limit) |
| baseToPow2 = baseToPow2.square().mod2(p); |
| } |
| |
| return result; |
| } |
| |
| /** |
| * Returns a BigInteger whose value is this mod(2**p). |
| * Assumes that this {@code BigInteger >= 0} and {@code p > 0}. |
| */ |
| private BigInteger mod2(int p) { |
| if (bitLength() <= p) |
| return this; |
| |
| // Copy remaining ints of mag |
| int numInts = (p + 31) >>> 5; |
| int[] mag = new int[numInts]; |
| for (int i=0; i<numInts; i++) |
| mag[i] = this.mag[i + (this.mag.length - numInts)]; |
| |
| // Mask out any excess bits |
| int excessBits = (numInts << 5) - p; |
| mag[0] &= (1L << (32-excessBits)) - 1; |
| |
| return (mag[0]==0 ? new BigInteger(1, mag) : new BigInteger(mag, 1)); |
| } |
| |
| /** |
| * Returns a BigInteger whose value is {@code (this}<sup>-1</sup> {@code mod m)}. |
| * |
| * @param m the modulus. |
| * @return {@code this}<sup>-1</sup> {@code mod m}. |
| * @throws ArithmeticException {@code m} ≤ 0, or this BigInteger |
| * has no multiplicative inverse mod m (that is, this BigInteger |
| * is not <i>relatively prime</i> to m). |
| */ |
| public BigInteger modInverse(BigInteger m) { |
| if (m.signum != 1) |
| throw new ArithmeticException("BigInteger: modulus not positive"); |
| |
| if (m.equals(ONE)) |
| return ZERO; |
| |
| // Calculate (this mod m) |
| BigInteger modVal = this; |
| if (signum < 0 || (this.compareMagnitude(m) >= 0)) |
| modVal = this.mod(m); |
| |
| if (modVal.equals(ONE)) |
| return ONE; |
| |
| MutableBigInteger a = new MutableBigInteger(modVal); |
| MutableBigInteger b = new MutableBigInteger(m); |
| |
| MutableBigInteger result = a.mutableModInverse(b); |
| return result.toBigInteger(1); |
| } |
| |
| // Shift Operations |
| |
| /** |
| * Returns a BigInteger whose value is {@code (this << n)}. |
| * The shift distance, {@code n}, may be negative, in which case |
| * this method performs a right shift. |
| * (Computes <tt>floor(this * 2<sup>n</sup>)</tt>.) |
| * |
| * @param n shift distance, in bits. |
| * @return {@code this << n} |
| * @throws ArithmeticException if the shift distance is {@code |
| * Integer.MIN_VALUE}. |
| * @see #shiftRight |
| */ |
| public BigInteger shiftLeft(int n) { |
| if (signum == 0) |
| return ZERO; |
| if (n==0) |
| return this; |
| if (n<0) { |
| if (n == Integer.MIN_VALUE) { |
| throw new ArithmeticException("Shift distance of Integer.MIN_VALUE not supported."); |
| } else { |
| return shiftRight(-n); |
| } |
| } |
| |
| int nInts = n >>> 5; |
| int nBits = n & 0x1f; |
| int magLen = mag.length; |
| int newMag[] = null; |
| |
| if (nBits == 0) { |
| newMag = new int[magLen + nInts]; |
| for (int i=0; i<magLen; i++) |
| newMag[i] = mag[i]; |
| } else { |
| int i = 0; |
| int nBits2 = 32 - nBits; |
| int highBits = mag[0] >>> nBits2; |
| if (highBits != 0) { |
| newMag = new int[magLen + nInts + 1]; |
| newMag[i++] = highBits; |
| } else { |
| newMag = new int[magLen + nInts]; |
| } |
| int j=0; |
| while (j < magLen-1) |
| newMag[i++] = mag[j++] << nBits | mag[j] >>> nBits2; |
| newMag[i] = mag[j] << nBits; |
| } |
| |
| return new BigInteger(newMag, signum); |
| } |
| |
| /** |
| * Returns a BigInteger whose value is {@code (this >> n)}. Sign |
| * extension is performed. The shift distance, {@code n}, may be |
| * negative, in which case this method performs a left shift. |
| * (Computes <tt>floor(this / 2<sup>n</sup>)</tt>.) |
| * |
| * @param n shift distance, in bits. |
| * @return {@code this >> n} |
| * @throws ArithmeticException if the shift distance is {@code |
| * Integer.MIN_VALUE}. |
| * @see #shiftLeft |
| */ |
| public BigInteger shiftRight(int n) { |
| if (n==0) |
| return this; |
| if (n<0) { |
| if (n == Integer.MIN_VALUE) { |
| throw new ArithmeticException("Shift distance of Integer.MIN_VALUE not supported."); |
| } else { |
| return shiftLeft(-n); |
| } |
| } |
| |
| int nInts = n >>> 5; |
| int nBits = n & 0x1f; |
| int magLen = mag.length; |
| int newMag[] = null; |
| |
| // Special case: entire contents shifted off the end |
| if (nInts >= magLen) |
| return (signum >= 0 ? ZERO : negConst[1]); |
| |
| if (nBits == 0) { |
| int newMagLen = magLen - nInts; |
| newMag = new int[newMagLen]; |
| for (int i=0; i<newMagLen; i++) |
| newMag[i] = mag[i]; |
| } else { |
| int i = 0; |
| int highBits = mag[0] >>> nBits; |
| if (highBits != 0) { |
| newMag = new int[magLen - nInts]; |
| newMag[i++] = highBits; |
| } else { |
| newMag = new int[magLen - nInts -1]; |
| } |
| |
| int nBits2 = 32 - nBits; |
| int j=0; |
| while (j < magLen - nInts - 1) |
| newMag[i++] = (mag[j++] << nBits2) | (mag[j] >>> nBits); |
| } |
| |
| if (signum < 0) { |
| // Find out whether any one-bits were shifted off the end. |
| boolean onesLost = false; |
| for (int i=magLen-1, j=magLen-nInts; i>=j && !onesLost; i--) |
| onesLost = (mag[i] != 0); |
| if (!onesLost && nBits != 0) |
| onesLost = (mag[magLen - nInts - 1] << (32 - nBits) != 0); |
| |
| if (onesLost) |
