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-// BigInteger.java -- an arbitrary-precision integer
-
-/* Copyright (C) 1999, 2000 Free Software Foundation
-
- This file is part of libgcj.
-
-This software is copyrighted work licensed under the terms of the
-Libgcj License. Please consult the file "LIBGCJ_LICENSE" for
-details. */
-
-package java.math;
-import gnu.gcj.math.*;
-import java.util.Random;
-
-/**
- * @author Warren Levy <warrenl@cygnus.com>
- * @date December 20, 1999.
- */
-
-/**
- * Written using on-line Java Platform 1.2 API Specification, as well
- * as "The Java Class Libraries", 2nd edition (Addison-Wesley, 1998) and
- * "Applied Cryptography, Second Edition" by Bruce Schneier (Wiley, 1996).
-
- *
- * Based primarily on IntNum.java BitOps.java by Per Bothner <per@bothner.com>
- * (found in Kawa 1.6.62).
- *
- * Status: Believed complete and correct.
- */
-
-public class BigInteger extends Number implements Comparable
-{
- /** All integers are stored in 2's-complement form.
- * If words == null, the ival is the value of this BigInteger.
- * Otherwise, the first ival elements of words make the value
- * of this BigInteger, stored in little-endian order, 2's-complement form. */
- private int ival;
- private int[] words;
-
-
- /** We pre-allocate integers in the range minFixNum..maxFixNum. */
- private static final int minFixNum = -100;
- private static final int maxFixNum = 1024;
- private static final int numFixNum = maxFixNum-minFixNum+1;
- private static final BigInteger[] smallFixNums = new BigInteger[numFixNum];
-
- static {
- for (int i = numFixNum; --i >= 0; )
- smallFixNums[i] = new BigInteger(i + minFixNum);
- }
-
- // JDK1.2
- public static final BigInteger ZERO = smallFixNums[-minFixNum];
-
- // JDK1.2
- public static final BigInteger ONE = smallFixNums[1 - minFixNum];
-
- /* Rounding modes: */
- private static final int FLOOR = 1;
- private static final int CEILING = 2;
- private static final int TRUNCATE = 3;
- private static final int ROUND = 4;
-
- /** When checking the probability of primes, it is most efficient to
- * first check the factoring of small primes, so we'll use this array.
- */
- private static final int[] primes =
- { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,
- 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107,
- 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181,
- 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251 };
-
- private BigInteger()
- {
- }
-
- /* Create a new (non-shared) BigInteger, and initialize to an int. */
- private BigInteger(int value)
- {
- ival = value;
- }
-
- public BigInteger(String val, int radix)
- {
- BigInteger result = valueOf(val, radix);
- this.ival = result.ival;
- this.words = result.words;
- }
-
- public BigInteger(String val)
- {
- this(val, 10);
- }
-
- /* Create a new (non-shared) BigInteger, and initialize from a byte array. */
- public BigInteger(byte[] val)
- {
- if (val == null || val.length < 1)
- throw new NumberFormatException();
-
- words = byteArrayToIntArray(val, val[0] < 0 ? -1 : 0);
- BigInteger result = make(words, words.length);
- this.ival = result.ival;
- this.words = result.words;
- }
-
- public BigInteger(int signum, byte[] magnitude)
- {
- if (magnitude == null || signum > 1 || signum < -1)
- throw new NumberFormatException();
-
- if (signum == 0)
- {
- int i;
- for (i = magnitude.length - 1; i >= 0 && magnitude[i] == 0; --i)
- ;
- if (i >= 0)
- throw new NumberFormatException();
- return;
- }
-
- // Magnitude is always positive, so don't ever pass a sign of -1.
- words = byteArrayToIntArray(magnitude, 0);
- BigInteger result = make(words, words.length);
- this.ival = result.ival;
- this.words = result.words;
-
- if (signum < 0)
- setNegative();
- }
-
- public BigInteger(int numBits, Random rnd)
- {
- if (numBits < 0)
- throw new IllegalArgumentException();
-
- // Result is always positive so tack on an extra zero word, it will be
- // canonicalized out later if necessary.
- int nwords = numBits / 32 + 2;
- words = new int[nwords];
- words[--nwords] = 0;
- words[--nwords] = rnd.nextInt() >>> (numBits % 32);
- while (--nwords >= 0)
- words[nwords] = rnd.nextInt();
-
- BigInteger result = make(words, words.length);
- this.ival = result.ival;
- this.words = result.words;
- }
-
- public BigInteger(int bitLength, int certainty, Random rnd)
- {
- this(bitLength, rnd);
-
- // Keep going until we find a probable prime.
- while (true)
- {
- if (isProbablePrime(certainty))
- return;
-
- BigInteger next = new BigInteger(bitLength, rnd);
- this.ival = next.ival;
- this.words = next.words;
- }
- }
-
- /** Return a (possibly-shared) BigInteger with a given long value. */
- private static BigInteger make(long value)
- {
- if (value >= minFixNum && value <= maxFixNum)
- return smallFixNums[(int)value - minFixNum];
- int i = (int) value;
- if ((long)i == value)
- return new BigInteger(i);
- BigInteger result = alloc(2);
- result.ival = 2;
- result.words[0] = i;
- result.words[1] = (int) (value >> 32);
- return result;
- }
-
- // FIXME: Could simply rename 'make' method above as valueOf while
- // changing all instances of 'make'. Don't do this until this class
- // is done as the Kawa class this is based on has 'make' methods
- // with other parameters; wait to see if they are used in BigInteger.
- public static BigInteger valueOf(long val)
- {
- return make(val);
- }
-
- /** Make a canonicalized BigInteger from an array of words.
- * The array may be reused (without copying). */
- private static BigInteger make(int[] words, int len)
- {
- if (words == null)
- return make(len);
- len = BigInteger.wordsNeeded(words, len);
- if (len <= 1)
- return len == 0 ? ZERO : make(words[0]);
- BigInteger num = new BigInteger();
- num.words = words;
- num.ival = len;
- return num;
- }
-
- /** Convert a big-endian byte array to a little-endian array of words. */
- private static int[] byteArrayToIntArray(byte[] bytes, int sign)
- {
- // Determine number of words needed.
- int[] words = new int[(bytes.length + 3) / 4 + 1];
- int nwords = words.length;
-
- // For simplicity, tack on an extra word of sign at the front,
- // it will be canonicalized out later. */
- words[--nwords] = sign;
-
- // Create a int out of modulo 4 high order bytes.
- int bptr = 0;
- int word = sign;
- for (int i = bytes.length % 4; i > 0; --i, bptr++)
- word = (word << 8) | (((int) bytes[bptr]) & 0xff);
- words[--nwords] = word;
-
- // Elements remaining in byte[] are a multiple of 4.
- while (nwords > 0)
- words[--nwords] = bytes[bptr++] << 24 |
- (((int) bytes[bptr++]) & 0xff) << 16 |
- (((int) bytes[bptr++]) & 0xff) << 8 |
- (((int) bytes[bptr++]) & 0xff);
- return words;
- }
-
- /** Allocate a new non-shared BigInteger.
- * @param nwords number of words to allocate
- */
- private static BigInteger alloc(int nwords)
- {
- if (nwords <= 1)
- return new BigInteger();
- BigInteger result = new BigInteger();
- result.words = new int[nwords];
- return result;
- }
-
- /** Change words.length to nwords.
- * We allow words.length to be upto nwords+2 without reallocating.
