Some CUDA/HIP constants fail on device with `constexpr` since they
internally rely on non-constexpr functions, e.g.
```
\#define CUDART_INF_F __int_as_float(0x7f800000)
```
This fails for cuda-clang (though passes with nvcc). These constants are
currently used by `device::numeric_limits`. For portability, we
need to remove `constexpr` from the affected functions.
For C++11 or higher, we should be able to rely on the `std::numeric_limits`
versions anyways, since the methods themselves are now `constexpr`, so
should be supported on device (clang/hipcc natively, nvcc with
`--expr-relaxed-constexpr`).
NVCC and older versions of clang do not fully support `std::complex` on device,
leading to either compile errors (Cannot call `__host__` function) or worse,
runtime errors (Illegal instruction). For most functions, we can
implement specialized `numext` versions. Here we specialize the standard
operators (with the exception of stream operators and member function operators
with a scalar that are already specialized in `<complex>`) so they can be used
in device code as well.
To import these operators into the current scope, use
`EIGEN_USING_STD_COMPLEX_OPERATORS`. By default, these are imported into
the `Eigen`, `Eigen:internal`, and `Eigen::numext` namespaces.
This allow us to remove specializations of the
sum/difference/product/quotient ops, and allow us to treat complex
numbers like most other scalars (e.g. in tests).
This is to support scalar `sqrt` of complex numbers `std::complex<T>` on
device, requested by Tensorflow folks.
Technically `std::complex` is not supported by NVCC on device
(though it is by clang), so the default `sqrt(std::complex<T>)` function only
works on the host. Here we create an overload to add back the
functionality.
Also modified the CMake file to add `--relaxed-constexpr` (or
equivalent) flag for NVCC to allow calling constexpr functions from
device functions, and added support for specifying compute architecture for
NVCC (was already available for clang).
This provide several advantages:
- more flexibility in designing unit tests
- unit tests can be glued to speed up compilation
- unit tests are compiled with same predefined macros, which is a requirement for zapcc
The major changes are
1. Moving CUDA/PacketMath.h to GPU/PacketMath.h
2. Moving CUDA/MathFunctions.h to GPU/MathFunction.h
3. Moving CUDA/CudaSpecialFunctions.h to GPU/GpuSpecialFunctions.h
The above three changes effectively enable the Eigen "Packet" layer for the HIP platform
4. Merging the "hip_basic" and "cuda_basic" unit tests into one ("gpu_basic")
5. Updating the "EIGEN_DEVICE_FUNC" marking in some places
The change has been tested on the HIP and CUDA platforms.
