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Switch to log2 with table lookup and interpolation #31

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83 changes: 59 additions & 24 deletions src/mcts.c
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Original file line number Diff line number Diff line change
Expand Up @@ -50,46 +50,80 @@ static fixed_point_t fixed_sqrt(fixed_point_t x)
return s;
}

static fixed_point_t fixed_log(fixed_point_t v)
#define LOG2_TABLE_SIZE 10
static unsigned log2_table[1U << LOG2_TABLE_SIZE];
static void log2_table_init(void)
{
/*
* Q0.32 fixed-point representation of
* 2^{1/2}-1, 2^{1/4}-1, ..., 2^{2^{-32}}-1
*/
const unsigned jump[32] = {
1779033704, 812638371, 388727752, 190154448, 94047537, 46769127,
23321248, 11644838, 5818478, 2908254, 1453881, 726879,
363424, 181708, 90853, 45426, 22713, 11357,
5678, 2839, 1420, 710, 355, 177,
89, 44, 22, 11, 6, 3,
1, 1};

for (unsigned i = 0; i < (1U << LOG2_TABLE_SIZE); ++i) {
/*
* Use binary search to find the largest log2(1+x) <= log2(1+i/1024)
*/
u64 target = (u64) i << (64 - LOG2_TABLE_SIZE), now = 0;
unsigned log = 0;
for (unsigned j = 0; j < 32; ++j) {
/* (1+now) * (1+jump) = 1 + now + jump + now*jump */
u64 t = ((now + (1U << 31)) >> 32) * jump[j];
if (now + ((u64) jump[j] << 32) + t <= target) {
now += ((u64) jump[j] << 32) + t;
log |= 1U << (31 - j);
}
}
log2_table[i] = log;
}
}

static fixed_point_t fixed_log2(fixed_point_t v)
{
if (!v || v == (1U << FIXED_SCALE_BITS))
return 0;

fixed_point_t numerator = (v - (1U << FIXED_SCALE_BITS));
int neg = 0;
if (GET_SIGN(numerator)) {
neg = 1;
numerator = CLR_SIGN(numerator);
numerator = (1U << 31) - numerator;
}
int log2_v = 15 - __builtin_clz(v);
v <<= (15 - log2_v);
fixed_point_t int_part = (unsigned) log2_v << FIXED_SCALE_BITS;

fixed_point_t y = ((u64) numerator << FIXED_SCALE_BITS) /
((u64) v + (1U << FIXED_SCALE_BITS));
unsigned index = (v ^ (1U << 31)) >> (31 - LOG2_TABLE_SIZE);
unsigned lower = log2_table[index];
unsigned upper =
index == (1 << LOG2_TABLE_SIZE) - 1 ? 0 : log2_table[index + 1];

fixed_point_t ans = 0U;
for (unsigned i = 1; i < 20; i += 2) {
fixed_point_t z = (1U << FIXED_SCALE_BITS);
for (int j = 0; j < i; j++) {
z = ((u64) z * y) >> FIXED_SCALE_BITS;
}
z = ((u64) z << FIXED_SCALE_BITS) / (i << FIXED_SCALE_BITS);
unsigned offset = v & ((1U << (31 - LOG2_TABLE_SIZE)) - 1);
u64 frac_part =
lower +
(((u64) (upper - lower) * offset + (1U << (30 - LOG2_TABLE_SIZE))) >>
(31 - LOG2_TABLE_SIZE));

ans += z;
}
ans <<= 1;
ans = neg ? SET_SIGN(ans) : ans;
return ans;
unsigned result = int_part + ((frac_part + (1U << 15)) >> 16);

/* Convert from 2's complement to signed representation */
if (GET_SIGN(result))
result = SET_SIGN(-result);

return result;
}

#define EXPLORATION_FACTOR fixed_sqrt(1U << (FIXED_SCALE_BITS + 1))
#define SQRT_LOG_2 54562
#define EXPLORATION_FACTOR \
(fixed_sqrt(1U << (FIXED_SCALE_BITS + 1)) * SQRT_LOG_2 >> FIXED_SCALE_BITS)

static inline fixed_point_t uct_score(int n_total, int n_visits, u64 score)
{
if (n_visits == 0)
return FIXED_MAX;

fixed_point_t result = (fixed_point_t) (score / n_visits);
fixed_point_t log_val = fixed_log(
fixed_point_t log_val = fixed_log2(
(n_total < 65536) ? (n_total << FIXED_SCALE_BITS) : FIXED_MAX);
fixed_point_t tmp =
((u64) EXPLORATION_FACTOR * fixed_sqrt(log_val / n_visits)) >>
Expand Down Expand Up @@ -219,5 +253,6 @@ int mcts(uint32_t table, char player)
void mcts_init(void)
{
xoro_init(&(mcts_obj.xoro_obj));
log2_table_init();
mcts_obj.nr_active_nodes = 0;
}