exprtk_factorize_pollard.cpp

Go to the documentation of this file.

/*
 **************************************************************
 *         C++ Mathematical Expression Toolkit Library        *
 *                                                            *
 * ExprTk Pollard's Rho Factorization Example                 *
 * 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 <cstdio>
#include <string>
 
#include "exprtk.hpp"
 
 
template <typename T>
void factorize_pollards_rho()
{
   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;
 
   // Form: n = p*q where p,q are prime
   T composites[] =
   {
       199203677,  779234623,  843093203,  883543291, 1197162971,
      1282615157, 1552390397, 1765737859, 1878769589, 1993904873,
      2257133471, 2520523529, 2579094799, 2853450949, 2935025369,
      3095780533, 3164132249, 3408963511, 4260042859, 4608613981,
      4654875857, 5085931997, 7278175081, 7289187463, 9206112101
   };
 
   exprtk::rtl::io::println<T> println;
 
   symbol_table_t symbol_table;
 
   symbol_table.add_vector  ("composites", composites);
   symbol_table.add_function("println"   , println   );
 
   compositor_t compositor(symbol_table);
 
   compositor.add(function_t()
      .name("gcd")
      .var("x") .var("y")
      .expression
      (
         " x := abs(x);       "
         " y := abs(y);       "
         " while (0 != y)     "
         " {                  "
         "    var r := x % y; "
         "    x := y;         "
         "    y := r;         "
         " };                 "
         " x                  "
      ));
 
   compositor.add(function_t()
      .name("pollard_rho")
      .var("n")
      .expression
      (
         " var c  := 10;                "
         " var a1 := 1 + c;             "
         " var a2 := 11 + c;            "
         "                              "
         " while (gcd(n, a2 - a1) == 1) "
         " {                            "
         "    /* The Tortoise */        "
         "    a1 := (a1^2 + c) % n;     "
         "                              "
         "    /* The Hare */            "
         "    a2 := (a2^2 + c) % n;     "
         "    a2 := (a2^2 + c) % n;     "
         " };                           "
         "                              "
         " var g := gcd(n, a2 - a1);    "
         "                              "
         " n / g                        "
      ));
 
   const std::string factorize_composites_program =
      " for (var i := 0; i < composites[]; i += 1)                               "
      " {                                                                        "
      "    var n       := composites[i];                                         "
      "    var factor0 := pollard_rho(n);                                        "
      "    var factor1 := n / factor0;                                           "
      "                                                                          "
      "    if ((factor0 * factor1 == n) and (factor0 != 1))                      "
      "    {                                                                     "
      "       println('n: ', n, ' factors: { ', factor0 ,' , ', factor1 ,' } '); "
      "    }                                                                     "
      "    else                                                                  "
      "    {                                                                     "
      "       println('failed to factorize ', n);                                "
      "    }                                                                     "
      " }                                                                        "
      "                                                                          ";
   expression_t expression;
   expression.register_symbol_table(symbol_table);
 
   parser_t parser;
   parser.compile(factorize_composites_program,expression);
 
   expression.value();
}
 
int main()
{
   factorize_pollards_rho<double>();
   return 0;
}