InfIntMath.hpp

#ifndef INFINTMATH_HPP
#define INFINTMATH_HPP

// C++ std
#include <string>
#include <stdexcept>

// InfInt libs
#include "InfInt.hpp"
#include "InfIntResult.hpp"
#include "InfIntRandom.hpp"

namespace InfIntMath {

InfInt abs(const InfInt& infint);

const InfInt& min(const InfInt& a, const InfInt& b);
InfInt& min(InfInt& a, InfInt& b);

const InfInt& max(const InfInt& a, const InfInt& b);
InfInt& max(InfInt& a, InfInt& b);

InfInt pow(const InfInt& _a, const InfInt& _b);
InfInt modpow(const InfInt& _a, const InfInt& _b, const InfInt& m);

InfInt sqrt(const InfInt& n);
InfInt root(const InfInt& a, const InfInt& b);

InfInt log2(const InfInt& a);
InfInt log(const InfInt& a, const InfInt& b);

InfInt modulo(const InfInt& a, const InfInt& b);

InfInt lcm(const InfInt& a, const InfInt& b);
InfInt gcd(const InfInt& _a, const InfInt& _b);
InfIntEGCDResult egcd(const InfInt& a, const InfInt& b);
InfInt modinv(const InfInt& a, const InfInt& b);

bool congruent_modulo(const InfInt& a, const InfInt& b, const InfInt& n);
bool coprime(const InfInt& a, const InfInt& b);

bool probable_prime_base(const InfInt& n, const InfInt& a);
bool probable_prime(const InfInt& n);

} // namesapce InfIntMath



namespace InfIntMath {

const std::vector<InfInt> first_primes = {
	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, 1009, 1013,
	1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069,
	1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151,
	1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223,
	1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291,
	1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373,
	1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451,
	1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511,
	1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583,
	1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657,
	1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733,
	1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811,
	1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889,
	1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987,
	1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053,
	2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129,
	2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213,
	2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287,
	2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357,
	2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423,
	2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531,
	2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617,
	2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687,
	2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741,
	2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819,
	2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903,
	2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999,
	3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079,
	3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181,
	3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257,
	3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331,
	3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413,
	3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511,
	3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571,
	3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643,
	3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727,
	3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821,
	3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907,
	3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989,
	4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057,
	4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139,
	4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231,
	4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297,
	4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409,
	4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493,
	4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583,
	4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657,
	4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751,
	4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831,
	4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937,
	4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003,
	5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087,
	5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179,
	5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279,
	5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387,
	5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443,
	5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521,
	5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639,
	5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693,
	5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791,
	5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857,
	5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939,
	5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053,
	6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133,
	6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221,
	6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301,
	6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367,
	6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473,
	6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571,
	6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673,
	6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761,
	6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833,
	6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917,
	6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997,
	7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103,
	7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207,
	7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297,
	7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411,
	7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499,
	7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561,
	7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643,
	7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723,
	7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829,
	7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919
};

InfInt abs(const InfInt& infint) {
	InfInt tmp(infint);
	if (tmp.sign())
		tmp.twos_complement();
	return tmp;
}

InfInt& min(InfInt& a, InfInt& b) {
	if (a <= b)
		return a;
	else
		return b;
}

const InfInt& min(const InfInt& a, const InfInt& b) {
	if (a <= b)
		return a;
	else
		return b;
}

InfInt& max(InfInt& a, InfInt& b) {
	if (a >= b)
		return a;
	else
		return b;
}

const InfInt& max(const InfInt& a, const InfInt& b) {
	if (a >= b)
		return a;
	else
		return b;
}

InfInt pow(const InfInt& _a, const InfInt& _b) {
	if (_b == InfInt::zero) {
		if (_a == InfInt::zero)
			throw std::domain_error("InfInt InfIntMath::pow(const InfInt& _a, const InfInt& _b): Division by zero");
		return InfInt::pos_one;
	}
	if (_b < InfInt::zero) {
		if (_a == InfInt::zero)
			throw std::domain_error("InfInt InfIntMath::pow(const InfInt& _a, const InfInt& _b): Division by zero");
		return InfInt::zero;
	}

	InfInt a(_a);
	InfInt b(_b);
	InfInt r(InfInt::pos_one);

	while (b.size() != 1) {
		if (b.get(0))
			r *= a;
		a *= a;
		b >>= 1;
	}
	if (b.get(0))
		r *= a;

	return r;
}

InfInt modpow(const InfInt& _a, const InfInt& _b, const InfInt& m) {
	if (_b == InfInt::zero) {
		if (_a == InfInt::zero)
			throw std::domain_error("InfInt InfIntMath::modpow(const InfInt& _a, const InfInt& _b, const InfInt& m): Division by zero");
		return InfInt::pos_one;
	}
	if (_b < InfInt::zero) {
		if (_a == InfInt::zero)
			throw std::domain_error("InfInt InfIntMath::modpow(const InfInt& _a, const InfInt& _b, const InfInt& m): Division by zero");
		return InfInt::zero;
	}

	InfInt a(_a);
	InfInt b(_b);
	InfInt r(InfInt::pos_one);

	while (b.size() != 1) {
		if (b.get(0))
			r = r * a % m;
		a = a * a % m;
		b >>= 1;
	}
	if (b.get(0))
		r = r * a % m;

	return r;
}

InfInt sqrt(const InfInt& n) {
	if (n < InfInt::zero)
		throw std::domain_error("InfInt sqrt(const InfInt& n): must have n >= 0 (n=" + n.str() + ")");
	InfInt x = n;
	InfInt old_x;
	while (old_x != x) {
		old_x = x;
		x = x - ( x * x - n ) / ( 2_infint * x );
	}
	if (x * x > n) --x;
	return x;
}

