#704894 (C) No.3030 ミラー・ラビン素数判定法のテスト

提出ソース

結果

問題	No.3030 ミラー・ラビン素数判定法のテスト
ユーザー	nonamae
提出日時	2021-10-07 08:49:23
言語	C (gcc 12.3.0)
結果	AC
実行時間	27 ms / 9,973 ms
コード長	8,921 bytes
コンパイル時間	519 ms
コンパイル使用メモリ	38,776 KB
実行使用メモリ	5,248 KB
最終ジャッジ日時	2024-11-16 23:40:35
合計ジャッジ時間	1,033 ms
ジャッジサーバーID （参考情報）	judge1 / judge5

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	1 ms 5,248 KB
testcase_01	AC	1 ms 5,248 KB
testcase_02	AC	1 ms 5,248 KB
testcase_03	AC	1 ms 5,248 KB
testcase_04	AC	17 ms 5,248 KB
testcase_05	AC	17 ms 5,248 KB
testcase_06	AC	10 ms 5,248 KB
testcase_07	AC	10 ms 5,248 KB
testcase_08	AC	10 ms 5,248 KB
testcase_09	AC	27 ms 5,248 KB

権限があれば一括ダウンロードができます

コンパイルメッセージ

main.c: In function 'read_int':
main.c:38:14: warning: implicit declaration of function 'getchar_unlocked' [-Wimplicit-function-declaration]
   38 |   while (c = getchar_unlocked(), c < 48 || c > 57) if (c == 45) f = -f;
      |              ^~~~~~~~~~~~~~~~
main.c: In function 'write_int':
main.c:65:5: warning: implicit declaration of function 'putchar_unlocked' [-Wimplicit-function-declaration]
   65 |     putchar_unlocked('-');
      |     ^~~~~~~~~~~~~~~~

ソースコード

raw source code

#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")

#include <assert.h>
#include <math.h>
#include <stdbool.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>

/* signed integer */
typedef   int8_t      i8;
typedef   int16_t     i16;
typedef   int32_t     i32;
typedef   int64_t     i64;
typedef __int128_t    i128;

/* unsigned integer */
typedef   uint8_t     u8;
typedef   uint16_t    u16;
typedef   uint32_t    u32;
typedef   uint64_t    u64;
typedef __uint128_t   u128;

/* floating point number */
typedef   float       f32;
typedef   double      f64;
typedef   long double f80;

typedef   int         FastInt;

/* io */
static inline FastInt read_int(void) {
  FastInt c, x = 0, f = 1;
  while (c = getchar_unlocked(), c < 48 || c > 57) if (c == 45) f = -f;
  while (47 < c && c < 58) {
    x = x * 10 + c - 48;
    c = getchar_unlocked();
  }
  return f * x;
}
static inline i64 in(void) {
  i64 c, x = 0, f = 1;
  while (c = getchar_unlocked(), c < 48 || c > 57) if (c == 45) f = -f;
  while (47 < c && c < 58) {
    x = x * 10 + c - 48;
    c = getchar_unlocked();
  }
  return f * x;
}
static inline u64 inu(void) {
  u64 c, x = 0;
  while (c = getchar_unlocked(), c < 48 || c > 57);
  while (47 < c && c < 58) {
    x = x * 10 + c - 48;
    c = getchar_unlocked();
  }
  return x;
}
static inline void write_int(FastInt x) {
  if (x < 0) {
    putchar_unlocked('-');
    x = -x;
  }
  if (x >= 10) write_int(x / 10);
  putchar_unlocked(x - x / 10 * 10 + 48);
}
static inline void out(i64 x) {
  if (x < 0) {
    putchar_unlocked('-');
    x = -x;
  }
  if (x >= 10) out(x / 10);
  putchar_unlocked(x - x / 10 * 10 + 48);
}
static inline void outu(u64 x) {
  if (x >= 10) outu(x / 10);
  putchar_unlocked(x - x / 10 * 10 + 48);
}
static inline void NL(void) { putchar_unlocked('\n'); }
static inline void SP(void) { putchar_unlocked(' '); }

/* MACROS */
#define POPCNT(a) __builtin_popcountll((a))
#define CTZ(a) __builtin_ctzll((a))
#define CLZ(a) __builtin_clzll((a))
#define LSBit(a) ((a)&(-(a)))
#define CLSBit(a) ((a)&((a)-(1)))
#define HAS_SINGLE_BIT(a) (POPCNT((a))==1)
#define BIT_CEIL(a) ((!(a))?(1):((POPCNT(a))==(1)?((1ull)<<((63)-CLZ((a)))):((1ull)<<((64)-CLZ(a)))))
#define BIT_FLOOR(a) ((!(a))?(0):((1ull)<<((63)-CLZ((a)))))
#define BIT_WIDTH(a) ((a)?((64)-CLZ((a))):(0))
#define _ROTL(x, s) (((x)<<((s)%(64)))|(((x)>>((64)-((s)%(64))))))
#define _ROTR(x, s) (((x)>>((s)%(64)))|(((x)<<((64)-((s)%(64))))))
#define ROTL(x, s) (((s)==(0))?(0):(((s)<(0))?(_ROTR((x),-(s))):(_ROTL((x),(s)))))
#define ROTR(x, s) (((s)==(0))?(0):(((s)<(0))?(_ROTL((x),-(s))):(_ROTR((x),(s)))))
#define SWAP(a, b) (((a)^=(b)),((b)^=(a)),((a)^=(b)))
#define MAX(a, b) ((a)>(b)?(a):(b))
#define MIN(a, b) ((a)<(b)?(a):(b))

