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 specialization of array class in the different namespace for GCC<=6.4
* The implicit call to `std::array` constructor using the initializer list for GCC <=6.1
The errors were introduced by this commit :
After the above mentioned commit, some of the tests started failing with the following error
```
Built target cxx11_tensor_reduction
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:117:
/home/rocm-user/eigen/unsupported/Eigen/CXX11/src/Tensor/TensorBlockV2.h:155:5: error: the field type is not amp-compatible
DestinationBufferKind m_kind;
^
/home/rocm-user/eigen/unsupported/Eigen/CXX11/src/Tensor/TensorBlockV2.h:211:3: error: the field type is not amp-compatible
DestinationBuffer m_destination;
^
```
For some reason HIPCC does not like device code to contain enum types which do not have the base-type explicitly declared. The fix is trivial, explicitly state "int" as the basetype
