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Diffstat (limited to 'core/src/main/java/org/bouncycastle/pqc/math/linearalgebra/IntegerFunctions.java')
| -rw-r--r-- | core/src/main/java/org/bouncycastle/pqc/math/linearalgebra/IntegerFunctions.java | 1423 |
1 files changed, 0 insertions, 1423 deletions
diff --git a/core/src/main/java/org/bouncycastle/pqc/math/linearalgebra/IntegerFunctions.java b/core/src/main/java/org/bouncycastle/pqc/math/linearalgebra/IntegerFunctions.java deleted file mode 100644 index 779f384a..00000000 --- a/core/src/main/java/org/bouncycastle/pqc/math/linearalgebra/IntegerFunctions.java +++ /dev/null @@ -1,1423 +0,0 @@ -package org.bouncycastle.pqc.math.linearalgebra; - -import java.math.BigInteger; -import java.security.SecureRandom; - -/** - * Class of number-theory related functions for use with integers represented as - * <tt>int</tt>'s or <tt>BigInteger</tt> objects. - */ -public final class IntegerFunctions -{ - - private static final BigInteger ZERO = BigInteger.valueOf(0); - - private static final BigInteger ONE = BigInteger.valueOf(1); - - private static final BigInteger TWO = BigInteger.valueOf(2); - - private static final BigInteger FOUR = BigInteger.valueOf(4); - - private static final int[] SMALL_PRIMES = {3, 5, 7, 11, 13, 17, 19, 23, - 29, 31, 37, 41}; - - private static final long SMALL_PRIME_PRODUCT = 3L * 5 * 7 * 11 * 13 * 17 - * 19 * 23 * 29 * 31 * 37 * 41; - - private static SecureRandom sr = null; - - // the jacobi function uses this lookup table - private static final int[] jacobiTable = {0, 1, 0, -1, 0, -1, 0, 1}; - - private IntegerFunctions() - { - // empty - } - - /** - * Computes the value of the Jacobi symbol (A|B). The following properties - * hold for the Jacobi symbol which makes it a very efficient way to - * evaluate the Legendre symbol - * <p> - * (A|B) = 0 IF gcd(A,B) > 1<br> - * (-1|B) = 1 IF n = 1 (mod 1)<br> - * (-1|B) = -1 IF n = 3 (mod 4)<br> - * (A|B) (C|B) = (AC|B)<br> - * (A|B) (A|C) = (A|CB)<br> - * (A|B) = (C|B) IF A = C (mod B)<br> - * (2|B) = 1 IF N = 1 OR 7 (mod 8)<br> - * (2|B) = 1 IF N = 3 OR 5 (mod 8) - * - * @param A integer value - * @param B integer value - * @return value of the jacobi symbol (A|B) - */ - public static int jacobi(BigInteger A, BigInteger B) - { - BigInteger a, b, v; - long k = 1; - - k = 1; - - // test trivial cases - if (B.equals(ZERO)) - { - a = A.abs(); - return a.equals(ONE) ? 1 : 0; - } - - if (!A.testBit(0) && !B.testBit(0)) - { - return 0; - } - - a = A; - b = B; - - if (b.signum() == -1) - { // b < 0 - b = b.negate(); // b = -b - if (a.signum() == -1) - { - k = -1; - } - } - - v = ZERO; - while (!b.testBit(0)) - { - v = v.add(ONE); // v = v + 1 - b = b.divide(TWO); // b = b/2 - } - - if (v.testBit(0)) - { - k = k * jacobiTable[a.intValue() & 7]; - } - - if (a.signum() < 0) - { // a < 0 - if (b.testBit(1)) - { - k = -k; // k = -k - } - a = a.negate(); // a = -a - } - - // main loop - while (a.signum() != 0) - { - v = ZERO; - while (!a.testBit(0)) - { // a is even - v = v.add(ONE); - a = a.divide(TWO); - } - if (v.testBit(0)) - { - k = k * jacobiTable[b.intValue() & 7]; - } - - if (a.compareTo(b) < 0) - { // a < b - // swap and correct intermediate result - BigInteger x = a; - a = b; - b = x; - if (a.testBit(1) && b.testBit(1)) - { - k = -k; - } - } - a = a.subtract(b); - } - - return b.equals(ONE) ? (int)k : 0; - } - - /** - * Computes the square root of a BigInteger modulo a prime employing the - * Shanks-Tonelli algorithm. - * - * @param a value out of which