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Diffstat (limited to 'third_party/eigen3/Eigen/src/Core/arch/SSE/MathFunctions.h')
| -rw-r--r-- | third_party/eigen3/Eigen/src/Core/arch/SSE/MathFunctions.h | 529 |
1 files changed, 529 insertions, 0 deletions
diff --git a/third_party/eigen3/Eigen/src/Core/arch/SSE/MathFunctions.h b/third_party/eigen3/Eigen/src/Core/arch/SSE/MathFunctions.h new file mode 100644 index 0000000000..0baa7b4b58 --- /dev/null +++ b/third_party/eigen3/Eigen/src/Core/arch/SSE/MathFunctions.h @@ -0,0 +1,529 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2007 Julien Pommier +// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +/* The sin, cos, exp, and log functions of this file come from + * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/ + */ + +#ifndef EIGEN_MATH_FUNCTIONS_SSE_H +#define EIGEN_MATH_FUNCTIONS_SSE_H + +namespace Eigen { + +namespace internal { + +template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED +Packet4f plog<Packet4f>(const Packet4f& _x) +{ + Packet4f x = _x; + _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f); + _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f); + _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f); + + _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000); + + /* 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 + */ + _EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f); + _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f); + _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f); + _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f); + _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f); + _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f); + _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f); + _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f); + _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f); + _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f); + _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f); + _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f); + + + Packet4i emm0; + + // invalid_mask is set to true when x is NaN + Packet4f invalid_mask = _mm_cmpnge_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); + + /* keep only the fractional part */ + x = _mm_and_ps(x, p4f_inv_mant_mask); + x = _mm_or_ps(x, p4f_half); + + emm0 = _mm_sub_epi32(emm0, p4i_0x7f); + Packet4f e = padd(Packet4f(_mm_cvtepi32_ps(emm0)), p4f_1); + + /* part2: + if( x < SQRTHF ) { + e -= 1; + x = x + x - 1.0; + } else { x = x - 1.0; } + */ + Packet4f mask = _mm_cmplt_ps(x, p4f_cephes_SQRTHF); + Packet4f tmp = pand(x, mask); + x = psub(x, p4f_1); + e = psub(e, pand(p4f_1, mask)); + x = padd(x, tmp); + + Packet4f x2 = pmul(x,x); + Packet4f x3 = pmul(x2,x); + + Packet4f y, y1, y2; + y = pmadd(p4f_cephes_log_p0, x, p4f_cephes_log_p1); + y1 = pmadd(p4f_cephes_log_p3, x, p4f_cephes_log_p4); + y2 = pmadd(p4f_cephes_log_p6, x, p4f_cephes_log_p7); + y = pmadd(y , x, p4f_cephes_log_p2); + y1 = pmadd(y1, x, p4f_cephes_log_p5); + y2 = pmadd(y2, x, p4f_cephes_log_p8); + y = pmadd(y, x3, y1); + y = pmadd(y, x3, y2); + y = pmul(y, x3); + + y1 = pmul(e, p4f_cephes_log_q1); + tmp = pmul(x2, p4f_half); + y = padd(y, y1); + x = psub(x, tmp); + y2 = pmul(e, p4f_cephes_log_q2); + x = padd(x, y); + x = padd(x, y2); + // 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 +Packet4f pexp<Packet4f>(const Packet4f& _x) +{ + Packet4f x = _x; + _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f); + _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f); + _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f); + + + _EIGEN_DECLARE_CONST_Packet4f(exp_hi, 88.3762626647950f); + _EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f); + + _EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f); + _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f); + _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f); + + _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f); + _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f); + _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f); + _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f); + _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f); + _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f); + + Packet4f tmp, fx; + Packet4i emm0; + + // clamp x + x = pmax(pmin(x, p4f_exp_hi), p4f_exp_lo); + + /* express exp(x) as exp(g + n*log(2)) */ + fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half); + +#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); + x = psub(x, tmp); + x = psub(x, z); + + z = pmul(x,x); + + Packet4f y = p4f_cephes_exp_p0; + y = pmadd(y, x, p4f_cephes_exp_p1); + y = pmadd(y, x, p4f_cephes_exp_p2); + y = pmadd(y, x, p4f_cephes_exp_p3); + y = pmadd(y, x, p4f_cephes_exp_p4); + y = pmadd(y, x, p4f_cephes_exp_p5); + y = pmadd(y, z, x); + y = padd(y, p4f_1); + + // build 2^n + emm0 = _mm_cvttps_epi32(fx); + emm0 = _mm_add_epi32(emm0, p4i_0x7f); + emm0 = _mm_slli_epi32(emm0, 23); + return pmax(pmul(y, Packet4f(_mm_castsi128_ps(emm0))), _x); +} +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, 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 pmax(pmul(x, Packet2d(_mm_castsi128_pd(emm0))), _x); +} + +/* evaluation of 4 sines at onces, using SSE2 intrinsics. + + The code is the exact rewriting of the cephes sinf function. + Precision is excellent as long as x < 8192 (I did not bother to + take into account the special handling they have for greater values + -- it does not return garbage for arguments over 8192, though, but + the extra precision is missing). + + Note that it is such that sinf((float)M_PI) = 8.74e-8, which is the + surprising but correct result. +*/ + +template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED +Packet4f psin<Packet4f>(const Packet4f& _x) +{ + Packet4f x = _x; + _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f); + _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f); + + _EIGEN_DECLARE_CONST_Packet4i(1, 1); + _EIGEN_DECLARE_CONST_Packet4i(not1, ~1); + _EIGEN_DECLARE_CONST_Packet4i(2, 2); + _EIGEN_DECLARE_CONST_Packet4i(4, 4); + + _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(sign_mask, 0x80000000); + + _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f); + _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f); + _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f); + _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f); + _EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736E-3f); + _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f); + _EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948E-005f); + _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f); + _EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827E-002f); + _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f); // 4 / M_PI + + Packet4f xmm1, xmm2, xmm3, sign_bit, y; + + Packet4i emm0, emm2; + sign_bit = x; + /* take the absolute value */ + x = pabs(x); + + /* take the modulo */ + + /* extract the sign bit (upper one) */ + sign_bit = _mm_and_ps(sign_bit, p4f_sign_mask); + + /* scale by 4/Pi */ + y = pmul(x, p4f_cephes_FOPI); + + /* store the integer part of y in mm0 */ + emm2 = _mm_cvttps_epi32(y); + /* j=(j+1) & (~1) (see the cephes sources) */ + emm2 = _mm_add_epi32(emm2, p4i_1); + emm2 = _mm_and_si128(emm2, p4i_not1); + y = _mm_cvtepi32_ps(emm2); + /* get the swap sign flag */ + emm0 = _mm_and_si128(emm2, p4i_4); + emm0 = _mm_slli_epi32(emm0, 29); + /* get the polynom selection mask + there is one polynom for 0 <= x <= Pi/4 + and another one for Pi/4<x<=Pi/2 + + Both branches will be computed. + */ + emm2 = _mm_and_si128(emm2, p4i_2); + emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128()); + + Packet4f swap_sign_bit = _mm_castsi128_ps(emm0); + Packet4f poly_mask = _mm_castsi128_ps(emm2); + sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit); + + /* The magic pass: "Extended precision modular arithmetic" + x = ((x - y * DP1) - y * DP2) - y * DP3; */ + xmm1 = pmul(y, p4f_minus_cephes_DP1); + xmm2 = pmul(y, p4f_minus_cephes_DP2); + xmm3 = pmul(y, p4f_minus_cephes_DP3); + x = padd(x, xmm1); + x = padd(x, xmm2); + x = padd(x, xmm3); + + /* Evaluate the first polynom (0 <= x <= Pi/4) */ + y = p4f_coscof_p0; + Packet4f z = _mm_mul_ps(x,x); + + y = pmadd(y, z, p4f_coscof_p1); + y = pmadd(y, z, p4f_coscof_p2); + y = pmul(y, z); + y = pmul(y, z); + Packet4f tmp = pmul(z, p4f_half); + y = psub(y, tmp); + y = padd(y, p4f_1); + + /* Evaluate the second polynom (Pi/4 <= x <= 0) */ + + Packet4f y2 = p4f_sincof_p0; + y2 = pmadd(y2, z, p4f_sincof_p1); + y2 = pmadd(y2, z, p4f_sincof_p2); + y2 = pmul(y2, z); + y2 = pmul(y2, x); + y2 = padd(y2, x); + + /* select the correct result from the two polynoms */ + y2 = _mm_and_ps(poly_mask, y2); + y = _mm_andnot_ps(poly_mask, y); + y = _mm_or_ps(y,y2); + /* update the sign */ + return _mm_xor_ps(y, sign_bit); +} + +/* almost the same as psin */ +template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED +Packet4f pcos<Packet4f>(const Packet4f& _x) +{ + Packet4f x = _x; + _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f); + _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f); + + _EIGEN_DECLARE_CONST_Packet4i(1, 