#708064 (C) No.8030 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.8030 ミラー・ラビン素数判定法のテスト
ユーザー	nonamae
提出日時	2021-10-18 10:13:34
言語	C (gcc 13.3.0)
結果	AC
実行時間	41 ms / 9,973 ms
コード長	12,877 bytes
コンパイル時間	659 ms
コンパイル使用メモリ	38,016 KB
実行使用メモリ	5,248 KB
最終ジャッジ日時	2024-11-16 23:40:51
合計ジャッジ時間	1,238 ms
ジャッジサーバーID （参考情報）	judge2 / judge3

このコードへのチャレンジ
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ファイルパターン	結果
other	AC * 10

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:44:16: warning: implicit declaration of function 'getchar_unlocked' [-Wimplicit-function-declaration]
   44 |     while (c = getchar_unlocked(), c < 48 || c > 57)
      |                ^~~~~~~~~~~~~~~~
main.c: In function '_write_int':
main.c:98:5: warning: implicit declaration of function 'putchar_unlocked' [-Wimplicit-function-declaration]
   98 |     putchar_unlocked(x - x / 10 * 10 + 48);
      |     ^~~~~~~~~~~~~~~~

ソースコード

raw source code

#define LOCAL

#ifndef LOCAL
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC optimize("fast-math")
#endif

#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>

/* 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;

/* io */
static inline 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;
}
static inline u32 in_u32(void)
{
    // 0 ～ 4294967295 (> 10 ^ 9)
    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 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;
}
static inline 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(int x)
{
    if (x >= 10)
        _write_int(x / 10);
    putchar_unlocked(x - x / 10 * 10 + 48);
}
static inline void write_int(int x)
{
    if (x < 0)
    {
        putchar_unlocked('-');
        x = -x;
    }
    _write_int(x);
}
static inline void out_u32(u32 x)
{
    if (x >= 10)
        out_u32(x / 10);
    putchar_unlocked(x - x / 10 * 10 + 48);
}
static inline void _out_i64(i64 x)
{
    if (x >= 10)
        _out_i64(x / 10);
    putchar_unlocked(x - x / 10 * 10 + 48);
}
static inline void out_i64(i64 x)
{
    if (x < 0)
    {
        putchar_unlocked('-');
        x = -x;
    }
    _out_i64(x);
}
static inline void out_u64(u64 x)
{
    if (x >= 10)
        out_u64(x / 10);
    putchar_unlocked(x - x / 10 * 10 + 48);
}
static inline void NL(void) { putchar_unlocked('\n'); }
static inline void SP(void) { putchar_unlocked(' '); }

/* macro */
#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))

/* bit macro */
#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 MSB32(a) ((31) - __builtin_clz((a)))
#define MSB64(a) ((63) - __builtin_clzll((a)))
#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) : ((((i128)(s)) < (0)) ? (_ROTR((x), -(s))) : (_ROTL((x), (s)))))
#define ROTR(x, s) (((s) == (0)) ? (0) : ((((i128)(s)) < (0)) ? (_ROTL((x), -(s))) : (_ROTR((x), (s)))))

/* debug */
#ifdef LOCAL
void dump_int(int x)
{
    fprintf(stderr, "\033[1;36m%d\033[0m\n", x);
}
void dump_i64(i64 x)
{
    fprintf(stderr, "\033[1;36m%ld\033[0m\n", x);
}
void dump_u32(u32 x)
{
    fprintf(stderr, "\033[1;36m%u\033[0m\n", x);
}
void dump_u64(u64 x)
{
    fprintf(stderr, "\033[1;36m%lu\033[0m\n", x);
}
void dump_int_array(int *a, int a_len)
{
    for (int i = 0; i < a_len; i++)
    {
        if (i == a_len - 1)
            fprintf(stderr, "\033[1;36m%d\033[0m\n", a[i]);
        else
            fprintf(stderr, "\033[1;36m%d\033[0m ", a[i]);
    }
}
void dump_i64_array(i64 *a, int a_len)
{
    for (int i = 0; i < a_len; i++)
    {
        if (i == a_len - 1)
            fprintf(stderr, "\033[1;36m%ld\033[0m\n", a[i]);
        else
            fprintf(stderr, "\033[1;36m%ld\033[0m ", a[i]);
    }
}
void dump_u32_array(u32 *a, int a_len)
{
    for (int i = 0; i < a_len; i++)
    {
        if (i == a_len - 1)
            fprintf(stderr, "\033[1;36m%u\033[0m\n", a[i]);
        else
            fprintf(stderr, "\033[1;36m%u\033[0m ", a[i]);
    }
}
void dump_u64_array(u64 *a, int a_len)
{
    for (int i = 0; i < a_len; i++)
    {
        if (i == a_len - 1)
            fprintf(stderr, "\033[1;36m%lu\033[0m\n", a[i]);
        else
            fprintf(stderr, "\033[1;36m%lu\033[0m ", a[i]);
    }
}
void printb(u32 v)
{
    u32 mask = (int)1 << (sizeof(v) * CHAR_BIT - 1);
    do
        putchar(mask & v ? '1' : '0');
    while (mask >>= 1);
}
void putb(u32 v)
{
    putchar('0'), putchar('b'), printb(v), putchar('\n');
}
#endif

