Loading data from random memory locations became too expensive compared to computations. For log, exp, trigonometry, and similar, I think people rarely use any lookup tables. Instead, they use some high-poly approximations, and for log/exp abuse IEEE binary floats representation.
LUTs at least do well in microbenchmarks, but I do worry that they may do comparatively much worse in real code.
That said, that's another advantage of small tables using vpermi2pd.
The Julia/base implementations of log and exp both use LUTs.
The SIMD AVX512 implementation of exp used by LoopVectorization.jl will sometimes use the 16 element table.
I experimented with log, but had some difficulty getting accuracy and performance, so the version LoopVectorization.jl currently uses doesn't use a table.
Here's a log() function from the standard library in OpenBSD: https://github.com/openbsd/src/blob/master/lib/libm/src/e_lo...