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- // This file is part of Eigen, a lightweight C++ template library
- // for linear algebra.
- //
- // Copyright (C) 2014 Pedro Gonnet (pedro.gonnet@gmail.com)
- // Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
- //
- // 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_MATHFUNCTIONSIMPL_H
- #define EIGEN_MATHFUNCTIONSIMPL_H
- namespace Eigen {
- namespace internal {
- /** \internal \returns the hyperbolic tan of \a a (coeff-wise)
- Doesn't do anything fancy, just a 13/6-degree rational interpolant which
- is accurate up to a couple of ulp in the range [-9, 9], outside of which
- the tanh(x) = +/-1.
- This implementation works on both scalars and packets.
- */
- template<typename T>
- T generic_fast_tanh_float(const T& a_x)
- {
- // Clamp the inputs to the range [-9, 9] since anything outside
- // this range is +/-1.0f in single-precision.
- const T plus_9 = pset1<T>(9.f);
- const T minus_9 = pset1<T>(-9.f);
- // NOTE GCC prior to 6.3 might improperly optimize this max/min
- // step such that if a_x is nan, x will be either 9 or -9,
- // and tanh will return 1 or -1 instead of nan.
- // This is supposed to be fixed in gcc6.3,
- // see: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=72867
- const T x = pmax(minus_9,pmin(plus_9,a_x));
- // The monomial coefficients of the numerator polynomial (odd).
- const T alpha_1 = pset1<T>(4.89352455891786e-03f);
- const T alpha_3 = pset1<T>(6.37261928875436e-04f);
- const T alpha_5 = pset1<T>(1.48572235717979e-05f);
- const T alpha_7 = pset1<T>(5.12229709037114e-08f);
- const T alpha_9 = pset1<T>(-8.60467152213735e-11f);
- const T alpha_11 = pset1<T>(2.00018790482477e-13f);
- const T alpha_13 = pset1<T>(-2.76076847742355e-16f);
- // The monomial coefficients of the denominator polynomial (even).
- const T beta_0 = pset1<T>(4.89352518554385e-03f);
- const T beta_2 = pset1<T>(2.26843463243900e-03f);
- const T beta_4 = pset1<T>(1.18534705686654e-04f);
- const T beta_6 = pset1<T>(1.19825839466702e-06f);
- // Since the polynomials are odd/even, we need x^2.
- const T x2 = pmul(x, x);
- // Evaluate the numerator polynomial p.
- T p = pmadd(x2, alpha_13, alpha_11);
- p = pmadd(x2, p, alpha_9);
- p = pmadd(x2, p, alpha_7);
- p = pmadd(x2, p, alpha_5);
- p = pmadd(x2, p, alpha_3);
- p = pmadd(x2, p, alpha_1);
- p = pmul(x, p);
- // Evaluate the denominator polynomial p.
- T q = pmadd(x2, beta_6, beta_4);
- q = pmadd(x2, q, beta_2);
- q = pmadd(x2, q, beta_0);
- // Divide the numerator by the denominator.
- return pdiv(p, q);
- }
- template<typename RealScalar>
- EIGEN_STRONG_INLINE
- RealScalar positive_real_hypot(const RealScalar& x, const RealScalar& y)
- {
- EIGEN_USING_STD_MATH(sqrt);
- RealScalar p, qp;
- p = numext::maxi(x,y);
- if(p==RealScalar(0)) return RealScalar(0);
- qp = numext::mini(y,x) / p;
- return p * sqrt(RealScalar(1) + qp*qp);
- }
- template<typename Scalar>
- struct hypot_impl
- {
- typedef typename NumTraits<Scalar>::Real RealScalar;
- static inline RealScalar run(const Scalar& x, const Scalar& y)
- {
- EIGEN_USING_STD_MATH(abs);
- return positive_real_hypot<RealScalar>(abs(x), abs(y));
- }
- };
- } // end namespace internal
- } // end namespace Eigen
- #endif // EIGEN_MATHFUNCTIONSIMPL_H
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