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ckpts/universal/global_step120/zero/1.word_embeddings.weight/exp_avg.pt

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+oid sha256:26fa04eeadf9328273156571c6bdda26a708eeceab40d27d154baeebd0146941
+size 415237404

ckpts/universal/global_step120/zero/25.attention.dense.weight/exp_avg_sq.pt

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+version https://git-lfs.github.com/spec/v1
+oid sha256:1e9bd4a9faa76ff2d7d8d492e5511db35f0a0ae9b318b1f8090157d19e11865d
+size 16778411

ckpts/universal/global_step120/zero/3.attention.query_key_value.weight/exp_avg.pt

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+version https://git-lfs.github.com/spec/v1
+oid sha256:604df502700ab22fc781bc1f33d7a06bb90d9e02f99d6167537b34b90d0d0c8d
+size 50332828

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/AtomicAddFloat.h

@@ -0,0 +1,37 @@
+#ifndef ATOMIC_ADD_FLOAT
+#define ATOMIC_ADD_FLOAT
+
+#if (defined(__x86_64__) || defined(__i386__) || defined(__aarch64__))
+#include <ATen/native/cpu/Intrinsics.h>
+#else
+#define _mm_pause()
+#endif
+
+#include <atomic>
+
+static inline void cpu_atomic_add_float(float* dst, float fvalue)
+{
+  typedef union {
+    unsigned intV;
+    float floatV;
+  } uf32_t;
+
+  uf32_t new_value, old_value;
+  std::atomic<unsigned>* dst_intV = (std::atomic<unsigned>*)(dst);
+
+  old_value.floatV = *dst;
+  new_value.floatV = old_value.floatV + fvalue;
+
+  unsigned* old_intV = (unsigned*)(&old_value.intV);
+  while (!std::atomic_compare_exchange_strong(dst_intV, old_intV, new_value.intV)) {
+#ifdef __aarch64__
+    __asm__ __volatile__("yield;" : : : "memory");
+#else
+    _mm_pause();
+#endif
+    old_value.floatV = *dst;
+    new_value.floatV = old_value.floatV + fvalue;
+  }
+}
+
+#endif

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/CatKernel.h

@@ -0,0 +1,12 @@
+#pragma once
+
+#include <ATen/core/Tensor.h>
+#include <ATen/native/DispatchStub.h>
+#include <ATen/core/IListRef.h>
+
+namespace at { namespace native {
+
+using cat_serial_fn = void(*)(const Tensor &, const MaterializedITensorListRef&, int64_t);
+DECLARE_DISPATCH(cat_serial_fn, cat_serial_stub);
+
+}}  // namespace at::native

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/ChannelShuffleKernel.h

@@ -0,0 +1,14 @@
+#pragma once
+#include <ATen/native/DispatchStub.h>
+#include <cstdint>
+
+namespace at {
+class TensorBase;
+}
+
+namespace at { namespace native {
+
+using channel_shuffle_fn = void(*)(TensorBase&, const TensorBase&, int64_t);
+DECLARE_DISPATCH(channel_shuffle_fn, channel_shuffle_kernel);
+
+}} // at::native

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/CopyKernel.h

@@ -0,0 +1,12 @@
+#pragma once
+
+namespace at {
+struct TensorIteratorBase;
+
+namespace native {
+inline namespace CPU_CAPABILITY {
+
+void direct_copy_kernel(TensorIteratorBase &iter);
+void copy_kernel(TensorIterator& iter, bool /*non_blocking*/);
+
+}}}  // namespace at::native::CPU_CAPABILITY

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/DepthwiseConvKernel.h

@@ -0,0 +1,21 @@
+#pragma once
+
+#include <ATen/native/DispatchStub.h>
+#include <c10/util/ArrayRef.h>
+
+/*
+  Depthwise 3x3 Winograd convolution operator
+*/
+
+namespace at {
+class Tensor;
+
+namespace native {
+
+using convolution_depthwise3x3_winograd_fn =
+    Tensor (*)(const Tensor &, const Tensor &, const Tensor &, IntArrayRef, IntArrayRef, int64_t);
+
+DECLARE_DISPATCH(convolution_depthwise3x3_winograd_fn, convolution_depthwise3x3_winograd_stub);
+
+}  // namespace native
+}  // namespace at

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/DistributionTemplates.h

@@ -0,0 +1,369 @@
+#pragma once
+
+#include <ATen/CPUApplyUtils.h>
+#include <ATen/Dispatch.h>
+#include <ATen/Dispatch_v2.h>
+#include <ATen/ExpandBase.h>
+#include <ATen/core/DistributionsHelper.h>
+#include <ATen/native/TensorIterator.h>
+#include <ATen/native/cpu/Loops.h>
+#include <limits>
+#include <mutex>
+
+#ifdef CPU_CAPABILITY_AVX2
+#include <ATen/native/cpu/avx_mathfun.h>
+#include <c10/util/irange.h>
+#endif
+
+
+namespace at {
+namespace native {
+namespace templates {
+namespace cpu {
+namespace {
+
+// ==================================================== Random ========================================================
+
+template<typename RNG>
+void random_from_to_kernel(TensorIteratorBase& iter, uint64_t range, int64_t base, RNG generator) {
+  AT_DISPATCH_V2(iter.dtype(), "random_from_to_kernel_cpu", AT_WRAP([&] {
+    std::lock_guard<std::mutex> lock(generator->mutex_);
+    cpu_serial_kernel(iter, [range, base, generator]() -> scalar_t {
+      uniform_int_from_to_distribution<scalar_t> random(range, base);
+      return random(generator);
+    });
+  }), kBool, kHalf, kBFloat16, AT_EXPAND(AT_ALL_TYPES), AT_EXPAND(AT_BAREBONES_UNSIGNED_TYPES));
+}
+
+// This is the special kernel to handle single specific case:
+// from(inclusive) = std::numeric_limits<int64_t>::lowest()
+// to(exclusive) = None (= std::numeric_limits<int64_t>::max() + 1)
+template<typename RNG>
+void random_full_64_bits_range_kernel(TensorIteratorBase& iter, RNG generator) {
+  AT_DISPATCH_ALL_TYPES_AND(at::ScalarType::BFloat16, iter.dtype(), "random_full_64_bits_range_kernel_cpu", [&] {
+    if constexpr (std::is_same<scalar_t, int64_t>::value ||
+        std::is_same<scalar_t, double>::value ||
+        std::is_same<scalar_t, float>::value ||
+        std::is_same<scalar_t, at::BFloat16>::value) {
+      std::lock_guard<std::mutex> lock(generator->mutex_);
+      cpu_serial_kernel(iter, [generator]() -> scalar_t {
+        uniform_int_full_range_distribution<scalar_t> random;
+        return random(generator);
+      });
+    } else {
+      TORCH_CHECK(false, "random_full_64_bits_range_kernel_cpu handles only int64, double, float and bfloat16");
+    }
+  });
+}
+
+template<typename RNG>
+struct RandomFromToKernel {
+  void operator()(TensorIteratorBase& iter, uint64_t range, int64_t base, c10::optional<Generator> gen) {
+    random_from_to_kernel(iter, range, base, check_generator<RNG>(gen));
+  }
+  void operator()(TensorIteratorBase& iter, c10::optional<Generator> gen) {
+    random_full_64_bits_range_kernel(iter, check_generator<RNG>(gen));
+  }
+};
+
+template<typename RNG>
+void random_kernel(TensorIteratorBase& iter, RNG generator) {
+  std::lock_guard<std::mutex> lock(generator->mutex_);
+  AT_DISPATCH_ALL_TYPES_AND3(at::ScalarType::Half, at::ScalarType::BFloat16, at::ScalarType::Bool, iter.dtype(), "random_kernel_cpu", [&] {
+    cpu_serial_kernel(iter, [generator]() -> scalar_t {
+      uniform_int_distribution<scalar_t> random;
+      return random(generator);
+    });
+  });
+}
+
+template<typename RNG>
+struct RandomKernel {
+  void operator()(TensorIteratorBase& iter, c10::optional<Generator> gen) {
+    random_kernel(iter, check_generator<RNG>(gen));
+  }
+};
+
+// ==================================================== Normal ========================================================
+
+#ifdef CPU_CAPABILITY_AVX2
+static void normal_fill_16_AVX2(float *data,
+                         const __m256* two_pi,
+                         const __m256* one,
+                         const __m256* minus_two,
+                         const __m256* mean,
+                         const __m256* std_v) {
+  const __m256 u1 = _mm256_sub_ps(*one, _mm256_loadu_ps(data));
+  const __m256 u2 = _mm256_loadu_ps(data + 8);
+  // sincos256_ps and log256_ps are from avx_mathfun.h
+  const __m256 radius = _mm256_sqrt_ps(_mm256_mul_ps(*minus_two, log256_ps(u1)));
+  const __m256 theta = _mm256_mul_ps(*two_pi, u2);
+  __m256 sintheta, costheta;
+  sincos256_ps(theta, &sintheta, &costheta);
+  const __m256 n1 = _mm256_mul_ps(radius, costheta);
+  const __m256 n2 = _mm256_mul_ps(radius, sintheta);
+  _mm256_storeu_ps(data, _mm256_fmadd_ps(n1, *std_v, *mean));
+  _mm256_storeu_ps(data + 8, _mm256_fmadd_ps(n2, *std_v, *mean));
+}
+
+template<typename RNG>
+void normal_fill_AVX2(const TensorBase &self, const float mean, const float std, RNG generator) {
+  float *data = self.data_ptr<float>();
+  auto size = self.numel();
+  std::lock_guard<std::mutex> lock(generator->mutex_);
+  for (const auto i : c10::irange(size)) {
+    at::uniform_real_distribution<float> uniform(0, 1);
+    data[i] = uniform(generator);
+  }
+  const __m256 two_pi = _mm256_set1_ps(2.0f * c10::pi<double>);
+  const __m256 one = _mm256_set1_ps(1.0f);
+  const __m256 minus_two = _mm256_set1_ps(-2.0f);
+  const __m256 mean_v = _mm256_set1_ps(mean);
+  const __m256 std_v = _mm256_set1_ps(std);
+
+  for (int64_t i = 0; i < size - 15; i += 16) {
+    normal_fill_16_AVX2(data + i, &two_pi, &one, &minus_two, &mean_v, &std_v);
+  }
+
+  if (size % 16 != 0) {
+    // Recompute the last 16 values.
+    data = data + size - 16;
+    for (const auto i : c10::irange(16)) {
+      at::uniform_real_distribution<float> uniform(0, 1);
+      data[i] = uniform(generator);
+    }
+    normal_fill_16_AVX2(data, &two_pi, &one, &minus_two, &mean_v, &std_v);
+  }
+}
+#endif
+
+template <typename scalar_t>
+static void normal_fill_16(scalar_t *data, const scalar_t mean, const scalar_t std) {
+  for (const auto j : c10::irange(8)) {
+    const scalar_t u1 = 1 - data[j]; // [0, 1) -> (0, 1] for log.
+    const scalar_t u2 = data[j + 8];
+    const scalar_t radius = std::sqrt(-2 * std::log(u1));
+    const scalar_t theta = 2.0f * c10::pi<double> * u2;
+    data[j] = radius * std::cos(theta) * std + mean;
+    data[j + 8] = radius * std::sin(theta) * std + mean;
+  }
+}
+
+template <typename scalar_t, typename RNG>
+void normal_fill(const TensorBase &self, const scalar_t mean, const scalar_t std, RNG generator) {
+  scalar_t *data = self.data_ptr<scalar_t>();
+  auto size = self.numel();
+  std::lock_guard<std::mutex> lock(generator->mutex_);
+  for (const auto i : c10::irange(size)) {
+    at::uniform_real_distribution<scalar_t> uniform(0, 1);
+    data[i] = uniform(generator);
+  }
+
+  for (int64_t i = 0; i < size - 15; i += 16) {
+    normal_fill_16<scalar_t>(data + i, mean, std);
+  }
+  if (size % 16 != 0) {
+    // Recompute the last 16 values.
+    data = data + size - 16;
+    for (const auto i : c10::irange(16)) {
+      at::uniform_real_distribution<scalar_t> uniform(0, 1);
+      data[i] = uniform(generator);
+    }
+    normal_fill_16<scalar_t>(data, mean, std);
+  }
+}
+
+template<typename RNG>
+void normal_kernel(const TensorBase &self, double mean, double std, RNG generator) {
+  auto size = self.numel();
+  if (self.scalar_type() == ScalarType::Float && size >= 16 && self.is_contiguous()) {
+#ifdef CPU_CAPABILITY_AVX2
+    normal_fill_AVX2(self, static_cast<float>(mean), static_cast<float>(std), generator);
+#else
+    normal_fill(self, static_cast<float>(mean), static_cast<float>(std), generator);
+#endif
+  } else {
+    AT_DISPATCH_FLOATING_TYPES_AND2(kHalf, kBFloat16, self.scalar_type(), "normal_kernel_cpu", [&] {
+      if (size >= 16 && self.is_contiguous()) {
+        normal_fill<scalar_t>(self, static_cast<scalar_t>(mean), static_cast<scalar_t>(std), generator);
+      } else {
+        auto iter = TensorIterator::borrowing_nullary_op(self);
+        std::lock_guard<std::mutex> lock(generator->mutex_);
+        cpu_serial_kernel(iter, [mean, std, generator]() -> scalar_t {
+          at::normal_distribution<double> normal(mean, std);
+          return static_cast<scalar_t>(normal(generator));
+        });
+      }
+    });
+  }
+}
+
+template<typename RNG>
+struct NormalKernel {
+  void operator()(Tensor& self, double mean, double std, c10::optional<Generator> gen) {
+    normal_kernel(self, mean, std, check_generator<RNG>(gen));
+  }
+};
+
+// ==================================================== Uniform =======================================================
+
+template<typename RNG>
+void uniform_kernel(TensorIteratorBase& iter, double from_, double to_, RNG generator) {
+  AT_DISPATCH_FLOATING_TYPES_AND2(kHalf, kBFloat16, iter.dtype(), "uniform_kernel_cpu", [&]() {
+    std::lock_guard<std::mutex> lock(generator->mutex_);
+    auto from = static_cast<scalar_t>(from_);
+    auto to = static_cast<scalar_t>(to_);
+    at::uniform_real_distribution<scalar_t> uniform(from, to);
+    cpu_serial_kernel(iter, [&uniform, generator]() -> scalar_t {
+      return static_cast<scalar_t>(uniform(generator));
+    });
+  });
+}
+
+template<typename RNG>
+struct UniformKernel {
+  void operator()(TensorIteratorBase& iter, double from, double to, c10::optional<Generator> gen) {
+    uniform_kernel(iter, from, to, check_generator<RNG>(gen));
+  }
+};
+
+// ==================================================== Cauchy ========================================================
+
+template<typename RNG>
+void cauchy_kernel(TensorIteratorBase& iter, double median, double sigma, RNG generator) {
+  AT_DISPATCH_FLOATING_TYPES_AND2(kHalf, kBFloat16, iter.dtype(), "cauchy_cpu", [&]() {
+    std::lock_guard<std::mutex> lock(generator->mutex_);
+    at::cauchy_distribution<double> cauchy(median, sigma);
+    cpu_serial_kernel(iter, [&cauchy, generator]() -> scalar_t {
+      return static_cast<scalar_t>(cauchy(generator));
+    });
+  });
+}
+
+template<typename RNG>
+struct CauchyKernel {
+  void operator()(TensorIteratorBase& iter, double median, double sigma, c10::optional<Generator> gen) {
+    cauchy_kernel(iter, median, sigma, check_generator<RNG>(gen));
+  }
+};
+
+// ================================================== LogNormal =======================================================
+
+template<typename RNG>
+void log_normal_kernel(TensorIteratorBase& iter, double mean, double std, RNG generator) {
+  AT_DISPATCH_FLOATING_TYPES_AND2(at::ScalarType::Half, at::ScalarType::BFloat16, iter.dtype(), "log_normal_cpu", [&]() {
+    std::lock_guard<std::mutex> lock(generator->mutex_);
+    at::lognormal_distribution<double> logNormal(mean, std);
+    cpu_serial_kernel(iter, [&logNormal, generator]() -> scalar_t {
+      return static_cast<scalar_t>(logNormal(generator));
+    });
+  });
+}
+
+template<typename RNG>
+struct LogNormalKernel {
+  void operator()(TensorIteratorBase& iter, double mean, double std, c10::optional<Generator> gen) {
+    log_normal_kernel(iter, mean, std, check_generator<RNG>(gen));
+  }
+};
+
+// =================================================== Geometric ======================================================
+
+template<typename RNG>
+void geometric_kernel(TensorIteratorBase& iter, double p, RNG generator) {
+  AT_DISPATCH_ALL_TYPES_AND2(at::ScalarType::Half, at::ScalarType::BFloat16, iter.dtype(), "geometric_cpu", [&]() {
+    std::lock_guard<std::mutex> lock(generator->mutex_);
+    at::geometric_distribution<double> geometric(p);
+    cpu_serial_kernel(iter, [&geometric, generator]() -> scalar_t {
+      return static_cast<scalar_t>(geometric(generator));
+    });
+  });
+}
+
+template<typename RNG>
+struct GeometricKernel {
+  void operator()(TensorIteratorBase& iter, double p, c10::optional<Generator> gen) {
+    geometric_kernel(iter, p, check_generator<RNG>(gen));
+  }
+};
+
+// ================================================== Exponential =====================================================
+
+template<typename RNG>
+void exponential_kernel(TensorIteratorBase& iter, double lambda, RNG generator) {
+  TORCH_CHECK(isFloatingType(iter.dtype()), "Exponential distribution is a continuous probability distribution. dtype must be a floating point but you specified ", iter.dtype());
+  AT_DISPATCH_FLOATING_TYPES_AND2(at::ScalarType::Half, at::ScalarType::BFloat16, iter.dtype(), "exponential_cpu", [&]() {
+    std::lock_guard<std::mutex> lock(generator->mutex_);
+    at::exponential_distribution<double> exponential(lambda);
+    cpu_serial_kernel(iter, [&exponential, generator]() -> scalar_t {
+      return static_cast<scalar_t>(exponential(generator));
+    });
+  });
+}
+
+template<typename RNG>
+struct ExponentialKernel {
+  void operator()(TensorIteratorBase& iter, double lambda, c10::optional<Generator> gen) {
+    exponential_kernel(iter, lambda, check_generator<RNG>(gen));
+  }
+};
+
+// ================================================== Bernoulli =======================================================
+
+template<typename RNG>
+void bernoulli_kernel(const TensorBase &self, const TensorBase &p_, RNG generator) {
+  AT_DISPATCH_ALL_TYPES_AND3(at::ScalarType::Bool, at::ScalarType::BFloat16, at::ScalarType::Half,
+  self.scalar_type(), "bernoulli_tensor_cpu_self_", [&] {
+    // See Note [Acquire lock when using random generators]
+    std::lock_guard<std::mutex> lock(generator->mutex_);
+    using self_t = scalar_t;
+    auto p_cpu = p_.to(kCPU);
+    auto p = expand_inplace(self, p_cpu);
+    auto iter = TensorIteratorConfig()
+        .add_output(self)
+        .add_input(*p)
+        .check_all_same_dtype(false)
+        .build();
+    if (p->scalar_type() == kDouble) {
+      cpu_serial_kernel(iter, [&](const double p_val) -> self_t {
+        at::bernoulli_distribution<double> bernoulli(p_val);
+        return static_cast<self_t>(bernoulli(generator));
+      });
+    } else {
+      AT_DISPATCH_FLOATING_TYPES_AND2(at::ScalarType::BFloat16, at::ScalarType::Half,
+      p->scalar_type(), "bernoulli_tensor_cpu_p_", [&] {
+        using p_t = scalar_t;
+        cpu_serial_kernel(iter, [&](const p_t p_val) -> self_t {
+          at::bernoulli_distribution<float> bernoulli(p_val);
+          return static_cast<self_t>(bernoulli(generator));
+        });
+      });
+    }
+  });
+}
+
+template<typename RNG>
+void bernoulli_kernel(const TensorBase &self, double p, RNG generator) {
+  AT_DISPATCH_ALL_TYPES_AND3(at::ScalarType::Bool, at::ScalarType::BFloat16, at::ScalarType::Half,
+  self.scalar_type(), "bernoulli_scalar_cpu_", [&] {
+    // See Note [Acquire lock when using random generators]
+    std::lock_guard<std::mutex> lock(generator->mutex_);
+    auto iter = TensorIterator::borrowing_nullary_op(self);
+    cpu_serial_kernel(iter, [p, generator]() -> scalar_t {
+      at::bernoulli_distribution<double> bernoulli(p);
+      return static_cast<scalar_t>(bernoulli(generator));
+    });
+  });
+}
+
+template<typename RNG>
+struct BernoulliKernel {
+  void operator()(const TensorBase &self, double p, c10::optional<Generator> gen) {
+    bernoulli_kernel(self, p, check_generator<RNG>(gen));
+  }
+  void operator()(const TensorBase &self, const TensorBase &p_, c10::optional<Generator> gen) {
+    bernoulli_kernel(self, p_, check_generator<RNG>(gen));
+  }
+};
+
+}}}}}

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/GridSamplerKernel.h

@@ -0,0 +1,34 @@
+#pragma once
+
+#include <ATen/native/DispatchStub.h>
+
+#include <array>
+#include <cstdint>
+
+namespace at {
+class TensorBase;
+}
+
+namespace at { namespace native {
+
+using forward_2d_fn = void (*) (
+    const TensorBase &output,
+    const TensorBase &input,
+    const TensorBase &grid,
+    int64_t interpolation_mode,
+    int64_t padding_mode,
+    bool align_corners);
+using backward_2d_fn = void (*) (
+    const TensorBase &grad_input,
+    const TensorBase &grad_grid,
+    const TensorBase &grad_output,
+    const TensorBase &input,
+    const TensorBase &grid,
+    int64_t interpolation_mode,
+    int64_t padding_mode,
+    bool align_corners,
+    std::array<bool, 2> output_mask);
+DECLARE_DISPATCH(forward_2d_fn, grid_sampler_2d_cpu_kernel);
+DECLARE_DISPATCH(backward_2d_fn, grid_sampler_2d_backward_cpu_kernel);
+
+}}  // namespace at::native

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/IndexKernelUtils.h

@@ -0,0 +1,88 @@
+#pragma once
+#include <ATen/native/TensorIterator.h>
+#include <c10/util/irange.h>
+
+namespace at {
+namespace native {
+
+namespace {
+static bool is_constant_index(int ntensor, const int64_t* strides) {
+  AT_ASSERT(ntensor >= 3);
+  for (const auto arg : c10::irange(2, ntensor)) {
+    if (strides[arg] != 0) {
+      return false;
+    }
+  }
+  return true;
+}
+
+
+struct Indexer {
+  Indexer(int64_t num_indexers, char** indexers, const int64_t* indexer_strides,
+          IntArrayRef original_sizes, IntArrayRef original_strides)
+    : num_indexers(num_indexers)
+    , indexers(indexers)
+    , indexer_strides(indexer_strides)
+    , original_strides(original_strides.data())
+    , original_sizes(original_sizes.data()) {
+    AT_ASSERT(static_cast<int64_t>(original_strides.size()) == num_indexers);
+    AT_ASSERT(static_cast<int64_t>(original_sizes.size()) == num_indexers);
+  }
+
+  int64_t num_indexers;
+  char** indexers;
+  const int64_t* indexer_strides;
+  const int64_t* original_strides;
+  const int64_t* original_sizes;
+
+  int64_t get(int64_t idx) {
+    int64_t offset = 0;
+    for (const auto j : c10::irange(num_indexers)) {
+      int64_t value = *(int64_t*)&indexers[j][idx * indexer_strides[j]];
+      int64_t size = original_sizes[j];
+      TORCH_CHECK_INDEX(value >= -size && value < size,
+                        "index ", value, " is out of bounds for dimension ", j, " with size ", size);
+      if (value < 0) {
+        value += size;
+      }
+      offset += value * original_strides[j];
+    }
+    return offset;
+  }
+};
+} // anonymous namespace
+
+template <typename scalar_t, typename func_t>
+void cpu_index_kernel(TensorIteratorBase& iter, IntArrayRef index_size, IntArrayRef index_stride,
+                      const func_t& f, bool serial_execution=false)
+{
+  int ntensor = iter.ntensors();
+  // When launch the index parallel version, set a relative small grain size less than the INTERNAL::GRAIN_SIZE
+  // to make the whole available thread numbers get more balanced work load and a better cache location.
+  // The grain size here is chosen by the op benchmark to overcome the thread launch overhead
+  const int index_parallel_grain_size = 3000;
+  auto loop = [&](char** data, const int64_t* strides, int64_t n) {
+    auto indexer = Indexer(ntensor - 2, &data[2], &strides[2], index_size, index_stride);
+    char* dst = data[0];
+    char* src = data[1];
+    if (is_constant_index(ntensor, strides)) {
+      // specialization for when every element uses the same index
+      int64_t offset = indexer.get(0);
+      for (const auto i : c10::irange(n)) {
+        f(dst + strides[0] * i, src + strides[1] * i, offset);
+      }
+    } else {
+      for (const auto i : c10::irange(n)) {
+        int64_t offset = indexer.get(i);
+        f(dst + strides[0] * i, src + strides[1] * i, offset);
+      }
+    }
+  };
+  if (serial_execution) {
+    iter.serial_for_each(loop, {0, iter.numel()});
+  } else {
+    iter.for_each(loop, index_parallel_grain_size);
+  }
+}
+} // at
+} // native

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/Intrinsics.h

@@ -0,0 +1,33 @@
+#pragma once
+
+#if defined(__clang__) && (defined(__x86_64__) || defined(__i386__))
+/* Clang-compatible compiler, targeting x86/x86-64 */
+#include <x86intrin.h>
+#elif defined(_MSC_VER)
+/* Microsoft C/C++-compatible compiler */
+#include <intrin.h>
+#if _MSC_VER <= 1900
+#define _mm256_extract_epi64(X, Y) (((uint64_t*)&X)[Y])
+#endif
+#elif defined(__GNUC__) && (defined(__x86_64__) || defined(__i386__))
+/* GCC-compatible compiler, targeting x86/x86-64 */
+#include <x86intrin.h>
+#elif defined(__GNUC__) && defined(__ARM_NEON__)
+/* GCC-compatible compiler, targeting ARM with NEON */
+#include <arm_neon.h>
+#elif defined(__GNUC__) && defined(__IWMMXT__)
+/* GCC-compatible compiler, targeting ARM with WMMX */
+#include <mmintrin.h>
+#elif (defined(__GNUC__) || defined(__xlC__)) && \
+    (defined(__VEC__) || defined(__ALTIVEC__))
+/* XLC or GCC-compatible compiler, targeting PowerPC with VMX/VSX */
+#include <altivec.h>
+/* We need to undef those tokens defined by <altivec.h> to avoid conflicts
+   with the C++ types. => Can still use __bool/__vector */
+#undef bool
+#undef vector
+#undef pixel
+#elif defined(__GNUC__) && defined(__SPE__)
+/* GCC-compatible compiler, targeting PowerPC with SPE */
+#include <spe.h>
+#endif

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/IsContiguous.h

@@ -0,0 +1,62 @@
+#pragma once
+
+namespace at { namespace native { inline namespace CPU_CAPABILITY {
+
+// n: number of function arguments (arity)
+// traits: function_traits (see FunctionTraits.h)
+// s: index of scalar argument or -1
+template <int n, int stride_index, typename traits, int s=-1>
+struct IsContiguous {
+  static bool eval(const int64_t* strides) {
+    using type = typename traits::template arg<n - 1>::type;
+    return strides[stride_index] == (s == n ? 0 : sizeof(type)) &&
+           IsContiguous<n - 1, stride_index - 1, traits, s>::eval(strides);
+  }
+};
+
+// will be called when there is an output exists
+template <typename traits, int s>
+struct IsContiguous<0, 0, traits, s> {
+  static bool eval(const int64_t* strides) {
+    return strides[0] == sizeof(typename traits::result_type);
+  }
+};
+
+// will be called when there is no output
+template <typename traits, int s>
+struct IsContiguous<0, -1, traits, s> {
+  static bool eval(const int64_t* /*strides*/) {
+    return true;
+  }
+};
+
+// output and all inputs are contiguous
+template <typename traits,
+    typename std::enable_if<std::is_void<typename traits::result_type>::value>::type* = nullptr>
+static inline bool is_contiguous(const int64_t* strides) {
+  return IsContiguous<traits::arity, traits::arity - 1, traits>::eval(strides);
+}
+
+template <typename traits,
+    typename std::enable_if<!std::is_void<typename traits::result_type>::value>::type* = nullptr>
+static inline bool is_contiguous(const int64_t* strides) {
+  return IsContiguous<traits::arity, traits::arity, traits>::eval(strides);
+}
+
+// input at `s` is scalar (stride 0); output and other inputs are contiguous
+// NB: output is typically at strides[0] so first input corresponds to s=1
+template <typename traits, int s,
+    typename std::enable_if<std::is_void<typename traits::result_type>::value>::type* = nullptr>
+static inline bool is_contiguous_scalar(const int64_t* strides) {
+  static_assert(s > 0 && s <= traits::arity, "scalar argument index out of bounds");
+  return IsContiguous<traits::arity, traits::arity - 1, traits, s>::eval(strides);
+}
+
+template <typename traits, int s,
+    typename std::enable_if<!std::is_void<typename traits::result_type>::value>::type* = nullptr>
+static inline bool is_contiguous_scalar(const int64_t* strides) {
+  static_assert(s > 0 && s <= traits::arity, "scalar argument index out of bounds");
+  return IsContiguous<traits::arity, traits::arity, traits, s>::eval(strides);
+}
+
+}}}

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/LogAddExp.h

@@ -0,0 +1,61 @@
+#pragma once
+
+#include <c10/util/complex.h>
+#include <ATen/NumericUtils.h>
+
+namespace at { namespace native {
+inline namespace CPU_CAPABILITY {
+
+// custom min and max to be used in logcumsumexp for complex arguments
+template <typename scalar_t>
+std::pair<c10::complex<scalar_t>, c10::complex<scalar_t>> _logcumsumexp_minmax(c10::complex<scalar_t> x, c10::complex<scalar_t> y) {
+  if (at::_isnan(y)) {  // either real is nan or imag is nan
+    return std::make_pair(y, y);
+  } else if (at::_isnan(x)) {  // either real is nan or imag is nan
+    return std::make_pair(x, x);
+  } else {
+    return (x.real() < y.real()) ? std::make_pair(x, y) : std::make_pair(y, x);
+  }
+}
+
+template <typename scalar_t>
+scalar_t _log_add_exp_helper(scalar_t x, scalar_t y) {
+  // Reference : https://www.tensorflow.org/api_docs/python/tf/math/cumulative_logsumexp
+  scalar_t min = at::_isnan(y) ? y : std::min(x, y); // std::min returns first arg if one of the args is nan
+  scalar_t max = at::_isnan(y) ? y : std::max(x, y); // std::max returns first arg if one of the args is nan
+  if (min != max || std::isfinite(min)) {
+    // nan will be propagated here
+    return std::log1p(std::exp(min - max)) + max;
+  } else {
+    // special case to correctly handle infinite cases
+    return x;
+  }
+}
+
+template <typename scalar_t>
+c10::complex<scalar_t> _log_add_exp_helper(const c10::complex<scalar_t>& x, const c10::complex<scalar_t>& y) {
+  auto [min, max] = _logcumsumexp_minmax<scalar_t>(x, y);
+  auto min_real = std::real(min);
+  auto max_real = std::real(max);
+
+  if (at::_isnan(min)) {  // either real is nan or imag is nan
+    // handling the "infectious" NaNs
+    return {std::numeric_limits<scalar_t>::quiet_NaN(), std::numeric_limits<scalar_t>::quiet_NaN()};
+  } else if (!std::isfinite(min_real) && (min_real == max_real)) {
+    if (min_real < 0) {
+      // handle the -inf case, the imaginary part here does not really matter as the exp(value)
+      // will be around 0.0 and the angle (i.e. the imaginary part) cannot be determined.
+      // It does not matter if we're taking the exp of this value
+      return min;
+    } else {
+      // handle the +inf case, we don't need the special precision for log1p for small values
+      // and to avoid producing nan in case of real(max) == real(min) == +inf
+      return std::log(std::exp(min) + std::exp(max));
+    }
+  } else {
+    return std::log1p(std::exp(min - max)) + max;
+  }
+}
+
+} // end namespace
+}} //end at::native