we extract the square root - * @param p prime modulus that determines the underlying field - * @return a number <tt>b</tt> such that b<sup>2</sup> = a (mod p) if - * <tt>a</tt> is a quadratic residue modulo <tt>p</tt>. - * @throws NoQuadraticResidueException if <tt>a</tt> is a quadratic non-residue modulo <tt>p</tt> - */ - public static BigInteger ressol(BigInteger a, BigInteger p) - throws IllegalArgumentException - { - - BigInteger v = null; - - if (a.compareTo(ZERO) < 0) - { - a = a.add(p); - } - - if (a.equals(ZERO)) - { - return ZERO; - } - - if (p.equals(TWO)) - { - return a; - } - - // p = 3 mod 4 - if (p.testBit(0) && p.testBit(1)) - { - if (jacobi(a, p) == 1) - { // a quadr. residue mod p - v = p.add(ONE); // v = p+1 - v = v.shiftRight(2); // v = v/4 - return a.modPow(v, p); // return a^v mod p - // return --> a^((p+1)/4) mod p - } - throw new IllegalArgumentException("No quadratic residue: " + a + ", " + p); - } - - long t = 0; - - // initialization - // compute k and s, where p = 2^s (2k+1) +1 - - BigInteger k = p.subtract(ONE); // k = p-1 - long s = 0; - while (!k.testBit(0)) - { // while k is even - s++; // s = s+1 - k = k.shiftRight(1); // k = k/2 - } - - k = k.subtract(ONE); // k = k - 1 - k = k.shiftRight(1); // k = k/2 - - // initial values - BigInteger r = a.modPow(k, p); // r = a^k mod p - - BigInteger n = r.multiply(r).remainder(p); // n = r^2 % p - n = n.multiply(a).remainder(p); // n = n * a % p - r = r.multiply(a).remainder(p); // r = r * a %p - - if (n.equals(ONE)) - { - return r; - } - - // non-quadratic residue - BigInteger z = TWO; // z = 2 - while (jacobi(z, p) == 1) - { - // while z quadratic residue - z = z.add(ONE); // z = z + 1 - } - - v = k; - v = v.multiply(TWO); // v = 2k - v = v.add(ONE); // v = 2k + 1 - BigInteger c = z.modPow(v, p); // c = z^v mod p - - // iteration - while (n.compareTo(ONE) == 1) - { // n > 1 - k = n; // k = n - t = s; // t = s - s = 0; - - while (!k.equals(ONE)) - { // k != 1 - k = k.multiply(k).mod(p); // k = k^2 % p - s++; // s = s + 1 - } - - t -= s; // t = t - s - if (t == 0) - { - throw new IllegalArgumentException("No quadratic residue: " + a + ", " + p); - } - - v = ONE; - for (long i = 0; i < t - 1; i++) - { - v = v.shiftLeft(1); // v = 1 * 2^(t - 1) - } - c = c.modPow(v, p); // c = c^v mod p - r = r.multiply(c).remainder(p); // r = r * c % p - c = c.multiply(c).remainder(p); // c = c^2 % p - n = n.multiply(c).mod(p); // n = n * c % p - } - return r; - } - - /** - * Computes the greatest common divisor of the two specified integers - * - * @param u - first integer - * @param v - second integer - * @return gcd(a, b) - */ - public static int gcd(int u, int v) - { - return BigInteger.valueOf(u).gcd(BigInteger.valueOf(v)).intValue(); - } - - /** - * Extended euclidian algorithm (computes gcd and representation). - * - * @param a the first integer - * @param b the second integer - * @return <tt>(g,u,v)</tt>, where <tt>g = gcd(abs(a),abs(b)) = ua + vb</tt> - */ - public static int[] extGCD(int a, int b) - { - BigInteger ba = BigInteger.valueOf(a); - BigInteger bb = BigInteger.valueOf(b); - BigInteger[] bresult = extgcd(ba, bb); - int[] result = new int[3]; - result[0] = bresult[0].intValue(); - result[1] = bresult[1].intValue(); - result[2] = bresult[2].intValue(); - return result; - } - - public static BigInteger divideAndRound(BigInteger a, BigInteger b) - { - if (a.signum() < 0) - { - return divideAndRound(a.negate(), b).negate(); - } - if (b.signum() < 0) - { - return divideAndRound(a, b.negate()).negate(); - } - return