- */
- private void realloc(int nwords)
- {
- if (nwords == 0)
- {
- if (words != null)
- {
- if (ival > 0)
- ival = words[0];
- words = null;
- }
- }
- else if (words == null
- || words.length < nwords
- || words.length > nwords + 2)
- {
- int[] new_words = new int [nwords];
- if (words == null)
- {
- new_words[0] = ival;
- ival = 1;
- }
- else
- {
- if (nwords < ival)
- ival = nwords;
- System.arraycopy(words, 0, new_words, 0, ival);
- }
- words = new_words;
- }
- }
-
- private final boolean isNegative()
- {
- return (words == null ? ival : words[ival - 1]) < 0;
- }
-
- public int signum()
- {
- int top = words == null ? ival : words[ival-1];
- if (top == 0 && words == null)
- return 0;
- return top < 0 ? -1 : 1;
- }
-
- private static int compareTo(BigInteger x, BigInteger y)
- {
- if (x.words == null && y.words == null)
- return x.ival < y.ival ? -1 : x.ival > y.ival ? 1 : 0;
- boolean x_negative = x.isNegative();
- boolean y_negative = y.isNegative();
- if (x_negative != y_negative)
- return x_negative ? -1 : 1;
- int x_len = x.words == null ? 1 : x.ival;
- int y_len = y.words == null ? 1 : y.ival;
- if (x_len != y_len)
- return (x_len > y_len) != x_negative ? 1 : -1;
- return MPN.cmp(x.words, y.words, x_len);
- }
-
- // JDK1.2
- public int compareTo(Object obj)
- {
- if (obj instanceof BigInteger)
- return compareTo(this, (BigInteger) obj);
- throw new ClassCastException();
- }
-
- public int compareTo(BigInteger val)
- {
- return compareTo(this, val);
- }
-
- public BigInteger min(BigInteger val)
- {
- return compareTo(this, val) < 0 ? this : val;
- }
-
- public BigInteger max(BigInteger val)
- {
- return compareTo(this, val) > 0 ? this : val;
- }
-
- private final boolean isOdd()
- {
- int low = words == null ? ival : words[0];
- return (low & 1) != 0;
- }
-
- private final boolean isZero()
- {
- return words == null && ival == 0;
- }
-
- private final boolean isOne()
- {
- return words == null && ival == 1;
- }
-
- private final boolean isMinusOne()
- {
- return words == null && ival == -1;
- }
-
- /** Calculate how many words are significant in words[0:len-1].
- * Returns the least value x such that x>0 && words[0:x-1]==words[0:len-1],
- * when words is viewed as a 2's complement integer.
- */
- private static int wordsNeeded(int[] words, int len)
- {
- int i = len;
- if (i > 0)
- {
- int word = words[--i];
- if (word == -1)
- {
- while (i > 0 && (word = words[i - 1]) < 0)
- {
- i--;
- if (word != -1) break;
- }
- }
- else
- {
- while (word == 0 && i > 0 && (word = words[i - 1]) >= 0) i--;
- }
- }
- return i + 1;
- }
-
- private BigInteger canonicalize()
- {
- if (words != null
- && (ival = BigInteger.wordsNeeded(words, ival)) <= 1)
- {
- if (ival == 1)
- ival = words[0];
- words = null;
- }
- if (words == null && ival >= minFixNum && ival <= maxFixNum)
- return smallFixNums[(int) ival - minFixNum];
- return this;
- }
-
- /** Add two ints, yielding a BigInteger. */
- private static final BigInteger add(int x, int y)
- {
- return BigInteger.make((long) x + (long) y);
- }
-
- /** Add a BigInteger and an int, yielding a new BigInteger. */
- private static BigInteger add(BigInteger x, int y)
- {
- if (x.words == null)
- return BigInteger.add(x.ival, y);
- BigInteger result = new BigInteger(0);
- result.setAdd(x, y);
- return result.canonicalize();
- }
-
- /** Set this to the sum of x and y.
- * OK if x==this. */
- private void setAdd(BigInteger x, int y)
- {
- if (x.words == null)
- {
- set((long) x.ival + (long) y);
- return;
- }
- int len = x.ival;
- realloc(len + 1);
- long carry = y;
- for (int i = 0; i < len; i++)
- {
- carry += ((long) x.words[i] & 0xffffffffL);
- words[i] = (int) carry;
- carry >>= 32;
- }
- if (x.words[len - 1] < 0)
- carry--;
- words[len] = (int) carry;
- ival = wordsNeeded(words, len + 1);
- }
-
- /** Destructively add an int to this. */
- private final void setAdd(int y)
- {
- setAdd(this, y);
- }
-
- /** Destructively set the value of this to a long. */
- private final void set(long y)
- {
- int i = (int) y;
- if ((long) i == y)
- {
- ival = i;
- words = null;
- }
- else
- {
- realloc(2);
- words[0] = i;
- words[1] = (int) (y >> 32);
- ival = 2;
- }
- }
-
- /** Destructively set the value of this to the given words.
- * The words array is reused, not copied. */
- private final void set(int[] words, int length)
- {
- this.ival = length;
- this.words = words;
- }
-
- /** Destructively set the value of this to that of y. */
- private final void set(BigInteger y)
- {
- if (y.words == null)
- set(y.ival);
- else if (this != y)
- {
- realloc(y.ival);
- System.arraycopy(y.words, 0, words, 0, y.ival);
- ival = y.ival;
- }
- }
-
- /** Add two BigIntegers, yielding their sum as another BigInteger. */
- private static BigInteger add(BigInteger x, BigInteger y, int k)
- {
- if (x.words == null && y.words == null)
- return BigInteger.make((long) k * (long) y.ival + (long) x.ival);
- if (k != 1)
- {
- if (k == -1)
- y = BigInteger.neg(y);
- else
- y = BigInteger.times(y, BigInteger.make(k));
- }
- if (x.words == null)
- return BigInteger.add(y, x.ival);
- if (y.words == null)
- return BigInteger.add(x, y.ival);
- // Both are big
- int len;
- if (y.ival > x.ival)
- { // Swap so x is longer then y.
- BigInteger tmp = x; x = y; y = tmp;
- }
- BigInteger result = alloc(x.ival + 1);
- int i = y.ival;
- long carry = MPN.add_n(result.words, x.words, y.words, i);
- long y_ext = y.words[i - 1] < 0 ? 0xffffffffL : 0;
- for (; i < x.ival; i++)
- {
- carry += ((long) x.words[i] & 0xffffffffL) + y_ext;;
- result.words[i] = (int) carry;
- carry >>>= 32;
- }
- if (x.words[i - 1] < 0)
- y_ext--;
- result.words[i] = (int) (carry + y_ext);
- result.ival = i+1;
- return result.canonicalize();
- }
-
- public BigInteger add(BigInteger val)
- {
- return add(this, val, 1);
- }
-
- public BigInteger subtract(BigInteger val)
- {
- return add(this, val, -1);
- }
-
- private static final BigInteger times(BigInteger x, int y)
- {
- if (y == 0)
- return ZERO;
- if (y == 1)
- return x;
- int[] xwords = x.words;
- int xlen = x.ival;
- if (xwords == null)
- return BigInteger.make((long) xlen * (long) y);
- boolean negative;
- BigInteger result = BigInteger.alloc(xlen + 1);
- if (xwords[xlen - 1] < 0)
- {
- negative = true;
- negate(result.words, xwords, xlen);
- xwords = result.words;
- }
- else
- negative = false;
- if (y < 0)
- {
- negative = !negative;
- y = -y;
- }
- result.words[xlen] = MPN.mul_1(result.words, xwords, xlen, y);
- result.ival = xlen + 1;
- if (negative)
- result.setNegative();
- return result.canonicalize();
- }
-
- private static final BigInteger times(BigInteger x, BigInteger y)
- {
- if (y.words == null)
- return times(x, y.ival);
- if (x.words == null)
- return times(y, x.ival);
- boolean negative = false;
- int[] xwords;
- int[] ywords;
- int xlen = x.ival;
- int ylen = y.ival;
- if (x.isNegative())
- {
- negative = true;
- xwords = new int[xlen];
- negate(xwords, x.words, xlen);
- }
- else
- {
- negative = false;
- xwords = x.words;
- }
- if (y.isNegative())
- {
- negative = !negative;
- ywords = new int[ylen];
- negate(ywords, y.words, ylen);
- }
- else
- ywords = y.words;
- // Swap if x is shorter then y.
