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Diffstat (limited to 'Eigen/src/Core/arch/MSA/MathFunctions.h')
| -rw-r--r-- | Eigen/src/Core/arch/MSA/MathFunctions.h | 387 |
1 files changed, 387 insertions, 0 deletions
diff --git a/Eigen/src/Core/arch/MSA/MathFunctions.h b/Eigen/src/Core/arch/MSA/MathFunctions.h new file mode 100644 index 000000000..f5181b90e --- /dev/null +++ b/Eigen/src/Core/arch/MSA/MathFunctions.h @@ -0,0 +1,387 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2007 Julien Pommier +// Copyright (C) 2014 Pedro Gonnet (pedro.gonnet@gmail.com) +// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// Copyright (C) 2018 Wave Computing, Inc. +// Written by: +// Chris Larsen +// Alexey Frunze (afrunze@wavecomp.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/. + +/* The sin, cos, exp, and log functions of this file come from + * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/ + */ + +/* The tanh function of this file is an adaptation of + * template<typename T> T generic_fast_tanh_float(const T&) + * from MathFunctionsImpl.h. + */ + +#ifndef EIGEN_MATH_FUNCTIONS_MSA_H +#define EIGEN_MATH_FUNCTIONS_MSA_H + +namespace Eigen { + +namespace internal { + +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f +plog<Packet4f>(const Packet4f& _x) { + static _EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f); + static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292e-2f); + static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, -1.1514610310e-1f); + static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740e-1f); + static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, -1.2420140846e-1f); + static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, +1.4249322787e-1f); + static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, -1.6668057665e-1f); + static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, +2.0000714765e-1f); + static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, -2.4999993993e-1f); + static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, +3.3333331174e-1f); + static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f); + static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f); + static _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f); + static _EIGEN_DECLARE_CONST_Packet4f(1, 1.0f); + + // Convert negative argument into NAN (quiet negative, to be specific). + Packet4f zero = (Packet4f)__builtin_msa_ldi_w(0); + Packet4i neg_mask = __builtin_msa_fclt_w(_x, zero); + Packet4i zero_mask = __builtin_msa_fceq_w(_x, zero); + Packet4f non_neg_x_or_nan = padd(_x, (Packet4f)neg_mask); // Add 0.0 or NAN. + Packet4f x = non_neg_x_or_nan; + + // Extract exponent from x = mantissa * 2**exponent, where 1.0 <= mantissa < 2.0. + // N.B. the exponent is one less of what frexpf() would return. + Packet4i e_int = __builtin_msa_ftint_s_w(__builtin_msa_flog2_w(x)); + // Multiply x by 2**(-exponent-1) to get 0.5 <= x < 1.0 as from frexpf(). + x = __builtin_msa_fexp2_w(x, (Packet4i)__builtin_msa_nori_b((v16u8)e_int, 0)); + + /* + if (x < SQRTHF) { + x = x + x - 1.0; + } else { + e += 1; + x = x - 1.0; + } + */ + Packet4f xx = padd(x, x); + Packet4i ge_mask = __builtin_msa_fcle_w(p4f_cephes_SQRTHF, x); + e_int = psub(e_int, ge_mask); + x = (Packet4f)__builtin_msa_bsel_v((v16u8)ge_mask, (v16u8)xx, (v16u8)x); + x = psub(x, p4f_1); + Packet4f e = __builtin_msa_ffint_s_w(e_int); + + 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); + + y = pmadd(e, p4f_cephes_log_q1, y); + x = __builtin_msa_fmsub_w(x, x2, p4f_half); + x = padd(x, y); + x = pmadd(e, p4f_cephes_log_q2, x); + + // x is now the logarithm result candidate. We still