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/Loops.h

@@ -0,0 +1,394 @@
+#pragma once
+
+// This file provides two functions to help write elementwise kernels:
+//
+//   cpu_kernel(TensorIterator iter, <lambda>)
+//   cpu_kernel_vec(TensorIterator iter, <lambda>, <vec_lambda>)
+//
+// Both functions may generate vectorized code. The cpu_kernel implementation
+// relies on the compiler's auto-vectorization. The cpu_kernel_vec
+// implementation uses x86 SIMD intrinsics when available. These functions
+// are only intended to be used in the ATen/native/cpu subdirectory, since files
+// in other directories are not compiled with AVX/AVX2 enabled. See README.md
+// for more details.
+//
+// For example, to write a multiplication kernel for float:
+//
+//   cpu_kernel(iter, [](float a, float b) { return a * b; });
+//
+// Or you may write:
+//
+//   cpu_kernel_vec(iter,
+//     [](float a, float b) { return a * b; },
+//     [](Vectorized<float> a, Vectorized<float> b) { return a * b; });
+//
+// See BinaryOpsKernel.cpp for the complete implementation
+//
+//
+
+#include <stdint.h>
+#include <c10/util/C++17.h>
+#include <c10/util/Load.h>
+#include <c10/util/irange.h>
+#include <ATen/detail/FunctionTraits.h>
+#include <ATen/native/cpu/IsContiguous.h>
+#include <ATen/native/TensorIterator.h>
+#include <ATen/native/TensorIteratorDynamicCasting.h>
+#include <ATen/cpu/vec/vec.h>
+
+#include <utility>
+
+namespace at { namespace native { inline namespace CPU_CAPABILITY {
+
+using namespace vec;
+
+template <typename traits, std::size_t... INDEX>
+typename traits::ArgsTuple
+dereference_impl(char* C10_RESTRICT data[], const int64_t* strides, int64_t i,
+                 std::index_sequence<INDEX...>) {
+  return std::make_tuple(
+      c10::load<typename traits::template arg<INDEX>::type>(
+          data[INDEX] + i * strides[INDEX])...);
+}
+
+template <typename traits>
+typename traits::ArgsTuple
+dereference(char* C10_RESTRICT data[], const int64_t* strides, int64_t i) {
+  using Indices = std::make_index_sequence<traits::arity>;
+  return dereference_impl<traits>(data, strides, i, Indices{});
+}
+
+template <typename traits, std::size_t... INDEX>
+typename traits::ArgsTuple
+dereference_vec_impl(char* C10_RESTRICT data[],
+                     const typename traits::result_type& opt_scalar,
+                     size_t S,
+                     int64_t i,
+                     std::index_sequence<INDEX...>) {
+  using Vec = typename traits::result_type;
+  using scalar_t = typename Vec::value_type;
+  return std::make_tuple(
+      S == INDEX + 1 ?
+      opt_scalar :
+      Vec::loadu(data[INDEX] + i * sizeof(scalar_t))...);
+}
+
+template <typename traits>
+typename traits::ArgsTuple
+dereference_vec(char* C10_RESTRICT data[], const typename traits::result_type& opt_scalar, size_t S, int64_t i) {
+  using Indices = std::make_index_sequence<traits::arity>;
+  return dereference_vec_impl<traits>(data, opt_scalar, S, i, Indices{});
+}
+
+template <typename func_t,
+    typename std::enable_if<!std::is_void<typename function_traits<func_t>::result_type>::value>::type* = nullptr>
+static inline void
+execute_op(char* C10_RESTRICT data[], const int64_t* strides, int64_t i, int64_t n, func_t&& op) {
+  using traits = function_traits<func_t>;
+  using result_type = typename traits::result_type;
+  for (; i < n; i++) {
+    result_type* out_ptr = (result_type*)(data[0] + i * strides[0]);
+    *out_ptr = c10::guts::apply(std::forward<func_t>(op), dereference<traits>(
+        &data[1],
+        &strides[1],
+        i));
+  }
+}
+
+template <typename func_t,
+    typename std::enable_if<std::is_void<typename function_traits<func_t>::result_type>::value>::type* = nullptr>
+static inline void
+execute_op(char* C10_RESTRICT data[], const int64_t* strides, int64_t i, int64_t n, func_t&& op) {
+  using traits = function_traits<func_t>;
+  for (; i < n; i++) {
+    c10::guts::apply(std::forward<func_t>(op), dereference<traits>(
+        &data[0],
+        &strides[0],
+        i));
+  }
+}
+
+// Basic loop operation (one output, N inputs). May be auto-vectorized
+// by the compiler. Supports inputs and outputs of different types.
+template <typename func_t>
+static inline void
+basic_loop(char* C10_RESTRICT data[], const int64_t* strides_, int64_t i, int64_t n, func_t&& op) {
+  using traits = function_traits<func_t>;
+  constexpr int ntensors = traits::arity + 1;
+
+  // Copying strides to temporary array helps auto vectorization in older GCC
+  // versions.
+  int64_t strides[ntensors];
+  for (const auto arg : c10::irange(ntensors)) {
+    strides[arg] = strides_[arg];
+  }
+
+  execute_op(data, strides, i, n, std::forward<func_t>(op));
+}
+
+// the recursive variadic template for iterating over the returned tuple
+template<class T, size_t N>
+struct TupleOutput {
+  static void handle(char *C10_RESTRICT data[], const int64_t *strides, int64_t i,
+                     const T &tuple) {
+    TupleOutput<T, N - 1>::handle(data, strides, i, tuple);
+
+    auto output = std::get<N - 1>(tuple);
+    using output_type = decltype(output);
+    output_type * out_ptr = (output_type *)(data[N - 1] + i * strides[N - 1]);
+    *out_ptr = output;
+  }
+};
+
+// Base case for the above recursive template
+template<class T>
+struct TupleOutput<T, 1> {
+  static void handle(char *C10_RESTRICT data[], const int64_t *strides, int64_t i,
+                     const T &tuple) {
+    auto output = std::get<0>(tuple);
+    using output_type = decltype(output);
+    output_type* out_ptr = (output_type *)(data[0] + i * strides[0]);
+    *out_ptr = output;
+  }
+};
+
+template<class... Args>
+void handle_tuple_outputs(char* C10_RESTRICT data[],
+                          const int64_t* strides,
+                          int64_t i,
+                          const std::tuple<Args...> &tuple) {
+  TupleOutput<decltype(tuple), sizeof...(Args)>::handle(data, strides, i, tuple);
+}
+
+// Loop operation for `cpu_kernel_multiple_outputs`.
+// 1. Use `c10::guts::apply` to make dynamic method invocation
+//    for the lambda passed in `cpu_kernel_multiple_outputs`.
+// 2. Iterate over the members of the returned tuple, set the corresponding
+//    output tensor by the tuple member in `handle_tuple_outputs` function.
+template <typename func_t>
+static inline void
+multiple_outputs_loop(char* C10_RESTRICT data[], const int64_t* strides_, int64_t i, int64_t n, func_t&& op) {
+  using traits = function_traits<func_t>;
+
+  using result_type = typename traits::result_type;
+  constexpr int num_outputs = std::tuple_size<result_type>::value;
+  constexpr int ntensors = traits::arity + num_outputs;
+
+  // Copying strides to temporary array helps auto vectorization in older GCC
+  // versions.
+  int64_t strides[ntensors];
+  for (const auto arg : c10::irange(ntensors)) {
+    strides[arg] = strides_[arg];
+  }
+
+  for (; i < n; i++) {
+    auto output = c10::guts::apply(op, dereference<traits>(
+      &data[num_outputs],
+      &strides[num_outputs],
+      i));
+    handle_tuple_outputs(data, strides, i, output);
+  }
+}
+
+// Explicitly vectorized loop implementation. All inputs and outputs must be
+// the same type and contiguous with one exception: a single input may be
+// a scalar (stride 0). It's position is indicated by the argument `S`. If `S`
+// is 0, then there are no scalar inputs.
+template <typename func_t, typename vec_func_t>
+static inline void
+vectorized_loop(char** C10_RESTRICT data_, int64_t n, int64_t S, func_t&& op, vec_func_t&& vop) {
+  using traits = function_traits<vec_func_t>;
+  using scalar_t = typename function_traits<func_t>::result_type;
+  using Vec = Vectorized<scalar_t>;
+  constexpr int ntensors = traits::arity + 1;
+
+  char* C10_RESTRICT data[ntensors];
+  for (const auto arg : c10::irange(ntensors)) {
+    data[arg] = data_[arg];
+  }
+
+  Vec opt_scalar = Vec(S > 0 ? *(scalar_t*)data[S] : scalar_t(0));
+  int64_t i = 0;
+  for (; i <= n - 2 * Vec::size(); i += 2 * Vec::size()) {
+    auto args1 = dereference_vec<traits>(&data[1], opt_scalar, S, i);
+    auto args2 = dereference_vec<traits>(&data[1], opt_scalar, S, i + Vec::size());
+    auto out1 = c10::guts::apply(std::forward<vec_func_t>(vop), std::move(args1));
+    auto out2 = c10::guts::apply(std::forward<vec_func_t>(vop), std::move(args2));
+    out1.store(data[0] + i * sizeof(scalar_t));
+    out2.store(data[0] + (i + Vec::size()) * sizeof(scalar_t));
+  }
+  if (i < n) {
+    int64_t strides[ntensors];
+    for (const auto arg : c10::irange(ntensors)) {
+      strides[arg] = (S > 0 && arg == S) ? 0 : sizeof(scalar_t);
+    }
+    basic_loop(data, strides, i, n, std::forward<func_t>(op));
+  }
+}
+
+
+template <typename traits, typename cb_t>
+static inline void unroll_contiguous_scalar_checks(
+    const int64_t* /*strides*/,
+    std::index_sequence<>,
+    cb_t&& cb) {
+  cb(0);
+}
+
+template <typename traits, typename cb_t, size_t INDEX0, size_t ...INDEX>
+static inline void unroll_contiguous_scalar_checks(
+    const int64_t* strides,
+    std::index_sequence<INDEX0, INDEX...>,
+    cb_t&& cb) {
+  if (is_contiguous_scalar<traits, INDEX0 + 1>(strides)) {
+    cb(INDEX0 + 1);
+  } else {
+    unroll_contiguous_scalar_checks<traits>(strides, std::index_sequence<INDEX...>{}, std::forward<cb_t>(cb));
+  }
+}
+
+template <typename op_t, typename vop_t>
+struct VectorizedLoop2d {
+  op_t op;
+  vop_t vop;
+
+  using traits = function_traits<op_t>;
+  static constexpr int ntensors = traits::arity + 1;
+  using data_t = std::array<char*, ntensors>;
+
+  VectorizedLoop2d(const op_t &op, vop_t vop):
+    op(op), vop(std::move(vop)) {}
+
+  static void advance(data_t &data, const int64_t *outer_strides) {
+    for (const auto arg : c10::irange(data.size())) {
+      data[arg] += outer_strides[arg];
+    }
+  }
+
+  void operator()(char** base, const int64_t *strides, int64_t size0, int64_t size1) {
+    data_t data;
+    std::copy_n(base, ntensors, data.data());
+    const int64_t *outer_strides = &strides[ntensors];
+
+    if (is_contiguous<traits>(strides)) {
+      for (const auto i C10_UNUSED : c10::irange(size1)) {
+        vectorized_loop(data.data(), size0, 0, op, vop);
+        advance(data, outer_strides);
+      }
+    } else {
+      using Indices = std::make_index_sequence<traits::arity>;
+      unroll_contiguous_scalar_checks<traits>(strides, Indices{}, [&](size_t idx) {
+        if (idx) {
+          for (const auto i C10_UNUSED : c10::irange(size1)) {
+            vectorized_loop(data.data(), size0, idx, op, vop);
+            advance(data, outer_strides);
+          }
+        } else {
+          for (const auto i C10_UNUSED : c10::irange(size1)) {
+            basic_loop(data.data(), strides, 0, size0, op);
+            advance(data, outer_strides);
+          }
+        }
+      });
+    }
+  }
+};
+
+template <typename op_t, typename vop_t>
+VectorizedLoop2d<op_t, vop_t> make_vectorized_loop2d(
+    const op_t &op, const vop_t &vop) {
+  return VectorizedLoop2d<op_t, vop_t>(op, vop);
+}
+
+template <typename func_t>
+void cpu_kernel(TensorIteratorBase& iter, func_t&& op, int64_t grain_size = at::internal::GRAIN_SIZE) {
+  using traits = function_traits<func_t>;
+  // this could be extended to work with void return types
+  TORCH_INTERNAL_ASSERT(iter.ninputs() == traits::arity);
+  TORCH_INTERNAL_ASSERT(iter.noutputs() == 1);
+  // dynamic casting not currently supported on CPU
+  TORCH_INTERNAL_ASSERT(!needs_dynamic_casting<func_t>::check(iter));
+
+  iter.for_each([&](char** data, const int64_t* strides, int64_t n) {
+    // basic loop can handle 1d slices with arbitrary strides, and 1d slices is all that
+    // iter.for_each is ever sending to the loop lambda
+      basic_loop(data, strides, 0, n, std::forward<func_t>(op));
+  }, grain_size);
+  iter.cast_outputs();
+}
+
+// This function helps write elementwise kernels that requires multiple outputs.
+// It follows the similar structure of cpu_kernel.
+// Instead of `basic_loop` function, a new `multiple_outputs_loop` function is
+// manipulated to handle multiple return values.
+// For now `needs_dynamic_casting` check is not added as the passed lambda (`func_t`)
+// of `multiple_outputs_loop` returns `std::tuple` instead of `scalar_t`.
+// The `gpu_kernel_multiple_outputs` is also implemented without this check,
+// We could extend `needs_dynamic_casting` to support both `std::tuple` and
+// `thrust::tuple` in the future.
+template <typename func_t>
+void cpu_kernel_multiple_outputs(TensorIteratorBase& iter, func_t&& op, int64_t grain_size = at::internal::GRAIN_SIZE) {
+  using traits = function_traits<func_t>;
+  TORCH_INTERNAL_ASSERT(iter.ninputs() == traits::arity);
+
+  iter.for_each([&](char** data, const int64_t* strides, int64_t n) {
+    multiple_outputs_loop(data, strides, 0, n, std::forward<func_t>(op));
+  }, grain_size);
+  iter.cast_outputs();
+}
+
+template <bool check_dynamic_cast=true, typename func_t, typename vec_func_t>
+void cpu_kernel_vec(TensorIteratorBase& iter, func_t&& op, vec_func_t&& vop, int64_t grain_size = at::internal::GRAIN_SIZE) {
+  using traits = function_traits<func_t>;
+  // this could be extended to work with void return types
+  TORCH_INTERNAL_ASSERT(iter.ninputs() == traits::arity);
+  TORCH_INTERNAL_ASSERT(iter.noutputs() == 1);
+  // dynamic casting not currently supported on CPU, but some kernels (like Fill)
+  // explicitly dynamic_cast, so we give the opt-out of checking.
+  if constexpr (check_dynamic_cast) {
+    TORCH_INTERNAL_ASSERT(!needs_dynamic_casting<func_t>::check(iter));
+  }
+
+  iter.for_each(make_vectorized_loop2d(op, vop), grain_size);
+  iter.cast_outputs();
+}
+
+template <typename func_t>
+void cpu_serial_kernel(TensorIteratorBase& iter, func_t&& op, const Range& range) {
+  using traits = function_traits<func_t>;
+  constexpr bool result_void = std::is_void<typename traits::result_type>::value;
+  TORCH_INTERNAL_ASSERT(iter.ninputs() == traits::arity &&
+                        ((result_void && iter.noutputs() == 0) || (!result_void && iter.noutputs() == 1)));
+  // dynamic casting not currently supported on CPU
+  TORCH_INTERNAL_ASSERT(!needs_dynamic_casting<func_t>::check(iter));
+
+  iter.serial_for_each([&](char** data, const int64_t* strides, int64_t n) {
+    basic_loop(data, strides, 0, n, std::forward<func_t>(op));
+  }, range);
+  iter.cast_outputs();
+}
+
+template <typename func_t>
+void cpu_serial_kernel(TensorIteratorBase& iter, func_t&& op) {
+  cpu_serial_kernel(iter, op, {0, iter.numel()});
+}
+
+template <typename func_t, typename vec_func_t>
+void cpu_serial_kernel_vec(TensorIteratorBase& iter, func_t&& op, vec_func_t&& vop, const Range& range) {
+  using traits = function_traits<func_t>;
+  // this could be extended to work with void return types
+  TORCH_INTERNAL_ASSERT(iter.ninputs() == traits::arity);
+  TORCH_INTERNAL_ASSERT(iter.noutputs() == 1);
+  // dynamic casting not currently supported on CPU
+  TORCH_INTERNAL_ASSERT(!needs_dynamic_casting<func_t>::check(iter));
+
+  iter.serial_for_each(make_vectorized_loop2d(op, vop), range);
+  iter.cast_outputs();
+}
+
+template <typename func_t, typename vec_func_t>
+void cpu_serial_kernel_vec(TensorIteratorBase& iter, func_t&& op, vec_func_t&& vop) {
+  cpu_serial_kernel_vec(iter, op, vop, {0, iter.numel()});
+}
+
+}}}  // namespace at::native::<anonymous>

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/MaxUnpoolKernel.h

@@ -0,0 +1,14 @@
+#pragma once
+#include <ATen/native/DispatchStub.h>
+
+namespace at {
+class Tensor;
+
+namespace native {
+
+using max_unpooling_fn = void(*)(Tensor&, const Tensor&, const Tensor&);
+
+DECLARE_DISPATCH(max_unpooling_fn, max_unpool2d_kernel);
+DECLARE_DISPATCH(max_unpooling_fn, max_unpool3d_kernel);
+
+}} // at::native

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/PixelShuffleKernel.h

@@ -0,0 +1,14 @@
+#pragma once
+#include <ATen/native/DispatchStub.h>
+
+namespace at {
+class TensorBase;
+}
+
+namespace at { namespace native {
+
+using pixel_shuffle_fn = void(*)(TensorBase&, const TensorBase&, int64_t);
+DECLARE_DISPATCH(pixel_shuffle_fn, pixel_shuffle_kernel);
+DECLARE_DISPATCH(pixel_shuffle_fn, pixel_unshuffle_kernel);
+
+}} // at::native

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/Reduce.h

@@ -0,0 +1,314 @@
+#pragma once
+
+#include <ATen/native/cpu/Loops.h>
+#include <ATen/Parallel.h>
+#include <c10/util/TypeList.h>
+#include <c10/core/Scalar.h>
+#include <c10/util/irange.h>
+
+#include <sstream>
+#include <type_traits>
+
+namespace at { namespace native { inline namespace CPU_CAPABILITY {
+
+using namespace vec;
+
+#define VEC_LOOP_HEADER(func_t, data) \
+  using scalar_t = typename function_traits<func_t>::result_type; \
+  using Vec = Vectorized<scalar_t>; \
+  char* out_ptr = data[0]; \
+  (void) out_ptr;
+
+// reduction that is contiguous over the input in dim 0
+template <typename traits>
+static inline bool is_contiguous_reduction(const int64_t* strides) {
+  return strides[0] == 0 &&
+         strides[1] == sizeof(typename traits::arg2_t);
+}
+
+// reduction that is contiguous over the input in dim 1
+template <typename traits>
+static inline bool is_outer_reduction(const int64_t* strides) {
+  return strides[0] == 0 &&
+         strides[2] == sizeof(typename traits::result_type) &&
+         strides[3] == sizeof(typename traits::arg2_t);
+}
+
+template <typename func_t, typename vec_func_t>
+static inline void vectorized_reduction(char** data, int64_t n, int64_t stride,
+                                        func_t op, vec_func_t vop, bool reduce) {
+  VEC_LOOP_HEADER(func_t, data)
+  const char* in1_ptr = data[1];
+  Vec acc[4];
+  for (const auto j : c10::irange(4)) {
+    acc[j] = Vec::loadu(in1_ptr + j * Vec::size() * sizeof(scalar_t));
+  }
+  for (const auto i : c10::irange(1, n)) {
+    const char* ptr = in1_ptr + stride * i;
+    acc[0] = vop(acc[0], Vec::loadu(ptr + (0 * Vec::size() * sizeof(scalar_t))));
+    acc[1] = vop(acc[1], Vec::loadu(ptr + (1 * Vec::size() * sizeof(scalar_t))));
+    acc[2] = vop(acc[2], Vec::loadu(ptr + (2 * Vec::size() * sizeof(scalar_t))));
+    acc[3] = vop(acc[3], Vec::loadu(ptr + (3 * Vec::size() * sizeof(scalar_t))));
+  }
+  if (reduce) {
+    scalar_t buffer[Vec::size()];
+    acc[0] = vop(vop(acc[0], acc[1]), vop(acc[2], acc[3]));
+    acc[0].store(buffer);
+    for (const auto j : c10::irange(1, Vec::size())) {
+      buffer[0] = op(buffer[0], buffer[j]);
+    }
+    auto dst = (scalar_t*)out_ptr;
+    *dst = op(*dst, buffer[0]);
+  } else {
+    for (const auto j : c10::irange(4)) {
+      auto dst = out_ptr + j * Vec::size() * sizeof(scalar_t);
+      acc[j] = vop(acc[j], Vec::loadu(dst));
+      acc[j].store(dst);
+    }
+  }
+}
+
+template <typename F>
+static inline void UNARY_OUTER_LOOP(char* data[2], const int64_t strides[2], int64_t n, F f) {
+  for (const auto j C10_UNUSED : c10::irange(n)) {
+    f();
+    data[0] += strides[0];
+    data[1] += strides[1];
+  }
+}
+
+// computes the reduction out = op(out, in)
+template <typename func_t, typename vec_func_t>
+static inline void vectorized_inner_reduction(char** data, int64_t n, func_t op, vec_func_t vop) {
+  VEC_LOOP_HEADER(func_t, data)
+  int64_t vector_stride = 4 * Vec::size() * sizeof(scalar_t);
+  int64_t count = n / (4 * Vec::size());
+  if (count > 0) {
+    vectorized_reduction(data, count, vector_stride, op, vop, /*reduce=*/true);
+  }
+  char* ptrs[3] = { data[0], data[0], data[1] };
+  int64_t strides[] = { 0, 0, sizeof(scalar_t) };
+  basic_loop(ptrs, strides, count * 4 * Vec::size(), n, op);
+}
+
+// computes the reduction out = op(out, in)
+template <typename func_t, typename vec_func_t>
+static inline void vectorized_outer_reduction(char** data, int64_t inner_stride, int64_t size0, int64_t size1, func_t op, vec_func_t vop) {
+  VEC_LOOP_HEADER(func_t, data)
+
+  // reduce down each column of 4 * Vec::size() elements (128 or 256 bytes)
+#if defined(CPU_CAPABILITY_AVX512)
+  int64_t outer_stride[2] = { 256, 256 };
+#else
+  int64_t outer_stride[2] = { 128, 128 };
+#endif
+  UNARY_OUTER_LOOP(data, outer_stride, size1 / (4 * Vec::size()), [&] {
+    vectorized_reduction(data, size0, inner_stride, op, vop, /*reduce=*/false);
+  });
+
+  // reduce down the remaining columns
+  int64_t step[] = { sizeof(scalar_t), sizeof(scalar_t) };
+  int64_t remaining = size1 % (4 * Vec::size());
+  UNARY_OUTER_LOOP(data, step, remaining, [&] {
+    char* ptrs[3] = { data[0], data[0], data[1] };
+    int64_t strides[] = { 0, 0, inner_stride };
+    basic_loop(ptrs, strides, 0, size0, op);
+  });
+}
+
+template<typename traits, typename res_t>
+static void set_result(const int index, const res_t result, const TensorIteratorBase &iter, const int num_outputs) {
+  // static_assert(std::is_same<res_t, typename traits::arg2_t>::value, "data types must match");
+  if (index < num_outputs) {
+    char *out = (char *) iter.data_ptr(index);
+    *(res_t *) out = result;
+  }
+}
+
+template<typename traits, typename res_t>
+static void set_results(const res_t result, const TensorIteratorBase &iter, const int num_outputs) {
+  AT_ASSERT(num_outputs == 1);
+  set_result<traits>(0, result, iter, num_outputs);
+}
+
+template<typename traits, std::size_t i = 0, typename... tuple_t>
+static inline typename std::enable_if<i == sizeof...(tuple_t), std::size_t>::type
+for_each_in_tuple(const std::tuple<tuple_t...>& /*t*/, const TensorIteratorBase& /*iter*/, const int /*num_outputs*/) {
+  return i;
+}
+
+template<typename traits, std::size_t i = 0, typename... tuple_t>
+static inline typename std::enable_if<i < sizeof...(tuple_t), std::size_t>::type
+for_each_in_tuple(const std::tuple<tuple_t...>& t, const TensorIteratorBase &iter, const int num_outputs) {
+  if (i < (size_t)num_outputs) {
+    set_result<traits>(i, std::get<i>(t), iter, num_outputs);
+    return for_each_in_tuple<traits, i + 1, tuple_t...>(t, iter, num_outputs);
+  }
+  return i;
+}
+
+template<typename traits, typename... res_t>
+static void set_results(const std::tuple<res_t...>& result, const TensorIteratorBase &iter, const int num_outputs) {
+  AT_ASSERT(num_outputs >= 1);
+  std::size_t result_size = for_each_in_tuple<traits>(result, iter, num_outputs);
+  AT_ASSERT((size_t)num_outputs == result_size);
+}
+
+template <typename T, typename... Args>
+struct all_same : std::conjunction<
+  std::is_same<T, Args>...
+> {};
+
+// data_t is the input/output data type.
+// acc_t is a type that contains all the necessary data
+// to continue reducing.
+// index_t is a one-dimensional index
+//
+// ops_t is such that &ops_t::reduce, &ops_t::combine, and &ops_t::project exist and satisfy
+// the following.
+// reduce: (acc_t, data_t, index_t) -> acc_t adds one data point to the accumulated value.
+// combine: (acc_t, acc_t) -> acc_t combines two accumulated values into one.
+// project: acc_t -> out_t finishes the reduction, getting the required output.
+//
+// Additionally, acc_t must be default-constructible:
+// acc_t {} is an identity for combine,
+// and project(acc_t {}) is the value of the operation on zero elements.
+//
+// The point of `combine` is to support parallelization -
+// the idea is to one sequence of `reduce` calls per thread of execution,
+// and then to combine them at the end with `combine`.
+//
+// If there is more than one output element,
+// our parallelization strategy is to use one thread for each of them,
+// which means that `combine` will never be called.
+//
+// If, on the other hand, there is only one, then we split the input into
+// into several pieces, reduce each separately, and then combine them.
+
+template <typename ops_t, typename init_t>
+void binary_kernel_reduce(TensorIteratorBase& iter, ops_t ops, init_t init) {
+  using rf_t = decltype(&ops_t::reduce);
+  using cf_t = decltype(&ops_t::combine);
+  using pf_t = decltype(&ops_t::project);
+  using r_traits = binary_function_traits<rf_t>;
+  using c_traits = binary_function_traits<cf_t>;
+  using p_traits = unary_function_traits<pf_t>;
+  using acc_t = typename p_traits::arg1_t;
+  using data_t = typename r_traits::arg2_t;
+  static_assert(
+    all_same<
+      acc_t,
+      init_t,
+      typename r_traits::arg1_t,
+      typename r_traits::result_type,
+      typename c_traits::arg1_t,
+      typename c_traits::arg2_t,
+      typename c_traits::result_type>::value,
+    "all accumulate types must match");
+  static_assert(
+    std::is_default_constructible<acc_t>::value,
+    "the accumulate type must be default-constructible"
+  );
+  const int num_outputs = iter.noutputs();
+  iter.foreach_reduced_elt([&ops, &init, num_outputs](TensorIteratorBase &sub_iter) {
+    auto reduction_body = [&ops, &sub_iter, num_outputs](acc_t acc, int64_t begin, int64_t end) -> acc_t {
+      int ntensors = sub_iter.ntensors();
+      sub_iter.serial_for_each([&acc, &ops, num_outputs, ntensors, begin](char** data, const int64_t* strides, int64_t size) {
+        AT_ASSERT(ntensors - num_outputs == 1);
+        char *in = data[ntensors - 1];
+        int64_t stride = strides[ntensors - 1];
+        for (const auto i : c10::irange(size)) {
+          acc = ops.reduce(acc, c10::load<data_t>(in), begin + i);
+          in += stride;
+        }
+      }, {begin, end});
+      return ops.translate_idx(acc, sub_iter.view_offsets()[0]);
+    };
+    acc_t total_acc = init;
+    auto numel = sub_iter.numel();
+    if (numel < at::internal::GRAIN_SIZE || at::get_num_threads() == 1 ||
+        at::in_parallel_region()) {
+      total_acc = reduction_body(total_acc, 0, numel);
+    } else {
+      int max_threads = at::get_num_threads();
+      AT_ASSERT(max_threads > 0);
+      static_assert(
+        !std::is_same<acc_t, bool>::value,
+        "Concurrently modifying different references into std::vector<bool> is UB."
+      );
+      std::vector<acc_t> buffer((unsigned)max_threads, init);
+      at::parallel_for(0, numel, internal::GRAIN_SIZE,
+        [&](int64_t begin, int64_t end) {
+          auto& acc = buffer[at::get_thread_num()];
+          acc = reduction_body(acc, begin, end);
+        }
+      );
+      for (const auto i : c10::irange(max_threads)) {
+        total_acc = ops.combine(total_acc, buffer[i]);
+      }
+    }
+    set_results<r_traits>(ops.project(total_acc), sub_iter, num_outputs);
+  });
+}
+
+template <typename func_t, typename vec_func_t>
+void binary_kernel_reduce_vec(TensorIteratorBase& iter, func_t op, vec_func_t vop, double ident = 0) {
+  using traits = binary_function_traits<func_t>;
+  static_assert(
+    all_same<
+      typename traits::result_type,
+      typename traits::arg1_t,
+      typename traits::arg2_t>::value,
+    "all types must match");
+
+  iter.output_base().fill_(ident);
+  iter.parallel_reduce([&](char** data, const int64_t* strides, int64_t size0, int64_t size1) {
+    int64_t outer_strides[] = { strides[2], strides[3] };
+    if (is_contiguous_reduction<traits>(strides)) {
+      // input is contiguous in dim 0, output is reduced in dim 0
+      UNARY_OUTER_LOOP(data, outer_strides, size1, [&] {
+        vectorized_inner_reduction(data, size0, op, vop);
+      });
+    } else if (is_outer_reduction<traits>(strides)) {
+      // input and output are contiguous in dim 1
+      int64_t inner_stride = strides[1]; // stride of input in dim 0
+      vectorized_outer_reduction(data, inner_stride, size0, size1, op, vop);
+    } else {
+      UNARY_OUTER_LOOP(data, outer_strides, size1, [&] {
+        char* ptrs[3] = { data[0], data[0], data[1] };
+        int64_t inner_strides[3] = { strides[0], strides[0], strides[1] };
+        basic_loop(ptrs, inner_strides, 0, size0, op);
+      });
+    }
+  });
+}
+
+// when reduction is on most inner dimension (dim 0 in TensorIterator)
+// and input has contiguous most inner dimension, `binary_kernel_reduce_lastdim`
+// can be used.
+static inline bool is_reduce_lastdim(TensorIteratorBase& iter) {
+  return iter.num_reduce_dims() == 1 && iter.is_dim_reduced(0)
+      && iter.ninputs() == 1 && iter.strides(1)[0] == iter.element_size(1);
+}
+
+template <typename reduce_func_t>
+void binary_kernel_reduce_lastdim(TensorIteratorBase& iter, reduce_func_t reduce_op) {
+  auto shape = iter.shape();
+  int64_t dim_size = shape[0];
+  int64_t grain_size = std::max((int64_t) 1, at::internal::GRAIN_SIZE / dim_size);
+  TensorIterator sub_iter(iter);
+  // create sub iterator to parallel on all non-reduce-dims
+  sub_iter.narrow(0, 0, 1);
+  auto loop = [&](char** data, const int64_t* strides, int64_t size) {
+    char* out = data[0];
+    char* in = data[1];
+    for (int64_t i = 0; i < size; ++i) {
+      reduce_op(out, in, dim_size);
+      out += strides[0];
+      in += strides[1];
+    }
+  };
+  sub_iter.for_each(loop, grain_size);
+}
+
+}}}  // namespace at::native::<anonymous>

