Eigen  3.3.3
MathFunctionsImpl.h
00001 // This file is part of Eigen, a lightweight C++ template library
00002 // for linear algebra.
00003 //
00004 // Copyright (C) 2014 Pedro Gonnet (pedro.gonnet@gmail.com)
00005 // Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
00006 //
00007 // This Source Code Form is subject to the terms of the Mozilla
00008 // Public License v. 2.0. If a copy of the MPL was not distributed
00009 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
00010 
00011 #ifndef EIGEN_MATHFUNCTIONSIMPL_H
00012 #define EIGEN_MATHFUNCTIONSIMPL_H
00013 
00014 namespace Eigen {
00015 
00016 namespace internal {
00017 
00025 template<typename T>
00026 T generic_fast_tanh_float(const T& a_x)
00027 {
00028   // Clamp the inputs to the range [-9, 9] since anything outside
00029   // this range is +/-1.0f in single-precision.
00030   const T plus_9 = pset1<T>(9.f);
00031   const T minus_9 = pset1<T>(-9.f);
00032   // NOTE GCC prior to 6.3 might improperly optimize this max/min
00033   //      step such that if a_x is nan, x will be either 9 or -9,
00034   //      and tanh will return 1 or -1 instead of nan.
00035   //      This is supposed to be fixed in gcc6.3,
00036   //      see: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=72867
00037   const T x = pmax(minus_9,pmin(plus_9,a_x));
00038   // The monomial coefficients of the numerator polynomial (odd).
00039   const T alpha_1 = pset1<T>(4.89352455891786e-03f);
00040   const T alpha_3 = pset1<T>(6.37261928875436e-04f);
00041   const T alpha_5 = pset1<T>(1.48572235717979e-05f);
00042   const T alpha_7 = pset1<T>(5.12229709037114e-08f);
00043   const T alpha_9 = pset1<T>(-8.60467152213735e-11f);
00044   const T alpha_11 = pset1<T>(2.00018790482477e-13f);
00045   const T alpha_13 = pset1<T>(-2.76076847742355e-16f);
00046 
00047   // The monomial coefficients of the denominator polynomial (even).
00048   const T beta_0 = pset1<T>(4.89352518554385e-03f);
00049   const T beta_2 = pset1<T>(2.26843463243900e-03f);
00050   const T beta_4 = pset1<T>(1.18534705686654e-04f);
00051   const T beta_6 = pset1<T>(1.19825839466702e-06f);
00052 
00053   // Since the polynomials are odd/even, we need x^2.
00054   const T x2 = pmul(x, x);
00055 
00056   // Evaluate the numerator polynomial p.
00057   T p = pmadd(x2, alpha_13, alpha_11);
00058   p = pmadd(x2, p, alpha_9);
00059   p = pmadd(x2, p, alpha_7);
00060   p = pmadd(x2, p, alpha_5);
00061   p = pmadd(x2, p, alpha_3);
00062   p = pmadd(x2, p, alpha_1);
00063   p = pmul(x, p);
00064 
00065   // Evaluate the denominator polynomial p.
00066   T q = pmadd(x2, beta_6, beta_4);
00067   q = pmadd(x2, q, beta_2);
00068   q = pmadd(x2, q, beta_0);
00069 
00070   // Divide the numerator by the denominator.
00071   return pdiv(p, q);
00072 }
00073 
00074 } // end namespace internal
00075 
00076 } // end namespace Eigen
00077 
00078 #endif // EIGEN_MATHFUNCTIONSIMPL_H
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