eigen

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Rasmus Munk Larsen a566074480 Improve accuracy of fast approximate tanh and the logistic functions in Eigen, such that they preserve relative accuracy to within a few ULPs where their function values tend to zero (around x=0 for tanh, and for large negative x for the logistic function).

This change re-instates the fast rational approximation of the logistic function for float32 in Eigen (removed in 66f07efeae), but uses the more accurate approximation 1/(1+exp(-1)) ~= exp(x) below -9. The exponential is only calculated on the vectorized path if at least one element in the SIMD input vector is less than -9.

This change also contains a few improvements to speed up the original float specialization of logistic:
  - Introduce EIGEN_PREDICT_{FALSE,TRUE} for __builtin_predict and use it to predict that the logistic-only path is most likely (~2-3% speedup for the common case).
  - Carefully set the upper clipping point to the smallest x where the approximation evaluates to exactly 1. This saves the explicit clamping of the output (~7% speedup).

The increased accuracy for tanh comes at a cost of 10-20% depending on instruction set.

The benchmarks below repeated calls

   u = v.logistic()  (u = v.tanh(), respectively)

where u and v are of type Eigen::ArrayXf, have length 8k, and v contains random numbers in [-1,1].

Benchmark numbers for logistic:

Before:
Benchmark                  Time(ns)        CPU(ns)     Iterations
-----------------------------------------------------------------
SSE
BM_eigen_logistic_float        4467           4468         155835  model_time: 4827
AVX
BM_eigen_logistic_float        2347           2347         299135  model_time: 2926
AVX+FMA
BM_eigen_logistic_float        1467           1467         476143  model_time: 2926
AVX512
BM_eigen_logistic_float         805            805         858696  model_time: 1463

After:
Benchmark                  Time(ns)        CPU(ns)     Iterations
-----------------------------------------------------------------
SSE
BM_eigen_logistic_float        2589           2590         270264  model_time: 4827
AVX
BM_eigen_logistic_float        1428           1428         489265  model_time: 2926
AVX+FMA
BM_eigen_logistic_float        1059           1059         662255  model_time: 2926
AVX512
BM_eigen_logistic_float         673            673        1000000  model_time: 1463

Benchmark numbers for tanh:

Before:
Benchmark                  Time(ns)        CPU(ns)     Iterations
-----------------------------------------------------------------
SSE
BM_eigen_tanh_float        2391           2391         292624  model_time: 4242
AVX
BM_eigen_tanh_float        1256           1256         554662  model_time: 2633
AVX+FMA
BM_eigen_tanh_float         823            823         866267  model_time: 1609
AVX512
BM_eigen_tanh_float         443            443        1578999  model_time: 805

After:
Benchmark                  Time(ns)        CPU(ns)     Iterations
-----------------------------------------------------------------
SSE
BM_eigen_tanh_float        2588           2588         273531  model_time: 4242
AVX
BM_eigen_tanh_float        1536           1536         452321  model_time: 2633
AVX+FMA
BM_eigen_tanh_float        1007           1007         694681  model_time: 1609
AVX512
BM_eigen_tanh_float         471            471        1472178  model_time: 805

2019-12-16 21:33:42 +00:00

bench

update hg to git hashes

2019-12-05 16:33:24 +01:00

blas

STYLE: Remove CMake-language block-end command arguments

2019-10-31 11:36:27 -05:00

cmake

[SYCL] Rebasing the SYCL support branch on top of the Einge upstream master branch.

2019-11-28 10:08:54 +00:00

debug

MIsc. source and comment typos