- if (xlen < ylen)
- {
- int[] twords = xwords; xwords = ywords; ywords = twords;
- int tlen = xlen; xlen = ylen; ylen = tlen;
- }
- BigInteger result = BigInteger.alloc(xlen+ylen);
- MPN.mul(result.words, xwords, xlen, ywords, ylen);
- result.ival = xlen+ylen;
- if (negative)
- result.setNegative();
- return result.canonicalize();
- }
-
- public BigInteger multiply(BigInteger y)
- {
- return times(this, y);
- }
-
- private static void divide(long x, long y,
- BigInteger quotient, BigInteger remainder,
- int rounding_mode)
- {
- boolean xNegative, yNegative;
- if (x < 0)
- {
- xNegative = true;
- if (x == Long.MIN_VALUE)
- {
- divide(BigInteger.make(x), BigInteger.make(y),
- quotient, remainder, rounding_mode);
- return;
- }
- x = -x;
- }
- else
- xNegative = false;
-
- if (y < 0)
- {
- yNegative = true;
- if (y == Long.MIN_VALUE)
- {
- if (rounding_mode == TRUNCATE)
- { // x != Long.Min_VALUE implies abs(x) < abs(y)
- if (quotient != null)
- quotient.set(0);
- if (remainder != null)
- remainder.set(x);
- }
- else
- divide(BigInteger.make(x), BigInteger.make(y),
- quotient, remainder, rounding_mode);
- return;
- }
- y = -y;
- }
- else
- yNegative = false;
-
- long q = x / y;
- long r = x % y;
- boolean qNegative = xNegative ^ yNegative;
-
- boolean add_one = false;
- if (r != 0)
- {
- switch (rounding_mode)
- {
- case TRUNCATE:
- break;
- case CEILING:
- case FLOOR:
- if (qNegative == (rounding_mode == FLOOR))
- add_one = true;
- break;
- case ROUND:
- add_one = r > ((y - (q & 1)) >> 1);
- break;
- }
- }
- if (quotient != null)
- {
- if (add_one)
- q++;
- if (qNegative)
- q = -q;
- quotient.set(q);
- }
- if (remainder != null)
- {
- // The remainder is by definition: X-Q*Y
- if (add_one)
- {
- // Subtract the remainder from Y.
- r = y - r;
- // In this case, abs(Q*Y) > abs(X).
- // So sign(remainder) = -sign(X).
- xNegative = ! xNegative;
- }
- else
- {
- // If !add_one, then: abs(Q*Y) <= abs(X).
- // So sign(remainder) = sign(X).
- }
- if (xNegative)
- r = -r;
- remainder.set(r);
- }
- }
-
- /** Divide two integers, yielding quotient and remainder.
- * @param x the numerator in the division
- * @param y the denominator in the division
- * @param quotient is set to the quotient of the result (iff quotient!=null)
- * @param remainder is set to the remainder of the result
- * (iff remainder!=null)
- * @param rounding_mode one of FLOOR, CEILING, TRUNCATE, or ROUND.
- */
- private static void divide(BigInteger x, BigInteger y,
- BigInteger quotient, BigInteger remainder,
- int rounding_mode)
- {
- if ((x.words == null || x.ival <= 2)
- && (y.words == null || y.ival <= 2))
- {
- long x_l = x.longValue();
- long y_l = y.longValue();
- if (x_l != Long.MIN_VALUE && y_l != Long.MIN_VALUE)
- {
- divide(x_l, y_l, quotient, remainder, rounding_mode);
- return;
- }
- }
-
- boolean xNegative = x.isNegative();
- boolean yNegative = y.isNegative();
- boolean qNegative = xNegative ^ yNegative;
-
- int ylen = y.words == null ? 1 : y.ival;
- int[] ywords = new int[ylen];
- y.getAbsolute(ywords);
- while (ylen > 1 && ywords[ylen - 1] == 0) ylen--;
-
- int xlen = x.words == null ? 1 : x.ival;
- int[] xwords = new int[xlen+2];
- x.getAbsolute(xwords);
- while (xlen > 1 && xwords[xlen-1] == 0) xlen--;
-
- int qlen, rlen;
-
- int cmpval = MPN.cmp(xwords, xlen, ywords, ylen);
- if (cmpval < 0) // abs(x) < abs(y)
- { // quotient = 0; remainder = num.
- int[] rwords = xwords; xwords = ywords; ywords = rwords;
- rlen = xlen; qlen = 1; xwords[0] = 0;
- }
- else if (cmpval == 0) // abs(x) == abs(y)
- {
- xwords[0] = 1; qlen = 1; // quotient = 1
- ywords[0] = 0; rlen = 1; // remainder = 0;
- }
- else if (ylen == 1)
- {
- qlen = xlen;
- // Need to leave room for a word of leading zeros if dividing by 1
- // and the dividend has the high bit set. It might be safe to
- // increment qlen in all cases, but it certainly is only necessary
- // in the following case.
- if (ywords[0] == 1 && xwords[xlen-1] < 0)
- qlen++;
- rlen = 1;
- ywords[0] = MPN.divmod_1(xwords, xwords, xlen, ywords[0]);
- }
- else // abs(x) > abs(y)
- {
- // Normalize the denominator, i.e. make its most significant bit set by
- // shifting it normalization_steps bits to the left. Also shift the
- // numerator the same number of steps (to keep the quotient the same!).
-
- int nshift = MPN.count_leading_zeros(ywords[ylen - 1]);
- if (nshift != 0)
- {
- // Shift up the denominator setting the most significant bit of
- // the most significant word.
- MPN.lshift(ywords, 0, ywords, ylen, nshift);
-
- // Shift up the numerator, possibly introducing a new most
- // significant word.
- int x_high = MPN.lshift(xwords, 0, xwords, xlen, nshift);
- xwords[xlen++] = x_high;
- }
-
- if (xlen == ylen)
- xwords[xlen++] = 0;
- MPN.divide(xwords, xlen, ywords, ylen);
- rlen = ylen;
- if (remainder != null || rounding_mode != TRUNCATE)
- {
- if (nshift == 0)
- System.arraycopy(xwords, 0, ywords, 0, rlen);
- else
- MPN.rshift(ywords, xwords, 0, rlen, nshift);
- }
-
- qlen = xlen + 1 - ylen;
- if (quotient != null)
- {
- for (int i = 0; i < qlen; i++)
- xwords[i] = xwords[i+ylen];
- }
- }
-
- // Now the quotient is in xwords, and the remainder is in ywords.
-
- boolean add_one = false;
- if (rlen > 1 || ywords[0] != 0)
- { // Non-zero remainder i.e. in-exact quotient.
- switch (rounding_mode)
- {
- case TRUNCATE:
- break;
- case CEILING:
- case FLOOR:
- if (qNegative == (rounding_mode == FLOOR))
- add_one = true;
- break;
- case ROUND:
- // int cmp = compareTo(remainder<<1, abs(y));
- BigInteger tmp = remainder == null ? new BigInteger() : remainder;
- tmp.set(ywords, rlen);
- tmp = shift(tmp, 1);
- if (yNegative)
- tmp.setNegative();
- int cmp = compareTo(tmp, y);
- // Now cmp == compareTo(sign(y)*(remainder<<1), y)
- if (yNegative)
- cmp = -cmp;
- add_one = (cmp == 1) || (cmp == 0 && (xwords[0]&1) != 0);
- }
- }
- if (quotient != null)
- {
- quotient.set(xwords, qlen);
- if (qNegative)
- {
- if (add_one) // -(quotient + 1) == ~(quotient)
- quotient.setInvert();
- else
- quotient.setNegative();
- }
- else if (add_one)
- quotient.setAdd(1);
- }
- if (remainder != null)
- {
- // The remainder is by definition: X-Q*Y
- remainder.set(ywords, rlen);
- if (add_one)
- {
- // Subtract the remainder from Y:
- // abs(R) = abs(Y) - abs(orig_rem) = -(abs(orig_rem) - abs(Y)).