need to handle the + // extreme arguments of zero and positive infinity, though. + // N.B. if the argument is +INFINITY, x is NAN because the polynomial terms + // contain infinities of both signs (see the coefficients and code above). + // INFINITY - INFINITY is NAN. + + // If the argument is +INFINITY, make it the new result candidate. + // To achieve that we choose the smaller of the result candidate and the + // argument. + // This is correct for all finite pairs of values (the logarithm is smaller + // than the argument). + // This is also correct in the special case when the argument is +INFINITY + // and the result candidate is NAN. This is because the fmin.df instruction + // prefers non-NANs to NANs. + x = __builtin_msa_fmin_w(x, non_neg_x_or_nan); + + // If the argument is zero (including -0.0), the result becomes -INFINITY. + Packet4i neg_infs = __builtin_msa_slli_w(zero_mask, 23); + x = (Packet4f)__builtin_msa_bsel_v((v16u8)zero_mask, (v16u8)x, (v16u8)neg_infs); + + return x; +} + +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f +pexp<Packet4f>(const Packet4f& _x) { + // Limiting single-precision pexp's argument to [-128, +128] lets pexp + // reach 0 and INFINITY naturally. + static _EIGEN_DECLARE_CONST_Packet4f(exp_lo, -128.0f); + static _EIGEN_DECLARE_CONST_Packet4f(exp_hi, +128.0f); + static _EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f); + static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f); + static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f); + static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500e-4f); + static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507e-3f); + static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073e-3f); + static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894e-2f); + static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459e-1f); + static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201e-1f); + static _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f); + static _EIGEN_DECLARE_CONST_Packet4f(1, 1.0f); + + Packet4f x = _x; + + // Clamp x. + x = (Packet4f)__builtin_msa_bsel_v((v16u8)__builtin_msa_fclt_w(x, p4f_exp_lo), (v16u8)x, + (v16u8)p4f_exp_lo); + x = (Packet4f)__builtin_msa_bsel_v((v16u8)__builtin_msa_fclt_w(p4f_exp_hi, x), (v16u8)x, + (v16u8)p4f_exp_hi); + + // Round to nearest integer by adding 0.5 (with x's sign) and truncating. + Packet4f x2_add = (Packet4f)__builtin_msa_binsli_w((v4u32)p4f_half, (v4u32)x, 0); + Packet4f x2 = pmadd(x, p4f_cephes_LOG2EF, x2_add); + Packet4i x2_int = __builtin_msa_ftrunc_s_w(x2); + Packet4f x2_int_f = __builtin_msa_ffint_s_w(x2_int); + + x = __builtin_msa_fmsub_w(x, x2_int_f, p4f_cephes_exp_C1); + x = __builtin_msa_fmsub_w(x, x2_int_f, p4f_cephes_exp_C2); + + Packet4f 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); + + // y *= 2**exponent. + y = __builtin_msa_fexp2_w(y, x2_int); + + return y; +} + +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f +ptanh<Packet4f>(const Packet4f& _x) { + static _EIGEN_DECLARE_CONST_Packet4f(tanh_tiny, 1e-4f); + static _EIGEN_DECLARE_CONST_Packet4f(tanh_hi, 9.0f); + // The monomial coefficients of the numerator polynomial (odd). + static _EIGEN_DECLARE_CONST_Packet4f(alpha_1, 4.89352455891786e-3f); + static _EIGEN_DECLARE_CONST_Packet4f(alpha_3, 6.37261928875436e-4f); + static _EIGEN_DECLARE_CONST_Packet4f(alpha_5, 1.48572235717979e-5f); + static _EIGEN_DECLARE_CONST_Packet4f(alpha_7, 5.12229709037114e-8f); + static _EIGEN_DECLARE_CONST_Packet4f(alpha_9, -8.60467152213735e-11f); + static _EIGEN_DECLARE_CONST_Packet4f(alpha_11, 2.00018790482477e-13f); + static _EIGEN_DECLARE_CONST_Packet4f(alpha_13, -2.76076847742355e-16f); + // The