arch/MSA/MathFunctions.h

0001 // This file is part of Eigen, a lightweight C++ template library
0002 // for linear algebra.
0003 //
0004 // Copyright (C) 2007 Julien Pommier
0005 // Copyright (C) 2014 Pedro Gonnet (pedro.gonnet@gmail.com)
0006 // Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
0007 //
0008 // Copyright (C) 2018 Wave Computing, Inc.
0009 // Written by:
0010 //   Chris Larsen
0011 //   Alexey Frunze (afrunze@wavecomp.com)
0012 //
0013 // This Source Code Form is subject to the terms of the Mozilla
0014 // Public License v. 2.0. If a copy of the MPL was not distributed
0015 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
0016
0017 /* The sin, cos, exp, and log functions of this file come from
0018  * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/
0019  */
0020
0021 /* The tanh function of this file is an adaptation of
0022  * template<typename T> T generic_fast_tanh_float(const T&)
0023  * from MathFunctionsImpl.h.
0024  */
0025
0026 #ifndef EIGEN_MATH_FUNCTIONS_MSA_H
0027 #define EIGEN_MATH_FUNCTIONS_MSA_H
0028
0029 namespace RivetEigen {
0030
0031 namespace internal {
0032
0033 template <>
0034 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f
0035 plog<Packet4f>(const Packet4f& _x) {
0036   static _EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);
0037   static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292e-2f);
0038   static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, -1.1514610310e-1f);
0039   static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740e-1f);
0040   static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, -1.2420140846e-1f);
0041   static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, +1.4249322787e-1f);
0042   static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, -1.6668057665e-1f);
0043   static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, +2.0000714765e-1f);
0044   static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, -2.4999993993e-1f);
0045   static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, +3.3333331174e-1f);
0046   static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);
0047   static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);
0048   static _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
0049   static _EIGEN_DECLARE_CONST_Packet4f(1, 1.0f);
0050
0051   // Convert negative argument into NAN (quiet negative, to be specific).
0052   Packet4f zero = (Packet4f)__builtin_msa_ldi_w(0);
0053   Packet4i neg_mask = __builtin_msa_fclt_w(_x, zero);
0054   Packet4i zero_mask = __builtin_msa_fceq_w(_x, zero);
0055   Packet4f non_neg_x_or_nan = padd(_x, (Packet4f)neg_mask);  // Add 0.0 or NAN.
0056   Packet4f x = non_neg_x_or_nan;
0057
0058   // Extract exponent from x = mantissa * 2**exponent, where 1.0 <= mantissa < 2.0.
0059   // N.B. the exponent is one less of what frexpf() would return.
0060   Packet4i e_int = __builtin_msa_ftint_s_w(__builtin_msa_flog2_w(x));
0061   // Multiply x by 2**(-exponent-1) to get 0.5 <= x < 1.0 as from frexpf().
0062   x = __builtin_msa_fexp2_w(x, (Packet4i)__builtin_msa_nori_b((v16u8)e_int, 0));
0063
0064   /*
0065      if (x < SQRTHF) {
0066        x = x + x - 1.0;
0067      } else {
0068        e += 1;
0069        x = x - 1.0;
0070      }
0071   */
0072   Packet4f xx = padd(x, x);
0073   Packet4i ge_mask = __builtin_msa_fcle_w(p4f_cephes_SQRTHF, x);
0074   e_int = psub(e_int, ge_mask);
0075   x = (Packet4f)__builtin_msa_bsel_v((v16u8)ge_mask, (v16u8)xx, (v16u8)x);
0076   x = psub(x, p4f_1);
0077   Packet4f e = __builtin_msa_ffint_s_w(e_int);
0078
0079   Packet4f x2 = pmul(x, x);
0080   Packet4f x3 = pmul(x2, x);
0081
0082   Packet4f y, y1, y2;
0083   y = pmadd(p4f_cephes_log_p0, x, p4f_cephes_log_p1);
0084   y1 = pmadd(p4f_cephes_log_p3, x, p4f_cephes_log_p4);
0085   y2 = pmadd(p4f_cephes_log_p6, x, p4f_cephes_log_p7);
0086   y = pmadd(y, x, p4f_cephes_log_p2);
0087   y1 = pmadd(y1, x, p4f_cephes_log_p5);
0088   y2 = pmadd(y2, x, p4f_cephes_log_p8);
0089   y = pmadd(y, x3, y1);
0090   y = pmadd(y, x3, y2);
0091   y = pmul(y, x3);
0092
0093   y = pmadd(e, p4f_cephes_log_q1, y);
0094   x = __builtin_msa_fmsub_w(x, x2, p4f_half);
0095   x = padd(x, y);
0096   x = pmadd(e, p4f_cephes_log_q2, x);
0097
0098   // x is now the logarithm result candidate. We still need to handle the
0099   // extreme arguments of zero and positive infinity, though.