| newMag = javaIncrement(newMag); |
| } |
| |
| return new BigInteger(newMag, signum); |
| } |
| |
| int[] javaIncrement(int[] val) { |
| int lastSum = 0; |
| for (int i=val.length-1; i >= 0 && lastSum == 0; i--) |
| lastSum = (val[i] += 1); |
| if (lastSum == 0) { |
| val = new int[val.length+1]; |
| val[0] = 1; |
| } |
| return val; |
| } |
| |
| // Bitwise Operations |
| |
| /** |
| * Returns a BigInteger whose value is {@code (this & val)}. (This |
| * method returns a negative BigInteger if and only if this and val are |
| * both negative.) |
| * |
| * @param val value to be AND'ed with this BigInteger. |
| * @return {@code this & val} |
| */ |
| public BigInteger and(BigInteger val) { |
| int[] result = new int[Math.max(intLength(), val.intLength())]; |
| for (int i=0; i<result.length; i++) |
| result[i] = (getInt(result.length-i-1) |
| & val.getInt(result.length-i-1)); |
| |
| return valueOf(result); |
| } |
| |
| /** |
| * Returns a BigInteger whose value is {@code (this | val)}. (This method |
| * returns a negative BigInteger if and only if either this or val is |
| * negative.) |
| * |
| * @param val value to be OR'ed with this BigInteger. |
| * @return {@code this | val} |
| */ |
| public BigInteger or(BigInteger val) { |
| int[] result = new int[Math.max(intLength(), val.intLength())]; |
| for (int i=0; i<result.length; i++) |
| result[i] = (getInt(result.length-i-1) |
| | val.getInt(result.length-i-1)); |
| |
| return valueOf(result); |
| } |
| |
| /** |
| * Returns a BigInteger whose value is {@code (this ^ val)}. (This method |
| * returns a negative BigInteger if and only if exactly one of this and |
| * val are negative.) |
| * |
| * @param val value to be XOR'ed with this BigInteger. |
| * @return {@code this ^ val} |
| */ |
| public BigInteger xor(BigInteger val) { |
| int[] result = new int[Math.max(intLength(), val.intLength())]; |
| for (int i=0; i<result.length; i++) |
| result[i] = (getInt(result.length-i-1) |
| ^ val.getInt(result.length-i-1)); |
| |
| return valueOf(result); |
| } |
| |
| /** |
| * Returns a BigInteger whose value is {@code (~this)}. (This method |
| * returns a negative value if and only if this BigInteger is |
| * non-negative.) |
| * |
| * @return {@code ~this} |
| */ |
| public BigInteger not() { |
| int[] result = new int[intLength()]; |
| for (int i=0; i<result.length; i++) |
| result[i] = ~getInt(result.length-i-1); |
| |
| return valueOf(result); |
| } |
| |
| /** |
| * Returns a BigInteger whose value is {@code (this & ~val)}. This |
| * method, which is equivalent to {@code and(val.not())}, is provided as |
| * a convenience for masking operations. (This method returns a negative |
| * BigInteger if and only if {@code this} is negative and {@code val} is |
| * positive.) |
| * |
| * @param val value to be complemented and AND'ed with this BigInteger. |
| * @return {@code this & ~val} |
| */ |
| public BigInteger andNot(BigInteger val) { |
| int[] result = new int[Math.max(intLength(), val.intLength())]; |
| for (int i=0; i<result.length; i++) |
| result[i] = (getInt(result.length-i-1) |
| & ~val.getInt(result.length-i-1)); |
| |
| return valueOf(result); |
| } |
| |
| |
| // Single Bit Operations |
| |
| /** |
| * Returns {@code true} if and only if the designated bit is set. |
| * (Computes {@code ((this & (1<<n)) != 0)}.) |
| * |
| * @param n index of bit to test. |
| * @return {@code true} if and only if the designated bit is set. |
| * @throws ArithmeticException {@code n} is negative. |
| */ |
| public boolean testBit(int n) { |
| if (n<0) |
| throw new ArithmeticException("Negative bit address"); |
| |
| return (getInt(n >>> 5) & (1 << (n & 31))) != 0; |
| } |
| |
| /** |
| * Returns a BigInteger whose value is equivalent to this BigInteger |
| * with the designated bit set. (Computes {@code (this | (1<<n))}.) |
| * |
| * @param n index of bit to set. |
| * @return {@code this | (1<<n)} |
| * @throws ArithmeticException {@code n} is negative. |
| */ |
| public BigInteger setBit(int n) { |
| if (n<0) |
| throw new ArithmeticException("Negative bit address"); |
| |
| int intNum = n >>> 5; |
| int[] result = new int[Math.max(intLength(), intNum+2)]; |
| |
| for (int i=0; i<result.length; i++) |
| result[result.length-i-1] = getInt(i); |
| |
| result[result.length-intNum-1] |= (1 << (n & 31)); |
| |
| return valueOf(result); |
| } |
| |
| /** |
| * Returns a BigInteger whose value is equivalent to this BigInteger |
| * with the designated bit cleared. |
| * (Computes {@code (this & ~(1<<n))}.) |
| * |
| * @param n index of bit to clear. |
| * @return {@code this & ~(1<<n)} |
| * @throws ArithmeticException {@code n} is negative. |
| */ |
| public BigInteger clearBit(int n) { |
| if (n<0) |
| throw new ArithmeticException("Negative bit address"); |
| |
| int intNum = n >>> 5; |
| int[] result = new int[Math.max(intLength(), ((n + 1) >>> 5) + 1)]; |
| |
| for (int i=0; i<result.length; i++) |
