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Diffstat (limited to 'runtimes/nn/depend/external/eigen/Eigen/src/Core/arch/AVX512/MathFunctions.h')
| -rw-r--r-- | runtimes/nn/depend/external/eigen/Eigen/src/Core/arch/AVX512/MathFunctions.h | 396 |
1 files changed, 396 insertions, 0 deletions
diff --git a/runtimes/nn/depend/external/eigen/Eigen/src/Core/arch/AVX512/MathFunctions.h b/runtimes/nn/depend/external/eigen/Eigen/src/Core/arch/AVX512/MathFunctions.h new file mode 100644 index 000000000..399be0ee4 --- /dev/null +++ b/runtimes/nn/depend/external/eigen/Eigen/src/Core/arch/AVX512/MathFunctions.h @@ -0,0 +1,396 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2016 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 THIRD_PARTY_EIGEN3_EIGEN_SRC_CORE_ARCH_AVX512_MATHFUNCTIONS_H_ +#define THIRD_PARTY_EIGEN3_EIGEN_SRC_CORE_ARCH_AVX512_MATHFUNCTIONS_H_ + +namespace Eigen { + +namespace internal { + +// Disable the code for older versions of gcc that don't support many of the required avx512 instrinsics. +#if EIGEN_GNUC_AT_LEAST(5, 3) + +#define _EIGEN_DECLARE_CONST_Packet16f(NAME, X) \ + const Packet16f p16f_##NAME = pset1<Packet16f>(X) + +#define _EIGEN_DECLARE_CONST_Packet16f_FROM_INT(NAME, X) \ + const Packet16f p16f_##NAME = (__m512)pset1<Packet16i>(X) + +#define _EIGEN_DECLARE_CONST_Packet8d(NAME, X) \ + const Packet8d p8d_##NAME = pset1<Packet8d>(X) + +#define _EIGEN_DECLARE_CONST_Packet8d_FROM_INT64(NAME, X) \ + const Packet8d p8d_##NAME = _mm512_castsi512_pd(_mm512_set1_epi64(X)) + +// 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. +#if defined(EIGEN_VECTORIZE_AVX512DQ) +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet16f +plog<Packet16f>(const Packet16f& _x) { + Packet16f x = _x; + _EIGEN_DECLARE_CONST_Packet16f(1, 1.0f); + _EIGEN_DECLARE_CONST_Packet16f(half, 0.5f); + _EIGEN_DECLARE_CONST_Packet16f(126f, 126.0f); + + _EIGEN_DECLARE_CONST_Packet16f_FROM_INT(inv_mant_mask, ~0x7f800000); + + // The smallest non denormalized float number. + _EIGEN_DECLARE_CONST_Packet16f_FROM_INT(min_norm_pos, 0x00800000); + _EIGEN_DECLARE_CONST_Packet16f_FROM_INT(minus_inf, 0xff800000); + _EIGEN_DECLARE_CONST_Packet16f_FROM_INT(nan, 0x7fc00000); + + // Polynomial coefficients. + _EIGEN_DECLARE_CONST_Packet16f(cephes_SQRTHF, 0.707106781186547524f); + _EIGEN_DECLARE_CONST_Packet16f(cephes_log_p0, 7.0376836292E-2f); + _EIGEN_DECLARE_CONST_Packet16f(cephes_log_p1, -1.1514610310E-1f); + _EIGEN_DECLARE_CONST_Packet16f(cephes_log_p2, 1.1676998740E-1f); + _EIGEN_DECLARE_CONST_Packet16f(cephes_log_p3, -1.2420140846E-1f); + _EIGEN_DECLARE_CONST_Packet16f(cephes_log_p4, +1.4249322787E-1f); + _EIGEN_DECLARE_CONST_Packet16f(cephes_log_p5, -1.6668057665E-1f); + _EIGEN_DECLARE_CONST_Packet16f(cephes_log_p6, +2.0000714765E-1f); + _EIGEN_DECLARE_CONST_Packet16f(cephes_log_p7, -2.4999993993E-1f); + _EIGEN_DECLARE_CONST_Packet16f(cephes_log_p8, +3.3333331174E-1f); + _EIGEN_DECLARE_CONST_Packet16f(cephes_log_q1, -2.12194440e-4f); + _EIGEN_DECLARE_CONST_Packet16f(cephes_log_q2, 