a.shiftLeft(1).add(b).divide(b.shiftLeft(1)); - } - - public static BigInteger[] divideAndRound(BigInteger[] a, BigInteger b) - { - BigInteger[] out = new BigInteger[a.length]; - for (int i = 0; i < a.length; i++) - { - out[i] = divideAndRound(a[i], b); - } - return out; - } - - /** - * Compute the smallest integer that is greater than or equal to the - * logarithm to the base 2 of the given BigInteger. - * - * @param a the integer - * @return ceil[log(a)] - */ - public static int ceilLog(BigInteger a) - { - int result = 0; - BigInteger p = ONE; - while (p.compareTo(a) < 0) - { - result++; - p = p.shiftLeft(1); - } - return result; - } - - /** - * Compute the smallest integer that is greater than or equal to the - * logarithm to the base 2 of the given integer. - * - * @param a the integer - * @return ceil[log(a)] - */ - public static int ceilLog(int a) - { - int log = 0; - int i = 1; - while (i < a) - { - i <<= 1; - log++; - } - return log; - } - - /** - * Compute <tt>ceil(log_256 n)</tt>, the number of bytes needed to encode - * the integer <tt>n</tt>. - * - * @param n the integer - * @return the number of bytes needed to encode <tt>n</tt> - */ - public static int ceilLog256(int n) - { - if (n == 0) - { - return 1; - } - int m; - if (n < 0) - { - m = -n; - } - else - { - m = n; - } - - int d = 0; - while (m > 0) - { - d++; - m >>>= 8; - } - return d; - } - - /** - * Compute <tt>ceil(log_256 n)</tt>, the number of bytes needed to encode - * the long integer <tt>n</tt>. - * - * @param n the long integer - * @return the number of bytes needed to encode <tt>n</tt> - */ - public static int ceilLog256(long n) - { - if (n == 0) - { - return 1; - } - long m; - if (n < 0) - { - m = -n; - } - else - { - m = n; - } - - int d = 0; - while (m > 0) - { - d++; - m >>>= 8; - } - return d; - } - - /** - * Compute the integer part of the logarithm to the base 2 of the given - * integer. - * - * @param a the integer - * @return floor[log(a)] - */ - public static int floorLog(BigInteger a) - { - int result = -1; - BigInteger p = ONE; - while (p.compareTo(a) <= 0) - { - result++; - p = p.shiftLeft(1); - } - return result; - } - - /** - * Compute the integer part of the logarithm to the base 2 of the given - * integer. - * - * @param a the integer - * @return floor[log(a)] - */ - public static int floorLog(int a) - { - int h = 0; - if (a <= 0) - { - return -1; - } - int p = a >>> 1; - while (p > 0) - { - h++; - p >>>= 1; - } - - return h; - } - - /** - * Compute the largest <tt>h</tt> with <tt>2^h | a</tt> if <tt>a!=0</tt>. - * - * @param a an integer - * @return the largest <tt>h</tt> with <tt>2^h | a</tt> if <tt>a!=0</tt>, - * <tt>0</tt> otherwise - */ - public static int maxPower(int a) - { - int h = 0; - if (a != 0) - { - int p = 1; - while ((a & p) == 0) - { - h++; - p <<= 1; - } - } - - return h; - } - - /** - * @param a an integer - * @return the number of ones in the binary representation of an integer - * <tt>a</tt> - */ - public static int bitCount(int a) - { - int h = 0; - while (a != 0) - { - h += a & 1; - a >>>= 1; - } - - return h; - } - - /** - * determines the order of g modulo p, p prime and 1 < g < p. This algorithm - * is only efficient for small p (see X9.62-1998, p. 68). - * - * @param g an integer with 1 < g < p - * @param p a prime - * @return the order k of g (that is k is the smallest integer with - * g<sup>k</sup> = 1 mod p - */ - public static int order(int g, int p) - { - int b, j; - - b = g % p; // Reduce g mod p first. - j = 1; - - // Check