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#include "tensorflow/core/lib/random/weighted_picker.h"
#include <string.h>
#include <algorithm>
#include "tensorflow/core/lib/random/simple_philox.h"
namespace tensorflow {
namespace random {
WeightedPicker::WeightedPicker(int N) {
CHECK_GE(N, 0);
N_ = N;
// Find the number of levels
num_levels_ = 1;
while (LevelSize(num_levels_ - 1) < N) {
num_levels_++;
}
// Initialize the levels
level_ = new int32*[num_levels_];
for (int l = 0; l < num_levels_; l++) {
level_[l] = new int32[LevelSize(l)];
}
SetAllWeights(1);
}
WeightedPicker::~WeightedPicker() {
for (int l = 0; l < num_levels_; l++) {
delete[] level_[l];
}
delete[] level_;
}
static int32 UnbiasedUniform(SimplePhilox* r, int32 n) {
CHECK_LE(0, n);
const uint32 range = ~static_cast<uint32>(0);
if (n == 0) {
return r->Rand32() * n;
} else if (0 == (n & (n - 1))) {
// N is a power of two, so just mask off the lower bits.
return r->Rand32() & (n - 1);
} else {
// Reject all numbers that skew the distribution towards 0.
// Rand32's output is uniform in the half-open interval [0, 2^{32}).
// For any interval [m,n), the number of elements in it is n-m.
uint32 rem = (range % n) + 1;
uint32 rnd;
// rem = ((2^{32}-1) \bmod n) + 1
// 1 <= rem <= n
// NB: rem == n is impossible, since n is not a power of 2 (from
// earlier check).
do {
rnd = r->Rand32(); // rnd uniform over [0, 2^{32})
} while (rnd < rem); // reject [0, rem)
// rnd is uniform over [rem, 2^{32})
//
// The number of elements in the half-open interval is
//
// 2^{32} - rem = 2^{32} - ((2^{32}-1) \bmod n) - 1
// = 2^{32}-1 - ((2^{32}-1) \bmod n)
// = n \cdot \lfloor (2^{32}-1)/n \rfloor
//
// therefore n evenly divides the number of integers in the
// interval.
//
// The function v \rightarrow v % n takes values from [bias,
// 2^{32}) to [0, n). Each integer in the range interval [0, n)
// will have exactly \lfloor (2^{32}-1)/n \rfloor preimages from
// the domain interval.
//
// Therefore, v % n is uniform over [0, n). QED.
return rnd % n;
}
}
int WeightedPicker::Pick(SimplePhilox* rnd) const {
if (total_weight() == 0) return -1;
// using unbiased uniform distribution to avoid bias
// toward low elements resulting from a possible use
// of big weights.
return PickAt(UnbiasedUniform(rnd, total_weight()));
}
int WeightedPicker::PickAt(int32 weight_index) const {
if (weight_index < 0 || weight_index >= total_weight()) return -1;
int32 position = weight_index;
int index = 0;
for (int l = 1; l < num_levels_; l++) {
// Pick left or right child of "level_[l-1][index]"
const int32 left_weight = level_[l][2 * index];
if (position < left_weight) {
// Descend to left child
index = 2 * index;
} else {
// Descend to right child
index = 2 * index + 1;
position -= left_weight;
}
}
CHECK_GE(index, 0);
CHECK_LT(index, N_);
CHECK_LE(position, level_[num_levels_ - 1][index]);
return index;
}
void WeightedPicker::set_weight(int index, int32 weight) {
assert(index >= 0);
assert(index < N_);
// Adjust the sums all the way up to the root
const int32 delta = weight - get_weight(index);
for (int l = num_levels_ - 1; l >= 0; l--) {
level_[l][index] += delta;
index >>= 1;
}
}
void WeightedPicker::SetAllWeights(int32 weight) {
// Initialize leaves
int32* leaves = level_[num_levels_ - 1];
for (int i = 0; i < N_; i++) leaves[i] = weight;
for (int i = N_; i < LevelSize(num_levels_ - 1); i++) leaves[i] = 0;
// Now sum up towards the root
RebuildTreeWeights();
}
void WeightedPicker::SetWeightsFromArray(int N, const int32* weights) {
Resize(N);
// Initialize leaves
int32* leaves = level_[num_levels_ - 1];
for (int i = 0; i < N_; i++) leaves[i] = weights[i];
for (int i = N_; i < LevelSize(num_levels_ - 1); i++) leaves[i] = 0;
// Now sum up towards the root
RebuildTreeWeights();
}
void WeightedPicker::RebuildTreeWeights() {
for (int l = num_levels_ - 2; l >= 0; l--) {
int32* level = level_[l];
int32* children = level_[l + 1];
for (int i = 0; i < LevelSize(l); i++) {
level[i] = children[2 * i] + children[2 * i + 1];
}
}
}
void WeightedPicker::Append(int32 weight) {
Resize(num_elements() + 1);
set_weight(num_elements() - 1, weight);
}
void WeightedPicker::Resize(int new_size) {
CHECK_GE(new_size, 0);
if (new_size <= LevelSize(num_levels_ - 1)) {
// The new picker fits in the existing levels.
// First zero out any of the weights that are being dropped so
// that the levels are correct (only needed when shrinking)
for (int i = new_size; i < N_; i++) {
set_weight(i, 0);
}
// We do not need to set any new weights when enlarging because
// the unneeded entries always have weight zero.
N_ = new_size;
return;
}
// We follow the simple strategy of just copying the old
// WeightedPicker into a new WeightedPicker. The cost is
// O(N) regardless.
assert(new_size > N_);
WeightedPicker new_picker(new_size);
int32* dst = new_picker.level_[new_picker.num_levels_ - 1];
int32* src = this->level_[this->num_levels_ - 1];
memcpy(dst, src, sizeof(dst[0]) * N_);
memset(dst + N_, 0, sizeof(dst[0]) * (new_size - N_));
new_picker.RebuildTreeWeights();
// Now swap the two pickers
std::swap(new_picker.N_, this->N_);
std::swap(new_picker.num_levels_, this->num_levels_);
std::swap(new_picker.level_, this->level_);
assert(this->N_ == new_size);
}
} // namespace random
} // namespace tensorflow
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