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exprtk_miller_rabin_primality_test.cpp
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exprtk_miller_rabin_primality_test.cpp
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/*
**************************************************************
* C++ Mathematical Expression Toolkit Library *
* *
* ExprTk Miller-Rabin Probabilistic Primality Test *
* 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 <algorithm>
#include <array>
#include <cstdio>
#include <random>
#include <string>
#include "exprtk.hpp"
template <typename T>
struct random_uint final : public exprtk::ifunction<T>
{
using exprtk::ifunction<T>::operator();
random_uint()
: exprtk::ifunction<T>(2)
{
std::random_device device;
std::array<unsigned int,std::mt19937::state_size> seed;
std::generate_n(seed.data(), seed.size(), std::ref(device));
std::seed_seq seq(std::begin(seed), std::end(seed));
generator.seed(seq);
}
inline T operator() (const T& r0,const T& r1) override
{
std::uniform_int_distribution<std::uint64_t>
distribution { static_cast<std::uint64_t>(r0), static_cast<std::uint64_t>(r1) };
return static_cast<T>(distribution(generator));
}
std::mt19937 generator;
};
template <typename T>
void miller_rabin_probabilistic_primality_test()
{
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 prime_numbers[] =
{
5083823, 5083879, 5083889, 5083909, 5083913, 5083927, 5083931, 5083957,
5083973, 5083993, 5084017, 5084033, 5084069, 5084099, 5084111, 5084113,
5084117, 5084129, 5084141, 5084147, 5084171, 5084179, 5084197, 5084213,
5084221, 5084243, 5084249, 5084263, 5084269, 5084333, 5084371, 5084383,
5084393, 5084399, 5084407, 5084423, 5084437, 5084447, 5084461, 5084473,
5084477, 5084489, 5084501, 5084509, 5084531, 5084537, 5084543, 5084549,
5084551, 5084557, 5084567, 5084593, 5084617, 5084627, 5084641, 5084671,
5084689, 5084693, 5084711, 5084731, 5084743, 5084749, 5084753, 5084803,
5084809, 5084813, 5084843, 5084851, 5084867, 5084869, 5084897, 5084903,
6782807, 6782821, 6782827, 6782833, 6782869, 6782903, 6782911, 6782921,
6782929, 6782933, 6782939, 6782959, 6782969, 6782977, 6783011, 6783031,
6783047, 6783067, 6783083, 6783089, 6783097, 6783107, 6783131, 6783143,
6783149, 6783151, 6783169, 6783193, 6783211, 6783223, 6783239, 6783241,
6783253, 6783263, 6783299, 6783317, 6783331, 6783353, 6783421, 6783433,
6783449, 6783457, 6783461, 6783467, 6783481, 6783521, 6783529, 6783533,
9723667, 9723691, 9723697, 9723709, 9723713, 9723757, 9723761, 9723767,
9723773, 9723797, 9723799, 9723803, 9723809, 9723821, 9723829, 9723841,
9723851, 9723853, 9723869, 9723887, 9723893, 9723907, 9723913, 9723937,
9723941, 9723943, 9723979, 9723997, 9724021, 9724061, 9724079, 9724087,
9724097, 9724103, 9724129, 9724151, 9724171, 9724201, 9724207, 9724213,
9724223, 9724241, 9724259, 9724277, 9724279, 9724283, 9724291, 9724327,
10619129, 10619131, 10619137, 10619159, 10619177, 10619179, 10619209, 10619243,
10619251, 10619263, 10619291, 10619303, 10619327, 10619341, 10619381, 10619393,
10619431, 10619489, 10619501, 10619503, 10619513, 10619563, 10619573, 10619591,
10619599, 10619617, 10619621, 10619641, 10619647, 10619669, 10619681, 10619711,
10619723, 10619729, 10619731, 10619737, 10619759, 10619773, 10619783, 10619801,
10619863, 10619893, 10619897, 10619899, 10619911, 10619923, 10619927, 10619957,
10619971, 10619989, 10620007, 10620023, 10620041, 10620067, 10620131, 10620133,
10620139, 10620143, 10620149, 10620151, 10620157, 10620163, 10620179, 10620199,
10748671, 10748687, 10748693, 10748701, 10748707, 10748713, 10748747, 10748767,
10748779, 10748783, 10748791, 10748807, 10748809, 10748827, 10748849, 10748863,
10748867, 10748869, 10748873, 10748893, 10748897, 10748917, 10748921, 10748923,
10748951, 10748953, 10748957, 10748963, 10748987, 10748999, 10749001, 10749023,
10749029, 10749059, 10749061, 10749071, 10749077, 10749107, 10749121, 10749143,
