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.
- cleanup noise in imaginary part of real roots
- take into account the magnitude of the derivative to check roots.
- use <= instead of < at appropriate places
