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
- 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
Depending on instruction set, significant speedups are observed for the vectorized path:
log1p wall time is reduced 60-93% (2.5x - 15x speedup)
expm1 wall time is reduced 0-85% (1x - 7x speedup)
The scalar path is slower by 20-30% due to the extra branch needed to handle +infinity correctly.
Full benchmarks measured on Intel(R) Xeon(R) Gold 6154 here: https://bitbucket.org/snippets/rmlarsen/MXBkpM
1. Fix buggy pcmp_eq and unit test for half types.
2. Add unit test for pselect and add specializations for SSE 4.1, AVX512, and half types.
3. Get rid of FIXME: Implement faster pnegate for half by XOR'ing with a sign bit mask.
* Allow specifying multiple GPU architectures. E.g.:
cmake -DEIGEN_CUDA_COMPUTE_ARCH="60;70"
* Pass CUDA SDK path to clang. Without it it will default to /usr/local/cuda
which may not be the right location, if cmake was invoked with
-DCUDA_TOOLKIT_ROOT_DIR=/some/other/CUDA/path