1.Only computing about half of the factors and use complex conjugate symmetry for the rest instead of all to save time.
2.All twiddles are calculated in double because that gives the maximum achievable precision when doing float transforms.
3.Reducing all angles to the range 0<angle<pi/4 which gives even more precision.
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.