/* montgomery modular multiplication 32bit */
typedef uint32_t m32;

m32 _one_m32(u32 mod)
{
    return -1u % mod + 1;
}
m32 _r2_m32(u32 mod)
{
    return (u64)(i64)-1 % mod + 1;
}
m32 _inv_m32(u32 mod)
{
    u32 inv = mod;
    for (int ixjw82jwm = 0; ixjw82jwm < __builtin_ctz(sizeof(u32) * 8) - 1; ++ixjw82jwm)
        inv *= 2 - mod * inv;
    return inv;
}
m32 _reduce_m32(u64 a, m32 inv, u32 mod)
{
    i64 z = (a >> 32) - ((((u32)a * inv) * (u64)mod) >> 32);
    return z < 0 ? z + mod : (u32)z;
}
m32 to_m32(u32 a, m32 r2, m32 inv, u32 mod)
{
    return _reduce_m32((u64)a * r2, inv, mod);
}
m32 from_m32(m32 A, m32 inv, u32 mod)
{
    m32 t = _reduce_m32((u64)A, inv, mod) - mod;
    return t + (mod & -(t >> 31u));
}
m32 add_m32(m32 A, m32 B, u32 mod)
{
    A += B - (mod << 1u);
    A += (mod << 1u) & -(A >> 31u);
    return A;
}
m32 sub_m32(m32 A, m32 B, u32 mod)
{
    A -= B;
    A += (mod << 1u) & -(A >> 31u);
    return A;
}
m32 min_m32(m32 A, u32 mod)
{
    return sub_m32(0, A, mod);
}
m32 mul_m32(m32 A, m32 B, m32 inv, u32 mod)
{
    return _reduce_m32((u64)A * B, inv, mod);
}
m32 pow_m32(m32 A, i64 n, m32 inv, u32 mod)
{
    m32 ret = _one_m32(mod);
    while (n > 0)
    {
        if (n & 1)
            ret = mul_m32(ret, A, inv, mod);
        A = mul_m32(A, A, inv, mod);
        n >>= 1;
    }
    return ret;
}
m32 inv_m32(m32 A, m32 inv, u32 mod)
{
    return pow_m32(A, (i64)mod - 2, inv, mod);
}
m32 div_m32(m32 A, m32 B, m32 inv, u32 mod)
{
    /* assert(is_prime(mod)); */
    return mul_m32(A, inv_m32(B, inv, mod), inv, mod);
}
m32 in_m32(m32 r2, m32 inv, u32 mod)
{
    u32 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_m32(a, r2, inv, mod);
}
void out_m32(m32 A, m32 inv, u32 mod)
{
    u32 a = from_m32(A, inv, mod);
    out_u32(a);
}
#ifdef LOCAL
void dump_m32(m32 x, m32 inv, u32 mod)
{
    fprintf(stderr, "\033[1;36m(m32 = %u, u32 = %u)\033[0m\n", x, from_m32(x, inv, mod));
}
void dump_m32_array(m32 *x, int x_len, m32 inv, u32 mod)
{
    fprintf(stderr, "m32 * => ");
    for (int i = 0; i < x_len; i++)
    {
        if (i == x_len - 1)
            fprintf(stderr, "%u\n", x[i]);
        else
            fprintf(stderr, "%u ", x[i]);
    }
    fprintf(stderr, "u32 * => ");
    for (int i = 0; i < x_len; i++)
    {
        if (i == x_len - 1)
            fprintf(stderr, "%u\n", from_m32(x[i], inv, mod));
        else
            fprintf(stderr, "%u ", from_m32(x[i], inv, mod));
    }
}
#endif

