Replace usage of `std::numeric_limits<...>::min/max_exponent` in
codebase. Also replaced some other `numeric_limits` usages in
affected tests with the `NumTraits` equivalent.
Fixes#2148
Both CUDA and HIP require trivial default constructors for types used
in shared memory. Otherwise failing with
```
error: initialization is not supported for __shared__ variables.
```
Currently, when compiling with HIP, Eigen::half is derived from the `__half_raw` struct that is defined within the hip_fp16.h header file. This is true for both the "host" compile phase and the "device" compile phase. This was causing a very hard to detect bug in the ROCm TensorFlow build.
In the ROCm Tensorflow build,
* files that do not contain ant GPU code get compiled via gcc, and
* files that contnain GPU code get compiled via hipcc.
In certain case, we have a function that is defined in a file that is compiled by hipcc, and is called in a file that is compiled by gcc. If such a function had Eigen::half has a "pass-by-value" argument, its value was getting corrupted, when received by the function.
The reason for this seems to be that for the gcc compile, Eigen::half is derived from a `__half_raw` struct that has `uint16_t` as the data-store, and for hipcc the `__half_raw` implementation uses `_Float16` as the data store. There is some ABI incompatibility between gcc / hipcc (which is essentially latest clang), which results in the Eigen::half value (which is correct at the call-site) getting randomly corrupted when passed to the function.
Changing the Eigen::half argument to be "pass by reference" seems to workaround the error.
In order to fix it such that we do not run into it again in TF, this commit changes the Eigne::half implementation to use the same `__half_raw` implementation as the non-GPU compile, during host compile phase of the hipcc compile.
This is a new version of !423, which failed for MSVC.
Defined `EIGEN_OPTIMIZATION_BARRIER(X)` that uses inline assembly to
prevent operations involving `X` from crossing that barrier. Should
work on most `GNUC` compatible compilers (MSVC doesn't seem to need
this). This is a modified version adapted from what was used in
`psincos_float` and tested on more platforms
(see #1674, https://godbolt.org/z/73ezTG).
Modified `rint` to use the barrier to prevent the add/subtract rounding
trick from being optimized away.
Also fixed an edge case for large inputs that get bumped up a power of two
and ends up rounding away more than just the fractional part. If we are
over `2^digits` then just return the input. This edge case was missed in
the test since the test was comparing approximate equality, which was still
satisfied. Adding a strict equality option catches it.
Since `numeric_limits<half>::max_exponent` is a static inline constant,
it cannot be directly passed by reference. This triggers a linker error
in recent versions of `g++-powerpc64le`.
Changing `half` to take inputs by value fixes this. Wrapping
`max_exponent` with `int(...)` to make an addressable integer also fixes this
and may help with other custom `Scalar` types down-the-road.
Also eliminated some compile warnings for powerpc.
Added `EIGEN_HAS_STD_HASH` macro, checking for C++11 support and not
running on GPU.
`std::hash<float>` is not a device function, so cannot be used by
`std::hash<bfloat16>`. Removed `EIGEN_DEVICE_FUNC` and only
define if `EIGEN_HAS_STD_HASH`. Same for `half`.
Added `EIGEN_CUDA_HAS_FP16_ARITHMETIC` to improve readability,
eliminate warnings about `EIGEN_CUDA_ARCH` not being defined.
Replaced a couple C-style casts with `reinterpret_cast` for aligned
loading of `half*` to `half2*`. This eliminates `-Wcast-align`
warnings in clang. Although not ideal due to potential type aliasing,
this is how CUDA handles these conversions internally.
The original clamping bounds on `_x` actually produce finite values:
```
exp(88.3762626647950) = 2.40614e+38 < 3.40282e+38
exp(709.437) = 1.27226e+308 < 1.79769e+308
```
so with an accurate `ldexp` implementation, `pexp` fails for large
inputs, producing finite values instead of `inf`.
This adjusts the bounds slightly outside the finite range so that
the output will overflow to +/- `inf` as expected.
The previous implementations produced garbage values if the exponent did
not fit within the exponent bits. See #2131 for a complete discussion,
and !375 for other possible implementations.
Here we implement the 4-factor version. See `pldexp_impl` in
`GenericPacketMathFunctions.h` for a full description.
The SSE `pcmp*` methods were moved down since `pcmp_le<Packet4i>`
requires `por`.
