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/* ************************************************************** * C++ Mathematical Expression Toolkit Library * * * * ExprTk Nth-Root via Bisection Method * * Author: Arash Partow (1999-2024) * * URL: https://www.partow.net/programming/exprtk/index.html * * * * Copyright notice: * * Free use of the Mathematical Expression Toolkit Library is * * permitted under the guidelines and in accordance with the * * most current version of the MIT License. * * https://www.opensource.org/licenses/MIT * * SPDX-License-Identifier: MIT * * * ************************************************************** */ #include #include #include #include "exprtk.hpp" template void nthroot_via_bisection() { typedef exprtk::symbol_table symbol_table_t; typedef exprtk::expression expression_t; typedef exprtk::parser parser_t; typedef exprtk::function_compositor compositor_t; typedef typename compositor_t::function function_t; const std::string nthroot_via_bisection_program = " for (var x := -30; x <= 30; x += 1) " " { " " println('[', x, ']', " " ' sqrt = ', nthroot(x,2), " " ' cbrt = ', nthroot(x,3)); " " } "; exprtk::rtl::io::println println; symbol_table_t symbol_table; symbol_table.add_function("println",println); compositor_t compositor(symbol_table); // define function: nthroot(x,n) compositor.add( function_t("nthroot") .var("x") .var("n") .expression ( " if (abs(frac(n)) > 0) " " return [null]; " " else if (x < 0 and (n % 2 == 0)) " " return [null]; " " " " var lo := min(0,x); " " var hi := max(0,x); " " " " while (true) " " { " " var mid := avg(lo,hi); " " var y := pow(mid,n); " " " " if (equal(y, x)) " " break [mid]; " " else if (y < x) " " lo := mid; " " else " " hi := mid; " " }; " )); expression_t expression; expression.register_symbol_table(symbol_table); parser_t parser; parser.compile(nthroot_via_bisection_program, expression); expression.value(); } int main() { nthroot_via_bisection(); return 0; }