cp-library
競技プログラミング用 C++ ライブラリ
test/is_prime_light.test.cpp
test/is_prime_light.test.cpp · GitHub で見る
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コード
#define PROBLEM "https://judge.yosupo.jp/problem/primality_test"
#include "math/is_prime_light.hpp"
#include "components/fast_io.hpp"
#include <cstdint>
int main() {
FastInput input;
FastOutput output;
int q = 0;
input.read(q);
while (q--) {
std::uint64_t n = 0;
input.read(n);
output.println(light_is_prime(n) ? "Yes" : "No");
}
}
#line 1 "test/is_prime_light.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/primality_test"
#line 1 "math/is_prime_light.hpp"
#line 1 "components/is_prime_core.hpp"
#line 1 "components/montgomery.hpp"
#include <cassert>
#include <cstdint>
struct Montgomery64 {
using U = std::uint64_t;
using W = __uint128_t;
U mod, inverse = 1, r2, one;
explicit Montgomery64(U n) : mod(n), r2(-W(n) % n) {
for (int repeat_index = 0; repeat_index < 6; ++repeat_index) inverse *= 2 - n * inverse;
assert(n > 1 && (n & 1));
one = reduce(r2);
}
U reduce(W x) const {
U a = x >> 64, b = (W(U(x) * inverse) * mod) >> 64;
return a < b ? a - b + mod : a - b;
}
U in(U x) const { return reduce(W(x) * r2); }
U mul(U a, U b) const { return reduce(W(a) * b); }
U add(U a, U b) const {
U c = a + b;
return c < a || c >= mod ? c - mod : c;
}
U pow(U a, U e) const {
U r = one;
for (; e; e >>= 1, a = mul(a, a))
if (e & 1) r = mul(r, a);
return r;
}
};
#line 1 "components/montgomery32.hpp"
#line 6 "components/montgomery32.hpp"
struct Montgomery32 {
using U = std::uint32_t;
using W = std::uint64_t;
U mod, inverse = 1, r2, one;
explicit Montgomery32(U n) : mod(n), r2(-W(n) % n) {
for (int i = 0; i < 5; ++i) inverse *= 2 - n * inverse;
assert(n > 1 && (n & 1));
one = reduce(r2);
}
U reduce(W x) const {
U a = x >> 32, b = (W(U(x) * inverse) * mod) >> 32;
return a < b ? a - b + mod : a - b;
}
U in(U x) const { return reduce(W(x) * r2); }
U mul(U a, U b) const { return reduce(W(a) * b); }
U add(U a, U b) const {
U c = a + b;
return c < a || c >= mod ? c - mod : c;
}
U pow(U a, U e) const {
U r = one;
if (mod < (U(1) << 30)) {
U inverse = -this->inverse;
auto product = [&](U a, U b) {
W x = W(a) * b;
return U((x + W(U(x) * inverse) * mod) >> 32);
};
for (; e; e >>= 1, a = product(a, a)) if (e & 1) r = product(r, a);
return r < mod ? r : r - mod;
}
for (; e; e >>= 1, a = mul(a, a)) if (e & 1) r = mul(r, a);
return r;
}
};
#line 6 "components/is_prime_core.hpp"
#include <algorithm>
#include <array>
#include <bit>
#line 10 "components/is_prime_core.hpp"
namespace is_prime_detail {
using U = std::uint64_t;
inline constexpr U small_primes[] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37};
template <class Montgomery, class Multiply>
inline bool witness(const Montgomery &m, typename Montgomery::U x, int s, Multiply multiply) {
if (x >= m.mod) x -= m.mod;
if (x == m.one || x == m.mod - m.one) return true;
for (int j = 1; j < s; ++j) {
x = multiply(x, x);
if (x >= m.mod) x -= m.mod;
if (x == m.mod - m.one) return true;
}
return false;
}
template <class Multiply>
inline bool witness2(const Montgomery64 &m, U d, int s, Multiply multiply) {
int shift = std::max(0, int(std::bit_width(d)) - 6);
U x = m.in(U(1) << (d >> shift));
const U twice = m.mod + m.mod;
for (int bit = shift - 1; bit >= 0; --bit) {
x = multiply(x, x);
if ((d >> bit) & 1) {
x += x;
if (x >= twice) x -= twice;
}
}
return witness(m, x, s, multiply);
}
template <class Montgomery, std::size_t Count, class Multiply>
