79 lines
2.7 KiB
C++
79 lines
2.7 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2014 Pedro Gonnet (pedro.gonnet@gmail.com)
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// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#ifndef EIGEN_MATHFUNCTIONSIMPL_H
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#define EIGEN_MATHFUNCTIONSIMPL_H
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namespace Eigen {
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namespace internal {
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/** \internal \returns the hyperbolic tan of \a a (coeff-wise)
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Doesn't do anything fancy, just a 13/6-degree rational interpolant which
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is accurate up to a couple of ulp in the range [-9, 9], outside of which
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the tanh(x) = +/-1.
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This implementation works on both scalars and packets.
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*/
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template<typename T>
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T generic_fast_tanh_float(const T& a_x)
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{
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// Clamp the inputs to the range [-9, 9] since anything outside
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// this range is +/-1.0f in single-precision.
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const T plus_9 = pset1<T>(9.f);
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const T minus_9 = pset1<T>(-9.f);
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// NOTE GCC prior to 6.3 might improperly optimize this max/min
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// step such that if a_x is nan, x will be either 9 or -9,
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// and tanh will return 1 or -1 instead of nan.
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// This is supposed to be fixed in gcc6.3,
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// see: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=72867
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const T x = pmax(minus_9,pmin(plus_9,a_x));
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// The monomial coefficients of the numerator polynomial (odd).
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const T alpha_1 = pset1<T>(4.89352455891786e-03f);
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const T alpha_3 = pset1<T>(6.37261928875436e-04f);
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const T alpha_5 = pset1<T>(1.48572235717979e-05f);
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const T alpha_7 = pset1<T>(5.12229709037114e-08f);
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const T alpha_9 = pset1<T>(-8.60467152213735e-11f);
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const T alpha_11 = pset1<T>(2.00018790482477e-13f);
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const T alpha_13 = pset1<T>(-2.76076847742355e-16f);
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// The monomial coefficients of the denominator polynomial (even).
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const T beta_0 = pset1<T>(4.89352518554385e-03f);
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const T beta_2 = pset1<T>(2.26843463243900e-03f);
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const T beta_4 = pset1<T>(1.18534705686654e-04f);
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const T beta_6 = pset1<T>(1.19825839466702e-06f);
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// Since the polynomials are odd/even, we need x^2.
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const T x2 = pmul(x, x);
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// Evaluate the numerator polynomial p.
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T p = pmadd(x2, alpha_13, alpha_11);
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p = pmadd(x2, p, alpha_9);
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p = pmadd(x2, p, alpha_7);
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p = pmadd(x2, p, alpha_5);
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p = pmadd(x2, p, alpha_3);
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p = pmadd(x2, p, alpha_1);
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p = pmul(x, p);
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// Evaluate the denominator polynomial p.
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T q = pmadd(x2, beta_6, beta_4);
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q = pmadd(x2, q, beta_2);
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q = pmadd(x2, q, beta_0);
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// Divide the numerator by the denominator.
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return pdiv(p, q);
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}
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} // end namespace internal
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} // end namespace Eigen
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#endif // EIGEN_MATHFUNCTIONSIMPL_H
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