ArithmeticMod
umontreal.iro.lecuyer.util

Class ArithmeticMod



  • public class ArithmeticModextends Object
    This class provides facilities to compute multiplications of scalars, of vectors and of matrices modulo m. All algorithms are present in three different versions. These allow operations on double, int and long. The int and long versions work exactly like the double ones.
    • Method Summary

      Methods 
      Modifier and TypeMethod and Description
      static voidmatMatModM(double[][] A, double[][] B, double[][] C, double m)
      Computes A×B mod m and puts the result in C.
      static voidmatMatModM(int[][] A, int[][] B, int[][] C, int m)
      Exactly like matMatModM using double, but with int instead of double.
      static voidmatMatModM(long[][] A, long[][] B, long[][] C, long m)
      Exactly like matMatModM using double, but with long instead of double.
      static voidmatPowModM(double[][] A, double[][] B, double m, int c)
      Computes Ac mod m and puts the result in B.
      static voidmatPowModM(int[][] A, int[][] B, int m, int c)
      Exactly like matPowModM using double, but with int instead of double.
      static voidmatPowModM(long[][] A, long[][] B, long m, int c)
      Exactly like matPowModM using double, but with long instead of double.
      static voidmatTwoPowModM(double[][] A, double[][] B, double m, int e)
      Computes A2e mod m and puts the result in B.
      static voidmatTwoPowModM(int[][] A, int[][] B, int m, int e)
      Exactly like matTwoPowModM using double, but with int instead of double.
      static voidmatTwoPowModM(long[][] A, long[][] B, long m, int e)
      Exactly like matTwoPowModM using double, but with long instead of double.
      static voidmatVecModM(double[][] A, double[] s, double[] v, double m)
      Computes the result of A×s mod m and puts the result in v.
      static voidmatVecModM(int[][] A, int[] s, int[] v, int m)
      Exactly like matVecModM using double, but with int instead of double.
      static voidmatVecModM(long[][] A, long[] s, long[] v, long m)
      Exactly like matVecModM using double, but with long instead of double.
      static doublemultModM(double a, double s, double c, double m)
      Computes (a×s + c) mod m.
      static intmultModM(int a, int s, int c, int m)
      Computes (a×s + c) mod m.
      static longmultModM(long a, long s, long c, long m)
      Computes (a×s + c) mod m.
    • Method Detail

      • multModM

        public static double multModM(double a,              double s,              double c,              double m)
        Computes (a×s + c) mod m. Where m must be smaller than 235. Works also if s or c are negative. The result is always positive (and thus always between 0 and m - 1).
        Parameters:
        a - the first factor of the multiplication
        s - the second factor of the multiplication
        c - the second term of the addition
        m - the modulus
        Returns:
        the result of the multiplication and the addition modulo m
      • matVecModM

        public static void matVecModM(double[][] A,              double[] s,              double[] v,              double m)
        Computes the result of A×s mod m and puts the result in v. Where s and v are both column vectors. This method works even if s = v.
        Parameters:
        A - the multiplication matrix
        s - the multiplied vector
        v - the result of the multiplication
        m - the modulus
      • matMatModM

        public static void matMatModM(double[][] A,              double[][] B,              double[][] C,              double m)
        Computes A×B mod m and puts the result in C. Works even if A = C, B = C or A = B = C.
        Parameters:
        A - the first factor of the multiplication
        B - the second factor of the multiplication
        C - the result of the multiplication
        m - the modulus
      • matTwoPowModM

        public static void matTwoPowModM(double[][] A,                 double[][] B,                 double m,                 int e)
        Computes A2e mod m and puts the result in B. Works even if A = B.
        Parameters:
        A - the matrix to raise to a power
        B - the result of exponentiation
        m - the modulus
        e - the log2 of the exponent
      • matPowModM

        public static void matPowModM(double[][] A,              double[][] B,              double m,              int c)
        Computes Ac mod m and puts the result in B. Works even if A = B.
        Parameters:
        A - the matrix to raise to a power
        B - the result of the exponentiation
        m - the modulus
        c - the exponent
      • multModM

        public static int multModM(int a,           int s,           int c,           int m)
        Computes (a×s + c) mod m. Works also if s or c are negative. The result is always positive (and thus always between 0 and m - 1).
        Parameters:
        a - the first factor of the multiplication
        s - the second factor of the multiplication
        c - the second term of the addition
        m - the modulus
        Returns:
        the result of the multiplication and the addition modulo m
      • matVecModM

        public static void matVecModM(int[][] A,              int[] s,              int[] v,              int m)
        Exactly like matVecModM using double, but with int instead of double.
        Parameters:
        A - the multiplication matrix
        s - the multiplied vector
        v - the result of the multiplication
        m - the modulus
      • matMatModM

        public static void matMatModM(int[][] A,              int[][] B,              int[][] C,              int m)
        Exactly like matMatModM using double, but with int instead of double.
        Parameters:
        A - the first factor of the multiplication
        B - the second factor of the multiplication
        C - the result of the multiplication
        m - the modulus
      • matTwoPowModM

        public static void matTwoPowModM(int[][] A,                 int[][] B,                 int m,                 int e)
        Exactly like matTwoPowModM using double, but with int instead of double.
        Parameters:
        A - the matrix to raise to a power
        B - the result of exponentiation
        m - the modulus
        e - the log2 of the exponent
      • matPowModM

        public static void matPowModM(int[][] A,              int[][] B,              int m,              int c)
        Exactly like matPowModM using double, but with int instead of double.
        Parameters:
        A - the matrix to raise to a power
        B - the result of the exponentiation
        m - the modulus
        c - the exponent
      • multModM

        public static long multModM(long a,            long s,            long c,            long m)
        Computes (a×s + c) mod m. Works also if s or c are negative. The result is always positive (and thus always between 0 and m - 1).
        Parameters:
        a - the first factor of the multiplication
        s - the second factor of the multiplication
        c - the second term of the addition
        m - the modulus
        Returns:
        the result of the multiplication and the addition modulo m
      • matVecModM

        public static void matVecModM(long[][] A,              long[] s,              long[] v,              long m)
        Exactly like matVecModM using double, but with long instead of double.
        Parameters:
        A - the multiplication matrix
        s - the multiplied vector
        v - the result of the multiplication
        m - the modulus
      • matMatModM

        public static void matMatModM(long[][] A,              long[][] B,              long[][] C,              long m)
        Exactly like matMatModM using double, but with long instead of double.
        Parameters:
        A - the first factor of the multiplication
        B - the second factor of the multiplication
        C - the result of the multiplication
        m - the modulus
      • matTwoPowModM

        public static void matTwoPowModM(long[][] A,                 long[][] B,                 long m,                 int e)
        Exactly like matTwoPowModM using double, but with long instead of double.
        Parameters:
        A - the matrix to raise to a power
        B - the result of exponentiation
        m - the modulus
        e - the log2 of the exponent
      • matPowModM

        public static void matPowModM(long[][] A,              long[][] B,              long m,              int c)
        Exactly like matPowModM using double, but with long instead of double.
        Parameters:
        A - the matrix to raise to a power
        B - the result of the exponentiation
        m - the modulus
        c - the exponent

SCaVis 2.0 © jWork.ORG