clang-tidy: Return type 'const T' is 'const'-qualified at the top level,
which may reduce code readability without improving const correctness
The types are somewhat long, but the affected return types are of the form:
```
const T my_func() { /**/ }
```
Change to:
```
T my_func() { /**/ }
```
For custom scalars, zero is not necessarily represented by
a zeroed-out memory block (e.g. gnu MPFR). We therefore
cannot rely on `memset` if we want to fill a matrix or tensor
with zeroes. Instead, we should rely on `fill`, which for trivial
types does end up getting converted to a `memset` under-the-hood
(at least with gcc/clang).
Requires adding a `fill(begin, end, v)` to `TensorDevice`.
Replaced all potentially bad instances of memset with fill.
Fixes#2245.
The namespace declaration for googlehash is a configurable macro that
can be disabled. In particular, it is disabled within google, causing
compile errors since `dense_hash_map`/`sparse_hash_map` are then in
the global namespace instead of in `::google`.
Here we play a bit of gynastics to allow for both `google::*_hash_map`
and `*_hash_map`, while limiting namespace polution. Symbols within
the `::google` namespace are imported into `Eigen::google`.
We also remove checks based on `_SPARSE_HASH_MAP_H_`, as this is
fragile, and instead require `EIGEN_GOOGLEHASH_SUPPORT` to be
defined.
1.Only computing about half of the factors and use complex conjugate symmetry for the rest instead of all to save time.
2.All twiddles are calculated in double because that gives the maximum achievable precision when doing float transforms.
3.Reducing all angles to the range 0<angle<pi/4 which gives even more precision.
Current implementations fail to consider half-float packets, only
half-float scalars. Added specializations for packets on AVX, AVX512 and
NEON. Added tests to `special_packetmath`.
The current `special_functions` tests would fail for half and bfloat16 due to
lack of precision. The NEON tests also fail with precision issues and
due to different handling of `sqrt(inf)`, so special functions bessel, ndtri
have been disabled.
Tested with AVX, AVX512.
