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38abf2be42
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`.
827 lines
29 KiB
C++
827 lines
29 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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//
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// The conversion routines are Copyright (c) Fabian Giesen, 2016.
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// The original license follows:
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//
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// Copyright (c) Fabian Giesen, 2016
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// All rights reserved.
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted.
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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// HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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// Standard 16-bit float type, mostly useful for GPUs. Defines a new
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// type Eigen::half (inheriting either from CUDA's or HIP's __half struct) with
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// operator overloads such that it behaves basically as an arithmetic
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// type. It will be quite slow on CPUs (so it is recommended to stay
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// in fp32 for CPUs, except for simple parameter conversions, I/O
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// to disk and the likes), but fast on GPUs.
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#ifndef EIGEN_HALF_H
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#define EIGEN_HALF_H
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#if EIGEN_HAS_CXX11
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#define EIGEN_EXPLICIT_CAST(tgt_type) explicit operator tgt_type()
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#else
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#define EIGEN_EXPLICIT_CAST(tgt_type) operator tgt_type()
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#endif
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#include <sstream>
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#if defined(EIGEN_HAS_GPU_FP16) || defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)
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// When compiling with GPU support, the "__half_raw" base class as well as
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// some other routines are defined in the GPU compiler header files
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// (cuda_fp16.h, hip_fp16.h), and they are not tagged constexpr
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// As a consequence, we get compile failures when compiling Eigen with
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// GPU support. Hence the need to disable EIGEN_CONSTEXPR when building
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// Eigen with GPU support
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#pragma push_macro("EIGEN_CONSTEXPR")
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#undef EIGEN_CONSTEXPR
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#define EIGEN_CONSTEXPR
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#endif
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namespace Eigen {
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struct half;
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namespace half_impl {
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#if !defined(EIGEN_HAS_GPU_FP16)
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// Make our own __half_raw definition that is similar to CUDA's.
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struct __half_raw {
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EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __half_raw() : x(0) {}
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#if defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)
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explicit EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __half_raw(numext::uint16_t raw) : x(numext::bit_cast<__fp16>(raw)) {
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}
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__fp16 x;
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#else
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explicit EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __half_raw(numext::uint16_t raw) : x(raw) {}
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numext::uint16_t x;
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#endif
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};
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#elif defined(EIGEN_HAS_HIP_FP16)
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// Nothing to do here
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// HIP fp16 header file has a definition for __half_raw
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#elif defined(EIGEN_HAS_CUDA_FP16)
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#if defined(EIGEN_CUDA_SDK_VER) && EIGEN_CUDA_SDK_VER < 90000
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// In CUDA < 9.0, __half is the equivalent of CUDA 9's __half_raw
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typedef __half __half_raw;
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#endif // defined(EIGEN_HAS_CUDA_FP16)
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#elif defined(SYCL_DEVICE_ONLY)
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typedef cl::sycl::half __half_raw;
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#endif
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __half_raw raw_uint16_to_half(numext::uint16_t x);
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half_raw float_to_half_rtne(float ff);
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC float half_to_float(__half_raw h);
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struct half_base : public __half_raw {
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EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half_base() {}
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EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half_base(const __half_raw& h) : __half_raw(h) {}
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#if defined(EIGEN_HAS_GPU_FP16)
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#if defined(EIGEN_HAS_HIP_FP16)
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EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half_base(const __half& h) { x = __half_as_ushort(h); }
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#elif defined(EIGEN_HAS_CUDA_FP16)
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#if (defined(EIGEN_CUDA_SDK_VER) && EIGEN_CUDA_SDK_VER >= 90000)
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EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half_base(const __half& h) : __half_raw(*(__half_raw*)&h) {}
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#endif
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#endif
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#endif
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};
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} // namespace half_impl
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// Class definition.
