There are two major changes (and a few minor ones which are not listed here...see PR discussion for details)
1. Eigen::half implementations for HIP and CUDA have been merged.
This means that
- `CUDA/Half.h` and `HIP/hcc/Half.h` got merged to a new file `GPU/Half.h`
- `CUDA/PacketMathHalf.h` and `HIP/hcc/PacketMathHalf.h` got merged to a new file `GPU/PacketMathHalf.h`
- `CUDA/TypeCasting.h` and `HIP/hcc/TypeCasting.h` got merged to a new file `GPU/TypeCasting.h`
After this change the `HIP/hcc` directory only contains one file `math_constants.h`. That will go away too once that file becomes a part of the HIP install.
2. new macros EIGEN_GPUCC, EIGEN_GPU_COMPILE_PHASE and EIGEN_HAS_GPU_FP16 have been added and the code has been updated to use them where appropriate.
- `EIGEN_GPUCC` is the same as `(EIGEN_CUDACC || EIGEN_HIPCC)`
- `EIGEN_GPU_DEVICE_COMPILE` is the same as `(EIGEN_CUDA_ARCH || EIGEN_HIP_DEVICE_COMPILE)`
- `EIGEN_HAS_GPU_FP16` is the same as `(EIGEN_HAS_CUDA_FP16 or EIGEN_HAS_HIP_FP16)`
In addition to igamma(a, x), this code implements:
* igamma_der_a(a, x) = d igamma(a, x) / da -- derivative of igamma with respect to the parameter
* gamma_sample_der_alpha(alpha, sample) -- reparameterization derivative of a Gamma(alpha, 1) random variable sample with respect to the alpha parameter
The derivatives are computed by forward mode differentiation of the igamma(a, x) code. Although gamma_sample_der_alpha can be implemented via igamma_der_a, a separate function is more accurate and efficient due to analytical cancellation of some terms. All three functions are implemented by a method parameterized with "mode" that always computes the derivatives, but does not return them unless required by the mode. The compiler is expected to (and, based on benchmarks, does) skip the unnecessary computations depending on the mode.
This commit enables the use of Eigen on HIP kernels / AMD GPUs. Support has been added along the same lines as what already exists for using Eigen in CUDA kernels / NVidia GPUs.
Application code needs to explicitly define EIGEN_USE_HIP when using Eigen in HIP kernels. This is because some of the CUDA headers get picked up by default during Eigen compile (irrespective of whether or not the underlying compiler is CUDACC/NVCC, for e.g. Eigen/src/Core/arch/CUDA/Half.h). In order to maintain this behavior, the EIGEN_USE_HIP macro is used to switch to using the HIP version of those header files (see Eigen/Core and unsupported/Eigen/CXX11/Tensor)
Use the "-DEIGEN_TEST_HIP" cmake option to enable the HIP specific unit tests.
The functions are conventionally called i0e and i1e. The exponentially scaled version is more numerically stable. The standard Bessel functions can be obtained as i0(x) = exp(|x|) i0e(x)
The code is ported from Cephes and tested against SciPy.
