diff --git a/Eigen/Core b/Eigen/Core index 416e901ae..68748a3f6 100644 --- a/Eigen/Core +++ b/Eigen/Core @@ -290,6 +290,7 @@ using std::ptrdiff_t; #include "src/Core/arch/SSE/PacketMath.h" #include "src/Core/arch/SSE/Complex.h" #include "src/Core/arch/AVX/PacketMath.h" + #include "src/Core/arch/AVX/MathFunctions.h" #include "src/Core/arch/AVX/Complex.h" #elif defined EIGEN_VECTORIZE_SSE #include "src/Core/arch/SSE/PacketMath.h" diff --git a/Eigen/src/Core/arch/AVX/MathFunctions.h b/Eigen/src/Core/arch/AVX/MathFunctions.h new file mode 100644 index 000000000..2810a7a0b --- /dev/null +++ b/Eigen/src/Core/arch/AVX/MathFunctions.h @@ -0,0 +1,317 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2014 Pedro Gonnet (pedro.gonnet@gmail.com) +// +// 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/. + +#ifndef EIGEN_MATH_FUNCTIONS_AVX_H +#define EIGEN_MATH_FUNCTIONS_AVX_H + +// For some reason, this function didn't make it into the avxintirn.h +// used by the compiler, so we'll just wrap it. +#define _mm256_setr_m128(lo, hi) \ + _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1) + +/* The sin, cos, exp, and log functions of this file are loosely derived from + * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/ + */ + +namespace Eigen { + +namespace internal { + +// Sine function +// Computes sin(x) by wrapping x to the interval [-Pi/4,3*Pi/4] and +// evaluating interpolants in [-Pi/4,Pi/4] or [Pi/4,3*Pi/4]. The interpolants +// are (anti-)symmetric and thus have only odd/even coefficients +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f +psin(const Packet8f& _x) { + Packet8f x = _x; + + // Some useful values. + _EIGEN_DECLARE_CONST_Packet8i(one, 1); + _EIGEN_DECLARE_CONST_Packet8f(one, 1.0f); + _EIGEN_DECLARE_CONST_Packet8f(two, 2.0f); + _EIGEN_DECLARE_CONST_Packet8f(one_over_four, 0.25f); + _EIGEN_DECLARE_CONST_Packet8f(one_over_pi, 3.183098861837907e-01f); + _EIGEN_DECLARE_CONST_Packet8f(neg_pi_first, -3.140625000000000e+00); + _EIGEN_DECLARE_CONST_Packet8f(neg_pi_second, -9.670257568359375e-04); + _EIGEN_DECLARE_CONST_Packet8f(neg_pi_third, -6.278329571784980e-07); + _EIGEN_DECLARE_CONST_Packet8f(four_over_pi, 1.273239544735163e+00); + + // Map x from [-Pi/4,3*Pi/4] to z in [-1,3] and subtract the shifted period. + Packet8f z = pmul(x, p8f_one_over_pi); + Packet8f shift = _mm256_floor_ps(padd(z, p8f_one_over_four)); + x = pmadd(shift, p8f_neg_pi_first, x); + x = pmadd(shift, p8f_neg_pi_second, x); + x = pmadd(shift, p8f_neg_pi_third, x); + z = pmul(x, p8f_four_over_pi); + + // Make a mask for the entries that need flipping, i.e. wherever the shift + // is odd. + Packet8i shift_ints = _mm256_cvtps_epi32(shift); + Packet8i shift_isodd = + (__m256i)_mm256_and_ps((__m256)shift_ints, (__m256)p8i_one); +#ifdef EIGEN_VECTORIZE_AVX2 + Packet8i sign_flip_mask = _mm256_slli_epi32(shift_isodd, 31); +#else + __m128i lo = + _mm_slli_epi32(_mm256_extractf128_si256((__m256i)shift_isodd, 0), 31); + __m128i hi = + _mm_slli_epi32(_mm256_extractf128_si256((__m256i)shift_isodd, 1), 31); + Packet8i sign_flip_mask = _mm256_setr_m128(lo, hi); +#endif + + // Create a mask for which interpolant to use, i.e. if z > 1, then the mask + // is set to ones for that entry. + Packet8f ival_mask = _mm256_cmp_ps(z, p8f_one, _CMP_GT_OQ); + + // Evaluate the polynomial for the interval [1,3] in z. + _EIGEN_DECLARE_CONST_Packet8f(coeff_right_0, 9.999999724233232e-01f); + _EIGEN_DECLARE_CONST_Packet8f(coeff_right_2, -3.084242535619928e-01); + _EIGEN_DECLARE_CONST_Packet8f(coeff_right_4, 