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Introducing calculus::nInt.
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‎.idea/editor.xml

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‎CMakeLists.txt

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@@ -95,6 +95,7 @@ SET(COMPONENTS
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base::baseConvert
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base::decimalConvert
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calc::abs
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calculus::nInt
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calc::add
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calc::atan2
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calc::comparison

‎include/fn/calculus.hpp

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/**************************************************************************************************
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* Copyright (c) 2023-2024 NWSOFT *
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* *
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* Permission is hereby granted, free of charge, to any person obtaining a copy *
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* of this software and associated documentation files (the "Software"), to deal *
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* in the Software without restriction, including without limitation the rights *
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* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell *
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* copies of the Software, and to permit persons to whom the Software is *
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* furnished to do so, subject to the following conditions: *
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* *
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* The above copyright notice and this permission notice shall be included in all *
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* copies or substantial portions of the Software. *
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* *
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR *
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* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, *
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE *
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* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER *
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* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, *
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* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE *
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* SOFTWARE. *
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**************************************************************************************************/
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#pragma once
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#include <functional>
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#include <string>
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/**
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* @namespace steppable::__internals::calculus
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* @brief Contains calculus functions.
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*/
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namespace steppable::__internals::calculus
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{
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std::string romberg(const std::function<std::string(std::string)>& f,
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const std::string& a,
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const std::string& b,
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int max_steps,
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int decimals);
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}

‎src/calculus/nInt/nInt.cpp

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/**************************************************************************************************
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* Copyright (c) 2023-2024 NWSOFT *
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* *
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* Permission is hereby granted, free of charge, to any person obtaining a copy *
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* of this software and associated documentation files (the "Software"), to deal *
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* in the Software without restriction, including without limitation the rights *
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* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell *
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* copies of the Software, and to permit persons to whom the Software is *
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* furnished to do so, subject to the following conditions: *
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* *
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* The above copyright notice and this permission notice shall be included in all *
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* copies or substantial portions of the Software. *
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* *
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR *
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* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, *
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE *
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* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER *
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* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, *
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* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE *
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* SOFTWARE. *
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**************************************************************************************************/
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#include "fn/basicArithm.hpp"
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#include "rounding.hpp"
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#include <concepts>
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#include <functional>
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#include <string>
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#include <vector>
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using namespace steppable::__internals::arithmetic;
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using namespace steppable::__internals::numUtils;
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using namespace std::literals;
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namespace steppable::__internals::calculus
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{
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std::string romberg(const std::function<std::string(std::string)>& f,
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const std::string& a,
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const std::string& b,
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const int max_steps,
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const int decimals)
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{
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auto acc = "0." + std::string(decimals - 1, '0') + "1";
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auto Rp = std::vector(max_steps, "0"s);
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auto Rc = std::vector(max_steps, "0"s);
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auto h = subtract(b, a, 0);
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auto fAB = add(f(a), f(b), 0);
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auto halfH = multiply(h, "0.5", 0);
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Rp.front() = multiply(halfH, fAB, 0);
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for (int i = 1; i < max_steps; i++)
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{
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h = multiply(h, "0.5", 0);
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auto c = "0"s;
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long ep = 1 << (i - 1); // 2^(i - 1)
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for (long j = 1; j < (ep + 1); j++)
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{
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auto d = multiply(std::to_string((2 * j) - 1), h, 0);
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c = add(c, f(add(a, d, 0)), 0);
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}
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Rc.front() = add(multiply(h, c, 0), multiply("0.5", Rp.front(), 0), 0);
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for (int j = 1; j < (i + 1); j++)
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{
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long double n_k = pow(4, j);
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auto one = multiply(std::to_string(n_k), Rc.at(j - 1), 0);
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auto top = subtract(one, Rp.at(j - 1), 0);
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Rc.at(j) = divide(top, std::to_string(n_k - 1), 0, decimals + 1);
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if (i > 1 and compare(abs(subtract(Rp.at(i - 1), Rc.at(i), 0), 0), acc, 0) == "0")
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return roundOff(Rc.at(i), decimals);
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}
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std::ranges::swap(Rp, Rc);
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}
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return roundOff(Rp.at(max_steps - 1), decimals);
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}
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} // namespace steppable::__internals::calculus
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#ifndef NO_MAIN
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int main() {}
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#endif

‎src/calculus/nInt/nIntReport.cpp

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/**************************************************************************************************
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* Copyright (c) 2023-2024 NWSOFT *
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* *
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* Permission is hereby granted, free of charge, to any person obtaining a copy *
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* of this software and associated documentation files (the "Software"), to deal *
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* in the Software without restriction, including without limitation the rights *
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* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell *
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* copies of the Software, and to permit persons to whom the Software is *
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* furnished to do so, subject to the following conditions: *
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* *
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* The above copyright notice and this permission notice shall be included in all *
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* copies or substantial portions of the Software. *
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* *
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR *
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* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, *
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE *
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* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER *
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* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, *
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* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE *
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* SOFTWARE. *
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**************************************************************************************************/
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#include "nIntReport.hpp"
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#include <string>
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std::string reportNInt()
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{
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// Intentionally not implemented.
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return "";
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}

‎src/calculus/nInt/nIntReport.hpp

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/**************************************************************************************************
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* Copyright (c) 2023-2024 NWSOFT *
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* *
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* Permission is hereby granted, free of charge, to any person obtaining a copy *
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* of this software and associated documentation files (the "Software"), to deal *
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* in the Software without restriction, including without limitation the rights *
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* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell *
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* copies of the Software, and to permit persons to whom the Software is *
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* furnished to do so, subject to the following conditions: *
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* *
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* The above copyright notice and this permission notice shall be included in all *
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* copies or substantial portions of the Software. *
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* *
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR *
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* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, *
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE *
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* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER *
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* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, *
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* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE *
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* SOFTWARE. *
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**************************************************************************************************/
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#pragma once
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#include <string>
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std::string reportNInt();

‎tests/testNInt.cpp

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/**************************************************************************************************
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* Copyright (c) 2023-2024 NWSOFT *
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* *
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* Permission is hereby granted, free of charge, to any person obtaining a copy *
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* of this software and associated documentation files (the "Software"), to deal *
6+
* in the Software without restriction, including without limitation the rights *
7+
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell *
8+
* copies of the Software, and to permit persons to whom the Software is *
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* furnished to do so, subject to the following conditions: *
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* *
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* The above copyright notice and this permission notice shall be included in all *
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* copies or substantial portions of the Software. *
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* *
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR *
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* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, *
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE *
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* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER *
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* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, *
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* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE *
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* SOFTWARE. *
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**************************************************************************************************/
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#include "colors.hpp"
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#include "fn/basicArithm.hpp"
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#include "fn/calculus.hpp"
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#include "output.hpp"
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#include "testing.hpp"
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#include "util.hpp"
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#include <iomanip>
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#include <iostream>
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using namespace steppable::__internals::calculus;
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using namespace steppable::__internals::arithmetic;
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TEST_START()
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SECTION(Test Numerical Integration)
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const auto& result = romberg([](const std::string& x) { return add("1", multiply(x, "2", 0), 0); }, "0", "1", 10, 3);
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_.assertIsEqual(result, "2.000");
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SECTION_END()
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TEST_END()

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