Introducing calculus::nInt.

ZCG-coder · Aug 10, 2024 · a72bacb · a72bacb
1 parent c349d9e
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diff --git a/.idea/editor.xml b/.idea/editor.xml
diff --git a/CMakeLists.txt b/CMakeLists.txt
@@ -95,6 +95,7 @@ SET(COMPONENTS
     base::baseConvert
     base::decimalConvert
     calc::abs
+    calculus::nInt
     calc::add
     calc::atan2
     calc::comparison

diff --git a/include/fn/calculus.hpp b/include/fn/calculus.hpp
@@ -0,0 +1,39 @@
+/**************************************************************************************************
+ * Copyright (c) 2023-2024 NWSOFT                                                                 *
+ *                                                                                                *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy                   *
+ * of this software and associated documentation files (the "Software"), to deal                  *
+ * in the Software without restriction, including without limitation the rights                   *
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell                      *
+ * copies of the Software, and to permit persons to whom the Software is                          *
+ * furnished to do so, subject to the following conditions:                                       *
+ *                                                                                                *
+ * The above copyright notice and this permission notice shall be included in all                 *
+ * copies or substantial portions of the Software.                                                *
+ *                                                                                                *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR                     *
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,                       *
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE                    *
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER                         *
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,                  *
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE                  *
+ * SOFTWARE.                                                                                      *
+ **************************************************************************************************/
+
+#pragma once
+
+#include <functional>
+#include <string>
+
+/**
+ * @namespace steppable::__internals::calculus
+ * @brief Contains calculus functions.
+ */
+namespace steppable::__internals::calculus
+{
+    std::string romberg(const std::function<std::string(std::string)>& f,
+                        const std::string& a,
+                        const std::string& b,
+                        int max_steps,
+                        int decimals);
+}
diff --git a/src/calculus/nInt/nInt.cpp b/src/calculus/nInt/nInt.cpp
@@ -0,0 +1,84 @@
+/**************************************************************************************************
+ * Copyright (c) 2023-2024 NWSOFT                                                                 *
+ *                                                                                                *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy                   *
+ * of this software and associated documentation files (the "Software"), to deal                  *
+ * in the Software without restriction, including without limitation the rights                   *
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell                      *
+ * copies of the Software, and to permit persons to whom the Software is                          *
+ * furnished to do so, subject to the following conditions:                                       *
+ *                                                                                                *
+ * The above copyright notice and this permission notice shall be included in all                 *
+ * copies or substantial portions of the Software.                                                *
+ *                                                                                                *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR                     *
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,                       *
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE                    *
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER                         *
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,                  *
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE                  *
+ * SOFTWARE.                                                                                      *
+ **************************************************************************************************/
+
+#include "fn/basicArithm.hpp"
+#include "rounding.hpp"
+
+#include <concepts>
+#include <functional>
+#include <string>
+#include <vector>
+
+using namespace steppable::__internals::arithmetic;
+using namespace steppable::__internals::numUtils;
+using namespace std::literals;
+
+namespace steppable::__internals::calculus
+{
+    std::string romberg(const std::function<std::string(std::string)>& f,
+                        const std::string& a,
+                        const std::string& b,
+                        const int max_steps,
+                        const int decimals)
+    {
+        auto acc = "0." + std::string(decimals - 1, '0') + "1";
+        auto Rp = std::vector(max_steps, "0"s);
+        auto Rc = std::vector(max_steps, "0"s);
+
+        auto h = subtract(b, a, 0);
+        auto fAB = add(f(a), f(b), 0);
+        auto halfH = multiply(h, "0.5", 0);
+        Rp.front() = multiply(halfH, fAB, 0);
+
+        for (int i = 1; i < max_steps; i++)
+        {
+            h = multiply(h, "0.5", 0);
+            auto c = "0"s;
+            long ep = 1 << (i - 1); // 2^(i - 1)
+            for (long j = 1; j < (ep + 1); j++)
+            {
+                auto d = multiply(std::to_string((2 * j) - 1), h, 0);
+                c = add(c, f(add(a, d, 0)), 0);
+            }
+            Rc.front() = add(multiply(h, c, 0), multiply("0.5", Rp.front(), 0), 0);
+
+            for (int j = 1; j < (i + 1); j++)
+            {
+                long double n_k = pow(4, j);
+                auto one = multiply(std::to_string(n_k), Rc.at(j - 1), 0);
+                auto top = subtract(one, Rp.at(j - 1), 0);
+                Rc.at(j) = divide(top, std::to_string(n_k - 1), 0, decimals + 1);
+
+                if (i > 1 and compare(abs(subtract(Rp.at(i - 1), Rc.at(i), 0), 0), acc, 0) == "0")
+                    return roundOff(Rc.at(i), decimals);
+            }
+
+            std::ranges::swap(Rp, Rc);
+        }
+
+        return roundOff(Rp.at(max_steps - 1), decimals);
