exprtk_nthroot_bisection.cpp

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/*
 **************************************************************
 *         C++ Mathematical Expression Toolkit Library        *
 *                                                            *
 * ExprTk Nth-Root via Bisection Method                       *
 * Author: Arash Partow (1999-2025)                           *
 * 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 <cmath>
#include <cstdio>
#include <string>
 
#include "exprtk.hpp"
 
 
template <typename T>
void nthroot_via_bisection()
{
   typedef exprtk::symbol_table<T>         symbol_table_t;
   typedef exprtk::expression<T>           expression_t;
   typedef exprtk::parser<T>               parser_t;
   typedef exprtk::function_compositor<T>  compositor_t;
   typedef typename compositor_t::function function_t;
 
   const std::string nthroot_via_bisection_program =
      " for (var x := -30; x <= 30; x += 1/2) "
      " {                                     "
      "    println('[', x, ']',               "
      "            ' sqrt = ', nthroot(x,2),  "
      "            ' cbrt = ', nthroot(x,3)); "
      " }                                     ";
 
   exprtk::rtl::io::println<T> 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 ((n < 0) or (abs(frac(n)) > 0))   "
        "    return [null];                    "
        " else if (x < 0 and (n % 2 == 0))     "
        "    return [null];                    "
        "                                      "
        " var lo := (x >= 0) ? 0 : min(-1, x); "
        " var hi := (x  < 0) ? 0 : max( 1, 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<double>();
   return 0;
}