0100   // N.B. if the argument is +INFINITY, x is NAN because the polynomial terms
0101   // contain infinities of both signs (see the coefficients and code above).
0102   // INFINITY - INFINITY is NAN.
0103
0104   // If the argument is +INFINITY, make it the new result candidate.
0105   // To achieve that we choose the smaller of the result candidate and the
0106   // argument.
0107   // This is correct for all finite pairs of values (the logarithm is smaller
0108   // than the argument).
0109   // This is also correct in the special case when the argument is +INFINITY
0110   // and the result candidate is NAN. This is because the fmin.df instruction
0111   // prefers non-NANs to NANs.
0112   x = __builtin_msa_fmin_w(x, non_neg_x_or_nan);
0113
0114   // If the argument is zero (including -0.0), the result becomes -INFINITY.
0115   Packet4i neg_infs = __builtin_msa_slli_w(zero_mask, 23);
0116   x = (Packet4f)__builtin_msa_bsel_v((v16u8)zero_mask, (v16u8)x, (v16u8)neg_infs);
0117
0118   return x;
0119 }
0120
0121 template <>
0122 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f
0123 pexp<Packet4f>(const Packet4f& _x) {
0124   // Limiting single-precision pexp's argument to [-128, +128] lets pexp
0125   // reach 0 and INFINITY naturally.
0126   static _EIGEN_DECLARE_CONST_Packet4f(exp_lo, -128.0f);
0127   static _EIGEN_DECLARE_CONST_Packet4f(exp_hi, +128.0f);
0128   static _EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);
0129   static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);
0130   static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);
0131   static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500e-4f);
0132   static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507e-3f);
0133   static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073e-3f);
0134   static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894e-2f);
0135   static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459e-1f);
0136   static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201e-1f);
0137   static _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
0138   static _EIGEN_DECLARE_CONST_Packet4f(1, 1.0f);
0139
0140   Packet4f x = _x;
0141
0142   // Clamp x.
0143   x = (Packet4f)__builtin_msa_bsel_v((v16u8)__builtin_msa_fclt_w(x, p4f_exp_lo), (v16u8)x,
0144                                      (v16u8)p4f_exp_lo);
0145   x = (Packet4f)__builtin_msa_bsel_v((v16u8)__builtin_msa_fclt_w(p4f_exp_hi, x), (v16u8)x,
0146                                      (v16u8)p4f_exp_hi);
0147
0148   // Round to nearest integer by adding 0.5 (with x's sign) and truncating.
0149   Packet4f x2_add = (Packet4f)__builtin_msa_binsli_w((v4u32)p4f_half, (v4u32)x, 0);
0150   Packet4f x2 = pmadd(x, p4f_cephes_LOG2EF, x2_add);
0151   Packet4i x2_int = __builtin_msa_ftrunc_s_w(x2);
0152   Packet4f x2_int_f = __builtin_msa_ffint_s_w(x2_int);
0153
0154   x = __builtin_msa_fmsub_w(x, x2_int_f, p4f_cephes_exp_C1);
0155   x = __builtin_msa_fmsub_w(x, x2_int_f, p4f_cephes_exp_C2);
0156
0157   Packet4f z = pmul(x, x);
0158
0159   Packet4f y = p4f_cephes_exp_p0;
0160   y = pmadd(y, x, p4f_cephes_exp_p1);
0161   y = pmadd(y, x, p4f_cephes_exp_p2);
0162   y = pmadd(y, x, p4f_cephes_exp_p3);
0163   y = pmadd(y, x, p4f_cephes_exp_p4);
0164   y = pmadd(y, x, p4f_cephes_exp_p5);
0165   y = pmadd(y, z, x);
0166   y = padd(y, p4f_1);
0167
0168   // y *= 2**exponent.