+    }
+} // namespace steppable::__internals::calculus
+
+#ifndef NO_MAIN
+int main() {}
+#endif
diff --git a/src/calculus/nInt/nIntReport.cpp b/src/calculus/nInt/nIntReport.cpp
@@ -0,0 +1,31 @@
+/**************************************************************************************************
+ * Copyright (c) 2023-2024 NWSOFT                                                                 *
+ *                                                                                                *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy                   *
+ * of this software and associated documentation files (the "Software"), to deal                  *
+ * in the Software without restriction, including without limitation the rights                   *
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell                      *
+ * copies of the Software, and to permit persons to whom the Software is                          *
+ * furnished to do so, subject to the following conditions:                                       *
+ *                                                                                                *
+ * The above copyright notice and this permission notice shall be included in all                 *
+ * copies or substantial portions of the Software.                                                *
+ *                                                                                                *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR                     *
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,                       *
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE                    *
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER                         *
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,                  *
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE                  *
+ * SOFTWARE.                                                                                      *
+ **************************************************************************************************/
+
+#include "nIntReport.hpp"
+
+#include <string>
+
+std::string reportNInt()
+{
+    // Intentionally not implemented.
+    return "";
+}
diff --git a/src/calculus/nInt/nIntReport.hpp b/src/calculus/nInt/nIntReport.hpp
@@ -0,0 +1,27 @@
+/**************************************************************************************************
+ * Copyright (c) 2023-2024 NWSOFT                                                                 *
+ *                                                                                                *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy                   *
+ * of this software and associated documentation files (the "Software"), to deal                  *
+ * in the Software without restriction, including without limitation the rights                   *
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell                      *
+ * copies of the Software, and to permit persons to whom the Software is                          *
+ * furnished to do so, subject to the following conditions:                                       *
+ *                                                                                                *
+ * The above copyright notice and this permission notice shall be included in all                 *
+ * copies or substantial portions of the Software.                                                *
+ *                                                                                                *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR                     *
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,                       *
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE                    *
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER                         *
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,                  *
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE                  *
+ * SOFTWARE.                                                                                      *
+ **************************************************************************************************/
+
+#pragma once
+
+#include <string>
+
+std::string reportNInt();
diff --git a/tests/testNInt.cpp b/tests/testNInt.cpp
@@ -0,0 +1,43 @@
+/**************************************************************************************************
+ * Copyright (c) 2023-2024 NWSOFT                                                                 *
+ *                                                                                                *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy                   *
+ * of this software and associated documentation files (the "Software"), to deal                  *
+ * in the Software without restriction, including without limitation the rights                   *
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell                      *
+ * copies of the Software, and to permit persons to whom the Software is                          *
+ * furnished to do so, subject to the following conditions:                                       *
+ *                                                                                                *
+ * The above copyright notice and this permission notice shall be included in all                 *
+ * copies or substantial portions of the Software.                                                *
+ *                                                                                                *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR                     *
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,                       *
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE                    *
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER                         *
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,                  *
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE                  *
+ * SOFTWARE.                                                                                      *
+ **************************************************************************************************/
+
+#include "colors.hpp"
+#include "fn/basicArithm.hpp"
+#include "fn/calculus.hpp"
+#include "output.hpp"
+#include "testing.hpp"
+#include "util.hpp"
+
+#include <iomanip>
+#include <iostream>
+
+using namespace steppable::__internals::calculus;
+using namespace steppable::__internals::arithmetic;
+
+TEST_START()
+
+SECTION(Test Numerical Integration)
+const auto& result = romberg([](const std::string& x) { return add("1", multiply(x, "2", 0), 0); }, "0", "1", 10, 3);
+_.assertIsEqual(result, "2.000");
+SECTION_END()
+
+TEST_END()