Left as a "TODO" is to delegate to a faster version if we know the
exponent does fit within the exponent bits.
Fixes#2131.
The new `generic_pow` implementation was failing for half/bfloat16 since
their construction from int/float is not `constexpr`. Modified
in `GenericPacketMathFunctions` to remove `constexpr`.
While adding tests for half/bfloat16, found other issues related to
implicit conversions.
Also needed to implement `numext::arg` for non-integer, non-complex,
non-float/double/long double types. These seem to be implicitly
converted to `std::complex<T>`, which then fails for half/bfloat16.
The recent addition of vectorized pow (!330) relies on `pfrexp` and
`pldexp`. This was missing for `Eigen::half` and `Eigen::bfloat16`.
Adding tests for these packet ops also exposed an issue with handling
negative values in `pfrexp`, returning an incorrect exponent.
Added the missing implementations, corrected the exponent in `pfrexp1`,
and added `packetmath` tests.
I ran some testing (comparing to `std::pow(double(x), double(y)))` for `x` in the set of all (positive) floats in the interval `[std::sqrt(std::numeric_limits<float>::min()), std::sqrt(std::numeric_limits<float>::max())]`, and `y` in `{2, sqrt(2), -sqrt(2)}` I get the following error statistics:
```
max_rel_error = 8.34405e-07
rms_rel_error = 2.76654e-07
```
If I widen the range to all normal float I see lower accuracy for arguments where the result is subnormal, e.g. for `y = sqrt(2)`:
```
max_rel_error = 0.666667
rms = 6.8727e-05
count = 1335165689
argmax = 2.56049e-32, 2.10195e-45 != 1.4013e-45
```
which seems reasonable, since these results are subnormals with only couple of significant bits left.
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).
For these to exist we would need to define `_USE_MATH_DEFINES` before
`cmath` or `math.h` is first included. However, we don't
control the include order for projects outside Eigen, so even defining
the macro in `Eigen/Core` does not fix the issue for projects that
end up including `<cmath>` before Eigen does (explicitly or transitively).
To fix this, we define `EIGEN_LOG2E` and `EIGEN_LN2` ourselves.
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 `shfl*` functions are `__device__` only, and adjusted `#ifdef`s so
they are defined whenever the corresponding CUDA/HIP ones are.
Also changed the HIP/CUDA<9.0 versions to cast to int instead of
doing the conversion `half`<->`float`.
Fixes#2083
Adding the term e*ln(2) is split into two step for no obvious reason.
This dates back to the original Cephes code from which the algorithm is adapted.
It appears that this was done in Cephes to prevent the compiler from reordering
the addition of the 3 terms in the approximation
log(1+x) ~= x - 0.5*x^2 + x^3*P(x)/Q(x)
which must be added in reverse order since |x| < (sqrt(2)-1).
This allows rewriting the code to just 2 pmadd and 1 padd instructions,
which on a Skylake processor speeds up the code by 5-7%.
Prior to this fix, `TensorContractionGpu` and the `cxx11_tensor_of_float16_gpu`
test are broken, as well as several ops in Tensorflow. The gpu functions
`__shfl*` became ambiguous now that `Eigen::half` implicitly converts to float.
Here we add the required specializations.
`bit_cast` cannot be `constexpr`, so we need to remove `EIGEN_CONSTEXPR` from
`raw_half_as_uint16(...)`. This shouldn't affect anything else, since
it is only used in `a bit_cast<uint16_t,half>()` which is not itself
`constexpr`.
Fixes#2077.
The `half_float` test was failing with `-mcpu=cortex-a55` (native `__fp16`) due
to a bad NaN bit-pattern comparison (in the case of casting a float to `__fp16`,
the signaling `NaN` is quieted). There was also an inconsistency between
`numeric_limits<half>::quiet_NaN()` and `NumTraits::quiet_NaN()`. Here we
correct the inconsistency and compare NaNs according to the IEEE 754
definition.
Also modified the `bfloat16_float` test to match.
Tested with `cortex-a53` and `cortex-a55`.
Minimal implementation of AVX `Eigen::half` ops to bring in line
with `bfloat16`. Allows `packetmath_13` to pass.
Also adjusted `bfloat16` packet traits to match the supported set
of ops (e.g. Bessel is not actually implemented).
