/*
 **************************************************************
 *         C++ Mathematical Expression Toolkit Library        *
 *                                                            *
 * Simple Example 10                                          *
 * Author: Arash Partow (1999-2018)                           *
 * URL: http://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.                   *
 * http://www.opensource.org/licenses/MIT                     *
 *                                                            *
 **************************************************************
*/


#include <cmath>
#include <cstdio>
#include <string>

#include "exprtk.hpp"


template <typename T>
void newton_sqrt()
{
   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;

   T x = T(0);

   symbol_table_t symbol_table;

   symbol_table.add_constants();
   symbol_table.add_variable("x",x);

   compositor_t compositor(symbol_table);

   compositor
      .add(
      function_t( // define function: newton_sqrt(x)
           "newton_sqrt",
           " switch                                              "
           " {                                                   "
           "   case x < 0  : -inf;                               "
           "   case x == 0 : 0;                                  "
           "   case x == 1 : 1;                                  "
           "   default:                                          "
           "   ~{                                                "
           "      var z := 100;                                  "
           "      var sqrt_x := x / 2;                           "
           "      repeat                                         "
           "        sqrt_x := (1 / 2) * (sqrt_x + (x / sqrt_x)); "
           "        if (equal(sqrt_x^2, x))                      "
           "          break[sqrt_x];                             "
           "      until ((z -= 1) <= 0);                         "
           "    };                                               "
           " }                                                   ",
           "x"));

   std::string expression_str = "newton_sqrt(x)";

   expression_t expression;
   expression.register_symbol_table(symbol_table);

   parser_t parser;
   parser.compile(expression_str,expression);

   for (std::size_t i = 0; i < 100; ++i)
   {
      x = static_cast<T>(i);

      T result = expression.value();

      printf("sqrt(%03d) - Result: %12.10f\tReal: %12.10f\n",
             static_cast<unsigned int>(i),
             result,
             std::sqrt(x));
   }
}

int main()
{
   newton_sqrt<double>();
   return 0;
}