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number_theory/test/montgomery_64_stress.test.cpp
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- Last update: 2025-06-28 10:05:47+09:00
- Problem: https://onlinejudge.u-aizu.ac.jp/courses/lesson/2/ITP1/1/ITP1_1_A
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Code
#define PROBLEM \
"https://onlinejudge.u-aizu.ac.jp/courses/lesson/2/ITP1/1/ITP1_1_A"
#define FAST_IO
#define FIX_SEED
#include "../../number_theory/montgomery_64.hpp"
#include "../../template/random.hpp"
#include "../../template/template.hpp"
using M = MontgomeryModInt64<0>;
u64 add(u64 a, u64 b, u64 m) { return (a + b) % m; }
u64 sub(u64 a, u64 b, u64 m) { return (m + a - b) % m; }
u64 mul(u64 a, u64 b, u64 m) { return __uint128_t(a) * b % m; }
void test_small_mod(i32 m) {
M::set_mod(m);
REP(i, m) REP(j, m) {
M x(i), y(j);
assert((x + y).val() == add(i, j, m));
assert((x - y).val() == sub(i, j, m));
assert((x * y).val() == mul(i, j, m));
}
}
void test_large_mod(u64 m) {
M::set_mod(m);
constexpr int ITER = 1'000'000;
for (int i = 0; i < ITER; ++i) {
u64 x = uniform(m);
u64 y = uniform(m);
M x_(x), y_(y);
assert((x_ + y_).val() == add(x, y, m));
assert((x_ - y_).val() == sub(x, y, m));
assert((x_ * y_).val() == mul(x, y, m));
}
}
void test() {
for (i32 m = 3; m <= 99; m += 2) {
test_small_mod(m);
}
for (int i = 0; i < 10; ++i) {
u64 m = uniform<u64>(3, 1ULL << 63);
while (m % 2 == 0) {
m = uniform<u64>(3, 1ULL << 63);
}
test_large_mod(m);
}
test_large_mod((1ULL << 63) - 1);
}
int main() {
test();
cout << "Hello World\n";
}#line 1 "number_theory/test/montgomery_64_stress.test.cpp"
#define PROBLEM \
"https://onlinejudge.u-aizu.ac.jp/courses/lesson/2/ITP1/1/ITP1_1_A"
#define FAST_IO
#define FIX_SEED
#line 2 "number_theory/montgomery_64.hpp"
#include <cassert>
// mod: odd, < 2^{63}
template <int id>
struct MontgomeryModInt64 {
using u64 = unsigned long long;
using u128 = __uint128_t;
static u64 inv_64(u64 n) {
u64 r = n;
for (int i = 0; i < 5; ++i) {
r *= 2 - n * r;
}
return r;
}
static u64 mod, neg_inv, sq;
static void set_mod(u64 m) {
assert(m % 2 == 1 && m < (1ULL << 63));
mod = m;
neg_inv = -inv_64(m);
sq = -u128(mod) % mod;
}
static u64 get_mod() { return mod; }
static u64 reduce(u128 xr) {
u64 ret = (xr + u128(u64(xr) * neg_inv) * mod) >> 64;
if (ret >= mod) {
ret -= mod;
}
return ret;
}
using M = MontgomeryModInt64<id>;
u64 x;
MontgomeryModInt64() : x(0) {}
MontgomeryModInt64(u64 _x) : x(reduce(u128(_x) * sq)) {}
u64 val() const { return reduce(u128(x)); }
M &operator+=(M rhs) {
if ((x += rhs.x) >= mod) {
x -= mod;
}
return *this;
}
M &operator-=(M rhs) {
if ((x -= rhs.x) >= mod) {
x += mod;
}
return *this;
}
M &operator*=(M rhs) {
x = reduce(u128(x) * rhs.x);
return *this;
}
M operator+(M rhs) const { return M(*this) += rhs; }
M operator-(M rhs) const { return M(*this) -= rhs; }
M operator*(M rhs) const { return M(*this) *= rhs; }
M pow(u64 t) const {
M ret(1);
M self = *this;
while (t) {
if (t & 1) {
ret *= self;
}
self *= self;
t >>= 1;
}
return ret;
}
M inv() const {
assert(x);
return this->pow(mod - 2);
}
M &operator/=(M rhs) {
*this /= rhs.inv();
return *this;
}
M operator/(M rhs) const { return M(*this) /= rhs; }
};
template <int id> unsigned long long MontgomeryModInt64<id>::mod = 1;
template <int id> unsigned long long MontgomeryModInt64<id>::neg_inv = 1;
template <int id> unsigned long long MontgomeryModInt64<id>::sq = 1;
#line 2 "template/random.hpp"
#include <chrono>
#include <random>
#if defined(LOCAL) || defined(FIX_SEED)
std::mt19937_64 mt(123456789);
#else
std::mt19937_64 mt(std::chrono::steady_clock::now().time_since_epoch().count());
#endif
template <typename T>
T uniform(T l, T r) {
return std::uniform_int_distribution<T>(l, r - 1)(mt);
}
template <typename T>
T uniform(T n) {
