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45 lines
1.5 KiB
45 lines
1.5 KiB
3 months ago
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// David Eberly, Geometric Tools, Redmond WA 98052
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// Copyright (c) 1998-2021
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// Distributed under the Boost Software License, Version 1.0.
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// https://www.boost.org/LICENSE_1_0.txt
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// https://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
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// Version: 4.0.2019.12.23
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#pragma once
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#include <Mathematics/Exp2Estimate.h>
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// Minimax polynomial approximations to 2^x. The polynomial p(x) of
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// degree D minimizes the quantity maximum{|2^x - p(x)| : x in [0,1]}
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// over all polynomials of degree D. The natural exponential is
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// computed using exp(x) = 2^{x/log(2)}, where log(2) is the natural
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// logarithm of 2.
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namespace gte
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{
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template <typename Real>
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class ExpEstimate
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{
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public:
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// The input constraint is x in [0,1]. For example,
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// float x; // in [0,1]
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// float result = ExpEstimate<float>::Degree<3>(x);
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template <int D>
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inline static Real Degree(Real x)
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{
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return Exp2Estimate<Real>::Degree<D>(x * (Real)GTE_C_INV_LN_2);
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}
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// The input x can be any real number. Range reduction is used to
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// generate a value y in [0,1], call Degree(y), and combine the output
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// with the proper exponent to obtain the approximation. For example,
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// float x; // x >= 0
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// float result = ExpEstimate<float>::DegreeRR<3>(x);
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template <int D>
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inline static Real DegreeRR(Real x)
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{
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return Exp2Estimate<Real>::DegreeRR<D>(x * (Real)GTE_C_INV_LN_2);
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}
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};
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}
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