0169   y = __builtin_msa_fexp2_w(y, x2_int);
0170
0171   return y;
0172 }
0173
0174 template <>
0175 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f
0176 ptanh<Packet4f>(const Packet4f& _x) {
0177   static _EIGEN_DECLARE_CONST_Packet4f(tanh_tiny, 1e-4f);
0178   static _EIGEN_DECLARE_CONST_Packet4f(tanh_hi, 9.0f);
0179   // The monomial coefficients of the numerator polynomial (odd).
0180   static _EIGEN_DECLARE_CONST_Packet4f(alpha_1, 4.89352455891786e-3f);
0181   static _EIGEN_DECLARE_CONST_Packet4f(alpha_3, 6.37261928875436e-4f);
0182   static _EIGEN_DECLARE_CONST_Packet4f(alpha_5, 1.48572235717979e-5f);
0183   static _EIGEN_DECLARE_CONST_Packet4f(alpha_7, 5.12229709037114e-8f);
0184   static _EIGEN_DECLARE_CONST_Packet4f(alpha_9, -8.60467152213735e-11f);
0185   static _EIGEN_DECLARE_CONST_Packet4f(alpha_11, 2.00018790482477e-13f);
0186   static _EIGEN_DECLARE_CONST_Packet4f(alpha_13, -2.76076847742355e-16f);
0187   // The monomial coefficients of the denominator polynomial (even).
0188   static _EIGEN_DECLARE_CONST_Packet4f(beta_0, 4.89352518554385e-3f);
0189   static _EIGEN_DECLARE_CONST_Packet4f(beta_2, 2.26843463243900e-3f);
0190   static _EIGEN_DECLARE_CONST_Packet4f(beta_4, 1.18534705686654e-4f);
0191   static _EIGEN_DECLARE_CONST_Packet4f(beta_6, 1.19825839466702e-6f);
0192
0193   Packet4f x = pabs(_x);
0194   Packet4i tiny_mask = __builtin_msa_fclt_w(x, p4f_tanh_tiny);
0195
0196   // Clamp the inputs to the range [-9, 9] since anything outside
0197   // this range is -/+1.0f in single-precision.
0198   x = (Packet4f)__builtin_msa_bsel_v((v16u8)__builtin_msa_fclt_w(p4f_tanh_hi, x), (v16u8)x,
0199                                      (v16u8)p4f_tanh_hi);
0200
0201   // Since the polynomials are odd/even, we need x**2.
0202   Packet4f x2 = pmul(x, x);
0203
0204   // Evaluate the numerator polynomial p.
0205   Packet4f p = pmadd(x2, p4f_alpha_13, p4f_alpha_11);
0206   p = pmadd(x2, p, p4f_alpha_9);
0207   p = pmadd(x2, p, p4f_alpha_7);
0208   p = pmadd(x2, p, p4f_alpha_5);
0209   p = pmadd(x2, p, p4f_alpha_3);
0210   p = pmadd(x2, p, p4f_alpha_1);
0211   p = pmul(x, p);
0212
0213   // Evaluate the denominator polynomial q.
0214   Packet4f q = pmadd(x2, p4f_beta_6, p4f_beta_4);
0215   q = pmadd(x2, q, p4f_beta_2);
0216   q = pmadd(x2, q, p4f_beta_0);
0217
0218   // Divide the numerator by the denominator.
0219   p = pdiv(p, q);
0220
0221   // Reinstate the sign.
0222   p = (Packet4f)__builtin_msa_binsli_w((v4u32)p, (v4u32)_x, 0);
0223
0224   // When the argument is very small in magnitude it's more accurate to just return it.
0225   p = (Packet4f)__builtin_msa_bsel_v((v16u8)tiny_mask, (v16u8)p, (v16u8)_x);
0226
0227   return p;
0228 }
0229
0230 template <bool sine>
0231 Packet4f psincos_inner_msa_float(const Packet4f& _x) {
0232   static _EIGEN_DECLARE_CONST_Packet4f(sincos_max_arg, 13176795.0f);  // Approx. (2**24) / (4/Pi).
