diff options
author | Rasmus Munk Larsen <rmlarsen@google.com> | 2016-10-04 14:22:56 -0700 |
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committer | Rasmus Munk Larsen <rmlarsen@google.com> | 2016-10-04 14:22:56 -0700 |
commit | 3ed67cb0bb4af65fbf243df598604a8c7630bf7d (patch) | |
tree | 02c61529c1a3edab6c9894f271100a7488cd7cdc /Eigen/src/Core/arch/SSE/MathFunctions.h | |
parent | 6af5ac7e2749bdea7a31323855ef3b4333b91c3e (diff) |
Fix a bug in the implementation of Carmack's fast sqrt algorithm in Eigen (enabled by EIGEN_FAST_MATH), which causes the vectorized parts of the computation to return -0.0 instead of NaN for negative arguments.
Benchmark speed in Giga-sqrts/s
Intel(R) Xeon(R) CPU E5-1650 v3 @ 3.50GHz
-----------------------------------------
SSE AVX
Fast=1 2.529G 4.380G
Fast=0 1.944G 1.898G
Fast=1 fixed 2.214G 3.739G
This table illustrates the worst case in terms speed impact: It was measured by repeatedly computing the sqrt of an n=4096 float vector that fits in L1 cache. For large vectors the operation becomes memory bound and the differences between the different versions almost negligible.
Diffstat (limited to 'Eigen/src/Core/arch/SSE/MathFunctions.h')
-rw-r--r-- | Eigen/src/Core/arch/SSE/MathFunctions.h | 19 |
1 files changed, 11 insertions, 8 deletions
diff --git a/Eigen/src/Core/arch/SSE/MathFunctions.h b/Eigen/src/Core/arch/SSE/MathFunctions.h index ac2fd8103..2c34a869d 100644 --- a/Eigen/src/Core/arch/SSE/MathFunctions.h +++ b/Eigen/src/Core/arch/SSE/MathFunctions.h @@ -32,7 +32,7 @@ Packet4f plog<Packet4f>(const Packet4f& _x) /* the smallest non denormalized float number */ _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos, 0x00800000); _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_inf, 0xff800000);//-1.f/0.f); - + /* natural logarithm computed for 4 simultaneous float return NaN for x <= 0 */ @@ -451,18 +451,21 @@ template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f psqrt<Packet4f>(const Packet4f& _x) { Packet4f half = pmul(_x, pset1<Packet4f>(.5f)); + Packet4f denormal_mask = _mm_and_ps( + _mm_cmpge_ps(_x, _mm_setzero_ps()), + _mm_cmplt_ps(_x, pset1<Packet4f>((std::numeric_limits<float>::min)()))); - /* select only the inverse sqrt of non-zero inputs */ - Packet4f non_zero_mask = _mm_cmpge_ps(_x, pset1<Packet4f>((std::numeric_limits<float>::min)())); - Packet4f x = _mm_and_ps(non_zero_mask, _mm_rsqrt_ps(_x)); - + // Compute approximate reciprocal sqrt. + Packet4f x = _mm_rsqrt_ps(_x); + // Do a single step of Newton's iteration. x = pmul(x, psub(pset1<Packet4f>(1.5f), pmul(half, pmul(x,x)))); - return pmul(_x,x); + // Flush results for denormals to zero. + return _mm_andnot_ps(denormal_mask, pmul(_x,x)); } #else -template<>EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED +template<>EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f psqrt<Packet4f>(const Packet4f& x) { return _mm_sqrt_ps(x); } #endif @@ -491,7 +494,7 @@ Packet4f prsqrt<Packet4f>(const Packet4f& _x) { Packet4f neg_mask = _mm_cmplt_ps(_x, _mm_setzero_ps()); Packet4f zero_mask = _mm_andnot_ps(neg_mask, le_zero_mask); Packet4f infs_and_nans = _mm_or_ps(_mm_and_ps(neg_mask, p4f_nan), - _mm_and_ps(zero_mask, p4f_inf)); + _mm_and_ps(zero_mask, p4f_inf)); // Do a single step of Newton's iteration. x = pmul(x, pmadd(neg_half, pmul(x, x), p4f_one_point_five)); |