InfInt root(const InfInt& a, const InfInt& b) {
	if (a < InfInt::zero)
		throw std::domain_error("InfInt root(const InfInt& a, const InfInt& b): must have a >= 0 (a=" + a.str() + ")");
	InfInt x = InfInt::pos_one;
	InfInt old_x;
	while (old_x != x) {
		old_x = x;
		InfInt f = pow(x, b) - a;
		InfInt _f = b * pow(x, b - InfInt::pos_one);
		x -= f / _f;
	}
	while (pow(x, b) > a)
		--x;
	return x;
}

InfInt log2(const InfInt& a) {
	return a.size() - 1;
}

InfInt log(const InfInt& a, const InfInt& b) {
	return log2(a) / log2(b);
}

InfInt modulo(const InfInt& a, const InfInt& b) {
	InfInt r = a % b;
	if (r.sign() != b.sign())
		r += b;
	return r;
}

InfInt lcm(const InfInt& a, const InfInt& b) {
	return a / gcd(a, b) * b;
}

InfInt gcd(const InfInt& _a, const InfInt& _b) {
	InfInt a(_a);
	InfInt b(_b);
	while (b != InfInt::zero) {
		InfInt c = a % b;
		a = b;
		b = c;
	}
	return a;
}

InfIntEGCDResult egcd(const InfInt& a, const InfInt& b) {
	InfInt r = b;
	InfInt old_r = a;

	InfInt s = InfInt::zero;
	InfInt old_s = InfInt::pos_one;

	InfInt t = InfInt::pos_one;
	InfInt old_t = InfInt::zero;

	while (r != InfInt::zero) {
		InfInt tmp_r(r), tmp_s(s), tmp_t(t);
		auto result = InfInt::fulldiv(old_r, r);

		r = result.remainder();
		s = old_s - result.quotient() * s;
		t = old_t - result.quotient() * t;

		old_r = tmp_r;
		old_s = tmp_s;
		old_t = tmp_t;
	}

	/*std::cout
	<< std::endl
	<< "EGCD:" << std::endl
	<< "gdc: " << old_r << std::endl
	<< "x: " << old_s << std::endl
	<< "y: " << old_t << std::endl
	<< std::endl;*/

	return InfIntEGCDResult(old_r, old_s, old_t);
}

InfInt modinv(const InfInt& a, const InfInt& b) {
	InfInt r = b;
	InfInt old_r = a;

	InfInt s = InfInt::zero;
	InfInt old_s = InfInt::pos_one;

	while (r != InfInt::zero) {
		InfInt tmp_r(r), tmp_s(s);
		auto result = InfInt::fulldiv(old_r, r);

		r = result.remainder();
		s = old_s - result.quotient() * s;

		old_r = tmp_r;
		old_s = tmp_s;
	}

	return old_s;
}

bool congruent_modulo(const InfInt& a, const InfInt& b, const InfInt& n) {
	return modulo(a - b, n) == InfInt::zero;
}

bool coprime(const InfInt& a, const InfInt& b) {
	return gcd(a, b) == InfInt::pos_one;
	/*if (a == b)
	return false;
	if (!a.get(0) && !b.get(0))
	return false;
	const InfInt& min(min(a, b));
	const InfInt two(2);
	for (InfInt i = 3; i <= min; i += two)
	if (a % i == 0 && b % i == 0)
	return false;
	return true;*/
}

bool probable_prime_base(const InfInt& n, const InfInt& a) {
	InfInt n1 = n - InfInt::pos_one;
	if (!(InfInt::pos_one < a && a < n1))
		throw std::domain_error("must have 1 < a < n - 1");

	//std::cout << "n: " << n << std::endl;
	//std::cout << "a: " << a << std::endl;

	InfInt::size_type s = 0;
	InfInt d;
	for (InfInt::size_type i = 0; i < n1.size(); ++i) {
		if (!n1.get(i))
			continue;
		s = i;
		d = n1 >> i;
		break;
	}

	//std::cout << "s: " << s << std::endl;
	//std::cout << "d: " << d << std::endl;

	InfInt result = modpow(a, d, n);
	if (result == InfInt::pos_one)
		return true;

	for (InfInt::size_type r = 0; r < s; ++r) {
		//std::cout << "r: " << r << std::endl;
		InfInt result = modpow(a, d * (InfInt::pos_one << r), n);
		if (result == n1)
			return true;
	}

	return false;
}

bool probable_prime(const InfInt& n) {
	std::cout << "Testing: " << n << std::endl;

	for (unsigned long long i = 0; i < first_primes.size(); ++i) {
		if (n % first_primes[i] == InfInt::zero) {
			std::cout << "Div test failed with " << first_primes[i] << std::endl;
			return false;
		}
	}

	std::cout << "Div test up to " << first_primes.back() << std::endl;

	if (!probable_prime_base(n, 2))
		std::cout << "is probable prime base 2" << std::endl;
	else {
		std::cout << "is composite" << std::endl;
		return false;
	}

	return true;
}

} // namespace InfIntMath

#endif // INFINTMATH_HPP