[LEAPSECS] leap smear

[michael.deckers]

    On 2011-09-15 21:55, Poul-Henning Kamp wrote:

> Actually, the _really_ interesting thing is that they resort to using

> a cos() function to herd the NTPD pll's in their system, but that

> is more a testimony to how bogus that PLL code really is.

>

    The correction term is (1 - cos(t))/2 = sin(t/2)^2,
    hence Google's modification of UTC is four times
    continuously differentiable.

    The minimal rate is
       d(TAI)*(1 - pi/2/(window length in seconds))
    hence the slowdown is 57 % larger than with the
    piecewise linear method (as used by Markus Kuhn's
    SLS) over the same window. The piecewise linear
    method gives a time scale that is continuous but
    not differentiable.

    Michael Deckers.