The `half_float` test was failing with `-mcpu=cortex-a55` (native `__fp16`) due
to a bad NaN bit-pattern comparison (in the case of casting a float to `__fp16`,
the signaling `NaN` is quieted). There was also an inconsistency between
`numeric_limits<half>::quiet_NaN()` and `NumTraits::quiet_NaN()`. Here we
correct the inconsistency and compare NaNs according to the IEEE 754
definition.
Also modified the `bfloat16_float` test to match.
Tested with `cortex-a53` and `cortex-a55`.
Both, Eigen::half and Eigen::Bfloat16 are implicitly convertible to
float and can hence be converted to bool via the conversion chain
Eigen::{half,bfloat16} -> float -> bool
We thus remove the explicit cast operator to bool.
The existing `TensorRandom.h` implementation makes the assumption that
`half` (`bfloat16`) has a `uint16_t` member `x` (`value`), which is not
always true. This currently fails on arm64, where `x` has type `__fp16`.
Added `bit_cast` specializations to allow casting to/from `uint16_t`
for both `half` and `bfloat16`. Also added tests in
`half_float`, `bfloat16_float`, and `cxx11_tensor_random` to catch
these errors in the future.
When calling `internal::cast<S, std::complex<T>>(x)`, clang often
generates an implicit conversion warning due to an implicit cast
from type `S` to `T`. This currently affects the following tests:
- `basicstuff`
- `bfloat16_float`
- `cxx11_tensor_casts`
The implicit cast leads to widening/narrowing float conversions.
Widening warnings only seem to be generated by clang (`-Wdouble-promotion`).
To eliminate the warning, we explicitly cast the real-component first
from `S` to `T`. We also adjust tests to use `internal::cast` instead
of `static_cast` when a complex type may be involved.
The following commit breaks Eigen for ROCm (and probably CUDA too) with the following error
e265f7ed8e
```
Building HIPCC object test/CMakeFiles/gpu_basic.dir/gpu_basic_generated_gpu_basic.cu.o
In file included from /home/rocm-user/eigen/test/gpu_basic.cu:20:
In file included from /home/rocm-user/eigen/test/main.h:355:
In file included from /home/rocm-user/eigen/Eigen/QR:11:
In file included from /home/rocm-user/eigen/Eigen/Core:169:
/home/rocm-user/eigen/Eigen/src/Core/arch/Default/Half.h:825:76: error: use of undeclared identifier 'numext'; did you mean 'Eigen::numext'?
return Eigen::half_impl::raw_uint16_to_half(__ldg(reinterpret_cast<const numext::uint16_t*>(ptr)));
^~~~~~
Eigen::numext
/home/rocm-user/eigen/Eigen/src/Core/MathFunctions.h:968:11: note: 'Eigen::numext' declared here
namespace numext {
^
1 error generated when compiling for gfx900.
CMake Error at gpu_basic_generated_gpu_basic.cu.o.cmake:192 (message):
Error generating file
/home/rocm-user/eigen/build/test/CMakeFiles/gpu_basic.dir//./gpu_basic_generated_gpu_basic.cu.o
test/CMakeFiles/gpu_basic.dir/build.make:63: recipe for target 'test/CMakeFiles/gpu_basic.dir/gpu_basic_generated_gpu_basic.cu.o' failed
make[3]: *** [test/CMakeFiles/gpu_basic.dir/gpu_basic_generated_gpu_basic.cu.o] Error 1
CMakeFiles/Makefile2:16611: recipe for target 'test/CMakeFiles/gpu_basic.dir/all' failed
make[2]: *** [test/CMakeFiles/gpu_basic.dir/all] Error 2
CMakeFiles/Makefile2:16618: recipe for target 'test/CMakeFiles/gpu_basic.dir/rule' failed
make[1]: *** [test/CMakeFiles/gpu_basic.dir/rule] Error 2
Makefile:5401: recipe for target 'gpu_basic' failed
make: *** [gpu_basic] Error 2
```
The fix is in this commit is trivial. Please review and merge
Armv8.2-a provides a native half-precision floating point (__fp16 aka.
float16_t). This patch introduces
* __fp16 as underlying type of Eigen::half if this type is available
* the packet types Packet4hf and Packet8hf representing float16x4_t and
float16x8_t respectively
* packet-math for the above packets with corresponding scalar type Eigen::half
The packet-math functionality has been implemented by Ashutosh Sharma
<ashutosh.sharma@amperecomputing.com>.
This closes#1940.
