I am using polygon datatype with some very small values and discovered that the overlaps operator appears to break down and give false positives for values smaller than ~1e-6. I have tested this on 9.5 (.3 and .16) and 10.10.
To reproduce (these examples only differ in the x-axis exponents) and should be false but the first one is t(rue)
select '((3.0e-07,-2),(9.0e-07,-2),(9.0e-07,1),(3.0e-07,1))'::polygon
&& '((2.0e-07,-0.1),(2.0e-07,0.1),(2.01e-07,0.1),(2.01e-07,-0.1))'::polygon;
select '((3.0e-06,-2),(9.0e-06,-2),(9.0e-06,1),(3.0e-06,1))'::polygon
&& '((2.0e-06,-0.1),(2.0e-06,0.1),(2.01e-06,0.1),(2.01e-06,-0.1))'::polygon;
Maybe suggests some single-precision floating point use in the calculations...