1.584991525700324e-02); + _EIGEN_DECLARE_CONST_Packet8f(coeff_right_6, -3.188805084631342e-04); + Packet8f z_minus_two = psub(z, p8f_two); + Packet8f z_minus_two2 = pmul(z_minus_two, z_minus_two); + Packet8f right = pmadd(p8f_coeff_right_6, z_minus_two2, p8f_coeff_right_4); + right = pmadd(right, z_minus_two2, p8f_coeff_right_2); + right = pmadd(right, z_minus_two2, p8f_coeff_right_0); + + // Evaluate the polynomial for the interval [-1,1] in z. + _EIGEN_DECLARE_CONST_Packet8f(coeff_left_1, 7.853981525427295e-01); + _EIGEN_DECLARE_CONST_Packet8f(coeff_left_3, -8.074536727092352e-02); + _EIGEN_DECLARE_CONST_Packet8f(coeff_left_5, 2.489871967827018e-03); + _EIGEN_DECLARE_CONST_Packet8f(coeff_left_7, -3.587725841214251e-05); + Packet8f z2 = pmul(z, z); + Packet8f left = pmadd(p8f_coeff_left_7, z2, p8f_coeff_left_5); + left = pmadd(left, z2, p8f_coeff_left_3); + left = pmadd(left, z2, p8f_coeff_left_1); + left = pmul(left, z); + + // Assemble the results, i.e. select the left and right polynomials. + left = _mm256_andnot_ps(ival_mask, left); + right = _mm256_and_ps(ival_mask, right); + Packet8f res = _mm256_or_ps(left, right); + + // Flip the sign on the odd intervals and return the result. + res = _mm256_xor_ps(res, (__m256)sign_flip_mask); + return res; +} + +// Natural logarithm +// Computes log(x) as log(2^e * m) = C*e + log(m), where the constant C =log(2) +// and m is in the range [sqrt(1/2),sqrt(2)). In this range, the logarithm can +// be easily approximated by a polynomial centered on m=1 for stability. +// TODO(gonnet): Further reduce the interval allowing for lower-degree +// polynomial interpolants -> ... -> profit! +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f +plog(const Packet8f& _x) { + Packet8f x = _x; + _EIGEN_DECLARE_CONST_Packet8f(1, 1.0f); + _EIGEN_DECLARE_CONST_Packet8f(half, 0.5f); + _EIGEN_DECLARE_CONST_Packet8f(126f, 126.0f); + + _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(inv_mant_mask, ~0x7f800000); + + // The smallest non denormalized float number. + _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(min_norm_pos, 0x00800000); + _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(minus_inf, 0xff800000); + + // Polynomial coefficients. + _EIGEN_DECLARE_CONST_Packet8f(cephes_SQRTHF, 0.707106781186547524f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p0, 7.0376836292E-2f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p1, -1.1514610310E-1f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p2, 1.1676998740E-1f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p3, -1.2420140846E-1f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p4, +1.4249322787E-1f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p5, -1.6668057665E-1f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p6, +2.0000714765E-1f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p7, -2.4999993993E-1f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p8, +3.3333331174E-1f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_log_q1, -2.12194440e-4f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_log_q2, 0.693359375f); + + Packet8f invalid_mask = _mm256_cmp_ps(x, _mm256_setzero_ps(), _CMP_NGE_UQ); // not greater equal is true if x is NaN + Packet8f iszero_mask = _mm256_cmp_ps(x, _mm256_setzero_ps(), _CMP_EQ_OQ); + + // Truncate input values to the minimum positive normal. + x = pmax(x, p8f_min_norm_pos); + +// Extract the shifted exponents (No bitwise shifting in regular AVX, so +// convert to SSE and do it there). +#ifdef EIGEN_VECTORIZE_AVX2 + Packet8f emm0 = _mm256_cvtepi32_ps(_mm256_srli_epi32((__m256i)x, 