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struct half : public half_impl::half_base {
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// Writing this out as separate #if-else blocks to make the code easier to follow
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// The same applies to most #if-else blocks in this file
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#if !defined(EIGEN_HAS_GPU_FP16)
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typedef half_impl::__half_raw __half_raw;
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#elif defined(EIGEN_HAS_HIP_FP16)
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// Nothing to do here
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// HIP fp16 header file has a definition for __half_raw
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#elif defined(EIGEN_HAS_CUDA_FP16)
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// Note that EIGEN_CUDA_SDK_VER is set to 0 even when compiling with HIP, so
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// (EIGEN_CUDA_SDK_VER < 90000) is true even for HIP! So keeping this within
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// #if defined(EIGEN_HAS_CUDA_FP16) is needed
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#if defined(EIGEN_CUDA_SDK_VER) && EIGEN_CUDA_SDK_VER < 90000
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typedef half_impl::__half_raw __half_raw;
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#endif
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#endif
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EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half() {}
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EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half(const __half_raw& h) : half_impl::half_base(h) {}
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#if defined(EIGEN_HAS_GPU_FP16)
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#if defined(EIGEN_HAS_HIP_FP16)
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EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half(const __half& h) : half_impl::half_base(h) {}
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#elif defined(EIGEN_HAS_CUDA_FP16)
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#if defined(EIGEN_CUDA_SDK_VER) && EIGEN_CUDA_SDK_VER >= 90000
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EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half(const __half& h) : half_impl::half_base(h) {}
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#endif
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#endif
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#endif
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explicit EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR half(bool b)
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: half_impl::half_base(half_impl::raw_uint16_to_half(b ? 0x3c00 : 0)) {}
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template<class T>
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explicit EIGEN_DEVICE_FUNC half(const T& val)
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: half_impl::half_base(half_impl::float_to_half_rtne(static_cast<float>(val))) {}
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explicit EIGEN_DEVICE_FUNC half(float f)
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: half_impl::half_base(half_impl::float_to_half_rtne(f)) {}
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// Following the convention of numpy, converting between complex and
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// float will lead to loss of imag value.
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template<typename RealScalar>
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explicit EIGEN_DEVICE_FUNC half(std::complex<RealScalar> c)
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: half_impl::half_base(half_impl::float_to_half_rtne(static_cast<float>(c.real()))) {}
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EIGEN_DEVICE_FUNC operator float() const { // NOLINT: Allow implicit conversion to float, because it is lossless.
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return half_impl::half_to_float(*this);
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}
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};
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} // end namespace Eigen
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namespace std {
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template<>
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struct numeric_limits<Eigen::half> {
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static const bool is_specialized = true;
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static const bool is_signed = true;
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static const bool is_integer = false;
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static const bool is_exact = false;
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static const bool has_infinity = true;
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static const bool has_quiet_NaN = true;
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static const bool has_signaling_NaN = true;
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static const float_denorm_style has_denorm = denorm_present;
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static const bool has_denorm_loss = false;
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static const std::float_round_style round_style = std::round_to_nearest;
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static const bool is_iec559 = false;
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static const bool is_bounded = false;
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static const bool is_modulo = false;
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static const int digits = 11;
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static const int digits10 = 3; // according to http://half.sourceforge.net/structstd_1_1numeric__limits_3_01half__float_1_1half_01_4.html
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static const int max_digits10 = 5; // according to http://half.sourceforge.net/structstd_1_1numeric__limits_3_01half__float_1_1half_01_4.html
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static const int radix = 2;
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static const int min_exponent = -13;
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static const int min_exponent10 = -4;
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static const int max_exponent = 16;
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static const int max_exponent10 = 4;
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static const bool traps = true;
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static const bool tinyness_before = false;
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static Eigen::half (min)() { return Eigen::half_impl::raw_uint16_to_half(0x400); }
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static Eigen::half lowest() { return Eigen::half_impl::raw_uint16_to_half(0xfbff); }
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static Eigen::half (max)() { return Eigen::half_impl::raw_uint16_to_half(0x7bff); }
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static Eigen::half epsilon() { return Eigen::half_impl::raw_uint16_to_half(0x0800); }
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static Eigen::half round_error() { return Eigen::half(0.5); }
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static Eigen::half infinity() { return Eigen::half_impl::raw_uint16_to_half(0x7c00); }
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static Eigen::half quiet_NaN() { return Eigen::half_impl::raw_uint16_to_half(0x7e00); }
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static Eigen::half signaling_NaN() { return Eigen::half_impl::raw_uint16_to_half(0x7d00); }
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static Eigen::half denorm_min() { return Eigen::half_impl::raw_uint16_to_half(0x1); }
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};
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// If std::numeric_limits<T> is specialized, should also specialize
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// std::numeric_limits<const T>, std::numeric_limits<volatile T>, and
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// std::numeric_limits<const volatile T>
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// https://stackoverflow.com/a/16519653/
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template<>
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struct numeric_limits<const Eigen::half> : numeric_limits<Eigen::half> {};
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template<>
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struct numeric_limits<volatile Eigen::half> : numeric_limits<Eigen::half> {};
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template<>
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struct numeric_limits<const volatile Eigen::half> : numeric_limits<Eigen::half> {};
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} // end namespace std
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namespace Eigen {
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namespace half_impl {
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#if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && \
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EIGEN_CUDA_ARCH >= 530) || \
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(defined(EIGEN_HAS_HIP_FP16) && defined(HIP_DEVICE_COMPILE))
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// Note: We deliberatly do *not* define this to 1 even if we have Arm's native
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// fp16 type since GPU halfs are rather different from native CPU halfs.