| result[result.length-i-1] = getInt(i); |
| |
| result[result.length-intNum-1] &= ~(1 << (n & 31)); |
| |
| return valueOf(result); |
| } |
| |
| /** |
| * Returns a BigInteger whose value is equivalent to this BigInteger |
| * with the designated bit flipped. |
| * (Computes {@code (this ^ (1<<n))}.) |
| * |
| * @param n index of bit to flip. |
| * @return {@code this ^ (1<<n)} |
| * @throws ArithmeticException {@code n} is negative. |
| */ |
| public BigInteger flipBit(int n) { |
| if (n<0) |
| throw new ArithmeticException("Negative bit address"); |
| |
| int intNum = n >>> 5; |
| int[] result = new int[Math.max(intLength(), intNum+2)]; |
| |
| for (int i=0; i<result.length; i++) |
| result[result.length-i-1] = getInt(i); |
| |
| result[result.length-intNum-1] ^= (1 << (n & 31)); |
| |
| return valueOf(result); |
| } |
| |
| /** |
| * Returns the index of the rightmost (lowest-order) one bit in this |
| * BigInteger (the number of zero bits to the right of the rightmost |
| * one bit). Returns -1 if this BigInteger contains no one bits. |
| * (Computes {@code (this==0? -1 : log2(this & -this))}.) |
| * |
| * @return index of the rightmost one bit in this BigInteger. |
| */ |
| public int getLowestSetBit() { |
| @SuppressWarnings("deprecation") int lsb = lowestSetBit - 2; |
| if (lsb == -2) { // lowestSetBit not initialized yet |
| lsb = 0; |
| if (signum == 0) { |
| lsb -= 1; |
| } else { |
| // Search for lowest order nonzero int |
| int i,b; |
| for (i=0; (b = getInt(i))==0; i++) |
| ; |
| lsb += (i << 5) + Integer.numberOfTrailingZeros(b); |
| } |
| lowestSetBit = lsb + 2; |
| } |
| return lsb; |
| } |
| |
| |
| // Miscellaneous Bit Operations |
| |
| /** |
| * Returns the number of bits in the minimal two's-complement |
| * representation of this BigInteger, <i>excluding</i> a sign bit. |
| * For positive BigIntegers, this is equivalent to the number of bits in |
| * the ordinary binary representation. (Computes |
| * {@code (ceil(log2(this < 0 ? -this : this+1)))}.) |
| * |
| * @return number of bits in the minimal two's-complement |
| * representation of this BigInteger, <i>excluding</i> a sign bit. |
| */ |
| public int bitLength() { |
| @SuppressWarnings("deprecation") int n = bitLength - 1; |
| if (n == -1) { // bitLength not initialized yet |
| int[] m = mag; |
| int len = m.length; |
| if (len == 0) { |
| n = 0; // offset by one to initialize |
| } else { |
| // Calculate the bit length of the magnitude |
| int magBitLength = ((len - 1) << 5) + bitLengthForInt(mag[0]); |
| if (signum < 0) { |
| // Check if magnitude is a power of two |
| boolean pow2 = (Integer.bitCount(mag[0]) == 1); |
| for(int i=1; i< len && pow2; i++) |
| pow2 = (mag[i] == 0); |
| |
| n = (pow2 ? magBitLength -1 : magBitLength); |
| } else { |
| n = magBitLength; |
| } |
| } |
| bitLength = n + 1; |
| } |
| return n; |
| } |
| |
| /** |
| * Returns the number of bits in the two's complement representation |
| * of this BigInteger that differ from its sign bit. This method is |
| * useful when implementing bit-vector style sets atop BigIntegers. |
| * |
| * @return number of bits in the two's complement representation |
| * of this BigInteger that differ from its sign bit. |
| */ |
| public int bitCount() { |
| @SuppressWarnings("deprecation") int bc = bitCount - 1; |
| if (bc == -1) { // bitCount not initialized yet |
| bc = 0; // offset by one to initialize |
| // Count the bits in the magnitude |
| for (int i=0; i<mag.length; i++) |
| bc += Integer.bitCount(mag[i]); |
| if (signum < 0) { |
| // Count the trailing zeros in the magnitude |
| int magTrailingZeroCount = 0, j; |
| for (j=mag.length-1; mag[j]==0; j--) |
| magTrailingZeroCount += 32; |
| magTrailingZeroCount += Integer.numberOfTrailingZeros(mag[j]); |
| bc += magTrailingZeroCount - 1; |
| } |
| bitCount = bc + 1; |
| } |
| return bc; |
| } |
| |
| // Primality Testing |
| |
| /** |
| * Returns {@code true} if this BigInteger is probably prime, |
| * {@code false} if it's definitely composite. If |
| * {@code certainty} is ≤ 0, {@code true} is |
| * returned. |
| * |
| * @param certainty a measure of the uncertainty that the caller is |
| * willing to tolerate: if the call returns {@code true} |
| * the probability that this BigInteger is prime exceeds |
| * (1 - 1/2<sup>{@code certainty}</sup>). The execution time of |
| * this method is proportional to the value of this parameter. |
| * @return {@code true} if this BigInteger is probably prime, |
| * {@code false} if it's definitely composite. |
| */ |
| public boolean isProbablePrime(int certainty) { |
| if (certainty <= 0) |
| return true; |
| BigInteger w = this.abs(); |
| if (w.equals(TWO)) |
| return true; |
| if (!w.testBit(0) || w.equals(ONE)) |
| return false; |
| |
| return w.primeToCertainty(certainty, null); |
| } |
| |
| // Comparison Operations |
| |
| /** |
| * Compares this BigInteger with the specified BigInteger. This |
