In comparing the computation of vonmisesDistribution CDF using

N[CDF[VonMisesDistribution[0, 1], -0.78539816339744828], 17]

0.25614866519978797

I can integrate the PDF using

NIntegrate[ PDF[VonMisesDistribution[0,1],x], {x,-\Pi, Divide[-\Pi,4]}]

and by asking for more digits get a value 0.25615930008908783
that agrees with my calculation in C++ using a Boost tanhsinh integration, and with values computed by R and Python with machine precision (17 decimal digits).

I suspect that the integration is terminated after about 6 decimal digit precision rather than my expectation that it will use machine precision of 17 decimal digits.

I have experimented with trying to set $Tolerance, and $MaxExtraPrecision and $MaxPrecision but without success. Can anyone please confirm this diagnosis and perhaps tell me how to force computation of machine precision 17 decimal digits.