Package cc.redberry.rings.poly

Class MachineArithmetic

java.lang.Object
cc.redberry.rings.poly.MachineArithmetic
public final class MachineArithmetic
extends Object
Helper methods for arithmetic with machine numbers.
Since:
1.0

  • Field Summary

    Fields
    Modifier and Type Field Description
    static BigInteger b_MAX_SUPPORTED_MODULUS
    Max supported modulus
    static long MAX_SUPPORTED_MODULUS
    Max supported modulus which fits into machine word
    static int MAX_SUPPORTED_MODULUS_BITS
    Max supported modulus bits which fits into machine word

  • 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)

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Field Details

    • 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 Details

    • 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

    • safeMultiply

      public static long safeMultiply​(long x, long y)
      Delegates to Math.multiplyExact(long, long)
      Throws:
      ArithmeticException - if the result overflows a long

    • safeMultiply

      public static long safeMultiply​(long x, long y, long z)
      Delegates to Math.multiplyExact(long, long)
      Throws:
      ArithmeticException - if the result overflows a long

    • safeAdd

      public static long safeAdd​(long x, long y)
      Delegates to Math.addExact(long, long)
      Throws:
      ArithmeticException - if the result overflows a long

    • safeSubtract

      public static long safeSubtract​(long a, long b)
      Delegates to Math.subtractExact(long, long)
      Throws:
      ArithmeticException - if the result overflows a long

    • safeNegate

      public static long safeNegate​(long x)
      Delegates to Math.negateExact(long)
      Throws:
      ArithmeticException - if the result overflows a long

    • 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

    • mod

      public static long mod​(long num, long modulus)
      Delegates to Math.floorMod(long, long)

    • 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