0233   static _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1, -0.78515625f);
0234   static _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);
0235   static _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);
0236   static _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891e-4f);
0237   static _EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736e-3f);
0238   static _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611e-1f);
0239   static _EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948e-5f);
0240   static _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765e-3f);
0241   static _EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827e-2f);
0242   static _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f);  // 4/Pi.
0243   static _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
0244   static _EIGEN_DECLARE_CONST_Packet4f(1, 1.0f);
0245
0246   Packet4f x = pabs(_x);
0247
0248   // Translate infinite arguments into NANs.
0249   Packet4f zero_or_nan_if_inf = psub(_x, _x);
0250   x = padd(x, zero_or_nan_if_inf);
0251   // Prevent sin/cos from generating values larger than 1.0 in magnitude
0252   // for very large arguments by setting x to 0.0.
0253   Packet4i small_or_nan_mask = __builtin_msa_fcult_w(x, p4f_sincos_max_arg);
0254   x = pand(x, (Packet4f)small_or_nan_mask);
0255
0256   // Scale x by 4/Pi to find x's octant.
0257   Packet4f y = pmul(x, p4f_cephes_FOPI);
0258   // Get the octant. We'll reduce x by this number of octants or by one more than it.
0259   Packet4i y_int = __builtin_msa_ftrunc_s_w(y);
0260   // x's from even-numbered octants will translate to octant 0: [0, +Pi/4].
0261   // x's from odd-numbered octants will translate to octant -1: [-Pi/4, 0].
0262   // Adjustment for odd-numbered octants: octant = (octant + 1) & (~1).
0263   Packet4i y_int1 = __builtin_msa_addvi_w(y_int, 1);
0264   Packet4i y_int2 = (Packet4i)__builtin_msa_bclri_w((Packet4ui)y_int1, 0); // bclri = bit-clear
0265   y = __builtin_msa_ffint_s_w(y_int2);
0266
0267   // Compute the sign to apply to the polynomial.
0268   Packet4i sign_mask = sine ? pxor(__builtin_msa_slli_w(y_int1, 29), (Packet4i)_x)
0269                             : __builtin_msa_slli_w(__builtin_msa_addvi_w(y_int, 3), 29);
0270
0271   // Get the polynomial selection mask.
0272   // We'll calculate both (sin and cos) polynomials and then select from the two.
0273   Packet4i poly_mask = __builtin_msa_ceqi_w(__builtin_msa_slli_w(y_int2, 30), 0);
0274
0275   // Reduce x by y octants to get: -Pi/4 <= x <= +Pi/4.
0276   // The magic pass: "Extended precision modular arithmetic"
0277   // x = ((x - y * DP1) - y * DP2) - y * DP3
0278   Packet4f tmp1 = pmul(y, p4f_minus_cephes_DP1);
0279   Packet4f tmp2 = pmul(y, p4f_minus_cephes_DP2);
0280   Packet4f tmp3 = pmul(y, p4f_minus_cephes_DP3);
0281   x = padd(x, tmp1);
0282   x = padd(x, tmp2);
0283   x = padd(x, tmp3);
0284
0285   // Evaluate the cos(x) polynomial.
0286   y = p4f_coscof_p0;
0287   Packet4f z = pmul(x, x);
0288   y = pmadd(y, z, p4f_coscof_p1);
0289   y = pmadd(y, z, p4f_coscof_p2);
0290   y = pmul(y, z);
0291   y = pmul(y, z);
0292   y = __builtin_msa_fmsub_w(y, z, p4f_half);
0293   y = padd(y, p4f_1);
0294
0295   // Evaluate the sin(x) polynomial.
0296   Packet4f y2 = p4f_sincof_p0;
0297   y2 = pmadd(y2, z, p4f_sincof_p1);
0298   y2 = pmadd(y2, z, p4f_sincof_p2);
0299   y2 = pmul(y2, z);
0300   y2 = pmadd(y2, x, x);
0301
0302   // Select the correct result from the two polynomials.