| * method is provided in preference to individual methods for each |
| * of the six boolean comparison operators ({@literal <}, ==, |
| * {@literal >}, {@literal >=}, !=, {@literal <=}). The suggested |
| * idiom for performing these comparisons is: {@code |
| * (x.compareTo(y)} <<i>op</i>> {@code 0)}, where |
| * <<i>op</i>> is one of the six comparison operators. |
| * |
| * @param val BigInteger to which this BigInteger is to be compared. |
| * @return -1, 0 or 1 as this BigInteger is numerically less than, equal |
| * to, or greater than {@code val}. |
| */ |
| public int compareTo(BigInteger val) { |
| if (signum == val.signum) { |
| switch (signum) { |
| case 1: |
| return compareMagnitude(val); |
| case -1: |
| return val.compareMagnitude(this); |
| default: |
| return 0; |
| } |
| } |
| return signum > val.signum ? 1 : -1; |
| } |
| |
| /** |
| * Compares the magnitude array of this BigInteger with the specified |
| * BigInteger's. This is the version of compareTo ignoring sign. |
| * |
| * @param val BigInteger whose magnitude array to be compared. |
| * @return -1, 0 or 1 as this magnitude array is less than, equal to or |
| * greater than the magnitude aray for the specified BigInteger's. |
| */ |
| final int compareMagnitude(BigInteger val) { |
| int[] m1 = mag; |
| int len1 = m1.length; |
| int[] m2 = val.mag; |
| int len2 = m2.length; |
| if (len1 < len2) |
| return -1; |
| if (len1 > len2) |
| return 1; |
| for (int i = 0; i < len1; i++) { |
| int a = m1[i]; |
| int b = m2[i]; |
| if (a != b) |
| return ((a & LONG_MASK) < (b & LONG_MASK)) ? -1 : 1; |
| } |
| return 0; |
| } |
| |
| /** |
| * Compares this BigInteger with the specified Object for equality. |
| * |
| * @param x Object to which this BigInteger is to be compared. |
| * @return {@code true} if and only if the specified Object is a |
| * BigInteger whose value is numerically equal to this BigInteger. |
| */ |
| public boolean equals(Object x) { |
| // This test is just an optimization, which may or may not help |
| if (x == this) |
| return true; |
| |
| if (!(x instanceof BigInteger)) |
| return false; |
| |
| BigInteger xInt = (BigInteger) x; |
| if (xInt.signum != signum) |
| return false; |
| |
| int[] m = mag; |
| int len = m.length; |
| int[] xm = xInt.mag; |
| if (len != xm.length) |
| return false; |
| |
| for (int i = 0; i < len; i++) |
| if (xm[i] != m[i]) |
| return false; |
| |
| return true; |
| } |
| |
| /** |
| * Returns the minimum of this BigInteger and {@code val}. |
| * |
| * @param val value with which the minimum is to be computed. |
| * @return the BigInteger whose value is the lesser of this BigInteger and |
| * {@code val}. If they are equal, either may be returned. |
| */ |
| public BigInteger min(BigInteger val) { |
| return (compareTo(val)<0 ? this : val); |
| } |
| |
| /** |
| * Returns the maximum of this BigInteger and {@code val}. |
| * |
| * @param val value with which the maximum is to be computed. |
| * @return the BigInteger whose value is the greater of this and |
| * {@code val}. If they are equal, either may be returned. |
| */ |
| public BigInteger max(BigInteger val) { |
| return (compareTo(val)>0 ? this : val); |
| } |
| |
| |
| // Hash Function |
| |
| /** |
| * Returns the hash code for this BigInteger. |
| * |
| * @return hash code for this BigInteger. |
| */ |
| public int hashCode() { |
| int hashCode = 0; |
| |
| for (int i=0; i<mag.length; i++) |
| hashCode = (int)(31*hashCode + (mag[i] & LONG_MASK)); |
| |
| return hashCode * signum; |
| } |
| |
| /** |
| * Returns the String representation of this BigInteger in the |
| * given radix. If the radix is outside the range from {@link |
| * Character#MIN_RADIX} to {@link Character#MAX_RADIX} inclusive, |
| * it will default to 10 (as is the case for |
| * {@code Integer.toString}). The digit-to-character mapping |
| * provided by {@code Character.forDigit} is used, and a minus |
| * sign is prepended if appropriate. (This representation is |
| * compatible with the {@link #BigInteger(String, int) (String, |
| * int)} constructor.) |
| * |
| * @param radix radix of the String representation. |
| * @return String representation of this BigInteger in the given radix. |
| * @see Integer#toString |
| * @see Character#forDigit |
| * @see #BigInteger(java.lang.String, int) |
| */ |
| public String toString(int radix) { |
| if (signum == 0) |
| return "0"; |
| if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX) |
| radix = 10; |
| |
| // Compute upper bound on number of digit groups and allocate space |
| int maxNumDigitGroups = (4*mag.length + 6)/7; |
| String digitGroup[] = new String[maxNumDigitGroups]; |
| |
| // Translate number to string, a digit group at a time |
| BigInteger tmp = this.abs(); |
| int numGroups = 0; |
| while (tmp.signum != 0) { |
| BigInteger d = longRadix[radix]; |
| |
| MutableBigInteger q = new MutableBigInteger(), |
| a = new MutableBigInteger(tmp.mag), |
| b = new MutableBigInteger(d.mag); |