inline bool witnesses(const Montgomery &m, typename Montgomery::U d, int s,
const std::array<typename Montgomery::U, Count> &bases, Multiply multiply) {
using V = typename Montgomery::U;
std::array<V, Count> x;
if (Count <= 3 || d < 4096) {
std::array<V, Count> a;
#pragma GCC unroll 8
for (std::size_t i = 0; i < Count; ++i) a[i] = x[i] = m.in(bases[i] % m.mod);
for (V e = d >> 1; e; e >>= 1) {
#pragma GCC unroll 8
for (std::size_t i = 0; i < Count; ++i) a[i] = multiply(a[i], a[i]);
if (e & 1) {
#pragma GCC unroll 8
for (std::size_t i = 0; i < Count; ++i) x[i] = multiply(x[i], a[i]);
}
}
} else {
constexpr int window = 3;
std::array<std::array<V, Count>, 1 << window> powers;
for (std::size_t i = 0; i < Count; ++i) powers[1][i] = m.in(bases[i] % m.mod);
for (int k = 2; k < (1 << window); ++k)
for (std::size_t i = 0; i < Count; ++i) powers[k][i] = multiply(powers[k - 1][i], powers[1][i]);
int shift = ((std::bit_width(d) - 1) / window) * window;
x = powers[d >> shift];
for (shift -= window; shift >= 0; shift -= window) {
for (int k = 0; k < window; ++k) {
#pragma GCC unroll 8
for (std::size_t i = 0; i < Count; ++i) x[i] = multiply(x[i], x[i]);
}
int digit = (d >> shift) & ((1 << window) - 1);
if (digit) {
#pragma GCC unroll 8
for (std::size_t i = 0; i < Count; ++i) x[i] = multiply(x[i], powers[digit][i]);
}
}
}
#pragma GCC unroll 8
for (std::size_t i = 0; i < Count; ++i) {
V y = x[i] >= m.mod ? x[i] - m.mod : x[i];
if (!y && bases[i] % m.mod == 0) continue;
if (!witness(m, y, s, multiply)) return false;
}
return true;
}
inline bool prime(const Montgomery32 &m) {
using V = Montgomery32::U;
V d = m.mod - 1;
int s = std::countr_zero(d);
d >>= s;
auto check = [&](auto multiply) {
if (!witnesses(m, d, s, std::array<V, 1>{2}, multiply)) return false;
if (m.mod < 1373653) return witnesses(m, d, s, std::array<V, 1>{3}, multiply);
return witnesses(m, d, s, std::array<V, 2>{7, 61}, multiply);
};
if (m.mod < (V(1) << 30)) return check([&](V a, V b) {
U x = U(a) * b;
return V(x >> 32) + m.mod - V((U(V(x) * m.inverse) * m.mod) >> 32);
});
return check([&](V a, V b) { return m.mul(a, b); });
}
inline bool prime(const Montgomery64 &m) {
if (m.mod < (U(1) << 32)) return prime(Montgomery32(m.mod));
U d = m.mod - 1;
int s = std::countr_zero(d);
d >>= s;
const std::array<U, 6> bases{325, 9375, 28178, 450775, 9780504, 1795265022};
if (m.mod < (U(1) << 62)) {
if (!witness2(m, d, s, [&](U a, U b) {
__uint128_t x = __uint128_t(a) * b;
return U(x >> 64) + m.mod - U((__uint128_t(U(x) * m.inverse) * m.mod) >> 64);
})) return false;
U inverse = -m.inverse;
return witnesses(m, d, s, bases, [&](U a, U b) {
__uint128_t x = __uint128_t(a) * b;
return U((x + __uint128_t(U(x) * inverse) * m.mod) >> 64);
});
}
auto multiply = [&](U a, U b) { return m.mul(a, b); };
return witnesses(m, d, s, std::array<U, 1>{2}, multiply) && witnesses(m, d, s, bases, multiply);
}
template <class Check>
inline bool check(U n, Check prime) {
if (n < 2) return false;
#pragma GCC unroll 16
for (U p : small_primes)
if (n % p == 0) return n == p;
if (n < 1681) return true;
if (n < (std::uint64_t(1) << 32)) return prime(Montgomery32(n));
return prime(Montgomery64(n));
}
}
#line 5 "math/is_prime_light.hpp"
inline bool light_is_prime(std::uint64_t n) {
return is_prime_detail::check(n, [](const auto &m) { return is_prime_detail::prime(m); });
}
#line 1 "components/fast_io.hpp"
#line 8 "components/fast_io.hpp"
#include <charconv>
#include <cstddef>
#line 11 "components/fast_io.hpp"
#include <cstdio>
#include <cstring>
#include <memory>
#include <stdexcept>
