Type Members

1.  final class CMS extends Serializable

   The idealized formula for the updating current value for a key (y0 -> y1) is given as:

   The idealized formula for the updating current value for a key (y0 -> y1) is given as:

   delta = (t1 - t0) / halflife y1 = y0 * 2^(-delta) + n

   However, we want to avoid having to rescale every single cell every time we update; i.e. a cell with a zero value should continue to have a zero value when n=0.

   Therefore, we introduce a change of variable to cell values (z) along with a scale factor (scale), and the following formula:

   (1) zN = yN * scaleN

   Our constraint is expressed as:

   (2) If n=0, z1 = z0

   In that case:

   (3) If n=0, (y1 * scale1) = (y0 * scale0) (4) Substituting for y1, (y0 * 2^{(-delta) + 0) * scale1 = y0 * scale0 (5) 2}(-delta) * scale1 = scale0 (6) scale1 = scale0 * 2^(delta)

   Also, to express z1 in terms of z0, we say:

   (7) z1 = y1 * scale1 (8) z1 = (y0 * 2^{(-delta) + n) * scale1 (9) z1 = ((z0 / scale0) * 2}(-delta) + n) * scale1 (10) z1 / scale1 = (z0 / (scale1 * 2^{(-delta))) * 2}(-delta) + n (11) z1 / scale1 = z0 / scale1 + n (12) z1 = z0 + n * scale1

   So, for cells where n=0, we just update scale0 to scale1, and for cells where n is non-zero, we update z1 in terms of z0 and scale1.

   If we convert scale to logscale, we have:

   (13) logscale1 = logscale0 + delta * log(2) (14) z1 = z0 + n * exp(logscale1)

   When logscale1 gets big, we start to distort z1. For example, exp(36) is close to 2^53. We can measure when n * exp(logscale1) gets big, and in those cases we can rescale all our cells (set each z to its corresponding y) and set the logscale to 0.

   (15) y1 = z1 / scale1 (16) y1 = z1 / exp(logscale1) (17) y1 = z1 * exp(-logscale1)

2.  class DoubleAt extends Serializable

   Represents a decaying scalar value at a particular point in time.

   Represents a decaying scalar value at a particular point in time.

   The value decays according to halfLife. Another way to think about DoubleAt is that it represents a particular decay curve (and in particular, a point along that curve). Two DoubleAt values may be equivalent if they are two points on the same curve.

   The timeToZero and timeToUnit methods can be used to "normalize" DoubleAt values. If two DoubleAt values do not produce the same (approximate) Double values from these methods, they represent different curves.