| MutableBigInteger r = a.divide(b, q); |
| BigInteger q2 = q.toBigInteger(tmp.signum * d.signum); |
| BigInteger r2 = r.toBigInteger(tmp.signum * d.signum); |
| |
| digitGroup[numGroups++] = Long.toString(r2.longValue(), radix); |
| tmp = q2; |
| } |
| |
| // Put sign (if any) and first digit group into result buffer |
| StringBuilder buf = new StringBuilder(numGroups*digitsPerLong[radix]+1); |
| if (signum<0) |
| buf.append('-'); |
| buf.append(digitGroup[numGroups-1]); |
| |
| // Append remaining digit groups padded with leading zeros |
| for (int i=numGroups-2; i>=0; i--) { |
| // Prepend (any) leading zeros for this digit group |
| int numLeadingZeros = digitsPerLong[radix]-digitGroup[i].length(); |
| if (numLeadingZeros != 0) |
| buf.append(zeros[numLeadingZeros]); |
| buf.append(digitGroup[i]); |
| } |
| return buf.toString(); |
| } |
| |
| /* zero[i] is a string of i consecutive zeros. */ |
| private static String zeros[] = new String[64]; |
| static { |
| zeros[63] = |
| "000000000000000000000000000000000000000000000000000000000000000"; |
| for (int i=0; i<63; i++) |
| zeros[i] = zeros[63].substring(0, i); |
| } |
| |
| /** |
| * Returns the decimal String representation of this BigInteger. |
| * The digit-to-character mapping provided by |
| * {@code Character.forDigit} is used, and a minus sign is |
| * prepended if appropriate. (This representation is compatible |
| * with the {@link #BigInteger(String) (String)} constructor, and |
| * allows for String concatenation with Java's + operator.) |
| * |
| * @return decimal String representation of this BigInteger. |
| * @see Character#forDigit |
| * @see #BigInteger(java.lang.String) |
| */ |
| public String toString() { |
| return toString(10); |
| } |
| |
| /** |
| * Returns a byte array containing the two's-complement |
| * representation of this BigInteger. The byte array will be in |
| * <i>big-endian</i> byte-order: the most significant byte is in |
| * the zeroth element. The array will contain the minimum number |
| * of bytes required to represent this BigInteger, including at |
| * least one sign bit, which is {@code (ceil((this.bitLength() + |
| * 1)/8))}. (This representation is compatible with the |
| * {@link #BigInteger(byte[]) (byte[])} constructor.) |
| * |
| * @return a byte array containing the two's-complement representation of |
| * this BigInteger. |
| * @see #BigInteger(byte[]) |
| */ |
| public byte[] toByteArray() { |
| int byteLen = bitLength()/8 + 1; |
| byte[] byteArray = new byte[byteLen]; |
| |
| for (int i=byteLen-1, bytesCopied=4, nextInt=0, intIndex=0; i>=0; i--) { |
| if (bytesCopied == 4) { |
| nextInt = getInt(intIndex++); |
| bytesCopied = 1; |
| } else { |
| nextInt >>>= 8; |
| bytesCopied++; |
| } |
| byteArray[i] = (byte)nextInt; |
| } |
| return byteArray; |
| } |
| |
| /** |
| * Converts this BigInteger to an {@code int}. This |
| * conversion is analogous to a |
| * <i>narrowing primitive conversion</i> from {@code long} to |
| * {@code int} as defined in section 5.1.3 of |
| * <cite>The Java™ Language Specification</cite>: |
| * if this BigInteger is too big to fit in an |
| * {@code int}, only the low-order 32 bits are returned. |
| * Note that this conversion can lose information about the |
| * overall magnitude of the BigInteger value as well as return a |
| * result with the opposite sign. |
| * |
| * @return this BigInteger converted to an {@code int}. |
| */ |
| public int intValue() { |
| int result = 0; |
| result = getInt(0); |
| return result; |
| } |
| |
| /** |
| * Converts this BigInteger to a {@code long}. This |
| * conversion is analogous to a |
| * <i>narrowing primitive conversion</i> from {@code long} to |
| * {@code int} as defined in section 5.1.3 of |
| * <cite>The Java™ Language Specification</cite>: |
| * if this BigInteger is too big to fit in a |
| * {@code long}, only the low-order 64 bits are returned. |
| * Note that this conversion can lose information about the |
| * overall magnitude of the BigInteger value as well as return a |
| * result with the opposite sign. |
| * |
| * @return this BigInteger converted to a {@code long}. |
| */ |
| public long longValue() { |
| long result = 0; |
| |
| for (int i=1; i>=0; i--) |
| result = (result << 32) + (getInt(i) & LONG_MASK); |
| return result; |
| } |
| |
| /** |
| * Converts this BigInteger to a {@code float}. This |
| * conversion is similar to the |
| * <i>narrowing primitive conversion</i> from {@code double} to |
| * {@code float} as defined in section 5.1.3 of |
| * <cite>The Java™ Language Specification</cite>: |
| * if this BigInteger has too great a magnitude |
| * to represent as a {@code float}, it will be converted to |
| * {@link Float#NEGATIVE_INFINITY} or {@link |
| * Float#POSITIVE_INFINITY} as appropriate. Note that even when |
| * the return value is finite, this conversion can lose |
| * information about the precision of the BigInteger value. |