whether g == 0 mod p (avoiding endless loop). - if (b == 0) - { - throw new IllegalArgumentException(g + " is not an element of Z/(" - + p + "Z)^*; it is not meaningful to compute its order."); - } - - // Compute the order of g mod p: - while (b != 1) - { - b *= g; - b %= p; - if (b < 0) - { - b += p; - } - j++; - } - - return j; - } - - /** - * Reduces an integer into a given interval - * - * @param n - the integer - * @param begin - left bound of the interval - * @param end - right bound of the interval - * @return <tt>n</tt> reduced into <tt>[begin,end]</tt> - */ - public static BigInteger reduceInto(BigInteger n, BigInteger begin, - BigInteger end) - { - return n.subtract(begin).mod(end.subtract(begin)).add(begin); - } - - /** - * Compute <tt>a<sup>e</sup></tt>. - * - * @param a the base - * @param e the exponent - * @return <tt>a<sup>e</sup></tt> - */ - public static int pow(int a, int e) - { - int result = 1; - while (e > 0) - { - if ((e & 1) == 1) - { - result *= a; - } - a *= a; - e >>>= 1; - } - return result; - } - - /** - * Compute <tt>a<sup>e</sup></tt>. - * - * @param a the base - * @param e the exponent - * @return <tt>a<sup>e</sup></tt> - */ - public static long pow(long a, int e) - { - long result = 1; - while (e > 0) - { - if ((e & 1) == 1) - { - result *= a; - } - a *= a; - e >>>= 1; - } - return result; - } - - /** - * Compute <tt>a<sup>e</sup> mod n</tt>. - * - * @param a the base - * @param e the exponent - * @param n the modulus - * @return <tt>a<sup>e</sup> mod n</tt> - */ - public static int modPow(int a, int e, int n) - { - if (n <= 0 || (n * n) > Integer.MAX_VALUE || e < 0) - { - return 0; - } - int result = 1; - a = (a % n + n) % n; - while (e > 0) - { - if ((e & 1) == 1) - { - result = (result * a) % n; - } - a = (a * a) % n; - e >>>= 1; - } - return result; - } - - /** - * Extended euclidian algorithm (computes gcd and representation). - * - * @param a - the first integer - * @param b - the second integer - * @return <tt>(d,u,v)</tt>, where <tt>d = gcd(a,b) = ua + vb</tt> - */ - public static BigInteger[] extgcd(BigInteger a, BigInteger b) - { - BigInteger u = ONE; - BigInteger v = ZERO; - BigInteger d = a; - if (b.signum() != 0) - { - BigInteger v1 = ZERO; - BigInteger v3 = b; - while (v3.signum() != 0) - { - BigInteger[] tmp = d.divideAndRemainder(v3); - BigInteger q = tmp[0]; - BigInteger t3 = tmp[1]; - BigInteger t1 = u.subtract(q.multiply(v1)); - u = v1; - d = v3; - v1 = t1; - v3 = t3; - } - v = d.subtract(a.multiply(u)).divide(b); - } - return new BigInteger[]{d, u, v}; - } - - /** - * Computation of the least common multiple of a set of BigIntegers. - * - * @param numbers - the set of numbers - * @return the lcm(numbers) - */ - public static BigInteger leastCommonMultiple(BigInteger[] numbers) - { - int n = numbers.length; - BigInteger result = numbers[0]; - for (int i = 1; i < n; i++) - { - BigInteger gcd = result.gcd(numbers[i]); - result = result.multiply(numbers[i]).divide(gcd); - } - return result; - } - - /** - * Returns a long integer whose value is <tt>(a mod m</tt>). This method - * differs from <tt>%</tt> in that it always returns a <i>non-negative</i> - * integer. - * - * @param a value on which the modulo operation has to be performed. - * @param m the modulus. - * @return <tt>a mod m</tt> - */ - public static long mod(long a, long m) - { - long result = a % m; - if (result < 0) - { - result += m; - } - return result; - } - - /** - * Computes the modular inverse of an integer a - * - * @param a - the integer to