i64 _gcd_(i64 a, i64 b) {
  // assert(a >= 0 && b >= 0);
  if (!a || !b) return a | b;
  FastInt shift = CTZ(a | b);
  a >>= CTZ(a);
  do {
    b >>= CTZ(b);
    if (a > b) SWAP(a, b);
    b -= a;
  } while (b);
  return a << shift;
}
i64 _lcm_(i64 a, i64 b) {
  // assert(a >= 0 && b >= 0);
  return a / _gcd_(a, b) * b;
}

/* montgomery modular multiplication 32-bit */
typedef u32 Montgomery;

Montgomery _one(u32 mod) {
  return -1u % mod + 1;
}
Montgomery _r2(u32 mod) {
  return (u64)(i64)-1 % mod + 1;
}
Montgomery _inv(u32 mod) {
  u32 u = 1, v = 0, x = 1ULL << 31;
  for (FastInt i = 0; i < 32; i++) {
    if (u & 1) u = (u + mod) >> 1, v = (v >> 1) + x;
    else u >>= 1, v >>= 1;
  }
  return -v;
}
Montgomery _MR(u64 a, Montgomery inv, u32 mod) {
  i32 z = (a >> 32) - ((((u32)a * inv) * (u64)mod) >> 32);
  return z < 0 ? z + mod : (u64)z;
}
Montgomery _to_montgomery(u32 a, Montgomery r2, Montgomery inv, u32 mod) {
  return _MR((u64)a * r2, inv, mod);
}
u32 _from_montgomery(Montgomery A, Montgomery inv, u32 mod) {
  return _MR((u64)A, inv, mod) % mod;
}
Montgomery add_MR(Montgomery A, Montgomery B, Montgomery r2, Montgomery inv, u32 mod) {
  if ((i32)(A += B - 2 * mod) < 0) A += 2 * mod;
  return A;
}
Montgomery sub_MR(Montgomery A, Montgomery B, Montgomery r2, Montgomery inv, u32 mod) {
  if ((i32)(A -= B) < 0) A += 2 * mod;
  return A;
}
Montgomery min_MR(Montgomery A, Montgomery r2, Montgomery inv, u32 mod) {
  return sub_MR(0, A, r2, inv, mod);
}
Montgomery mul_MR(Montgomery A, Montgomery B, Montgomery inv, u32 mod) {
  return _MR((u64)A * B, inv, mod);
}
Montgomery pow_MR(Montgomery A, i64 n, Montgomery inv, u32 mod) {
  Montgomery ret = _one(mod);
  while (n > 0) {
    if (n & 1) ret = mul_MR(ret, A, inv, mod);
    A = mul_MR(A, A, inv, mod);
    n >>= 1;
  }
  return ret;
}
Montgomery inv_MR(Montgomery A, Montgomery inv, u32 mod) {
  return pow_MR(A, (i64)mod - 2, inv, mod);
}
Montgomery div_MR(Montgomery A, Montgomery B, Montgomery inv, u32 mod) {
  return mul_MR(A, inv_MR(B, inv, mod), inv, mod);
}
bool eq_MR(Montgomery A, Montgomery B, Montgomery inv, u32 mod) {
  return _from_montgomery(A, inv, mod) == _from_montgomery(B, inv, mod);
}
bool neq_MR(Montgomery A, Montgomery B, Montgomery inv, u32 mod) {
  return _from_montgomery(A, inv, mod) != _from_montgomery(B, inv, mod);
}
bool is_prime(u32 n) {
  // assert(n < 4759123141);
  if (n <= 3) return n == 2 || n == 3;
  if (!(n & 1)) return false;
  Montgomery r2 = _r2(n);
  Montgomery inv = _inv(n);
  u32 s = CTZ(n - 1);
  u32 d = (n - 1) >> s;
  u32 as[] = {2, 7, 61};
  Montgomery e = _one(n);
  Montgomery rev = _to_montgomery(n - 1, r2, inv, n);
  for (FastInt i = 0; i < 3; i++) {
    Montgomery A = _to_montgomery(as[i], r2, inv, n);
    if (A == 0) return true;
    Montgomery res = pow_MR(A, d, inv, n);
    if (res == e) continue;
    bool ok = true;
    for (u32 r = 0; r < s; r++) {
      if (res == rev) {
        ok = false;
        break;
      }
      res = mul_MR(res, res, inv, n);
    }
    if (ok) return false;
  }
  return true;
}


