diff options
Diffstat (limited to 'Eigen/src/Core/arch/SSE/MathFunctions.h')
-rw-r--r-- | Eigen/src/Core/arch/SSE/MathFunctions.h | 28 |
1 files changed, 18 insertions, 10 deletions
diff --git a/Eigen/src/Core/arch/SSE/MathFunctions.h b/Eigen/src/Core/arch/SSE/MathFunctions.h index ac2fd8103..7b5f948e1 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 */ @@ -444,25 +444,33 @@ Packet4f pcos<Packet4f>(const Packet4f& _x) #if EIGEN_FAST_MATH -// This is based on Quake3's fast inverse square root. +// Functions for sqrt. +// The EIGEN_FAST_MATH version uses the _mm_rsqrt_ps approximation and one step +// of Newton's method, at a cost of 1-2 bits of precision as opposed to the +// exact solution. It does not handle +inf, or denormalized numbers correctly. +// The main advantage of this approach is not just speed, but also the fact that +// it can be inlined and pipelined with other computations, further reducing its +// effective latency. This is similar to Quake3's fast inverse square root. // For detail see here: http://www.beyond3d.com/content/articles/8/ -// It lacks 1 (or 2 bits in some rare cases) of precision, and does not handle negative, +inf, or denormalized numbers correctly. 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 +499,7 @@ 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)); |