invert - * @param mod - the modulus - * @return <tt>a<sup>-1</sup> mod n</tt> - */ - public static int modInverse(int a, int mod) - { - return BigInteger.valueOf(a).modInverse(BigInteger.valueOf(mod)) - .intValue(); - } - - /** - * Computes the modular inverse of an integer a - * - * @param a - the integer to invert - * @param mod - the modulus - * @return <tt>a<sup>-1</sup> mod n</tt> - */ - public static long modInverse(long a, long mod) - { - return BigInteger.valueOf(a).modInverse(BigInteger.valueOf(mod)) - .longValue(); - } - - /** - * Tests whether an integer <tt>a</tt> is power of another integer - * <tt>p</tt>. - * - * @param a - the first integer - * @param p - the second integer - * @return n if a = p^n or -1 otherwise - */ - public static int isPower(int a, int p) - { - if (a <= 0) - { - return -1; - } - int n = 0; - int d = a; - while (d > 1) - { - if (d % p != 0) - { - return -1; - } - d /= p; - n++; - } - return n; - } - - /** - * Find and return the least non-trivial divisor of an integer <tt>a</tt>. - * - * @param a - the integer - * @return divisor p >1 or 1 if a = -1,0,1 - */ - public static int leastDiv(int a) - { - if (a < 0) - { - a = -a; - } - if (a == 0) - { - return 1; - } - if ((a & 1) == 0) - { - return 2; - } - int p = 3; - while (p <= (a / p)) - { - if ((a % p) == 0) - { - return p; - } - p += 2; - } - - return a; - } - - /** - * Miller-Rabin-Test, determines wether the given integer is probably prime - * or composite. This method returns <tt>true</tt> if the given integer is - * prime with probability <tt>1 - 2<sup>-20</sup></tt>. - * - * @param n the integer to test for primality - * @return <tt>true</tt> if the given integer is prime with probability - * 2<sup>-100</sup>, <tt>false</tt> otherwise - */ - public static boolean isPrime(int n) - { - if (n < 2) - { - return false; - } - if (n == 2) - { - return true; - } - if ((n & 1) == 0) - { - return false; - } - if (n < 42) - { - for (int i = 0; i < SMALL_PRIMES.length; i++) - { - if (n == SMALL_PRIMES[i]) - { - return true; - } - } - } - - if ((n % 3 == 0) || (n % 5 == 0) || (n % 7 == 0) || (n % 11 == 0) - || (n % 13 == 0) || (n % 17 == 0) || (n % 19 == 0) - || (n % 23 == 0) || (n % 29 == 0) || (n % 31 == 0) - || (n % 37 == 0) || (n % 41 == 0)) - { - return false; - } - - return BigInteger.valueOf(n).isProbablePrime(20); - } - - /** - * Short trial-division test to find out whether a number is not prime. This - * test is usually used before a Miller-Rabin primality test. - * - * @param candidate the number to test - * @return <tt>true</tt> if the number has no factor of the tested primes, - * <tt>false</tt> if the number is definitely composite - */ - public static boolean passesSmallPrimeTest(BigInteger candidate) - { - final int[] smallPrime = {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, 257, 263, 269, 271, 277, 281, 283, 293, 307, - 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, - 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, - 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, - 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, - 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, - 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, - 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, - 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, - 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, - 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, - 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, - 