- BigInteger tmp;
- if (y.words == null)
- {
- tmp = remainder;
- tmp.set(yNegative ? ywords[0] + y.ival : ywords[0] - y.ival);
- }
- else
- tmp = BigInteger.add(remainder, y, yNegative ? 1 : -1);
- // Now tmp <= 0.
- // In this case, abs(Q) = 1 + floor(abs(X)/abs(Y)).
- // Hence, abs(Q*Y) > abs(X).
- // So sign(remainder) = -sign(X).
- if (xNegative)
- remainder.setNegative(tmp);
- else
- remainder.set(tmp);
- }
- else
- {
- // If !add_one, then: abs(Q*Y) <= abs(X).
- // So sign(remainder) = sign(X).
- if (xNegative)
- remainder.setNegative();
- }
- }
- }
-
- public BigInteger divide(BigInteger val)
- {
- if (val.isZero())
- throw new ArithmeticException("divisor is zero");
-
- BigInteger quot = new BigInteger();
- divide(this, val, quot, null, TRUNCATE);
- return quot.canonicalize();
- }
-
- public BigInteger remainder(BigInteger val)
- {
- if (val.isZero())
- throw new ArithmeticException("divisor is zero");
-
- BigInteger rem = new BigInteger();
- divide(this, val, null, rem, TRUNCATE);
- return rem.canonicalize();
- }
-
- public BigInteger[] divideAndRemainder(BigInteger val)
- {
- if (val.isZero())
- throw new ArithmeticException("divisor is zero");
-
- BigInteger[] result = new BigInteger[2];
- result[0] = new BigInteger();
- result[1] = new BigInteger();
- divide(this, val, result[0], result[1], TRUNCATE);
- result[0].canonicalize();
- result[1].canonicalize();
- return result;
- }
-
- public BigInteger mod(BigInteger m)
- {
- if (m.isNegative() || m.isZero())
- throw new ArithmeticException("non-positive modulus");
-
- BigInteger rem = new BigInteger();
- divide(this, m, null, rem, FLOOR);
- return rem.canonicalize();
- }
-
- /** Calculate power for BigInteger exponents.
- * @param y exponent assumed to be non-negative. */
- private BigInteger pow(BigInteger y)
- {
- if (isOne())
- return this;
- if (isMinusOne())
- return y.isOdd () ? this : ONE;
- if (y.words == null && y.ival >= 0)
- return pow(y.ival);
-
- // Assume exponent is non-negative.
- if (isZero())
- return this;
-
- // Implemented by repeated squaring and multiplication.
- BigInteger pow2 = this;
- BigInteger r = null;
- for (;;) // for (i = 0; ; i++)
- {
- // pow2 == x**(2**i)
- // prod = x**(sum(j=0..i-1, (y>>j)&1))
- if (y.isOdd())
- r = r == null ? pow2 : times(r, pow2); // r *= pow2
- y = BigInteger.shift(y, -1);
- if (y.isZero())
- break;
- // pow2 *= pow2;
- pow2 = times(pow2, pow2);
- }
- return r == null ? ONE : r;
- }
-
- /** Calculate the integral power of a BigInteger.
- * @param exponent the exponent (must be non-negative)
- */
- public BigInteger pow(int exponent)
- {
- if (exponent <= 0)
- {
- if (exponent == 0)
- return ONE;
- else
- throw new ArithmeticException("negative exponent");
- }
- if (isZero())
- return this;
- int plen = words == null ? 1 : ival; // Length of pow2.
- int blen = ((bitLength() * exponent) >> 5) + 2 * plen;
- boolean negative = isNegative() && (exponent & 1) != 0;
- int[] pow2 = new int [blen];
- int[] rwords = new int [blen];
- int[] work = new int [blen];
- getAbsolute(pow2); // pow2 = abs(this);
- int rlen = 1;
- rwords[0] = 1; // rwords = 1;
- for (;;) // for (i = 0; ; i++)
- {
- // pow2 == this**(2**i)
- // prod = this**(sum(j=0..i-1, (exponent>>j)&1))
- if ((exponent & 1) != 0)
- { // r *= pow2
- MPN.mul(work, pow2, plen, rwords, rlen);
- int[] temp = work; work = rwords; rwords = temp;
- rlen += plen;
- while (rwords[rlen - 1] == 0) rlen--;
- }
- exponent >>= 1;
- if (exponent == 0)
- break;
- // pow2 *= pow2;
- MPN.mul(work, pow2, plen, pow2, plen);
- int[] temp = work; work = pow2; pow2 = temp; // swap to avoid a copy
- plen *= 2;
- while (pow2[plen - 1] == 0) plen--;
- }
- if (rwords[rlen - 1] < 0)
- rlen++;
- if (negative)
- negate(rwords, rwords, rlen);
- return BigInteger.make(rwords, rlen);
- }
-
- private static final int[] euclidInv(int a, int b, int prevDiv)
- {
- // Storage for return values, plus one slot for a temp int (see below).
- int[] xy;
-
- if (b == 0)
- throw new ArithmeticException("not invertible");
- else if (b == 1)
- {
- // Success: values are indeed invertible!
- // Bottom of the recursion reached; start unwinding.
- xy = new int[3];
- xy[0] = -prevDiv;
- xy[1] = 1;
- return xy;
- }
-
- xy = euclidInv(b, a % b, a / b); // Recursion happens here.
-
- // xy[2] is just temp storage for intermediate results in the following
- // calculation. This saves us a bit of space over having an int
- // allocated at every level of this recursive method.
- xy[2] = xy[0];
- xy[0] = xy[2] * -prevDiv + xy[1];
- xy[1] = xy[2];
- return xy;
- }
-
- private static final BigInteger[]
- euclidInv(BigInteger a, BigInteger b, BigInteger prevDiv)
- {
- // FIXME: This method could be more efficient memory-wise and should be
- // modified as such since it is recursive.
-
- // Storage for return values, plus one slot for a temp int (see below).
- BigInteger[] xy;
-
- if (b.isZero())
- throw new ArithmeticException("not invertible");
- else if (b.isOne())
- {
- // Success: values are indeed invertible!
- // Bottom of the recursion reached; start unwinding.
- xy = new BigInteger[3];
- xy[0] = neg(prevDiv);
- xy[1] = ONE;
- return xy;
- }
-
- // Recursion happens in the following conditional!
-
- // If a just contains an int, then use integer math for the rest.
- if (a.words == null)
- {
- int[] xyInt = euclidInv(b.ival, a.ival % b.ival, a.ival / b.ival);
- xy = new BigInteger[3];
- xy[0] = new BigInteger(xyInt[0]);
- xy[1] = new BigInteger(xyInt[1]);
- }
- else
- {
- BigInteger rem = new BigInteger();
- BigInteger quot = new BigInteger();
- divide(a, b, quot, rem, FLOOR);
- xy = euclidInv(b, rem, quot);
- }
-
- // xy[2] is just temp storage for intermediate results in the following
- // calculation. This saves us a bit of space over having a BigInteger
- // allocated at every level of this recursive method.