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/ReduceUtils.h

@@ -0,0 +1,238 @@
+#pragma once
+
+#include <ATen/Parallel.h>
+#include <ATen/NumericUtils.h>
+#include <ATen/cpu/vec/vec.h>
+#include <ATen/cpu/vec/functional.h>
+#include <ATen/native/ReductionType.h>
+#include <c10/util/irange.h>
+#include <ATen/OpMathType.h>
+#include <ATen/native/cpu/utils.h>
+#include <ATen/OpMathType.h>
+
+namespace at::native {
+inline namespace CPU_CAPABILITY {
+
+using namespace vec;
+
+#define AT_DISPATCH_REDUCTION_TYPES(op, ...)                                   \
+  [&] {                                                                        \
+    switch (op) {                                                              \
+      case ReductionType::SUM: {                                               \
+        static constexpr auto reduce = ReductionType::SUM;                     \
+        return __VA_ARGS__();                                                  \
+      }                                                                        \
+      case ReductionType::MEAN: {                                              \
+        static constexpr auto reduce = ReductionType::MEAN;                    \
+        return __VA_ARGS__();                                                  \
+      }                                                                        \
+      case ReductionType::MIN: {                                               \
+        static constexpr auto reduce = ReductionType::MIN;                     \
+        return __VA_ARGS__();                                                  \
+      }                                                                        \
+      case ReductionType::MAX: {                                               \
+        static constexpr auto reduce = ReductionType::MAX;                     \
+        return __VA_ARGS__();                                                  \
+      }                                                                        \
+      case ReductionType::PROD: {                                              \
+        static constexpr auto reduce = ReductionType::PROD;                    \
+        return __VA_ARGS__();                                                  \
+      }                                                                        \
+    }                                                                          \
+  }()
+
+template <typename scalar_t, ReductionType reduce>
+inline vec_scalar_t<scalar_t> init_value() {
+  using acc_t = vec_scalar_t<scalar_t>;
+  acc_t val;
+  if (reduce == ReductionType::SUM ||
+      reduce == ReductionType::MEAN) {
+    val = static_cast<acc_t>(0);
+  } else if (reduce == ReductionType::PROD) {
+    val = static_cast<acc_t>(1);
+  } else if (reduce == ReductionType::MAX) {
+    val = -std::numeric_limits<acc_t>::infinity();
+  } else {
+    TORCH_INTERNAL_ASSERT(reduce == ReductionType::MIN);
+    val = std::numeric_limits<acc_t>::infinity();
+  }
+  return val;
+}
+
+template <typename scalar_t, ReductionType reduce>
+inline vec_scalar_t<scalar_t> init_value(const c10::optional<Scalar>& initial) {
+  using acc_t = vec_scalar_t<scalar_t>;
+  if (initial.has_value()) {
+    return initial.value().to<acc_t>();
+  } else {
+    return init_value<scalar_t, reduce>();
+  }
+}
+
+template <typename scalar_t>
+inline void init(scalar_t* out, int64_t size, const vec_scalar_t<scalar_t>& val) {
+  using Vec = Vectorized<vec_scalar_t<scalar_t>>;
+  map<scalar_t>(
+      [val](Vec x) { return Vec(val); },
+      out,
+      out,
+      size);
+}
+
+template <typename scalar_t, ReductionType reduce>
+inline void init(scalar_t* out, int64_t size, const c10::optional<Scalar>& initial) {
+  using acc_t = vec_scalar_t<scalar_t>;
+  acc_t val = init_value<scalar_t, reduce>(initial);
+  init(out, size, val);
+}
+
+// overload with `include_self`, used by scatter_reduce
+template <typename scalar_t, ReductionType reduce>
+inline void init(scalar_t* out, int64_t size, bool include_self = false) {
+  using acc_t = vec_scalar_t<scalar_t>;
+  if (!include_self) {
+    acc_t val = init_value<scalar_t, reduce>();
+    init(out, size, val);
+  }
+}
+
+template <typename scalar_t, ReductionType reduce>
+inline void _init(scalar_t* self_ptr, at::opmath_type<scalar_t>* buffer_ptr, int64_t size, bool include_self) {
+  if (!include_self) {
+    init<at::opmath_type<scalar_t>, reduce>(buffer_ptr, size, include_self);
+  } else {
+    vec::convert(self_ptr, buffer_ptr, size);
+  }
+}
+
+template <typename scalar_t>
+inline typename std::enable_if<!std::is_same<scalar_t, Vec2>::value, scalar_t>::type
+_max(const scalar_t& x, const scalar_t& y) {
+  return at::_isnan(y) ? y : std::max(x, y);
+}
+
+template <typename scalar_t>
+inline Vectorized<scalar_t> _max(const Vectorized<scalar_t>& x, const Vectorized<scalar_t>& y) {
+  // vec::maximum propagates NaN
+  return vec::maximum(x, y);
+}
+
+template <typename vec_t>
+inline typename std::enable_if<std::is_same<vec_t, Vec2>::value, Vec2>::type
+_max(const vec_t& x, const vec_t& y) {
+  // vec::maximum propagates NaN
+  return maximum(x, y);
+}
+
+template <typename scalar_t>
+inline typename std::enable_if<!std::is_same<scalar_t, Vec2>::value, scalar_t>::type
+_min(const scalar_t& x, const scalar_t& y) {
+  return at::_isnan(y) ? y : std::min(x, y);
+}
+
+template <typename scalar_t>
+inline Vectorized<scalar_t> _min(const Vectorized<scalar_t>& x, const Vectorized<scalar_t>& y) {
+  // vec::minimum propagates NaN
+  return vec::minimum(x, y);
+}
+
+template <typename vec_t>
+inline typename std::enable_if<std::is_same<vec_t, Vec2>::value, Vec2>::type
+_min(const vec_t& x, const vec_t& y) {
+  // vec::minimum propagates NaN
+  return minimum(x, y);
+}
+
+template <typename scalar_t, typename accumut, typename Op,
+          typename std::enable_if_t<is_reduced_floating_point_v<scalar_t>, int> = 0>
+inline void map_acc(
+    const Op& vec_fun,
+    accumut* output_data,
+    const accumut* input_data,
+    const scalar_t* input_data2,
+    int64_t size) {
+  using Vec = vec::Vectorized<scalar_t>;
+  using aVec = vec::Vectorized<accumut>;
+  int64_t d = 0;
+  constexpr int64_t kVecSize = Vec::size();
+  constexpr int64_t kaVecSize = aVec::size();
+  for (d = 0; d < size - (size % kVecSize); d += kVecSize) {
+    Vec data2_vec = Vec::loadu(input_data2 + d);
+    auto [data2_avec0, data2_avec1] = convert_to_float<scalar_t>(data2_vec);
+    aVec input_vec0 = aVec::loadu(input_data + d);
+    aVec input_vec1 = aVec::loadu(input_data + d + kaVecSize);
+    vec_fun(input_vec0, data2_avec0).store(output_data + d);
+    vec_fun(input_vec1, data2_avec1).store(output_data + d + kaVecSize);
+  }
+  if (size - d > 0) {
+    int64_t tail_size = size - d;
+    Vec data2_vec = Vec::loadu(input_data2 + d, tail_size);
+    auto [data2_avec0, data2_avec1] = convert_to_float<scalar_t>(data2_vec);
+    if (tail_size > kaVecSize) {
+      aVec input_vec0 = aVec::loadu(input_data + d);
+      aVec input_vec1 = aVec::loadu(input_data + d + kaVecSize, tail_size - kaVecSize);
+      vec_fun(input_vec0, data2_avec0).store(output_data + d);
+      vec_fun(input_vec1, data2_avec1).store(output_data + d + kaVecSize, tail_size - kaVecSize);
+    } else {
+      aVec input_vec0 = aVec::loadu(input_data + d, tail_size);
+      vec_fun(input_vec0, data2_avec0).store(output_data + d, tail_size);
+    }
+  }
+}
+
+// for Max and Min, propagate NaN:
+template <typename T, ReductionType reduce>
+inline T update(const T& x, const T& y) {
+  if (reduce == ReductionType::SUM ||
+      reduce == ReductionType::MEAN) {
+    return x + y;
+  } else if (reduce == ReductionType::PROD) {
+    return x * y;
+  } else if (reduce == ReductionType::MAX) {
+    return _max(x, y);
+  } else {
+    TORCH_INTERNAL_ASSERT(reduce == ReductionType::MIN);
+    return _min(x, y);
+  }
+}
+
+template <typename scalar_t, ReductionType reduce>
+inline void update(scalar_t* out, const scalar_t* data, int64_t K) {
+  using Vec = vec::Vectorized<vec_scalar_t<scalar_t>>;
+  map2<scalar_t>(
+      [](Vec x, Vec y) { return update<Vec, reduce>(x, y); },
+      out,
+      out,
+      data,
+      K);
+}
+
+template <typename scalar_t, ReductionType reduce,
+          typename std::enable_if_t<is_reduced_floating_point_v<scalar_t>, int> = 0>
+inline void update(at::opmath_type<scalar_t>* out, const scalar_t* data, int64_t K) {
+  using opmath_t = at::opmath_type<scalar_t>;
+  using Vec = vec::Vectorized<opmath_t>;
+  map_acc<scalar_t, opmath_t>(
+      [](Vec x, Vec y) { return update<Vec, reduce>(x, y); },
+      out,
+      out,
+      data,
+      K);
+}
+
+template <typename scalar_t, ReductionType reduce>
+inline void write(scalar_t* out, int64_t count, int64_t K) {
+  using Vec = vec::Vectorized<vec_scalar_t<scalar_t>>;
+  if (reduce == ReductionType::MEAN) {
+    if (count > 0) {
+      vec::map<scalar_t>(
+          [count](Vec x) { return x / Vec(count); },
+          out,
+          out,
+          K);
+    }
+  }
+}
+
+} // namespace CPU_CAPABILITY
+} // namespace at::native

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/SampledAddmmKernel.h

@@ -0,0 +1,12 @@
+#pragma once
+
+#include <ATen/core/Tensor.h>
+#include <ATen/native/DispatchStub.h>
+
+namespace at { namespace native {
+
+using sampled_addmm_sparse_csr_fn = void(*)(const Tensor&, const Tensor&, const Scalar&, const Scalar&, const Tensor&);
+
+DECLARE_DISPATCH(sampled_addmm_sparse_csr_fn, sampled_addmm_sparse_csr_stub);
+
+}} // at::native

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/SerialStackImpl.h

@@ -0,0 +1,144 @@
+// Copyright 2004-present Facebook. All Rights Reserved.
+#pragma once
+
+#include <ATen/core/Tensor.h>
+
+#include <ATen/MemoryOverlap.h>
+#include <ATen/Parallel.h>
+#include <ATen/TensorIterator.h>
+#include <ATen/cpu/vec/functional.h>
+#include <ATen/cpu/vec/vec.h>
+#include <c10/util/irange.h>
+
+namespace at { namespace native { namespace detail {
+
+struct InputMeta {
+  void* data_ptr;
+  int64_t inner_size;
+
+  InputMeta(const Tensor& t, int64_t dim, int64_t inner)
+      : data_ptr(t.data_ptr()), inner_size(t.sizes()[dim] * inner) {}
+};
+
+// This kernel is used by two TensorList types:
+// 1. stack_serial_kernel uses at::ArrayRef<Tensor>
+// 2. Static runtime calls this kernel directly (csrc/jit/runtime/static/ops.cpp) with
+//    ProcessedNodeInputWrapper.
+// When making changes, make sure that they are compatible with both types!
+template <typename scalar_t, typename TensorListType>
+void stack_serial_kernel_impl(Tensor& result, TensorListType tensors, int64_t dim) {
+  TORCH_INTERNAL_ASSERT_DEBUG_ONLY(
+      dim >= 0 && dim <= result.dim(),
+      "dim out of range in stack_serial_kernel_impl");
+  int64_t outer =
+      result.numel() / (result.sizes()[dim] * result.strides()[dim]);
+  scalar_t* result_data = result.data_ptr<scalar_t>();
+  int64_t ninputs = tensors.size();
+  std::vector<InputMeta> inputs;
+  inputs.reserve(ninputs);
+  for (const auto& tensor : tensors) {
+    inputs.emplace_back(tensor, dim, tensor.strides()[dim]);
+  }
+
+  using Vec = vec::Vectorized<scalar_t>;
+  scalar_t* result_ptr = result_data;
+  for (const auto i : c10::irange(outer)) {
+    for (const auto j : c10::irange(ninputs)) {
+      int64_t local_inner = inputs[j].inner_size;
+      scalar_t* input_ptr = (scalar_t*)(inputs[j].data_ptr) + i * local_inner;
+
+      if (local_inner < Vec::size()) {
+        for (const auto k : c10::irange(local_inner)) {
+          result_ptr[k] = input_ptr[k];
+        }
+      } else {
+        vec::map(
+            [](Vec x) { return x; }, result_ptr, input_ptr, local_inner);
+      }
+      result_ptr += local_inner;
+    }
+  }
+}
+
+// Checks to see whether native stack can be invoked under these conditions:
+// - result and input tensors are contiguous
+// - only one thread is used
+// - no type promotion has to occur
+// - tensors dtype is Double or Float
+template <typename TensorListType>
+bool can_use_native_serial_stack_impl(Tensor& result, TensorListType tensors, int64_t dim) {
+  TORCH_CHECK(tensors.size() > 0, "expected a non-empty list of Tensors");
+  const Tensor& first_tensor = tensors[0];
+  // stack dimension should be in range [0,firstTensor.dim())
+  // dim == firstTensor.dim() is a valid input, but it is handled by default code path
+  // that uses unsqueeze
+  if (dim >= first_tensor.dim()) return false;
+  // Native stack doesn't apply any tensor is skipped.
+  if (first_tensor.numel() == 0 && first_tensor.dim() == 1) return false;
+  // there should be no type promotion
+  if (result.dtype() != first_tensor.dtype()) return false;
+
+  auto first_tensor_mem_format = first_tensor.suggest_memory_format();
+  ScalarType dtype = first_tensor.scalar_type();
+
+  if (!result.is_contiguous(first_tensor_mem_format)) {
+    return false;
+  }
+
+  // fast path only works for Double and Float
+  if (dtype != ScalarType::Double && dtype != ScalarType::Float) {
+    return false;
+  }
+
+  // check remainder of inputs
+  auto const &first_tensor_shape = first_tensor.sizes();
+  for (const auto i : c10::irange(1, tensors.size())) {
+    auto const &tensor = tensors[i];
+    TORCH_CHECK(tensors[i].sizes() == first_tensor.sizes(),
+      "stack expects each tensor to be equal size, but got ", first_tensor_shape,
+      " at entry 0 and ", tensor.sizes(), " at entry ", i);
+
+    // every tensor must be contiguous
+    // tensor sizes and strides must be the same
+    // there should be no type promotion
+    if (!tensor.is_contiguous(first_tensor_mem_format) ||
+      tensor.strides() != first_tensor.strides() ||
+      tensor.dtype() != dtype) {
+      return false;
+    }
+  }
+
+  // fast native stack should only be used when it is not worth using multiple threads
+  // or there is only one thread. Note that we aren't checking result.numel() here because
+  // it may not have been resized and we want to defer that cost till later.
+  int64_t numel_in_stack = first_tensor.numel() * tensors.size();
+  return numel_in_stack < at::internal::GRAIN_SIZE || at::get_num_threads() == 1;
+}
+
+template <typename TensorListType, bool should_skip_overlap_check>
+struct CanUseNativeSerialStack;
+
+template <typename TensorListType>
+struct CanUseNativeSerialStack<TensorListType, false> {
+  static bool call(Tensor& result, TensorListType tensors, int64_t dim) {
+    // Inputs cannot alias the output tensor
+    for (const auto i : c10::irange(tensors.size())) {
+      auto lap = at::get_overlap_status(result, tensors[i]);
+      TORCH_CHECK(lap != at::MemOverlapStatus::Partial &&
+          lap != at::MemOverlapStatus::Full, 0,
+          "unsupported operation: the input tensors cannot refer to any of the "
+          "output memory locations. Found overlap in input tensor ", i);
+    }
+
+    return can_use_native_serial_stack_impl(result, tensors, dim);
+  }
+};
+
+template <typename TensorListType>
+struct CanUseNativeSerialStack<TensorListType, true> {
+  static bool call(Tensor& result, TensorListType tensors, int64_t dim) {
+    return can_use_native_serial_stack_impl(result, tensors, dim);
+  }
+};
+
+}}}  // namespace at::native::detail

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/SoftmaxKernel.h

@@ -0,0 +1,28 @@
+#pragma once
+
+#include <ATen/native/DispatchStub.h>
+#include <cstdint>
+
+namespace at {
+class Tensor;
+
+namespace native {
+
+using forward_fn = void (*)(const Tensor&, const Tensor&);
+using backward_fn = void(*)(const Tensor &, const Tensor &, const Tensor&);
+
+DECLARE_DISPATCH(forward_fn, softmax_lastdim_kernel);
+DECLARE_DISPATCH(forward_fn, log_softmax_lastdim_kernel);
+DECLARE_DISPATCH(backward_fn, softmax_backward_lastdim_kernel);
+DECLARE_DISPATCH(backward_fn, log_softmax_backward_lastdim_kernel);
+
+using forward_fn_with_dim = void(*)(const Tensor &, const Tensor &, const int64_t);
+using backward_fn_with_dim =
+    void (*)(const Tensor&, const Tensor&, const Tensor&, const int64_t);
+
+DECLARE_DISPATCH(forward_fn_with_dim, softmax_kernel);
+DECLARE_DISPATCH(forward_fn_with_dim, log_softmax_kernel);
+DECLARE_DISPATCH(backward_fn_with_dim, softmax_backward_kernel);
+DECLARE_DISPATCH(backward_fn_with_dim, log_softmax_backward_kernel);
+}
+}

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/SpmmReduceKernel.h

@@ -0,0 +1,22 @@
+#pragma once
+
+#include <ATen/core/Tensor.h>
+#include <ATen/native/DispatchStub.h>
+#include <ATen/native/ReductionType.h>
+
+namespace at::native {
+
+using spmm_reduce_fn = void(*)(const Tensor&, const Tensor&, const Tensor&, const Tensor&, const Tensor&, ReductionType op);
+using spmm_reduce_arg_fn = void(*)(const Tensor&, const Tensor&, const Tensor&, const Tensor&, const Tensor&, const Tensor&, ReductionType op);
+using spmm_reduce_backward_input_fn = void(*)(const Tensor&, const Tensor&, const Tensor&, const Tensor&, const Tensor&, const Tensor&, ReductionType op);
+using spmm_reduce_backward_input_arg_fn = void(*)(const Tensor&, const Tensor&, const Tensor&, const Tensor&, const Tensor&, ReductionType op);
+using spmm_reduce_backward_other_fn = void(*)(const Tensor&, const Tensor&, const Tensor&, const Tensor&, const Tensor&, const Tensor&, const Tensor&, ReductionType op);
+
+DECLARE_DISPATCH(spmm_reduce_fn, spmm_reduce_stub);
+DECLARE_DISPATCH(spmm_reduce_arg_fn, spmm_reduce_arg_stub);
+DECLARE_DISPATCH(spmm_reduce_backward_input_fn, spmm_reduce_backward_input_stub);
+DECLARE_DISPATCH(spmm_reduce_backward_input_arg_fn, spmm_reduce_backward_input_arg_stub);
+DECLARE_DISPATCH(spmm_reduce_backward_other_fn, spmm_reduce_backward_other_stub);
+DECLARE_DISPATCH(spmm_reduce_backward_input_arg_fn, spmm_reduce_backward_other_arg_stub);
+
+} // at::native

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/StackKernel.h

@@ -0,0 +1,12 @@
+// Copyright 2004-present Facebook. All Rights Reserved.
+#pragma once
+
+#include <ATen/core/Tensor.h>
+#include <ATen/native/DispatchStub.h>
+
+namespace at { namespace native {
+
+using stack_serial_fn = void(*)(Tensor &, TensorList, int64_t);
+DECLARE_DISPATCH(stack_serial_fn, stack_serial_stub);
+
+}}  // namespace at::native

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/UpSampleKernelAVXAntialias.h

