#713793 (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	2021-11-06 15:26:27
言語	C (gcc 12.3.0)
結果	WA
実行時間	-
コード長	10,209 bytes
コンパイル時間	1,450 ms
コンパイル使用メモリ	45,160 KB
実行使用メモリ	4,384 KB
最終ジャッジ日時	2023-08-07 08:56:21
合計ジャッジ時間	2,527 ms
ジャッジサーバーID （参考情報）	judge11 / judge12
このコードへのチャレンジ（β）
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 4,380 KB
testcase_01	AC	1 ms 4,376 KB
testcase_02	AC	0 ms 4,376 KB
testcase_03	AC	1 ms 4,380 KB
testcase_04	WA	-
testcase_05	WA	-
testcase_06	WA	-
testcase_07	WA	-
testcase_08	WA	-
testcase_09	WA	-
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ソースコード

raw source code
#pragma region opt
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma endregion opt

#pragma region header
#define _GNU_SOURCE
#include <stdbool.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <assert.h>
#include <limits.h>
#include <math.h>
#include <string.h>
#include <time.h>
#pragma endregion header

#pragma region type
/* 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;
#pragma endregion type

#pragma region macro
#define MIN(a, b) (((a) < (b)) ? (a) : (b))
#define MAX(a, b) (((a) > (b)) ? (a) : (b))
#define SWAP(a, b) (((a) ^= (b)), ((b) ^= (a)), ((a) ^= (b)))
#define POPCNT32(a) __builtin_popcount((a))
#define POPCNT64(a) __builtin_popcountll((a))
#define CTZ32(a) __builtin_ctz((a))
#define CLZ32(a) __builtin_clz((a))
#define CTZ64(a) __builtin_ctzll((a))
#define CLZ64(a) __builtin_clzll((a))
#define HAS_SINGLE_BIT32(a) (__builtin_popcount((a)) == (1))
#define HAS_SINGLE_BIT64(a) (__builtin_popcountll((a)) == (1))
#define MSB32(a) ((31) - __builtin_clz((a)))
#define MSB64(a) ((63) - __builtin_clzll((a)))
#define BIT_WIDTH32(a) ((a) ? ((32) - __builtin_clz((a))) : (0))
#define BIT_WIDTH64(a) ((a) ? ((64) - __builtin_clzll((a))) : (0))
#define LSBit(a) ((a) & (-(a)))
#define CLSBit(a) ((a) & ((a) - (1)))
#define BIT_CEIL32(a) ((!(a)) ? (1) : ((POPCNT32(a)) == (1) ? ((1u) << ((31) - CLZ32((a)))) : ((1u) << ((32) - CLZ32(a)))))
#define BIT_CEIL64(a) ((!(a)) ? (1) : ((POPCNT64(a)) == (1) ? ((1ull) << ((63) - CLZ64((a)))) : ((1ull) << ((64) - CLZ64(a)))))
#define BIT_FLOOR32(a) ((!(a)) ? (0) : ((1u) << ((31) - CLZ32((a)))))
#define BIT_FLOOR64(a) ((!(a)) ? (0) : ((1ull) << ((63) - CLZ64((a)))))
#define _ROTL32(x, s) (((x) << ((s) % (32))) | (((x) >> ((32) - ((s) % (32))))))
#define _ROTR32(x, s) (((x) >> ((s) % (32))) | (((x) << ((32) - ((s) % (32))))))
#define ROTL32(x, s) (((s) == (0)) ? (x) : ((((i64)(s)) < (0)) ? (_ROTR32((x), -(s))) : (_ROTL32((x), (s)))))
#define ROTR32(x, s) (((s) == (0)) ? (x) : ((((i64)(s)) < (0)) ? (_ROTL32((x), -(s))) : (_ROTR32((x), (s)))))
#define _ROTL64(x, s) (((x) << ((s) % (64))) | (((x) >> ((64) - ((s) % (64))))))
#define _ROTR64(x, s) (((x) >> ((s) % (64))) | (((x) << ((64) - ((s) % (64))))))
#define ROTL64(x, s) (((s) == (0)) ? (x) : ((((i128)(s)) < (0)) ? (_ROTR64((x), -(s))) : (_ROTL64((x), (s)))))
#define ROTR64(x, s) (((s) == (0)) ? (x) : ((((i128)(s)) < (0)) ? (_ROTL64((x), -(s))) : (_ROTR64((x), (s)))))
#pragma endregion macro