- xy[2] = xy[0];
- xy[0] = add(xy[1], times(xy[2], prevDiv), -1);
- xy[1] = xy[2];
- return xy;
- }
-
- public BigInteger modInverse(BigInteger y)
- {
- if (y.isNegative() || y.isZero())
- throw new ArithmeticException("non-positive modulo");
-
- // Degenerate cases.
- if (y.isOne())
- return ZERO;
- else if (isOne())
- return ONE;
-
- // Use Euclid's algorithm as in gcd() but do this recursively
- // rather than in a loop so we can use the intermediate results as we
- // unwind from the recursion.
- // Used http://www.math.nmsu.edu/~crypto/EuclideanAlgo.html as reference.
- BigInteger result = new BigInteger();
- int xval = ival;
- int yval = y.ival;
- boolean swapped = false;
-
- if (y.words == null)
- {
- // The result is guaranteed to be less than the modulus, y (which is
- // an int), so simplify this by working with the int result of this
- // modulo y. Also, if this is negative, make it positive via modulo
- // math. Note that BigInteger.mod() must be used even if this is
- // already an int as the % operator would provide a negative result if
- // this is negative, BigInteger.mod() never returns negative values.
- if (words != null || isNegative())
- xval = mod(y).ival;
-
- // Swap values so x > y.
- if (yval > xval)
- {
- int tmp = xval; xval = yval; yval = tmp;
- swapped = true;
- }
- // Normally, the result is in the 2nd element of the array, but
- // if originally x < y, then x and y were swapped and the result
- // is in the 1st element of the array.
- result.ival =
- euclidInv(yval, xval % yval, xval / yval)[swapped ? 0 : 1];
-
- // Result can't be negative, so make it positive by adding the
- // original modulus, y.ival (not the possibly "swapped" yval).
- if (result.ival < 0)
- result.ival += y.ival;
- }
- else
- {
- BigInteger x = this;
-
- // As above, force this to be a positive value via modulo math.
- if (isNegative())
- x = mod(y);
-
- // Swap values so x > y.
- if (x.compareTo(y) < 0)
- {
- BigInteger tmp = x; x = y; y = tmp;
- swapped = true;
- }
- // As above (for ints), result will be in the 2nd element unless
- // the original x and y were swapped.
- BigInteger rem = new BigInteger();
- BigInteger quot = new BigInteger();
- divide(x, y, quot, rem, FLOOR);
- result = euclidInv(y, rem, quot)[swapped ? 0 : 1];
-
- // Result can't be negative, so make it positive by adding the
- // original modulus, y (which is now x if they were swapped).
- if (result.isNegative())
- result = add(result, swapped ? x : y, 1);
- }
-
- return result;
- }
-
- public BigInteger modPow(BigInteger exponent, BigInteger m)
- {
- if (m.isNegative() || m.isZero())
- throw new ArithmeticException("non-positive modulo");
-
- if (exponent.isNegative())
- return modInverse(m);
- if (exponent.isOne())
- return mod(m);
-
- // To do this naively by first raising this to the power of exponent
- // and then performing modulo m would be extremely expensive, especially
- // for very large numbers. The solution is found in Number Theory
- // where a combination of partial powers and modulos can be done easily.
- //
- // We'll use the algorithm for Additive Chaining which can be found on
- // p. 244 of "Applied Cryptography, Second Edition" by Bruce Schneier.
- BigInteger s, t, u;
- int i;
-
- s = ONE;
- t = this;
- u = exponent;
-
- while (!u.isZero())
- {
- if (u.and(ONE).isOne())
- s = times(s, t).mod(m);
- u = u.shiftRight(1);
- t = times(t, t).mod(m);
- }
-
- return s;
- }
-
- /** Calculate Greatest Common Divisor for non-negative ints. */
- private static final int gcd(int a, int b)
- {
- // Euclid's algorithm, copied from libg++.
- if (b > a)
- {
- int tmp = a; a = b; b = tmp;
- }
- for(;;)
- {
- if (b == 0)
- return a;
- else if (b == 1)
- return b;
- else
- {
- int tmp = b;
- b = a % b;
- a = tmp;
- }
- }
- }
-
- public BigInteger gcd(BigInteger y)
- {
- int xval = ival;
- int yval = y.ival;
- if (words == null)
- {
- if (xval == 0)
- return BigInteger.abs(y);
- if (y.words == null
- && xval != Integer.MIN_VALUE && yval != Integer.MIN_VALUE)
- {
- if (xval < 0)
- xval = -xval;
- if (yval < 0)
- yval = -yval;
- return BigInteger.make(BigInteger.gcd(xval, yval));
- }
- xval = 1;
- }
- if (y.words == null)
- {
- if (yval == 0)
- return BigInteger.abs(this);
- yval = 1;
- }
- int len = (xval > yval ? xval : yval) + 1;
- int[] xwords = new int[len];
- int[] ywords = new int[len];
- getAbsolute(xwords);
- y.getAbsolute(ywords);
- len = MPN.gcd(xwords, ywords, len);
- BigInteger result = new BigInteger(0);
- result.ival = len;
- result.words = xwords;
- return result.canonicalize();
- }
-
- public boolean isProbablePrime(int certainty)
- {
- /** We'll use the Rabin-Miller algorithm for doing a probabilistic
- * primality test. It is fast, easy and has faster decreasing odds of a
- * composite passing than with other tests. This means that this
- * method will actually have a probability much greater than the
- * 1 - .5^certainty specified in the JCL (p. 117), but I don't think
- * anyone will complain about better performance with greater certainty.
- *
- * The Rabin-Miller algorithm can be found on pp. 259-261 of "Applied
- * Cryptography, Second Edition" by Bruce Schneier.
- */
-
- // First rule out small prime factors and assure the number is odd.
- for (int i = 0; i < primes.length; i++)
- {
- if (words == null && ival == primes[i])
- return true;
- if (remainder(make(primes[i])).isZero())
- return false;
- }
-
- // Now perform the Rabin-Miller test.
- // NB: I know that this can be simplified programatically, but
- // I have tried to keep it as close as possible to the algorithm
- // as written in the Schneier book for reference purposes.
-
- // Set b to the number of times 2 evenly divides (this - 1).
- // I.e. 2^b is the largest power of 2 that divides (this - 1).
- BigInteger pMinus1 = add(this, -1);
- int b = pMinus1.getLowestSetBit();
-
- // Set m such that this = 1 + 2^b * m.
- BigInteger m = pMinus1.divide(make(2L << b - 1));
-
- Random rand = new Random();
- while (certainty-- > 0)
- {
- // Pick a random number greater than 1 and less than this.
- // The algorithm says to pick a small number to make the calculations
- // go faster, but it doesn't say how small; we'll use 2 to 1024.
- int a = rand.nextInt();
- a = (a < 0 ? -a : a) % 1023 + 2;
-
- BigInteger z = make(a).modPow(m, this);
- if (z.isOne() || z.equals(pMinus1))
- continue; // Passes the test; may be prime.
-
- int i;
- for (i = 0; i < b; )
- {
- if (z.isOne())
- return false;
- i++;
- if (z.equals(pMinus1))
- break; // Passes the test; may be prime.
-
- z = z.modPow(make(2), this);
- }
-
- if (i == b && !z.equals(pMinus1))
- return false;
- }
- return true;
- }
-
- private void setInvert()
- {
- if (words == null)
- ival = ~ival;
- else
- {
- for (int i = ival; --i >= 0; )
- words[i] = ~words[i];
- }
- }
-
- private void setShiftLeft(BigInteger x, int count)
- {
- int[] xwords;
- int xlen;
- if (x.words == null)
- {
- if (count < 32)
- {
- set((long) x.ival << count);
- return;
- }
- xwords = new int[1];
- xwords[0] = x.ival;
- xlen = 1;
- }
- else
- {
- xwords = x.words;
- xlen = x.ival;
- }
- int word_count = count >> 5;
- count &= 31;
- int new_len = xlen + word_count;
- if (count == 0)
- {
- realloc(new_len);
- for (int i = xlen; --i >= 0; )
- words[i+word_count] = xwords[i];
- }
- else
- {
- new_len++;
- realloc(new_len);
- int shift_out = MPN.lshift(words, word_count, xwords, xlen, count);
- count = 32 - count;
- words[new_len-1] = (shift_out << count) >> count; // sign-extend.
