Householder construction treated a tail as zero whenever its squared norm
underflowed, returning tau = 0 so the reflector did not eliminate the tail. For
complex inputs, squaring a small imaginary head could select the same shortcut
and leave a non-real head while returning a real beta.
When the tail norm is small enough that underflow or flush-to-zero can discard a
significant contribution, form beta, tau, and the essential vector from
scale-free ratios instead, widening float intermediates to double so every
finite float component can be squared. A finite trivial reflector is retained
where the tail is exactly zero, is insignificant relative to a dominant real
head, or the target flushes an entirely subnormal input.
The direct 2x2 and 3x3 float self-adjoint eigensolvers widen their scaling
division below min() / epsilon() so a flush-to-zero target does not discard a
coefficient that is subnormal in the original matrix but significant relative to
the scale.
HessenbergDecomposition deliberately keeps master's shortcut for a tail whose
squared norm and head's imaginary component are both negligible, so
Tridiagonalization receives the corrected complex-head behavior while Hessenberg
decomposition preserves its existing behavior.
Adds householder_12 and eigensolver_selfadjoint_13 regressions plus gpu_basic
device coverage.
MSVC does not support specializing compound assignments for
`std::complex`, since it already specializes them (contrary to the
standard).
Trying to use one of these on device will currently lead to a
duplicate definition error. This is still probably preferable
to no error though. If we remove the definitions for MSVC, then
it will compile, but the kernel will fail silently.
The only proper solution would be to define our own custom `Complex`
type.
Since `std::equal_to::operator()` is not a device function, it
fails on GPU. On my device, I seem to get a silent crash in the
kernel (no reported error, but the kernel does not complete).
Replacing this with a portable version enables comparisons on device.
Addresses #2292 - would need to be cherry-picked. The 3.3 branch
also requires adding `EIGEN_DEVICE_FUNC` in `BooleanRedux.h` to get
fully working.
Some CUDA/HIP constants fail on device with `constexpr` since they
internally rely on non-constexpr functions, e.g.
```
\#define CUDART_INF_F __int_as_float(0x7f800000)
```
This fails for cuda-clang (though passes with nvcc). These constants are
currently used by `device::numeric_limits`. For portability, we
need to remove `constexpr` from the affected functions.
For C++11 or higher, we should be able to rely on the `std::numeric_limits`
versions anyways, since the methods themselves are now `constexpr`, so
should be supported on device (clang/hipcc natively, nvcc with
`--expr-relaxed-constexpr`).
NVCC and older versions of clang do not fully support `std::complex` on device,
leading to either compile errors (Cannot call `__host__` function) or worse,
runtime errors (Illegal instruction). For most functions, we can
implement specialized `numext` versions. Here we specialize the standard
operators (with the exception of stream operators and member function operators
with a scalar that are already specialized in `<complex>`) so they can be used
in device code as well.
To import these operators into the current scope, use
`EIGEN_USING_STD_COMPLEX_OPERATORS`. By default, these are imported into
the `Eigen`, `Eigen:internal`, and `Eigen::numext` namespaces.
This allow us to remove specializations of the
sum/difference/product/quotient ops, and allow us to treat complex
numbers like most other scalars (e.g. in tests).
This is to support scalar `sqrt` of complex numbers `std::complex<T>` on
device, requested by Tensorflow folks.
Technically `std::complex` is not supported by NVCC on device
(though it is by clang), so the default `sqrt(std::complex<T>)` function only
works on the host. Here we create an overload to add back the
functionality.
Also modified the CMake file to add `--relaxed-constexpr` (or
equivalent) flag for NVCC to allow calling constexpr functions from
device functions, and added support for specifying compute architecture for
NVCC (was already available for clang).
This provide several advantages:
- more flexibility in designing unit tests
- unit tests can be glued to speed up compilation
- unit tests are compiled with same predefined macros, which is a requirement for zapcc
The major changes are
1. Moving CUDA/PacketMath.h to GPU/PacketMath.h
2. Moving CUDA/MathFunctions.h to GPU/MathFunction.h
3. Moving CUDA/CudaSpecialFunctions.h to GPU/GpuSpecialFunctions.h
The above three changes effectively enable the Eigen "Packet" layer for the HIP platform
4. Merging the "hip_basic" and "cuda_basic" unit tests into one ("gpu_basic")
5. Updating the "EIGEN_DEVICE_FUNC" marking in some places
The change has been tested on the HIP and CUDA platforms.
Florian Maurin