FM / cpu

/usr/local/lib64/python3.6/site-packages/torch/include/ATen/native/cpu/

/usr/local/lib64/python3.6/site-packages/torch/include/ATen/native/cpu

Name	Size	Mode	Actions
AtomicAddFloat.h	750	0644	edit dl rm
avx_mathfun.h	17448	0644	edit dl rm
CatKernel.h	252	0644	edit dl rm
DepthwiseConvKernel.h	447	0644	edit dl rm
DistributionTemplates.h	14051	0644	edit dl rm
GridSamplerKernel.h	592	0644	edit dl rm
Intrinsics.h	1212	0644	edit dl rm
IsContiguous.h	2414	0644	edit dl rm
Loops.h	14411	0644	edit dl rm
MaxUnpoolKernel.h	483	0644	edit dl rm
moments_utils.h	4245	0644	edit dl rm
Reduce.h	10955	0644	edit dl rm
SoftmaxKernel.h	636	0644	edit dl rm
StackKernel.h	315	0644	edit dl rm
utils.h	1093	0644	edit dl rm
zmath.h	6480	0644	edit dl rm

Edit: /usr/local/lib64/python3.6/site-packages/torch/include/ATen/native/cpu/moments_utils.h (4245B)

#pragma once

#include <array>
#include <cstring>
#include <numeric>
#include <utility>
#include <vector>

#include <ATen/Parallel.h>
#include <ATen/cpu/vec/vec.h>
#include <ATen/native/cpu/utils.h>
#include <c10/util/SmallVector.h>

namespace at {
namespace native {
namespace utils {

constexpr int64_t kChunkSize = 16;

template <typename T>
void AddMoments(
    int64_t m0_add,
    const T& m1_add,
    const T& m2_add,
    int64_t& m0,
    T& m1,
    T& m2) {
  const int64_t n = m0 + m0_add;
  const T c = n == 0 ? static_cast<T>(0) : static_cast<T>(m0_add) / static_cast<T>(n);
  const T delta = m1_add - m1;
  m1 += c * delta;
  m2 += m2_add + delta * delta * c * static_cast<T>(m0);
  m0 = n;
}

template <typename T>
void AddMomentsVec(
    int64_t m0_add,
    const vec::Vectorized<T>& m1_add,
    const vec::Vectorized<T>& m2_add,
    int64_t& m0,
    vec::Vectorized<T>& m1,
    vec::Vectorized<T>& m2) {
  using Vec = vec::Vectorized<T>;
  const int64_t n = m0 + m0_add;
  const T c = n == 0 ? static_cast<T>(0) : static_cast<T>(m0_add) / static_cast<T>(n);
  const Vec c_vec(c);
  const Vec delta = m1_add - m1;
  m1 += c_vec * delta;
  m2 += m2_add + delta * delta * c_vec * Vec(static_cast<T>(m0));
  m0 = n;
}

// Compute rowwise moments by Welford algorithm and cascade sum to improve
// numerical stability.
// https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance
// https://en.wikipedia.org/wiki/Pairwise_summation
template <typename T, int64_t kMaxDepth>
std::pair<T, T> RowwiseMomentsImpl(const T* X, int64_t N, int64_t ddof = 0) {
  using Vec = vec::Vectorized<T>;

constexpr int64_t kVecSize = Vec::size();
  const int64_t n = N / kVecSize;
  const int64_t m = divup(n, kChunkSize);
  const int64_t depth = CeilLog2(m);

const Vec kZeroVec(T(0));
  c10::SmallVector<int64_t, kMaxDepth> m0_stk(depth, 0);
  c10::SmallVector<Vec, kMaxDepth> m1_stk(depth, kZeroVec);
  c10::SmallVector<Vec, kMaxDepth> m2_stk(depth, kZeroVec);

for (int64_t i = 0; i < m; ++i) {
    const T* X_ptr = X + i * kChunkSize * kVecSize;
    const int64_t m0 = std::min(kChunkSize, n - i * kChunkSize);
    Vec m1_vec(0);
    Vec m2_vec(0);
    for (int64_t j = 0; j < m0; ++j) {
      const Vec x_vec = Vec::loadu(X_ptr + j * kVecSize);
      const Vec delta_vec = x_vec - m1_vec;
      const Vec c_vec = Vec(T(1) / static_cast<T>(j + 1));
      m1_vec += delta_vec * c_vec;
      m2_vec += delta_vec * (x_vec - m1_vec);
    }
    AddMomentsVec(m0, m1_vec, m2_vec, m0_stk[0], m1_stk[0], m2_stk[0]);
    int64_t mask = i + 1;
    for (int64_t j = 1; j < depth && (mask & 1) == 0; ++j) {
      AddMomentsVec(
          m0_stk[j - 1],
          m1_stk[j - 1],
          m2_stk[j - 1],
          m0_stk[j],
          m1_stk[j],
          m2_stk[j]);
      m0_stk[j - 1] = 0;
      m1_stk[j - 1] = kZeroVec;
      m2_stk[j - 1] = kZeroVec;
      mask >>= 1;
    }
  }
  for (int64_t i = 1; i < depth; ++i) {
    AddMomentsVec(
        m0_stk[i], m1_stk[i], m2_stk[i], m0_stk[0], m1_stk[0], m2_stk[0]);
  }

std::array<T, kVecSize> m1_arr{};
  std::array<T, kVecSize> m2_arr{};
  m1_stk[0].store(m1_arr.data());
  m2_stk[0].store(m2_arr.data());

int64_t m0 = 0;
  T m1 = 0;
  T m2 = 0;
  for (int64_t i = n * kVecSize; i < N; ++i) {
    const T delta = X[i] - m1;
    ++m0;
    m1 += delta / static_cast<T>(m0);
    m2 += delta * (X[i] - m1);
  }
  for (int64_t i = 0; i < kVecSize; ++i) {
    AddMoments(n, m1_arr[i], m2_arr[i], m0, m1, m2);
  }

return std::make_pair(m1, m2 / static_cast<T>(N - ddof));
}

template <typename T>
std::pair<T, T> RowwiseMoments(const T* X, int64_t N, int64_t ddof = 0) {
  using Vec = vec::Vectorized<T>;
  constexpr int64_t kVecSize = Vec::size();
  const int64_t n = N / kVecSize;
  const int64_t m = divup(n, kChunkSize);
  const int64_t depth = CeilLog2(m);
  if (depth <= 4) {
    return RowwiseMomentsImpl<T, 4>(X, N, ddof);
  } else if (depth <= 8) {
    return RowwiseMomentsImpl<T, 8>(X, N, ddof);
  } else if (depth <= 16) {
    return RowwiseMomentsImpl<T, 16>(X, N, ddof);
  } else if (depth <= 32) {
    return RowwiseMomentsImpl<T, 32>(X, N, ddof);
  } else {
    return RowwiseMomentsImpl<T, 64>(X, N, ddof);
  }
}

} // namespace utils
} // namespace native
} // namespace at

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