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, - 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, - 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, - 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, - 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499}; - - for (int i = 0; i < smallPrime.length; i++) - { - if (candidate.mod(BigInteger.valueOf(smallPrime[i])).equals( - ZERO)) - { - return false; - } - } - return true; - } - - /** - * Returns the largest prime smaller than the given integer - * - * @param n - upper bound - * @return the largest prime smaller than <tt>n</tt>, or <tt>1</tt> if - * <tt>n <= 2</tt> - */ - public static int nextSmallerPrime(int n) - { - if (n <= 2) - { - return 1; - } - - if (n == 3) - { - return 2; - } - - if ((n & 1) == 0) - { - n--; - } - else - { - n -= 2; - } - - while (n > 3 & !isPrime(n)) - { - n -= 2; - } - return n; - } - - /** - * Compute the next probable prime greater than <tt>n</tt> with the - * specified certainty. - * - * @param n a integer number - * @param certainty the certainty that the generated number is prime - * @return the next prime greater than <tt>n</tt> - */ - public static BigInteger nextProbablePrime(BigInteger n, int certainty) - { - - if (n.signum() < 0 || n.signum() == 0 || n.equals(ONE)) - { - return TWO; - } - - BigInteger result = n.add(ONE); - - // 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( - BigInteger.valueOf(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.isProbablePrime(certainty)) - { - return result; - } - - result = result.add(TWO); - } - } - - /** - * Compute the next probable prime greater than <tt>n</tt> with the default - * certainty (20). - * - * @param n a integer number - * @return the next prime greater than <tt>n</tt> - */ - public static BigInteger nextProbablePrime(BigInteger n) - { - return nextProbablePrime(n, 20); - } - - /** - * Computes the next prime greater than n. - * - * @param n a integer number - * @return the next prime greater than n - */ - public static BigInteger nextPrime(long n) - { - long i; - boolean found = false; - long result = 0; - - if (n <= 1) - { - return BigInteger.valueOf(2); - } - if (n == 2) - { - return BigInteger.valueOf(3); - } - - for (i = n + 1 + (n & 1); (i <= n << 1) && !found; i += 2) - { - for (long j = 3; (j <= i >> 1) && !found; j += 2) - { - if (i % j == 0) - { - found = true; - } - } - if (found) - { - found = false; - } - else - { - result = i; - found = true; - } - } - return BigInteger.valueOf(result); - } - - /** - * Computes the binomial coefficient (n|t) ("n over t"). Formula: - * <ul> - * <li>if n !=0 and t != 0 then (n|t) = Mult(i=1, t): (n-(i-1))/i</li> - * <li>if t = 0 then (n|t) = 1</li> - * <li>if n = 0 and t > 0 then (n|t) = 0</li> - * </ul> - * - * @param n - the "upper" integer - * @param t - the "lower" integer - * @return the binomialcoefficient "n over t" as BigInteger - */ - public static BigInteger binomial(int n, int t) - { - - BigInteger result = ONE; - - if (n == 0) - { - if (t == 0) - { - return result; - } - return ZERO; - } - - // the property (n|t) = (n|n-t) be used to reduce numbers of operations - if (t > (n >>> 1)) - { - t = n - t; - } - - for (int i = 1; i <= t; i++) - { - result = (result.multiply(BigInteger.valueOf(n - (i - 1)))) - .divide(BigInteger.valueOf(i)); - } - - return result; - } - - public static BigInteger randomize(BigInteger upperBound) - { - if (sr == null) - { - sr = new SecureRandom(); - } - return randomize(upperBound, sr); - } - - public static BigInteger randomize(BigInteger