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// TODO: Rename to something like EIGEN_HAS_NATIVE_GPU_FP16
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#define EIGEN_HAS_NATIVE_FP16
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#endif
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// Intrinsics for native fp16 support. Note that on current hardware,
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// these are no faster than fp32 arithmetic (you need to use the half2
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// versions to get the ALU speed increased), but you do save the
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// conversion steps back and forth.
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#if defined(EIGEN_HAS_NATIVE_FP16)
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EIGEN_STRONG_INLINE __device__ half operator + (const half& a, const half& b) {
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#if defined(EIGEN_CUDA_SDK_VER) && EIGEN_CUDA_SDK_VER >= 90000
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return __hadd(::__half(a), ::__half(b));
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#else
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return __hadd(a, b);
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#endif
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}
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EIGEN_STRONG_INLINE __device__ half operator * (const half& a, const half& b) {
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return __hmul(a, b);
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}
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EIGEN_STRONG_INLINE __device__ half operator - (const half& a, const half& b) {
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return __hsub(a, b);
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}
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EIGEN_STRONG_INLINE __device__ half operator / (const half& a, const half& b) {
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#if defined(EIGEN_CUDA_SDK_VER) && EIGEN_CUDA_SDK_VER >= 90000
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return __hdiv(a, b);
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#else
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float num = __half2float(a);
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float denom = __half2float(b);
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return __float2half(num / denom);
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#endif
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}
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EIGEN_STRONG_INLINE __device__ half operator - (const half& a) {
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return __hneg(a);
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}
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EIGEN_STRONG_INLINE __device__ half& operator += (half& a, const half& b) {
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a = a + b;
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return a;
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}
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EIGEN_STRONG_INLINE __device__ half& operator *= (half& a, const half& b) {
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a = a * b;
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return a;
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}
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EIGEN_STRONG_INLINE __device__ half& operator -= (half& a, const half& b) {
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a = a - b;
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return a;
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}
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EIGEN_STRONG_INLINE __device__ half& operator /= (half& a, const half& b) {
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a = a / b;
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return a;
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}
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EIGEN_STRONG_INLINE __device__ bool operator == (const half& a, const half& b) {
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return __heq(a, b);
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}
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EIGEN_STRONG_INLINE __device__ bool operator != (const half& a, const half& b) {
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return __hne(a, b);
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}
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EIGEN_STRONG_INLINE __device__ bool operator < (const half& a, const half& b) {
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return __hlt(a, b);
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}
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EIGEN_STRONG_INLINE __device__ bool operator <= (const half& a, const half& b) {
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return __hle(a, b);
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}
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EIGEN_STRONG_INLINE __device__ bool operator > (const half& a, const half& b) {
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return __hgt(a, b);
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}
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EIGEN_STRONG_INLINE __device__ bool operator >= (const half& a, const half& b) {
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return __hge(a, b);
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}
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#endif
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#if defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator + (const half& a, const half& b) {
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return half(vaddh_f16(a.x, b.x));
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}
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator * (const half& a, const half& b) {
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return half(vmulh_f16(a.x, b.x));
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}
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator - (const half& a, const half& b) {
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return half(vsubh_f16(a.x, b.x));
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}
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator / (const half& a, const half& b) {
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return half(vdivh_f16(a.x, b.x));
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}
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator - (const half& a) {
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return half(vnegh_f16(a.x));
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}
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator += (half& a, const half& b) {
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a = half(vaddh_f16(a.x, b.x));
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return a;
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}
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator *= (half& a, const half& b) {