#include <string>
#include <string_view>
#include <type_traits>
#if defined(__unix__) || defined(__APPLE__)
#include <sys/mman.h>
#include <sys/stat.h>
#include <unistd.h>
#endif
namespace fast_io_detail { struct BulkInput; struct BulkOutput; }
class FastInput {
friend struct fast_io_detail::BulkInput;
static constexpr std::size_t capacity = 1 << 16;
FILE *file = nullptr;
std::unique_ptr<char[]> buffer;
const char *current = "", *end = current;
std::string scratch;
void *mapping = nullptr;
std::size_t mapped_size = 0;
bool refill() {
if (!file) return false;
std::size_t n = std::fread(buffer.get(), 1, capacity, file);
current = buffer.get();
end = current + n;
return n;
}
static const char *scan(const char *p, const char *end) {
while (end - p >= 8) {
std::uint64_t x;
std::memcpy(&x, p, 8);
if ((x - 0x2121212121212121ULL) & ~x & 0x8080808080808080ULL) break;
p += 8;
}
while (p != end && static_cast<unsigned char>(*p) > ' ') ++p;
return p;
}
public:
explicit FastInput(FILE *input = stdin) {
#if defined(__unix__) || defined(__APPLE__)
struct stat status;
int fd = fileno(input);
auto offset = ftello(input);
if (fd >= 0 && offset >= 0 && !fstat(fd, &status) && S_ISREG(status.st_mode) && status.st_size > offset) {
mapped_size = status.st_size;
mapping = mmap(nullptr, mapped_size, PROT_READ, MAP_PRIVATE, fd, 0);
if (mapping != MAP_FAILED) {
current = static_cast<const char *>(mapping) + offset;
end = static_cast<const char *>(mapping) + mapped_size;
return;
}
mapping = nullptr;
}
#endif
file = input;
buffer = std::make_unique_for_overwrite<char[]>(capacity);
}
explicit FastInput(std::string_view input) : current(input.empty() ? "" : input.data()), end(current + input.size()) {}
FastInput(const FastInput &) = delete;
FastInput &operator=(const FastInput &) = delete;
~FastInput() {
#if defined(__unix__) || defined(__APPLE__)
if (mapping) munmap(mapping, mapped_size);
#endif
}
std::string_view token() {
while (true) {
while (current != end && static_cast<unsigned char>(*current) <= ' ') ++current;
if (current != end) break;
if (!refill()) return {};
}
const char *begin = current;
current = scan(current, end);
if (current != end || !file) return {begin, std::size_t(current - begin)};
scratch.assign(begin, end);
while (refill()) {
current = scan(current, end);
scratch.append(buffer.get(), std::size_t(current - buffer.get()));
if (current != end) break;
}
return scratch;
}
template <class T>
bool read(T &value) {
if constexpr (std::is_integral_v<T> && !std::is_same_v<T, bool>) {
while (true) {
while (current != end && static_cast<unsigned char>(*current) <= ' ') ++current;
if (current != end) break;
if (!refill()) return false;
}
if constexpr (std::is_unsigned_v<T> && sizeof(T) == 4 && std::endian::native == std::endian::little) {
if (end - current >= 11) {
std::uint64_t x;
std::memcpy(&x, current, 8);
if (!(((x + 0x4646464646464646ULL) | (x - 0x3030303030303030ULL)) & 0x8080808080808080ULL)) {
x &= 0x0f0f0f0f0f0f0f0fULL;
x = (x * 10 + (x >> 8)) & 0x00ff00ff00ff00ffULL;
x = (x * 100 + (x >> 16)) & 0x0000ffff0000ffffULL;
std::uint64_t v = std::uint32_t(x * 10000 + (x >> 32));
int n = 8;
for (; n < 10 && static_cast<unsigned char>(current[n]) - unsigned('0') < 10; ++n)
v = v * 10 + (current[n] - '0');
if (static_cast<unsigned char>(current[n]) <= ' ' && v <= 0xffffffffULL) {
current += n;
value = T(v);
return true;
}
}
}
}
T parsed{};
auto result = std::from_chars(current, end, parsed);
if (result.ec == std::errc{} && (result.ptr != end ? static_cast<unsigned char>(*result.ptr) <= ' ' : !file)) {
