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File indexing completed on 2025-08-05 08:19:07
0001 // TRENTO: Reduced Thickness Event-by-event Nuclear Topology 0002 // Copyright 2015 Jonah E. Bernhard, J. Scott Moreland 0003 // TRENTO3D: Three-dimensional extension of TRENTO by Weiyao Ke 0004 // MIT License 0005 0006 #ifndef FAST_EXP_H 0007 #define FAST_EXP_H 0008 0009 #include <cmath> 0010 #include <stdexcept> 0011 #include <vector> 0012 0013 namespace trento { 0014 0015 /// \rst 0016 /// Fast exponential approximation, to be used as a drop-in replacement for 0017 /// ``std::exp`` when it will be evaluated many times within a fixed range. 0018 /// Works by pre-tabulating exp() values and exploiting the leading-order Taylor 0019 /// expansion; for step size `dx` the error is `\mathcal O(dx^2)`. 0020 /// 0021 /// Example:: 0022 /// 0023 /// FastExp<double> fast_exp{0., 1., 11}; // tabulate at 0.0, 0.1, 0.2, ... 0024 /// fast_exp(0.50); // evaluate at table point -> exact result 0025 /// fast_exp(0.55); // midway between points -> worst-case error 0026 /// 0027 /// \endrst 0028 template <typename T = double> 0029 class FastExp { 0030 public: 0031 /// Pre-tabulate exp() values from \c xmin to \c xmax in \c nsteps 0032 /// evenly-spaced intervals. 0033 FastExp(T xmin, T xmax, std::size_t nsteps); 0034 0035 /// Evaluate the exponential at \em x (must be within range). 0036 T operator()(T x) const; 0037 0038 private: 0039 /// Minimum and maximum. 0040 const T xmin_, xmax_; 0041 0042 /// Step size. 0043 const T dx_; 0044 0045 /// Tabulated exp() values. 0046 std::vector<T> table_; 0047 }; 0048 0049 template <typename T> 0050 FastExp<T>::FastExp(T xmin, T xmax, std::size_t nsteps) 0051 : xmin_(xmin), 0052 xmax_(xmax), 0053 dx_((xmax-xmin)/(nsteps-1)), 0054 table_(nsteps) { 0055 // Tabulate evenly-spaced exp() values. 0056 for (std::size_t i = 0; i < nsteps; ++i) 0057 table_[i] = std::exp(xmin_ + i*dx_); 0058 } 0059 0060 template <typename T> 0061 inline T FastExp<T>::operator()(T x) const { 0062 #ifndef NDEBUG 0063 if (x < xmin_ || x > xmax_) 0064 throw std::out_of_range{"argument must be within [xmin, xmax]"}; 0065 #endif 0066 0067 // Determine the table index of the nearest tabulated value. 0068 auto index = static_cast<std::size_t>((x - xmin_)/dx_ + .5); 0069 0070 // Compute the leading-order Taylor expansion. 0071 // exp(x) = exp(x0) * exp(x-x0) =~ exp(x0) * (1 + x - x0) 0072 // exp(x0) = table_[index] 0073 // x0 = xmin_ + index*dx_ 0074 return table_[index] * (1. + x - xmin_ - index*dx_); 0075 } 0076 0077 } // namespace trento 0078 0079 #endif // FAST_EXP_H
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