Current implementations fail to consider half-float packets, only
half-float scalars. Added specializations for packets on AVX, AVX512 and
NEON. Added tests to `special_packetmath`.
The current `special_functions` tests would fail for half and bfloat16 due to
lack of precision. The NEON tests also fail with precision issues and
due to different handling of `sqrt(inf)`, so special functions bessel, ndtri
have been disabled.
Tested with AVX, AVX512.
The errors were introduced by this commit : d38e6fbc27
After the above mentioned commit, some of the tests started failing with the following error
```
Building HIPCC object unsupported/test/CMakeFiles/cxx11_tensor_reduction_gpu_5.dir/cxx11_tensor_reduction_gpu_5_generated_cxx11_tensor_reduction_gpu.cu.o
In file included from /home/rocm-user/eigen/unsupported/test/cxx11_tensor_reduction_gpu.cu:16:
In file included from /home/rocm-user/eigen/unsupported/Eigen/CXX11/Tensor:29:
In file included from /home/rocm-user/eigen/unsupported/Eigen/CXX11/../SpecialFunctions:70:
/home/rocm-user/eigen/unsupported/Eigen/CXX11/../src/SpecialFunctions/SpecialFunctionsHalf.h:28:22: error: call to 'erf' is ambiguous
return Eigen::half(Eigen::numext::erf(static_cast<float>(a)));
^~~~~~~~~~~~~~~~~~
/home/rocm-user/eigen/unsupported/test/../../Eigen/src/Core/MathFunctions.h:1600:7: note: candidate function [with T = float]
float erf(const float &x) { return ::erff(x); }
^
/home/rocm-user/eigen/unsupported/Eigen/CXX11/../src/SpecialFunctions/SpecialFunctionsImpl.h:1897:5: note: candidate function [with Scalar = float]
erf(const Scalar& x) {
^
In file included from /home/rocm-user/eigen/unsupported/test/cxx11_tensor_reduction_gpu.cu:16:
In file included from /home/rocm-user/eigen/unsupported/Eigen/CXX11/Tensor:29:
In file included from /home/rocm-user/eigen/unsupported/Eigen/CXX11/../SpecialFunctions:75:
/home/rocm-user/eigen/unsupported/Eigen/CXX11/../src/SpecialFunctions/arch/GPU/GpuSpecialFunctions.h:87:23: error: call to 'erf' is ambiguous
return make_double2(erf(a.x), erf(a.y));
^~~
/home/rocm-user/eigen/unsupported/test/../../Eigen/src/Core/MathFunctions.h:1603:8: note: candidate function [with T = double]
double erf(const double &x) { return ::erf(x); }
^
/home/rocm-user/eigen/unsupported/Eigen/CXX11/../src/SpecialFunctions/SpecialFunctionsImpl.h:1897:5: note: candidate function [with Scalar = double]
erf(const Scalar& x) {
^
In file included from /home/rocm-user/eigen/unsupported/test/cxx11_tensor_reduction_gpu.cu:16:
In file included from /home/rocm-user/eigen/unsupported/Eigen/CXX11/Tensor:29:
In file included from /home/rocm-user/eigen/unsupported/Eigen/CXX11/../SpecialFunctions:75:
/home/rocm-user/eigen/unsupported/Eigen/CXX11/../src/SpecialFunctions/arch/GPU/GpuSpecialFunctions.h:87:33: error: call to 'erf' is ambiguous
return make_double2(erf(a.x), erf(a.y));
^~~
/home/rocm-user/eigen/unsupported/test/../../Eigen/src/Core/MathFunctions.h:1603:8: note: candidate function [with T = double]
double erf(const double &x) { return ::erf(x); }
^
/home/rocm-user/eigen/unsupported/Eigen/CXX11/../src/SpecialFunctions/SpecialFunctionsImpl.h:1897:5: note: candidate function [with Scalar = double]
erf(const Scalar& x) {
^
3 errors generated.
```
This PR fixes the compile error by removing the "old" implementation for "erf" (assuming that the "new" implementation is what we want going forward. from a GPU point-of-view both implementations are the same).
This PR also fixes what seems like a cut-n-paste error in the aforementioned commit
- Split SpecialFunctions files in to a separate BesselFunctions file.
In particular add:
- Modified bessel functions of the second kind k0, k1, k0e, k1e
- Bessel functions of the first kind j0, j1
- Bessel functions of the second kind y0, y1
The fixes needed are
* adding EIGEN_DEVICE_FUNC attribute to a couple of funcs (else HIPCC will error out when non-device funcs are called from global/device funcs)
* switching to using ::<math_func> instead std::<math_func> (only for HIPCC) in cases where the std::<math_func> is not recognized as a device func by HIPCC
* removing an errant "j" from a testcase (don't know how that made it in to begin with!)
* Modifying TensorDeviceSYCL to use `EIGEN_THROW_X`.
* Modifying TensorMacro to use `EIGEN_TRY/CATCH(X)` macro.
* Modifying TensorReverse.h to use `EIGEN_DEVICE_REF` instead of `&`.
* Fixing the SYCL device macro in SpecialFunctionsImpl.h.
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)`
The commit with Bessel functions i0e and i1e placed the ifdef/endif incorrectly,
causing i0e/i1e to be undefined when EIGEN_HAS_C99_MATH=0. These functions do not
actually require C99 math, so now they are always available.
Previously, when computing the derivative, it used a relative error threshold. Now it uses an absolute error threshold. The behavior for computing the value is unchanged. This makes more sense since we do not expect the derivative to often be close to zero. This change makes the derivatives about 30% faster across the board. The error for the igamma_der_a is almost unchanged, while for gamma_sample_der_alpha it is a bit worse for float32 and unchanged for float64.
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.
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