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a = half(vmulh_f16(a.x, b.x));
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return a;
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}
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator -= (half& a, const half& b) {
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a = half(vsubh_f16(a.x, b.x));
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return a;
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}
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator /= (half& a, const half& b) {
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a = half(vdivh_f16(a.x, b.x));
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return a;
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}
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator == (const half& a, const half& b) {
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return vceqh_f16(a.x, b.x);
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}
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator != (const half& a, const half& b) {
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return !vceqh_f16(a.x, b.x);
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}
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator < (const half& a, const half& b) {
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return vclth_f16(a.x, b.x);
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}
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator <= (const half& a, const half& b) {
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return vcleh_f16(a.x, b.x);
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}
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator > (const half& a, const half& b) {
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return vcgth_f16(a.x, b.x);
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}
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator >= (const half& a, const half& b) {
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return vcgeh_f16(a.x, b.x);
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}
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// We need to distinguish ‘clang as the CUDA compiler’ from ‘clang as the host compiler,
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// invoked by NVCC’ (e.g. on MacOS). The former needs to see both host and device implementation
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// of the functions, while the latter can only deal with one of them.
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#elif !defined(EIGEN_HAS_NATIVE_FP16) || (EIGEN_COMP_CLANG && !EIGEN_COMP_NVCC) // Emulate support for half floats
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#if EIGEN_COMP_CLANG && defined(EIGEN_CUDACC)
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// We need to provide emulated *host-side* FP16 operators for clang.
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#pragma push_macro("EIGEN_DEVICE_FUNC")
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#undef EIGEN_DEVICE_FUNC
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#if defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_HAS_NATIVE_FP16)
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#define EIGEN_DEVICE_FUNC __host__
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#else // both host and device need emulated ops.
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#define EIGEN_DEVICE_FUNC __host__ __device__
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#endif
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#endif
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// Definitions for CPUs and older HIP+CUDA, mostly working through conversion
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// to/from fp32.
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator + (const half& a, const half& b) {
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return half(float(a) + float(b));
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}
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator * (const half& a, const half& b) {
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return half(float(a) * float(b));
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}
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator - (const half& a, const half& b) {
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return half(float(a) - float(b));
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}
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator / (const half& a, const half& b) {
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return half(float(a) / float(b));
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}
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator - (const half& a) {
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half result;
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result.x = a.x ^ 0x8000;
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return result;
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}
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator += (half& a, const half& b) {
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a = half(float(a) + float(b));
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return a;
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}
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator *= (half& a, const half& b) {
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a = half(float(a) * float(b));
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return a;
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}
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator -= (half& a, const half& b) {
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a = half(float(a) - float(b));
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return a;
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}
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half& operator /= (half& a, const half& b) {
|
||
a = half(float(a) / float(b));
|
||
return a;
|
||
}
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator == (const half& a, const half& b) {
|
||
return numext::equal_strict(float(a),float(b));
|
||
}
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator != (const half& a, const half& b) {
|
||
return numext::not_equal_strict(float(a), float(b));
|
||
}
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator < (const half& a, const half& b) {
|
||
return float(a) < float(b);
|
||
}
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator <= (const half& a, const half& b) {
|
||
return float(a) <= float(b);
|
||
}
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator > (const half& a, const half& b) {
|
||
return float(a) > float(b);
|
||
}
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool operator >= (const half& a, const half& b) {
|
||
return float(a) >= float(b);
|
||
}
|
||
|
||
#if defined(__clang__) && defined(__CUDA__)
|
||
#pragma pop_macro("EIGEN_DEVICE_FUNC")
|
||
#endif
|
||
#endif // Emulate support for half floats
|
||
|
||
// Division by an index. Do it in full float precision to avoid accuracy
|
||
// issues in converting the denominator to half.