/* montgomery modular multiplication 64bit */
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)
{
    u64 inv = mod;
    for (int h2zq6gm5d = 0; h2zq6gm5d < __builtin_ctz(sizeof(u64) * 8) - 1; ++h2zq6gm5d)
        inv *= 2 - mod * inv;
    return inv;
}
m64 _reduce_m64(u128 a, m64 inv, u64 mod)
{
    i128 A = (a >> 64) - ((((u64)a * inv) * (u128)mod) >> 64);
    return A < 0 ? (u64)(A + mod) : (u64)A;
}
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)
{
    m64 t = _reduce_m64((u128)A, inv, mod) - mod;
    return t + (mod & -(t >> 63u));
}
m64 add_m64(m64 A, m64 B, u64 mod)
{
    A += B - (mod << 1u);
    A += (mod << 1u) & -(A >> 63u);
    return A;
}
m64 sub_m64(m64 A, m64 B, u64 mod)
{
    A -= B;
    A += (mod << 1u) & -(A >> 63u);
    return A;
}
m64 min_m64(m64 A, u64 mod)
{
    return sub_m64(0, 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 recip_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)
{
    return mul_m64(A, recip_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);
}
#ifdef LOCAL
void dump_m64(m64 x, m64 inv, u64 mod)
{
    fprintf(stderr, "\033[1;36m(m64 = %lu, u64 = %lu)\033[0m\n", x, from_m64(x, inv, mod));
}
void dump_m64_array(m64 *x, int x_len, m64 inv, u64 mod)
{
    fprintf(stderr, "m64 * => ");
    for (int i = 0; i < x_len; i++)
    {
        if (i == x_len - 1)
            fprintf(stderr, "%lu\n", x[i]);
        else
            fprintf(stderr, "%lu ", x[i]);
    }
    fprintf(stderr, "u64 * => ");
    for (int i = 0; i < x_len; i++)
    {
        if (i == x_len - 1)
            fprintf(stderr, "%lu\n", from_m64(x[i], inv, mod));
        else
            fprintf(stderr, "%lu ", from_m64(x[i], inv, mod));
    }
}
#endif

/* miller-rabin primary test */
bool miller_rabin32(u32 n, u32 d, const u32 *bases, int bases_len, m32 r2, m32 inv, m32 one, m32 rev)
{
    for (int i = 0; i < bases_len; i++)
    {
        if (n <= bases[i])
            break;
        
        m32 a = to_m32(bases[i], r2, inv, n);
        u32 t = d;
        m32 y = pow_m32(a, t, inv, n);
        
        while (t != n - 1 && y != one && y != rev)
        {
            y = mul_m32(y, y, inv, n);
            t <<= 1;
        }
        if (y != rev && (!(t & 1)))
            return false;
    }
    return true;
}
bool is_prime32(u32 n)
{
    u32 m = n - 1;
    m32 r2 = _r2_m32(n);
    m32 inv = _inv_m32(n);
    m32 one = _one_m32(n);
    m32 rev = to_m32(m, r2, inv, n);
    u32 d = m >> CTZ(m);
    const u32 bases[] = { 2u, 7u, 61u };
    
    return miller_rabin32(n, d, bases, 3, r2, inv, one, rev);
}
bool miller_rabin64(u64 n, u64 d, const u64 *bases, int bases_len, m64 r2, m64 inv, m64 one, m64 rev)
{
    for (int i = 0; i < bases_len; i++)
    {
        if (n <= bases[i])
            break;
        
        m64 a = to_m64(bases[i], r2, inv, n);
        u64 t = d;
        m64 y = pow_m64(a, t, inv, n);
        
        while (t != n - 1 && y != one && y != rev)
        {
            y = mul_m64(y, y, inv, n);
            t <<= 1;
        }
        if (y != rev && (!(t & 1)))
            return false;
    }
    return true;
}
bool is_prime64(u64 n)
{
    u64 m = n - 1;
    m64 r2 = _r2_m64(n);
    m64 inv = _inv_m64(n);
    m64 one = _one_m64(n);
    m64 rev = to_m64(m, r2, inv, n);
    u64 d = m >> CTZ(m);
    const u64 bases[] = { 2ull, 325ull, 9375ull, 28178ull, 450775ull, 9780504ull, 1795265022ull };
    
    return miller_rabin64(n, d, bases, 7, r2, inv, one, rev);
}
bool is_prime(u64 n)
{
    if (n <= 3u)
        return n == 2u || n == 3u;

    if (!(n & 1))
        return false;

    if (n < ((u32)1u << 31))
        return is_prime32((u32)n);
    
    return is_prime64(n);
}

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

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

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