diff options
Diffstat (limited to 'Eigen/src/Core/arch/SSE/MathFunctions.h')
| -rw-r--r-- | Eigen/src/Core/arch/SSE/MathFunctions.h | 101 |
1 files changed, 96 insertions, 5 deletions
diff --git a/Eigen/src/Core/arch/SSE/MathFunctions.h b/Eigen/src/Core/arch/SSE/MathFunctions.h index 3f41a4e26..99cbd0d95 100644 --- a/Eigen/src/Core/arch/SSE/MathFunctions.h +++ b/Eigen/src/Core/arch/SSE/MathFunctions.h @@ -31,7 +31,8 @@ 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 */ @@ -51,7 +52,8 @@ Packet4f plog<Packet4f>(const Packet4f& _x) Packet4i emm0; - Packet4f invalid_mask = _mm_cmple_ps(x, _mm_setzero_ps()); + Packet4f invalid_mask = _mm_cmplt_ps(x, _mm_setzero_ps()); + Packet4f iszero_mask = _mm_cmpeq_ps(x, _mm_setzero_ps()); x = pmax(x, p4f_min_norm_pos); /* cut off denormalized stuff */ emm0 = _mm_srli_epi32(_mm_castps_si128(x), 23); @@ -96,7 +98,9 @@ Packet4f plog<Packet4f>(const Packet4f& _x) y2 = pmul(e, p4f_cephes_log_q2); x = padd(x, y); x = padd(x, y2); - return _mm_or_ps(x, invalid_mask); // negative arg will be NAN + // negative arg will be NAN, 0 will be -INF + return _mm_or_ps(_mm_andnot_ps(iszero_mask, _mm_or_ps(x, invalid_mask)), + _mm_and_ps(iszero_mask, p4f_minus_inf)); } template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED @@ -131,13 +135,16 @@ Packet4f pexp<Packet4f>(const Packet4f& _x) /* express exp(x) as exp(g + n*log(2)) */ fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half); - /* how to perform a floorf with SSE: just below */ +#ifdef EIGEN_VECTORIZE_SSE4_1 + fx = _mm_floor_ps(fx); +#else emm0 = _mm_cvttps_epi32(fx); tmp = _mm_cvtepi32_ps(emm0); /* if greater, substract 1 */ Packet4f mask = _mm_cmpgt_ps(tmp, fx); mask = _mm_and_ps(mask, p4f_1); fx = psub(tmp, mask); +#endif tmp = pmul(fx, p4f_cephes_exp_C1); Packet4f z = pmul(fx, p4f_cephes_exp_C2); @@ -161,6 +168,79 @@ Packet4f pexp<Packet4f>(const Packet4f& _x) emm0 = _mm_slli_epi32(emm0, 23); return pmul(y, _mm_castsi128_ps(emm0)); } +template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED +Packet2d pexp<Packet2d>(const Packet2d& _x) +{ + Packet2d x = _x; + + _EIGEN_DECLARE_CONST_Packet2d(1 , 1.0); + _EIGEN_DECLARE_CONST_Packet2d(2 , 2.0); + _EIGEN_DECLARE_CONST_Packet2d(half, 0.5); + + _EIGEN_DECLARE_CONST_Packet2d(exp_hi, 709.437); + _EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303); + + _EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599); + + _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4); + _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2); + _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1); + + _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6); + _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3); + _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1); + _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0); + + _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125); + _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6); + static const __m128i p4i_1023_0 = _mm_setr_epi32(1023, 1023, 0, 0); + + Packet2d tmp = _mm_setzero_pd(), fx; + Packet4i emm0; + + // clamp x + x = pmax(pmin(x, p2d_exp_hi), p2d_exp_lo); + /* express exp(x) as exp(g + n*log(2)) */ + fx = pmadd(p2d_cephes_LOG2EF, x, p2d_half); + +#ifdef EIGEN_VECTORIZE_SSE4_1 + fx = _mm_floor_pd(fx); +#else + emm0 = _mm_cvttpd_epi32(fx); + tmp = _mm_cvtepi32_pd(emm0); + /* if greater, substract 1 */ + Packet2d mask = _mm_cmpgt_pd(tmp, fx); + mask = _mm_and_pd(mask, p2d_1); + fx = psub(tmp, mask); +#endif + + tmp = pmul(fx, p2d_cephes_exp_C1); + Packet2d z = pmul(fx, p2d_cephes_exp_C2); + x = psub(x, tmp); + x = psub(x, z); + + Packet2d x2 = pmul(x,x); + + Packet2d px = p2d_cephes_exp_p0; + px = pmadd(px, x2, p2d_cephes_exp_p1); + px = pmadd(px, x2, p2d_cephes_exp_p2); + px = pmul (px, x); + + Packet2d qx = p2d_cephes_exp_q0; + qx = pmadd(qx, x2, p2d_cephes_exp_q1); + qx = pmadd(qx, x2, p2d_cephes_exp_q2); + qx = pmadd(qx, x2, p2d_cephes_exp_q3); + + x = pdiv(px,psub(qx,px)); + x = pmadd(p2d_2,x,p2d_1); + + // build 2^n + emm0 = _mm_cvttpd_epi32(fx); + emm0 = _mm_add_epi32(emm0, p4i_1023_0); + emm0 = _mm_slli_epi32(emm0, 20); + emm0 = _mm_shuffle_epi32(emm0, _MM_SHUFFLE(1,2,0,3)); + return pmul(x, _mm_castsi128_pd(emm0)); +} /* evaluation of 4 sines at onces, using SSE2 intrinsics. @@ -362,21 +442,32 @@ Packet4f pcos<Packet4f>(const Packet4f& _x) return _mm_xor_ps(y, sign_bit); } +#if EIGEN_FAST_MATH + // This is based on 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)); /* select only the inverse sqrt of non-zero inputs */ - Packet4f non_zero_mask = _mm_cmpgt_ps(_x, pset1<Packet4f>(std::numeric_limits<float>::epsilon())); + 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)); x = pmul(x, psub(pset1<Packet4f>(1.5f), pmul(half, pmul(x,x)))); return pmul(_x,x); } +#else + +template<> EIGEN_STRONG_INLINE Packet4f psqrt<Packet4f>(const Packet4f& x) { return _mm_sqrt_ps(x); } + +#endif + +template<> EIGEN_STRONG_INLINE Packet2d psqrt<Packet2d>(const Packet2d& x) { return _mm_sqrt_pd(x); } + } // end namespace internal } // end namespace Eigen |