| * |
| * @return this BigInteger converted to a {@code float}. |
| */ |
| public float floatValue() { |
| // Somewhat inefficient, but guaranteed to work. |
| return Float.parseFloat(this.toString()); |
| } |
| |
| /** |
| * Converts this BigInteger to a {@code double}. This |
| * conversion is similar to the |
| * <i>narrowing primitive conversion</i> from {@code double} to |
| * {@code float} as defined in section 5.1.3 of |
| * <cite>The Java™ Language Specification</cite>: |
| * if this BigInteger has too great a magnitude |
| * to represent as a {@code double}, it will be converted to |
| * {@link Double#NEGATIVE_INFINITY} or {@link |
| * Double#POSITIVE_INFINITY} as appropriate. Note that even when |
| * the return value is finite, this conversion can lose |
| * information about the precision of the BigInteger value. |
| * |
| * @return this BigInteger converted to a {@code double}. |
| */ |
| public double doubleValue() { |
| // Somewhat inefficient, but guaranteed to work. |
| return Double.parseDouble(this.toString()); |
| } |
| |
| /** |
| * Returns a copy of the input array stripped of any leading zero bytes. |
| */ |
| private static int[] stripLeadingZeroInts(int val[]) { |
| int vlen = val.length; |
| int keep; |
| |
| // Find first nonzero byte |
| for (keep = 0; keep < vlen && val[keep] == 0; keep++) |
| ; |
| return java.util.Arrays.copyOfRange(val, keep, vlen); |
| } |
| |
| /** |
| * Returns the input array stripped of any leading zero bytes. |
| * Since the source is trusted the copying may be skipped. |
| */ |
| private static int[] trustedStripLeadingZeroInts(int val[]) { |
| int vlen = val.length; |
| int keep; |
| |
| // Find first nonzero byte |
| for (keep = 0; keep < vlen && val[keep] == 0; keep++) |
| ; |
| return keep == 0 ? val : java.util.Arrays.copyOfRange(val, keep, vlen); |
| } |
| |
| /** |
| * Returns a copy of the input array stripped of any leading zero bytes. |
| */ |
| private static int[] stripLeadingZeroBytes(byte a[]) { |
| int byteLength = a.length; |
| int keep; |
| |
| // Find first nonzero byte |
| for (keep = 0; keep < byteLength && a[keep]==0; keep++) |
| ; |
| |
| // Allocate new array and copy relevant part of input array |
| int intLength = ((byteLength - keep) + 3) >>> 2; |
| int[] result = new int[intLength]; |
| int b = byteLength - 1; |
| for (int i = intLength-1; i >= 0; i--) { |
| result[i] = a[b--] & 0xff; |
| int bytesRemaining = b - keep + 1; |
| int bytesToTransfer = Math.min(3, bytesRemaining); |
| for (int j=8; j <= (bytesToTransfer << 3); j += 8) |
| result[i] |= ((a[b--] & 0xff) << j); |
| } |
| return result; |
| } |
| |
| /** |
| * Takes an array a representing a negative 2's-complement number and |
| * returns the minimal (no leading zero bytes) unsigned whose value is -a. |
| */ |
| private static int[] makePositive(byte a[]) { |
| int keep, k; |
| int byteLength = a.length; |
| |
| // Find first non-sign (0xff) byte of input |
| for (keep=0; keep<byteLength && a[keep]==-1; keep++) |
| ; |
| |
| |
| /* Allocate output array. If all non-sign bytes are 0x00, we must |
| * allocate space for one extra output byte. */ |
| for (k=keep; k<byteLength && a[k]==0; k++) |
| ; |
| |
| int extraByte = (k==byteLength) ? 1 : 0; |
| int intLength = ((byteLength - keep + extraByte) + 3)/4; |
| int result[] = new int[intLength]; |
| |
| /* Copy one's complement of input into output, leaving extra |
| * byte (if it exists) == 0x00 */ |
| int b = byteLength - 1; |
| for (int i = intLength-1; i >= 0; i--) { |
| result[i] = a[b--] & 0xff; |
| int numBytesToTransfer = Math.min(3, b-keep+1); |
| if (numBytesToTransfer < 0) |
| numBytesToTransfer = 0; |
| for (int j=8; j <= 8*numBytesToTransfer; j += 8) |
| result[i] |= ((a[b--] & 0xff) << j); |
| |
| // Mask indicates which bits must be complemented |
| int mask = -1 >>> (8*(3-numBytesToTransfer)); |
| result[i] = ~result[i] & mask; |
| } |
| |
| // Add one to one's complement to generate two's complement |
| for (int i=result.length-1; i>=0; i--) { |
| result[i] = (int)((result[i] & LONG_MASK) + 1); |
| if (result[i] != 0) |
| break; |
| } |
| |
| return result; |
| } |
| |
| /** |
| * Takes an array a representing a negative 2's-complement number and |
| * returns the minimal (no leading zero ints) unsigned whose value is -a. |
| */ |
| private static int[] makePositive(int a[]) { |
| int keep, j; |
| |
| // Find first non-sign (0xffffffff) int of input |
| for (keep=0; keep<a.length && a[keep]==-1; keep++) |
| ; |
| |
| /* Allocate output array. If all non-sign ints are 0x00, we must |
| * allocate space for one extra output int. */ |
| for (j=keep; j<a.length && a[j]==0; j++) |
| ; |
| int extraInt = (j==a.length ? 1 : 0); |
| int result[] = new int[a.length - keep + extraInt]; |
| |
| /* Copy one's complement of input into output, leaving extra |
| * int (if it exists) == 0x00 */ |
| for (int i = keep; i<a.length; i++) |
| result[i - keep + extraInt] = ~a[i]; |
