#783738 (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	2022-08-02 03:05:06
言語	C (gcc 12.3.0)
結果	AC
実行時間	30 ms / 9,973 ms
コード長	12,456 bytes
コンパイル時間	603 ms
コンパイル使用メモリ	45,092 KB
実行使用メモリ	5,376 KB
最終ジャッジ日時	2024-04-28 09:52:13
合計ジャッジ時間	1,194 ms
ジャッジサーバーID （参考情報）	judge3 / judge4
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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 5,376 KB
testcase_02	AC	1 ms 5,376 KB
testcase_03	AC	1 ms 5,376 KB
testcase_04	AC	18 ms 5,376 KB
testcase_05	AC	21 ms 5,376 KB
testcase_06	AC	15 ms 5,376 KB
testcase_07	AC	13 ms 5,376 KB
testcase_08	AC	14 ms 5,376 KB
testcase_09	AC	30 ms 5,376 KB
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ソースコード

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

#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>

typedef   int8_t      i8;
typedef   int16_t     i16;
typedef   int32_t     i32;
typedef   int64_t     i64;
typedef __int128_t    i128;
typedef   uint8_t     u8;
typedef   uint16_t    u16;
typedef   uint32_t    u32;
typedef   uint64_t    u64;
typedef __uint128_t   u128;
typedef   float       f32;
typedef   double      f64;
typedef   long double f80;

#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)))

static inline u64 get_bit_floor(u64 n) { if (n) return 1ull << (63 - __builtin_clzll(n)); return 0; }
static inline u64 get_bit_ceil(u64 n) { assert(n > 0); --n; n |= n >> 1; n |= n >> 2; n |= n >> 4; n |= n >> 8; n |= n >> 16; n |= n >> 32; ++n; return n; }
static inline u32 get_log2(u64 n) { assert(HAS_SINGLE_BIT64(n)); const u32 deBruijn[64] = {0,1,2,53,3,7,54,27,4,38,41,8,34,55,48,28,62,5,39,46,44,42,22,9,24,35,59,56,49,18,29,11,63,52,6,26,37,40,33,47,61,45,43,21,23,58,17,10,51,25,36,32,60,20,57,16,50,31,19,15,30,14,13,12}; return deBruijn[n * 0x022fdd63cc95386dull >> 58]; }
static inline u32 rotr32(u32 x, i64 r) { if (r < 0) { u64 l = ((u64)(-r)) % 32; return x << l | x >> (-l & 31); } r %= 32; return x >> r | x << (-r & 31); }
static inline u64 rotr64(u64 x, i64 r) { if (r < 0) { u64 l = ((u64)(-r)) % 64; return x << l | x >> (-l & 63); } r %= 64; return x >> r | x << (-r & 63); }
static inline u32 rotl32(u32 x, i64 r) { return rotr32(x, -r); }
static inline u64 rotl64(u64 x, i64 r) { return rotr64(x, -r); }
static inline int deBruijn_log2(u64 n) { static const u64 deBruijn = 0x022fdd63cc95386d; static const int convert[64] = {0, 1, 2, 53, 3, 7, 54, 27, 4, 38, 41, 8, 34, 55, 48, 28, 62, 5, 39, 46, 44, 42, 22, 9, 24, 35, 59, 56, 49, 18, 29, 11, 63, 52, 6, 26, 37, 40, 33, 47, 61, 45, 43, 21, 23, 58, 17, 10, 51, 25, 36, 32, 60, 20, 57, 16, 50, 31, 19, 15, 30, 14, 13, 12}; return convert[n * deBruijn >> 58]; }
static inline int bsf(u64 n) { return deBruijn_log2(n & ~(n - 1)); }

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; }
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); }
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 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); }
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; }
void out_u32(u32 x) { if (x >= 10) out_u32(x / 10); putchar_unlocked(x - x / 10 * 10 + 48); }
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; }
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 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 dump_int_array_range(int *a, int a_len, int l, int r) { if (a_len <= r) { r = a_len - 1; } if (l > r) { return; } for (int i = l; i <= r; i++) { if (i == r) { 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_range(i64 *a, int a_len, int l, int r) { if (a_len <= r) { r = a_len - 1; } if (l > r) { return; } for (int i = l; i <= r; i++) { if (i == r) { 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_range(u32 *a, int a_len, int l, int r) { if (a_len <= r) { r = a_len - 1; } if (l > r) { return; } for (int i = l; i <= r; i++) { if (i == r) { 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_range(u64 *a, int a_len, int l, int r) { if (a_len <= r) { r = a_len - 1; } if (l > r) { return; } for (int i = l; i <= r; i++) { if (i == r) { fprintf(stderr, "\033[1;36m%lu\033[0m\n", a[i]); } else { fprintf(stderr, "\033[1;36m%lu\033[0m ", a[i]); } } }
void printb_32bit(u32 v) { u32 mask = (u32)1 << (sizeof(v) * CHAR_BIT - 1); do { putchar_unlocked(mask & v ? '1' : '0'); } while (mask >>= 1); }
void printb_64bit(u64 v) { u64 mask = (u64)1 << (sizeof(v) * CHAR_BIT - 1); do { putchar_unlocked(mask & v ? '1' : '0'); } while (mask >>= 1); }
#pragma endregion template


///////////////////////////////////////////////////////////////////////////////
/// jacobi_symbol.c                                                         ///
///////////////////////////////////////////////////////////////////////////////
int jacobi_symbol(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 ((u64)(a) > n / 2) a -= n;
    }
    return n == 1 ? j : 0;
}