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half operator / (const half& a, Index b) {
|
||
return half(static_cast<float>(a) / static_cast<float>(b));
|
||
}
|
||
|
||
// Conversion routines, including fallbacks for the host or older CUDA.
|
||
// Note that newer Intel CPUs (Haswell or newer) have vectorized versions of
|
||
// these in hardware. If we need more performance on older/other CPUs, they are
|
||
// also possible to vectorize directly.
|
||
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __half_raw raw_uint16_to_half(numext::uint16_t x) {
|
||
// We cannot simply do a "return __half_raw(x)" here, because __half_raw is union type
|
||
// in the hip_fp16 header file, and that will trigger a compile error
|
||
// On the other hand, having anything but a return statement also triggers a compile error
|
||
// because this is constexpr function.
|
||
// Fortunately, since we need to disable EIGEN_CONSTEXPR for GPU anyway, we can get out
|
||
// of this catch22 by having separate bodies for GPU / non GPU
|
||
#if defined(EIGEN_HAS_GPU_FP16)
|
||
__half_raw h;
|
||
h.x = x;
|
||
return h;
|
||
#else
|
||
return __half_raw(x);
|
||
#endif
|
||
}
|
||
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR numext::uint16_t raw_half_as_uint16(const __half_raw& h) {
|
||
// HIP/CUDA/Default have a member 'x' of type uint16_t.
|
||
// For ARM64 native half, the member 'x' is of type __fp16, so we need to bit-cast.
|
||
// For SYCL, cl::sycl::half is _Float16, so cast directly.
|
||
#if defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)
|
||
return numext::bit_cast<numext::uint16_t>(h.x);
|
||
#elif defined(SYCL_DEVICE_ONLY)
|
||
return numext::bit_cast<numext::uint16_t>(h);
|
||
#else
|
||
return h.x;
|
||
#endif
|
||
}
|
||
|
||
union float32_bits {
|
||
unsigned int u;
|
||
float f;
|
||
};
|
||
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC __half_raw float_to_half_rtne(float ff) {
|
||
#if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 300) || \
|
||
(defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIP_DEVICE_COMPILE))
|
||
__half tmp_ff = __float2half(ff);
|
||
return *(__half_raw*)&tmp_ff;
|
||
|
||
#elif defined(EIGEN_HAS_FP16_C)
|
||
__half_raw h;
|
||
h.x = _cvtss_sh(ff, 0);
|
||
return h;
|
||
|
||
#elif defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)
|
||
__half_raw h;
|
||
h.x = static_cast<__fp16>(ff);
|
||
return h;
|
||
|
||
#else
|
||
float32_bits f; f.f = ff;
|
||
|
||
const float32_bits f32infty = { 255 << 23 };
|
||
const float32_bits f16max = { (127 + 16) << 23 };
|
||
const float32_bits denorm_magic = { ((127 - 15) + (23 - 10) + 1) << 23 };
|
||
unsigned int sign_mask = 0x80000000u;
|
||
__half_raw o;
|
||
o.x = static_cast<numext::uint16_t>(0x0u);
|
||
|
||
unsigned int sign = f.u & sign_mask;
|
||
f.u ^= sign;
|
||
|
||
// NOTE all the integer compares in this function can be safely
|
||
// compiled into signed compares since all operands are below
|
||
// 0x80000000. Important if you want fast straight SSE2 code
|
||
// (since there's no unsigned PCMPGTD).
|
||
|
||
if (f.u >= f16max.u) { // result is Inf or NaN (all exponent bits set)
|
||
o.x = (f.u > f32infty.u) ? 0x7e00 : 0x7c00; // NaN->qNaN and Inf->Inf
|
||
} else { // (De)normalized number or zero
|
||
if (f.u < (113 << 23)) { // resulting FP16 is subnormal or zero
|
||
// use a magic value to align our 10 mantissa bits at the bottom of
|
||
// the float. as long as FP addition is round-to-nearest-even this
|
||
// just works.
|
||
f.f += denorm_magic.f;
|
||
|
||
// and one integer subtract of the bias later, we have our final float!
|
||
o.x = static_cast<numext::uint16_t>(f.u - denorm_magic.u);
|
||
} else {
|
||
unsigned int mant_odd = (f.u >> 13) & 1; // resulting mantissa is odd
|
||
|
||
// update exponent, rounding bias part 1
|
||
// Equivalent to `f.u += ((unsigned int)(15 - 127) << 23) + 0xfff`, but
|
||
// without arithmetic overflow.
