Package cern.jet.math

Class Arithmetic

java.lang.Object
cern.jet.math.Constants
cern.jet.math.Arithmetic
public class Arithmetic
extends Constants
Arithmetic functions.

  • Field Summary

    Fields 
    Modifier and Type Field Description
    protected static double[] doubleFactorials  
    protected static double[] logFactorials  
    protected static long[] longFactorials  

    Fields inherited from class cern.jet.math.Constants

    big, biginv, LOGPI, MACHEP, MAXGAM, MAXLOG, MINLOG, SQRTH, SQTPI

  • Constructor Summary

    Constructors 
    Modifier Constructor Description
    protected Arithmetic()
    Makes this class non instantiable, but still let's others inherit from it.

  • Method Summary

    Modifier and Type Method Description
    static double binomial​(double n, long k)
    Efficiently returns the binomial coefficient, often also referred to as "n over k" or "n choose k".
    static double binomial​(long n, long k)
    Efficiently returns the binomial coefficient, often also referred to as "n over k" or "n choose k".
    static long ceil​(double value)
    Returns the smallest long >= value.
    static double chbevl​(double x, double[] coef, int N)
    Evaluates the series of Chebyshev polynomials Ti at argument x/2.
    static double factorial​(int k)
    Instantly returns the factorial k!
    static long floor​(double value)
    Returns the largest long <= value.
    static double log​(double base, double value)
    Returns logbasevalue.
    static double log10​(double value)
    Returns log10value.
    static double log2​(double value)
    Returns log2value.
    static double logFactorial​(int k)
    Returns log(k!)
    static long longFactorial​(int k)
    Instantly returns the factorial k!
    static double stirlingCorrection​(int k)
    Returns the StirlingCorrection.

    Methods inherited from class java.lang.Object

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

  • Field Details

  • Constructor Details

    • Arithmetic

      protected Arithmetic()
      Makes this class non instantiable, but still let's others inherit from it.

  • Method Details

    • binomial

      public static double binomial​(double n, long k)
      Efficiently returns the binomial coefficient, often also referred to as "n over k" or "n choose k". The binomial coefficient is defined as (n * n-1 * ... * n-k+1 ) / ( 1 * 2 * ... * k ).
      • k<0: 0.
      • k==0: 1.
      • k==1: n.
      • else: (n * n-1 * ... * n-k+1 ) / ( 1 * 2 * ... * k ).
      Returns:
      the binomial coefficient.

    • binomial

      public static double binomial​(long n, long k)
      Efficiently returns the binomial coefficient, often also referred to as "n over k" or "n choose k". The binomial coefficient is defined as
      • k<0: 0.
      • k==0 || k==n: 1.
      • k==1 || k==n-1: n.
      • else: (n * n-1 * ... * n-k+1 ) / ( 1 * 2 * ... * k ).
      Returns:
      the binomial coefficient.

    • ceil

      public static long ceil​(double value)
      Returns the smallest long >= value. Examples: 1.0 -> 1, 1.2 -> 2, 1.9 -> 2. This method is safer than using (long) Math.ceil(value), because of possible rounding error.

    • chbevl

      public static double chbevl​(double x, double[] coef, int N) throws ArithmeticException
      Evaluates the series of Chebyshev polynomials Ti at argument x/2. The series is given by 
              N-1
         - '
  y  =   >   coef[i] T (x/2)
         -            i
        i=0
      Coefficients are stored in reverse order, i.e. the zero order term is last in the array. Note N is the number of coefficients, not the order.

      If coefficients are for the interval a to b, x must have been transformed to x -> 2(2x - b - a)/(b-a) before entering the routine. This maps x from (a, b) to (-1, 1), over which the Chebyshev polynomials are defined.

      If the coefficients are for the inverted interval, in which (a, b) is mapped to (1/b, 1/a), the transformation required is x -> 2(2ab/x - b - a)/(b-a). If b is infinity, this becomes x -> 4a/x - 1.

      SPEED:

      Taking advantage of the recurrence properties of the Chebyshev polynomials, the routine requires one more addition per loop than evaluating a nested polynomial of the same degree.

      Parameters:
      x - argument to the polynomial.
      coef - the coefficients of the polynomial.
      N - the number of coefficients.
      Throws:
      ArithmeticException

    • factorial

      public static double factorial​(int k)
      Instantly returns the factorial k!.
      Parameters:
      k - must hold k >= 0.

    • floor

      public static long floor​(double value)
      Returns the largest long <= value. Examples: 1.0 -> 1, 1.2 -> 1, 1.9 -> 1 2.0 -> 2, 2.2 -> 2, 2.9 -> 2 This method is safer than using (long) Math.floor(value), because of possible rounding error.

    • log

      public static double log​(double base, double value)
      Returns logbasevalue.

    • log10

      public static double log10​(double value)
      Returns log10value.

    • log2

      public static double log2​(double value)
      Returns log2value.

    • logFactorial

      public static double logFactorial​(int k)
      Returns log(k!). Tries to avoid overflows. For k<30 simply looks up a table in O(1). For k>=30 uses stirlings approximation.
      Parameters:
      k - must hold k >= 0.

    • longFactorial

      public static long longFactorial​(int k) throws IllegalArgumentException
      Instantly returns the factorial k!.
      Parameters:
      k - must hold k >= 0 && k < 21.
      Throws:
      IllegalArgumentException

    • stirlingCorrection

      public static double stirlingCorrection​(int k)
      Returns the StirlingCorrection.

      Correction term of the Stirling approximation for log(k!) (series in 1/k, or table values for small k) with int parameter k.

      log k! = (k + 1/2)log(k + 1) - (k + 1) + (1/2)log(2Pi) + stirlingCorrection(k + 1)

      log k! = (k + 1/2)log(k) - k + (1/2)log(2Pi) + stirlingCorrection(k)