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/* ************************************************************** * C++ Mathematical Expression Toolkit Library * * * * ExprTk Archimedes Approximation Of Pi * * 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 "exprtk.hpp" template void archimedes_pi() { 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; exprtk::rtl::io::println println("%25.23f"); symbol_table_t symbol_table; symbol_table.add_function("println", println); symbol_table.add_constants(); compositor_t compositor(symbol_table); compositor.add( function_t("archimedes_pi") .var("iterations") .expression ( " var s := 1.0; " " var approx_pi := 0.0; " " " " for (var i := 0; i < iterations; i += 1) " " { " " var n := 6 * 2^i; " " var s2 := (s / 2)^2; " " var t := sqrt(1 - s2); " " var q := 1 - t; " " var p := n * s; " " " " approx_pi := p / 2; " " s := sqrt(q^2 + s2); " " }; " " " " approx_pi; " )); const std::string archimedes_pi_program = " const var n := 30; " " " " for (var i := 1; i <= n; i += 1) " " { " " var approx_pi := archimedes_pi(i); " " var abs_error := abs(approx_pi - pi); " " " " println('approx pi: ', approx_pi, ' abs error:', abs_error); " " } "; expression_t expression; expression.register_symbol_table(symbol_table); parser_t parser; parser.compile(archimedes_pi_program,expression); expression.value(); } int main() { archimedes_pi(); return 0; }