///////////////////////////////////////////////////////////////////////////////
/// m64.c                                                                   ///
///////////////////////////////////////////////////////////////////////////////
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 N_m64(u64 mod) { m64 N = mod; for (int i = 0; i < 5; i++) { N *= 2 - N * mod; } return N; }
m64 reduce_m64(u128 a, m64 N, u64 mod) { u64 y = (u64)(a >> 64) - (u64)(((u128)((u64)a * N) * mod) >> 64); return (i64)y < 0 ? y + mod : y; }
m64 to_m64(u64 a, m64 r2, m64 N, u64 mod) { return reduce_m64((u128)a * r2, N, mod); }
u64 from_m64(m64 A, m64 N, u64 mod) { return reduce_m64((u128)A, N, mod); }
m64 add_m64(m64 A, m64 B, u64 mod) { return (A + B >= mod) ? (A + B) % mod : A + B; }
m64 sub_m64(m64 A, m64 B, u64 mod) { return (A >= B) ? (A - B) % mod : (mod + A - B) % mod; }
m64 min_m64(m64 A, u64 mod) { return sub_m64(0ull, A, mod); }
m64 mul_m64(m64 A, m64 B, m64 N, u64 mod) { return reduce_m64((u128)A * B, N, mod); }
m64 pow_m64(m64 A, i64 n, m64 one, m64 N, u64 mod) { m64 ret = one; while (n > 0) { if (n & 1) ret = mul_m64(ret, A, N, mod); A = mul_m64(A, A, N, mod); n >>= 1; } return ret; }
m64 inv_m64(m64 A, m64 one, m64 N, u64 mod) { return pow_m64(A, (i64)mod - 2, one, N, mod); }
m64 div_m64(m64 A, m64 B, m64 one, m64 N, u64 mod) { /* assert(is_prime(mod)); */ return mul_m64(A, inv_m64(B, one, N, mod), N, mod); }
bool eq_m64(m64 A, m64 B, m64 N, u64 mod) { return from_m64(A, N, mod) == from_m64(B, N, mod); }
bool neq_m64(m64 A, m64 B, m64 N, u64 mod) { return from_m64(A, N, mod) != from_m64(B, N, mod); }
m64 in_m64(m64 r2, m64 N, u64 mod) { u64 c = 0; u64 a = 0; while (c = getchar(), c < 48 || c > 57); while (47 < c && c < 58) { a = a * 10 + c - 48; c = getchar(); } return to_m64(a, r2, N, mod); }
void out_m64(m64 A, m64 N, u64 mod) { u64 a = from_m64(A, N, mod); out_u64(a); }



///////////////////////////////////////////////////////////////////////////////
/// Baillie-PSW.c                                                           ///
///////////////////////////////////////////////////////////////////////////////
bool baillie_psw(u64 n) {
    {
        if (n <= 1) return false;
        if (n <= 3) return true;
        if (!(n & 1)) return false;
    }
    const u64 mod = n;
    const m64 one = one_m64(n);
    const m64 r2 = r2_m64(n);
    const m64 N = N_m64(n);
    {
        u64 d = (mod - 1) << __builtin_clzll(mod - 1);
        m64 t = one << 1;
        if (t >= mod) t -= mod;
        for (d <<= 1; d; d <<= 1) {
            t = mul_m64(t, t, N, mod);
            if (d >> 63) {
                t <<= 1;
                if (t >= mod) t -= mod;
            }
        }
        if (t != one) {
            u64 x = (n - 1) & -(n - 1);
            m64 rev = mod - one;
            for (x >>= 1; t != rev; x >>= 1) {
                if (x == 0) return false;
                t = mul_m64(t, t, N, mod);
            }
        }
    }
    {
        i64 D = 5;
        for (int i = 0; jacobi_symbol(D, n) != -1 && i < 64; ++i) {
            if (i == 32) {
                u32 k = round(sqrtl(n));
                if (k * k == n) return false;
            }
            if (i & 1) D -= 2;
            else       D += 2;
            D = -D;
        }
        m64 Q = to_m64(D < 0 ? (1 - D) / 4 % mod : mod - (D - 1) / 4 % mod, r2, N, mod);
        m64 u = one, v = one, Qn = Q;
        u64 k = (n + 1) << __builtin_clzll(n + 1);
        D %= (i64)mod;
        D = to_m64(D < 0 ? mod + D : D, r2, N, mod);
        for (k <<= 1; k; k <<= 1) {
            u = mul_m64(u, v, N, mod);
            v = sub_m64(mul_m64(v, v, N, mod), add_m64(Qn, Qn, mod), mod);
            Qn = mul_m64(Qn, Qn, N, mod);
            if (k >> 63) {
                u64 uu = add_m64(u, v, mod);
                if (uu & 1) uu += mod;
                uu >>= 1;
                v = add_m64(mul_m64(D, u, N, mod), v, mod);
                if (v & 1) v += mod;
                v >>= 1;
                u = uu;
                Qn = mul_m64(Qn, Q, N, mod);
            }
        }
        if (u == 0 || v == 0) return true;
        u64 x = (n + 1) & ~n;
        for (x >>= 1; x; x >>= 1) {
            u = mul_m64(u, v, N, mod);
            v = sub_m64(mul_m64(v, v, N, mod), add_m64(Qn, Qn, mod), mod);
            if (v == 0) return true;
            Qn = mul_m64(Qn, Qn, N, mod);
        }
    }
    return false;
}


int main(void) {
    u64 Q = in_u64();
    while (Q--) {
        u64 x = in_u64();
        out_u64(x);
        SP();
        out_u32(baillie_psw(x) ? 1u : 0u);
        NL();
    }
    return 0;
}
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結果

テストケース

ソースコード
