Ancient versions of CMake required else(), endif(), and similar block
termination commands to have arguments matching the command starting the block.
This is no longer the preferred style.
2. Simplify handling of special cases by taking advantage of the fact that the
builtin vrsqrt approximation handles negative, zero and +inf arguments correctly.
This speeds up the SSE and AVX implementations by ~20%.
3. Make the Newton-Raphson formula used for rsqrt more numerically robust:
Before: y = y * (1.5 - x/2 * y^2)
After: y = y * (1.5 - y * (x/2) * y)
Forming y^2 can overflow for very large or very small (denormalized) values of x, while x*y ~= 1. For AVX512, this makes it possible to compute accurate results for denormal inputs down to ~1e-42 in single precision.
4. Add a faster double precision implementation for Knights Landing using the vrsqrt28 instruction and a single Newton-Raphson iteration.
Benchmark results: https://bitbucket.org/snippets/rmlarsen/5LBq9o
Add a new EIGEN_HAS_INTRINSIC_INT128 macro, and use this instead of __SIZEOF_INT128__. This fixes related issues with TensorIntDiv.h when building with Clang for Windows, where support for 128-bit integer arithmetic is advertised but broken in practice.
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!)
- Move colamd implementation in its own namespace to avoid polluting the internal namespace with Ok, Status, etc.
- Fix signed/unsigned warning
- move some ugly free functions as member functions
