Implemented fast size-4 matrix inverse (mimicking Inverse_SSE.h) using NEON intrinsics.
```
Benchmark Time CPU Time Old Time New CPU Old CPU New
--------------------------------------------------------------------------------------------------------
BM_float -0.1285 -0.1275 568 495 572 499
BM_double -0.2265 -0.2254 638 494 641 496
```
PR 181 ( https://gitlab.com/libeigen/eigen/-/merge_requests/181 ) adds `__launch_bounds__(1024)` attribute to GPU kernels, that did not have that attribute explicitly specified.
That PR seems to cause regressions on the CUDA platform. This PR/commit makes the changes in PR 181, to be applicable for HIP only
Some platforms define int64_t to be long long even for C++03. If this is
the case we miss the definition of internal::make_unsigned for this
type. If we just define the template we get duplicated definitions
errors for platforms defining int64_t as signed long for C++03.
We need to find a way to distinguish both cases at compile-time.
The NEON implementation mimics the SSE implementation, but didn't mention the caveat that due to the unsigned of signed integer conversions, not all values in the original floating point represented are supported.
If we have explicit conversion operators available (C++11) we define
explicit casts from bfloat16 to other types. If not (C++03), we don't
define conversion operators but rely on implicit conversion chains from
bfloat16 over float to other types.
Specialized `bfloat16_impl::float_to_bfloat16_rtne(float)` for normal floating point numbers, infinity and zero, in order to improve the performance of `bfloat16::bfloat16(const T&)` for integer argument types.
A reduction of more than 20% of the runtime duration of conversion from int to bfloat16 was observed, using Visual C++ 2019 on Windows 10.
Conversion from `bfloat16` to `float` and `double` is lossless. It seems natural to allow the conversion to be implicit, as the C++ language also support implicit conversion from a smaller to a larger floating point type.
Intel's OneDLL bfloat16 implementation also has an implicit `operator float()`: https://github.com/oneapi-src/oneDNN/blob/v1.5/src/common/bfloat16.hpp
- Guard fundamental types that are not available pre C++11
- Separate subsequent angle brackets >> by spaces
- Allow casting of Eigen::half and Eigen::bfloat16 to complex types
The original tensor casts were only defined for
`SrcCoeffRatio`:`TgtCoeffRatio` 1:1, 1:2, 2:1, 4:1. Here we add the
missing 1:N and 8:1.
We also add casting `Eigen::half` to/from `std::complex<T>`, which
was missing to make it consistent with `Eigen:bfloat16`, and
generalize the overload to work for any complex type.
Tests were added to `basicstuff`, `packetmath`, and
`cxx11_tensor_casts` to test all cast configurations.
Added missing `pmadd<Packet2f>` for NEON. This leads to significant
improvement in precision than previous `pmul+padd`, which was causing
the `pcos` tests to fail. Also added an approx test with
`std::sin`/`std::cos` since otherwise returning any `a^2+b^2=1` would
pass.
Modified `log(denorm)` tests. Denorms are not always supported by all
systems (returns `::min`), are always flushed to zero on 32-bit arm,
and configurably flush to zero on sse/avx/aarch64. This leads to
inconsistent results across different systems (i.e. `-inf` vs `nan`).
Added a check for existence and exclude ARM.
Removed logistic exactness test, since scalar and vectorized versions
follow different code-paths due to differences in `pexp` and `pmadd`,
which result in slightly different values. For example, exactness always
fails on arm, aarch64, and altivec.
The NEON `pcast` operators are all implemented and tested for existing
packets. This requires adding a `pcast(a,b,c,d,e,f,g,h)` for casting
between `int64_t` and `int8_t` in `GenericPacketMath.h`.
Removed incorrect `HasHalfPacket` definition for NEON's
`Packet2l`/`Packet2ul`.
Adjustments were also made to the `packetmath` tests. These include
- minor bug fixes for cast tests (i.e. 4:1 casts, only casting for
packets that are vectorizable)
- added 8:1 cast tests
- random number generation
- original had uninteresting 0 to 0 casts for many casts between
floating-point and integers, and exhibited signed overflow
undefined behavior
Tested:
```
$ aarch64-linux-gnu-g++ -static -I./ '-DEIGEN_TEST_PART_ALL=1' test/packetmath.cpp -o packetmath
$ adb push packetmath /data/local/tmp/
$ adb shell "/data/local/tmp/packetmath"
```
The use of the `packet_traits<>::HasCast` field is currently inconsistent with
`type_casting_traits<>`, and is unused apart from within
`test/packetmath.cpp`. In addition, those packetmath cast tests do not
currently reflect how casts are performed in practice: they ignore the
`SrcCoeffRatio` and `TgtCoeffRatio` fields, assuming a 1:1 ratio.
Here we remove the unsed `HasCast`, and modify the packet cast tests to
better reflect their usage.
