// Probabilistic Miller-Rabin primality test.


// Number of checks in Miller-Rabin test.
var times_confident = 10;

var primes_below_1000 = new Array (
				   2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
				   73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
				   157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233,
				   239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317,
				   331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419,
				   421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503,
				   509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607,
				   613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701,
				   709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811,
				   821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911,
				   919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997
				   );

var big_primes_below_1000 = new Array();

function init_big_primes()
{
    big_primes_below_1000.length = primes_below_1000.length;

    for (var i = 0; i < primes_below_1000.length; i++) {
	big_primes_below_1000[i] = biFromNumber(primes_below_1000[i]);
    }
}

init_big_primes();

// Makes unnecesasary work for numbers below 1.000.000
function passes_heuristic_primality_check(number, callback)
{
    var length = big_primes_below_1000.length;
    var i = 0;

    iter();

    function iter() {
	if (i < length) {
	    biModulo(number, big_primes_below_1000[i],
		     function (modulo)
		     {
			 if (biCompare(modulo, big_zero) == 0) {
			     if (biCompare(number, big_primes_below_1000[i]) != big_zero) {
				 callback(false);
			     }
			 }
			 i++;
			 ensure_response(iter);
		     }
		    );
	}
	else {
	    callback(true);
	}
    }
}

function least_significant_bit(number)
{
    return number.digits[0] & 0x1;
}

function two_factors_decomp(number)
{
    var factors_count = 0;

    while (least_significant_bit(number) == 0) {
	number = biShiftRight(number, 1);

	++factors_count;
    }

    return new Array (factors_count, number);
}

function is_composite_witness(number, witness, barrett_mu, callback)
{
    var decreased_num = biSubtract(number, big_one);
    var decomp = two_factors_decomp(decreased_num);
    var two_factors_count = decomp[0];
    var residue = decomp[1];
    var tmp;

    barrett_mu.powMod(witness, residue,
		     function(result)
		     {
			 tmp = result;
			 ensure_response(f2);
		     }
		    );

    function f2() {
	if (biCompare(tmp, big_one) != 0) {
	    var s = 0;

	    function iter () {

		function iter_continuation() {
		    if (biCompare(tmp, decreased_num) == 0) {
			callback(false);
		    }

		    ++s;

		    if (s == two_factors_count) {
			callback(true);
		    }

		    ensure_response(iter);
		}

		if (s != 0) {

		    barrett_mu.multiplyMod(tmp, tmp,
					   function(result)
					   {
					       tmp = result;
					       ensure_response(iter_continuation);
					   }
					  );
		}
		else {
		    ensure_response(iter_continuation);
		}


	    }

	    ensure_response(iter);
	}

	callback(false);
    }
}

function is_probable_prime(number, times, randpool, callback)
{
    ensure_response(f);

    function f() {
	function callback_fun_1(is_witness) {
	    if (is_witness) {
		callback(false);
	    }
	    else {
		ensure_response(iter);
	    }
	}

	function callback_fun_2(result) {
	    if (result) {
		ensure_response(iter);
	    }
	    else {
		callback(false);
	    }
	}

	var barrett_mu;
	var i = 0;

	new BarrettMu(number,
		     function(mu)
		     {
			 barrett_mu = mu;
			 ensure_response(heuristic_check);
		     }
		    );

	function heuristic_check() {
	    passes_heuristic_primality_check(number, callback_fun_2);
	}

	function iter() {
	    var witness = random_bigint_below(number, randpool);

	    if (i < times) {
		i++;
		is_composite_witness(number, witness, barrett_mu, callback_fun_1);
	    }
	    else {
		callback(true);
	    }
	}


    }
}

function generate_random_prime(numbits, randpool, callback)
{
    var prime_candidate;

    function callback_fun(result) {
	if (result) {
	    callback(prime_candidate);
	}
	else {
	    ensure_response(f);
	}
    }

    function f() {

	do {
	    prime_candidate = random_bigint(numbits, randpool);
	    if (least_significant_bit(prime_candidate) != 1) {
		prime_candidate = biAdd(prime_candidate, big_one);
	    }

	    is_probable_prime(prime_candidate, times_confident, randpool, callback_fun);
	} while (true);


	callback(prime_candidate);
    }

    f();
}