Package cc.redberry.rings.poly

Class MachineArithmetic

  • public final class MachineArithmetic
extends Object
    Helper methods for arithmetic with machine numbers.
    Since:
    1.0

    • Method Summary

      Modifier and Type Method Description
      static boolean fits31bitWord​(long val)
      Returns true if val fits into 32-bit machine word (unsigned) and false otherwise
      static boolean fits32bitWord​(long val)
      Returns true if val fits into 32-bit machine word (unsigned) and false otherwise
      static long gcd​(int... integers)
      Returns the greatest common an array of integers
      static long gcd​(int[] integers, int from, int to)
      Returns the greatest common an array of integers
      static int gcd​(int p, int q)
      Computes the greatest common divisor of the absolute value of two numbers, using a modified version of the "binary gcd" method.
      static long gcd​(long... integers)
      Returns the greatest common an array of longs
      static long gcd​(long[] integers, int from, int to)
      Returns the greatest common an array of longs
      static long gcd​(long p, long q)
      Returns the greatest common divisor of two longs.
      static long[] gcdExtended​(long a, long b)
      Runs extended Euclidean algorithm to compute [gcd(a,b), x, y] such that x * a + y * b = gcd(a, b)
      static boolean isOverflowAdd​(long x, long y)
      Tests whether the addition of x + y will cause long overflow
      static boolean isOverflowMultiply​(long x, long y)
      Tests whether the multiplication of x*y will cause long overflow
      static int lcm​(int a, int b)
      Returns the least common multiple of two integers
      static long lcm​(long a, long b)
      Returns the least common multiple of two longs
      static long mod​(long num, long modulus)
      Delegates to Math.floorMod(long, long)
      static long modInverse​(long num, long modulus)
      Returns a solution of congruence num * x = 1 mod modulus
      static long[] perfectPowerDecomposition​(long n)
      Tests whether n is a perfect power n == a^b and returns {a, b} if so and null otherwise
      static long powMod​(long base, long exponent, long modulus)
      Returns base in a power of non-negative e modulo modulus
      static long powModSigned​(long base, long exponent, cc.redberry.libdivide4j.FastDivision.Magic magic)
      Returns base in a power of non-negative e modulo magic.modulus
      static long powModUnsigned​(long base, long exponent, cc.redberry.libdivide4j.FastDivision.Magic magic)
      Returns base in a power of non-negative e modulo magic.modulus
      static long safeAdd​(long x, long y)
      Delegates to Math.addExact(long, long)
      static long safeMultiply​(long x, long y)
      Delegates to Math.multiplyExact(long, long)
      static long safeMultiply​(long x, long y, long z)
      Delegates to Math.multiplyExact(long, long)
      static long safeNegate​(long x)
      Delegates to Math.negateExact(long)
      static long safePow​(long base, long exponent)
      Returns base in a power of e (non negative)
      static long safeSubtract​(long a, long b)
      Delegates to Math.subtractExact(long, long)
      static int safeToInt​(long value)
      Casts long to signed int throwing exception in case of overflow.
      static long symMod​(long value, long modulus)
      Returns value mod modulus in the symmetric representation (-modulus/2 <= result <= modulus/2)
      static long unsafePow​(long base, long exponent)
      Returns base in a power of e (non negative)

    • Field Detail

      • MAX_SUPPORTED_MODULUS_BITS

        public static final int MAX_SUPPORTED_MODULUS_BITS
        Max supported modulus bits which fits into machine word
        See Also:
        Constant Field Values

      • MAX_SUPPORTED_MODULUS

        public static final long MAX_SUPPORTED_MODULUS
        Max supported modulus which fits into machine word
        See Also:
        Constant Field Values

      • b_MAX_SUPPORTED_MODULUS

        public static final BigInteger b_MAX_SUPPORTED_MODULUS
        Max supported modulus

    • Method Detail

      • fits32bitWord

        public static boolean fits32bitWord​(long val)
        Returns true if val fits into 32-bit machine word (unsigned) and false otherwise
        Parameters:
        val - the value
        Returns:
        true if val fits into 32-bit machine word (unsigned) and false otherwise

      • fits31bitWord

        public static boolean fits31bitWord​(long val)
        Returns true if val fits into 32-bit machine word (unsigned) and false otherwise
        Parameters:
        val - the value
        Returns:
        true if val fits into 32-bit machine word (unsigned) and false otherwise

      • isOverflowMultiply

        public static boolean isOverflowMultiply​(long x,
                                         long y)
        Tests whether the multiplication of x*y will cause long overflow

      • isOverflowAdd

        public static boolean isOverflowAdd​(long x,
                                    long y)
        Tests whether the addition of x + y will cause long overflow

      • safePow

        public static long safePow​(long base,
                           long exponent)
        Returns base in a power of e (non negative)
        Parameters:
        base - base
        exponent - exponent (non negative)
        Returns:
        base in a power of e
        Throws:
        ArithmeticException - if the result overflows a long