upperBound, - SecureRandom prng) - { - int blen = upperBound.bitLength(); - BigInteger randomNum = BigInteger.valueOf(0); - - if (prng == null) - { - prng = sr != null ? sr : new SecureRandom(); - } - - for (int i = 0; i < 20; i++) - { - randomNum = new BigInteger(blen, prng); - if (randomNum.compareTo(upperBound) < 0) - { - return randomNum; - } - } - return randomNum.mod(upperBound); - } - - /** - * Extract the truncated square root of a BigInteger. - * - * @param a - value out of which we extract the square root - * @return the truncated square root of <tt>a</tt> - */ - public static BigInteger squareRoot(BigInteger a) - { - int bl; - BigInteger result, remainder, b; - - if (a.compareTo(ZERO) < 0) - { - throw new ArithmeticException( - "cannot extract root of negative number" + a + "."); - } - - bl = a.bitLength(); - result = ZERO; - remainder = ZERO; - - // if the bit length is odd then extra step - if ((bl & 1) != 0) - { - result = result.add(ONE); - bl--; - } - - while (bl > 0) - { - remainder = remainder.multiply(FOUR); - remainder = remainder.add(BigInteger.valueOf((a.testBit(--bl) ? 2 - : 0) - + (a.testBit(--bl) ? 1 : 0))); - b = result.multiply(FOUR).add(ONE); - result = result.multiply(TWO); - if (remainder.compareTo(b) != -1) - { - result = result.add(ONE); - remainder = remainder.subtract(b); - } - } - - return result; - } - - /** - * Takes an approximation of the root from an integer base, using newton's - * algorithm - * - * @param base the base to take the root from - * @param root the root, for example 2 for a square root - */ - public static float intRoot(int base, int root) - { - float gNew = base / root; - float gOld = 0; - int counter = 0; - while (Math.abs(gOld - gNew) > 0.0001) - { - float gPow = floatPow(gNew, root); - while (Float.isInfinite(gPow)) - { - gNew = (gNew + gOld) / 2; - gPow = floatPow(gNew, root); - } - counter += 1; - gOld = gNew; - gNew = gOld - (gPow - base) / (root * floatPow(gOld, root - 1)); - } - return gNew; - } - - /** - * Calculation of a logarithmus of a float param - * - * @param param - * @return - */ - public static float floatLog(float param) - { - double arg = (param - 1) / (param + 1); - double arg2 = arg; - int counter = 1; - float result = (float)arg; - - while (arg2 > 0.001) - { - counter += 2; - arg2 *= arg * arg; - result += (1. / counter) * arg2; - } - return 2 * result; - } - - /** - * int power of a base float, only use for small ints - * - * @param f - * @param i - * @return - */ - public static float floatPow(float f, int i) - { - float g = 1; - for (; i > 0; i--) - { - g *= f; - } - return g; - } - - /** - * calculate the logarithm to the base 2. - * - * @param x any double value - * @return log_2(x) - * @deprecated use MathFunctions.log(double) instead - */ - public static double log(double x) - { - if (x > 0 && x < 1) - { - double d = 1 / x; - double result = -log(d); - return result; - } - - int tmp = 0; - double tmp2 = 1; - double d = x; - - while (d > 2) - { - d = d / 2; - tmp += 1; - tmp2 *= 2; - } - double rem = x / tmp2; - rem = logBKM(rem); - return tmp + rem; - } - - /** - * calculate the logarithm to the base 2. - * - * @param x any long value >=1 - * @return log_2(x) - * @deprecated use MathFunctions.log(long) instead - */ - public static double log(long x) - { - int tmp = floorLog(BigInteger.valueOf(x)); - long tmp2 = 1 << tmp; - double rem = (double)x / (double)tmp2; - rem = logBKM(rem); - return tmp + rem; - } - - /** - * BKM Algorithm to calculate logarithms to the base 