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.
The AVX512 version of ptranpose for PacketBlock<Packet16h,16> was
reordering the PacketBlock argument incorrectly. This lead to errors in
the multiplication of matrices composed of 16 bit floats on AVX512
machines, if at least of the matrices was using RowMajor order. This
error is responsible for one tensorflow unit test failure on AVX512
machines:
//tensorflow/python/kernel_tests:batch_matmul_op_test
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.
