From 05754100fecf00e13b2a5799e31570a980e4dd72 Mon Sep 17 00:00:00 2001 From: Rasmus Munk Larsen Date: Wed, 16 Dec 2020 18:16:11 +0000 Subject: * Add iterative psqrt for AVX and SSE when FMA is available. This provides a ~10% speedup. * Write iterative sqrt explicitly in terms of pmadd. This gives up to 7% speedup for psqrt with AVX & SSE with FMA. * Remove iterative psqrt for NEON, because the initial rsqrt apprimation is not accurate enough for convergence in 2 Newton-Raphson steps and with 3 steps, just calling the builtin sqrt insn is faster. MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit The following benchmarks were compiled with clang "-O2 -fast-math -mfma" and with and without -mavx. AVX+FMA (float) name old cpu/op new cpu/op delta BM_eigen_sqrt_float/1 1.08ns ± 0% 1.09ns ± 1% ~ BM_eigen_sqrt_float/8 2.07ns ± 0% 2.08ns ± 1% ~ BM_eigen_sqrt_float/64 12.4ns ± 0% 12.4ns ± 1% ~ BM_eigen_sqrt_float/512 95.7ns ± 0% 95.5ns ± 0% ~ BM_eigen_sqrt_float/4k 776ns ± 0% 763ns ± 0% -1.67% BM_eigen_sqrt_float/32k 6.57µs ± 1% 6.13µs ± 0% -6.69% BM_eigen_sqrt_float/256k 83.7µs ± 3% 83.3µs ± 2% ~ BM_eigen_sqrt_float/1M 335µs ± 2% 332µs ± 2% ~ SSE+FMA (float) name old cpu/op new cpu/op delta BM_eigen_sqrt_float/1 1.08ns ± 0% 1.09ns ± 0% ~ BM_eigen_sqrt_float/8 2.07ns ± 0% 2.06ns ± 0% ~ BM_eigen_sqrt_float/64 12.4ns ± 0% 12.4ns ± 1% ~ BM_eigen_sqrt_float/512 95.7ns ± 0% 96.3ns ± 4% ~ BM_eigen_sqrt_float/4k 774ns ± 0% 763ns ± 0% -1.50% BM_eigen_sqrt_float/32k 6.58µs ± 2% 6.11µs ± 0% -7.06% BM_eigen_sqrt_float/256k 82.7µs ± 1% 82.6µs ± 1% ~ BM_eigen_sqrt_float/1M 330µs ± 1% 329µs ± 2% ~ SSE+FMA (double) BM_eigen_sqrt_double/1 1.63ns ± 0% 1.63ns ± 0% ~ BM_eigen_sqrt_double/8 6.51ns ± 0% 6.08ns ± 0% -6.68% BM_eigen_sqrt_double/64 52.1ns ± 0% 46.5ns ± 1% -10.65% BM_eigen_sqrt_double/512 417ns ± 0% 374ns ± 1% -10.29% BM_eigen_sqrt_double/4k 3.33µs ± 0% 2.97µs ± 1% -11.00% BM_eigen_sqrt_double/32k 26.7µs ± 0% 23.7µs ± 0% -11.07% BM_eigen_sqrt_double/256k 213µs ± 0% 206µs ± 1% -3.31% BM_eigen_sqrt_double/1M 862µs ± 0% 870µs ± 2% +0.96% AVX+FMA (double) name old cpu/op new cpu/op delta BM_eigen_sqrt_double/1 1.63ns ± 0% 1.63ns ± 0% ~ BM_eigen_sqrt_double/8 6.51ns ± 0% 6.06ns ± 0% -6.95% BM_eigen_sqrt_double/64 52.1ns ± 0% 46.5ns ± 1% -10.80% BM_eigen_sqrt_double/512 417ns ± 0% 373ns ± 1% -10.59% BM_eigen_sqrt_double/4k 3.33µs ± 0% 2.97µs ± 1% -10.79% BM_eigen_sqrt_double/32k 26.7µs ± 0% 23.8µs ± 0% -10.94% BM_eigen_sqrt_double/256k 214µs ± 0% 208µs ± 2% -2.76% BM_eigen_sqrt_double/1M 866µs ± 3% 923µs ± 7% ~ --- Eigen/src/Core/arch/SSE/MathFunctions.h | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) (limited to 'Eigen/src/Core/arch/SSE') diff --git a/Eigen/src/Core/arch/SSE/MathFunctions.h b/Eigen/src/Core/arch/SSE/MathFunctions.h index 2d7df2f7b..9f66d8ab3 100644 --- a/Eigen/src/Core/arch/SSE/MathFunctions.h +++ b/Eigen/src/Core/arch/SSE/MathFunctions.h @@ -86,17 +86,17 @@ Packet4f pcos(const Packet4f& _x) template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f psqrt(const Packet4f& _x) { - Packet4f half = pmul(_x, pset1(.5f)); - Packet4f denormal_mask = _mm_and_ps( - _mm_cmpge_ps(_x, _mm_setzero_ps()), - _mm_cmplt_ps(_x, pset1((std::numeric_limits::min)()))); + Packet4f minus_half_x = pmul(_x, pset1(-0.5f)); + Packet4f denormal_mask = pandnot( + pcmp_lt(_x, pset1((std::numeric_limits::min)())), + pcmp_lt(_x, pzero(_x))); // Compute approximate reciprocal sqrt. Packet4f x = _mm_rsqrt_ps(_x); // Do a single step of Newton's iteration. - x = pmul(x, psub(pset1(1.5f), pmul(half, pmul(x,x)))); + x = pmul(x, pmadd(minus_half_x, pmul(x,x), pset1(1.5f))); // Flush results for denormals to zero. - return _mm_andnot_ps(denormal_mask, pmul(_x,x)); + return pandnot(pmul(_x,x), denormal_mask); } #else -- cgit v1.2.3