      • unsafePow

        public static long unsafePow​(long base,
                             long exponent)
        Returns base in a power of e (non negative)
        Parameters:
        base - base
        exponent - exponent (non negative)
        Returns:
        base in a power of e

      • gcd

        public static long gcd​(long p,
                       long q)
        Returns the greatest common divisor of two longs.
        Parameters:
        p - a long
        q - a long
        Returns:
        greatest common divisor of a and b

      • gcd

        public static int gcd​(int p,
                      int q)
        Computes the greatest common divisor of the absolute value of two numbers, using a modified version of the "binary gcd" method. See Knuth 4.5.2 algorithm B. The algorithm is due to Josef Stein (1961).
        Special cases:
        • The invocations gcd(Integer.MIN_VALUE, Integer.MIN_VALUE), gcd(Integer.MIN_VALUE, 0) and gcd(0, Integer.MIN_VALUE) throw an ArithmeticException, because the result would be 2^31, which is too large for an int value.
        • The result of gcd(x, x), gcd(0, x) and gcd(x, 0) is the absolute value of x, except for the special cases above.
        • The invocation gcd(0, 0) is the only one which returns 0.
        Parameters:
        p - Number.
        q - Number.
        Returns:
        the greatest common divisor (never negative).

      • gcdExtended

        public static long[] gcdExtended​(long a,
                                 long b)
        Runs extended Euclidean algorithm to compute [gcd(a,b), x, y] such that x * a + y * b = gcd(a, b)
        Parameters:
        a - a long
        b - a long
        Returns:
        array of [gcd(a,b), x, y] such that x * a + y * b = gcd(a, b)

      • lcm

        public static long lcm​(long a,
                       long b)
        Returns the least common multiple of two longs
        Parameters:
        a - a long
        b - a long
        Returns:
        least common multiple of a and b
        Throws:
        ArithmeticException - if the result overflows a long

      • lcm

        public static int lcm​(int a,
                      int b)
        Returns the least common multiple of two integers
        Parameters:
        a - a number
        b - a number
        Returns:
        least common multiple of a and b

      • gcd

        public static long gcd​(long[] integers,
                       int from,
                       int to)
        Returns the greatest common an array of longs
        Parameters:
        integers - array of longs
        from - from position (inclusive)
        to - to position (exclusive)
        Returns:
        greatest common divisor of array

      • gcd

        public static long gcd​(long... integers)
        Returns the greatest common an array of longs
        Parameters:
        integers - array of longs
        Returns:
        greatest common divisor of array

      • gcd

        public static long gcd​(int[] integers,
                       int from,
                       int to)
        Returns the greatest common an array of integers
        Parameters:
        integers - array of integers
        from - from position (inclusive)
        to - to position (exclusive)
        Returns:
        greatest common divisor of array

      • gcd

        public static long gcd​(int... integers)
        Returns the greatest common an array of integers
        Parameters:
        integers - array of integers
        Returns:
        greatest common divisor of array

      • symMod

        public static long symMod​(long value,
                          long modulus)
        Returns value mod modulus in the symmetric representation (-modulus/2 <= result <= modulus/2)
        Parameters:
        value - a long
        modulus - modulus
        Returns:
        value mod modulus in the symmetric representation (-modulus/2 <= result <= modulus/2)

      • modInverse

        public static long modInverse​(long num,
                              long modulus)
        Returns a solution of congruence num * x = 1 mod modulus
        Parameters:
        num - base
        modulus - modulus
        Returns:
        a^(-1) mod p
        Throws:
        IllegalArgumentException - a and modulus are not coprime

      • safeToInt

        public static int safeToInt​(long value)
        Casts long to signed int throwing exception in case of overflow.
        Parameters:
        value - the long
        Returns:
        int value
        Throws:
        ArithmeticException - if the result overflows a long

      • powMod

        public static long powMod​(long base,
                          long exponent,
                          long modulus)
        Returns base in a power of non-negative e modulo modulus
        Parameters:
        base - the base
        exponent - the non-negative exponent
        modulus - the modulus
        Returns:
        base in a power of e

      • powModSigned

        public static long powModSigned​(long base,
                                long exponent,
                                cc.redberry.libdivide4j.FastDivision.Magic magic)
        Returns base in a power of non-negative e modulo magic.modulus
        Parameters:
        base - the base
        exponent - the non-negative exponent
        magic - magic modulus
        Returns:
        base in a power of e

      • powModUnsigned

        public static long powModUnsigned​(long base,
                                  long exponent,
                                  cc.redberry.libdivide4j.FastDivision.Magic magic)
        Returns base in a power of non-negative e modulo magic.modulus
        Parameters:
        base - the base
        exponent - the non-negative exponent
        magic - magic modulus
        Returns:
        base in a power of e

      • perfectPowerDecomposition

        public static long[] perfectPowerDecomposition​(long n)
        Tests whether n is a perfect power n == a^b and returns {a, b} if so and null otherwise
        Parameters:
        n - the number
        Returns:
        array {a, b} so that n = a^b or null is n is not a perfect power