1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
|
namespace nim {
using u64 = uint64_t;
template <int k, typename Out> struct Reducer {
static_assert(k <= 6, "");
u64 multiply(u64 a, u64 b) const {
static const u64 P = 1ULL << (1 << k - 1);
u64 a1 = a / P, a0 = a % P, b1 = b / P, b0 = b % P,
c = out.multiply(a0, b0);
return out.multiply(out.multiply(a1, b1), P / 2) ^
(out.multiply(a0 ^ a1, b0 ^ b1) ^ c) * P ^ c;
}
private:
Out out;
};
template <int k> struct QuadraticMemorizedNim {
static_assert(k <= 3, "");
static const int N = 1 << (1 << k);
QuadraticMemorizedNim() : table() {
static Reducer<k, QuadraticMemorizedNim<k - 1>> out;
for (int i = 0; i < N; ++i) {
for (int j = 0; j < N; ++j) {
table[i][j] = out.multiply(i, j);
}
}
}
u64 multiply(u64 a, u64 b) const { return table[a][b]; }
u64 table[N][N];
};
template <> struct QuadraticMemorizedNim<0> {
static const int N = 2;
QuadraticMemorizedNim() {}
u64 multiply(u64 a, u64 b) const { return a && b; }
};
// k == 4
template <u64 G> struct LinearMemorizedNim {
static const int N = 1 << 16;
LinearMemorizedNim() : exp(), log() {
static Reducer<4, Reducer<3, QuadraticMemorizedNim<3>>> reduced;
log[exp[0] = 1] = 0;
for (int i = 1; i < N - 1; ++i) {
log[exp[i] = reduced.multiply(exp[i - 1], G)] = i;
}
}
u64 multiply(u64 a, u64 b) const {
return a == 0 || b == 0 ? 0 : exp[(log[a] + log[b]) % (N - 1)];
}
private:
int exp[N], log[N];
};
u64 multiply(u64 a, u64 b) {
static Reducer<6, Reducer<5, Reducer<4, LinearMemorizedNim<258>>>> reduced;
return reduced.multiply(a, b);
}
} // namespace nim
|