0.693359375f); + + // invalid_mask is set to true when x is NaN + __mmask16 invalid_mask = + _mm512_cmp_ps_mask(x, _mm512_setzero_ps(), _CMP_NGE_UQ); + __mmask16 iszero_mask = + _mm512_cmp_ps_mask(x, _mm512_setzero_ps(), _CMP_EQ_UQ); + + // Truncate input values to the minimum positive normal. + x = pmax(x, p16f_min_norm_pos); + + // Extract the shifted exponents. + Packet16f emm0 = _mm512_cvtepi32_ps(_mm512_srli_epi32((__m512i)x, 23)); + Packet16f e = _mm512_sub_ps(emm0, p16f_126f); + + // Set the exponents to -1, i.e. x are in the range [0.5,1). + x = _mm512_and_ps(x, p16f_inv_mant_mask); + x = _mm512_or_ps(x, p16f_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; } + __mmask16 mask = _mm512_cmp_ps_mask(x, p16f_cephes_SQRTHF, _CMP_LT_OQ); + Packet16f tmp = _mm512_mask_blend_ps(mask, x, _mm512_setzero_ps()); + x = psub(x, p16f_1); + e = psub(e, _mm512_mask_blend_ps(mask, p16f_1, _mm512_setzero_ps())); + x = padd(x, tmp); + + Packet16f x2 = pmul(x, x); + Packet16f x3 = pmul(x2, x); + + // Evaluate the polynomial approximant of degree 8 in three parts, probably + // to improve instruction-level parallelism. + Packet16f y, y1, y2; + y = pmadd(p16f_cephes_log_p0, x, p16f_cephes_log_p1); + y1 = pmadd(p16f_cephes_log_p3, x, p16f_cephes_log_p4); + y2 = pmadd(p16f_cephes_log_p6, x, p16f_cephes_log_p7); + y = pmadd(y, x, p16f_cephes_log_p2); + y1 = pmadd(y1, x, p16f_cephes_log_p5); + y2 = pmadd(y2, x, p16f_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, p16f_cephes_log_q1); + tmp = pmul(x2, p16f_half); + y = padd(y, y1); + x = psub(x, tmp); + y2 = pmul(e, p16f_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 _mm512_mask_blend_ps(iszero_mask, p16f_minus_inf, + _mm512_mask_blend_ps(invalid_mask, p16f_nan, x)); +} +#endif + +// 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 Packet16f +pexp<Packet16f>(const Packet16f& _x) { + _EIGEN_DECLARE_CONST_Packet16f(1, 1.0f); + _EIGEN_DECLARE_CONST_Packet16f(half, 0.5f); + _EIGEN_DECLARE_CONST_Packet16f(127, 127.0f); + + _EIGEN_DECLARE_CONST_Packet16f(exp_hi, 88.3762626647950f); + _EIGEN_DECLARE_CONST_Packet16f(exp_lo, -88.3762626647949f); + + _EIGEN_DECLARE_CONST_Packet16f(cephes_LOG2EF, 1.44269504088896341f); + + _EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p0, 1.9875691500E-4f); + _EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p1, 1.3981999507E-3f); + _EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p2, 8.3334519073E-3f); + _EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p3, 4.1665795894E-2f); + _EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p4, 1.6666665459E-1f); + _EIGEN_DECLARE_CONST_Packet16f(cephes_exp_p5, 5.0000001201E-1f); + + // Clamp x. + Packet16f x = pmax(pmin(_x, p16f_exp_hi), p16f_exp_lo); + + // Express exp(x) as exp(m*ln(2) + r), start by extracting + // m = floor(x/ln(2) + 0.5). + Packet16f m = _mm512_floor_ps(pmadd(x, p16f_cephes_LOG2EF, p16f_half)); + + // Get r = x - m*ln(2). Note that we can do this without losing more than one + // ulp precision due to the FMA instruction. + _EIGEN_DECLARE_CONST_Packet16f(nln2, -0.6931471805599453f); + Packet16f r = _mm512_fmadd_ps(m, p16f_nln2, x); + Packet16f r2 = pmul(r, r); + + // TODO(gonnet): Split into odd/even polynomials and try to exploit + // instruction-level parallelism. + Packet16f y = p16f_cephes_exp_p0; + y = pmadd(y, r, p16f_cephes_exp_p1); + y = pmadd(y, r, p16f_cephes_exp_p2); + y = pmadd(y, r, p16f_cephes_exp_p3); + y = pmadd(y, r, p16f_cephes_exp_p4); + y = pmadd(y, r, p16f_cephes_exp_p5); + y = pmadd(y, r2, r); + y = padd(y, p16f_1); + + // Build emm0 = 2^m. + Packet16i emm0 = _mm512_cvttps_epi32(padd(m, p16f_127)); + emm0 = _mm512_slli_epi32(emm0, 23); + + // Return 2^m * exp(r). + return pmax(pmul(y, _mm512_castsi512_ps(emm0)), _x); +} + +/*template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8d +pexp<Packet8d>(const Packet8d& _x) { + Packet8d x = _x; + + _EIGEN_DECLARE_CONST_Packet8d(1, 1.0); + _EIGEN_DECLARE_CONST_Packet8d(2, 2.0); + + _EIGEN_DECLARE_CONST_Packet8d(exp_hi, 709.437); + _EIGEN_DECLARE_CONST_Packet8d(exp_lo, -709.436139303); + + _EIGEN_DECLARE_CONST_Packet8d(cephes_LOG2EF, 1.4426950408889634073599); + + _EIGEN_DECLARE_CONST_Packet8d(cephes_exp_p0, 1.26177193074810590878e-4); + _EIGEN_DECLARE_CONST_Packet8d(cephes_exp_p1, 3.02994407707441961300e-2); + _EIGEN_DECLARE_CONST_Packet8d(cephes_exp_p2, 9.99999999999999999910e-1); + + _EIGEN_DECLARE_CONST_Packet8d(cephes_exp_q0, 3.00198505138664455042e-6); + _EIGEN_DECLARE_CONST_Packet8d(cephes_exp_q1, 2.52448340349684104192e-3); + _EIGEN_DECLARE_CONST_Packet8d(cephes_exp_q2, 2.27265548208155028766e-1); + _EIGEN_DECLARE_CONST_Packet8d(cephes_exp_q3, 2.00000000000000000009e0); + + _EIGEN_DECLARE_CONST_Packet8d(cephes_exp_C1, 0.693145751953125); + _EIGEN_DECLARE_CONST_Packet8d(cephes_exp_C2, 1.42860682030941723212e-6); + + // clamp x + x = pmax(pmin(x, p8d_exp_hi), p8d_exp_lo); + + // Express exp(x) as exp(g + n*log(2)). + const Packet8d n = + _mm512_mul_round_pd(p8d_cephes_LOG2EF, x, _MM_FROUND_TO_NEAREST_INT); + + // Get the remainder modulo log(2), i.e. the "g" described above. Subtract + // n*log(2) out in two steps, i.e. n*C1 + n*C2, C1+C2=log2 to get the last + // digits right. + const Packet8d nC1 = pmul(n, p8d_cephes_exp_C1); + const Packet8d nC2 = pmul(n, p8d_cephes_exp_C2); + x = psub(x, nC1); + x = psub(x, nC2); + + const Packet8d x2 = pmul(x, x); + + // Evaluate the numerator polynomial of the rational interpolant. + Packet8d px = p8d_cephes_exp_p0; + px = pmadd(px, x2, p8d_cephes_exp_p1); + px = pmadd(px, x2, p8d_cephes_exp_p2); + px = pmul(px, x); + + // Evaluate the denominator polynomial of the rational interpolant. + Packet8d qx = p8d_cephes_exp_q0; + qx = pmadd(qx, x2, p8d_cephes_exp_q1); + qx = pmadd(qx, x2, p8d_cephes_exp_q2); + qx = pmadd(qx, x2, p8d_cephes_exp_q3); + + // I don't really get this bit, copied from the SSE2 routines, so... + // TODO(gonnet): Figure out what is going on here, perhaps find a better + // rational interpolant? + x = _mm512_div_pd(px, psub(qx, px)); + x = pmadd(p8d_2, x, p8d_1); + + // Build e=2^n. + const Packet8d e = _mm512_castsi512_pd(_mm512_slli_epi64( + _mm512_add_epi64(_mm512_cvtpd_epi64(n), _mm512_set1_epi64(1023)), 52)); + + // Construct the result 2^n * exp(g) = e * x. The max is used to catch + // non-finite values in the input. + return pmax(pmul(x, e), _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 Packet16f +psqrt<Packet16f>(const Packet16f& _x) { + _EIGEN_DECLARE_CONST_Packet16f(one_point_five, 1.5f); + _EIGEN_DECLARE_CONST_Packet16f(minus_half, -0.5f); + _EIGEN_DECLARE_CONST_Packet16f_FROM_INT(flt_min, 0x00800000); + + Packet16f neg_half = pmul(_x, p16f_minus_half); + + // select only the inverse sqrt of positive normal inputs (denormals are + // flushed to zero and cause infs as well). + __mmask16 non_zero_mask = _mm512_cmp_ps_mask(_x, p16f_flt_min, _CMP_GE_OQ); + Packet16f x = _mm512_mask_blend_ps(non_zero_mask, _mm512_rsqrt14_ps(_x), + _mm512_setzero_ps()); + + // Do a single step of Newton's iteration. + x = pmul(x, pmadd(neg_half, pmul(x, x), p16f_one_point_five)); + + // Multiply the original _x by it's reciprocal square root to extract the + // square root. + return pmul(_x, x); +} + +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8d +psqrt<Packet8d>(const Packet8d& _x) { + _EIGEN_DECLARE_CONST_Packet8d(one_point_five, 1.5); + _EIGEN_DECLARE_CONST_Packet8d(minus_half, -0.5); + _EIGEN_DECLARE_CONST_Packet8d_FROM_INT64(dbl_min, 0x0010000000000000LL); + + Packet8d neg_half = pmul(_x, p8d_minus_half); + + // select only the inverse sqrt of positive normal inputs (denormals are + // flushed to zero and cause infs as well). + __mmask8 non_zero_mask = _mm512_cmp_pd_mask(_x, p8d_dbl_min, _CMP_GE_OQ); + Packet8d x = _mm512_mask_blend_pd(non_zero_mask, _mm512_rsqrt14_pd(_x), + _mm512_setzero_pd()); + + // Do a first step of Newton's iteration. + x = pmul(x, pmadd(neg_half, pmul(x, x), p8d_one_point_five)); + + // Do a second step of Newton's iteration. + x = pmul(x, pmadd(neg_half, pmul(x, x), p8d_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 Packet16f psqrt<Packet16f>(const Packet16f& x) { + return _mm512_sqrt_ps(x); +} +template <> +EIGEN_STRONG_INLINE Packet8d psqrt<Packet8d>(const Packet8d& x) { + return _mm512_sqrt_pd(x); +} +#endif + +// Functions for rsqrt. +// Almost identical to the sqrt routine, just leave out the last multiplication +// and fill in NaN/Inf where needed. Note that this function only exists as an +// iterative version for doubles since there is no instruction for diretly +// computing the reciprocal square root in AVX-512. +#ifdef EIGEN_FAST_MATH +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet16f +prsqrt<Packet16f>(const Packet16f& _x) { + _EIGEN_DECLARE_CONST_Packet16f_FROM_INT(inf, 0x7f800000); + _EIGEN_DECLARE_CONST_Packet16f_FROM_INT(nan, 0x7fc00000); + _EIGEN_DECLARE_CONST_Packet16f(one_point_five, 1.5f); + _EIGEN_DECLARE_CONST_Packet16f(minus_half, -0.5f); + _EIGEN_DECLARE_CONST_Packet16f_FROM_INT(flt_min, 0x00800000); + + Packet16f neg_half = pmul(_x, p16f_minus_half); + + // select only the inverse sqrt of positive normal inputs (denormals are + // flushed to zero and cause infs as well). + __mmask16 le_zero_mask = _mm512_cmp_ps_mask(_x, p16f_flt_min, _CMP_LT_OQ); + Packet16f x = _mm512_mask_blend_ps(le_zero_mask, _mm512_setzero_ps(), + _mm512_rsqrt14_ps(_x)); + + // Fill in NaNs and Infs for the negative/zero entries. + __mmask16 neg_mask = _mm512_cmp_ps_mask(_x, _mm512_setzero_ps(), _CMP_LT_OQ); + Packet16f infs_and_nans = _mm512_mask_blend_ps( + neg_mask, p16f_nan, + _mm512_mask_blend_ps(le_zero_mask, p16f_inf, _mm512_setzero_ps())); + + // Do a single step of Newton's iteration. + x = pmul(x, pmadd(neg_half, pmul(x, x), p16f_one_point_five)); + + // Insert NaNs and Infs in all the right places. + return _mm512_mask_blend_ps(le_zero_mask, infs_and_nans, x); +} + +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8d +prsqrt<Packet8d>(const Packet8d& _x) { + _EIGEN_DECLARE_CONST_Packet8d_FROM_INT64(inf, 0x7ff0000000000000LL); + _EIGEN_DECLARE_CONST_Packet8d_FROM_INT64(nan, 0x7ff1000000000000LL); + _EIGEN_DECLARE_CONST_Packet8d(one_point_five, 1.5); + _EIGEN_DECLARE_CONST_Packet8d(minus_half, -0.5); + _EIGEN_DECLARE_CONST_Packet8d_FROM_INT64(dbl_min, 0x0010000000000000LL); + + Packet8d neg_half = pmul(_x, p8d_minus_half); + + // select only the inverse sqrt of positive normal inputs (denormals are + // flushed to zero and cause infs as well). + __mmask8 le_zero_mask = _mm512_cmp_pd_mask(_x, p8d_dbl_min, _CMP_LT_OQ); + Packet8d x = _mm512_mask_blend_pd(le_zero_mask, _mm512_setzero_pd(), + _mm512_rsqrt14_pd(_x)); + + // Fill in NaNs and Infs for the negative/zero entries. + __mmask8 neg_mask = _mm512_cmp_pd_mask(_x, _mm512_setzero_pd(), _CMP_LT_OQ); + Packet8d infs_and_nans = _mm512_mask_blend_pd( + neg_mask, p8d_nan, + _mm512_mask_blend_pd(le_zero_mask, p8d_inf, _mm512_setzero_pd())); + + // Do a first step of Newton's iteration. + x = pmul(x, pmadd(neg_half, pmul(x, x), p8d_one_point_five)); + + // Do a second step of Newton's iteration. + x = pmul(x, pmadd(neg_half, pmul(x, x), p8d_one_point_five)); + + // Insert NaNs and Infs in all the right places. + return _mm512_mask_blend_pd(le_zero_mask, infs_and_nans, x); +} +#else +template <> +EIGEN_STRONG_INLINE Packet16f prsqrt<Packet16f>(const Packet16f& x) { + return _mm512_rsqrt28_ps(x); +} +#endif +#endif + +} // end namespace internal + +} // end namespace Eigen + +#endif // THIRD_PARTY_EIGEN3_EIGEN_SRC_CORE_ARCH_AVX512_MATHFUNCTIONS_H_ |