current = result.ptr;
value = parsed;
return true;
}
}
auto s = token();
if (s.empty()) return false;
if constexpr (std::is_same_v<T, bool>) {
assert(s == "0" || s == "1");
value = s[0] == '1';
} else if constexpr (std::is_integral_v<T>) {
auto result = std::from_chars(s.data(), s.data() + s.size(), value);
assert(result.ec == std::errc{} && result.ptr == s.data() + s.size());
(void)result;
} else value = T(s);
return true;
}
};
class FastOutput {
friend struct fast_io_detail::BulkOutput;
inline static constexpr auto quads = [] {
std::array<std::array<char, 4>, 10000> table{};
for (int i = 0; i < 10000; ++i)
table[i] = {char('0' + i / 1000), char('0' + i / 100 % 10), char('0' + i / 10 % 10), char('0' + i % 10)};
return table;
}();
FILE *file;
std::unique_ptr<char[]> buffer = std::make_unique_for_overwrite<char[]>(1 << 16);
std::size_t capacity = 1 << 16, length = 0;
char *reserve(std::size_t n) {
if (n > capacity - length) {
if (!flush()) throw std::runtime_error("output failed");
if (n > capacity) {
std::size_t next = std::max(n, 2 * capacity);
buffer = std::make_unique_for_overwrite<char[]>(next);
capacity = next;
}
}
return buffer.get() + length;
}
public:
explicit FastOutput(FILE *output = stdout) : file(output) {}
FastOutput(const FastOutput &) = delete;
FastOutput &operator=(const FastOutput &) = delete;
~FastOutput() { flush(); }
bool flush() {
std::size_t offset = 0;
while (offset < length) {
auto n = std::fwrite(buffer.get() + offset, 1, length - offset, file);
if (!n) {
std::memmove(buffer.get(), buffer.get() + offset, length - offset);
length -= offset;
return false;
}
offset += n;
}
length = 0;
return std::fflush(file) == 0;
}
void write(char c) { *reserve(1) = c; ++length; }
void write(__uint128_t value) {
char digits[40];
char *end = digits + sizeof(digits), *begin = end;
do { *--begin = char('0' + value % 10); value /= 10; } while (value);
write(std::string_view(begin, end - begin));
}
void write(__int128_t value) {
__uint128_t magnitude = __uint128_t(value);
if (value < 0) write('-'), magnitude = 0 - magnitude;
write(magnitude);
}
void write(std::string_view s) {
char *out = reserve(s.size());
if (!s.empty()) std::memcpy(out, s.data(), s.size());
length += s.size();
}
template <class T> requires std::is_integral_v<T>
void write(T value) {
char *out = reserve(32);
if constexpr (std::is_same_v<T, bool>) *out = '0' + value, ++length;
else if constexpr (std::is_unsigned_v<T> && sizeof(T) == 4) {
char *p = out;
if (value >= 100000000) {
auto high = value / 100000000, low = value % 100000000;
p = std::to_chars(p, p + 2, high).ptr;
std::memcpy(p, quads[low / 10000].data(), 4);
std::memcpy(p + 4, quads[low % 10000].data(), 4);
p += 8;
} else if (value >= 10000) {
p = std::to_chars(p, p + 4, value / 10000).ptr;
std::memcpy(p, quads[value % 10000].data(), 4);
p += 4;
} else p = std::to_chars(p, p + 4, value).ptr;
length += p - out;
} else length += std::to_chars(out, out + 32, value).ptr - out;
}
template <class T> requires requires(const T &value, char *out) { value.decimal_capacity(); value.to_chars(out); }
void write(const T &value) {
char *out = reserve(value.decimal_capacity());
length += value.to_chars(out) - out;
}
template <class T>
void println(const T &value) { write(value); write('\n'); }
};
#line 5 "test/is_prime_light.test.cpp"
int main() {
FastInput input;
FastOutput output;
int q = 0;
input.read(q);
while (q--) {
std::uint64_t n = 0;
input.read(n);
output.println(light_is_prime(n) ? "Yes" : "No");
}
}