@@ -0,0 +1,1376 @@
+/*
+The Python Imaging Library (PIL) is
+
+    Copyright © 1997-2011 by Secret Labs AB
+    Copyright © 1995-2011 by Fredrik Lundh
+
+Pillow is the friendly PIL fork. It is
+
+    Copyright © 2010-2022 by Alex Clark and contributors
+
+Like PIL, Pillow is licensed under the open source HPND License
+*/
+
+// This code is heavily inspired from PILLOW-SIMD's implementation:
+// https://github.com/uploadcare/pillow-simd/blob/simd/master/src/libImaging/Resample.c
+
+#pragma once
+#ifdef CPU_CAPABILITY_AVX2
+// TODO: This file only supports AVX2. We could split the AVX kernels into
+// smaller logical blocks in order to port them into the Vec.h logic. This would
+// allow to support other vectorization architectures and perhaps also support
+// the non-vectorized fallback (we'd need to make sure it's not slower than the
+// current fallback).
+
+#include <ATen/core/Tensor.h>
+#include <ATen/cpu/vec/intrinsics.h>
+#include <c10/util/irange.h>
+
+#ifndef AT_PER_OPERATOR_HEADERS
+#include <ATen/Functions.h>
+#else
+#include <ATen/ops/empty.h>
+#endif
+
+
+namespace {
+
+static inline __m128i mm_cvtsi32_si128(const uint8_t* C10_RESTRICT ptr, bool i32_aligned) {
+  int32_t v;
+  if (i32_aligned) {
+    v = *(const int32_t*)ptr;
+  } else {
+    std::memcpy(&v, ptr, 4);
+  }
+  return _mm_cvtsi32_si128(v);
+}
+
+static inline __m128i mm_cvtepu8_epi32(const uint8_t* C10_RESTRICT ptr, bool i32_aligned) {
+  return _mm_cvtepu8_epi32(mm_cvtsi32_si128(ptr, i32_aligned));
+}
+
+static inline void _write_endline_rgb_as_uint32(
+    uint8_t* C10_RESTRICT output,
+    uint32_t data
+) {
+  // data is (R G B X), output is (X1 X2 X3 | R1 B1 G1 R2 ...)
+  // Here we explicitly set X as R1
+  uint8_t* data_ptr = reinterpret_cast<uint8_t*>(&data);
+  data_ptr[3] = output[3];
+  std::memcpy(output, data_ptr, 4);
+}
+
+at::Tensor unpack_rgb(const at::Tensor& packed_tensor) {
+  // Convert a "packed" tensor (typically RGBRGBRGB if channels_last) into
+  // RGBARGBARGBA format where A is hard-coded to 0. Each pixel is encoded
+  // into as 32 bits. This generalizes to num_channels <= 4 and also works for
+  // non-channels_last tensors.
+
+  const uint8_t* packed = (const uint8_t*)packed_tensor.data_ptr<uint8_t>();
+  auto num_pixels = packed_tensor.size(1) * packed_tensor.size(2);
+  auto num_channels = packed_tensor.size(0);
+
+  constexpr int rgba_size = 4;
+  auto unpacked_tensor = at::empty({rgba_size, packed_tensor.size(1), packed_tensor.size(2)}, at::CPU(at::kByte));
+  uint8_t* unpacked = (uint8_t*) unpacked_tensor.data_ptr<uint8_t>();
+
+  auto stride_i = packed_tensor.stride(2);
+  auto stride_j = packed_tensor.stride(0);
+
+  for (const auto i : c10::irange(num_pixels)) {
+    for (const auto j : c10::irange(rgba_size)) {
+      unpacked[rgba_size * i + j] = (j < num_channels) ? packed[stride_i * i + stride_j * j] : 0;
+    }
+  }
+  return unpacked_tensor;
+}
+
+void pack_rgb(
+    const at::Tensor& unpacked_tensor, // IN
+    const at::Tensor& packed_tensor // OUT
+) {
+  // Convert from unpacked channels last 3-channels or 4-channels tensor into original data layout.
+
+  uint8_t* unpacked = (uint8_t*)unpacked_tensor.data_ptr<uint8_t>();
+  uint8_t* packed = (uint8_t*)packed_tensor.data_ptr<uint8_t>();
+  auto num_pixels = packed_tensor.size(1) * packed_tensor.size(2);
+  auto num_channels = packed_tensor.size(0);
+
+  auto unpacked_increment = unpacked_tensor.size(0);
+  auto packed_increment = packed_tensor.stride(2);
+  auto packed_stride = packed_tensor.stride(0);
+
+  TORCH_INTERNAL_ASSERT(unpacked_increment == 3 || unpacked_increment == 4);
+
+  for (const auto i C10_UNUSED : c10::irange(num_pixels)) {
+    for (const auto j : c10::irange(num_channels)) {
+      packed[j * packed_stride] = unpacked[j];
+    }
+    unpacked += unpacked_increment;
+    packed += packed_increment;
+  }
+}
+
+void ImagingResampleHorizontalConvolution8u4x(
+    uint8_t* C10_RESTRICT lineOut0,
+    uint8_t* C10_RESTRICT lineOut1,
+    uint8_t* C10_RESTRICT lineOut2,
+    uint8_t* C10_RESTRICT lineOut3,
+    int64_t out_xsize,
+    const uint8_t* C10_RESTRICT lineIn0,
+    const uint8_t* C10_RESTRICT lineIn1,
+    const uint8_t* C10_RESTRICT lineIn2,
+    const uint8_t* C10_RESTRICT lineIn3,
+    int64_t in_xsize,
+    const int64_t* idx_ptr_xmin,
+    const int64_t* idx_ptr_size,
+    const int16_t* kk,
+    int kmax,
+    unsigned int coefs_precision,
+    int64_t num_channels,
+    bool is_last_line);
+
+void ImagingResampleHorizontalConvolution8u(
+    uint8_t* C10_RESTRICT lineOut,
+    int64_t out_xsize,
+    const uint8_t* C10_RESTRICT lineIn,
+    int64_t in_xsize,
+    const int64_t* idx_ptr_xmin,
+    const int64_t* idx_ptr_size,
+    const int16_t* kk,
+    int kmax,
+    unsigned int coefs_precision,
+    int64_t num_channels,
+    bool is_last_line);
+
+void ImagingResampleVerticalConvolution8u(
+    uint8_t* C10_RESTRICT lineOut,
+    const uint8_t* C10_RESTRICT lineIn,
+    int64_t xsize,
+    int64_t ids_min,
+    int64_t ids_size,
+    const int16_t* k,
+    unsigned int coefs_precision,
+    int64_t num_channels);
+
+template<int num_channels>
+void ImagingResampleHorizontal(
+    const at::Tensor & unpacked_output,
+    const at::Tensor & unpacked_input,
+    int ksize,
+    const std::vector<at::Tensor>& horiz_indices_weights,
+    unsigned int horiz_weights_precision) {
+
+  // Interpolation horizontal pass: we compute x-axis (image width) interpolation outputs.
+
+  // Input data is stored as
+  //   input = [r[0], g[0], b[0], a[0], r[1], g[1], b[1], a[1], r[2], g[2], b[2], a[2], ...]
+  // Weights are float values computed for each output pixel and rescaled to uint16:
+  //   weights[i] = [w[i, 0], w[i, 1], ..., w[i, K-1]]
+  // We want to compute the output as following:
+  //   output = [oR[0], oG[0], oB[0], oA[0], oR[1], oG[1], oB[1], oA[1], ...]
+  // where
+  //   oR[yoffset + i] = r[yoffset + xmin[i]] * w[i, 0] + ... + r[yoffset + xmin[i] + K-1] * w[i, K-1]
+  //   oG[yoffset + i] = g[yoffset + xmin[i]] * w[i, 0] + ... + g[yoffset + xmin[i] + K-1] * w[i, K-1]
+  //   oB[yoffset + i] = b[yoffset + xmin[i]] * w[i, 0] + ... + b[yoffset + xmin[i] + K-1] * w[i, K-1]
+  //
+
+  // TODO: we may want to merge that into the fallback code (currently called
+  // basic_loop_aa_horizontal<uint8_t>)
+  // Although this may not be needed if / when we port all this code to use
+  // Vec.h since this would potentially give us another fall-back implem
+
+  const int16_t* kk = (int16_t*)(horiz_indices_weights[3].data_ptr<double>());
+
+  auto xout = unpacked_output.size(2);
+  auto yout = unpacked_output.size(1);
+  auto xin = unpacked_input.size(2);
+  TORCH_INTERNAL_ASSERT(num_channels == unpacked_input.size(0));
+
+  const int64_t* idx_ptr_xmin = horiz_indices_weights[0].data_ptr<int64_t>();
+  const int64_t* idx_ptr_size = horiz_indices_weights[1].data_ptr<int64_t>();
+
+  uint8_t* unpacked_output_p = unpacked_output.data_ptr<uint8_t>();
+  const uint8_t* unpacked_input_p = unpacked_input.data_ptr<uint8_t>();
+
+  int64_t yy = 0;
+  auto xout_stride = xout * num_channels;
+  auto xin_stride = xin * num_channels;
+  for (; yy < yout - 3; yy += 4) {
+    ImagingResampleHorizontalConvolution8u4x(
+        unpacked_output_p + yy * xout_stride,
+        unpacked_output_p + (yy + 1) * xout_stride,
+        unpacked_output_p + (yy + 2) * xout_stride,
+        unpacked_output_p + (yy + 3) * xout_stride,
+        xout,
+        unpacked_input_p + yy * xin_stride,
+        unpacked_input_p + (yy + 1) * xin_stride,
+        unpacked_input_p + (yy + 2) * xin_stride,
+        unpacked_input_p + (yy + 3) * xin_stride,
+        xin,
+        idx_ptr_xmin,
+        idx_ptr_size,
+        kk,
+        ksize,
+        horiz_weights_precision,
+        num_channels,
+        yy + 3 == yout - 1);
+  }
+  for (; yy < yout; yy++) {
+    ImagingResampleHorizontalConvolution8u(
+        unpacked_output_p + yy * xout_stride,
+        xout,
+        unpacked_input_p + yy * xin_stride,
+        xin,
+        idx_ptr_xmin,
+        idx_ptr_size,
+        kk,
+        ksize,
+        horiz_weights_precision,
+        num_channels,
+        yy == yout - 1);
+  }
+}
+
+void ImagingResampleVertical(
+    const at::Tensor & unpacked_output,
+    const at::Tensor & unpacked_input,
+    int ksize,
+    const std::vector<at::Tensor>& vert_indices_weights,
+    unsigned int vert_weights_precision) {
+
+  // Interpolation vertical pass: we compute y-axis interpolation outputs.
+  // Input data is stored as
+  //   input = [r[0], g[0], b[0], a[0], r[1], g[1], b[1], a[1], r[2], g[2], b[2], a[2], ...]
+  // Weights are float values computed for each output pixel and rescaled to uint16:
+  //   weights[i] = [w[i, 0], w[i, 1], ..., w[i, K-1]]
+  // We want to compute the output as following:
+  //   output = [oR[0], oG[0], oB[0], oA[0], oR[1], oG[1], oB[1], oA[1], ...]
+  // where
+  //   oR[xoffset + i] = r[xoffset + ymin[i]] * w[i, 0] + ... + r[xoffset + ymin[i] + (K-1) * xsize] * w[i, K-1]
+  //   oG[xoffset + i] = g[xoffset + ymin[i]] * w[i, 0] + ... + g[xoffset + ymin[i] + (K-1) * xsize] * w[i, K-1]
+  //   oB[xoffset + i] = b[xoffset + ymin[i]] * w[i, 0] + ... + b[xoffset + ymin[i] + (K-1) * xsize] * w[i, K-1]
+
+  // TODO: we may want to merge that into the fallback code (currently called
+  // basic_loop_aa_vertical<uint8_t>)
+  // Although this may not be needed if / when we port all this code to use
+  // Vec.h since this would potentially give us another fall-back implem
+  const int16_t* kk = (int16_t*)(vert_indices_weights[3].data_ptr<double>());
+
+  const int64_t* idx_ptr_xmin = vert_indices_weights[0].data_ptr<int64_t>();
+  const int64_t* idx_ptr_size = vert_indices_weights[1].data_ptr<int64_t>();
+
+  uint8_t* unpacked_output_p = unpacked_output.data_ptr<uint8_t>();
+  const uint8_t* unpacked_input_p = unpacked_input.data_ptr<uint8_t>();
+
+  auto xout = unpacked_output.size(2);
+  auto yout = unpacked_output.size(1);
+  const auto num_channels = unpacked_input.size(0);
+  TORCH_INTERNAL_ASSERT(num_channels == unpacked_output.size(0));
+
+  auto xout_stride = xout * num_channels;
+  for (const auto yy : c10::irange(yout)) {
+    const auto* k = &kk[yy * ksize];
+    auto ids_min = idx_ptr_xmin[yy];
+    auto ids_size = idx_ptr_size[yy];
+    ImagingResampleVerticalConvolution8u(
+        unpacked_output_p + yy * xout_stride,
+        unpacked_input_p,
+        xout,
+        ids_min,
+        ids_size,
+        k,
+        vert_weights_precision,
+        num_channels);
+  }
+}
+
+// This is the only public entry point in this file.  It supports bilinear or bicubic
+// mode for uint8 dtype when C <= 4, with or without antialias. The
+// implem is based on PIL-SIMD.
+// Its equivalent implementation (fallback) for when AVX isn't supported or when
+// C > 4 is separable_upsample_generic_Nd_kernel_impl()  There are a bunch of
+// future improvement that can be done: look for the TODOs in this file.
+// For details on how the weights are computed and how the multiplications are
+// run on int (instead of float weights), see
+// [ Weights computation for uint8_t and multiplication trick ]
+// For details on how the AVX kernels are implemented, see
+// https://gist.github.com/NicolasHug/47c97d731f05eaad5694c173849b86f5
+// See also [ Support for antialias=False as a subcase of antialias=True ] to
+// learn more about how the antialias=False case is computed. The same holds
+// here: all these kernels are general enough to handle an arbitrary number of
+// weights, but when aa=False they could be optimized further.
+template <typename scale_type, class F>
+void upsample_avx_bilinear_bicubic_uint8(
+    const at::Tensor& input_,
+    const at::Tensor& output,
+    bool align_corners,
+    const scale_type& scales,
+    bool antialias) {
+  auto batch_size = input_.size(0);
+  auto num_channels = input_.size(1);
+  auto xin = input_.size(3);
+  auto yin = input_.size(2);
+  auto xout = output.size(3);
+  auto yout = output.size(2);
+
+  if (xin == xout && yin == yout) {
+    output.copy_(input_);
+    return;
+  }
+
+  at::Tensor input = input_;
+  if (!(input.is_contiguous() || input.is_contiguous(at::MemoryFormat::ChannelsLast))) {
+    // If input is not contiguous with memory format channels first or channels last,
+    // we explicitly convert the input to contiguous channels last memory format.
+    // This simplifies the rest of the code and let us assume that the format is only contiguous channels first or channels last,
+    // Most tensors going through this `if` block won't need to go through unpacking, but those having C < 3 may
+    // have to (this means 2 copies are made). We could avoid the extra copy by handling non-contiguous input
+    // directly within unpack_rgb() and pack_rgb(), but initial attempts showed that this is fairly complex.
+    input = input.contiguous(at::MemoryFormat::ChannelsLast);
+  }
+
+  auto need_horizontal = xout != xin;
+  auto need_vertical = yout != yin;
+
+  int ksize_horiz, ksize_vert;
+  std::vector<at::Tensor> horiz_indices_weights, vert_indices_weights;
+  unsigned int horiz_weights_precision, vert_weights_precision;
+
+  bool skip_unpacking = (num_channels == 3 || num_channels == 4) && input.is_contiguous(at::MemoryFormat::ChannelsLast);
+  bool skip_packing = (num_channels == 3 || num_channels == 4) && output.is_contiguous(at::MemoryFormat::ChannelsLast);
+
+  if (need_horizontal) {
+    int interp_dim = 3;
+    auto stride = (skip_unpacking) ? num_channels : 4;
+    std::tie(horiz_indices_weights, ksize_horiz, horiz_weights_precision) =
+        F::compute_index_ranges_int16_weights(
+            /*input_size=*/xin,
+            /*output_size=*/xout,
+            /*stride=*/stride,
+            /*ndims=*/4,
+            /*reshape_dim=*/interp_dim,
+            /*align_corners=*/align_corners,
+            /*opt_scale=*/scales[interp_dim - 2],
+            /*antialias=*/antialias,
+            /*align_i32=*/true);
+  }
+
+  if (need_vertical) {
+    int interp_dim = 2;
+    auto stride = (skip_unpacking) ? num_channels * xout : 4 * xout;
+    std::tie(vert_indices_weights, ksize_vert, vert_weights_precision) =
+        F::compute_index_ranges_int16_weights(
+            /*input_size=*/yin,
+            /*output_size=*/yout,
+            /*stride=*/stride,
+            /*ndims=*/4,
+            /*reshape_dim=*/interp_dim,
+            /*align_corners=*/align_corners,
+            /*opt_scale=*/scales[interp_dim - 2],
+            /*antialias=*/antialias,
+            /*align_i32=*/true);
+  }
+
+  at::Tensor buffer_horiz, buffer_vert;
+  // Minor optimization: we can avoid allocating an extra buffer if we're performing
+  // horizontal-only or vertical-only interpolation, and if the tensor doesn't
+  // need repacking
+  if (need_horizontal && (need_vertical || !skip_packing)) {
+    auto c = (skip_unpacking) ? num_channels : 4;
+    buffer_horiz = at::empty({c, yin, xout}, input.options());
+  }
+  if (need_vertical && !skip_packing) {
+    auto c = (skip_unpacking) ? num_channels : 4;
+    buffer_vert = at::empty({c, yout, xout}, input.options());
+  }
+
+  for (const auto i : c10::irange(batch_size)) {
+
+    at::Tensor unpacked_input = (skip_unpacking) ? input[i] : unpack_rgb(input[i]);
+    at::Tensor unpacked_output;
+
+    if (need_horizontal) {
+      at::Tensor unpacked_output_temp = (need_vertical || !skip_packing) ? buffer_horiz : output[i];
+
+      if (skip_unpacking && num_channels == 3) {
+        ImagingResampleHorizontal<3>(
+          unpacked_output_temp,
+          unpacked_input,
+          ksize_horiz,
+          horiz_indices_weights,
+          horiz_weights_precision);
+      } else {
+        ImagingResampleHorizontal<4>(
+            unpacked_output_temp,
+            unpacked_input,
+            ksize_horiz,
+            horiz_indices_weights,
+            horiz_weights_precision);
+      }
+      unpacked_output = unpacked_input = unpacked_output_temp;
+    }
+    if (need_vertical) {
+      unpacked_output = (skip_packing) ? output[i] : buffer_vert;
+
+      ImagingResampleVertical(
+          unpacked_output,
+          unpacked_input,
+          ksize_vert,
+          vert_indices_weights,
+          vert_weights_precision
+      );
+    }
+
+    TORCH_INTERNAL_ASSERT(unpacked_output.defined());
+
+    if (!skip_packing) {
+      pack_rgb(unpacked_output, output[i]);
+    }
+  }
+}
+
+void ImagingResampleHorizontalConvolution8u4x(
+    uint8_t* C10_RESTRICT lineOut0,
+    uint8_t* C10_RESTRICT lineOut1,
+    uint8_t* C10_RESTRICT lineOut2,
+    uint8_t* C10_RESTRICT lineOut3,
+    int64_t out_xsize,
+    const uint8_t* C10_RESTRICT lineIn0,
+    const uint8_t* C10_RESTRICT lineIn1,
+    const uint8_t* C10_RESTRICT lineIn2,
+    const uint8_t* C10_RESTRICT lineIn3,
+    int64_t in_xsize,
+    const int64_t* idx_ptr_xmin,
+    const int64_t* idx_ptr_size,
+    const int16_t* kk,
+    int kmax,
+    unsigned int coefs_precision,
+    int64_t num_channels,
+    bool is_last_line) {
+
+  // Interpolation horizontal pass processing together 4 vertical lines.
+  // - Input data format is RGBA or RGB with R,G,B,A being uint8. In case of RGBA
+  //   we can encode 4 values as a single uint32 value.
+  // - We split the size of weight vector for a given output index as a sum:
+  //   ids_size = num_blocks_4 * 4 + num_blocks_2 * 2 + num_blocks_1.
+  // - We load and process 4 weights values in a loop ("block 4") then we process 2 weights values
+  // in another loop ("block 2") and finally we process 1 weights value in the final loop ("block 1").
+
+  // Define shuffling masks (low/high) for num_channels 4 and 3
+  // Mask low casts lower half of each lane to epi16 and reorder RGBARGBA -> RRGGBBAA:
+  //   [r1 g1 b1 a1  r2 g2 b2 a2  ... | R1 G1 B1 A1  R2 G2 B2 A2 ... ] ->
+  //   [r1 0 r2 0  g1 0 g2 0  b1 0 b2 0  a1 0 a2 0 | R1 0 R2 0  G1 0 G2 0  B1 0 B2 0  A1 0 A2 0]
+  // Mask high casts upper half of each lane to epi16 and reorder RGBARGBA -> RRGGBBAA::
+  //   [ ... r3 g3 b3 a3  r4 g4 b4 a4 | ... R3 G3 B3 A3  R4 G4 B4 A4 ] ->
+  //   [r3 0 r4 0  g3 0 g4 0  b3 0 b4 0  a3 0 a4 0 | R3 0 R4 0  G3 0 G4 0  B3 0 B4 0  A3 0 A4 0]
+
+  const auto mask_low_c4 = _mm256_set_epi8(
+      -1, 7, -1, 3, -1, 6, -1, 2, -1, 5, -1, 1, -1, 4, -1, 0,
+      -1, 7, -1, 3, -1, 6, -1, 2, -1, 5, -1, 1, -1, 4, -1, 0);
+  const auto mask_high_c4 = _mm256_set_epi8(
+      -1, 15, -1, 11, -1, 14, -1, 10, -1, 13, -1, 9, -1, 12, -1, 8,
+      -1, 15, -1, 11, -1, 14, -1, 10, -1, 13, -1, 9, -1, 12, -1, 8);
+  const auto mask_low_c3 = _mm256_set_epi8(
+      -1, -1, -1, -1, -1, 5, -1, 2, -1, 4, -1, 1, -1, 3, -1, 0,
+      -1, -1, -1, -1, -1, 5, -1, 2, -1, 4, -1, 1, -1, 3, -1, 0);
+  const auto mask_high_c3 = _mm256_set_epi8(
+      -1, -1, -1, -1, -1, 11, -1, 8, -1, 10, -1, 7, -1, 9, -1, 6,
+      -1, -1, -1, -1, -1, 11, -1, 8, -1, 10, -1, 7, -1, 9, -1, 6);
+
+  const auto mask_low = (num_channels == 3) ? mask_low_c3 : mask_low_c4;
+  const auto mask_high = (num_channels == 3) ? mask_high_c3 : mask_high_c4;
+
+  const auto stride = num_channels * sizeof(uint8_t);
+
+  TORCH_INTERNAL_ASSERT(stride == 3 || stride == 4);
+
+  // out_xsize = output width, out_x = output x index
+  // ids_min is the input offset index corresponding to out_x
+  // ids_size is the interpolation size for out_x
+
+  // Let's precompute ids_size limits for block 4 and block 2.
+  //
+  // In block 4 (4 means we process 4 weight values together), we read input data
+  // with _mm_loadu_si128, i.e. 16 bytes, per one line:
+  // lineIn0 + stride * (i + ids_min) + 16 <= lineIn0 + stride * (ids_size + ids_min)
+  // --> i <= ids_size - 16.0 / stride
+  // Strict boundary:
+  // --> i < ids_size + 1 - int(ceil(16.0 / stride)) = ids_size - b4_delta
+  // Soft boundary for reading inside the buffer except its boundaries:
+  // --> i < ids_size + 1 - int(16.0 / stride) = ids_size - b4_delta_soft
+  // RGBA: b4_delta = b4_delta_soft = 3
+  // RGB : b4_delta = 5
+  // RGB : b4_delta_soft = 4
+  const auto b4_delta = (stride == 4) ? 3 : ((is_last_line) ? 5 : 4);
+
+  // In block 2 (2 means we process 2 weights values together), we read input data
+  // with _mm_loadl_epi64, i.e. 8 bytes, per one line:
+  // lineIn0 + stride * (i + ids_min) + 8 <= lineIn0 + stride * (ids_size + ids_min)
+  // --> i <= ids_size - 8.0 / stride
+  // Strict boundary:
+  // --> i < ids_size + 1 - int(ceil(8.0 / stride)) = ids_size - b2_delta
+  // Soft boundary for reading inside the buffer except its boundaries:
+  // --> i < ids_size + 1 - int(8.0 / stride) = ids_size - b2_delta_soft
+  // RGBA: b2_delta = b2_delta_soft = 1
+  // RGB : b2_delta = 2
+  // RGB : b2_delta_soft = 1
+  const auto b2_delta = (stride == 4) ? 1 : ((is_last_line) ? 2 : 1);
+
+  const auto max_out_x_strided = out_xsize * stride;
+  const auto max_in_x_strided = in_xsize * stride;
+
+  const auto zero = _mm256_setzero_si256();
+  const auto initial = _mm256_set1_epi32(1 << (coefs_precision - 1));
+
+  for (const auto out_x : c10::irange(out_xsize)) {
+    const auto ids_min = idx_ptr_xmin[out_x];
+    const auto ids_size = idx_ptr_size[out_x];
+    const auto * k = &kk[out_x * kmax];
+    int64_t i = 0;
+
+    auto sss0 = initial;
+    auto sss1 = initial;
+
+    const auto * lineIn0_min = lineIn0 + ids_min;
+    const auto * lineIn1_min = lineIn1 + ids_min;
+    const auto * lineIn2_min = lineIn2 + ids_min;
+    const auto * lineIn3_min = lineIn3 + ids_min;
+
+    // block 4
+    for (; i < ids_size - b4_delta; i += 4) {
+      // Load 4 values from weight vector
+      // mmk0 = [wl_0 wh_0 wl_1 wh_1  wl_0 wh_0 wl_1 wh_1  ...]
+      // mmk1 = [wl_2 wh_2 wl_3 wh_3  wl_2 wh_2 wl_3 wh_3  ...]
+      const auto mmk0 = _mm256_set1_epi32(*(int32_t*)&k[i]);
+      const auto mmk1 = _mm256_set1_epi32(*(int32_t*)&k[i + 2]);
+
+      // RGBA: Load 8 pixels (4 per line) from input lines 0 and 1:
+      // source = [
+      //   r0 g0 b0 a0  r1 g1 b1 a1  r2 g2 b2 a2  r3 g3 b3 a3
+      //   R0 G0 B0 A0  R1 G1 B1 A1  R2 G2 B2 A2  R3 G3 B3 A3
+      // ]
+      // RGB: Load 10 pixels (5 per line)
+      // source = [
+      //   r0 g0 b0 r1  g1 b1 r2 g2  b2 r3 g3 b3  r4 g4 b4 r5
+      //   R0 G0 B0 R1  G1 B1 R2 G2  B2 R3 G3 B3  R4 G4 B4 R5
+      // ]
+      auto source = _mm256_inserti128_si256(_mm256_castsi128_si256(
+          _mm_loadu_si128((__m128i *) (lineIn0_min + stride * i))),
+          _mm_loadu_si128((__m128i *) (lineIn1_min + stride * i)), 1);
+
+      // Apply mask_low:
+      // RGBA:
+      //   [r0 0 r1 0  g0 0 g1 0  b0 0 b1 0  a0 0 a1 0 | R0 0 R1 0  G0 0 G1 0  B0 0 B1 0  A0 0 A1 0]
+      // RGB:
+      //   [r0 0 r1 0  g0 0 g1 0  b0 0 b1 0  0 0 0 0 | R0 0 R1 0  G0 0 G1 0  B0 0 B1 0  0 0 0 0]
+      auto pix1 = _mm256_shuffle_epi8(source, mask_low);
+      // Compute output value as C += w0 * C0 + w1 * C1 for each channel in 32-bit precision
+      sss0 = _mm256_add_epi32(sss0, _mm256_madd_epi16(pix1, mmk0));
+
+      // Apply mask_high:
+      // RGBA:
+      //   [r2 0 r3 0  g2 0 g3 0  b2 0 b3 0  a2 0 a3 0 | R2 0 R3 0  G2 0 G3 0  B2 0 B3 0  A2 0 A3 0]
+      // RGB:
+      //   [r2 0 r3 0  g2 0 g3 0  b2 0 b3 0  0 0 0 0 | R2 0 R3 0  G2 0 G3 0  B2 0 B3 0  0 0 0 0]
+      auto pix2 = _mm256_shuffle_epi8(source, mask_high);
+      // Compute output value as C += w2 * C2 + w3 * C3 for each channel in 32-bit precision
+      sss0 = _mm256_add_epi32(sss0, _mm256_madd_epi16(pix2, mmk1));
+
+      // Same as above to next lines 2 and 3:
+      auto source2 = _mm256_inserti128_si256(_mm256_castsi128_si256(
+          _mm_loadu_si128((__m128i *) (lineIn2_min + stride * i))),
+          _mm_loadu_si128((__m128i *) (lineIn3_min + stride * i)), 1);
+      auto pix3 = _mm256_shuffle_epi8(source2, mask_low);
+      sss1 = _mm256_add_epi32(sss1, _mm256_madd_epi16(pix3, mmk0));
+      auto pix4 = _mm256_shuffle_epi8(source2, mask_high);
+      sss1 = _mm256_add_epi32(sss1, _mm256_madd_epi16(pix4, mmk1));
+    }
+
+    // block 2
+    for (; i < ids_size - b2_delta; i += 2) {
+      // Load 2 values from weight vector
+      // mmk = [wl_0 wh_0 wl_1 wh_1  wl_0 wh_0 wl_1 wh_1  ...]
+      const auto mmk = _mm256_set1_epi32(*(int32_t*)&k[i]);
+
+      // Load 4 pixels (2 per line) from input lines 0 and 1:
+      // RGBA: source1 = [
+      //   r0 g0 b0 a0  r1 g1 b1 a1  0 0 0 0  0 0 0 0
+      //   R0 G0 B0 A0  R1 G1 B1 A1  0 0 0 0  0 0 0 0
+      // ]
+      // RGB: source1 = [
+      //   r0 g0 b0 r1  g1 b1 r2  0 0 0 0  0 0 0 0
+      //   R0 G0 B0 R1  G1 B1 R2  0 0 0 0  0 0 0 0
+      // ]
+      auto source1 = _mm256_inserti128_si256(_mm256_castsi128_si256(
+          _mm_loadl_epi64((__m128i *) (lineIn0_min + stride * i))),
+          _mm_loadl_epi64((__m128i *) (lineIn1_min + stride * i)), 1);
+      // Apply mask_low:
+      // RGBA:
+      //   [r0 0 r1 0  g0 0 g1 0  b0 0 b1 0  a0 0 a1 0 | R0 0 R1 0  G0 0 G1 0  B0 0 B1 0  A0 0 A1 0]
+      // RGB:
+      //   [r0 0 r1 0  g0 0 g1 0  b0 0 b1 0  0 0 0 0 | R0 0 R1 0  G0 0 G1 0  B0 0 B1 0  0 0 0 0]
+      auto pix1 = _mm256_shuffle_epi8(source1, mask_low);
+      // Compute output value as C += w0 * C0 + w1 * C1 for each channel in 32-bit precision
+      sss0 = _mm256_add_epi32(sss0, _mm256_madd_epi16(pix1, mmk));
+
+      // Same as above for lines 2 and 3:
+      auto source2 = _mm256_inserti128_si256(_mm256_castsi128_si256(
+          _mm_loadl_epi64((__m128i *) (lineIn2_min + stride * i))),
+          _mm_loadl_epi64((__m128i *) (lineIn3_min + stride * i)), 1);
+      auto pix2 = _mm256_shuffle_epi8(source2, mask_low);
+      sss1 = _mm256_add_epi32(sss1, _mm256_madd_epi16(pix2, mmk));
+    }
+
+    // block 1
+    const auto i32_aligned = num_channels == 4;
+    for (; i < ids_size - 1; i++) {
+      // Load 1 value from weight vector
+      // mmk = [wl_0 wh_0 0 0  wl_0 wh_0 0 0  ...]
+      const auto mmk = _mm256_set1_epi32(k[i]);
+
+      // Load 2 pixels (one per line) from input lines 0 and 1:
+      // RGBA: pix1 = [
+      //   r0 0 0 0  g0 0 0 0  b0 0 0 0  a0 0 0 0
+      //   R0 0 0 0  G0 0 0 0  B0 0 0 0  A0 0 0 0
+      // ]
+      // RGB: pix1 = [
+      //   r0 0 0 0  g0 0 0 0  b0 0 0 0  r1 0 0 0
+      //   R0 0 0 0  G0 0 0 0  B0 0 0 0  R1 0 0 0
+      // ]
+      auto pix1 = _mm256_inserti128_si256(_mm256_castsi128_si256(
+          mm_cvtepu8_epi32(lineIn0_min + stride * i, i32_aligned)),
+          mm_cvtepu8_epi32(lineIn1_min + stride * i, i32_aligned), 1);
+      // Compute output value as C += w0 * C0 for each channel in 32-bit precision
+      sss0 = _mm256_add_epi32(sss0, _mm256_madd_epi16(pix1, mmk));
+
+      // Same as above for lines 2 and 3
+      auto pix2 = _mm256_inserti128_si256(_mm256_castsi128_si256(
+          mm_cvtepu8_epi32(lineIn2_min + stride * i, i32_aligned)),
+          mm_cvtepu8_epi32(lineIn3_min + stride * i, i32_aligned), 1);
+      sss1 = _mm256_add_epi32(sss1, _mm256_madd_epi16(pix2, mmk));
+    }
+
+    if (i == ids_size - 1) {
+      // last element
+      auto mmk = _mm256_set1_epi32(k[i]);
+      // For num_channels == 3 (3 bytes = one pixel) we tolerate to read 4 bytes
+      // lines 0, 1 and 2 wont go out of allocated memory bounds
+      auto pix = _mm256_inserti128_si256(_mm256_castsi128_si256(
+          mm_cvtepu8_epi32(lineIn0_min + stride * i, i32_aligned)),
+          mm_cvtepu8_epi32(lineIn1_min + stride * i, i32_aligned), 1);
+      sss0 = _mm256_add_epi32(sss0, _mm256_madd_epi16(pix, mmk));
+
+      auto p0 = mm_cvtepu8_epi32(lineIn2_min + stride * i, i32_aligned);
+      __m128i p1;
+      if (num_channels == 3 && C10_UNLIKELY(is_last_line && ids_min + stride * i + 4 >= max_in_x_strided)) {
+        uint8_t input[4];
+        std::memcpy(input, lineIn3_min + stride * i, 3);
+        p1 = mm_cvtepu8_epi32(input, true);
+      } else {
+        p1 = mm_cvtepu8_epi32(lineIn3_min + stride * i, i32_aligned);
+      }
+      auto pix2 = _mm256_inserti128_si256(_mm256_castsi128_si256(p0), p1, 1);
+      sss1 = _mm256_add_epi32(sss1, _mm256_madd_epi16(pix2, mmk));
+    }
+
+    // Convert fixed point values back to integers (truncating)
+    sss0 = _mm256_srai_epi32(sss0, coefs_precision);
+    sss1 = _mm256_srai_epi32(sss1, coefs_precision);
+    // Convert packed signed 32-bit integers to packed 16-bit integers using signed saturation
+    // (a a a a b b b b c c c c d d d d) -> (a a b b c c d d 0 0 0 0 0 0 0 0)
+    sss0 = _mm256_packs_epi32(sss0, zero);
+    sss1 = _mm256_packs_epi32(sss1, zero);
+    // Convert packed signed 16-bit integers to packed 8-bit integers using unsigned saturation
+    // (a a b b c c d d) -> (a b c d 0 0 0 0)
+    sss0 = _mm256_packus_epi16(sss0, zero);
+    sss1 = _mm256_packus_epi16(sss1, zero);
+
+    // Write the output into single uint32
+    // (a b c d) -> x_uint32
+    auto o0 = _mm_cvtsi128_si32(_mm256_castsi256_si128(sss0));
+    auto o1 = _mm_cvtsi128_si32(_mm256_extracti128_si256(sss0, 1));
+    auto o2 = _mm_cvtsi128_si32(_mm256_castsi256_si128(sss1));
+    auto o3 = _mm_cvtsi128_si32(_mm256_extracti128_si256(sss1, 1));
+
+    const auto out_x_strided = stride * out_x;
+
+    if (num_channels == 3 && C10_UNLIKELY(out_x_strided + 4 >= max_out_x_strided)) {
+      // Memcpy 4-bytes is faster than 3-bytes and this is a boundary case when we want to write
+      // 4 bytes (R G B | X) to the output buffer (X1 X2 X3 | R1).
+      // The 4th byte in the register (X) has a garbage value and 4th byte in the output buffer (R1) has a correct
+      // value which was previously computed by another line. In other words, it means that we can not overwrite
+      // it by simply writing 4 bytes from the register to the output. We'll do the following:
+      //               v----------|
+      // Output = [... X1 X2 X3 | R1 G1 B1 R2 ...]