10749161, 10749163, 10749173, 10749191, 10749197, 10749199, 10749241, 10749251,
10749259, 10749283, 10749313, 10749317, 10749337, 10749367, 10749371, 10749373,
10749379, 10749391, 10749433, 10749437, 10749449, 10749461, 10749493, 10749581,
10749587, 10749601, 10749617, 10749631, 10749659, 10749677, 10749679, 10749703,
10749709, 10749719, 10749727, 10749743, 10749773, 10749779, 10749811, 10749821,
10749833, 10749853, 10749857, 10749863, 10749881, 10749883, 10749889, 10749917,
10749971, 10749983, 10749989, 10749997, 10750009, 10750021, 10750031, 10750037,
10750049, 10750057, 10750073, 10750099, 10750127, 10750141, 10750147, 10750189,
10750193, 10750249, 10750279, 10750303, 10750309, 10750319, 10750349, 10750373,
};
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;
random_uint<T> random;
symbol_table_t symbol_table;
symbol_table.add_vector ("prime_numbers" , prime_numbers);
symbol_table.add_vector ("composite_numbers", composites );
symbol_table.add_function("println" , println );
symbol_table.add_function("random" , random );
compositor_t compositor(symbol_table);
compositor.add(function_t()
.name("modexp") // (base^exponent) mod m
.var("b") // base
.var("e") // exponent
.var("m") // modulo
.expression
(
" if (m == 1) "
" { "
" return [0]; "
" }; "
" "
" var result := 1; "
" b %= m; "
" "
" while (e > 0) "
" { "
" if ((e % 2) == 1) "
" { "
" result := (result * b) % m; "
" }; "
" "
" b := b^2 % m; "
" e := floor(e / 2); "
" }; "
" "
" result "
));
compositor.add(function_t()
.name("is_probable_prime")
.var("n") // Number to test for primaility
.var("k") // Number of iterations to perform
.expression
(
" switch "
" { "
" case n <= 1 : return [false]; "
" case frac(n) != 0 : return [false]; "
" case n == 2 : return [true ]; "
" }; "
" "
" var primes[18] := "
" { "
" 2, 3, 5, 7, 11, 13, 17, 19, 23, "
" 29, 31, 37, 41, 43, 47, 53, 59, 61 "
" }; "
" "
" var upper_bound := min(n - 1, trunc(sqrt(n)) + 1); "
" "
" for (var i := 0; i < primes[]; i += 1) "
" { "
" if (primes[i] >= upper_bound) "
" return [true]; "
" else if ((n % primes[i]) == 0) "
" return [false]; "
" }; "
" "
" var s := n - 1; "
" var t := 0; "
" "
" while ((s % 2) == 0) "
" { "
" s := floor(s / 2); "
" t += 1; "
" }; "
" "
" for (var trials := 0; trials < k; trials += 1) "
" { "
" var a := random(2, n - 2); "
" var x := modexp(a, s, n); "
" "
" if ((x == 1) or (x == (n - 1))) "
" { "
" continue; "
" }; "
" "
" for (var r := 1; r < t; r += 1) "
" { "
" x := modexp(x, 2, n); "
" "
" if (x == 1) "
" return [false]; "
" else if (x == (n - 1)) "
" break; "
" }; "
" "
" if (x != (n - 1)) "
" { "
" return [false]; "
" }; "
" }; "
" "
" return [true]; "
));
const std::string miller_rabin_primality_test_program =
" "
" println('Testing prime numbers...'); "
" for (var i := 0; i < prime_numbers[]; i += 1) "
" { "
" var n := prime_numbers[i]; "
" "
" if (is_probable_prime(n,1000)) "
" { "
" println(n, ' is correctly a prime number'); "
" } "
" else "
" { "
" println(n, ' is NOT a prime number (error)'); "
" } "
" }; "
" "
" println('Testing composite numbers...'); "
" for (var i := 0; i < composite_numbers[]; i += 1) "
" { "
" var n := composite_numbers[i]; "
" "
" if (not(is_probable_prime(n,1000))) "
" { "
" println(n, ' is correctly a composite'); "
" } "
" else "
" { "
" println(n, ' is a prime number (error)'); "
" } "
" }; "
" "
" for (var i := 0; i < prime_numbers[]; i += 1) "
" { "
" for (var j := i; j < prime_numbers[]; j += 1) "
" { "
" var n := prime_numbers[i] * prime_numbers[j]; "
" "
" if (not(is_probable_prime(n,1000))) "
" { "
" println(n, ' is correctly a composite'); "
" } "
" else "
" { "
" println(n, ' is a prime number (error)'); "
" } "
" } "
" }; ";
expression_t expression;
expression.register_symbol_table(symbol_table);
parser_t parser;
parser.compile(miller_rabin_primality_test_program,expression);
expression.value();
}
int main()
{
miller_rabin_probabilistic_primality_test<double>();
return 0;
}