Package org.apache.commons.rng.sampling.distribution

Class StableSampler.SpecialMath

java.lang.Object
org.apache.commons.rng.sampling.distribution.StableSampler.SpecialMath
Enclosing class:
StableSampler
static final class StableSampler.SpecialMath extends Object
Implement special math functions required by the CMS algorithm.

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    private static final double
    FOUR_PI
    4/pi.
    private static final double
    P0
    tan2 product constant.
    private static final double
    P1
    tan2 product constant.
    private static final double
    P2
    tan2 product constant.
    private static final double
    P3
    tan2 product constant.
    private static final double
    P4
    tan2 product constant.
    private static final double
    PI_4
    pi/4.
    private static final double
    Q0
    tan2 quotient constant.
    private static final double
    Q1
    tan2 quotient constant.
    private static final double
    Q2
    tan2 quotient constant.
    private static final double
    Q3
    tan2 quotient constant.
    private static final double
    Q4
    tan2 quotient constant.
    private static final double
    SWITCH_TO_EXPM1
    The threshold to switch to using Math.expm1(double).

  • Constructor Summary

    Constructors
    Modifier
    Constructor
    Description
    private
    SpecialMath()
    No instances.

  • Method Summary

    Modifier and Type
    Method
    Description
    (package private) static double
    d2(double x)
    Evaluate (exp(x) - 1) / x.
    (package private) static double
    tan2(double x)
    Evaluate tan(x) / x.

    Methods inherited from class java.lang.Object

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

  • Field Details

    • PI_4

      private static final double PI_4
      pi/4.
      See Also:

    • FOUR_PI

      private static final double FOUR_PI
      4/pi.
      See Also:

    • P0

      private static final double P0
      tan2 product constant.
      See Also:

    • P1

      private static final double P1
      tan2 product constant.
      See Also:

    • P2

      private static final double P2
      tan2 product constant.
      See Also:

    • P3

      private static final double P3
      tan2 product constant.
      See Also:

    • P4

      private static final double P4
      tan2 product constant.
      See Also:

    • Q0

      private static final double Q0
      tan2 quotient constant.
      See Also:

    • Q1

      private static final double Q1
      tan2 quotient constant.
      See Also:

    • Q2

      private static final double Q2
      tan2 quotient constant.
      See Also:

    • Q3

      private static final double Q3
      tan2 quotient constant.
      See Also:

    • Q4

      private static final double Q4
      tan2 quotient constant.
      See Also:

    • SWITCH_TO_EXPM1

      private static final double SWITCH_TO_EXPM1
      The threshold to switch to using Math.expm1(double). The following table shows the mean (max) ULP difference between using expm1 and exp using random +/-x with different exponents (n=2^30): 
       x        exp  positive x                 negative x
 64.0      6   0.10004021506756544  (2)   0.0                   (0)
 32.0      5   0.11177831795066595  (2)   0.0                   (0)
 16.0      4   0.0986650362610817   (2)   9.313225746154785E-10 (1)
 8.0       3   0.09863092936575413  (2)   4.9658119678497314E-6 (1)
 4.0       2   0.10015273280441761  (2)   4.547201097011566E-4  (1)
 2.0       1   0.14359260816127062  (2)   0.005623611621558666  (2)
 1.0       0   0.20160607434809208  (2)   0.03312791418284178   (2)
 0.5      -1   0.3993037799373269   (2)   0.28186883218586445   (2)
 0.25     -2   0.6307008266448975   (2)   0.5192863345146179    (2)
 0.125    -3   1.3862918205559254   (4)   1.386285437270999     (4)
 0.0625   -4   2.772640804760158    (8)   2.772612397558987     (8)

      The threshold of 0.5 has a mean ULP below 0.5 and max ULP of 2. The transition is monotonic. Neither is true for the next threshold of 0.25.

      See Also:

  • Constructor Details

    • SpecialMath

      private SpecialMath()
      No instances.

  • Method Details

    • d2

      static double d2(double x)
      Evaluate (exp(x) - 1) / x. For x in the range [-inf, inf] returns a result in [0, inf].
      • For x=-inf this returns 0.
      • For x=0 this returns 1.
      • For x=inf this returns inf.
      • For x=nan this returns nan.

      This corrects 0 / 0 and inf / inf division from NaN to either 1 or the upper bound respectively.

      Parameters:
      x - value to evaluate
      Returns:
      (exp(x) - 1) / x.

    • tan2

      static double tan2(double x)
      Evaluate tan(x) / x.

      For x in the range [0, pi/4] this returns a value in the range [1, 4 / pi].

      The following properties are desirable for the CMS algorithm:

      • For x=0 this returns 1.
      • For x=pi/4 this returns 4/pi.
      • For x=pi/4 this multiplied by x returns 1.

      This method is called by the CMS algorithm when x < pi/4. In this case the method is almost as accurate as Math.tan(x) / x, does not require checking for x=0 and is faster.

      Parameters:
      x - the x
      Returns:
      tan(x) / x.