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#include "kl_minimization.h"
#include "caffe2/core/logging.h"
using namespace std;
namespace dnnlowp {
TensorQuantizationParams KLDivergenceMinimization::ChooseQuantizationParams(
const Histogram& hist,
bool preserve_sparsity,
int precision) {
const vector<uint64_t> bins = *hist.GetHistogram();
int nbins = bins.size();
int dst_nbins = 1 << precision;
float min = hist.Min(), max = hist.Max();
assert(min <= 0.f);
assert(max >= 0.f);
// NOLINTNEXTLINE(bugprone-narrowing-conversions,cppcoreguidelines-narrowing-conversions)
double bin_width = (max - min) / nbins;
// NOLINTNEXTLINE(bugprone-narrowing-conversions,cppcoreguidelines-narrowing-conversions)
int zero_bin = round(-min / bin_width);
double total_sum = 0;
for (int i = 0; i < nbins; ++i) {
total_sum += bins[i];
}
vector<pair<int, double>> best_start_bins(nbins + 1);
// Look at mapping [start_bin, start_bin + nbins_selected) to
// [0, 1 << precision) for every (start_bin, nbins_selected) combination and
// pick the one with smallest KL divergence
#ifdef _OPENMP
#pragma omp parallel for
#endif
for (int nbins_selected = 1; nbins_selected <= nbins; ++nbins_selected) {
// if (nbins_selected % dst_nbins != 0) continue;
double kl_min = numeric_limits<double>::max();
int best_start_bin = 0;
int start_bin_begin = 0, start_bin_end = nbins - nbins_selected + 1;
if (preserve_sparsity) {
if (min == 0) {
start_bin_begin = 0;
start_bin_end = 1;
} else {
start_bin_begin = zero_bin - nbins_selected / 2;
start_bin_end = start_bin_begin + 1;
}
}
// NOLINTNEXTLINE(cppcoreguidelines-init-variables)
int start_bin;
for (start_bin = start_bin_begin; start_bin < start_bin_end; ++start_bin) {
double kl = 0;
// sum outliers
uint64_t left_outliers = 0;
// NOLINTNEXTLINE(cppcoreguidelines-init-variables)
int src_bin;
for (src_bin = 0; src_bin < start_bin; ++src_bin) {
left_outliers += bins[src_bin];
}
uint64_t right_outliers = 0;
for (src_bin = start_bin + nbins_selected; src_bin < nbins; ++src_bin) {
right_outliers += bins[src_bin];
}
// each destination bin corresponds to a quantized value
for (int dst_bin = 0; dst_bin < dst_nbins; ++dst_bin) {
double non_zero_length = 0;
double sum = 0;
double src_bin_begin_not_rounded =
start_bin + (double)dst_bin * nbins_selected / dst_nbins;
// NOLINTNEXTLINE(bugprone-narrowing-conversions,cppcoreguidelines-narrowing-conversions)
int src_bin_begin = src_bin_begin_not_rounded;
double src_bin_end_not_rounded =
start_bin + (double)(dst_bin + 1) * nbins_selected / dst_nbins;
int src_bin_end = ceil(src_bin_end_not_rounded);
for (src_bin = src_bin_begin; src_bin < src_bin_end; ++src_bin) {
if (src_bin >= 0 && src_bin < nbins) {
double bin = bins[src_bin];
double fraction = 1;
if (src_bin == src_bin_begin && src_bin == src_bin_end - 1) {
fraction = src_bin_end_not_rounded - src_bin_begin_not_rounded;
} else if (src_bin == src_bin_begin) {
fraction = (src_bin_begin + 1) - src_bin_begin_not_rounded;
assert(fraction >= 0);
} else if (src_bin == src_bin_end - 1) {
fraction = src_bin_end_not_rounded - (src_bin_end - 1);
assert(fraction >= 0);
}
bin *= fraction;
sum += bin;
if (src_bin == std::max(start_bin, 0)) {
bin += left_outliers;
}
if (src_bin ==
std::min(start_bin + nbins_selected - 1, nbins - 1)) {
bin += right_outliers;
}
if (bin > 0) {
non_zero_length += fraction;
}
}
} // src_bin
for (src_bin = src_bin_begin; src_bin < src_bin_end; ++src_bin) {
if (src_bin >= 0 && src_bin < nbins) {
uint64_t bin = bins[src_bin];
double fraction = 1;
if (src_bin == src_bin_begin && src_bin == src_bin_end - 1) {
fraction = src_bin_end_not_rounded - src_bin_begin_not_rounded;
} else if (src_bin == src_bin_begin) {
fraction = (src_bin_begin + 1) - src_bin_begin_not_rounded;
} else if (src_bin == src_bin_end - 1) {
fraction = src_bin_end_not_rounded - (src_bin_end - 1);
}
if (src_bin == std::max(start_bin, 0)) {
bin += left_outliers;
}
if (src_bin ==
std::min(start_bin + nbins_selected - 1, nbins - 1)) {
bin += right_outliers;
}
bin *= fraction;
if (bin > 0) {
double p = (double)bin / total_sum;
double q = sum * fraction / non_zero_length / total_sum;
kl += p * log(p / q);
}
}
} // src_bin
} // dst_bin
assert(kl >= 0);
if (kl < kl_min) {
kl_min = kl;
best_start_bin = start_bin;
}
} // for each start_bin
best_start_bins[nbins_selected] = {best_start_bin, kl_min};
} // for each nbins_selected
double kl_min = numeric_limits<double>::max();
int best_nbins_selected = dst_nbins, best_start_bin = 0;
for (int nbins_selected = 1; nbins_selected <= nbins; ++nbins_selected) {
double kl = best_start_bins[nbins_selected].second;
if (kl < kl_min) {
kl_min = kl;
best_start_bin = best_start_bins[nbins_selected].first;
best_nbins_selected = nbins_selected;
}
}
double selected_sum = 0;
int i_begin = std::max(0, best_start_bin);
int i_end = std::min(nbins, best_start_bin + best_nbins_selected);
for (int i = i_begin; i < i_end; ++i) {
selected_sum += bins[i];
}
VLOG(2) << "best quantization range covers "
<< (double)selected_sum / total_sum * 100 << " %%";
VLOG(2) << "best start_bin " << best_start_bin << " nbins_selected "
<< best_nbins_selected;
// NOLINTNEXTLINE(cppcoreguidelines-avoid-magic-numbers,bugprone-narrowing-conversions,cppcoreguidelines-narrowing-conversions)
min = hist.Min() + bin_width * (best_start_bin + 0.5);
// NOLINTNEXTLINE(cppcoreguidelines-avoid-magic-numbers,bugprone-narrowing-conversions,cppcoreguidelines-narrowing-conversions)
max = hist.Min() + bin_width * (best_start_bin + best_nbins_selected + 0.5);
QuantizationFactory* qfactory = QuantizationFactory::GetDefaultInstance();
return qfactory->ChooseQuantizationParams(min, max);
} // ChooseQuantizationParams
} // namespace dnnlowp
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