#pragma region io
int read_int(void) {
  // -2147483648 ～ 2147483647 (> 10 ^ 9)
  int 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;
}
i32 in_i32(void) {
  // -2147483648 ～ 2147483647 (> 10 ^ 9)
  i32 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;
}
u32 in_u32(void) {
  // 0 ～ 4294967295 (> 10 ^ 9)
  u32 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;
}
i64 in_i64(void) {
  // -9223372036854775808 ～ 9223372036854775807 (> 10 ^ 18)
  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;
}
u64 in_u64(void) {
  // 0 ～ 18446744073709551615 (> 10 ^ 19)
  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_inner(int x) {
  if (x >= 10) write_int_inner(x / 10);
  putchar_unlocked(x - x / 10 * 10 + 48);
}
void write_int(int x) {
  if (x < 0) {
    putchar_unlocked('-');
    x = -x;
  }
  write_int_inner(x);
}
static inline void out_i32_inner(i32 x) {
  if (x >= 10) out_i32_inner(x / 10);
  putchar_unlocked(x - x / 10 * 10 + 48);
}
void out_i32(i32 x) {
  if (x < 0) {
    putchar_unlocked('-');
    x = -x;
  }
  out_i32_inner(x);
}
void out_u32(u32 x) {
  if (x >= 10) out_u32(x / 10);
  putchar_unlocked(x - x / 10 * 10 + 48);
}
static inline void out_i64_inner(i64 x) {
  if (x >= 10) out_i64_inner(x / 10);
  putchar_unlocked(x - x / 10 * 10 + 48);
}
void out_i64(i64 x) {
  if (x < 0) {
    putchar_unlocked('-');
    x = -x;
  }
  out_i64_inner(x);
}
void out_u64(u64 x) {
  if (x >= 10) out_u64(x / 10);
  putchar_unlocked(x - x / 10 * 10 + 48);
}
void NL(void) { putchar_unlocked('\n'); }
void SP(void) { putchar_unlocked(' '); }
void write_int_array(int *a, int a_len) {
  for (int i = 0; i < a_len; i++) {
    if (i) SP();
    write_int(a[i]);
  }
  NL();
}
void out_i32_array(i32 *a, int a_len) {
  for (int i = 0; i < a_len; i++) {
    if (i) SP();
    out_i32(a[i]);
  }
  NL();
}
void out_u32_array(u32 *a, int a_len) {
  for (int i = 0; i < a_len; i++) {
    if (i) SP();
    out_u32(a[i]);
  }
  NL();
}
void out_i64_array(i64 *a, int a_len) {
  for (int i = 0; i < a_len; i++) {
    if (i) SP();
    out_i64(a[i]);
  }
  NL();
}
void out_u64_array(u64 *a, int a_len) {
  for (int i = 0; i < a_len; i++) {
    if (i) SP();
    out_u64(a[i]);
  }
  NL();
}
#pragma endregion io

#pragma region m64
typedef uint64_t m64;
m64 _one_m64(u64 mod) { return (u64)-1ull % mod + 1; }
m64 _r2_m64(u64 mod) { return (u128)(i128)-1 % mod + 1; }
m64 _inv_m64(u64 mod) {
  m64 inv = mod;
  for (int i = 0; i < 5; i++) inv *= 2 - inv * mod;
  return inv;
}
m64 _reduce_m64(u128 a, m64 inv, u64 mod) {
  u64 y = (u64)(a >> 64) - (u64)(((u128)((u64)a * inv) * mod) >> 64);
  return (i64)y < 0 ? y + mod : y;
}
m64 to_m64(u64 a, m64 r2, m64 inv, u64 mod) { return _reduce_m64((u128)a * r2, inv, mod); }
u64 from_m64(m64 A, m64 inv, u64 mod) { return _reduce_m64(A, inv, mod); }
m64 add_m64(m64 A, m64 B, u64 mod) {
  A += B - mod;
  if ((i64)A < 0) A += mod;
  return A;
}
m64 sub_m64(m64 A, m64 B, u64 mod) {
  if ((i64)(A -= B) < 0) A += 2 * mod;
  return A;
}
m64 min_m64(m64 A, u64 mod) { return sub_m64(0ull, A, mod); }
m64 mul_m64(m64 A, m64 B, m64 inv, u64 mod) { return _reduce_m64((u128)A * B, inv, mod); }
m64 pow_m64(m64 A, i64 n, m64 inv, u64 mod) {
  m64 ret = _one_m64(mod);
  while (n > 0) {
    if (n & 1) ret = mul_m64(ret, A, inv, mod);
    A = mul_m64(A, A, inv, mod);
    n >>= 1;
  }
  return ret;
}
m64 inv_m64(m64 A, m64 inv, u64 mod) { return pow_m64(A, (i64)mod - 2, inv, mod); }
m64 div_m64(m64 A, m64 B, m64 inv, u64 mod) {
  /* assert(is_prime(mod)); */
  return mul_m64(A, inv_m64(B, inv, mod), inv, mod);
}
m64 in_m64(m64 r2, m64 inv, u64 mod) {
  u64 c, a = 0;
  while (c = getchar_unlocked(), c < 48 || c > 57);
  while (47 < c && c < 58) {
    a = a * 10 + c - 48;
    c = getchar_unlocked();
  }
  return to_m64(a, r2, inv, mod);
}
void out_m64(m64 A, m64 inv, u64 mod) {
  u64 a = from_m64(A, inv, mod);
  out_u64(a);
}
#pragma endregion m64