- }
- ival = new_len;
- for (int i = word_count; --i >= 0; )
- words[i] = 0;
- }
-
- private void setShiftRight(BigInteger x, int count)
- {
- if (x.words == null)
- set(count < 32 ? x.ival >> count : x.ival < 0 ? -1 : 0);
- else if (count == 0)
- set(x);
- else
- {
- boolean neg = x.isNegative();
- int word_count = count >> 5;
- count &= 31;
- int d_len = x.ival - word_count;
- if (d_len <= 0)
- set(neg ? -1 : 0);
- else
- {
- if (words == null || words.length < d_len)
- realloc(d_len);
- if (count == 0)
- System.arraycopy(x.words, word_count, words, 0, d_len);
- else
- MPN.rshift(words, x.words, word_count, d_len, count);
- ival = d_len;
- if (neg)
- words[ival-1] |= -1 << (32 - count);
- }
- }
- }
-
- private void setShift(BigInteger x, int count)
- {
- if (count > 0)
- setShiftLeft(x, count);
- else
- setShiftRight(x, -count);
- }
-
- private static BigInteger shift(BigInteger x, int count)
- {
- if (x.words == null)
- {
- if (count <= 0)
- return make(count > -32 ? x.ival >> (-count) : x.ival < 0 ? -1 : 0);
- if (count < 32)
- return make((long) x.ival << count);
- }
- if (count == 0)
- return x;
- BigInteger result = new BigInteger(0);
- result.setShift(x, count);
- return result.canonicalize();
- }
-
- public BigInteger shiftLeft(int n)
- {
- return shift(this, n);
- }
-
- public BigInteger shiftRight(int n)
- {
- return shift(this, -n);
- }
-
- private void format(int radix, StringBuffer buffer)
- {
- if (words == null)
- buffer.append(Integer.toString(ival, radix));
- else if (ival <= 2)
- buffer.append(Long.toString(longValue(), radix));
- else
- {
- boolean neg = isNegative();
- int[] work;
- if (neg || radix != 16)
- {
- work = new int[ival];
- getAbsolute(work);
- }
- else
- work = words;
- int len = ival;
-
- int buf_size = len * (MPN.chars_per_word(radix) + 1);
- if (radix == 16)
- {
- if (neg)
- buffer.append('-');
- int buf_start = buffer.length();
- for (int i = len; --i >= 0; )
- {
- int word = work[i];
- for (int j = 8; --j >= 0; )
- {
- int hex_digit = (word >> (4 * j)) & 0xF;
- // Suppress leading zeros:
- if (hex_digit > 0 || buffer.length() > buf_start)
- buffer.append(Character.forDigit(hex_digit, 16));
- }
- }
- }
- else
- {
- int i = buffer.length();
- for (;;)
- {
- int digit = MPN.divmod_1(work, work, len, radix);
- buffer.append(Character.forDigit(digit, radix));
- while (len > 0 && work[len-1] == 0) len--;
- if (len == 0)
- break;
- }
- if (neg)
- buffer.append('-');
- /* Reverse buffer. */
- int j = buffer.length() - 1;
- while (i < j)
- {
- char tmp = buffer.charAt(i);
- buffer.setCharAt(i, buffer.charAt(j));
- buffer.setCharAt(j, tmp);
- i++; j--;
- }
- }
- }
- }
-
- public String toString()
- {
- return toString(10);
- }
-
- public String toString(int radix)
- {
- if (words == null)
- return Integer.toString(ival, radix);
- else if (ival <= 2)
- return Long.toString(longValue(), radix);
- int buf_size = ival * (MPN.chars_per_word(radix) + 1);
- StringBuffer buffer = new StringBuffer(buf_size);
- format(radix, buffer);
- return buffer.toString();
- }
-
- public int intValue()
- {
- if (words == null)
- return ival;
- return words[0];
- }
-
- public long longValue()
- {
- if (words == null)
- return ival;
- if (ival == 1)
- return words[0];
- return ((long)words[1] << 32) + ((long)words[0] & 0xffffffffL);
- }
-
- public int hashCode()
- {
- // FIXME: May not match hashcode of JDK.
- return words == null ? ival : (words[0] + words[ival - 1]);
- }
-
- /* Assumes x and y are both canonicalized. */
- private static boolean equals(BigInteger x, BigInteger y)
- {
- if (x.words == null && y.words == null)
- return x.ival == y.ival;
- if (x.words == null || y.words == null || x.ival != y.ival)
- return false;
- for (int i = x.ival; --i >= 0; )
- {
- if (x.words[i] != y.words[i])
- return false;
- }
- return true;
- }
-
- /* Assumes this and obj are both canonicalized. */
- public boolean equals(Object obj)
- {
- if (obj == null || ! (obj instanceof BigInteger))
- return false;
- return BigInteger.equals(this, (BigInteger) obj);
- }
-
- private static BigInteger valueOf(String s, int radix)
- throws NumberFormatException
- {
- int len = s.length();
- // Testing (len < MPN.chars_per_word(radix)) would be more accurate,
- // but slightly more expensive, for little practical gain.
- if (len <= 15 && radix <= 16)
- return BigInteger.make(Long.parseLong(s, radix));
-
- int byte_len = 0;
- byte[] bytes = new byte[len];
- boolean negative = false;
- for (int i = 0; i < len; i++)
- {
- char ch = s.charAt(i);
- if (ch == '-')
- negative = true;
- else if (ch == '_' || (byte_len == 0 && (ch == ' ' || ch == '\t')))
- continue;
- else
- {
- int digit = Character.digit(ch, radix);
- if (digit < 0)
- break;
- bytes[byte_len++] = (byte) digit;
- }
- }
- return valueOf(bytes, byte_len, negative, radix);
- }
-
- private static BigInteger valueOf(byte[] digits, int byte_len,
- boolean negative, int radix)
- {
- int chars_per_word = MPN.chars_per_word(radix);
- int[] words = new int[byte_len / chars_per_word + 1];
- int size = MPN.set_str(words, digits, byte_len, radix);
- if (size == 0)
- return ZERO;
- if (words[size-1] < 0)
- words[size++] = 0;
- if (negative)
- negate(words, words, size);
- return make(words, size);
- }
-
- public double doubleValue()
- {
- if (words == null)
- return (double) ival;
- if (ival <= 2)
- return (double) longValue();
- if (isNegative())
- return BigInteger.neg(this).roundToDouble(0, true, false);
- else
- return roundToDouble(0, false, false);
- }
-
- public float floatValue()
- {
- return (float) doubleValue();
- }
-
- /** Return true if any of the lowest n bits are one.
- * (false if n is negative). */
- private boolean checkBits(int n)
- {
- if (n <= 0)
- return false;
- if (words == null)
- return n > 31 || ((ival & ((1 << n) - 1)) != 0);
- int i;
- for (i = 0; i < (n >> 5) ; i++)
- if (words[i] != 0)
- return true;
- return (n & 31) != 0 && (words[i] & ((1 << (n & 31)) - 1)) != 0;
- }
-
- /** Convert a semi-processed BigInteger to double.
- * Number must be non-negative. Multiplies by a power of two, applies sign,
- * and converts to double, with the usual java rounding.
