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.
1. Added new packet functions using SIMD for NByOne, OneByN cases
2. Modified existing packet functions to reduce index calculations when input stride is non-SIMD
3. Added 4 test cases to cover the new packet functions
Also, a few minor fixes for GPU tests running in HIP mode.
1. Adding an include for hip/hip_runtime.h in the Macros.h file
For HIP __host__ and __device__ are macros which are defined in hip headers.
Their definitions need to be included before their use in the file.
2. Fixing the compile failure in TensorContractionGpu introduced by the commit to
"Fuse computations into the Tensor contractions using output kernel"
3. Fixing a HIP/clang specific compile error by making the struct-member assignment explicit
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
Check for nan inputs and propagate them immediately. Limit the number of internal iterations to 2000 (same number as used by scipy.special.gammainc). This prevents an infinite loop when the function is called with nan or very large arguments.
Original change by mfirgunov@google.com
If the cost is large enough then the thread count can be larger than the maximum
representable int, so just casting it to an int is undefined behavior.
Contributed by phurst@google.com.
bug #1464 : Fixes construction of EulerAngles from 3D vector expression.
Approved-by: Tal Hadad <tal_hd@hotmail.com>
Approved-by: Abhijit Kundu <abhijit.kundu@gatech.edu>