| |
| // Add one to one's complement to generate two's complement |
| for (int i=result.length-1; ++result[i]==0; i--) |
| ; |
| |
| return result; |
| } |
| |
| /* |
| * The following two arrays are used for fast String conversions. Both |
| * are indexed by radix. The first is the number of digits of the given |
| * radix that can fit in a Java long without "going negative", i.e., the |
| * highest integer n such that radix**n < 2**63. The second is the |
| * "long radix" that tears each number into "long digits", each of which |
| * consists of the number of digits in the corresponding element in |
| * digitsPerLong (longRadix[i] = i**digitPerLong[i]). Both arrays have |
| * nonsense values in their 0 and 1 elements, as radixes 0 and 1 are not |
| * used. |
| */ |
| private static int digitsPerLong[] = {0, 0, |
| 62, 39, 31, 27, 24, 22, 20, 19, 18, 18, 17, 17, 16, 16, 15, 15, 15, 14, |
| 14, 14, 14, 13, 13, 13, 13, 13, 13, 12, 12, 12, 12, 12, 12, 12, 12}; |
| |
| private static BigInteger longRadix[] = {null, null, |
| valueOf(0x4000000000000000L), valueOf(0x383d9170b85ff80bL), |
| valueOf(0x4000000000000000L), valueOf(0x6765c793fa10079dL), |
| valueOf(0x41c21cb8e1000000L), valueOf(0x3642798750226111L), |
| valueOf(0x1000000000000000L), valueOf(0x12bf307ae81ffd59L), |
| valueOf( 0xde0b6b3a7640000L), valueOf(0x4d28cb56c33fa539L), |
| valueOf(0x1eca170c00000000L), valueOf(0x780c7372621bd74dL), |
| valueOf(0x1e39a5057d810000L), valueOf(0x5b27ac993df97701L), |
| valueOf(0x1000000000000000L), valueOf(0x27b95e997e21d9f1L), |
| valueOf(0x5da0e1e53c5c8000L), valueOf( 0xb16a458ef403f19L), |
| valueOf(0x16bcc41e90000000L), valueOf(0x2d04b7fdd9c0ef49L), |
| valueOf(0x5658597bcaa24000L), valueOf( 0x6feb266931a75b7L), |
| valueOf( 0xc29e98000000000L), valueOf(0x14adf4b7320334b9L), |
| valueOf(0x226ed36478bfa000L), valueOf(0x383d9170b85ff80bL), |
| valueOf(0x5a3c23e39c000000L), valueOf( 0x4e900abb53e6b71L), |
| valueOf( 0x7600ec618141000L), valueOf( 0xaee5720ee830681L), |
| valueOf(0x1000000000000000L), valueOf(0x172588ad4f5f0981L), |
| valueOf(0x211e44f7d02c1000L), valueOf(0x2ee56725f06e5c71L), |
| valueOf(0x41c21cb8e1000000L)}; |
| |
| /* |
| * These two arrays are the integer analogue of above. |
| */ |
| private static int digitsPerInt[] = {0, 0, 30, 19, 15, 13, 11, |
| 11, 10, 9, 9, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, |
| 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5}; |
| |
| private static int intRadix[] = {0, 0, |
| 0x40000000, 0x4546b3db, 0x40000000, 0x48c27395, 0x159fd800, |
| 0x75db9c97, 0x40000000, 0x17179149, 0x3b9aca00, 0xcc6db61, |
| 0x19a10000, 0x309f1021, 0x57f6c100, 0xa2f1b6f, 0x10000000, |
| 0x18754571, 0x247dbc80, 0x3547667b, 0x4c4b4000, 0x6b5a6e1d, |
| 0x6c20a40, 0x8d2d931, 0xb640000, 0xe8d4a51, 0x1269ae40, |
| 0x17179149, 0x1cb91000, 0x23744899, 0x2b73a840, 0x34e63b41, |
| 0x40000000, 0x4cfa3cc1, 0x5c13d840, 0x6d91b519, 0x39aa400 |
| }; |
| |
| /** |
| * These routines provide access to the two's complement representation |
| * of BigIntegers. |
| */ |
| |
| /** |
| * Returns the length of the two's complement representation in ints, |
| * including space for at least one sign bit. |
| */ |
| private int intLength() { |
| return (bitLength() >>> 5) + 1; |
| } |
| |
| /* Returns sign bit */ |
| private int signBit() { |
| return signum < 0 ? 1 : 0; |
| } |
| |
| /* Returns an int of sign bits */ |
| private int signInt() { |
| return signum < 0 ? -1 : 0; |
| } |
| |
| /** |
| * Returns the specified int of the little-endian two's complement |
| * representation (int 0 is the least significant). The int number can |
| * be arbitrarily high (values are logically preceded by infinitely many |
| * sign ints). |
| */ |
| private int getInt(int n) { |
| if (n < 0) |
| return 0; |
| if (n >= mag.length) |
| return signInt(); |
| |
| int magInt = mag[mag.length-n-1]; |
| |
| return (signum >= 0 ? magInt : |
| (n <= firstNonzeroIntNum() ? -magInt : ~magInt)); |
| } |
| |
| /** |
| * Returns the index of the int that contains the first nonzero int in the |
| * little-endian binary representation of the magnitude (int 0 is the |
| * least significant). If the magnitude is zero, return value is undefined. |
| */ |
| private int firstNonzeroIntNum() { |
| int fn = firstNonzeroIntNum - 2; |
| if (fn == -2) { // firstNonzeroIntNum not initialized yet |
| fn = 0; |
| |
| // Search for the first nonzero int |
| int i; |
| int mlen = mag.length; |
| for (i = mlen - 1; i >= 0 && mag[i] == 0; i--) |
| ; |
| fn = mlen - i - 1; |
| firstNonzeroIntNum = fn + 2; // offset by two to initialize |
| } |
| return fn; |
| } |
| |
| /** use serialVersionUID from JDK 1.1. for interoperability */ |
| private static final long serialVersionUID = -8287574255936472291L; |
| |
| /** |
| * Serializable fields for BigInteger. |
| * |
| * @serialField signum int |
| * signum of this BigInteger. |
| * @serialField magnitude int[] |