+      // First, we write R1 value to the 4th byte of (R G B | X) -> (R G B | R1)
+      // Second, we write 4 bytes from the register to the output: (X1 X2 X3 | R1) -> (R G B | R1)
+      // Output = [... R G B | R1 G1 B1 R2 ...]
+
+      _write_endline_rgb_as_uint32(lineOut0 + out_x_strided, o0);
+      _write_endline_rgb_as_uint32(lineOut1 + out_x_strided, o1);
+      _write_endline_rgb_as_uint32(lineOut2 + out_x_strided, o2);
+
+      if (C10_UNLIKELY(is_last_line)) {
+        // When we handle the last line, we can not access the next 4 bytes
+        // as they are out of memory bounds.
+        std::memcpy(lineOut3 + out_x_strided, (uint8_t *) &o3, num_channels);
+      } else {
+        _write_endline_rgb_as_uint32(lineOut3 + out_x_strided, o3);
+      }
+    } else if (num_channels == 3) {
+      // Memcpy 4-bytes is faster than 3-bytes and here
+      // we simply write 4 bytes (... R G B X 0 0 0 0 0 ...) where X is a garbage value
+      // that we will overwrite on the next iteration: (... R G B R G B X 0 0 ...)
+      std::memcpy(lineOut0 + out_x_strided, (uint8_t *) &o0, 4);
+      std::memcpy(lineOut1 + out_x_strided, (uint8_t *) &o1, 4);
+      std::memcpy(lineOut2 + out_x_strided, (uint8_t *) &o2, 4);
+      std::memcpy(lineOut3 + out_x_strided, (uint8_t *) &o3, 4);
+    } else {
+      // num_channels = 4 -> lineOutX + out_x_strided should be uint32 aligned
+      *(uint32_t *)(lineOut0 + out_x_strided) = o0;
+      *(uint32_t *)(lineOut1 + out_x_strided) = o1;
+      *(uint32_t *)(lineOut2 + out_x_strided) = o2;
+      *(uint32_t *)(lineOut3 + out_x_strided) = o3;
+    }
+  }
+}
+
+void ImagingResampleHorizontalConvolution8u(
+    uint8_t* C10_RESTRICT lineOut,
+    int64_t out_xsize,
+    const uint8_t* C10_RESTRICT lineIn,
+    int64_t in_xsize,
+    const int64_t* idx_ptr_xmin,
+    const int64_t* idx_ptr_size,
+    const int16_t* kk,
+    int kmax,
+    unsigned int coefs_precision,
+    int64_t num_channels,
+    bool is_last_line) {
+
+  // Interpolation horizontal pass processing only one vertical line.
+  // - Input data format is RGBA or RGB with R,G,B,A being uint8. In case of RGBA
+  //   we can encode 4 values as a single uint32 value.
+  // - We split the size of weight vector for a given output index as a sum:
+  //   ids_size = num_blocks_8 * 8 + num_blocks_4 * 4 + num_blocks_2 * 2 + num_blocks_1
+  // - We load and process 8 weights values in a loop ("block 8") then 4 weights and 2 weights values in
+  // in another loops ("block 4" and "block 2") and finally we process 1 weight value in the final loop ("block 1").
+
+  // Define various shuffling masks
+  const auto kmask_low = _mm256_set_epi8(
+      11, 10, 9, 8, 11, 10, 9, 8, 11, 10, 9, 8, 11, 10, 9, 8,
+      3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0);
+  const auto kmask_high = _mm256_set_epi8(
+      15, 14, 13, 12, 15, 14, 13, 12, 15, 14, 13, 12, 15, 14, 13, 12,
+      7, 6, 5, 4, 7, 6, 5, 4, 7, 6, 5, 4, 7, 6, 5, 4);
+  const auto kmask_hl = _mm256_set_epi8(
+      7, 6, 5, 4, 7, 6, 5, 4, 7, 6, 5, 4, 7, 6, 5, 4,
+      3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0);
+
+  const auto mask_low_c4 = _mm256_set_epi8(
+      -1, 7, -1, 3, -1, 6, -1, 2, -1, 5, -1, 1, -1, 4, -1, 0,
+      -1, 7, -1, 3, -1, 6, -1, 2, -1, 5, -1, 1, -1, 4, -1, 0);
+  const auto mask_high_c4 = _mm256_set_epi8(
+      -1, 15, -1, 11, -1, 14, -1, 10, -1, 13, -1, 9, -1, 12, -1, 8,
+      -1, 15, -1, 11, -1, 14, -1, 10, -1, 13, -1, 9, -1, 12, -1, 8);
+  const auto mask_low_c3 = _mm256_set_epi8(
+      -1, -1, -1, -1, -1, 5, -1, 2, -1, 4, -1, 1, -1, 3, -1, 0,
+      -1, -1, -1, -1, -1, 5, -1, 2, -1, 4, -1, 1, -1, 3, -1, 0);
+  const auto mask_high_c3 = _mm256_set_epi8(
+      -1, -1, -1, -1, -1, 11, -1, 8, -1, 10, -1, 7, -1, 9, -1, 6,
+      -1, -1, -1, -1, -1, 11, -1, 8, -1, 10, -1, 7, -1, 9, -1, 6);
+  const auto mask_hl_c3 = _mm256_set_epi8(
+      -1, -1, -1, -1, -1, 11, -1, 8, -1, 10, -1, 7, -1, 9, -1, 6,
+      -1, -1, -1, -1, -1, 5, -1, 2, -1, 4, -1, 1, -1, 3, -1, 0);
+  const auto mask_hl_c4 = _mm256_set_epi8(
+      -1, 15, -1, 11, -1, 14, -1, 10, -1, 13, -1, 9, -1, 12, -1, 8,
+      -1, 7, -1, 3, -1, 6, -1, 2, -1, 5, -1, 1, -1, 4, -1, 0);
+
+  const auto mask_low128_c3 = _mm_set_epi8(
+      -1, -1, -1, -1, -1, 5, -1, 2, -1, 4, -1, 1, -1, 3, -1, 0);
+  const auto mask_low128_c4 = _mm_set_epi8(
+      -1, 7, -1, 3, -1, 6, -1, 2, -1, 5, -1, 1, -1, 4, -1, 0);
+
+  const auto mask_low = (num_channels == 3) ? mask_low_c3 : mask_low_c4;
+  const auto mask_high = (num_channels == 3) ? mask_high_c3 : mask_high_c4;
+  const auto mask_hl = (num_channels == 3) ? mask_hl_c3 : mask_hl_c4;
+  const auto mask_low128 = (num_channels == 3) ? mask_low128_c3 : mask_low128_c4;
+
+  // out_xsize = output width, out_x = output x index
+  // ids_min is the input offset index corresponding to out_x
+  // ids_size is the interpolation size for out_x
+
+  const auto stride = num_channels * sizeof(uint8_t);
+  const auto zero = _mm_setzero_si128();
+
+  TORCH_INTERNAL_ASSERT(stride == 3 || stride == 4);
+
+  // Let's precompute ids_size limits for block 8, block 4 and block 2
+  //
+  // In block 8 (8 means we process 8 weight values together), we read at
+  // most 32 bytes input data (16 + 16 bytes for RGBA and 12 + 16 bytes for RGB)
+  // lineIn + stride * (i + ids_min) + 32 <= lineIn + stride * (ids_size + ids_min)
+  // --> i <= ids_size - 32.0 / stride
+  // Strict boundary:
+  // --> i < ids_size + 1 - int(ceil(32.0 / stride)) = ids_size - b8_delta
+  // Soft boundary for reading inside the buffer except its boundaries:
+  // --> i < ids_size + 1 - int(32.0 / stride) = ids_size - b8_delta_soft
+  // RGBA: b8_delta = b8_delta_soft = 7
+  // RGB : b8_delta = 10
+  // RGB : b8_delta_soft = 9
+  const auto b8_delta = (stride == 4) ? 7 : ((is_last_line) ? 10 : 9);
+
+  // In block 4 (4 means we process 4 weight values together), we read
+  // 16 bytes of input data.
+  // lineIn + stride * (i + ids_min) + 16 <= lineIn0 + stride * (ids_size + ids_min)
+  // --> i <= ids_size - 16.0 / stride
+  // Strict boundary:
+  // --> i < ids_size + 1 - int(ceil(16.0 / stride)) = ids_size - b4_delta
+  // Soft boundary for reading inside the buffer except its boundaries:
+  // --> i < ids_size + 1 - int(16.0 / stride) = ids_size - b4_delta_soft
+  // RGBA: b4_delta = b4_delta_soft = 3
+  // RGB : b4_delta = 5
+  // RGB : b4_delta_soft = 4
+  const auto b4_delta = (stride == 4) ? 3 : ((is_last_line) ? 5 : 4);
+
+  // In block 2 (2 means we process 2 weight values together), we read
+  // 8 bytes of input data.
+  // lineIn0 + stride * (i + ids_min) + 8 <= lineIn0 + stride * (ids_size + ids_min)
+  // --> i <= ids_size - 8.0 / stride
+  // Strict boundary:
+  // --> i < ids_size + 1 - int(ceil(8.0 / stride)) = ids_size - b2_delta
+  // Soft boundary for reading inside the buffer except its boundaries:
+  // --> i < ids_size + 1 - int(8.0 / stride) = ids_size - b2_delta_soft
+  // RGBA: b2_delta = b2_delta_soft = 1
+  // RGB : b2_delta = 2
+  // RGB : b2_delta_soft = 1
+  const auto b2_delta = (stride == 4) ? 1 : ((is_last_line) ? 2 : 1);
+
+  const auto max_out_x_strided = out_xsize * stride;
+  const auto max_in_x_strided = in_xsize * stride;
+
+  for (const auto out_x : c10::irange(out_xsize)) {
+    __m128i sss;
+    const auto ids_min = idx_ptr_xmin[out_x];
+    const auto ids_size = idx_ptr_size[out_x];
+    const auto * k = &kk[out_x * kmax];
+    int64_t i = 0;
+
+    const auto * lineIn_min = lineIn + ids_min;
+
+    if (ids_size < 8) {
+      sss = _mm_set1_epi32(1 << (coefs_precision - 1));
+    } else {
+      // Lower part will be added to higher, use only half of the error
+      auto sss256 = _mm256_set1_epi32(1 << (coefs_precision - 2));
+
+      // block 8
+      for (; i < ids_size - b8_delta; i += 8) {
+        // Load 8 values from weight vector
+        auto tmp = _mm_loadu_si128((__m128i*)&k[i]);
+        // ksource = [
+        //    wl_0 wh_0 wl_1 wh_1  wl_2 wh_2 wl_3 wh_3  wl_4 wh_4 wl_5 wh_5  wl_6 wh_6 wl_7 wh_7
+        //    wl_0 wh_0 wl_1 wh_1  wl_2 wh_2 wl_3 wh_3  wl_4 wh_4 wl_5 wh_5  wl_6 wh_6 wl_7 wh_7
+        // ]
+        auto ksource = _mm256_insertf128_si256(_mm256_castsi128_si256(tmp), tmp, 1);
+
+        // RGBA: Load 8 pixels from input:
+        // source = [
+        //    r0 g0 b0 a0  r1 g1 b1 a1  r2 g2 b2 a2  r3 g3 b3 a3
+        //    r4 g4 b4 a4  r5 g5 b5 a5  r6 g6 b6 a6  r7 g7 b7 a7
+        // ]
+        // RGB: Load 10 pixels from input (however we can process only 8 pixels):
+        // source = [
+        //    r0 g0 b0 r1  g1 b1 r2 g2  b2 r3 g3 b3  r4 g4 b4 r5
+        //    r4 g4 b4 r5  g5 b5 r6 g6  b6 r7 g7 b7  r8 g8 b8 r9
+        // ]
+        auto source = _mm256_inserti128_si256(_mm256_castsi128_si256(
+            _mm_loadu_si128((__m128i *) (lineIn_min + stride * i))),
+            _mm_loadu_si128((__m128i *) (lineIn_min + stride * (i + 4))), 1);
+
+        // Extract lower part of each lane, cast to epi16 and reoder RGBARGBA -> RRGGBBAA
+        // RGBA: pix1 = [
+        //   r0 0 r1 0  g0 0 g1 0  b0 0 b1 0  a0 0 a1 0
+        //   r4 0 r5 0  g4 0 g5 0  b4 0 b5 0  a4 0 a5 0
+        // ]
+        // RGB: pix1 = [
+        //   r0 0 r1 0  g0 0 g1 0  b0 0 b1 0  0 0 0 0
+        //   r4 0 r5 0  g4 0 g5 0  b4 0 b5 0  0 0 0 0
+        // ]
+        auto pix1 = _mm256_shuffle_epi8(source, mask_low);
+        // mmk1 = [
+        //   wl_0 wh_0 wl_1 wh_1  wl_0 wh_0 wl_1 wh_1  ...  ...
+        //   wl_4 wh_4 wl_5 wh_5  wl_4 wh_4 wl_5 wh_5  ...  ...
+        // ]
+        auto mmk1 = _mm256_shuffle_epi8(ksource, kmask_low);
+        // Compute output value as
+        //   C += w0 * C0 + w1 * C1
+        //   C += w4 * C4 + w5 * C5 for each channel in 32-bit precision
+        sss256 = _mm256_add_epi32(sss256, _mm256_madd_epi16(pix1, mmk1));
+
+        // Same as above for higher part of each lane
+        auto pix2 = _mm256_shuffle_epi8(source, mask_high);
+        auto mmk2 = _mm256_shuffle_epi8(ksource, kmask_high);
+        // Compute output value as
+        //    C += w2 * C2 + w3 * C3
+        //    C += w6 * C6 + w7 * C7 for each channel in 32-bit precision
+        sss256 = _mm256_add_epi32(sss256, _mm256_madd_epi16(pix2, mmk2));
+      }
+
+      // block 4
+      for (; i < ids_size - b4_delta; i += 4) {
+        // Load 4 values from weight vector
+        auto tmp = _mm_loadl_epi64((__m128i *) &k[i]);
+        // ksource = [
+        //    wl_0 wh_0 wl_1 wh_1  wl_2 wh_2 wl_3 wh_3  0 0 0 0  0 0 0 0
+        //    wl_0 wh_0 wl_1 wh_1  wl_2 wh_2 wl_3 wh_3  0 0 0 0  0 0 0 0
+        // ]
+        auto ksource = _mm256_insertf128_si256(_mm256_castsi128_si256(tmp), tmp, 1);
+
+        // Load pixels from input line
+        tmp = _mm_loadu_si128((__m128i *) (lineIn_min + stride * i));
+        // RGBA: source = [
+        //   r0 g0 b0 a0  r1 g1 b1 a1  r2 g2 b2 a2  r3 g3 b3 a3
+        //   r0 g0 b0 a0  r1 g1 b1 a1  r2 g2 b2 a2  r3 g3 b3 a3
+        // ]
+        // RGB: source = [
+        //   r0 g0 b0 r1  g1 b1 r2 g2  b2 r3 g3 b3  r4 g4 b4 r5
+        //   r0 g0 b0 r1  g1 b1 r2 g2  b2 r3 g3 b3  r4 g4 b4 r5
+        // ]
+        auto source = _mm256_insertf128_si256(_mm256_castsi128_si256(tmp), tmp, 1);
+
+        // Cast source to epi16 and reorder RGBARGBA -> RRGGBBAA
+        // RGBA: pix = [
+        //   r0 0 r1 0  g0 0 g1 0  b0 0 b1 0  a0 0 a1 0
+        //   r2 0 r3 0  g2 0 g3 0  b2 0 b3 0  a2 0 a3 0
+        // ]
+        // RGB: pix = [
+        //   r0 0 r1 0  g0 0 g1 0  b0 0 b1 0  0 0 0 0
+        //   r2 0 r3 0  g2 0 g3 0  b2 0 b3 0  0 0 0 0
+        // ]
+        auto pix = _mm256_shuffle_epi8(source, mask_hl);
+        // mmk = [
+        //   wl_0 wh_0 wl_1 wh_1  wl_0 wh_0 wl_1 wh_1  ... ...
+        //   wl_2 wh_2 wl_3 wh_3  wl_2 wh_2 wl_3 wh_3  ... ...
+        // ]
+        auto mmk = _mm256_shuffle_epi8(ksource, kmask_hl);
+        // Compute output value as
+        //   C += w0 * C0 + w1 * C1
+        //   C += w2 * C2 + w3 * C3 for each channel in 32-bit precision
+        sss256 = _mm256_add_epi32(sss256, _mm256_madd_epi16(pix, mmk));
+      }
+
+      // Sum results between the lanes
+      sss = _mm_add_epi32(
+          _mm256_extracti128_si256(sss256, 0),
+          _mm256_extracti128_si256(sss256, 1));
+    }
+
+    // block 2
+    for (; i < ids_size - b2_delta; i += 2) {
+      // Load 2 values from weight vector
+      // mmk = [wl_0 wh_0 wl_1 wh_1  wl_0 wh_0 wl_1 wh_1  ...]
+      auto mmk = _mm_set1_epi32(*(int32_t*)&k[i]);
+      // Load pixels from input line
+      // RGBA: source = [
+      //   r0 g0 b0 a0  r1 g1 b1 a1  0 0 0 0  0 0 0 0
+      // ]
+      // RGB: source = [
+      //   r0 g0 b0 r1  g1 b1 r2 g2  0 0 0 0  0 0 0 0
+      // ]
+      auto source = _mm_loadl_epi64((__m128i *) (lineIn_min + stride * i));
+      // Cast source to epi16 and reorder RGBARGBA -> RRGGBBAA
+      auto pix = _mm_shuffle_epi8(source, mask_low128);
+      // Compute output value as C += w0 * C0 + w1 * C1 for each channel in 32-bit precision
+      sss = _mm_add_epi32(sss, _mm_madd_epi16(pix, mmk));
+    }
+
+    // block 1
+    const auto i32_aligned = num_channels == 4;
+    for (; i < ids_size - 1; i++) {
+      // Load 1 value from weight vector
+      // mmk = [wl_0 wh_0 0 0  wl_0 wh_0 0 0  ...]
+      auto mmk = _mm_set1_epi32(k[i]);
+      // Load one pixel from input line
+      // RGBA: pix = [
+      //   r0 0 0 0  g0 0 0 0  b0 0 0 0  a0 0 0 0
+      // ]
+      // RGB: pix = [
+      //   r0 0 0 0  g0 0 0 0  b0 0 0 0  r1 0 0 0
+      // ]
+      auto pix = mm_cvtepu8_epi32(lineIn_min + stride * i, i32_aligned);
+      // Compute output value as C += w0 * C0 for each channel in 32-bit precision
+      sss = _mm_add_epi32(sss, _mm_madd_epi16(pix, mmk));
+    }
+
+    if (i == ids_size - 1) {
+      // last element
+      auto mmk = _mm_set1_epi32(k[i]);
+      __m128i pix;
+      auto p = lineIn_min + stride * i;
+      if (num_channels == 3 && C10_UNLIKELY(is_last_line && ids_min + stride * i + 4 >= max_in_x_strided)) {
+        uint8_t input[4];
+        std::memcpy(input, p, 3);
+        pix = mm_cvtepu8_epi32(input, true);
+      } else {
+        pix = mm_cvtepu8_epi32(p, i32_aligned);
+      }
+      sss = _mm_add_epi32(sss, _mm_madd_epi16(pix, mmk));
+    }
+
+    // Convert fixed point values back to integers (truncating)
+    sss = _mm_srai_epi32(sss, coefs_precision);
+    // Convert packed signed 32-bit integers to packed 16-bit integers using signed saturation
+    // (a a a a b b b b c c c c d d d d) -> (a a b b c c d d 0 0 0 0 0 0 0 0)
+    sss = _mm_packs_epi32(sss, zero);
+    // Convert packed signed 16-bit integers to packed 8-bit integers using unsigned saturation
+    // (a a b b c c d d) -> (a b c d 0 0 0 0)
+    sss = _mm_packus_epi16(sss, zero);
+    // Write the output into single uint32
+    // (a b c d) -> x_uint32
+    auto o = _mm_cvtsi128_si32(sss);
+    const auto out_x_strided = stride * out_x;
+    if (num_channels == 3 && C10_UNLIKELY(out_x_strided + 4 >= max_out_x_strided)) {
+      if (C10_UNLIKELY(is_last_line)) {
+        // When we handle the last line, we can not access the next 4 bytes
+        // as they are out of memory bounds.
+        std::memcpy(lineOut + out_x_strided, (uint8_t *) &o, 3);
+      } else {
+        // Memcpy 4-bytes is faster than 3-bytes and this is a boundary case when we want to write
+        // 4 bytes (R G B | X) to the output buffer (X1 X2 X3 | R1).
+        // The 4th byte in the register (X) has a garbage value and 4th byte in the output buffer (R1) has a correct
+        // value which was previously computed by another line. In other words, it means that we can not overwrite
+        // it by simply writing 4 bytes from the register to the output. We'll do the following:
+        //               v----------|
+        // Output = [... X1 X2 X3 | R1 G1 B1 R2 ...]
+        // First, we write R1 value to the 4th byte of (R G B | X) -> (R G B | R1)
+        // Second, we write 4 bytes from the register to the output: (X1 X2 X3 | R1) -> (R G B | R1)
+        // Output = [... R G B | R1 G1 B1 R2 ...]
+        _write_endline_rgb_as_uint32(lineOut + out_x_strided, o);
+      }
+    } else if (num_channels == 3) {
+      // Memcpy 4-bytes is faster than 3-bytes and here
+      // we simply write 4 bytes (... R G B X 0 0 0 0 0 ...) where X is a garbage value
+      // that we will overwrite on the next iteration: (... R G B R G B X 0 0 ...)
+      std::memcpy(lineOut + out_x_strided, (uint8_t *) &o, 4);
+    } else {
+      // num_channels = 4 -> lineOut + out_x_strided should be uint32 aligned
+      *(uint32_t *)(lineOut + out_x_strided) = o;
+    }
+  }
+}
+
+void ImagingResampleVerticalConvolution8u(
+    uint8_t* C10_RESTRICT lineOut,
+    const uint8_t* C10_RESTRICT lineIn,
+    int64_t xsize,
+    int64_t ids_min,
+    int64_t ids_size,
+    const int16_t* k,
+    unsigned int coefs_precision,
+    int64_t num_channels) {
+
+  // Interpolation vertical pass processing one line.
+  // - We process x-axis data with blocks of 8, 2 and 1
+  // - We split the size of weight vector for a given output index as a sum: K = n * 2 + m.
+
+  // xsize = output width, also equals to input width
+  // ids_size = interpolation size
+  // ids_min = input y start index
+  const auto stride = num_channels * sizeof(uint8_t);
+
+  TORCH_INTERNAL_ASSERT(stride == 3 || stride == 4);
+
+  const int64_t data_size = xsize * stride;
+  const int64_t data_stride = stride;
+  constexpr auto vec_size = 256 / 8;
+
+  const auto initial = _mm_set1_epi32(1 << (coefs_precision - 1));
+  const auto initial_256 = _mm256_set1_epi32(1 << (coefs_precision - 1));
+  const auto zero = _mm_setzero_si128();
+  const auto zero_256 = _mm256_setzero_si256();
+
+  int64_t j = 0;
+  // block 8
+  const auto b8_usable_vec_stride = (vec_size / data_stride) * data_stride;
+  for (; j < data_size - vec_size; j += b8_usable_vec_stride) {
+    auto sss0 = initial_256;
+    auto sss1 = initial_256;
+    auto sss2 = initial_256;
+    auto sss3 = initial_256;
+    int64_t i = 0;
+    const auto * lineIn_min = lineIn + j + ids_min;
+
+    for (; i < ids_size - 1; i += 2) {
+      // Load 2 values from weight vector
+      auto mmk = _mm256_set1_epi32(*(int32_t*)&k[i]);
+
+      // RGBA: Load 8 pixels per line
+      // source1 = [
+      //    r0 g0 b0 a0  r1 g1 b1 a1  r2 g2 b2 a2  r3 g3 b3 a3
+      //    r4 g4 b4 a4  r5 g5 b5 a5  r6 g6 b6 a6  r7 g7 b7 a7
+      // ]
+      // RGB: Load 10 pixels per line (however we can process only 8 pixels):
+      // source1 = [
+      //    r0 g0 b0 r1  g1 b1 r2 g2  b2 r3 g3 b3  r4 g4 b4 r5
+      //    r4 g4 b4 r5  g5 b5 r6 g6  b6 r7 g7 b7  r8 g8 b8 r9
+      // ]
+      auto source1 =
+          _mm256_loadu_si256((__m256i*)(lineIn_min + data_size * i));
+      auto source2 =
+          _mm256_loadu_si256((__m256i*)(lineIn_min + data_size * (i + 1)));
+
+      // Interleave source1 and source2 from the low half of each 128-bit lane
+      // and cast the result to epi16
+      // RGBA: pix1 = [
+      //    r0 0 R0 0  g0 0 G0 0  b0 0 B0 0  a0 0 A0 0
+      //    r1 0 R1 0  g1 0 G1 0  b1 0 B1 0  a1 0 A1 0
+      // ]
+      // RGB: pix1 = [
+      //    r0 0 R0 0  g0 0 G0 0  b0 0 B0 0  0 0 0 0
+      //    r1 0 R1 0  g1 0 G1 0  b1 0 B1 0  0 0 0 0
+      // ]
+      auto source_lo = _mm256_unpacklo_epi8(source1, source2);
+      auto pix1 = _mm256_unpacklo_epi8(source_lo, zero_256);
+      // Compute output value as
+      //   C += w0 * c0 + w1 * C0
+      //   C += w0 * c1 + w1 * C1 for each channel in 32-bit precision
+      sss0 = _mm256_add_epi32(sss0, _mm256_madd_epi16(pix1, mmk));
+
+      // RGBA: pix2 = [
+      //    r2 0 R2 0  g2 0 G2 0  b2 0 B2 0  a2 0 A2 0
+      //    r3 0 R3 0  g3 0 G3 0  b3 0 B3 0  a3 0 A3 0
+      // ]
+      // RGB: pix2 = [
+      //    r2 0 R2 0  g2 0 G2 0  b2 0 B2 0  0 0 0 0
+      //    r3 0 R3 0  g3 0 G3 0  b3 0 B3 0  0 0 0 0
+      // ]
+      auto pix2 = _mm256_unpackhi_epi8(source_lo, zero_256);
+      // Compute output value as
+      //   C += w0 * c2 + w1 * C2
+      //   C += w0 * c3 + w1 * C3 for each channel in 32-bit precision
+      sss1 = _mm256_add_epi32(sss1, _mm256_madd_epi16(pix2, mmk));
+
+      // Same as above for the high half of each 128-bit lane
+      auto source_hi = _mm256_unpackhi_epi8(source1, source2);
+      auto pix3 = _mm256_unpacklo_epi8(source_hi, zero_256);
+      sss2 = _mm256_add_epi32(sss2, _mm256_madd_epi16(pix3, mmk));
+      auto pix4 = _mm256_unpackhi_epi8(source_hi, zero_256);
+      sss3 = _mm256_add_epi32(sss3, _mm256_madd_epi16(pix4, mmk));
+    }
+    // Same processing as above but with a single weight value
+    for (; i < ids_size; i += 1) {
+      auto mmk = _mm256_set1_epi32(k[i]);
+
+      auto source1 = _mm256_loadu_si256((__m256i*)(lineIn_min + i * data_size));
+
+      auto source_lo = _mm256_unpacklo_epi8(source1, zero_256);
+      auto pix1 = _mm256_unpacklo_epi8(source_lo, zero_256);
+      sss0 = _mm256_add_epi32(sss0, _mm256_madd_epi16(pix1, mmk));
+      auto pix2 = _mm256_unpackhi_epi8(source_lo, zero_256);
+      sss1 = _mm256_add_epi32(sss1, _mm256_madd_epi16(pix2, mmk));
+
+      auto source_hi = _mm256_unpackhi_epi8(source1, zero_256);
+      auto pix3 = _mm256_unpacklo_epi8(source_hi, _mm256_setzero_si256());
+      sss2 = _mm256_add_epi32(sss2, _mm256_madd_epi16(pix3, mmk));
+      auto pix4 = _mm256_unpackhi_epi8(source_hi, _mm256_setzero_si256());
+      sss3 = _mm256_add_epi32(sss3, _mm256_madd_epi16(pix4, mmk));
+    }
+    // Convert fixed point values back to integers (truncating)
+    sss0 = _mm256_srai_epi32(sss0, coefs_precision);
+    sss1 = _mm256_srai_epi32(sss1, coefs_precision);
+    sss2 = _mm256_srai_epi32(sss2, coefs_precision);
+    sss3 = _mm256_srai_epi32(sss3, coefs_precision);
+    // Convert packed signed 32-bit integers to packed 16-bit integers using signed saturation
+    // (a a a a b b b b c c c c d d d d) -> (a a b b c c d d)
+    sss0 = _mm256_packs_epi32(sss0, sss1);
+    sss2 = _mm256_packs_epi32(sss2, sss3);
+    // Convert packed signed 16-bit integers to packed 8-bit integers using unsigned saturation
+    // (a a b b c c d d) -> (a b c d)
+    sss0 = _mm256_packus_epi16(sss0, sss2);
+
+    // Stores 32 bytes
+    _mm256_storeu_si256((__m256i*)(lineOut + j), sss0);
+  }
+
+  // TODO: Do we also need block 4 ???
+  // block 2
+  const auto b2_usable_vec_stride = (8 / data_stride) * data_stride;
+  for (; j < data_size - vec_size / 4; j += b2_usable_vec_stride) {
+    auto sss0 = initial;
+    auto sss1 = initial;
+    int64_t i = 0;
+    const auto * lineIn_min = lineIn + j + ids_min;
+
+    for (; i < ids_size - 1; i += 2) {
+      // Load 2 values from weight vector
+      // mmk = [wl_0 wh_0 wl_1 wh_1  wl_0 wh_0 wl_1 wh_1  ... ]
+      auto mmk = _mm_set1_epi32(*(int32_t*)&k[i]);
+
+      // Load 2 pixels per line
+      // RGBA: source1 = [
+      //    r0 g0 b0 a0  r1 g1 b1 a1  0 0 0 0  0 0 0 0
+      // ]
+      // RGB: source1 = [
+      //    r0 g0 b0 r1  g1 b1 r2 g2  0 0 0 0  0 0 0 0
+      // ]
+      auto source1 = _mm_loadl_epi64((__m128i *) (lineIn_min + i * data_size));
+      auto source2 = _mm_loadl_epi64((__m128i *) (lineIn_min + (i + 1) * data_size));
+      // Interleave source1 and source2 and cast the result to epi16
+      // RGBA: pix = [
+      //    r0 0 R0 0  g0 0 G0 0  b0 0 B0 0  a0 0 A0 0
+      // ]
+      // RGB: pix = [
+      //    r0 0 R0 0  g0 0 G0 0  b0 0 B0 0  0 0 0 0
+      // ]
+      auto source = _mm_unpacklo_epi8(source1, source2);
+      auto pix = _mm_unpacklo_epi8(source, zero);
+      // Compute output value as C += w0 * c0 + w1 * C0 for each channel in 32-bit precision
+      sss0 = _mm_add_epi32(sss0, _mm_madd_epi16(pix, mmk));
+      // RGBA: pix = [
+      //    r1 0 R1 0  g1 0 G1 0  b1 0 B1 0  a1 0 A1 0
+      // ]
+      // RGB: pix = [
+      //    r1 0 R1 0  g1 0 G1 0  b1 0 B1 0  0 0 0 0
+      // ]
+      pix = _mm_unpackhi_epi8(source, zero);
+      // Compute output value as C += w0 * c1 + w1 * C1 for each channel in 32-bit precision
+      sss1 = _mm_add_epi32(sss1, _mm_madd_epi16(pix, mmk));
+    }
+    // Same processing as above but with a single weight value
+    for (; i < ids_size; i += 1) {
+      auto mmk = _mm_set1_epi32(k[i]);
+
+      auto source1 = _mm_loadl_epi64((__m128i*) (lineIn_min + i * data_size));
+
+      auto source = _mm_unpacklo_epi8(source1, zero);
+      auto pix1 = _mm_unpacklo_epi8(source, zero);
+      sss0 = _mm_add_epi32(sss0, _mm_madd_epi16(pix1, mmk));
+      auto pix2 = _mm_unpackhi_epi8(source, zero);
+      sss1 = _mm_add_epi32(sss1, _mm_madd_epi16(pix2, mmk));
+    }
+    // Convert fixed point values back to integers (truncating)
+    sss0 = _mm_srai_epi32(sss0, coefs_precision);
+    sss1 = _mm_srai_epi32(sss1, coefs_precision);
+    // Convert packed signed 32-bit integers to packed 16-bit integers using signed saturation
+    // (a a a a b b b b c c c c d d d d) -> (a a b b c c d d)
+    sss0 = _mm_packs_epi32(sss0, sss1);
+    // Convert packed signed 16-bit integers to packed 8-bit integers using unsigned saturation
+    // (a a b b c c d d) -> (a b c d)
+    sss0 = _mm_packus_epi16(sss0, sss0);
+    // Store 2 pixels to the output
+    _mm_storel_epi64((__m128i*)(lineOut + j), sss0);
+  }
+
+  // block 1
+  const auto b1_usable_vec_stride = (4 / data_stride) * data_stride;
+  const auto i32_aligned = num_channels == 4;
+  for (; j < data_size - 4; j += b1_usable_vec_stride) {
+    auto sss = initial;
+    int64_t i = 0;
+    const auto * lineIn_min = lineIn + j + ids_min;
+
+    for (; i < ids_size - 1; i += 2) {
+      // Load 2 values from weight vector
+      // mmk = [wl_0 wh_0 wl_1 wh_1  wl_0 wh_0 wl_1 wh_1  ... ]
+      auto mmk = _mm_set1_epi32(*(int32_t*)&k[i]);
+
+      // Load one pixel per line
+      // RGBA: source1 = [
+      //    r0 g0 b0 a0  0 0 0 0  0 0 0 0  0 0 0 0
+      // ]
+      // RGB: source1 = [
+      //    r0 g0 b0 r1  0 0 0 0  0 0 0 0  0 0 0 0
+      // ]
+      auto source1 = mm_cvtsi32_si128(lineIn_min + i * data_size, i32_aligned);
+      auto source2 = mm_cvtsi32_si128(lineIn_min + (i + 1) * data_size, i32_aligned);
+
+      // Interleave source1 and source2 and cast the result to epi16
+      // RGBA: pix = [
+      //    r0 0 R0 0  g0 0 G0 0  b0 0 B0 0  a0 0 A0 0
+      // ]
+      // RGB: pix = [
+      //    r0 0 R0 0  g0 0 G0 0  b0 0 B0 0  0 0 0 0
+      // ]
+      auto source = _mm_unpacklo_epi8(source1, source2);
+      auto pix = _mm_unpacklo_epi8(source, zero);
+      // Compute output value as C += w0 * c0 + w1 * C0 for each channel in 32-bit precision
+      sss = _mm_add_epi32(sss, _mm_madd_epi16(pix, mmk));
+    }
+
+    for (; i < ids_size; i++) {
+      auto mmk = _mm_set1_epi32(k[i]);
+      auto pix = mm_cvtepu8_epi32(lineIn_min + i * data_size, i32_aligned);
+      sss = _mm_add_epi32(sss, _mm_madd_epi16(pix, mmk));
+    }
+    sss = _mm_srai_epi32(sss, coefs_precision);
+    sss = _mm_packs_epi32(sss, zero);
+    sss = _mm_packus_epi16(sss, zero);
+
+    auto o = _mm_cvtsi128_si32(sss);
+
+    // Here we write 4 bytes to the output even if num_channels < 4, e.g o = {r,g,b,X} for num_channels=3
+    // It is OK to write 4th byte (e.g. X) as on the next step we will overwrite it with new data.
+    // We also wont go out of bounds of lineOut memory allocation
+    std::memcpy(lineOut + j, (uint8_t *) &o, 4);
+  }
+
+  for (; j < data_size; j += data_stride) {
+    auto sss = initial;
+    int64_t i = 0;
+    const auto * lineIn_min = lineIn + j + ids_min;
+    // For RGBA we can use (ids_size - 1) as tighter limit but for RGB we can read outside memory boundary
+    // for the last remaining line
+    for (; i < ids_size - 2; i += 2) {
+      // Load two coefficients at once
+      auto mmk = _mm_set1_epi32(*(int32_t*)&k[i]);
+
+      // Load 2 lines
+      auto source1 = mm_cvtsi32_si128(lineIn_min + i * data_size, i32_aligned);
+      auto source2 = mm_cvtsi32_si128(lineIn_min + (i + 1) * data_size, i32_aligned);
+
+      auto source = _mm_unpacklo_epi8(source1, source2);
+      auto pix = _mm_unpacklo_epi8(source, zero);
+      sss = _mm_add_epi32(sss, _mm_madd_epi16(pix, mmk));
+    }
+
+    // Same processing as above but with a single weight value
+    for (; i < ids_size; i++) {
+      auto mmk = _mm_set1_epi32(k[i]);
+
+      const uint8_t * p = lineIn_min + i * data_size;
+      __m128i pix;
+      // There is no much perf gain using more detailed condition like
+      // num_channels == 3 && ids_min + j + data_size * i + 4 >= in_max_size
+      // const int64_t in_max_size = data_size * in_ysize;
+      if (num_channels == 3) {
+        uint8_t input[4];
+        std::memcpy(input, p, 3);
+        pix = mm_cvtepu8_epi32(input, true);
+      } else {
+        pix = mm_cvtepu8_epi32(p, true);
+      }
+      sss = _mm_add_epi32(sss, _mm_madd_epi16(pix, mmk));
+    }
+
+    // Convert fixed point values back to integers (truncating)
+    sss = _mm_srai_epi32(sss, coefs_precision);
+    // Convert packed signed 32-bit integers to packed 16-bit integers using signed saturation
+    // (a a a a b b b b c c c c d d d d) -> (a a b b c c d d)
+    sss = _mm_packs_epi32(sss, zero);
+    // Convert packed signed 16-bit integers to packed 8-bit integers using unsigned saturation
+    // (a a b b c c d d) -> (a b c d)
+    sss = _mm_packus_epi16(sss, zero);
+    // Store one pixel to the output
+    auto o = _mm_cvtsi128_si32(sss);
+    if (num_channels == 3 && C10_UNLIKELY(j + 4 >= data_size)) {
+      std::memcpy(lineOut + j, (uint8_t *) &o, 3);
+    } else {
+      std::memcpy(lineOut + j, (uint8_t *) &o, 4);
+    }
+  }
+}
+
+} // anonymous namespace
+#endif // CPU_CAPABILITY_AVX2