|
||
f.u += 0xc8000fffU;
|
||
// rounding bias part 2
|
||
f.u += mant_odd;
|
||
// take the bits!
|
||
o.x = static_cast<numext::uint16_t>(f.u >> 13);
|
||
}
|
||
}
|
||
|
||
o.x |= static_cast<numext::uint16_t>(sign >> 16);
|
||
return o;
|
||
#endif
|
||
}
|
||
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC float half_to_float(__half_raw h) {
|
||
#if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 300) || \
|
||
(defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIP_DEVICE_COMPILE))
|
||
return __half2float(h);
|
||
#elif defined(EIGEN_HAS_FP16_C)
|
||
return _cvtsh_ss(h.x);
|
||
#elif defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)
|
||
return static_cast<float>(h.x);
|
||
#else
|
||
const float32_bits magic = { 113 << 23 };
|
||
const unsigned int shifted_exp = 0x7c00 << 13; // exponent mask after shift
|
||
float32_bits o;
|
||
|
||
o.u = (h.x & 0x7fff) << 13; // exponent/mantissa bits
|
||
unsigned int exp = shifted_exp & o.u; // just the exponent
|
||
o.u += (127 - 15) << 23; // exponent adjust
|
||
|
||
// handle exponent special cases
|
||
if (exp == shifted_exp) { // Inf/NaN?
|
||
o.u += (128 - 16) << 23; // extra exp adjust
|
||
} else if (exp == 0) { // Zero/Denormal?
|
||
o.u += 1 << 23; // extra exp adjust
|
||
o.f -= magic.f; // renormalize
|
||
}
|
||
|
||
o.u |= (h.x & 0x8000) << 16; // sign bit
|
||
return o.f;
|
||
#endif
|
||
}
|
||
|
||
// --- standard functions ---
|
||
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (isinf)(const half& a) {
|
||
#ifdef EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC
|
||
return (numext::bit_cast<numext::uint16_t>(a.x) & 0x7fff) == 0x7c00;
|
||
#else
|
||
return (a.x & 0x7fff) == 0x7c00;
|
||
#endif
|
||
}
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (isnan)(const half& a) {
|
||
#if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 530) || \
|
||
(defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIP_DEVICE_COMPILE))
|
||
return __hisnan(a);
|
||
#elif defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)
|
||
return (numext::bit_cast<numext::uint16_t>(a.x) & 0x7fff) > 0x7c00;
|
||
#else
|
||
return (a.x & 0x7fff) > 0x7c00;
|
||
#endif
|
||
}
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bool (isfinite)(const half& a) {
|
||
return !(isinf EIGEN_NOT_A_MACRO (a)) && !(isnan EIGEN_NOT_A_MACRO (a));
|
||
}
|
||
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half abs(const half& a) {
|
||
#if defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)
|
||
return half(vabsh_f16(a.x));
|
||
#else
|
||
half result;
|
||
result.x = a.x & 0x7FFF;
|
||
return result;
|
||
#endif
|
||
}
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half exp(const half& a) {
|
||
#if (EIGEN_CUDA_SDK_VER >= 80000 && defined EIGEN_CUDA_ARCH && EIGEN_CUDA_ARCH >= 530) || \
|
||
defined(EIGEN_HIP_DEVICE_COMPILE)
|
||
return half(hexp(a));
|
||
#else
|
||
return half(::expf(float(a)));
|
||
#endif
|
||
}
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half expm1(const half& a) {
|
||
return half(numext::expm1(float(a)));
|
||
}
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half log(const half& a) {
|
||
#if (defined(EIGEN_HAS_CUDA_FP16) && EIGEN_CUDA_SDK_VER >= 80000 && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 530) || \
|
||
(defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIP_DEVICE_COMPILE))
|
||
return half(::hlog(a));
|
||
#else
|
||
return half(::logf(float(a)));
|
||
#endif
|
||
}
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half log1p(const half& a) {
|
||
return half(numext::log1p(float(a)));
|
||
}
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half log10(const half& a) {
|
||
return half(::log10f(float(a)));
|
||
}