23)); +#else + __m128i lo = _mm_srli_epi32(_mm256_extractf128_si256((__m256i)x, 0), 23); + __m128i hi = _mm_srli_epi32(_mm256_extractf128_si256((__m256i)x, 1), 23); + Packet8f emm0 = _mm256_cvtepi32_ps(_mm256_setr_m128(lo, hi)); +#endif + Packet8f e = _mm256_sub_ps(emm0, p8f_126f); + + // Set the exponents to -1, i.e. x are in the range [0.5,1). + x = _mm256_and_ps(x, p8f_inv_mant_mask); + x = _mm256_or_ps(x, p8f_half); + + // part2: Shift the inputs from the range [0.5,1) to [sqrt(1/2),sqrt(2)) + // and shift by -1. The values are then centered around 0, which improves + // the stability of the polynomial evaluation. + // if( x < SQRTHF ) { + // e -= 1; + // x = x + x - 1.0; + // } else { x = x - 1.0; } + Packet8f mask = _mm256_cmp_ps(x, p8f_cephes_SQRTHF, _CMP_LT_OQ); + Packet8f tmp = _mm256_and_ps(x, mask); + x = psub(x, p8f_1); + e = psub(e, _mm256_and_ps(p8f_1, mask)); + x = padd(x, tmp); + + Packet8f x2 = pmul(x, x); + Packet8f x3 = pmul(x2, x); + + // Evaluate the polynomial approximant of degree 8 in three parts, probably + // to improve instruction-level parallelism. + Packet8f y, y1, y2; + y = pmadd(p8f_cephes_log_p0, x, p8f_cephes_log_p1); + y1 = pmadd(p8f_cephes_log_p3, x, p8f_cephes_log_p4); + y2 = pmadd(p8f_cephes_log_p6, x, p8f_cephes_log_p7); + y = pmadd(y, x, p8f_cephes_log_p2); + y1 = pmadd(y1, x, p8f_cephes_log_p5); + y2 = pmadd(y2, x, p8f_cephes_log_p8); + y = pmadd(y, x3, y1); + y = pmadd(y, x3, y2); + y = pmul(y, x3); + + // Add the logarithm of the exponent back to the result of the interpolation. + y1 = pmul(e, p8f_cephes_log_q1); + tmp = pmul(x2, p8f_half); + y = padd(y, y1); + x = psub(x, tmp); + y2 = pmul(e, p8f_cephes_log_q2); + x = padd(x, y); + x = padd(x, y2); + + // Filter out invalid inputs, i.e. negative arg will be NAN, 0 will be -INF. + return _mm256_or_ps( + _mm256_andnot_ps(iszero_mask, _mm256_or_ps(x, invalid_mask)), + _mm256_and_ps(iszero_mask, p8f_minus_inf)); +} + +// Exponential function. Works by writing "x = m*log(2) + r" where +// "m = floor(x/log(2)+1/2)" and "r" is the remainder. The result is then +// "exp(x) = 2^m*exp(r)" where exp(r) is in the range [-1,1). +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f +pexp(const Packet8f& _x) { + _EIGEN_DECLARE_CONST_Packet8f(1, 1.0f); + _EIGEN_DECLARE_CONST_Packet8f(half, 0.5f); + _EIGEN_DECLARE_CONST_Packet8f(127, 127.0f); + + _EIGEN_DECLARE_CONST_Packet8f(exp_hi, 88.3762626647950f); + _EIGEN_DECLARE_CONST_Packet8f(exp_lo, -88.3762626647949f); + + _EIGEN_DECLARE_CONST_Packet8f(cephes_LOG2EF, 1.44269504088896341f); + + _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_p0, 1.9875691500E-4f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_p1, 1.3981999507E-3f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_p2, 8.3334519073E-3f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_p3, 4.1665795894E-2f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_p4, 1.6666665459E-1f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_p5, 5.0000001201E-1f); + + // Clamp x. + Packet8f x = pmax(pmin(_x, p8f_exp_hi), p8f_exp_lo); + + // Express exp(x) as exp(m*ln(2) + r), start by extracting + // m = floor(x/ln(2) + 0.5). + Packet8f m = _mm256_floor_ps(pmadd(x, p8f_cephes_LOG2EF, p8f_half)); + +// Get r = x - m*ln(2). If no FMA instructions are available, m*ln(2) is +// subtracted out in two parts, m*C1+m*C2 = m*ln(2), to avoid accumulating +// truncation errors. Note that we don't use the "pmadd" function here to +// ensure that a precision-preserving FMA instruction is used. +#ifdef EIGEN_VECTORIZE_FMA + _EIGEN_DECLARE_CONST_Packet8f(nln2, -0.6931471805599453f); + Packet8f r = _mm256_fmadd_ps(m, p8f_nln2, x); +#else + _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_C1, 0.693359375f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_C2, -2.12194440e-4f); + Packet8f r = psub(x, pmul(m, p8f_cephes_exp_C1)); + r = psub(r, pmul(m, p8f_cephes_exp_C2)); +#endif + + Packet8f r2 = pmul(r, r); + + // TODO(gonnet): Split into odd/even polynomials and try to exploit + // instruction-level parallelism. + Packet8f y = p8f_cephes_exp_p0; + y = pmadd(y, r, p8f_cephes_exp_p1); + y = pmadd(y, r, p8f_cephes_exp_p2); + y = pmadd(y, r, p8f_cephes_exp_p3); + y = pmadd(y, r, p8f_cephes_exp_p4); + y = pmadd(y, r, p8f_cephes_exp_p5); + y = pmadd(y, r2, r); + y = padd(y, p8f_1); + + // Build emm0 = 2^m. + Packet8i emm0 = _mm256_cvttps_epi32(padd(m, p8f_127)); +#ifdef EIGEN_VECTORIZE_AVX2 + emm0 = _mm256_slli_epi32(emm0, 23); +#else + __m128i lo = _mm_slli_epi32(_mm256_extractf128_si256(emm0, 0), 23); + __m128i hi = _mm_slli_epi32(_mm256_extractf128_si256(emm0, 1), 23); + emm0 = _mm256_setr_m128(lo, hi); +#endif + + // Return 2^m * exp(r). + return pmax(pmul(y, _mm256_castsi256_ps(emm0)), _x); +} + +// 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. 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. +#if EIGEN_FAST_MATH +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f +psqrt(const Packet8f& _x) { + _EIGEN_DECLARE_CONST_Packet8f(one_point_five, 1.5f); + _EIGEN_DECLARE_CONST_Packet8f(minus_half, -0.5f); + _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(flt_min, 0x00800000); + + Packet8f neg_half = pmul(_x, p8f_minus_half); + + // select only the inverse sqrt of positive normal inputs (denormals are + // flushed to zero and cause infs as well). + Packet8f non_zero_mask = _mm256_cmp_ps(_x, p8f_flt_min, _CMP_GE_OQ); + Packet8f x = _mm256_and_ps(non_zero_mask, _mm256_rsqrt_ps(_x)); + + // Do a single step of Newton's iteration. + x = pmul(x, pmadd(neg_half, pmul(x, x), p8f_one_point_five)); + + // Multiply the original _x by it's reciprocal square root to extract the + // square root. + return pmul(_x, x); +} +#else +template <> +EIGEN_STRONG_INLINE Packet8f psqrt(const Packet8f& x) { + return _mm256_sqrt_ps(x); +} +#endif +template <> +EIGEN_STRONG_INLINE Packet4d psqrt(const Packet4d& x) { + return _mm256_sqrt_pd(x); +} + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_MATH_FUNCTIONS_AVX_H diff --git a/Eigen/src/Core/arch/AVX/PacketMath.h b/Eigen/src/Core/arch/AVX/PacketMath.h index fc2e78b2d..c404676c4 100644 --- a/Eigen/src/Core/arch/AVX/PacketMath.h +++ b/Eigen/src/Core/arch/AVX/PacketMath.h @@ -42,6 +42,12 @@ template<> struct is_arithmetic<__m256d> { enum { value = true }; }; #define _EIGEN_DECLARE_CONST_Packet4d(NAME,X) \ const Packet4d p4d_##NAME = pset1(X) +#define _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(NAME,X) \ + const Packet8f p8f_##NAME = (__m256)pset1(X) + +#define _EIGEN_DECLARE_CONST_Packet8i(NAME,X) \ + const Packet8i p8i_##NAME = pset1(X) + template<> struct packet_traits : default_packet_traits { @@ -54,13 +60,13 @@ template<> struct packet_traits : default_packet_traits HasHalfPacket = 1, HasDiv = 1, - HasSin = 0, + HasSin = 1, HasCos = 0, - HasLog = 0, - HasExp = 0, - HasSqrt = 0 + HasLog = 1, + HasExp = 1, + HasSqrt = 1 }; - }; +}; template<> struct packet_traits : default_packet_traits { typedef Packet4d type; @@ -72,7 +78,8 @@ template<> struct packet_traits : default_packet_traits HasHalfPacket = 1, HasDiv = 1, - HasExp = 0 + HasExp = 0, + HasSqrt = 1 }; };