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/WeightNormKernel.h

@@ -0,0 +1,20 @@
+#pragma once
+#include <ATen/native/DispatchStub.h>
+#include <cstdint>
+
+namespace at {
+class TensorBase;
+}
+
+namespace at { namespace native {
+
+using weight_norm_fn = void(*)(
+    TensorBase&, TensorBase&, const TensorBase&, const TensorBase&, int64_t);
+using weight_norm_backward_fn = void(*)(
+    TensorBase&, TensorBase&, const TensorBase&, const TensorBase&,
+    const TensorBase&, const TensorBase&, int64_t);
+
+DECLARE_DISPATCH(weight_norm_fn, weight_norm_stub);
+DECLARE_DISPATCH(weight_norm_backward_fn, weight_norm_backward_stub);
+
+}}  // namespace at::native

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/avx_mathfun.h

@@ -0,0 +1,522 @@
+#pragma once
+/*
+   AVX implementation of sin, cos, sincos, exp and log
+
+   Based on "sse_mathfun.h", by Julien Pommier
+   http://gruntthepeon.free.fr/ssemath/
+
+   Copyright (C) 2012 Giovanni Garberoglio
+   Interdisciplinary Laboratory for Computational Science (LISC)
+   Fondazione Bruno Kessler and University of Trento
+   via Sommarive, 18
+   I-38123 Trento (Italy)
+
+  This software is provided 'as-is', without any express or implied
+  warranty.  In no event will the authors be held liable for any damages
+  arising from the use of this software.
+
+  Permission is granted to anyone to use this software for any purpose,
+  including commercial applications, and to alter it and redistribute it
+  freely, subject to the following restrictions:
+
+  1. The origin of this software must not be misrepresented; you must not
+     claim that you wrote the original software. If you use this software
+     in a product, an acknowledgment in the product documentation would be
+     appreciated but is not required.
+  2. Altered source versions must be plainly marked as such, and must not be
+     misrepresented as being the original software.
+  3. This notice may not be removed or altered from any source distribution.
+
+  (this is the zlib license)
+*/
+
+#include <ATen/native/cpu/Intrinsics.h>
+
+/* The original source of this file has been modified. */
+#if defined(CPU_CAPABILITY_AVX2)
+
+#if defined(__GNUC__)
+# define ALIGN32_BEG __attribute__((aligned(32)))
+#elif defined(_WIN32)
+# define ALIGN32_BEG __declspec(align(32))
+#endif
+
+typedef __m256  v8sf; // vector of 8 float (avx2)
+typedef __m256i v8si; // vector of 8 int   (avx2)
+
+/* declare some AVX constants -- why can't I figure a better way to do that? */
+#define _PS256_CONST(Name, Val)                                            \
+  static const ALIGN32_BEG float _ps256_##Name[8] = { Val, Val, Val, Val, Val, Val, Val, Val }
+#define _PI32_CONST256(Name, Val)                                            \
+  static const ALIGN32_BEG int _pi32_256_##Name[8] = { Val, Val, Val, Val, Val, Val, Val, Val }
+#define _PS256_CONST_TYPE(Name, Type, Val)                                 \
+  static const ALIGN32_BEG Type _ps256_##Name[8] = { Val, Val, Val, Val, Val, Val, Val, Val }
+
+_PS256_CONST(1  , 1.0f);
+_PS256_CONST(0p5, 0.5f);
+/* the smallest non denormalized float number */
+_PS256_CONST_TYPE(min_norm_pos, int, 0x00800000);
+_PS256_CONST_TYPE(mant_mask, int, 0x7f800000);
+_PS256_CONST_TYPE(inv_mant_mask, int, ~0x7f800000);
+
+_PS256_CONST_TYPE(sign_mask, int, (int)0x80000000);
+_PS256_CONST_TYPE(inv_sign_mask, int, ~0x80000000);
+
+_PI32_CONST256(0, 0);
+_PI32_CONST256(1, 1);
+_PI32_CONST256(inv1, ~1);
+_PI32_CONST256(2, 2);
+_PI32_CONST256(4, 4);
+_PI32_CONST256(0x7f, 0x7f);
+
+_PS256_CONST(cephes_SQRTHF, 0.707106781186547524);
+_PS256_CONST(cephes_log_p0, 7.0376836292E-2);
+_PS256_CONST(cephes_log_p1, - 1.1514610310E-1);
+_PS256_CONST(cephes_log_p2, 1.1676998740E-1);
+_PS256_CONST(cephes_log_p3, - 1.2420140846E-1);
+_PS256_CONST(cephes_log_p4, + 1.4249322787E-1);
+_PS256_CONST(cephes_log_p5, - 1.6668057665E-1);
+_PS256_CONST(cephes_log_p6, + 2.0000714765E-1);
+_PS256_CONST(cephes_log_p7, - 2.4999993993E-1);
+_PS256_CONST(cephes_log_p8, + 3.3333331174E-1);
+_PS256_CONST(cephes_log_q1, -2.12194440e-4);
+_PS256_CONST(cephes_log_q2, 0.693359375);
+
+
+/* natural logarithm computed for 8 simultaneous float
+   return NaN for x <= 0
+*/
+inline v8sf log256_ps(v8sf x) {
+  v8si imm0;
+  v8sf one = *(v8sf*)_ps256_1;
+
+  //v8sf invalid_mask = _mm256_cmple_ps(x, _mm256_setzero_ps());
+  v8sf invalid_mask = _mm256_cmp_ps(x, _mm256_setzero_ps(), _CMP_LE_OS);
+
+  x = _mm256_max_ps(x, *(v8sf*)_ps256_min_norm_pos);  /* cut off denormalized stuff */
+
+  // can be done with AVX2
+  imm0 = _mm256_srli_epi32(_mm256_castps_si256(x), 23);
+
+  /* keep only the fractional part */
+  x = _mm256_and_ps(x, *(v8sf*)_ps256_inv_mant_mask);
+  x = _mm256_or_ps(x, *(v8sf*)_ps256_0p5);
+
+  // this is again another AVX2 instruction
+  imm0 = _mm256_sub_epi32(imm0, *(v8si*)_pi32_256_0x7f);
+  v8sf e = _mm256_cvtepi32_ps(imm0);
+
+  e = _mm256_add_ps(e, one);
+
+  /* part2:
+     if( x < SQRTHF ) {
+       e -= 1;
+       x = x + x - 1.0;
+     } else { x = x - 1.0; }
+  */
+  //v8sf mask = _mm256_cmplt_ps(x, *(v8sf*)_ps256_cephes_SQRTHF);
+  v8sf mask = _mm256_cmp_ps(x, *(v8sf*)_ps256_cephes_SQRTHF, _CMP_LT_OS);
+  v8sf tmp = _mm256_and_ps(x, mask);
+  x = _mm256_sub_ps(x, one);
+  e = _mm256_sub_ps(e, _mm256_and_ps(one, mask));
+  x = _mm256_add_ps(x, tmp);
+
+  v8sf z = _mm256_mul_ps(x,x);
+
+  v8sf y = *(v8sf*)_ps256_cephes_log_p0;
+  y = _mm256_mul_ps(y, x);
+  y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_log_p1);
+  y = _mm256_mul_ps(y, x);
+  y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_log_p2);
+  y = _mm256_mul_ps(y, x);
+  y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_log_p3);
+  y = _mm256_mul_ps(y, x);
+  y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_log_p4);
+  y = _mm256_mul_ps(y, x);
+  y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_log_p5);
+  y = _mm256_mul_ps(y, x);
+  y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_log_p6);
+  y = _mm256_mul_ps(y, x);
+  y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_log_p7);
+  y = _mm256_mul_ps(y, x);
+  y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_log_p8);
+  y = _mm256_mul_ps(y, x);
+
+  y = _mm256_mul_ps(y, z);
+
+  tmp = _mm256_mul_ps(e, *(v8sf*)_ps256_cephes_log_q1);
+  y = _mm256_add_ps(y, tmp);
+
+
+  tmp = _mm256_mul_ps(z, *(v8sf*)_ps256_0p5);
+  y = _mm256_sub_ps(y, tmp);
+
+  tmp = _mm256_mul_ps(e, *(v8sf*)_ps256_cephes_log_q2);
+  x = _mm256_add_ps(x, y);
+  x = _mm256_add_ps(x, tmp);
+  x = _mm256_or_ps(x, invalid_mask); // negative arg will be NAN
+  return x;
+}
+
+_PS256_CONST(exp_hi,        88.3762626647949f);
+_PS256_CONST(exp_lo,        -88.3762626647949f);
+
+_PS256_CONST(cephes_LOG2EF, 1.44269504088896341);
+_PS256_CONST(cephes_exp_C1, 0.693359375);
+_PS256_CONST(cephes_exp_C2, -2.12194440e-4);
+
+_PS256_CONST(cephes_exp_p0, 1.9875691500E-4);
+_PS256_CONST(cephes_exp_p1, 1.3981999507E-3);
+_PS256_CONST(cephes_exp_p2, 8.3334519073E-3);
+_PS256_CONST(cephes_exp_p3, 4.1665795894E-2);
+_PS256_CONST(cephes_exp_p4, 1.6666665459E-1);
+_PS256_CONST(cephes_exp_p5, 5.0000001201E-1);
+
+inline v8sf exp256_ps(v8sf x) {
+  v8sf tmp = _mm256_setzero_ps(), fx;
+  v8si imm0;
+  v8sf one = *(v8sf*)_ps256_1;
+
+  x = _mm256_min_ps(x, *(v8sf*)_ps256_exp_hi);
+  x = _mm256_max_ps(x, *(v8sf*)_ps256_exp_lo);
+
+  /* express exp(x) as exp(g + n*log(2)) */
+  fx = _mm256_mul_ps(x, *(v8sf*)_ps256_cephes_LOG2EF);
+  fx = _mm256_add_ps(fx, *(v8sf*)_ps256_0p5);
+
+  /* how to perform a floorf with SSE: just below */
+  //imm0 = _mm256_cvttps_epi32(fx);
+  //tmp  = _mm256_cvtepi32_ps(imm0);
+
+  tmp = _mm256_floor_ps(fx);
+
+  /* if greater, subtract 1 */
+  //v8sf mask = _mm256_cmpgt_ps(tmp, fx);
+  v8sf mask = _mm256_cmp_ps(tmp, fx, _CMP_GT_OS);
+  mask = _mm256_and_ps(mask, one);
+  fx = _mm256_sub_ps(tmp, mask);
+
+  tmp = _mm256_mul_ps(fx, *(v8sf*)_ps256_cephes_exp_C1);
+  v8sf z = _mm256_mul_ps(fx, *(v8sf*)_ps256_cephes_exp_C2);
+  x = _mm256_sub_ps(x, tmp);
+  x = _mm256_sub_ps(x, z);
+
+  z = _mm256_mul_ps(x,x);
+
+  v8sf y = *(v8sf*)_ps256_cephes_exp_p0;
+  y = _mm256_mul_ps(y, x);
+  y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_exp_p1);
+  y = _mm256_mul_ps(y, x);
+  y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_exp_p2);
+  y = _mm256_mul_ps(y, x);
+  y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_exp_p3);
+  y = _mm256_mul_ps(y, x);
+  y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_exp_p4);
+  y = _mm256_mul_ps(y, x);
+  y = _mm256_add_ps(y, *(v8sf*)_ps256_cephes_exp_p5);
+  y = _mm256_mul_ps(y, z);
+  y = _mm256_add_ps(y, x);
+  y = _mm256_add_ps(y, one);
+
+  /* build 2^n */
+  imm0 = _mm256_cvttps_epi32(fx);
+  // another two AVX2 instructions
+  imm0 = _mm256_add_epi32(imm0, *(v8si*)_pi32_256_0x7f);
+  imm0 = _mm256_slli_epi32(imm0, 23);
+  v8sf pow2n = _mm256_castsi256_ps(imm0);
+  y = _mm256_mul_ps(y, pow2n);
+  return y;
+}
+
+_PS256_CONST(minus_cephes_DP1, -0.78515625);
+_PS256_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
+_PS256_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
+_PS256_CONST(sincof_p0, -1.9515295891E-4);
+_PS256_CONST(sincof_p1,  8.3321608736E-3);
+_PS256_CONST(sincof_p2, -1.6666654611E-1);
+_PS256_CONST(coscof_p0,  2.443315711809948E-005);
+_PS256_CONST(coscof_p1, -1.388731625493765E-003);
+_PS256_CONST(coscof_p2,  4.166664568298827E-002);
+_PS256_CONST(cephes_FOPI, 1.27323954473516); // 4 / M_PI
+
+
+/* evaluation of 8 sines at onces using AVX intrinsics
+
+   The code is the exact rewriting of the cephes sinf function.
+   Precision is excellent as long as x < 8192 (I did not bother to
+   take into account the special handling they have for greater values
+   -- it does not return garbage for arguments over 8192, though, but
+   the extra precision is missing).
+
+   Note that it is such that sinf((float)M_PI) = 8.74e-8, which is the
+   surprising but correct result.
+
+*/
+inline v8sf sin256_ps(v8sf x) { // any x
+  v8sf xmm1, xmm2 = _mm256_setzero_ps(), xmm3, sign_bit, y;
+  v8si imm0, imm2;
+
+  sign_bit = x;
+  /* take the absolute value */
+  x = _mm256_and_ps(x, *(v8sf*)_ps256_inv_sign_mask);
+  /* extract the sign bit (upper one) */
+  sign_bit = _mm256_and_ps(sign_bit, *(v8sf*)_ps256_sign_mask);
+
+  /* scale by 4/Pi */
+  y = _mm256_mul_ps(x, *(v8sf*)_ps256_cephes_FOPI);
+
+  /*
+    Here we start a series of integer operations, which are in the
+    realm of AVX2.
+    If we don't have AVX, let's perform them using SSE2 directives
+  */
+
+  /* store the integer part of y in mm0 */
+  imm2 = _mm256_cvttps_epi32(y);
+  /* j=(j+1) & (~1) (see the cephes sources) */
+  // another two AVX2 instruction
+  imm2 = _mm256_add_epi32(imm2, *(v8si*)_pi32_256_1);
+  imm2 = _mm256_and_si256(imm2, *(v8si*)_pi32_256_inv1);
+  y = _mm256_cvtepi32_ps(imm2);
+
+  /* get the swap sign flag */
+  imm0 = _mm256_and_si256(imm2, *(v8si*)_pi32_256_4);
+  imm0 = _mm256_slli_epi32(imm0, 29);
+  /* get the polynom selection mask
+     there is one polynom for 0 <= x <= Pi/4
+     and another one for Pi/4<x<=Pi/2
+
+     Both branches will be computed.
+  */
+  imm2 = _mm256_and_si256(imm2, *(v8si*)_pi32_256_2);
+  imm2 = _mm256_cmpeq_epi32(imm2,*(v8si*)_pi32_256_0);
+
+  v8sf swap_sign_bit = _mm256_castsi256_ps(imm0);
+  v8sf poly_mask = _mm256_castsi256_ps(imm2);
+  sign_bit = _mm256_xor_ps(sign_bit, swap_sign_bit);
+
+  /* The magic pass: "Extended precision modular arithmetic"
+     x = ((x - y * DP1) - y * DP2) - y * DP3; */
+  xmm1 = *(v8sf*)_ps256_minus_cephes_DP1;
+  xmm2 = *(v8sf*)_ps256_minus_cephes_DP2;
+  xmm3 = *(v8sf*)_ps256_minus_cephes_DP3;
+  xmm1 = _mm256_mul_ps(y, xmm1);
+  xmm2 = _mm256_mul_ps(y, xmm2);
+  xmm3 = _mm256_mul_ps(y, xmm3);
+  x = _mm256_add_ps(x, xmm1);
+  x = _mm256_add_ps(x, xmm2);
+  x = _mm256_add_ps(x, xmm3);
+
+  /* Evaluate the first polynom  (0 <= x <= Pi/4) */
+  y = *(v8sf*)_ps256_coscof_p0;
+  v8sf z = _mm256_mul_ps(x,x);
+
+  y = _mm256_mul_ps(y, z);
+  y = _mm256_add_ps(y, *(v8sf*)_ps256_coscof_p1);
+  y = _mm256_mul_ps(y, z);
+  y = _mm256_add_ps(y, *(v8sf*)_ps256_coscof_p2);
+  y = _mm256_mul_ps(y, z);
+  y = _mm256_mul_ps(y, z);
+  v8sf tmp = _mm256_mul_ps(z, *(v8sf*)_ps256_0p5);
+  y = _mm256_sub_ps(y, tmp);
+  y = _mm256_add_ps(y, *(v8sf*)_ps256_1);
+
+  /* Evaluate the second polynom  (Pi/4 <= x <= 0) */
+
+  v8sf y2 = *(v8sf*)_ps256_sincof_p0;
+  y2 = _mm256_mul_ps(y2, z);
+  y2 = _mm256_add_ps(y2, *(v8sf*)_ps256_sincof_p1);
+  y2 = _mm256_mul_ps(y2, z);
+  y2 = _mm256_add_ps(y2, *(v8sf*)_ps256_sincof_p2);
+  y2 = _mm256_mul_ps(y2, z);
+  y2 = _mm256_mul_ps(y2, x);
+  y2 = _mm256_add_ps(y2, x);
+
+  /* select the correct result from the two polynoms */
+  xmm3 = poly_mask;
+  y2 = _mm256_and_ps(xmm3, y2); //, xmm3);
+  y = _mm256_andnot_ps(xmm3, y);
+  y = _mm256_add_ps(y,y2);
+  /* update the sign */
+  y = _mm256_xor_ps(y, sign_bit);
+
+  return y;
+}
+
+/* almost the same as sin_ps */
+inline v8sf cos256_ps(v8sf x) { // any x
+  v8sf xmm1, xmm2 = _mm256_setzero_ps(), xmm3, y;
+  v8si imm0, imm2;
+
+  /* take the absolute value */
+  x = _mm256_and_ps(x, *(v8sf*)_ps256_inv_sign_mask);
+
+  /* scale by 4/Pi */
+  y = _mm256_mul_ps(x, *(v8sf*)_ps256_cephes_FOPI);
+
+  /* store the integer part of y in mm0 */
+  imm2 = _mm256_cvttps_epi32(y);
+  /* j=(j+1) & (~1) (see the cephes sources) */
+  imm2 = _mm256_add_epi32(imm2, *(v8si*)_pi32_256_1);
+  imm2 = _mm256_and_si256(imm2, *(v8si*)_pi32_256_inv1);
+  y = _mm256_cvtepi32_ps(imm2);
+  imm2 = _mm256_sub_epi32(imm2, *(v8si*)_pi32_256_2);
+
+  /* get the swap sign flag */
+  imm0 =  _mm256_andnot_si256(imm2, *(v8si*)_pi32_256_4);
+  imm0 = _mm256_slli_epi32(imm0, 29);
+  /* get the polynom selection mask */
+  imm2 = _mm256_and_si256(imm2, *(v8si*)_pi32_256_2);
+  imm2 = _mm256_cmpeq_epi32(imm2, *(v8si*)_pi32_256_0);
+
+  v8sf sign_bit = _mm256_castsi256_ps(imm0);
+  v8sf poly_mask = _mm256_castsi256_ps(imm2);
+
+  /* The magic pass: "Extended precision modular arithmetic"
+     x = ((x - y * DP1) - y * DP2) - y * DP3; */
+  xmm1 = *(v8sf*)_ps256_minus_cephes_DP1;
+  xmm2 = *(v8sf*)_ps256_minus_cephes_DP2;
+  xmm3 = *(v8sf*)_ps256_minus_cephes_DP3;
+  xmm1 = _mm256_mul_ps(y, xmm1);
+  xmm2 = _mm256_mul_ps(y, xmm2);
+  xmm3 = _mm256_mul_ps(y, xmm3);
+  x = _mm256_add_ps(x, xmm1);
+  x = _mm256_add_ps(x, xmm2);
+  x = _mm256_add_ps(x, xmm3);
+
+  /* Evaluate the first polynom  (0 <= x <= Pi/4) */
+  y = *(v8sf*)_ps256_coscof_p0;
+  v8sf z = _mm256_mul_ps(x,x);
+
+  y = _mm256_mul_ps(y, z);
+  y = _mm256_add_ps(y, *(v8sf*)_ps256_coscof_p1);
+  y = _mm256_mul_ps(y, z);
+  y = _mm256_add_ps(y, *(v8sf*)_ps256_coscof_p2);
+  y = _mm256_mul_ps(y, z);
+  y = _mm256_mul_ps(y, z);
+  v8sf tmp = _mm256_mul_ps(z, *(v8sf*)_ps256_0p5);
+  y = _mm256_sub_ps(y, tmp);
+  y = _mm256_add_ps(y, *(v8sf*)_ps256_1);
+
+  /* Evaluate the second polynom  (Pi/4 <= x <= 0) */
+
+  v8sf y2 = *(v8sf*)_ps256_sincof_p0;
+  y2 = _mm256_mul_ps(y2, z);
+  y2 = _mm256_add_ps(y2, *(v8sf*)_ps256_sincof_p1);
+  y2 = _mm256_mul_ps(y2, z);
+  y2 = _mm256_add_ps(y2, *(v8sf*)_ps256_sincof_p2);
+  y2 = _mm256_mul_ps(y2, z);
+  y2 = _mm256_mul_ps(y2, x);
+  y2 = _mm256_add_ps(y2, x);
+
+  /* select the correct result from the two polynoms */
+  xmm3 = poly_mask;
+  y2 = _mm256_and_ps(xmm3, y2); //, xmm3);
+  y = _mm256_andnot_ps(xmm3, y);
+  y = _mm256_add_ps(y,y2);
+  /* update the sign */
+  y = _mm256_xor_ps(y, sign_bit);
+
+  return y;
+}
+
+/* since sin256_ps and cos256_ps are almost identical, sincos256_ps could replace both of them..
+   it is almost as fast, and gives you a free cosine with your sine */
+inline void sincos256_ps(v8sf x, v8sf *s, v8sf *c) {
+
+  v8sf xmm1, xmm2, xmm3 = _mm256_setzero_ps(), sign_bit_sin, y;
+  v8si imm0, imm2, imm4;
+
+  sign_bit_sin = x;
+  /* take the absolute value */
+  x = _mm256_and_ps(x, *(v8sf*)_ps256_inv_sign_mask);
+  /* extract the sign bit (upper one) */
+  sign_bit_sin = _mm256_and_ps(sign_bit_sin, *(v8sf*)_ps256_sign_mask);
+
+  /* scale by 4/Pi */
+  y = _mm256_mul_ps(x, *(v8sf*)_ps256_cephes_FOPI);
+
+  /* store the integer part of y in imm2 */
+  imm2 = _mm256_cvttps_epi32(y);
+
+  /* j=(j+1) & (~1) (see the cephes sources) */
+  imm2 = _mm256_add_epi32(imm2, *(v8si*)_pi32_256_1);
+  imm2 = _mm256_and_si256(imm2, *(v8si*)_pi32_256_inv1);
+
+  y = _mm256_cvtepi32_ps(imm2);
+  imm4 = imm2;
+
+  /* get the swap sign flag for the sine */
+  imm0 = _mm256_and_si256(imm2, *(v8si*)_pi32_256_4);
+  imm0 = _mm256_slli_epi32(imm0, 29);
+  //v8sf swap_sign_bit_sin = _mm256_castsi256_ps(imm0);
+
+  /* get the polynom selection mask for the sine*/
+  imm2 = _mm256_and_si256(imm2, *(v8si*)_pi32_256_2);
+  imm2 = _mm256_cmpeq_epi32(imm2, *(v8si*)_pi32_256_0);
+  //v8sf poly_mask = _mm256_castsi256_ps(imm2);
+
+  v8sf swap_sign_bit_sin = _mm256_castsi256_ps(imm0);
+  v8sf poly_mask = _mm256_castsi256_ps(imm2);
+
+  /* The magic pass: "Extended precision modular arithmetic"
+     x = ((x - y * DP1) - y * DP2) - y * DP3; */
+  xmm1 = *(v8sf*)_ps256_minus_cephes_DP1;
+  xmm2 = *(v8sf*)_ps256_minus_cephes_DP2;
+  xmm3 = *(v8sf*)_ps256_minus_cephes_DP3;
+  xmm1 = _mm256_mul_ps(y, xmm1);
+  xmm2 = _mm256_mul_ps(y, xmm2);
+  xmm3 = _mm256_mul_ps(y, xmm3);
+  x = _mm256_add_ps(x, xmm1);
+  x = _mm256_add_ps(x, xmm2);
+  x = _mm256_add_ps(x, xmm3);
+
+  imm4 = _mm256_sub_epi32(imm4, *(v8si*)_pi32_256_2);
+  imm4 =  _mm256_andnot_si256(imm4, *(v8si*)_pi32_256_4);
+  imm4 = _mm256_slli_epi32(imm4, 29);
+
+  v8sf sign_bit_cos = _mm256_castsi256_ps(imm4);
+
+  sign_bit_sin = _mm256_xor_ps(sign_bit_sin, swap_sign_bit_sin);
+
+  /* Evaluate the first polynom  (0 <= x <= Pi/4) */
+  v8sf z = _mm256_mul_ps(x,x);
+  y = *(v8sf*)_ps256_coscof_p0;
+
+  y = _mm256_mul_ps(y, z);
+  y = _mm256_add_ps(y, *(v8sf*)_ps256_coscof_p1);
+  y = _mm256_mul_ps(y, z);
+  y = _mm256_add_ps(y, *(v8sf*)_ps256_coscof_p2);
+  y = _mm256_mul_ps(y, z);
+  y = _mm256_mul_ps(y, z);
+  v8sf tmp = _mm256_mul_ps(z, *(v8sf*)_ps256_0p5);
+  y = _mm256_sub_ps(y, tmp);
+  y = _mm256_add_ps(y, *(v8sf*)_ps256_1);
+
+  /* Evaluate the second polynom  (Pi/4 <= x <= 0) */
+
+  v8sf y2 = *(v8sf*)_ps256_sincof_p0;
+  y2 = _mm256_mul_ps(y2, z);
+  y2 = _mm256_add_ps(y2, *(v8sf*)_ps256_sincof_p1);
+  y2 = _mm256_mul_ps(y2, z);
+  y2 = _mm256_add_ps(y2, *(v8sf*)_ps256_sincof_p2);
+  y2 = _mm256_mul_ps(y2, z);
+  y2 = _mm256_mul_ps(y2, x);
+  y2 = _mm256_add_ps(y2, x);
+
+  /* select the correct result from the two polynoms */
+  xmm3 = poly_mask;
+  v8sf ysin2 = _mm256_and_ps(xmm3, y2);
+  v8sf ysin1 = _mm256_andnot_ps(xmm3, y);
+  y2 = _mm256_sub_ps(y2,ysin2);
+  y = _mm256_sub_ps(y, ysin1);
+
+  xmm1 = _mm256_add_ps(ysin1,ysin2);
+  xmm2 = _mm256_add_ps(y,y2);
+
+  /* update the sign */
+  *s = _mm256_xor_ps(xmm1, sign_bit_sin);
+  *c = _mm256_xor_ps(xmm2, sign_bit_cos);
+}
+
+#endif // CPU_CAPABILITY_AVX2

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/int_mm_kernel.h

@@ -0,0 +1,16 @@
+#pragma once
+
+#include <ATen/core/Tensor.h>
+#include <ATen/native/DispatchStub.h>
+
+namespace at::native {
+
+using weight_to_int4pack_fn = void(*)(const Tensor&, const Tensor&, int, int);
+using int4pack_mm_fn = void(*)(const Tensor&, const Tensor&, const Tensor&, int, const Tensor&, int, int);
+using int8pack_mm_fn = void(*)(const Tensor&, const Tensor&, const Tensor&, const Tensor&);
+
+DECLARE_DISPATCH(weight_to_int4pack_fn, weight_to_int4pack_stub);
+DECLARE_DISPATCH(int4pack_mm_fn, int4pack_mm_stub);
+DECLARE_DISPATCH(int8pack_mm_fn, int8pack_mm_stub);
+
+} // namespace at::native

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/mixed_data_type.h

@@ -0,0 +1,41 @@
+#pragma once
+
+#include <ATen/core/Tensor.h>
+
+namespace at { namespace native {
+
+inline ScalarType first_type() {
+  return ScalarType::Undefined;
+}
+
+template <typename... Args>
+inline ScalarType first_type(const Tensor& arg, const Args&... parameters) {
+  return arg.defined() ? arg.scalar_type() : first_type(parameters...);
+}
+
+template <typename... Args>
+inline bool is_mixed_type(const Tensor& input, const Args&... parameters) {
+  const auto parameter_type = first_type(parameters...);
+  return ((parameter_type != ScalarType::Undefined) &&
+          (parameter_type != input.scalar_type()));
+}
+
+// currently on CPU, mixed data type is only supported
+// when input is 'BFloat16' or 'Half' and parameters are 'Float'
+inline void check_mixed_data_type(const Tensor& input) {
+  TORCH_CHECK(at::isReducedFloatingType(input.scalar_type()),
+      "mixed dtype (CPU): all inputs must share same datatype.");
+}
+
+template <typename... Args>
+inline void check_mixed_data_type(const Tensor& input, const Tensor& parameter, const Args&... parameters) {
+  TORCH_CHECK(!parameter.defined() || parameter.scalar_type() == ScalarType::Float,
+      "mixed dtype (CPU): expect parameter to have scalar type of Float");
+  check_mixed_data_type(input, parameters...);
+}
+
+inline ScalarType param_scalar_type(const Tensor& t, bool is_mixed_type) {
+  return is_mixed_type ? ScalarType::Float : t.scalar_type();
+}
+
+}}  // namespace at::native

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/moments_utils.h

@@ -0,0 +1,206 @@
+#pragma once
+
+#include <array>
+#include <cstring>
+#include <numeric>
+#include <utility>
+#include <vector>
+
+#include <ATen/Parallel.h>
+#include <ATen/OpMathType.h>
+#include <ATen/cpu/vec/vec.h>
+#include <ATen/native/cpu/utils.h>
+#include <c10/util/SmallVector.h>
+#include <c10/util/irange.h>
+
+namespace at {
+namespace native {
+inline namespace CPU_CAPABILITY {
+
+template<typename T> using opmath_t = at::opmath_type<T>;
+
+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>
+C10_ALWAYS_INLINE 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;
+}
+
+template <typename T>
+inline typename std::enable_if<std::is_same<T, opmath_t<T>>::value, void>::type
+UpdateMomentsVec(
+    int64_t m0,
+    const T* X_ptr,
+    const std::array<vec::Vectorized<opmath_t<T>>, kChunkSize>& c_vecs,
+    int64_t& m0_stk0,
+    vec::Vectorized<opmath_t<T>>& m1_stk0,
+    vec::Vectorized<opmath_t<T>>& m2_stk0) {
+  using Vec = vec::Vectorized<opmath_t<T>>;
+  Vec m1_vec(0);
+  Vec m2_vec(0);
+  for (const auto j : c10::irange(m0)) {
+    const Vec x_vec = Vec::loadu(X_ptr + j * Vec::size());
+    const Vec delta_vec = x_vec - m1_vec;
+    m1_vec += delta_vec * c_vecs[j];
+    m2_vec += delta_vec * (x_vec - m1_vec);
+  }
+  AddMomentsVec(m0, m1_vec, m2_vec, m0_stk0, m1_stk0, m2_stk0);
+}
+
+// each bfloat16/half vector will be converted to two float vectors,
+// and accumulated successively on m1_stk0/m2_stk0.
+template <typename T>
+inline typename std::enable_if<!std::is_same<T, at::opmath_type<T>>::value, void>::type
+UpdateMomentsVec(
+    int64_t m0,
+    const T* X_ptr,
+    const std::array<vec::Vectorized<at::opmath_type<T>>, kChunkSize>& c_vecs,
+    int64_t& m0_stk0,
+    vec::Vectorized<at::opmath_type<T>>& m1_stk0,
+    vec::Vectorized<at::opmath_type<T>>& m2_stk0) {
+  using Vec = vec::Vectorized<T>;
+  using fVec = vec::Vectorized<at::opmath_type<T>>;
+  fVec m1_fvec0(0), m1_fvec1(0);
+  fVec m2_fvec0(0), m2_fvec1(0);
+  for (const auto j : c10::irange(m0)) {
+    const Vec x_bvec = Vec::loadu(X_ptr + j * Vec::size());
+    auto [x_fvec0, x_fvec1] = convert_to_float<T>(x_bvec);
+    const fVec delta_fvec0 = x_fvec0 - m1_fvec0;
+    const fVec delta_fvec1 = x_fvec1 - m1_fvec1;
+    m1_fvec0 += delta_fvec0 * c_vecs[j];
+    m1_fvec1 += delta_fvec1 * c_vecs[j];
+    m2_fvec0 += delta_fvec0 * (x_fvec0 - m1_fvec0);
+    m2_fvec1 += delta_fvec1 * (x_fvec1 - m1_fvec1);
+  }
+  AddMomentsVec(m0, m1_fvec0, m2_fvec0, m0_stk0, m1_stk0, m2_stk0);
+  AddMomentsVec(m0, m1_fvec1, m2_fvec1, m0_stk0, m1_stk0, m2_stk0);
+}
+
+// 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<opmath_t<T>, opmath_t<T>> RowwiseMomentsImpl(const T* X, int64_t N, int64_t ddof = 0) {
+  using math_t = opmath_t<T>;
+
+  constexpr int64_t kVecSize = vec::Vectorized<T>::size();
+  constexpr int64_t kAccVecSize = vec::Vectorized<math_t>::size();
+  const int64_t n = N / kVecSize;
+  const int64_t m = divup(n, kChunkSize);
+  const int64_t depth = utils::CeilLog2(m);
+
+  using Vec = vec::Vectorized<math_t>;
+  const Vec kZeroVec(math_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 (const auto i : c10::irange(m)) {
+    const T* X_ptr = X + i * kChunkSize * kVecSize;
+    const int64_t m0 = std::min(kChunkSize, n - i * kChunkSize);
+    static std::array<Vec, kChunkSize> c_vecs = ([]() {
+      std::array<Vec, kChunkSize> result;
+      for (const auto i : c10::irange(kChunkSize)) {
+        result[i] = Vec(math_t(1) / static_cast<math_t>(i + 1));
+      }
+      return result;
+    })();
+    UpdateMomentsVec(m0, X_ptr, c_vecs, 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 (const auto i : c10::irange(1, depth)) {
+    AddMomentsVec(
+        m0_stk[i], m1_stk[i], m2_stk[i], m0_stk[0], m1_stk[0], m2_stk[0]);
+  }
+
+  std::array<math_t, kAccVecSize> m1_arr{};
+  std::array<math_t, kAccVecSize> m2_arr{};
+  m1_stk[0].store(m1_arr.data());
+  m2_stk[0].store(m2_arr.data());
+
+  int64_t m0 = 0;
+  math_t m1 = 0;
+  math_t m2 = 0;
+  for (int64_t i = n * kVecSize; i < N; ++i) {
+    math_t x = static_cast<math_t>(X[i]);
+    const math_t delta = x - m1;
+    ++m0;
+    m1 += delta / static_cast<math_t>(m0);
+    m2 += delta * (x - m1);
+  }
+  // for BFloat16, each vector in m1_arr/m2_arr holds 2*n accumulated result
+  int64_t m0_add = n * kVecSize / kAccVecSize;
+  for (const auto i : c10::irange(kAccVecSize)) {
+    AddMoments(m0_add, m1_arr[i], m2_arr[i], m0, m1, m2);
+  }
+
+  return std::make_pair(m1, m2 / static_cast<math_t>(N - ddof));
+}
+
+template <typename T>
+std::pair<opmath_t<T>, opmath_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 = utils::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 CPU_CAPABILITY
+} // namespace native
+} // namespace at