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half sqrt(const half& a) {
|
||
#if (EIGEN_CUDA_SDK_VER >= 80000 && defined EIGEN_CUDA_ARCH && EIGEN_CUDA_ARCH >= 530) || \
|
||
defined(EIGEN_HIP_DEVICE_COMPILE)
|
||
return half(hsqrt(a));
|
||
#else
|
||
return half(::sqrtf(float(a)));
|
||
#endif
|
||
}
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half pow(const half& a, const half& b) {
|
||
return half(::powf(float(a), float(b)));
|
||
}
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half sin(const half& a) {
|
||
return half(::sinf(float(a)));
|
||
}
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half cos(const half& a) {
|
||
return half(::cosf(float(a)));
|
||
}
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half tan(const half& a) {
|
||
return half(::tanf(float(a)));
|
||
}
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half tanh(const half& a) {
|
||
return half(::tanhf(float(a)));
|
||
}
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half asin(const half& a) {
|
||
return half(::asinf(float(a)));
|
||
}
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half acos(const half& a) {
|
||
return half(::acosf(float(a)));
|
||
}
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half floor(const half& a) {
|
||
#if (EIGEN_CUDA_SDK_VER >= 80000 && defined EIGEN_CUDA_ARCH && EIGEN_CUDA_ARCH >= 300) || \
|
||
defined(EIGEN_HIP_DEVICE_COMPILE)
|
||
return half(hfloor(a));
|
||
#else
|
||
return half(::floorf(float(a)));
|
||
#endif
|
||
}
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half rint(const half& a) {
|
||
return half(::rintf(float(a)));
|
||
}
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half ceil(const half& a) {
|
||
#if (EIGEN_CUDA_SDK_VER >= 80000 && defined EIGEN_CUDA_ARCH && EIGEN_CUDA_ARCH >= 300) || \
|
||
defined(EIGEN_HIP_DEVICE_COMPILE)
|
||
return half(hceil(a));
|
||
#else
|
||
return half(::ceilf(float(a)));
|
||
#endif
|
||
}
|
||
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half (min)(const half& a, const half& b) {
|
||
#if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 530) || \
|
||
(defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIP_DEVICE_COMPILE))
|
||
return __hlt(b, a) ? b : a;
|
||
#else
|
||
const float f1 = static_cast<float>(a);
|
||
const float f2 = static_cast<float>(b);
|
||
return f2 < f1 ? b : a;
|
||
#endif
|
||
}
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC half (max)(const half& a, const half& b) {
|
||
#if (defined(EIGEN_HAS_CUDA_FP16) && defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 530) || \
|
||
(defined(EIGEN_HAS_HIP_FP16) && defined(EIGEN_HIP_DEVICE_COMPILE))
|
||
return __hlt(a, b) ? b : a;
|
||
#else
|
||
const float f1 = static_cast<float>(a);
|
||
const float f2 = static_cast<float>(b);
|
||
return f1 < f2 ? b : a;
|
||
#endif
|
||
}
|
||
|
||
#ifndef EIGEN_NO_IO
|
||
EIGEN_ALWAYS_INLINE std::ostream& operator << (std::ostream& os, const half& v) {
|
||
os << static_cast<float>(v);
|
||
return os;
|
||
}
|
||
#endif
|
||
|
||
} // end namespace half_impl
|
||
|
||
// import Eigen::half_impl::half into Eigen namespace
|
||
// using half_impl::half;
|
||
|
||
namespace internal {
|
||
|
||
template<>
|
||
struct random_default_impl<half, false, false>
|
||
{
|
||
static inline half run(const half& x, const half& y)
|
||
{
|
||
return x + (y-x) * half(float(std::rand()) / float(RAND_MAX));
|
||
}
|
||
static inline half run()
|
||
{
|
||
return run(half(-1.f), half(1.f));
|
||
}
|
||
};
|
||
|
||
template<> struct is_arithmetic<half> { enum { value = true }; };
|
||
|
||
} // end namespace internal
|
||
|
||
template<> struct NumTraits<Eigen::half>
|
||
: GenericNumTraits<Eigen::half>
|
||
{
|
||
enum {
|
||
IsSigned = true,
