Since `numeric_limits<half>::max_exponent` is a static inline constant,
it cannot be directly passed by reference. This triggers a linker error
in recent versions of `g++-powerpc64le`.
Changing `half` to take inputs by value fixes this. Wrapping
`max_exponent` with `int(...)` to make an addressable integer also fixes this
and may help with other custom `Scalar` types down-the-road.
Also eliminated some compile warnings for powerpc.
Added `EIGEN_HAS_STD_HASH` macro, checking for C++11 support and not
running on GPU.
`std::hash<float>` is not a device function, so cannot be used by
`std::hash<bfloat16>`. Removed `EIGEN_DEVICE_FUNC` and only
define if `EIGEN_HAS_STD_HASH`. Same for `half`.
Added `EIGEN_CUDA_HAS_FP16_ARITHMETIC` to improve readability,
eliminate warnings about `EIGEN_CUDA_ARCH` not being defined.
Replaced a couple C-style casts with `reinterpret_cast` for aligned
loading of `half*` to `half2*`. This eliminates `-Wcast-align`
warnings in clang. Although not ideal due to potential type aliasing,
this is how CUDA handles these conversions internally.
For these to exist we would need to define `_USE_MATH_DEFINES` before
`cmath` or `math.h` is first included. However, we don't
control the include order for projects outside Eigen, so even defining
the macro in `Eigen/Core` does not fix the issue for projects that
end up including `<cmath>` before Eigen does (explicitly or transitively).
To fix this, we define `EIGEN_LOG2E` and `EIGEN_LN2` ourselves.
Both, Eigen::half and Eigen::Bfloat16 are implicitly convertible to
float and can hence be converted to bool via the conversion chain
Eigen::{half,bfloat16} -> float -> bool
We thus remove the explicit cast operator to bool.
The existing `TensorRandom.h` implementation makes the assumption that
`half` (`bfloat16`) has a `uint16_t` member `x` (`value`), which is not
always true. This currently fails on arm64, where `x` has type `__fp16`.
Added `bit_cast` specializations to allow casting to/from `uint16_t`
for both `half` and `bfloat16`. Also added tests in
`half_float`, `bfloat16_float`, and `cxx11_tensor_random` to catch
these errors in the future.
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.
