mp.asin is inaccurate for small complex inputs #787
Description
As in the title.
Reproducer:
>>> mpmath.mp.asin(mpmath.mpc(0, 1e-22))
mpc(real='0.0', imag='0.0')
>>> mpmath.fp.asin(mpmath.mpc(0, 1e-22)) # expected result
1e-22jA workaround is to increase precision:
>>> mpmath.mp.prec=80
>>> mpmath.mp.asin(mpmath.mpc(0, 1e-22))
mpc(real='0.0', imag='9.9999996826552253889673883e-23')Points z=x+yj in the following (approximate) region
|x| < |y| < 1e-19
of the complex plane suffer from the defect reported here.