|
||
IsInteger = false,
|
||
IsComplex = false,
|
||
RequireInitialization = false
|
||
};
|
||
|
||
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static EIGEN_STRONG_INLINE Eigen::half epsilon() {
|
||
return half_impl::raw_uint16_to_half(0x0800);
|
||
}
|
||
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static EIGEN_STRONG_INLINE Eigen::half dummy_precision() {
|
||
return half_impl::raw_uint16_to_half(0x211f); // Eigen::half(1e-2f);
|
||
}
|
||
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static EIGEN_STRONG_INLINE Eigen::half highest() {
|
||
return half_impl::raw_uint16_to_half(0x7bff);
|
||
}
|
||
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static EIGEN_STRONG_INLINE Eigen::half lowest() {
|
||
return half_impl::raw_uint16_to_half(0xfbff);
|
||
}
|
||
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static EIGEN_STRONG_INLINE Eigen::half infinity() {
|
||
return half_impl::raw_uint16_to_half(0x7c00);
|
||
}
|
||
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static EIGEN_STRONG_INLINE Eigen::half quiet_NaN() {
|
||
return half_impl::raw_uint16_to_half(0x7e00);
|
||
}
|
||
};
|
||
|
||
} // end namespace Eigen
|
||
|
||
#if defined(EIGEN_HAS_GPU_FP16) || defined(EIGEN_HAS_ARM64_FP16_SCALAR_ARITHMETIC)
|
||
#pragma pop_macro("EIGEN_CONSTEXPR")
|
||
#endif
|
||
|
||
namespace std {
|
||
|
||
#if __cplusplus > 199711L
|
||
template <>
|
||
struct hash<Eigen::half> {
|
||
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE std::size_t operator()(const Eigen::half& a) const {
|
||
return static_cast<std::size_t>(a.x);
|
||
}
|
||
};
|
||
#endif
|
||
|
||
} // end namespace std
|
||
|
||
// Add the missing shfl_xor intrinsic
|
||
#if (defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 300) || \
|
||
defined(EIGEN_HIPCC)
|
||
|
||
__device__ EIGEN_STRONG_INLINE Eigen::half __shfl_xor(Eigen::half var, int laneMask, int width=warpSize) {
|
||
#if (EIGEN_CUDA_SDK_VER < 90000) || \
|
||
defined(EIGEN_HAS_HIP_FP16)
|
||
return static_cast<Eigen::half>(__shfl_xor(static_cast<float>(var), laneMask, width));
|
||
#else
|
||
return static_cast<Eigen::half>(__shfl_xor_sync(0xFFFFFFFF, static_cast<float>(var), laneMask, width));
|
||
#endif
|
||
}
|
||
#endif
|
||
|
||
// ldg() has an overload for __half_raw, but we also need one for Eigen::half.
|
||
#if (defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 350) || defined(EIGEN_HIPCC)
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half __ldg(const Eigen::half* ptr) {
|
||
return Eigen::half_impl::raw_uint16_to_half(__ldg(reinterpret_cast<const Eigen::numext::uint16_t*>(ptr)));
|
||
}
|
||
#endif
|
||
|
||
namespace Eigen {
|
||
namespace numext {
|
||
|
||
#if defined(EIGEN_GPU_COMPILE_PHASE)
|
||
|
||
template <>
|
||
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool(isnan)(const Eigen::half& h) {
|
||
return (half_impl::isnan)(h);
|
||
}
|
||
|
||
template <>
|
||
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool(isinf)(const Eigen::half& h) {
|
||
return (half_impl::isinf)(h);
|
||
}
|
||
|
||
template <>
|
||
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE bool(isfinite)(const Eigen::half& h) {
|
||
return (half_impl::isfinite)(h);
|
||
}
|
||
|
||
#endif
|
||
|
||
template <>
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bit_cast<Eigen::half, uint16_t>(const uint16_t& src) {
|
||
return Eigen::half(Eigen::half_impl::raw_uint16_to_half(src));
|
||
}
|
||
|
||
template <>
|
||
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC uint16_t bit_cast<uint16_t, Eigen::half>(const Eigen::half& src) {
|
||
return Eigen::half_impl::raw_half_as_uint16(src);
|
||
}
|
||
|
||
} // namespace numext
|
||
} // namespace Eigen
|
||
|
||
#endif // EIGEN_HALF_H
|