| * magnitude array of this BigInteger. |
| * @serialField bitCount int |
| * number of bits in this BigInteger |
| * @serialField bitLength int |
| * the number of bits in the minimal two's-complement |
| * representation of this BigInteger |
| * @serialField lowestSetBit int |
| * lowest set bit in the twos complement representation |
| */ |
| private static final ObjectStreamField[] serialPersistentFields = { |
| new ObjectStreamField("signum", Integer.TYPE), |
| new ObjectStreamField("magnitude", byte[].class), |
| new ObjectStreamField("bitCount", Integer.TYPE), |
| new ObjectStreamField("bitLength", Integer.TYPE), |
| new ObjectStreamField("firstNonzeroByteNum", Integer.TYPE), |
| new ObjectStreamField("lowestSetBit", Integer.TYPE) |
| }; |
| |
| /** |
| * Reconstitute the {@code BigInteger} instance from a stream (that is, |
| * deserialize it). The magnitude is read in as an array of bytes |
| * for historical reasons, but it is converted to an array of ints |
| * and the byte array is discarded. |
| * Note: |
| * The current convention is to initialize the cache fields, bitCount, |
| * bitLength and lowestSetBit, to 0 rather than some other marker value. |
| * Therefore, no explicit action to set these fields needs to be taken in |
| * readObject because those fields already have a 0 value be default since |
| * defaultReadObject is not being used. |
| */ |
| private void readObject(java.io.ObjectInputStream s) |
| throws java.io.IOException, ClassNotFoundException { |
| /* |
| * In order to maintain compatibility with previous serialized forms, |
| * the magnitude of a BigInteger is serialized as an array of bytes. |
| * The magnitude field is used as a temporary store for the byte array |
| * that is deserialized. The cached computation fields should be |
| * transient but are serialized for compatibility reasons. |
| */ |
| |
| // prepare to read the alternate persistent fields |
| ObjectInputStream.GetField fields = s.readFields(); |
| |
| // Read the alternate persistent fields that we care about |
| int sign = fields.get("signum", -2); |
| byte[] magnitude = (byte[])fields.get("magnitude", null); |
| |
| // Validate signum |
| if (sign < -1 || sign > 1) { |
| String message = "BigInteger: Invalid signum value"; |
| if (fields.defaulted("signum")) |
| message = "BigInteger: Signum not present in stream"; |
| throw new java.io.StreamCorruptedException(message); |
| } |
| if ((magnitude.length == 0) != (sign == 0)) { |
| String message = "BigInteger: signum-magnitude mismatch"; |
| if (fields.defaulted("magnitude")) |
| message = "BigInteger: Magnitude not present in stream"; |
| throw new java.io.StreamCorruptedException(message); |
| } |
| |
| // Commit final fields via Unsafe |
| unsafe.putIntVolatile(this, signumOffset, sign); |
| |
| // Calculate mag field from magnitude and discard magnitude |
| unsafe.putObjectVolatile(this, magOffset, |
| stripLeadingZeroBytes(magnitude)); |
| } |
| |
| // Support for resetting final fields while deserializing |
| private static final sun.misc.Unsafe unsafe = sun.misc.Unsafe.getUnsafe(); |
| private static final long signumOffset; |
| private static final long magOffset; |
| static { |
| try { |
| signumOffset = unsafe.objectFieldOffset |
| (BigInteger.class.getDeclaredField("signum")); |
| magOffset = unsafe.objectFieldOffset |
| (BigInteger.class.getDeclaredField("mag")); |
| } catch (Exception ex) { |
| throw new Error(ex); |
| } |
| } |
| |
| /** |
| * Save the {@code BigInteger} instance to a stream. |
| * The magnitude of a BigInteger is serialized as a byte array for |
| * historical reasons. |
| * |
| * @serialData two necessary fields are written as well as obsolete |
| * fields for compatibility with older versions. |
| */ |
| private void writeObject(ObjectOutputStream s) throws IOException { |
| // set the values of the Serializable fields |
| ObjectOutputStream.PutField fields = s.putFields(); |
| fields.put("signum", signum); |
| fields.put("magnitude", magSerializedForm()); |
| // The values written for cached fields are compatible with older |
| // versions, but are ignored in readObject so don't otherwise matter. |
| fields.put("bitCount", -1); |
| fields.put("bitLength", -1); |
| fields.put("lowestSetBit", -2); |
| fields.put("firstNonzeroByteNum", -2); |
| |
| // save them |
| s.writeFields(); |
| } |
| |
| /** |
| * Returns the mag array as an array of bytes. |
| */ |
| private byte[] magSerializedForm() { |
| int len = mag.length; |
| |
| int bitLen = (len == 0 ? 0 : ((len - 1) << 5) + bitLengthForInt(mag[0])); |
| int byteLen = (bitLen + 7) >>> 3; |
| byte[] result = new byte[byteLen]; |
| |
| for (int i = byteLen - 1, bytesCopied = 4, intIndex = len - 1, nextInt = 0; |
| i>=0; i--) { |
| if (bytesCopied == 4) { |
| nextInt = mag[intIndex--]; |
| bytesCopied = 1; |
| } else { |
| nextInt >>>= 8; |
| bytesCopied++; |
| } |
| result[i] = (byte)nextInt; |
| } |
| return result; |
| } |
| } |