/* montgomery modular multiplication 64-bit */
typedef u64 Montgomery64;

Montgomery64 _one_64(u64 mod) {
  return -1ull % mod + 1;
}
Montgomery64 _r2_64(u64 mod) {
  return (u128)(i128)-1 % mod + 1;
}
Montgomery64 _inv_64(u64 mod) {
  u64 u = 1, v = 0, x = 1ULL << 63;
  for (FastInt i = 0; i < 64; i++) {
    if (u & 1) u = (u + mod) >> 1, v = (v >> 1) + x;
    else u >>= 1, v >>= 1;
  }
  return -v;
}
Montgomery64 _MR_64(u128 a, Montgomery64 inv, u64 mod) {
  i64 A = (a >> 64) - ((((u64)a * inv) * (u128)mod) >> 64);
  return A < 0 ? A + mod : (u64)A;
}
Montgomery64 _to_montgomery_64(u64 a, Montgomery64 r2, Montgomery64 inv, u64 mod) {
  return _MR_64((u128)a * r2, inv, mod);
}
u64 _from_montgomery_64(Montgomery64 A, Montgomery64 inv, u64 mod) {
  return _MR_64((u128)A, inv, mod) % mod;
}
Montgomery64 add_MR_64(Montgomery64 A, Montgomery64 B, Montgomery64 r2, Montgomery64 inv, u64 mod) {
  if ((i64)(A += B - 2 * mod) < 0) A += 2 * mod;
  return A;
}
Montgomery64 sub_MR_64(Montgomery64 A, Montgomery64 B, Montgomery64 r2, Montgomery64 inv, u64 mod) {
  if ((i64)(A -= B) < 0) A += 2 * mod;
  return A;
}
Montgomery64 min_MR_64(Montgomery64 A, Montgomery64 r2, Montgomery64 inv, u64 mod) {
  return sub_MR_64(0, A, r2, inv, mod);
}
Montgomery64 mul_MR_64(Montgomery64 A, Montgomery64 B, Montgomery64 inv, u64 mod) {
  return _MR_64((u128)A * B, inv, mod);
}
Montgomery64 pow_MR_64(Montgomery64 A, i64 n, Montgomery64 inv, u64 mod) {
  Montgomery64 ret = _one_64(mod), mul = A;
  while (n > 0) {
    if (n & 1) ret = mul_MR_64(ret, mul, inv, mod);
    mul = mul_MR_64(mul, mul, inv, mod);
    n >>= 1;
  }
  return ret;
}
Montgomery64 inv_MR_64(Montgomery64 A, Montgomery64 inv, u64 mod) {
  return pow_MR_64(A, (i64)mod - 2, inv, mod);
}
Montgomery64 div_MR_64(Montgomery64 A, Montgomery64 B, Montgomery64 inv, u64 mod) {
  return mul_MR_64(A, inv_MR_64(B, inv, mod), inv, mod);
}
bool eq_MR_64(Montgomery64 A, Montgomery64 B, Montgomery64 inv, u64 mod) {
  return _from_montgomery_64(A, inv, mod) == _from_montgomery_64(B, inv, mod);
}
bool neq_MR_64(Montgomery64 A, Montgomery64 B, Montgomery64 inv, u64 mod) {
  return _from_montgomery_64(A, inv, mod) != _from_montgomery_64(B, inv, mod);
}
bool is_prime_64(u64 n) {
  if (n < 4759123141ull) return is_prime((u32)n);
  if (!(n & 1)) return false;
  Montgomery64 r2 = _r2_64(n), inv = _inv_64(n);
  u64 s = CTZ(n - 1);
  u64 d = (n - 1) >> s;
  u64 as[] = { 2, 325, 9375, 28178, 450775, 9780504, 1795265022 };
  Montgomery64 e = _one_64(n), rev = _to_montgomery_64(n - 1, r2, inv, n);
  for (FastInt i = 0; i < 7; i++) {
    Montgomery A = _to_montgomery_64(as[i], r2, inv, n);
    u64 t = d;
    Montgomery64 y = pow_MR_64(A, t, inv, n);
    while (t != n - 1 && y != e && y != rev) {
      y = mul_MR_64(y, y, inv, n);
      t <<= 1;
    }
    if (y != rev && !(t & 1)) return false;
  }
  return true;
}

void Main(void) {
  FastInt Q = read_int();
  while (Q--) {
    u64 x = inu();
    outu(x); SP(); outu(is_prime_64(x));
    NL();
  }
}

int main(void) {
  Main();
  return 0;
}

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結果

テストケース

コンパイルメッセージ

ソースコード