0303   y = sine ? (Packet4f)__builtin_msa_bsel_v((v16u8)poly_mask, (v16u8)y, (v16u8)y2)
0304            : (Packet4f)__builtin_msa_bsel_v((v16u8)poly_mask, (v16u8)y2, (v16u8)y);
0305
0306   // Update the sign.
0307   sign_mask = pxor(sign_mask, (Packet4i)y);
0308   y = (Packet4f)__builtin_msa_binsli_w((v4u32)y, (v4u32)sign_mask, 0); // binsli = bit-insert-left
0309   return y;
0310 }
0311
0312 template <>
0313 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f
0314 psin<Packet4f>(const Packet4f& x) {
0315   return psincos_inner_msa_float</* sine */ true>(x);
0316 }
0317
0318 template <>
0319 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f
0320 pcos<Packet4f>(const Packet4f& x) {
0321   return psincos_inner_msa_float</* sine */ false>(x);
0322 }
0323
0324 template <>
0325 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet2d
0326 pexp<Packet2d>(const Packet2d& _x) {
0327   // Limiting double-precision pexp's argument to [-1024, +1024] lets pexp
0328   // reach 0 and INFINITY naturally.
0329   static _EIGEN_DECLARE_CONST_Packet2d(exp_lo, -1024.0);
0330   static _EIGEN_DECLARE_CONST_Packet2d(exp_hi, +1024.0);
0331   static _EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599);
0332   static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125);
0333   static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);
0334   static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4);
0335   static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2);
0336   static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1);
0337   static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6);
0338   static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3);
0339   static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1);
0340   static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0);
0341   static _EIGEN_DECLARE_CONST_Packet2d(half, 0.5);
0342   static _EIGEN_DECLARE_CONST_Packet2d(1, 1.0);
0343   static _EIGEN_DECLARE_CONST_Packet2d(2, 2.0);
0344
0345   Packet2d x = _x;
0346
0347   // Clamp x.
0348   x = (Packet2d)__builtin_msa_bsel_v((v16u8)__builtin_msa_fclt_d(x, p2d_exp_lo), (v16u8)x,
0349                                      (v16u8)p2d_exp_lo);
0350   x = (Packet2d)__builtin_msa_bsel_v((v16u8)__builtin_msa_fclt_d(p2d_exp_hi, x), (v16u8)x,
0351                                      (v16u8)p2d_exp_hi);
0352
0353   // Round to nearest integer by adding 0.5 (with x's sign) and truncating.
0354   Packet2d x2_add = (Packet2d)__builtin_msa_binsli_d((v2u64)p2d_half, (v2u64)x, 0);
0355   Packet2d x2 = pmadd(x, p2d_cephes_LOG2EF, x2_add);
0356   Packet2l x2_long = __builtin_msa_ftrunc_s_d(x2);
0357   Packet2d x2_long_d = __builtin_msa_ffint_s_d(x2_long);
0358
0359   x = __builtin_msa_fmsub_d(x, x2_long_d, p2d_cephes_exp_C1);
0360   x = __builtin_msa_fmsub_d(x, x2_long_d, p2d_cephes_exp_C2);
0361
0362   x2 = pmul(x, x);
0363
0364   Packet2d px = p2d_cephes_exp_p0;
0365   px = pmadd(px, x2, p2d_cephes_exp_p1);
0366   px = pmadd(px, x2, p2d_cephes_exp_p2);
0367   px = pmul(px, x);
0368
0369   Packet2d qx = p2d_cephes_exp_q0;
0370   qx = pmadd(qx, x2, p2d_cephes_exp_q1);
0371   qx = pmadd(qx, x2, p2d_cephes_exp_q2);
0372   qx = pmadd(qx, x2, p2d_cephes_exp_q3);
0373
0374   x = pdiv(px, psub(qx, px));
0375   x = pmadd(p2d_2, x, p2d_1);
0376
0377   // x *= 2**exponent.
0378   x = __builtin_msa_fexp2_d(x, x2_long);
0379
0380   return x;
0381 }
0382
0383 }  // end namespace internal
0384
0385 }  // end namespace RivetEigen
0386
0387 #endif  // EIGEN_MATH_FUNCTIONS_MSA_H