// David Eberly, Geometric Tools, Redmond WA 98052 // Copyright (c) 1998-2020 // Distributed under the Boost Software License, Version 1.0. // https://www.boost.org/LICENSE_1_0.txt // https://www.geometrictools.com/License/Boost/LICENSE_1_0.txt // Version: 4.0.2019.08.13 #pragma once #include // Minimax polynomial approximations to 2^x. The polynomial p(x) of // degree D minimizes the quantity maximum{|2^x - p(x)| : x in [0,1]} // over all polynomials of degree D. namespace WwiseGTE { template class Exp2Estimate { public: // The input constraint is x in [0,1]. For example, // float x; // in [0,1] // float result = Exp2Estimate::Degree<3>(x); template inline static Real Degree(Real x) { return Evaluate(degree(), x); } // The input x can be any real number. Range reduction is used to // generate a value y in [0,1], call Degree(y), and combine the output // with the proper exponent to obtain the approximation. For example, // float x; // x >= 0 // float result = Exp2Estimate::DegreeRR<3>(x); template inline static Real DegreeRR(Real x) { Real p = std::floor(x); Real y = x - p; Real poly = Degree(y); Real result = std::ldexp(poly, (int)p); return result; } private: // Metaprogramming and private implementation to allow specialization // of a template member function. template struct degree {}; inline static Real Evaluate(degree<1>, Real t) { Real poly; poly = (Real)GTE_C_EXP2_DEG1_C1; poly = (Real)GTE_C_EXP2_DEG1_C0 + poly * t; return poly; } inline static Real Evaluate(degree<2>, Real t) { Real poly; poly = (Real)GTE_C_EXP2_DEG2_C2; poly = (Real)GTE_C_EXP2_DEG2_C1 + poly * t; poly = (Real)GTE_C_EXP2_DEG2_C0 + poly * t; return poly; } inline static Real Evaluate(degree<3>, Real t) { Real poly; poly = (Real)GTE_C_EXP2_DEG3_C3; poly = (Real)GTE_C_EXP2_DEG3_C2 + poly * t; poly = (Real)GTE_C_EXP2_DEG3_C1 + poly * t; poly = (Real)GTE_C_EXP2_DEG3_C0 + poly * t; return poly; } inline static Real Evaluate(degree<4>, Real t) { Real poly; poly = (Real)GTE_C_EXP2_DEG4_C4; poly = (Real)GTE_C_EXP2_DEG4_C3 + poly * t; poly = (Real)GTE_C_EXP2_DEG4_C2 + poly * t; poly = (Real)GTE_C_EXP2_DEG4_C1 + poly * t; poly = (Real)GTE_C_EXP2_DEG4_C0 + poly * t; return poly; } inline static Real Evaluate(degree<5>, Real t) { Real poly; poly = (Real)GTE_C_EXP2_DEG5_C5; poly = (Real)GTE_C_EXP2_DEG5_C4 + poly * t; poly = (Real)GTE_C_EXP2_DEG5_C3 + poly * t; poly = (Real)GTE_C_EXP2_DEG5_C2 + poly * t; poly = (Real)GTE_C_EXP2_DEG5_C1 + poly * t; poly = (Real)GTE_C_EXP2_DEG5_C0 + poly * t; return poly; } inline static Real Evaluate(degree<6>, Real t) { Real poly; poly = (Real)GTE_C_EXP2_DEG6_C6; poly = (Real)GTE_C_EXP2_DEG6_C5 + poly * t; poly = (Real)GTE_C_EXP2_DEG6_C4 + poly * t; poly = (Real)GTE_C_EXP2_DEG6_C3 + poly * t; poly = (Real)GTE_C_EXP2_DEG6_C2 + poly * t; poly = (Real)GTE_C_EXP2_DEG6_C1 + poly * t; poly = (Real)GTE_C_EXP2_DEG6_C0 + poly * t; return poly; } inline static Real Evaluate(degree<7>, Real t) { Real poly; poly = (Real)GTE_C_EXP2_DEG7_C7; poly = (Real)GTE_C_EXP2_DEG7_C6 + poly * t; poly = (Real)GTE_C_EXP2_DEG7_C5 + poly * t; poly = (Real)GTE_C_EXP2_DEG7_C4 + poly * t; poly = (Real)GTE_C_EXP2_DEG7_C3 + poly * t; poly = (Real)GTE_C_EXP2_DEG7_C2 + poly * t; poly = (Real)GTE_C_EXP2_DEG7_C1 + poly * t; poly = (Real)GTE_C_EXP2_DEG7_C0 + poly * t; return poly; } }; }