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0001 // This file is part of the ACTS project. 0002 // 0003 // Copyright (C) 2016 CERN for the benefit of the ACTS project 0004 // 0005 // This Source Code Form is subject to the terms of the Mozilla Public 0006 // License, v. 2.0. If a copy of the MPL was not distributed with this 0007 // file, You can obtain one at https://mozilla.org/MPL/2.0/. 0008 0009 #pragma once 0010 0011 #include <cmath> 0012 0013 namespace Acts { 0014 0015 /// @brief Returns the absolute of a number 0016 /// (Can be removed for c++ 23) 0017 /// @param n The number to take absolute value of 0018 /// @return The absolute value of the input 0019 template <typename T> 0020 constexpr T abs(const T n) { 0021 if constexpr (std::is_signed_v<T>) { 0022 if (n < 0) { 0023 return -n; 0024 } 0025 } 0026 return n; 0027 } 0028 0029 /// @brief Calculates the ordinary power of the number x. 0030 /// @param x: Number to take the power from 0031 /// @param p: Power to take 0032 /// @return x raised to the power p 0033 template <typename T, std::integral P> 0034 constexpr T pow(T x, P p) { 0035 constexpr T one = 1; 0036 if constexpr (std::is_signed_v<P>) { 0037 if (p < 0 && abs(x) > std::numeric_limits<T>::epsilon()) { 0038 x = one / x; 0039 p = -p; 0040 } 0041 } 0042 using unsigned_p = std::make_unsigned_t<P>; 0043 return p == 0 ? one : x * pow(x, static_cast<unsigned_p>(p) - 1); 0044 } 0045 0046 /// @brief Returns the square of the passed number 0047 /// @param x The number to square 0048 /// @return The square of the input 0049 template <typename T> 0050 constexpr auto square(T x) { 0051 return x * x; 0052 } 0053 0054 /// @brief Calculates the sum of squares of arguments 0055 /// @param args Variable number of arguments to square and sum 0056 /// @return Sum of squares of all arguments 0057 template <typename... T> 0058 constexpr auto hypotSquare(T... args) { 0059 return (square(args) + ...); 0060 } 0061 0062 /// @brief Fast hypotenuse calculation for multiple arguments 0063 /// @param args Variable number of arguments 0064 /// @return Square root of sum of squares of arguments 0065 template <typename... T> 0066 constexpr auto fastHypot(T... args) { 0067 return std::sqrt(hypotSquare(args...)); 0068 } 0069 0070 /// @brief Calculates the sum of 1 + 2 + 3+ ... + N using the 0071 /// Gaussian sum formula 0072 /// @param N: Number until which the sum runs 0073 /// @return Sum of integers from 1 to N 0074 template <std::integral T> 0075 constexpr T sumUpToN(const T N) { 0076 return N * (N + 1) / 2; 0077 } 0078 /// @brief Calculates the factorial of a number 0079 /// N!= N*(N-1)....*3*2*1 0080 /// @param upperN: Upper factor until which the factorial is calculated 0081 /// @param lowerN: Optional argument to remove the first factors from the calculation 0082 /// @return Factorial result 0083 template <std::integral T> 0084 constexpr T factorial(const T upperN, const T lowerN = 1) { 0085 constexpr T one = 1; 0086 const T& limit = std::max(one, lowerN); 0087 return upperN >= limit ? upperN * factorial(upperN - 1, limit) : one; 0088 } 0089 /// @brief Calculate the binomial coefficient 0090 /// n n! 0091 /// = -------- 0092 /// k k!(n-k)! 0093 /// @param n Upper value in binomial coefficient 0094 /// @param k Lower value in binomial coefficient 0095 /// @return Binomial coefficient n choose k 0096 template <std::integral T> 0097 constexpr T binomial(const T n, const T k) { 0098 return factorial<T>(n, n - k + 1) / factorial<T>(k); 0099 } 0100 0101 } // namespace Acts
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