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128 lines
4.3 KiB
128 lines
4.3 KiB
// 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: 4.0.2019.08.13
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#pragma once
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#include <Mathematics/Math.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.
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namespace gte
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{
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template <typename Real>
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class Exp2Estimate
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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 = Exp2Estimate<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 Evaluate(degree<D>(), x);
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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 = Exp2Estimate<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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Real p = std::floor(x);
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Real y = x - p;
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Real poly = Degree<D>(y);
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Real result = std::ldexp(poly, (int)p);
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return result;
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}
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private:
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// Metaprogramming and private implementation to allow specialization
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// of a template member function.
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template <int D> struct degree {};
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inline static Real Evaluate(degree<1>, Real t)
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{
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Real poly;
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poly = (Real)GTE_C_EXP2_DEG1_C1;
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poly = (Real)GTE_C_EXP2_DEG1_C0 + poly * t;
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return poly;
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}
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inline static Real Evaluate(degree<2>, Real t)
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{
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Real poly;
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poly = (Real)GTE_C_EXP2_DEG2_C2;
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poly = (Real)GTE_C_EXP2_DEG2_C1 + poly * t;
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poly = (Real)GTE_C_EXP2_DEG2_C0 + poly * t;
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return poly;
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}
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inline static Real Evaluate(degree<3>, Real t)
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{
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Real poly;
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poly = (Real)GTE_C_EXP2_DEG3_C3;
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poly = (Real)GTE_C_EXP2_DEG3_C2 + poly * t;
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poly = (Real)GTE_C_EXP2_DEG3_C1 + poly * t;
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poly = (Real)GTE_C_EXP2_DEG3_C0 + poly * t;
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return poly;
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}
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inline static Real Evaluate(degree<4>, Real t)
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{
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Real poly;
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poly = (Real)GTE_C_EXP2_DEG4_C4;
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poly = (Real)GTE_C_EXP2_DEG4_C3 + poly * t;
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poly = (Real)GTE_C_EXP2_DEG4_C2 + poly * t;
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poly = (Real)GTE_C_EXP2_DEG4_C1 + poly * t;
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poly = (Real)GTE_C_EXP2_DEG4_C0 + poly * t;
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return poly;
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}
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inline static Real Evaluate(degree<5>, Real t)
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{
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Real poly;
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poly = (Real)GTE_C_EXP2_DEG5_C5;
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poly = (Real)GTE_C_EXP2_DEG5_C4 + poly * t;
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poly = (Real)GTE_C_EXP2_DEG5_C3 + poly * t;
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poly = (Real)GTE_C_EXP2_DEG5_C2 + poly * t;
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poly = (Real)GTE_C_EXP2_DEG5_C1 + poly * t;
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poly = (Real)GTE_C_EXP2_DEG5_C0 + poly * t;
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return poly;
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}
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inline static Real Evaluate(degree<6>, Real t)
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{
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Real poly;
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poly = (Real)GTE_C_EXP2_DEG6_C6;
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poly = (Real)GTE_C_EXP2_DEG6_C5 + poly * t;
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poly = (Real)GTE_C_EXP2_DEG6_C4 + poly * t;
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poly = (Real)GTE_C_EXP2_DEG6_C3 + poly * t;
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poly = (Real)GTE_C_EXP2_DEG6_C2 + poly * t;
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poly = (Real)GTE_C_EXP2_DEG6_C1 + poly * t;
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poly = (Real)GTE_C_EXP2_DEG6_C0 + poly * t;
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return poly;
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}
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inline static Real Evaluate(degree<7>, Real t)
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{
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Real poly;
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poly = (Real)GTE_C_EXP2_DEG7_C7;
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poly = (Real)GTE_C_EXP2_DEG7_C6 + poly * t;
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poly = (Real)GTE_C_EXP2_DEG7_C5 + poly * t;
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poly = (Real)GTE_C_EXP2_DEG7_C4 + poly * t;
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poly = (Real)GTE_C_EXP2_DEG7_C3 + poly * t;
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poly = (Real)GTE_C_EXP2_DEG7_C2 + poly * t;
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poly = (Real)GTE_C_EXP2_DEG7_C1 + poly * t;
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poly = (Real)GTE_C_EXP2_DEG7_C0 + poly * t;
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return poly;
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}
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};
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}
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