1); + _EIGEN_DECLARE_CONST_Packet4i(not1, ~1); + _EIGEN_DECLARE_CONST_Packet4i(2, 2); + _EIGEN_DECLARE_CONST_Packet4i(4, 4); + + _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f); + _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f); + _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f); + _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f); + _EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736E-3f); + _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f); + _EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948E-005f); + _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f); + _EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827E-002f); + _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f); // 4 / M_PI + + Packet4f xmm1, xmm2, xmm3, y; + Packet4i emm0, emm2; + + x = pabs(x); + + /* scale by 4/Pi */ + y = pmul(x, p4f_cephes_FOPI); + + /* get the integer part of y */ + emm2 = _mm_cvttps_epi32(y); + /* j=(j+1) & (~1) (see the cephes sources) */ + emm2 = _mm_add_epi32(emm2, p4i_1); + emm2 = _mm_and_si128(emm2, p4i_not1); + y = _mm_cvtepi32_ps(emm2); + + emm2 = _mm_sub_epi32(emm2, p4i_2); + + /* get the swap sign flag */ + emm0 = _mm_andnot_si128(emm2, p4i_4); + emm0 = _mm_slli_epi32(emm0, 29); + /* get the polynom selection mask */ + emm2 = _mm_and_si128(emm2, p4i_2); + emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128()); + + Packet4f sign_bit = _mm_castsi128_ps(emm0); + Packet4f poly_mask = _mm_castsi128_ps(emm2); + + /* The magic pass: "Extended precision modular arithmetic" + x = ((x - y * DP1) - y * DP2) - y * DP3; */ + xmm1 = pmul(y, p4f_minus_cephes_DP1); + xmm2 = pmul(y, p4f_minus_cephes_DP2); + xmm3 = pmul(y, p4f_minus_cephes_DP3); + x = padd(x, xmm1); + x = padd(x, xmm2); + x = padd(x, xmm3); + + /* Evaluate the first polynom (0 <= x <= Pi/4) */ + y = p4f_coscof_p0; + Packet4f z = pmul(x,x); + + y = pmadd(y,z,p4f_coscof_p1); + y = pmadd(y,z,p4f_coscof_p2); + y = pmul(y, z); + y = pmul(y, z); + Packet4f tmp = _mm_mul_ps(z, p4f_half); + y = psub(y, tmp); + y = padd(y, p4f_1); + + /* Evaluate the second polynom (Pi/4 <= x <= 0) */ + Packet4f y2 = p4f_sincof_p0; + y2 = pmadd(y2, z, p4f_sincof_p1); + y2 = pmadd(y2, z, p4f_sincof_p2); + y2 = pmul(y2, z); + y2 = pmadd(y2, x, x); + + /* select the correct result from the two polynoms */ + y2 = _mm_and_ps(poly_mask, y2); + y = _mm_andnot_ps(poly_mask, y); + y = _mm_or_ps(y,y2); + + /* update the sign */ + 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_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); } + + +#if EIGEN_FAST_MATH + +template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED +Packet4f prsqrt<Packet4f>(const Packet4f& _x) { + _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inf, 0x7f800000); + _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(nan, 0x7fc00000); + _EIGEN_DECLARE_CONST_Packet4f(one_point_five, 1.5f); + _EIGEN_DECLARE_CONST_Packet4f(minus_half, -0.5f); + _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(flt_min, 0x00800000); + + Packet4f neg_half = pmul(_x, p4f_minus_half); + + // select only the inverse sqrt of positive normal inputs (denormals are + // flushed to zero and cause infs as well). + Packet4f le_zero_mask = _mm_cmple_ps(_x, p4f_flt_min); + Packet4f x = _mm_andnot_ps(le_zero_mask, _mm_rsqrt_ps(_x)); + + // Fill in NaNs and Infs for the negative/zero entries. + 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)); + + // Do a single step of Newton's iteration. + x = pmul(x, pmadd(neg_half, pmul(x, x), p4f_one_point_five)); + + // Insert NaNs and Infs in all the right places. + return _mm_or_ps(x, infs_and_nans); +} + +#else + +template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED +Packet4f prsqrt<Packet4f>(const Packet4f& x) { + // Unfortunately we can't use the much faster mm_rqsrt_ps since it only provides an approximation. + return _mm_div_ps(pset1<Packet4f>(1.0f), _mm_sqrt_ps(x)); +} + +#endif + +template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED +Packet2d prsqrt<Packet2d>(const Packet2d& x) { + // Unfortunately we can't use the much faster mm_rqsrt_pd since it only provides an approximation. + return _mm_div_pd(pset1<Packet2d>(1.0), _mm_sqrt_pd(x)); +} + +// Identical to the ptanh in GenericPacketMath.h, but for doubles use +// a small/medium approximation threshold of 0.001. +template<> EIGEN_STRONG_INLINE Packet2d ptanh_approx_threshold() { + return pset1<Packet2d>(0.001); +} + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_MATH_FUNCTIONS_SSE_H |