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/utils.h

@@ -0,0 +1,198 @@
+#pragma once
+
+#include <ATen/Parallel.h>
+#include <ATen/cpu/vec/vec.h>
+#include <c10/util/llvmMathExtras.h>
+
+#ifdef USE_FBGEMM
+#include <fbgemm/Fbgemm.h>
+#endif
+
+namespace at {
+namespace native {
+
+template <typename T>
+inline void _store(T* dst, at::vec::Vectorized<T> src) {
+  src.store(dst);
+}
+
+inline void _store(at::BFloat16* dst, at::vec::Vectorized<float> src) {
+  auto res = at::vec::convert_float_bfloat16(src, src);
+  res.store(dst, at::vec::Vectorized<float>::size());
+}
+
+inline void _store(at::Half* dst, at::vec::Vectorized<float> src) {
+  auto res = at::vec::convert_float_half(src, src);
+  res.store(dst, at::vec::Vectorized<float>::size());
+}
+
+inline namespace CPU_CAPABILITY {
+
+template <typename T>
+inline T data_index_init(T offset) {
+  return offset;
+}
+
+template <typename T, typename... Args>
+inline T data_index_init(T offset, T& x, const T& X, Args&&... args) {
+  offset = data_index_init(offset, std::forward<Args>(args)...);
+  x = offset % X;
+  return offset / X;
+}
+
+inline bool data_index_step() {
+  return true;
+}
+
+template <typename T, typename... Args>
+inline bool data_index_step(T& x, const T& X, Args&&... args) {
+  if (data_index_step(std::forward<Args>(args)...)) {
+    x = ((x + 1) == X) ? 0 : (x + 1);
+    return x == 0;
+  }
+  return false;
+}
+
+// Helper struct for bfloat16 vectorization
+// Useful when you need float as immediate dtype or accumulate dtype
+using namespace vec;
+struct Vec2 {
+  Vectorized<float> val0, val1;
+  Vec2(Vectorized<float> v0, Vectorized<float> v1) : val0(v0), val1(v1) {}
+  Vec2(float v) : val0(v), val1(v) {}
+  static Vec2 loadu(const BFloat16* ptr) {
+    auto [v0, v1] = convert_bfloat16_float(Vectorized<BFloat16>::loadu(ptr));
+    return {v0, v1};
+  }
+  static Vec2 loadu(const float* ptr) {
+    return {Vectorized<float>::loadu(ptr), Vectorized<float>::loadu(ptr + Vectorized<float>::size())};
+  }
+  void store(BFloat16* ptr) const {
+    Vectorized<BFloat16> val = convert_float_bfloat16(val0, val1);
+    val.store(ptr);
+  }
+  void store(float* ptr) const {
+    val0.store(ptr);
+    val1.store(ptr + Vectorized<float>::size());
+  }
+};
+inline Vec2 operator+(const Vec2& a, const Vec2& b) { return {a.val0 + b.val0, a.val1 + b.val1}; }
+inline Vec2 operator*(const Vec2& a, const Vec2& b) { return {a.val0 * b.val0, a.val1 * b.val1}; }
+inline Vec2 operator-(const Vec2& a, const Vec2& b) { return {a.val0 - b.val0, a.val1 - b.val1}; }
+inline Vec2 operator/(const Vec2& a, const Vec2& b) { return {a.val0 / b.val0, a.val1 / b.val1}; }
+inline Vec2 maximum(const Vec2& a, const Vec2& b) { return {vec::maximum(a.val0, b.val0), vec::maximum(a.val1, b.val1)}; }
+inline Vec2 minimum(const Vec2& a, const Vec2& b) { return {vec::minimum(a.val0, b.val0), vec::minimum(a.val1, b.val1)}; }
+
+template <typename scalar_t> struct VectorizedType { using type = Vectorized<scalar_t>; };
+template <> struct VectorizedType<BFloat16> { using type = Vec2; };
+template <typename scalar_t> using VecType = typename VectorizedType<scalar_t>::type;
+
+// Helper for mixed data type parameter Vec::load
+inline std::tuple<Vectorized<float>, Vectorized<float>> load2f(const BFloat16* ptr) {
+  return convert_bfloat16_float(Vectorized<BFloat16>::loadu(ptr));
+}
+
+inline std::tuple<Vectorized<float>, Vectorized<float>> load2f(const Half* ptr) {
+  return convert_half_float(Vectorized<Half>::loadu(ptr));
+}
+
+inline std::tuple<Vectorized<float>, Vectorized<float>> load2f(const float* ptr) {
+  using Vec = Vectorized<float>;
+  return std::make_tuple(Vec::loadu(ptr), Vec::loadu(ptr + Vec::size()));
+}
+
+inline std::tuple<Vectorized<float>, Vectorized<float>> load2f(const BFloat16* ptr, int64_t count) {
+  return convert_bfloat16_float(Vectorized<BFloat16>::loadu(ptr, count));
+}
+
+inline std::tuple<Vectorized<float>, Vectorized<float>> load2f(const Half* ptr, int64_t count) {
+  return convert_half_float(Vectorized<Half>::loadu(ptr, count));
+}
+
+inline std::tuple<Vectorized<float>, Vectorized<float>> load2f(const float* ptr, int64_t count) {
+  using Vec = Vectorized<float>;
+  if (count > Vec::size()) {
+  return std::make_tuple(Vec::loadu(ptr), Vec::loadu(ptr + Vec::size(), count - Vec::size()));
+  } else {
+    return std::make_tuple(Vec::loadu(ptr, count), Vec(0));
+  }
+}
+
+} // namespace
+
+namespace utils {
+
+template <typename T>
+T CeilLog2(const T& x) {
+  if (x <= 2) {
+    return 1;
+  }
+  // Last set bit is floor(log2(x)), floor + 1 is ceil
+  // except when x is an exact powers of 2, so subtract 1 first
+  return static_cast<T>(llvm::findLastSet(static_cast<uint64_t>(x) - 1)) + 1;
+}
+
+// matrix transpose:
+//   src has shape of M by N, with leading dimension of ld_src
+//   dst has shape of N by M, with leading dimension of ld_dst
+template <typename T>
+inline void transpose(int64_t M, int64_t N, const T* src, int64_t ld_src, T* dst, int64_t ld_dst) {
+  for (int64_t j = 0; j < N; j++) {
+    for (int64_t i = 0; i < M; i++) {
+      dst[j * ld_dst + i] = src[i * ld_src + j];
+    }
+  }
+}
+
+#ifdef USE_FBGEMM
+template <>
+inline void transpose<float>(int64_t M, int64_t N, const float* src, int64_t ld_src, float* dst, int64_t ld_dst) {
+  TORCH_CHECK(fbgemm::fbgemmSupportedCPU(), "Your CPU does not support FBGEMM.");
+  fbgemm::transpose_simd<float>(M, N, src, ld_src, dst, ld_dst);
+}
+#endif
+
+template <typename index_t, typename F>
+inline void parallel_sparse_csr(
+    const TensorAccessor<index_t, 1>& crow_acc,
+    const int64_t M,
+    const int64_t nnz,
+    const F& f) {
+  TORCH_CHECK(crow_acc.size(0) == M + 1);
+
+  // directly parallel on `M` may lead to load imbalance,
+  // statically determine thread partition here to average payload
+  // for each thread.
+  int num_threads = at::get_num_threads();
+  std::vector<int64_t> thread_splits(num_threads + 1, M);
+
+  int64_t thread_averge_payload = std::max((int64_t)1, divup(nnz, num_threads));
+
+  thread_splits[0] = 0;
+  int64_t sum = 0;
+  int64_t t = 1;
+  for (const auto m : c10::irange(M)) {
+    int64_t row_start = crow_acc[m];
+    int64_t row_end = crow_acc[m + 1];
+    sum += row_end - row_start;
+    if (sum > t * thread_averge_payload) {
+      thread_splits[t] = m;
+      t++;
+    }
+  }
+  // need to restore the last index,
+  // due to rounding error when calculating `thread_averge_payload`.
+  thread_splits[num_threads] = M;
+
+  at::parallel_for(0, num_threads, 1, [&](int64_t cbegin, int64_t cend) {
+    int tid = at::get_thread_num();
+    int64_t begin = thread_splits[tid];
+    int64_t end = thread_splits[tid + 1];
+    f(begin, end);
+  });
+}
+
+} // namespace utils
+
+} // namespace native
+} // namespace at

venv/lib/python3.10/site-packages/torch/include/ATen/native/cpu/zmath.h

@@ -0,0 +1,250 @@
+#pragma once
+
+// Complex number math operations that act as no-ops for other dtypes.
+#include <c10/util/complex.h>
+#include <c10/util/MathConstants.h>
+#include<ATen/NumericUtils.h>
+
+namespace at { namespace native {
+inline namespace CPU_CAPABILITY {
+
+template <typename SCALAR_TYPE, typename VALUE_TYPE=SCALAR_TYPE>
+inline VALUE_TYPE zabs (SCALAR_TYPE z) {
+  return z;
+}
+
+template<>
+inline c10::complex<float> zabs <c10::complex<float>> (c10::complex<float> z) {
+  return c10::complex<float>(std::abs(z));
+}
+
+template<>
+inline float zabs <c10::complex<float>, float> (c10::complex<float> z) {
+  return std::abs(z);
+}
+
+template<>
+inline c10::complex<double> zabs <c10::complex<double>> (c10::complex<double> z) {
+  return c10::complex<double>(std::abs(z));
+}
+
+template<>
+inline double zabs <c10::complex<double>, double> (c10::complex<double> z) {
+  return std::abs(z);
+}
+
+// This overload corresponds to non-complex dtypes.
+// The function is consistent with its NumPy equivalent
+// for non-complex dtypes where `pi` is returned for
+// negative real numbers and `0` is returned for 0 or positive
+// real numbers.
+// Note: `nan` is propagated.
+template <typename SCALAR_TYPE, typename VALUE_TYPE=SCALAR_TYPE>
+inline VALUE_TYPE angle_impl (SCALAR_TYPE z) {
+  if (at::_isnan(z)) {
+    return z;
+  }
+  return z < 0 ? c10::pi<double> : 0;
+}
+
+template<>
+inline c10::complex<float> angle_impl <c10::complex<float>> (c10::complex<float> z) {
+  return c10::complex<float>(std::arg(z), 0.0);
+}
+
+template<>
+inline float angle_impl <c10::complex<float>, float> (c10::complex<float> z) {
+  return std::arg(z);
+}
+
+template<>
+inline c10::complex<double> angle_impl <c10::complex<double>> (c10::complex<double> z) {
+  return c10::complex<double>(std::arg(z), 0.0);
+}
+
+template<>
+inline double angle_impl <c10::complex<double>, double> (c10::complex<double> z) {
+  return std::arg(z);
+}
+
+template <typename SCALAR_TYPE, typename VALUE_TYPE=SCALAR_TYPE>
+constexpr VALUE_TYPE real_impl (SCALAR_TYPE z) {
+  return z; //No-Op
+}
+
+template<>
+constexpr c10::complex<float> real_impl <c10::complex<float>> (c10::complex<float> z) {
+  return c10::complex<float>(z.real(), 0.0);
+}
+
+template<>
+constexpr float real_impl <c10::complex<float>, float> (c10::complex<float> z) {
+  return z.real();
+}
+
+template<>
+constexpr c10::complex<double> real_impl <c10::complex<double>> (c10::complex<double> z) {
+  return c10::complex<double>(z.real(), 0.0);
+}
+
+template<>
+constexpr double real_impl <c10::complex<double>, double> (c10::complex<double> z) {
+  return z.real();
+}
+
+template <typename SCALAR_TYPE, typename VALUE_TYPE=SCALAR_TYPE>
+constexpr VALUE_TYPE imag_impl (SCALAR_TYPE /*z*/) {
+  return 0;
+}
+
+template<>
+constexpr c10::complex<float> imag_impl <c10::complex<float>> (c10::complex<float> z) {
+  return c10::complex<float>(z.imag(), 0.0);
+}
+
+template<>
+constexpr float imag_impl <c10::complex<float>, float> (c10::complex<float> z) {
+  return z.imag();
+}
+
+template<>
+constexpr c10::complex<double> imag_impl <c10::complex<double>> (c10::complex<double> z) {
+  return c10::complex<double>(z.imag(), 0.0);
+}
+
+template<>
+constexpr double imag_impl <c10::complex<double>, double> (c10::complex<double> z) {
+  return z.imag();
+}
+
+template <typename TYPE>
+inline TYPE conj_impl (TYPE z) {
+  return z; //No-Op
+}
+
+template<>
+inline c10::complex<at::Half> conj_impl <c10::complex<at::Half>> (c10::complex<at::Half> z) {
+  return c10::complex<at::Half>{z.real(), -z.imag()};
+}
+
+template<>
+inline c10::complex<float> conj_impl <c10::complex<float>> (c10::complex<float> z) {
+  return c10::complex<float>(z.real(), -z.imag());
+}
+
+template<>
+inline c10::complex<double> conj_impl <c10::complex<double>> (c10::complex<double> z) {
+  return c10::complex<double>(z.real(), -z.imag());
+}
+
+template <typename TYPE>
+inline TYPE ceil_impl (TYPE z) {
+  return std::ceil(z);
+}
+
+template <>
+inline c10::complex<float> ceil_impl (c10::complex<float> z) {
+  return c10::complex<float>(std::ceil(z.real()), std::ceil(z.imag()));
+}
+
+template <>
+inline c10::complex<double> ceil_impl (c10::complex<double> z) {
+  return c10::complex<double>(std::ceil(z.real()), std::ceil(z.imag()));
+}
+
+template<typename T>
+inline c10::complex<T> sgn_impl (c10::complex<T> z) {
+  if (z == c10::complex<T>(0, 0)) {
+    return c10::complex<T>(0, 0);
+  } else {
+    return z / zabs(z);
+  }
+}
+
+template <typename TYPE>
+inline TYPE floor_impl (TYPE z) {
+  return std::floor(z);
+}
+
+template <>
+inline c10::complex<float> floor_impl (c10::complex<float> z) {
+  return c10::complex<float>(std::floor(z.real()), std::floor(z.imag()));
+}
+
+template <>
+inline c10::complex<double> floor_impl (c10::complex<double> z) {
+  return c10::complex<double>(std::floor(z.real()), std::floor(z.imag()));
+}
+
+template <typename TYPE>
+inline TYPE round_impl (TYPE z) {
+  return std::nearbyint(z);
+}
+
+template <>
+inline c10::complex<float> round_impl (c10::complex<float> z) {
+  return c10::complex<float>(std::nearbyint(z.real()), std::nearbyint(z.imag()));
+}
+
+template <>
+inline c10::complex<double> round_impl (c10::complex<double> z) {
+  return c10::complex<double>(std::nearbyint(z.real()), std::nearbyint(z.imag()));
+}
+
+template <typename TYPE>
+inline TYPE trunc_impl (TYPE z) {
+  return std::trunc(z);
+}
+
+template <>
+inline c10::complex<float> trunc_impl (c10::complex<float> z) {
+  return c10::complex<float>(std::trunc(z.real()), std::trunc(z.imag()));
+}
+
+template <>
+inline c10::complex<double> trunc_impl (c10::complex<double> z) {
+  return c10::complex<double>(std::trunc(z.real()), std::trunc(z.imag()));
+}
+
+template <typename TYPE, std::enable_if_t<!c10::is_complex<TYPE>::value, int> = 0>
+inline TYPE max_impl (TYPE a, TYPE b) {
+  if (_isnan<TYPE>(a) || _isnan<TYPE>(b)) {
+    return std::numeric_limits<TYPE>::quiet_NaN();
+  } else {
+    return std::max(a, b);
+  }
+}
+
+template <typename TYPE, std::enable_if_t<c10::is_complex<TYPE>::value, int> = 0>
+inline TYPE max_impl (TYPE a, TYPE b) {
+  if (_isnan<TYPE>(a)) {
+    return a;
+  } else if (_isnan<TYPE>(b)) {
+    return b;
+  } else {
+    return std::abs(a) > std::abs(b) ? a : b;
+  }
+}
+
+template <typename TYPE, std::enable_if_t<!c10::is_complex<TYPE>::value, int> = 0>
+inline TYPE min_impl (TYPE a, TYPE b) {
+  if (_isnan<TYPE>(a) || _isnan<TYPE>(b)) {
+    return std::numeric_limits<TYPE>::quiet_NaN();
+  } else {
+    return std::min(a, b);
+  }
+}
+
+template <typename TYPE, std::enable_if_t<c10::is_complex<TYPE>::value, int> = 0>
+inline TYPE min_impl (TYPE a, TYPE b) {
+  if (_isnan<TYPE>(a)) {
+    return a;
+  } else if (_isnan<TYPE>(b)) {
+    return b;
+  } else {
+    return std::abs(a) < std::abs(b) ? a : b;
+  }
+}
+
+} // end namespace
+}} //end at::native

venv/lib/python3.10/site-packages/torch/include/ATen/native/cuda/BinaryInternal.h

@@ -0,0 +1,48 @@
+// DON'T include this except from Binary*.cu files. It should not leak into
+// headers.
+#pragma once
+#define TORCH_ASSERT_NO_OPERATORS
+#include <ATen/AccumulateType.h>
+#include <ATen/Dispatch.h>
+#include <ATen/native/BinaryOps.h>
+#include <ATen/native/DispatchStub.h>
+#include <ATen/native/TensorIterator.h>
+#include <c10/cuda/CUDAGuard.h>
+#include <c10/cuda/CUDAMathCompat.h>
+#include <c10/util/TypeSafeSignMath.h>
+#include <ATen/native/cuda/JitLoops.cuh>
+#include <ATen/native/cuda/Loops.cuh>
+
+#include <type_traits>
+
+namespace at {
+namespace native {
+namespace binary_internal {
+
+template <typename scalar_t>
+struct DivFunctor {
+  __device__ scalar_t operator()(scalar_t a, scalar_t b) const {
+    return a / b;
+  }
+};
+
+template <typename T>
+struct MulFunctor {
+  __device__ T operator()(T a, T b) const {
+    return a * b;
+  }
+};
+
+// Workaround for the error: '*' in boolean context, suggest '&&' instead
+// [-Werror=int-in-bool-context]
+template <>
+struct MulFunctor<bool> {
+  __device__ bool operator()(bool a, bool b) const {
+    return a && b;
+  }
+};
+void div_true_kernel_cuda(TensorIteratorBase& iter);
+void div_trunc_kernel_cuda(TensorIteratorBase& iter);
+} // namespace binary_internal
+} // namespace native
+} // namespace at

venv/lib/python3.10/site-packages/torch/include/ATen/native/cuda/CompositeRandomAccessor.h

@@ -0,0 +1,35 @@
+#pragma once
+
+#include <ATen/native/CompositeRandomAccessorCommon.h>
+#include <thrust/tuple.h>
+
+namespace at { namespace native {
+
+struct TupleInfoCPU {
+  template <typename ...Types>
+  using tuple = thrust::tuple<Types...>;
+
+  template <typename ...Types>
+  static constexpr auto tie(Types&... args) noexcept {
+    return thrust::tie(args...);
+  }
+};
+
+template <typename KeyAccessor, typename ValueAccessor>
+using CompositeRandomAccessorCPU =
+  CompositeRandomAccessor<KeyAccessor, ValueAccessor, TupleInfoCPU>;
+
+template <typename Values, typename References>
+void swap(
+  references_holder<Values, References> rh1,
+  references_holder<Values, References> rh2
+) {
+  return thrust::swap(rh1.data(), rh2.data());
+}
+
+template <int N, typename Values, typename References>
+auto get(references_holder<Values, References> rh) -> decltype(thrust::get<N>(rh.data())) {
+  return thrust::get<N>(rh.data());
+}
+
+}} // namespace at::native

venv/lib/python3.10/site-packages/torch/include/ATen/native/cuda/Copy.h

@@ -0,0 +1,10 @@
+#pragma once
+
+namespace at {
+struct TensorIteratorBase;
+
+namespace native {
+
+void direct_copy_kernel_cuda(TensorIteratorBase &iter);
+
+}}  // namespace at::native

venv/lib/python3.10/site-packages/torch/include/ATen/native/cuda/CuFFTPlanCache.h

@@ -0,0 +1,494 @@
+#include <ATen/Config.h>
+#include <ATen/core/DimVector.h>
+#include <ATen/cuda/CUDAContext.h>
+#include <ATen/native/cuda/CuFFTUtils.h>
+#include <ATen/native/utils/ParamsHash.h>
+#include <c10/util/accumulate.h>
+#include <c10/util/irange.h>
+
+#include <cufft.h>
+#include <cufftXt.h>
+
+#include <limits>
+#include <list>
+#include <sstream>
+#include <stdexcept>
+#include <string>
+#include <unordered_map>
+
+namespace at { namespace native { namespace detail {
+
+// Enum representing the FFT type
+enum class CuFFTTransformType : int8_t {
+  C2C,  // Complex-to-complex
+  R2C,  // Real-to-complex
+  C2R,  // Complex-to-real
+};
+
+// This struct is used to let us easily compute hashes of the
+// parameters.
+// It will be the **key** to the plan cache.
+struct CuFFTParams
+{
+  int64_t signal_ndim_; // between 1 and max_rank, i.e., 1 <= signal_ndim <= 3
+  // These include additional batch dimension as well.
+  int64_t sizes_[max_rank + 1];
+  int64_t input_strides_[max_rank + 1];
+  int64_t output_strides_[max_rank + 1];
+  CuFFTTransformType fft_type_;
+  ScalarType value_type_;
+
+  CuFFTParams() = default;
+
+  CuFFTParams(IntArrayRef in_strides, IntArrayRef out_strides,
+      IntArrayRef signal_sizes, CuFFTTransformType fft_type, ScalarType value_type) {
+    // Padding bits must be zeroed for hashing
+    memset(this, 0, sizeof(*this));
+    signal_ndim_ = signal_sizes.size() - 1;
+    fft_type_ = fft_type;
+    value_type_ = value_type;
+
+    TORCH_INTERNAL_ASSERT(in_strides.size() == signal_sizes.size());
+    TORCH_INTERNAL_ASSERT(out_strides.size() == signal_sizes.size());
+    TORCH_INTERNAL_ASSERT(1 <= signal_ndim_ && signal_ndim_ <= max_rank);
+
+    std::copy(signal_sizes.cbegin(), signal_sizes.cend(), sizes_);
+    std::copy(in_strides.cbegin(), in_strides.cend(), input_strides_);
+    std::copy(out_strides.cbegin(), out_strides.cend(), output_strides_);
+  }
+};
+
+static_assert(std::is_trivial<CuFFTParams>::value, "");
+
+// Returns true if the transform type has complex input
+inline bool cufft_complex_input(CuFFTTransformType type) {
+  switch (type) {
+    case CuFFTTransformType::C2C:
+    case CuFFTTransformType::C2R:
+      return true;
+
+    case CuFFTTransformType::R2C:
+      return false;
+  }
+  TORCH_INTERNAL_ASSERT(false);
+}
+
+// Returns true if the transform type has complex output
+inline bool cufft_complex_output(CuFFTTransformType type) {
+  switch (type) {
+    case CuFFTTransformType::C2C:
+    case CuFFTTransformType::R2C:
+      return true;
+
+    case CuFFTTransformType::C2R:
+      return false;
+  }
+  TORCH_INTERNAL_ASSERT(false);
+}
+
+// Create transform type enum from bools representing if input and output are complex
+inline CuFFTTransformType GetCuFFTTransformType(bool complex_input, bool complex_output) {
+  if (complex_input && complex_output) {
+    return CuFFTTransformType::C2C;
+  } else if (complex_input && !complex_output) {
+    return CuFFTTransformType::C2R;
+  } else if (!complex_input && complex_output) {
+    return CuFFTTransformType::R2C;
+  }
+  TORCH_INTERNAL_ASSERT(false, "Real to real FFTs are not supported");
+}
+
+
+class CuFFTHandle {
+  ::cufftHandle handle_;
+public:
+
+  CuFFTHandle() {
+    CUFFT_CHECK(cufftCreate(&handle_));
+  }
+
+  ::cufftHandle & get() { return handle_; }
+  const ::cufftHandle & get() const { return handle_; }
+
+  ~CuFFTHandle() {
+// Not using fftDestroy() for rocFFT to work around double freeing of handles
+#if !defined(USE_ROCM)
+    cufftDestroy(handle_);
+#endif
+  }
+};
+
+__forceinline__
+static bool is_pow_of_two(int64_t x) {
+  return (x & (x - 1)) == 0;
+}
+
+using cufft_size_type = long long int;
+
+using CuFFTDimVector = c10::SmallVector<cufft_size_type, at::kDimVectorStaticSize>;
+
+// Struct representing a tensor in CuFFT's data layout for planning transforms
+// See NOTE [ cuFFT Embedded Strides ].
+struct CuFFTDataLayout {
+  CuFFTDimVector embed;
+  cufft_size_type stride, dist;
+  bool must_clone, simple;
+};
+
+// Returns a cufft embedding for a contiguous signal of the given size.
+// e.g. if the input is cloned, this will be the resulting data layout
+// See NOTE [ cuFFT Embedded Strides ].
+inline CuFFTDataLayout cufft_simple_embed(IntArrayRef sizes, bool onesided) {
+  CuFFTDataLayout layout;
+  layout.simple = true;
+  layout.must_clone = false;
+  layout.embed.assign(sizes.cbegin() + 1, sizes.cend());
+  if (onesided) {
+    layout.embed.back() = sizes.back() / 2 + 1;
+  }
+  layout.stride = 1;
+  layout.dist = 1;
+  for (const auto& len : layout.embed) {
+    layout.dist *= len;
+  }
+  return layout;
+}
+
+// Convert strides to a CuFFT embedded representation.
+// If strides cannot be embedded, returns a simple layout and sets must_clone flag
+// See NOTE [ cuFFT Embedded Strides ].
+inline CuFFTDataLayout as_cufft_embed(IntArrayRef strides, IntArrayRef sizes, bool onesided) {
+  const auto signal_ndim = strides.size() - 1;
+  CuFFTDataLayout layout;
+  auto last_stride = strides[signal_ndim];
+  layout.must_clone = (last_stride <= 0);
+
+  const auto last_dim_size = onesided ?
+      sizes[signal_ndim] / 2 + 1 : sizes[signal_ndim];
+  const auto signal_numel = c10::multiply_integers(sizes.slice(1, sizes.size() - 2)) * last_dim_size;
+
+  // Zero stides are not allowed, even if the batch size is one.
+  // If that happens just set a dummy case
+  if (sizes[0] == 1) {
+    layout.dist = signal_numel;
+  } else if (strides[0] == 0) {
+    layout.must_clone = true;
+  } else {
+    layout.dist = strides[0];
+  }
+
+  // Calculate the embedding shape, or set must_clone if the strides cannot be embedded
+  layout.embed.resize(signal_ndim);
+  for (auto i = signal_ndim - 1; !layout.must_clone && i > 0; i--) {
+    auto stride = strides[i];
+    if (sizes[i] == 1) {
+      layout.embed[i] = 1;
+    } else if (stride > 0 && stride % last_stride == 0) {
+      layout.embed[i] = stride / last_stride;
+      last_stride = stride;
+    } else {
+      layout.must_clone = true;
+    }
+  }
+
+  if (layout.must_clone) {
+    // If the input needs to be cloned, assume it will be contiguous
+    layout = cufft_simple_embed(sizes, onesided);
+    layout.must_clone = true;
+  } else {
+    layout.embed[0] = sizes[1];
+    layout.stride = strides[signal_ndim];
+    // Determine if layout represents a simple embedding (contiguous data)
+    layout.simple = [&] {
+      for (const auto i : c10::irange(1, signal_ndim - 1)) {
+        if (layout.embed[i] != sizes[i + 1]) {
+          return false;
+        }
+      }
+
+      return (layout.stride == 1 && layout.dist == signal_numel &&
+          layout.embed.back() == last_dim_size);
+    }();
+  }
+  return layout;
+}
+
+// This class contains all the information needed to execute a cuFFT plan:
+//   1. the plan
+//   2. whether to clone input before executing the plan
+//   3. the workspace size needed
+//
+// This class will be the **value** in the plan cache.
+// It **owns** the raw plan via a unique_ptr.
+class CuFFTConfig {
+public:
+
+  // Only move semantics is enought for this class. Although we already use
+  // unique_ptr for the plan, still remove copy constructor and assignment op so
+  // we don't accidentally copy and take perf hit.
+  CuFFTConfig(const CuFFTConfig&) = delete;
+  CuFFTConfig& operator=(CuFFTConfig const&) = delete;
+
+  explicit CuFFTConfig(const CuFFTParams& params):
+      CuFFTConfig(
+          IntArrayRef(params.input_strides_, params.signal_ndim_ + 1),
+          IntArrayRef(params.output_strides_, params.signal_ndim_ + 1),
+          IntArrayRef(params.sizes_, params.signal_ndim_ + 1),
+          params.fft_type_,
+          params.value_type_) {}
+
+  // For complex types, strides are in units of 2 * element_size(dtype)
+  // sizes are for the full signal, including batch size and always two-sided
+  CuFFTConfig(IntArrayRef in_strides, IntArrayRef out_strides,
+      IntArrayRef sizes, CuFFTTransformType fft_type, ScalarType dtype):
+        fft_type_(fft_type), value_type_(dtype) {
+
+    // signal sizes (excluding batch dim)
+    CuFFTDimVector signal_sizes(sizes.begin() + 1, sizes.end());
+
+    // input batch size
+    const int64_t batch = sizes[0];
+    const int64_t signal_ndim = sizes.size() - 1;
+
+    // Since cuFFT has limited non-unit stride support and various constraints, we
+    // use a flag to keep track throughout this function to see if we need to
+    // input = input.clone();
+
+#if defined(USE_ROCM)
+    // clone input to avoid issues with hipfft clobering the input and failing tests
+    clone_input = true;
+#else
+    clone_input = false;
+#endif
+
+    // For half, base strides on the real part of real-to-complex and
+    // complex-to-real transforms are not supported. Since our output is always
+    // contiguous, only need to check real-to-complex case.
+    if (dtype == ScalarType::Half) {
+      // cuFFT on half requires compute capability of at least SM_53
+      auto dev_prop = at::cuda::getCurrentDeviceProperties();
+      TORCH_CHECK(dev_prop->major >= 5 && !(dev_prop->major == 5 && dev_prop->minor < 3),
+               "cuFFT doesn't support signals of half type with compute "
+               "capability less than SM_53, but the device containing input half "
+               "tensor only has SM_", dev_prop->major, dev_prop->minor);
+      for (const auto i : c10::irange(signal_ndim)) {
+        TORCH_CHECK(is_pow_of_two(sizes[i + 1]),
+            "cuFFT only supports dimensions whose sizes are powers of two when"
+            " computing in half precision, but got a signal size of",
+            sizes.slice(1));
+      }
+      clone_input |= in_strides.back() != 1;
+    }
+
+    CuFFTDataLayout in_layout;
+    if (clone_input) {
+      in_layout = cufft_simple_embed(sizes, fft_type == CuFFTTransformType::C2R);
+    } else {
+      in_layout = as_cufft_embed(in_strides, sizes, fft_type == CuFFTTransformType::C2R);
+    }
+    auto out_layout = as_cufft_embed(out_strides, sizes, fft_type == CuFFTTransformType::R2C);
+    TORCH_INTERNAL_ASSERT(!out_layout.must_clone, "Out strides cannot be represented as CuFFT embedding");
+    clone_input |= in_layout.must_clone;
+
+    // Check if we can take advantage of simple data layout.
+    //
+    // See NOTE [ cuFFT Embedded Strides ] in native/cuda/SpectralOps.cu.
+
+    const bool simple_layout = in_layout.simple && out_layout.simple;
+    cudaDataType itype, otype, exec_type;
+    const auto complex_input = cufft_complex_input(fft_type);
+    const auto complex_output = cufft_complex_output(fft_type);
+    if (dtype == ScalarType::Float) {
+      itype = complex_input ? CUDA_C_32F : CUDA_R_32F;
+      otype = complex_output ? CUDA_C_32F : CUDA_R_32F;
+      exec_type = CUDA_C_32F;
+    } else if (dtype == ScalarType::Double) {
+      itype = complex_input ? CUDA_C_64F : CUDA_R_64F;
+      otype = complex_output ? CUDA_C_64F : CUDA_R_64F;
+      exec_type = CUDA_C_64F;
+    } else if (dtype == ScalarType::Half) {
+      itype = complex_input ? CUDA_C_16F : CUDA_R_16F;
+      otype = complex_output ? CUDA_C_16F : CUDA_R_16F;
+      exec_type = CUDA_C_16F;
+    } else {
+      TORCH_CHECK(false, "cuFFT doesn't support tensor of type: ", dtype);
+    }
+
+    // disable auto allocation of workspace to use THC allocator
+    CUFFT_CHECK(cufftSetAutoAllocation(plan(), /* autoAllocate */ 0));
+
+    size_t ws_size_t;
+
+    // make plan
+    if (simple_layout) {
+      // If with unit-stride, we tell cuFFT by setting inembed == onembed == NULL.
+      // In such case, cuFFT ignores istride, ostride, idist, and odist
+      // by assuming istride = ostride = 1.
+      //
+      // See NOTE [ cuFFT Embedded Strides ] in native/cuda/SpectralOps.cu.
+      CUFFT_CHECK(cufftXtMakePlanMany(plan(), signal_ndim, signal_sizes.data(),
+        /* inembed */ nullptr, /* base_istride */ 1, /* idist */ 1, itype,
+        /* onembed */ nullptr, /* base_ostride */ 1, /* odist */ 1, otype,
+        batch, &ws_size_t, exec_type));
+    } else {
+      CUFFT_CHECK(cufftXtMakePlanMany(plan(), signal_ndim, signal_sizes.data(),
+            in_layout.embed.data(), in_layout.stride, in_layout.dist, itype,
+            out_layout.embed.data(), out_layout.stride, out_layout.dist, otype,
+            batch, &ws_size_t, exec_type));
+    }
+    ws_size = static_cast<int64_t>(ws_size_t);
+  }
+
+  const cufftHandle &plan() const { return plan_ptr.get(); }
+
+  CuFFTTransformType transform_type() const { return fft_type_; }
+  ScalarType data_type() const { return value_type_; }
+  bool should_clone_input() const { return clone_input; }
+  int64_t workspace_size() const { return ws_size; }
+
+private:
+  CuFFTHandle plan_ptr;
+  bool clone_input;
+  int64_t ws_size;
+  CuFFTTransformType fft_type_;
+  ScalarType value_type_;
+};
+
+#if defined(USE_ROCM)
+  // Note that the max plan number for CUDA version < 10 has to be 1023
+  // due to a bug that fails on the 1024th plan
+  constexpr int64_t CUFFT_MAX_PLAN_NUM = 1023;
+  constexpr int64_t CUFFT_DEFAULT_CACHE_SIZE = CUFFT_MAX_PLAN_NUM;
+#else
+  constexpr int64_t CUFFT_MAX_PLAN_NUM = std::numeric_limits<int64_t>::max();
+  // The default max cache size chosen for CUDA version > 10 is arbitrary.
+  // This number puts a limit on how big of a plan cache should we maintain by
+  // default. Users can always configure it via cufft_set_plan_cache_max_size.
+  constexpr int64_t CUFFT_DEFAULT_CACHE_SIZE = 4096;
+#endif
+static_assert(0 <= CUFFT_MAX_PLAN_NUM && CUFFT_MAX_PLAN_NUM <= std::numeric_limits<int64_t>::max(),
+              "CUFFT_MAX_PLAN_NUM not in size_t range");
+static_assert(CUFFT_DEFAULT_CACHE_SIZE >= 0 && CUFFT_DEFAULT_CACHE_SIZE <= CUFFT_MAX_PLAN_NUM,
+              "CUFFT_DEFAULT_CACHE_SIZE not in [0, CUFFT_MAX_PLAN_NUM] range");
+
+// This cache assumes that the mapping from key to value never changes.
+// This is **NOT** thread-safe. Please use a mutex when using it **AND** the
+// value returned from try_emplace_value.
+// The contract of using this cache is that try_emplace_value should only be
+// used when the max_size is positive.
+class CuFFTParamsLRUCache {
+public:
+  using kv_t = typename std::pair<CuFFTParams, CuFFTConfig>;
+  using map_t = typename std::unordered_map<std::reference_wrapper<CuFFTParams>,
+                                            typename std::list<kv_t>::iterator,
+                                            ParamsHash<CuFFTParams>,
+                                            ParamsEqual<CuFFTParams>>;
+  using map_kkv_iter_t = typename map_t::iterator;
+
+
+  CuFFTParamsLRUCache() : CuFFTParamsLRUCache(CUFFT_DEFAULT_CACHE_SIZE) {}
+
+  CuFFTParamsLRUCache(int64_t max_size) {
+    _set_max_size(max_size);
+  }
+
+  CuFFTParamsLRUCache(CuFFTParamsLRUCache&& other) noexcept :
+    _usage_list(std::move(other._usage_list)),
+    _cache_map(std::move(other._cache_map)),
+    _max_size(other._max_size) {}
+
+  CuFFTParamsLRUCache& operator=(CuFFTParamsLRUCache&& other) noexcept {
+    _usage_list = std::move(other._usage_list);
+    _cache_map = std::move(other._cache_map);
+    _max_size = other._max_size;
+    return *this;
+  }
+
+  // If key is in this cache, return the cached config. Otherwise, emplace the
+  // config in this cache and return it.
+  // Return const reference because CuFFTConfig shouldn't be tampered with once
+  // created.
+  const CuFFTConfig &lookup(CuFFTParams params) {
+    AT_ASSERT(_max_size > 0);
+
+    map_kkv_iter_t map_it = _cache_map.find(params);
+    // Hit, put to list front
+    if (map_it != _cache_map.end()) {
+      _usage_list.splice(_usage_list.begin(), _usage_list, map_it->second);
+      return map_it->second->second;
+    }
+
+    // Miss
+    // remove if needed
+    if (_usage_list.size() >= _max_size) {
+      auto last = _usage_list.end();
+      last--;
+      _cache_map.erase(last->first);
+      _usage_list.pop_back();
+    }
+
+    // construct new plan at list front, then insert into _cache_map
+    _usage_list.emplace_front(std::piecewise_construct,
+                       std::forward_as_tuple(params),
+                       std::forward_as_tuple(params));
+    auto kv_it = _usage_list.begin();
+    _cache_map.emplace(std::piecewise_construct,
+                std::forward_as_tuple(kv_it->first),
+                std::forward_as_tuple(kv_it));
+    return kv_it->second;
+  }
+
+  void clear() {
+    _cache_map.clear();
+    _usage_list.clear();
+  }
+
+  void resize(int64_t new_size) {
+    _set_max_size(new_size);
+    auto cur_size = _usage_list.size();
+    if (cur_size > _max_size) {
+      auto delete_it = _usage_list.end();
+      for (size_t i = 0; i < cur_size - _max_size; i++) {
+        delete_it--;
+        _cache_map.erase(delete_it->first);
+      }
+      _usage_list.erase(delete_it, _usage_list.end());
+    }
+  }
+
+  size_t size() const { return _cache_map.size(); }
+
+  size_t max_size() const noexcept { return _max_size; }
+
+  std::mutex mutex;
+
+private:
+  // Only sets size and does value check. Does not resize the data structures.
+  void _set_max_size(int64_t new_size) {
+    // We check that 0 <= new_size <= CUFFT_MAX_PLAN_NUM here. Since
+    // CUFFT_MAX_PLAN_NUM is of type size_t, we need to do non-negativity check
+    // first.
+    TORCH_CHECK(new_size >= 0,
+             "cuFFT plan cache size must be non-negative, but got ", new_size);
+    TORCH_CHECK(new_size <= CUFFT_MAX_PLAN_NUM,
+             "cuFFT plan cache size can not be larger than ", CUFFT_MAX_PLAN_NUM, ", but got ", new_size);
+    _max_size = static_cast<size_t>(new_size);
+  }
+
+  std::list<kv_t> _usage_list;
+  map_t _cache_map;
+  size_t _max_size;
+};
+
+// Since ATen is separated into CPU build and CUDA build, we need a way to call
+// these functions only when CUDA is loaded. We use CUDA hooks for this purpose
+// (at cuda/detail/CUDAHooks.cpp), and call the hooked functions from the actual
+// native function counterparts (at native/SpectralOps.cpp), i.e.,
+// _cufft_get_plan_cache_max_size, _cufft_set_plan_cache_max_size
+// _cufft_get_plan_cache_size, and _cufft_clear_plan_cache.
+int64_t cufft_get_plan_cache_max_size_impl(DeviceIndex device_index);
+void cufft_set_plan_cache_max_size_impl(DeviceIndex device_index, int64_t max_size);
+int64_t cufft_get_plan_cache_size_impl(DeviceIndex device_index);
+void cufft_clear_plan_cache_impl(DeviceIndex device_index);
+
+}}} // namespace at::native::detail