2. - * - * @param arg a double value with 1<= arg<= 4.768462058 - * @return log_2(arg) - * @deprecated use MathFunctions.logBKM(double) instead - */ - private static double logBKM(double arg) - { - double ae[] = // A_e[k] = log_2 (1 + 0.5^k) - { - 1.0000000000000000000000000000000000000000000000000000000000000000000000000000, - 0.5849625007211561814537389439478165087598144076924810604557526545410982276485, - 0.3219280948873623478703194294893901758648313930245806120547563958159347765589, - 0.1699250014423123629074778878956330175196288153849621209115053090821964552970, - 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0.0000000000000000000000002983423419124370148392307506484490384140516252814304, - 0.0000000000000000000000001491711709562185074196153830361933046331030629430117, - 0.0000000000000000000000000745855854781092537098076934460888486730708440475045, - 0.0000000000000000000000000372927927390546268549038472050424734256652501673274, - 0.0000000000000000000000000186463963695273134274519237230207489851150821191330, - 0.0000000000000000000000000093231981847636567137259618916352525606281553180093, - 0.0000000000000000000000000046615990923818283568629809533488457973317312233323, - 0.0000000000000000000000000023307995461909141784314904785572277779202790023236, - 0.0000000000000000000000000011653997730954570892157452397493151087737428485431, - 0.0000000000000000000000000005826998865477285446078726199923328593402722606924, - 0.0000000000000000000000000002913499432738642723039363100255852559084863397344, - 0.0000000000000000000000000001456749716369321361519681550201473345138307215067, - 0.0000000000000000000000000000728374858184660680759840775119123438968122488047, - 0.0000000000000000000000000000364187429092330340379920387564158411083803465567, - 0.0000000000000000000000000000182093714546165170189960193783228378441837282509, - 0.0000000000000000000000000000091046857273082585094980096891901482445902524441, - 0.0000000000000000000000000000045523428636541292547490048446022564529197237262, - 0.0000000000000000000000000000022761714318270646273745024223029238091160103901}; - int n = 53; - double x = 1; - double y = 0; - double z; - double s = 1; - int k; - - for (k = 0; k < n; k++) - { - z = x + x * s; - if (z <= arg) - { - x = z; - y += ae[k]; - } - s *= 0.5; - } - return y; - } - - public static boolean isIncreasing(int[] a) - { - for (int i = 1; i < a.length; i++) - { - if (a[i - 1] >= a[i]) - { - System.out.println("a[" + (i - 1) + "] = " + a[i - 1] + " >= " - + a[i] + " = a[" + i + "]"); - return false; - } - } - return true; - } - - public static byte[] integerToOctets(BigInteger val) - { - byte[] valBytes = val.abs().toByteArray(); - - // check whether the array includes a sign bit - if ((val.bitLength() & 7) != 0) - { - return valBytes; - } - // get rid of the sign bit (first byte) - byte[] tmp = new byte[val.bitLength() >> 3]; - System.arraycopy(valBytes, 1, tmp, 0, tmp.length); - return tmp; - } - - public static BigInteger octetsToInteger(byte[] data, int offset, - int length) - { - byte[] val = new byte[length + 1]; - - val[0] = 0; - System.arraycopy(data, offset, val, 1, length); - return new BigInteger(val); - } - - public static BigInteger octetsToInteger(byte[] data) - { - return octetsToInteger(data, 0, data.length); - } - - public static void main(String[] args) - { - System.out.println("test"); - // System.out.println(intRoot(37, 5)); - // System.out.println(floatPow((float)2.5, 4)); - System.out.println(floatLog(10)); - System.out.println("test2"); - } -} |