return std::uniform_int_distribution<T>(0, n - 1)(mt);
}
#line 2 "template/template.hpp"
#include <bits/stdc++.h>
#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER2(i, n) for (i32 i = (i32)(n)-1; i >= 0; --i)
#define PER3(i, m, n) for (i32 i = (i32)(n)-1; i >= (i32)(m); --i)
#define PER(...) OVERRIDE(__VA_ARGS__, PER3, PER2)(__VA_ARGS__)
#define ALL(x) begin(x), end(x)
#define LEN(x) (i32)(x.size())
using namespace std;
using u32 = unsigned int;
using u64 = unsigned long long;
using i32 = signed int;
using i64 = signed long long;
using f64 = double;
using f80 = long double;
using pi = pair<i32, i32>;
using pl = pair<i64, i64>;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = V<V<T>>;
template <typename T>
using VVV = V<V<V<T>>>;
template <typename T>
using VVVV = V<V<V<V<T>>>>;
template <typename T>
using PQR = priority_queue<T, V<T>, greater<T>>;
template <typename T>
bool chmin(T &x, const T &y) {
if (x > y) {
x = y;
return true;
}
return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
if (x < y) {
x = y;
return true;
}
return false;
}
template <typename T>
i32 lob(const V<T> &arr, const T &v) {
return (i32)(lower_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
i32 upb(const V<T> &arr, const T &v) {
return (i32)(upper_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
V<i32> argsort(const V<T> &arr) {
V<i32> ret(arr.size());
iota(ALL(ret), 0);
sort(ALL(ret), [&](i32 i, i32 j) -> bool {
if (arr[i] == arr[j]) {
return i < j;
} else {
return arr[i] < arr[j];
}
});
return ret;
}
#ifdef INT128
using u128 = __uint128_t;
using i128 = __int128_t;
#endif
[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
SetUpIO() {
#ifdef FAST_IO
ios::sync_with_stdio(false);
cin.tie(nullptr);
#endif
cout << fixed << setprecision(15);
}
} set_up_io;
void scan(char &x) { cin >> x; }
void scan(u32 &x) { cin >> x; }
void scan(u64 &x) { cin >> x; }
void scan(i32 &x) { cin >> x; }
void scan(i64 &x) { cin >> x; }
void scan(f64 &x) { cin >> x; }
void scan(string &x) { cin >> x; }
template <typename T>
void scan(V<T> &x) {
for (T &ele : x) {
scan(ele);
}
}
void read() {}
template <typename Head, typename... Tail>
void read(Head &head, Tail &...tail) {
scan(head);
read(tail...);
}
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__);
#define U32(...) \
u32 __VA_ARGS__; \
read(__VA_ARGS__);
#define U64(...) \
u64 __VA_ARGS__; \
read(__VA_ARGS__);
#define I32(...) \
i32 __VA_ARGS__; \
read(__VA_ARGS__);
#define I64(...) \
i64 __VA_ARGS__; \
read(__VA_ARGS__);
#define F64(...) \
f64 __VA_ARGS__; \
read(__VA_ARGS__);
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__);
#define VEC(type, name, size) \
V<type> name(size); \
read(name);
#define VVEC(type, name, size1, size2) \
VV<type> name(size1, V<type>(size2)); \
read(name);
#line 9 "number_theory/test/montgomery_64_stress.test.cpp"
using M = MontgomeryModInt64<0>;
u64 add(u64 a, u64 b, u64 m) { return (a + b) % m; }
u64 sub(u64 a, u64 b, u64 m) { return (m + a - b) % m; }
u64 mul(u64 a, u64 b, u64 m) { return __uint128_t(a) * b % m; }
void test_small_mod(i32 m) {
M::set_mod(m);
REP(i, m) REP(j, m) {
M x(i), y(j);
assert((x + y).val() == add(i, j, m));
assert((x - y).val() == sub(i, j, m));
assert((x * y).val() == mul(i, j, m));
}
}
void test_large_mod(u64 m) {
M::set_mod(m);
constexpr int ITER = 1'000'000;
for (int i = 0; i < ITER; ++i) {
u64 x = uniform(m);
u64 y = uniform(m);
M x_(x), y_(y);
assert((x_ + y_).val() == add(x, y, m));
assert((x_ - y_).val() == sub(x, y, m));
assert((x_ * y_).val() == mul(x, y, m));
}
}
void test() {
for (i32 m = 3; m <= 99; m += 2) {
test_small_mod(m);
}
for (int i = 0; i < 10; ++i) {
u64 m = uniform<u64>(3, 1ULL << 63);
while (m % 2 == 0) {
m = uniform<u64>(3, 1ULL << 63);
}
test_large_mod(m);
}
test_large_mod((1ULL << 63) - 1);
}
int main() {
test();
cout << "Hello World\n";
}