- * @param exp power of two, positive or negative, by which to multiply
- * @param neg true if negative
- * @param remainder true if the BigInteger is the result of a truncating
- * division that had non-zero remainder. To ensure proper rounding in
- * this case, the BigInteger must have at least 54 bits. */
- private double roundToDouble(int exp, boolean neg, boolean remainder)
- {
- // Compute length.
- int il = bitLength();
-
- // Exponent when normalized to have decimal point directly after
- // leading one. This is stored excess 1023 in the exponent bit field.
- exp += il - 1;
-
- // Gross underflow. If exp == -1075, we let the rounding
- // computation determine whether it is minval or 0 (which are just
- // 0x0000 0000 0000 0001 and 0x0000 0000 0000 0000 as bit
- // patterns).
- if (exp < -1075)
- return neg ? -0.0 : 0.0;
-
- // gross overflow
- if (exp > 1023)
- return neg ? Double.NEGATIVE_INFINITY : Double.POSITIVE_INFINITY;
-
- // number of bits in mantissa, including the leading one.
- // 53 unless it's denormalized
- int ml = (exp >= -1022 ? 53 : 53 + exp + 1022);
-
- // Get top ml + 1 bits. The extra one is for rounding.
- long m;
- int excess_bits = il - (ml + 1);
- if (excess_bits > 0)
- m = ((words == null) ? ival >> excess_bits
- : MPN.rshift_long(words, ival, excess_bits));
- else
- m = longValue() << (- excess_bits);
-
- // Special rounding for maxval. If the number exceeds maxval by
- // any amount, even if it's less than half a step, it overflows.
- if (exp == 1023 && ((m >> 1) == (1L << 53) - 1))
- {
- if (remainder || checkBits(il - ml))
- return neg ? Double.NEGATIVE_INFINITY : Double.POSITIVE_INFINITY;
- else
- return neg ? - Double.MAX_VALUE : Double.MAX_VALUE;
- }
-
- // Normal round-to-even rule: round up if the bit dropped is a one, and
- // the bit above it or any of the bits below it is a one.
- if ((m & 1) == 1
- && ((m & 2) == 2 || remainder || checkBits(excess_bits)))
- {
- m += 2;
- // Check if we overflowed the mantissa
- if ((m & (1L << 54)) != 0)
- {
- exp++;
- // renormalize
- m >>= 1;
- }
- // Check if a denormalized mantissa was just rounded up to a
- // normalized one.
- else if (ml == 52 && (m & (1L << 53)) != 0)
- exp++;
- }
-
- // Discard the rounding bit
- m >>= 1;
-
- long bits_sign = neg ? (1L << 63) : 0;
- exp += 1023;
- long bits_exp = (exp <= 0) ? 0 : ((long)exp) << 52;
- long bits_mant = m & ~(1L << 52);
- return Double.longBitsToDouble(bits_sign | bits_exp | bits_mant);
- }
-
- /** Copy the abolute value of this into an array of words.
- * Assumes words.length >= (this.words == null ? 1 : this.ival).
- * Result is zero-extended, but need not be a valid 2's complement number.
- */
-
- private void getAbsolute(int[] words)
- {
- int len;
- if (this.words == null)
- {
- len = 1;
- words[0] = this.ival;
- }
- else
- {
- len = this.ival;
- for (int i = len; --i >= 0; )
- words[i] = this.words[i];
- }
- if (words[len - 1] < 0)
- negate(words, words, len);
- for (int i = words.length; --i > len; )
- words[i] = 0;
- }
-
- /** Set dest[0:len-1] to the negation of src[0:len-1].
- * Return true if overflow (i.e. if src is -2**(32*len-1)).
- * Ok for src==dest. */
- private static boolean negate(int[] dest, int[] src, int len)
- {
- long carry = 1;
- boolean negative = src[len-1] < 0;
- for (int i = 0; i < len; i++)
- {
- carry += ((long) (~src[i]) & 0xffffffffL);
- dest[i] = (int) carry;
- carry >>= 32;
- }
- return (negative && dest[len-1] < 0);
- }
-
- /** Destructively set this to the negative of x.
- * It is OK if x==this.*/
- private void setNegative(BigInteger x)
- {
- int len = x.ival;
- if (x.words == null)
- {
- if (len == Integer.MIN_VALUE)
- set(- (long) len);
- else
- set(-len);
- return;
- }
- realloc(len + 1);
- if (BigInteger.negate(words, x.words, len))
- words[len++] = 0;
- ival = len;
- }
-
- /** Destructively negate this. */
- private final void setNegative()
- {
- setNegative(this);
- }
-
- private static BigInteger abs(BigInteger x)
- {
- return x.isNegative() ? neg(x) : x;
- }
-
- public BigInteger abs()
- {
- return abs(this);
- }
-
- private static BigInteger neg(BigInteger x)
- {
- if (x.words == null && x.ival != Integer.MIN_VALUE)
- return make(- x.ival);
- BigInteger result = new BigInteger(0);
- result.setNegative(x);
- return result.canonicalize();
- }
-
- public BigInteger negate()
- {
- return BigInteger.neg(this);
- }
-
- /** Calculates ceiling(log2(this < 0 ? -this : this+1))
- * See Common Lisp: the Language, 2nd ed, p. 361.
- */
- public int bitLength()
- {
- if (words == null)
- return MPN.intLength(ival);
- else
- return MPN.intLength(words, ival);
- }
-
- public byte[] toByteArray()
- {
- // Determine number of bytes needed. The method bitlength returns
- // the size without the sign bit, so add one bit for that and then
- // add 7 more to emulate the ceil function using integer math.
- byte[] bytes = new byte[(bitLength() + 1 + 7) / 8];
- int nbytes = bytes.length;
-
- int wptr = 0;
- int word;
-
- // Deal with words array until one word or less is left to process.
- // If BigInteger is an int, then it is in ival and nbytes will be <= 4.
- while (nbytes > 4)
- {
- word = words[wptr++];
- for (int i = 4; i > 0; --i, word >>= 8)
- bytes[--nbytes] = (byte) word;
- }
-
- // Deal with the last few bytes. If BigInteger is an int, use ival.
- word = (words == null) ? ival : words[wptr];
- for ( ; nbytes > 0; word >>= 8)
- bytes[--nbytes] = (byte) word;
-
- return bytes;
- }
-
- /** Return the boolean opcode (for bitOp) for swapped operands.
- * I.e. bitOp(swappedOp(op), x, y) == bitOp(op, y, x).
- */
- private static int swappedOp(int op)
- {
- return
- "\000\001\004\005\002\003\006\007\010\011\014\015\012\013\016\017"
- .charAt(op);
- }
-
- /** Do one the the 16 possible bit-wise operations of two BigIntegers. */
- private static BigInteger bitOp(int op, BigInteger x, BigInteger y)
- {
- switch (op)
- {
- case 0: return ZERO;
- case 1: return x.and(y);
- case 3: return x;
- case 5: return y;
- case 15: return make(-1);
- }
- BigInteger result = new BigInteger();
- setBitOp(result, op, x, y);
- return result.canonicalize();
- }
-
- /** Do one the the 16 possible bit-wise operations of two BigIntegers. */
- private static void setBitOp(BigInteger result, int op,
- BigInteger x, BigInteger y)
- {
- if (y.words == null) ;
- else if (x.words == null || x.ival < y.ival)
- {
- BigInteger temp = x; x = y; y = temp;
- op = swappedOp(op);
- }
- int xi;
- int yi;
- int xlen, ylen;
- if (y.words == null)
- {
- yi = y.ival;
- ylen = 1;
- }
- else
- {
- yi = y.words[0];
- ylen = y.ival;
- }
- if (x.words == null)
- {
- xi = x.ival;
- xlen = 1;
- }
- else
- {
- xi = x.words[0];
- xlen = x.ival;
- }
- if (xlen > 1)
- result.realloc(xlen);
- int[] w = result.words;
- int i = 0;
- // Code for how to handle the remainder of x.