monomial coefficients of the denominator polynomial (even). + static _EIGEN_DECLARE_CONST_Packet4f(beta_0, 4.89352518554385e-3f); + static _EIGEN_DECLARE_CONST_Packet4f(beta_2, 2.26843463243900e-3f); + static _EIGEN_DECLARE_CONST_Packet4f(beta_4, 1.18534705686654e-4f); + static _EIGEN_DECLARE_CONST_Packet4f(beta_6, 1.19825839466702e-6f); + + Packet4f x = pabs(_x); + Packet4i tiny_mask = __builtin_msa_fclt_w(x, p4f_tanh_tiny); + + // Clamp the inputs to the range [-9, 9] since anything outside + // this range is -/+1.0f in single-precision. + x = (Packet4f)__builtin_msa_bsel_v((v16u8)__builtin_msa_fclt_w(p4f_tanh_hi, x), (v16u8)x, + (v16u8)p4f_tanh_hi); + + // Since the polynomials are odd/even, we need x**2. + Packet4f x2 = pmul(x, x); + + // Evaluate the numerator polynomial p. + Packet4f p = pmadd(x2, p4f_alpha_13, p4f_alpha_11); + p = pmadd(x2, p, p4f_alpha_9); + p = pmadd(x2, p, p4f_alpha_7); + p = pmadd(x2, p, p4f_alpha_5); + p = pmadd(x2, p, p4f_alpha_3); + p = pmadd(x2, p, p4f_alpha_1); + p = pmul(x, p); + + // Evaluate the denominator polynomial q. + Packet4f q = pmadd(x2, p4f_beta_6, p4f_beta_4); + q = pmadd(x2, q, p4f_beta_2); + q = pmadd(x2, q, p4f_beta_0); + + // Divide the numerator by the denominator. + p = pdiv(p, q); + + // Reinstate the sign. + p = (Packet4f)__builtin_msa_binsli_w((v4u32)p, (v4u32)_x, 0); + + // When the argument is very small in magnitude it's more accurate to just return it. + p = (Packet4f)__builtin_msa_bsel_v((v16u8)tiny_mask, (v16u8)p, (v16u8)_x); + + return p; +} + +template <bool sine> +Packet4f psincos_inner_msa_float(const Packet4f& _x) { + static _EIGEN_DECLARE_CONST_Packet4f(sincos_max_arg, 13176795.0f); // Approx. (2**24) / (4/Pi). + static _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1, -0.78515625f); + static _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f); + static _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f); + static _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891e-4f); + static _EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736e-3f); + static _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611e-1f); + static _EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948e-5f); + static _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765e-3f); + static _EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827e-2f); + static _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f); // 4/Pi. + static _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f); + static _EIGEN_DECLARE_CONST_Packet4f(1, 1.0f); + + Packet4f x = pabs(_x); + + // Translate infinite arguments into NANs. + Packet4f zero_or_nan_if_inf = psub(_x, _x); + x = padd(x, zero_or_nan_if_inf); + // Prevent sin/cos from generating values larger than 1.0 in magnitude + // for very large arguments by setting x to 0.0. + Packet4i small_or_nan_mask = __builtin_msa_fcult_w(x, p4f_sincos_max_arg); + x = pand(x, (Packet4f)small_or_nan_mask); + + // Scale x by 4/Pi to find x's octant. + Packet4f y = pmul(x, p4f_cephes_FOPI); + // Get the octant. We'll reduce x by this number of octants or by one more than it. + Packet4i y_int = __builtin_msa_ftrunc_s_w(y); + // x's from even-numbered octants will translate to octant 0: [0, +Pi/4]. + // x's from odd-numbered octants will translate to octant -1: [-Pi/4, 0]. + // Adjustment for odd-numbered octants: octant = (octant + 1) & (~1). + Packet4i y_int1 = __builtin_msa_addvi_w(y_int, 1); + Packet4i y_int2 = (Packet4i)__builtin_msa_bclri_w((Packet4ui)y_int1, 0); // bclri = bit-clear + y = __builtin_msa_ffint_s_w(y_int2); + + // Compute the sign to apply to the polynomial. + Packet4i sign_mask = sine ? pxor(__builtin_msa_slli_w(y_int1, 29), (Packet4i)_x) + : __builtin_msa_slli_w(__builtin_msa_addvi_w(y_int, 3), 29); + + // Get the polynomial selection mask. + // We'll calculate both (sin and cos) polynomials and then select from the two. + Packet4i poly_mask = __builtin_msa_ceqi_w(__builtin_msa_slli_w(y_int2, 30), 0); + + // Reduce x by y octants to get: -Pi/4 <= x <= +Pi/4. + // The magic pass: "Extended precision modular arithmetic" + // x = ((x - y * DP1) - y * DP2) - y * DP3 + Packet4f tmp1 = pmul(y, p4f_minus_cephes_DP1); + Packet4f tmp2 = pmul(y, p4f_minus_cephes_DP2); + Packet4f tmp3 = pmul(y, p4f_minus_cephes_DP3); + x = padd(x, tmp1); + x = padd(x, tmp2); + x = padd(x, tmp3); + + // Evaluate the cos(x) polynomial. + 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); + y = __builtin_msa_fmsub_w(y, z, p4f_half); + y = padd(y, p4f_1); + + // Evaluate the sin(x) polynomial. + 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 polynomials. + y = sine ? (Packet4f)__builtin_msa_bsel_v((v16u8)poly_mask, (v16u8)y, (v16u8)y2) + : (Packet4f)__builtin_msa_bsel_v((v16u8)poly_mask, (v16u8)y2, (v16u8)y); + + // Update the sign. + sign_mask = pxor(sign_mask, (Packet4i)y); + y = (Packet4f)__builtin_msa_binsli_w((v4u32)y, (v4u32)sign_mask, 0); // binsli = bit-insert-left + return y; +} + +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f +psin<Packet4f>(const Packet4f& x) { + return psincos_inner_msa_float</* sine */ true>(x); +} + +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f +pcos<Packet4f>(const Packet4f& x) { + return psincos_inner_msa_float</* sine */ false>(x); +} + +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet2d +pexp<Packet2d>(const Packet2d& _x) { + // Limiting double-precision pexp's argument to [-1024, +1024] lets pexp + // reach 0 and INFINITY naturally. + static _EIGEN_DECLARE_CONST_Packet2d(exp_lo, -1024.0); + static _EIGEN_DECLARE_CONST_Packet2d(exp_hi, +1024.0); + static _EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599); + static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125); + static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6); + static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4); + static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2); + static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1); + static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6); + static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3); + static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1); + static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0); + static _EIGEN_DECLARE_CONST_Packet2d(half, 0.5); + static _EIGEN_DECLARE_CONST_Packet2d(1, 1.0); + static _EIGEN_DECLARE_CONST_Packet2d(2, 2.0); + + Packet2d x = _x; + + // Clamp x. + x = (Packet2d)__builtin_msa_bsel_v((v16u8)__builtin_msa_fclt_d(x, p2d_exp_lo), (v16u8)x, + (v16u8)p2d_exp_lo); + x = (Packet2d)__builtin_msa_bsel_v((v16u8)__builtin_msa_fclt_d(p2d_exp_hi, x), (v16u8)x, + (v16u8)p2d_exp_hi); + + // Round to nearest integer by adding 0.5 (with x's sign) and truncating. + Packet2d x2_add = (Packet2d)__builtin_msa_binsli_d((v2u64)p2d_half, (v2u64)x, 0); + Packet2d x2 = pmadd(x, p2d_cephes_LOG2EF, x2_add); + Packet2l x2_long = __builtin_msa_ftrunc_s_d(x2); + Packet2d x2_long_d = __builtin_msa_ffint_s_d(x2_long); + + x = __builtin_msa_fmsub_d(x, x2_long_d, p2d_cephes_exp_C1); + x = __builtin_msa_fmsub_d(x, x2_long_d, p2d_cephes_exp_C2); + + 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); + + // x *= 2**exponent. + x = __builtin_msa_fexp2_d(x, x2_long); + + return x; +} + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_MATH_FUNCTIONS_MSA_H |