#pragma region Baillie_PSW primality test
int jacobi(i64 a, u64 n) {
  u64 t;
  int j = 1;
  while (a) {
    if (a < 0) {
      a = -a;
      if ((n & 3) == 3) j = -j;
    }
    int s = __builtin_ctzll(a);
    a >>= s;
    if (((n & 7) == 3 || (n & 7) == 5) && (s & 1)) j = -j;
    if ((a & n & 3) == 3) j = -j;
    t = a, a = n, n = t;
    a %= n;
    if (a > n / 2) a -= n;
  }
  return n == 1 ? j : 0;
}
bool is_prime(const u64 n) {
  // https://en.wikipedia.org/wiki/Baillie%E2%80%93PSW_primality_test
  // step 1.
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (!(n & 1)) return false;
  
  // step 2.
  const m64 one = _one_m64(n);
  const m64 r2 = _r2_m64(n);
  const m64 inv = _inv_m64(n);
  {
    // https://en.wikipedia.org/wiki/Strong_pseudoprime#Formal_definition
    // n = d * (2 ^ s) + 1
    u64 d = (n - 1) << __builtin_clzll(n - 1);
    m64 t = one << 1;
    if (t >= n) t -= n;
    for (d <<= 1; d; d <<= 1) {
      t = mul_m64(t, t, inv, n);
      if (d >> 63) {
        t <<= 1;
        if (t >= n) t -= n;
      }
    }
    if (t != one) {
      u64 x = (n - 1) & -(n - 1);
      m64 rev = n - one;
      for (x >>= 1; t != rev; x >>= 1) {
        if (x == 0) return false;
        t = mul_m64(t, t, inv, n);
      }
    }
  }

  // step 3.
  {
    i64 D = 5;
    for (int i = 0; jacobi(D, n) != -1 && i < 64; i++) {
      if (i == 32) {
        u32 k = round(sqrtl(n));
        if (k * k == n) return 0;
      }
      if (i & 1) D -= 2;
      else D += 2;
      D = -D;
    }
    m64 Q = to_m64(D < 0 ? (1 - D) / 4 % n : n - (D - 1) / 4 % n, r2, inv, n);
    m64 u, v, Qn;
    u64 k = (n + 1) << __builtin_clzll(n + 1);
    u = one;
    v = one;
    Qn = Q;
    D %= (i64)n;
    D = to_m64(D < 0 ? n + D : D, r2, inv, n);
    
    // step 4.
    // https://en.wikipedia.org/wiki/Lucas_pseudoprime#Strong_Lucas_pseudoprimes
    for (k <<= 1; k; k <<= 1) {
      u = mul_m64(u, v, inv, n);
      v = sub_m64(mul_m64(v, v, inv, n), add_m64(Qn, Qn, n), n);
      Qn = mul_m64(Qn, Qn, inv, n);
      if (k >> 63) {
        u64 uu = add_m64(u, v, n);
        if (uu & 1) uu += n;
        uu >>= 1;
        v = add_m64(mul_m64(D, u, inv, n), v, n);
        if (v & 1) v += n;
        v >>= 1;
        u = uu;
        Qn = mul_m64(Qn, Q, inv, n);
      }
    }
    if (u == 0 || v == 0) return true;
    u64 x = (n + 1) & ~n;
    for (x >>= 1; x; x >>= 1) {
      u = mul_m64(u, v, inv, n);
      v = sub_m64(mul_m64(v, v, inv, n), add_m64(Qn, Qn, n), n);
      if (v == 0) return true;
      Qn = mul_m64(Qn, Qn, inv, n);
    }
  }
  return false;
}
#pragma endregion Baillie_PSW primality test

void Main(void) {
  int T = read_int();
  while (T--) {
    u64 x = in_u64();
    out_u64(x);
    SP();
    write_int(is_prime(x));
    NL();
  }  
}

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

テストケース

ソースコード