- // 0: Truncate to length of y.
- // 1: Copy rest of x.
- // 2: Invert rest of x.
- int finish = 0;
- int ni;
- switch (op)
- {
- case 0: // clr
- ni = 0;
- break;
- case 1: // and
- for (;;)
- {
- ni = xi & yi;
- if (i+1 >= ylen) break;
- w[i++] = ni; xi = x.words[i]; yi = y.words[i];
- }
- if (yi < 0) finish = 1;
- break;
- case 2: // andc2
- for (;;)
- {
- ni = xi & ~yi;
- if (i+1 >= ylen) break;
- w[i++] = ni; xi = x.words[i]; yi = y.words[i];
- }
- if (yi >= 0) finish = 1;
- break;
- case 3: // copy x
- ni = xi;
- finish = 1; // Copy rest
- break;
- case 4: // andc1
- for (;;)
- {
- ni = ~xi & yi;
- if (i+1 >= ylen) break;
- w[i++] = ni; xi = x.words[i]; yi = y.words[i];
- }
- if (yi < 0) finish = 2;
- break;
- case 5: // copy y
- for (;;)
- {
- ni = yi;
- if (i+1 >= ylen) break;
- w[i++] = ni; xi = x.words[i]; yi = y.words[i];
- }
- break;
- case 6: // xor
- for (;;)
- {
- ni = xi ^ yi;
- if (i+1 >= ylen) break;
- w[i++] = ni; xi = x.words[i]; yi = y.words[i];
- }
- finish = yi < 0 ? 2 : 1;
- break;
- case 7: // ior
- for (;;)
- {
- ni = xi | yi;
- if (i+1 >= ylen) break;
- w[i++] = ni; xi = x.words[i]; yi = y.words[i];
- }
- if (yi >= 0) finish = 1;
- break;
- case 8: // nor
- for (;;)
- {
- ni = ~(xi | yi);
- if (i+1 >= ylen) break;
- w[i++] = ni; xi = x.words[i]; yi = y.words[i];
- }
- if (yi >= 0) finish = 2;
- break;
- case 9: // eqv [exclusive nor]
- for (;;)
- {
- ni = ~(xi ^ yi);
- if (i+1 >= ylen) break;
- w[i++] = ni; xi = x.words[i]; yi = y.words[i];
- }
- finish = yi >= 0 ? 2 : 1;
- break;
- case 10: // c2
- for (;;)
- {
- ni = ~yi;
- if (i+1 >= ylen) break;
- w[i++] = ni; xi = x.words[i]; yi = y.words[i];
- }
- break;
- case 11: // orc2
- for (;;)
- {
- ni = xi | ~yi;
- if (i+1 >= ylen) break;
- w[i++] = ni; xi = x.words[i]; yi = y.words[i];
- }
- if (yi < 0) finish = 1;
- break;
- case 12: // c1
- ni = ~xi;
- finish = 2;
- break;
- case 13: // orc1
- for (;;)
- {
- ni = ~xi | yi;
- if (i+1 >= ylen) break;
- w[i++] = ni; xi = x.words[i]; yi = y.words[i];
- }
- if (yi >= 0) finish = 2;
- break;
- case 14: // nand
- for (;;)
- {
- ni = ~(xi & yi);
- if (i+1 >= ylen) break;
- w[i++] = ni; xi = x.words[i]; yi = y.words[i];
- }
- if (yi < 0) finish = 2;
- break;
- default:
- case 15: // set
- ni = -1;
- break;
- }
- // Here i==ylen-1; w[0]..w[i-1] have the correct result;
- // and ni contains the correct result for w[i+1].
- if (i+1 == xlen)
- finish = 0;
- switch (finish)
- {
- case 0:
- if (i == 0 && w == null)
- {
- result.ival = ni;
- return;
- }
- w[i++] = ni;
- break;
- case 1: w[i] = ni; while (++i < xlen) w[i] = x.words[i]; break;
- case 2: w[i] = ni; while (++i < xlen) w[i] = ~x.words[i]; break;
- }
- result.ival = i;
- }
-
- /** Return the logical (bit-wise) "and" of a BigInteger and an int. */
- private static BigInteger and(BigInteger x, int y)
- {
- if (x.words == null)
- return BigInteger.make(x.ival & y);
- if (y >= 0)
- return BigInteger.make(x.words[0] & y);
- int len = x.ival;
- int[] words = new int[len];
- words[0] = x.words[0] & y;
- while (--len > 0)
- words[len] = x.words[len];
- return BigInteger.make(words, x.ival);
- }
-
- /** Return the logical (bit-wise) "and" of two BigIntegers. */
- public BigInteger and(BigInteger y)
- {
- if (y.words == null)
- return and(this, y.ival);
- else if (words == null)
- return and(y, ival);
-
- BigInteger x = this;
- if (ival < y.ival)
- {
- BigInteger temp = this; x = y; y = temp;
- }
- int i;
- int len = y.isNegative() ? x.ival : y.ival;
- int[] words = new int[len];
- for (i = 0; i < y.ival; i++)
- words[i] = x.words[i] & y.words[i];
- for ( ; i < len; i++)
- words[i] = x.words[i];
- return BigInteger.make(words, len);
- }
-
- /** Return the logical (bit-wise) "(inclusive) or" of two BigIntegers. */
- public BigInteger or(BigInteger y)
- {
- return bitOp(7, this, y);
- }
-
- /** Return the logical (bit-wise) "exclusive or" of two BigIntegers. */
- public BigInteger xor(BigInteger y)
- {
- return bitOp(6, this, y);
- }
-
- /** Return the logical (bit-wise) negation of a BigInteger. */
- public BigInteger not()
- {
- return bitOp(12, this, ZERO);
- }
-
- public BigInteger andNot(BigInteger val)
- {
- return and(val.not());
- }
-
- public BigInteger clearBit(int n)
- {
- if (n < 0)
- throw new ArithmeticException();
-
- return and(ONE.shiftLeft(n).not());
- }
-
- public BigInteger setBit(int n)
- {
- if (n < 0)
- throw new ArithmeticException();
-
- return or(ONE.shiftLeft(n));
- }
-
- public boolean testBit(int n)
- {
- if (n < 0)
- throw new ArithmeticException();
-
- return !and(ONE.shiftLeft(n)).isZero();
- }
-
- public BigInteger flipBit(int n)
- {
- if (n < 0)
- throw new ArithmeticException();
-
- return xor(ONE.shiftLeft(n));
- }
-
- public int getLowestSetBit()
- {
- if (isZero())
- return -1;
-
- if (words == null)
- return MPN.findLowestBit(ival);
- else
- return MPN.findLowestBit(words);
- }
-
- // bit4count[I] is number of '1' bits in I.
- private static final byte[] bit4_count = { 0, 1, 1, 2, 1, 2, 2, 3,
- 1, 2, 2, 3, 2, 3, 3, 4};
-
- private static int bitCount(int i)
- {
- int count = 0;
- while (i != 0)
- {
- count += bit4_count[i & 15];
- i >>>= 4;
- }
- return count;
- }
-
- private static int bitCount(int[] x, int len)
- {
- int count = 0;
- while (--len >= 0)
- count += bitCount(x[len]);
- return count;
- }
-
- /** Count one bits in a BigInteger.
- * If argument is negative, count zero bits instead. */
- public int bitCount()
- {
- int i, x_len;
- int[] x_words = words;
- if (x_words == null)
- {
- x_len = 1;
- i = bitCount(ival);
- }
- else
- {
- x_len = ival;
- i = bitCount(x_words, x_len);
- }
- return isNegative() ? x_len * 32 - i : i;
- }
-}
generated by cgit v1.2.3 (git 2.25.1) at 2024-05-20 19:15:21 +0000