venv/lib/python3.10/site-packages/torch/include/ATen/native/cuda/CuFFTUtils.h

@@ -0,0 +1,73 @@
+#pragma once
+
+#include <ATen/Config.h>
+
+#include <string>
+#include <stdexcept>
+#include <sstream>
+#include <cufft.h>
+#include <cufftXt.h>
+
+namespace at { namespace native {
+
+// This means that max dim is 3 + 2 = 5 with batch dimension and possible
+// complex dimension
+constexpr int max_rank = 3;
+
+static inline std::string _cudaGetErrorEnum(cufftResult error)
+{
+  switch (error)
+  {
+    case CUFFT_SUCCESS:
+      return "CUFFT_SUCCESS";
+    case CUFFT_INVALID_PLAN:
+      return "CUFFT_INVALID_PLAN";
+    case CUFFT_ALLOC_FAILED:
+      return "CUFFT_ALLOC_FAILED";
+    case CUFFT_INVALID_TYPE:
+      return "CUFFT_INVALID_TYPE";
+    case CUFFT_INVALID_VALUE:
+      return "CUFFT_INVALID_VALUE";
+    case CUFFT_INTERNAL_ERROR:
+      return "CUFFT_INTERNAL_ERROR";
+    case CUFFT_EXEC_FAILED:
+      return "CUFFT_EXEC_FAILED";
+    case CUFFT_SETUP_FAILED:
+      return "CUFFT_SETUP_FAILED";
+    case CUFFT_INVALID_SIZE:
+      return "CUFFT_INVALID_SIZE";
+    case CUFFT_UNALIGNED_DATA:
+      return "CUFFT_UNALIGNED_DATA";
+    case CUFFT_INCOMPLETE_PARAMETER_LIST:
+      return "CUFFT_INCOMPLETE_PARAMETER_LIST";
+    case CUFFT_INVALID_DEVICE:
+      return "CUFFT_INVALID_DEVICE";
+    case CUFFT_PARSE_ERROR:
+      return "CUFFT_PARSE_ERROR";
+    case CUFFT_NO_WORKSPACE:
+      return "CUFFT_NO_WORKSPACE";
+    case CUFFT_NOT_IMPLEMENTED:
+      return "CUFFT_NOT_IMPLEMENTED";
+#if !defined(USE_ROCM)
+    case CUFFT_LICENSE_ERROR:
+      return "CUFFT_LICENSE_ERROR";
+#endif
+    case CUFFT_NOT_SUPPORTED:
+      return "CUFFT_NOT_SUPPORTED";
+    default:
+      std::ostringstream ss;
+      ss << "unknown error " << error;
+      return ss.str();
+  }
+}
+
+static inline void CUFFT_CHECK(cufftResult error)
+{
+  if (error != CUFFT_SUCCESS) {
+    std::ostringstream ss;
+    ss << "cuFFT error: " << _cudaGetErrorEnum(error);
+    AT_ERROR(ss.str());
+  }
+}
+
+}} // at::native

venv/lib/python3.10/site-packages/torch/include/ATen/native/cuda/ForeachMinMaxFunctors.cuh

@@ -0,0 +1,22 @@
+#pragma once
+
+#include <ATen/NumericUtils.h>
+
+namespace at::native {
+
+// std:: does not have clamp functors
+template <typename T>
+struct minimum {
+  __device__ T operator()(const T& a, const T& b) const {
+    return (_isnan(a) || a < b) ? a : b;
+  }
+};
+
+template <typename T>
+struct maximum {
+  __device__ T operator()(const T& a, const T& b) const {
+    return (_isnan(a) || a > b) ? a : b;
+  }
+};
+
+} // namespace at::native

venv/lib/python3.10/site-packages/torch/include/ATen/native/cuda/GridSampler.cuh

@@ -0,0 +1,321 @@
+#pragma once
+#include <ATen/native/cuda/KernelUtils.cuh>
+#include <ATen/native/GridSamplerUtils.h>
+
+namespace at { namespace native {
+
+using detail::GridSamplerInterpolation;
+using detail::GridSamplerPadding;
+
+// Unnormalizes a coordinate from the -1 to +1 scale to its pixel index value,
+// where we view each pixel as an area between (idx - 0.5) and (idx + 0.5).
+// if align_corners: -1 and +1 get sent to the centers of the corner pixels
+//     -1 --> 0
+//     +1 --> (size - 1)
+//     scale_factor = (size - 1) / 2
+// if not align_corners: -1 and +1 get sent to the image edges
+//     -1 --> -0.5
+//     +1 --> (size - 1) + 0.5 == size - 0.5
+//     scale_factor = size / 2
+template <typename scalar_t>
+static __forceinline__ __device__
+scalar_t grid_sampler_unnormalize(scalar_t coord, int size, bool align_corners) {
+  if (align_corners) {
+    // unnormalize coord from [-1, 1] to [0, size - 1]
+    return ((coord + 1.f) / 2) * (size - 1);
+  } else {
+    // unnormalize coord from [-1, 1] to [-0.5, size - 0.5]
+    return ((coord + 1.f) * size - 1) / 2;
+  }
+}
+
+// grid_sampler_unnormalize_set_grad works the same as grid_sampler_unnormalize
+// except that it also returns the `d output / d input` via pointer argument
+// `grad_in`.
+// This is useful in the backward pass of grid_sampler.
+template <typename scalar_t>
+static __forceinline__ __device__
+scalar_t grid_sampler_unnormalize_set_grad(scalar_t coord, int size,
+                                           bool align_corners, scalar_t *grad_in) {
+  if (align_corners) {
+    // unnormalize coord from [-1, 1] to [0, size - 1]
+    *grad_in = static_cast<scalar_t>(size - 1) / 2;
+    return ((coord + 1.f) / 2) * (size - 1);
+  } else {
+    // unnormalize coord from [-1, 1] to [-0.5, size - 0.5]
+    *grad_in = static_cast<scalar_t>(size) / 2;
+    return ((coord + 1.f) * size - 1) / 2;
+  }
+}
+
+// Clips coordinates to between 0 and clip_limit - 1
+template <typename scalar_t>
+static __forceinline__ __device__
+scalar_t clip_coordinates(scalar_t in, int clip_limit) {
+  return ::min(static_cast<scalar_t>(clip_limit - 1), ::max(in, static_cast<scalar_t>(0)));
+}
+
+// clip_coordinates_set_grad works similarly to clip_coordinates except that
+// it also returns the `d output / d input` via pointer argument `grad_in`.
+// This is useful in the backward pass of grid_sampler.
+template <typename scalar_t>
+static __forceinline__ __device__
+scalar_t clip_coordinates_set_grad(scalar_t in, int clip_limit, scalar_t *grad_in) {
+  // Note that it is important for the gradient calculation that borders
+  // are considered out of bounds.
+  if (in <= static_cast<scalar_t>(0)) {
+    *grad_in = static_cast<scalar_t>(0);
+    return static_cast<scalar_t>(0);
+  } else {
+    scalar_t max = static_cast<scalar_t>(clip_limit - 1);
+    if (in >= max) {
+      *grad_in = static_cast<scalar_t>(0);
+      return max;
+    } else {
+      *grad_in = static_cast<scalar_t>(1);
+      return in;
+    }
+  }
+}
+
+// Reflects coordinates until they fall between low and high (inclusive).
+// The bounds are passed as twice their value so that half-integer values
+// can be represented as ints.
+template <typename scalar_t>
+static __forceinline__ __device__
+scalar_t reflect_coordinates(scalar_t in, int twice_low, int twice_high) {
+  if (twice_low == twice_high) {
+    return static_cast<scalar_t>(0);
+  }
+  scalar_t min = static_cast<scalar_t>(twice_low) / 2;
+  scalar_t span = static_cast<scalar_t>(twice_high - twice_low) / 2;
+  in = ::fabs(in - min);
+  // `fmod` returns same sign as `in`, which is positive after the `fabs` above.
+  scalar_t extra = ::fmod(in, span);
+  int flips = static_cast<int>(::floor(in / span));
+  if (flips % 2 == 0) {
+    return extra + min;
+  } else {
+    return span - extra + min;
+  }
+}
+
+// reflect_coordinates_set_grad works similarly to reflect_coordinates except
+// that it also returns the `d output / d input` via pointer argument
+// `grad_in`.
+// This is useful in the backward pass of grid_sampler.
+template <typename scalar_t>
+static __forceinline__ __device__
+scalar_t reflect_coordinates_set_grad(scalar_t in, int twice_low, int twice_high,
+                                      scalar_t *grad_in) {
+  if (twice_low == twice_high) {
+    *grad_in = static_cast<scalar_t>(0);
+    return static_cast<scalar_t>(0);
+  }
+  int grad_in_mult_;
+  scalar_t min = static_cast<scalar_t>(twice_low) / 2;
+  scalar_t span = static_cast<scalar_t>(twice_high - twice_low) / 2;
+  in = in - min;
+  if (in < static_cast<scalar_t>(0)) {
+    grad_in_mult_ = -1;
+    in = -in;
+  } else {
+    grad_in_mult_ = 1;
+  }
+  // `fmod` returns same sign as `in`, which is positive after the `if` above.
+  scalar_t extra = ::fmod(in, span);
+  int flips = static_cast<int>(::floor(in / span));
+  if (flips % 2 == 0) {
+    *grad_in = static_cast<scalar_t>(grad_in_mult_);
+    return extra + min;
+  } else {
+    *grad_in = static_cast<scalar_t>(-grad_in_mult_);
+    return span - extra + min;
+  }
+}
+
+template<typename scalar_t>
+static __forceinline__ __device__
+scalar_t safe_downgrade_to_int_range(scalar_t x){
+  // -100.0 does not have special meaning. This is just to make sure
+  // it's not within_bounds_2d or within_bounds_3d, and does not cause
+  // undefined behavior. See #35506.
+  if (x > INT_MAX-1 || x < INT_MIN || !::isfinite(static_cast<double>(x)))
+    return static_cast<scalar_t>(-100.0);
+  return x;
+}
+
+template<typename scalar_t>
+static __forceinline__ __device__
+scalar_t compute_coordinates(scalar_t coord, int size,
+                             GridSamplerPadding padding_mode,
+                             bool align_corners) {
+  if (padding_mode == GridSamplerPadding::Border) {
+    // clip coordinates to image borders
+    coord = clip_coordinates(coord, size);
+  } else if (padding_mode == GridSamplerPadding::Reflection) {
+    // reflect coordinates by image borders
+    if (align_corners) {
+      coord = reflect_coordinates(coord, 0, 2*(size - 1));
+    } else {
+      coord = reflect_coordinates(coord, -1, 2*size - 1);
+    }
+    // clip coordinates to image borders
+    coord = clip_coordinates(coord, size);
+  }
+
+  coord = safe_downgrade_to_int_range(coord);
+  return coord;
+}
+
+// Computes the pixel source index value for a grid coordinate
+template <typename scalar_t>
+static __forceinline__ __device__
+scalar_t grid_sampler_compute_source_index(
+    scalar_t coord,
+    int size,
+    GridSamplerPadding padding_mode,
+    bool align_corners) {
+  coord = grid_sampler_unnormalize(coord, size, align_corners);
+  coord = compute_coordinates(coord, size, padding_mode, align_corners);
+  return coord;
+}
+
+// grid_sampler_compute_source_index_set_grad works similarly to
+// grid_sampler_compute_source_index except that it also returns the
+// `d output / d input` via pointer argument `grad_in`.
+// This is useful in the backward pass of grid_sampler.
+template <typename scalar_t>
+static __forceinline__ __device__
+scalar_t grid_sampler_compute_source_index_set_grad(
+    scalar_t coord,
+    int size,
+    GridSamplerPadding padding_mode,
+    bool align_corners,
+    scalar_t *grad_in) {
+  scalar_t grad_clip, grad_refl;
+  coord = grid_sampler_unnormalize_set_grad(coord, size, align_corners, grad_in);
+  if (padding_mode == GridSamplerPadding::Border) {
+    // clip coordinates to image borders
+    coord = clip_coordinates_set_grad(coord, size, &grad_clip);
+    *grad_in = (*grad_in) * grad_clip;
+  } else if (padding_mode == GridSamplerPadding::Reflection) {
+    // reflect coordinates by image borders
+    if (align_corners) {
+      coord = reflect_coordinates_set_grad(coord, 0, 2*(size - 1), &grad_refl);
+    } else {
+      coord = reflect_coordinates_set_grad(coord, -1, 2*size - 1, &grad_refl);
+    }
+    // clip coordinates to image borders
+    coord = clip_coordinates_set_grad(coord, size, &grad_clip);
+    *grad_in = (*grad_in) * grad_refl * grad_clip;
+  }
+
+  coord = safe_downgrade_to_int_range(coord);
+  return coord;
+}
+
+static __forceinline__ __device__
+bool within_bounds_2d(int h, int w, int H, int W) {
+  return h >= 0 && h < H && w >= 0 && w < W;
+}
+
+static __forceinline__ __device__
+bool within_bounds_3d(int d, int h, int w, int D, int H, int W) {
+  return d >= 0 && d < D && h >= 0 && h < H && w >= 0 && w < W;
+}
+
+template<typename scalar_t>
+static __forceinline__ __device__
+scalar_t get_value_bounded(
+    scalar_t *data, scalar_t x, scalar_t y, int W, int H, int sW, int sH,
+    GridSamplerPadding padding_mode,
+    bool align_corners) {
+
+  x = compute_coordinates(x, W, padding_mode, align_corners);
+  y = compute_coordinates(y, H, padding_mode, align_corners);
+
+  int ix = static_cast<int>(x);
+  int iy = static_cast<int>(y);
+
+  if (within_bounds_2d(iy, ix, H, W)) {
+    return data[iy * sH + ix * sW];
+  }
+  return static_cast<scalar_t>(0);
+}
+
+template<typename scalar_t, typename index_t>
+static __forceinline__ __device__
+void safe_add_2d(scalar_t *data, int h, int w,
+                 int sH, int sW, int H, int W,
+                 scalar_t delta,
+                 const index_t NC_offset,
+                 const index_t memory_span) {
+  if (within_bounds_2d(h, w, H, W)) {
+    fastAtomicAdd(data,
+                  NC_offset + h * sH + w * sW,
+                  memory_span,
+                  delta,
+                  true);
+  }
+}
+
+template<typename scalar_t, typename index_t>
+static __forceinline__ __device__
+void safe_add_3d(scalar_t *data, int d, int h, int w,
+                 int sD, int sH, int sW, int D, int H, int W,
+                 scalar_t delta,
+                 const index_t NC_offset,
+                 const index_t memory_span) {
+  if (within_bounds_3d(d, h, w, D, H, W)) {
+    fastAtomicAdd(data,
+                  NC_offset + d * sD + h * sH + w * sW,
+                  memory_span,
+                  delta,
+                  true);
+  }
+}
+
+template<typename scalar_t, typename index_t>
+static __forceinline__ __device__
+void add_value_bounded(
+    scalar_t* data, scalar_t x, scalar_t y, int W, int H, int sW, int sH,
+    scalar_t delta,
+    GridSamplerPadding padding_mode,
+    bool align_corners,
+    const index_t NC_offset,
+    const index_t memory_span) {
+
+  x = compute_coordinates(x, W, padding_mode, align_corners);
+  y = compute_coordinates(y, H, padding_mode, align_corners);
+
+  int ix = static_cast<int>(x);
+  int iy = static_cast<int>(y);
+
+  safe_add_2d(data, iy, ix, sH, sW, H, W, delta, NC_offset, memory_span);
+}
+
+// Calculate the differential of the cubic convolution, i.e. `d coeff / d x`
+template<typename scalar_t>
+static __forceinline__ __device__
+void get_cubic_coefficients_grad(
+    scalar_t coeffs[4],
+    scalar_t t) {
+
+  // Must be the same as forward calculation in
+  // aten/src/ATen/native/cuda/UpSample.cuh:get_cubic_upsample_coefficients
+  scalar_t A = -0.75;
+
+  scalar_t x;
+  x = -1 - t;  // 1 < x = |-1 - tx| < 2
+  coeffs[0] = (-3 * A * x - 10 * A ) * x - 8 * A;
+  x = -t;     // x = |0 - tx| <= 1
+  coeffs[1] = (-3 * (A + 2) * x - 2 * (A + 3)) * x;
+  x = 1 - t;  // x = |1 - tx| <= 1
+  coeffs[2] = (3 * (A + 2) * x - 2 * (A + 3)) * x;
+  x = 2 - t;  // 1 < x = |2 - tx| < 2
+  coeffs[3] = (3 * A * x - 10 * A) * x + 8 * A;
+}
+
+
+}}  // namespace at::native

venv/lib/python3.10/site-packages/torch/include/ATen/native/cuda/GridSampler.h

@@ -0,0 +1,32 @@
+#pragma once
+#include <array>
+#include <cstdint>
+
+namespace at {
+class TensorBase;
+}
+
+namespace at {
+namespace native {
+
+void launch_grid_sampler_2d_forward_kernel(
+    const TensorBase &output, const TensorBase &input, const TensorBase &grid,
+    int64_t interpolation_mode, int64_t padding_mode, bool align_corners);
+
+void launch_grid_sampler_3d_forward_kernel(
+    const TensorBase &output, const TensorBase &input, const TensorBase &grid,
+    int64_t interpolation_mode, int64_t padding_mode, bool align_corners);
+
+void launch_grid_sampler_2d_backward_kernel(
+    const TensorBase &grad_input, const TensorBase &grad_grid,
+    const TensorBase &grad_output, const TensorBase &input,
+    const TensorBase &grid, int64_t interpolation_mode, int64_t padding_mode,
+    bool align_corners, std::array<bool, 2> output_mask);
+
+void launch_grid_sampler_3d_backward_kernel(
+    const TensorBase &grad_input, const TensorBase &grad_grid,
+    const TensorBase &grad_output, const TensorBase &input,
+    const TensorBase &grid, int64_t interpolation_mode, int64_t padding_mode,
+    bool align_corners, std::array<bool, 2> output_mask);
+
+}}  // namespace at::native

venv/lib/python3.10/site-packages/torch/include/ATen/native/cuda/IndexKernel.h

@@ -0,0 +1,16 @@
+#pragma once
+#include <c10/core/ScalarType.h>
+#include <cstdint>
+
+namespace at {
+struct TensorIteratorBase;
+class TensorBase;
+}
+
+namespace at {
+namespace native {
+/// @param maskPrefixSum[in,out]
+void launch_masked_scatter_kernel(
+    const TensorBase &self, const TensorBase &mask,
+    const TensorBase &maskPrefixSum, const TensorBase &source);
+}}

venv/lib/python3.10/site-packages/torch/include/ATen/native/cuda/JitLoops.cuh

@@ -0,0 +1,187 @@
+#pragma once
+
+#include <ATen/jit_macros.h>
+
+#if AT_USE_JITERATOR()
+
+#include <ATen/cuda/CUDAConfig.h>
+
+#include <ATen/OpMathType.h>
+#include <ATen/TensorIterator.h>
+#include <ATen/native/TensorIteratorDynamicCasting.h>
+
+#include <ATen/native/cuda/MemoryAccess.cuh>
+
+#include <ATen/native/cuda/CUDAJitLoops.cuh>
+
+namespace at {
+namespace native {
+
+/* Note [Jiterator]
+The "jiterator" simply just-in-time compiles the same kernels that
+Loops.cuh (and CUDALoops.cuh) usually build. This reduces build time,
+build size, and initial CUDA context size.
+
+By default on non-Windows systems, it also caches compiled kernels in ~/.cache/torch/kernels.
+This behavior is controlled with two environment variables:
+  - USE_PYTORCH_KERNEL_CACHE, if set to zero then this will disable all cache use
+  - PYTORCH_KERNEL_CACHE_PATH, if set specifies the folder to use for cached kernels
+
+The jiterator currently has some limitations, however. It cannot:
+  - handle math on complex datatypes
+  - handle kernels with scalar parameters
+
+These improvements will likely come soon.
+
+For examples of how to use the jiterator see the i1 and gcd kernel
+implementations, which pass jittable strings implementing their
+operations instead of the typical CUDA functors.
+
+To pass a runtime argument (similar to lambda captures in non-JIT kernels),
+we need to pass to additional arguments to `jitted_gpu_kernel` by value.
+Currently only primitive C++ types used for computation are valid.
+The order of these extra arguments should be same as the order they appear
+in kernel's function signature. (look at polygamma for example)
+
+NOTE: One big restriction being that these arguments should be after the
+arguments provided by TensorIterator. Eg. While capturing `n`, where
+`scalar_t x` and `scalar_t y` are provided by TensorIterator,
+* foo(scalar_t x, scalar_t y, int n) works!
+* foo(int n, scalar_t x, scalar_y) doesn't work
+* foo(scalar_t x, int n, scalar_y) doesn't work
+
+*/
+
+// Entrypoint for jitted GPU kernels.
+// Only handles elementwise unary and binary kernels with a
+//   common dtype and a single output.
+// NOTE: this assumes the op's iterator has a common_dtype.
+// NOTE: We use std::tuple instead of parameter pack
+//  for `extra_args` due to following
+// bug on older versions of clang
+// https://bugs.llvm.org/show_bug.cgi?id=23029
+template <
+    char const* name,
+    typename return_type,
+    typename f_inputs_type,
+    int arity,
+    typename... Args>
+void jitted_gpu_kernel(
+    TensorIteratorBase& iter,
+    const std::string& f,
+    at::cuda::jit::BinaryFuncVariant scalar_pos =
+        at::cuda::jit::BinaryFuncVariant::NoScalar,
+    at::opmath_type<f_inputs_type> scalar_val = 0,
+    std::tuple<Args...> extra_args = std::make_tuple()) {
+  // TODO: much of preamble is common to both jitted_gpu_kernel and gpu_kernel
+  //   Maybe it could be refactored?
+  for (int arg = 0; arg < iter.ntensors(); arg++) {
+    TORCH_INTERNAL_ASSERT(
+      iter.device(arg).is_cuda(),
+      "argument ", arg, ": expected a CUDA device but found ", iter.device(arg));
+  }
+
+  if (iter.numel() == 0) {
+    return;
+  }
+
+  if (!iter.can_use_32bit_indexing()) {
+    for (auto& sub_iter : iter.with_32bit_indexing()) {
+      jitted_gpu_kernel<name, return_type, f_inputs_type, arity>(
+          sub_iter, f, scalar_pos, scalar_val, extra_args);
+    }
+
+    return;
+  }
+
+  // Computes if dynamic casting is needed
+  // Dynamic casting is needed if an input's dtype differs from the common dtype
+  //   or if the result dtype differs from the output's dtype
+  // Note: this is intentionally divergent from calling needs_dynamic_casting,
+  //   which is more general and inspects a lambda to determine if dynamic
+  //   casting is needed.
+  bool needs_dynamic_casting = false;
+
+  // Checks output
+  const ScalarType return_scalar_type = c10::CppTypeToScalarType<return_type>::value;
+  const auto dtype0 = iter.dtype(0);
+  if (dtype0 != return_scalar_type) {
+    needs_dynamic_casting = true;
+  }
+
+  // Checks input(s)
+  const ScalarType inputs_scalar_type = c10::CppTypeToScalarType<f_inputs_type>::value;
+  for (auto i = decltype(arity){1}; i < (arity + 1); ++i) {
+    const auto dtypei = iter.dtype(i);
+    if (dtypei != inputs_scalar_type) {
+      needs_dynamic_casting = true;
+      break;
+    }
+  }
+  if (scalar_pos == at::cuda::jit::BinaryFuncVariant::NoScalar) {
+    // NOTE: With `scalar_pos=NoScalar`,`scalar_val` is not used
+    // for computation in the generated code and hence we pass a dummy
+    // value of `0`.
+    jitted_gpu_kernel_impl<
+        /*name*/ name,
+        /*return_type=*/return_type,
+        /*f_inputs_type=*/f_inputs_type,
+        arity,
+        at::cuda::jit::BinaryFuncVariant::NoScalar>(
+        iter, f, needs_dynamic_casting, /*scalar_val=*/scalar_val, extra_args);
+  } else if (scalar_pos == at::cuda::jit::BinaryFuncVariant::RhsScalar) {
+    jitted_gpu_kernel_impl<
+        /*name*/ name,
+        /*return_type=*/return_type,
+        /*f_inputs_type=*/f_inputs_type,
+        arity,
+        at::cuda::jit::BinaryFuncVariant::RhsScalar>(
+        iter,
+        f,
+        needs_dynamic_casting,
+        scalar_val,
+        extra_args);
+
+  } else {
+    jitted_gpu_kernel_impl<
+        /*name*/ name,
+        /*return_type=*/return_type,
+        /*f_inputs_type=*/f_inputs_type,
+        arity,
+        at::cuda::jit::BinaryFuncVariant::LhsScalar>(
+        iter,
+        f,
+        needs_dynamic_casting,
+        scalar_val,
+        extra_args);
+  }
+}
+
+// TODO: support runtime state capture similar to `jitted_gpu_kernel`.
+template <char const *name, typename return_type, typename f_inputs_type>
+void opmath_jitted_gpu_kernel_with_scalars(TensorIteratorBase& iter, const std::string& f) {
+  TORCH_INTERNAL_ASSERT(iter.ntensors() == 3);
+  //currently jiterator only handles binary functions where both inputs are of the same type (f_inputs_type)
+  using opmath_t = at::opmath_type<f_inputs_type>;
+  if (iter.is_cpu_scalar(1)) {
+    auto scalar_val = iter.scalar_value<opmath_t>(1);
+    iter.remove_operand(1);
+    // TODO: When all kernels that use gpu_kernel_with_scalars are
+    // ported to structured, this device guard can be deleted.  This
+    // works around incorrect device guard generation for pre-structured
+    // kernels device guards, but structured kernels do it right and
+    // we can assume the device is already set correctly
+    const OptionalDeviceGuard device_guard(iter.device(1));
+    jitted_gpu_kernel<name, return_type, f_inputs_type, 1>(iter, f, at::cuda::jit::BinaryFuncVariant::LhsScalar, scalar_val);
+  } else if (iter.is_cpu_scalar(2)) {
+    auto scalar_val = iter.scalar_value<opmath_t>(2);
+    iter.remove_operand(2);
+    jitted_gpu_kernel<name, return_type, f_inputs_type, 1>(iter, f, at::cuda::jit::BinaryFuncVariant::RhsScalar, scalar_val);
+  } else {
+    jitted_gpu_kernel<name, return_type, f_inputs_type, 2>(iter, f);
+  }
+}
+
+}}  // at::native
+
+#endif // AT_USE_JITERATOR()

venv/lib/python3.10/site-packages/torch/include/ATen/native/cuda/KernelUtils.cuh

@@ -0,0 +1,149 @@
+#pragma once
+#include <ATen/cuda/Atomic.cuh>
+
+#if !(defined(USE_ROCM) || ((defined(__CUDA_ARCH__) && (__CUDA_ARCH__ < 800))))
+#include <cuda_bf16.h>
+#endif
+
+namespace at {
+namespace native {
+
+__device__ __forceinline__ size_t
+idx(const size_t nc,
+    const size_t height,
+    const size_t width,
+    const size_t h,
+    const size_t w) {
+  return (nc * height + h) * width + w;
+}
+
+// for channels-last
+__device__ __forceinline__ size_t
+idx_cl(
+  const size_t n, const size_t h, const size_t w, const size_t c,
+  const size_t height, const size_t width, const size_t channel
+) {
+  return ((n * height + h) * width + w) * channel + c;
+}
+
+// fastSpecializedAtomicAdd (and fastAtomicAdd) are an optimization
+// that speed up half-precision atomics.  The situation with half
+// precision atomics is that we have a slow __half atomic, and
+// a fast vectored __half2 atomic (this can be worth up to a 6x
+// speedup, see https://github.com/pytorch/pytorch/pull/21879).
+// We can convert a __half atomic into a __half2 atomic by simply
+// pairing the __half with a zero entry on the left/right depending
+// on alignment... but only if this wouldn't cause an out of bounds
+// access!  Thus, you must specify tensor and numel so we can check
+// if you would be out-of-bounds and use a plain __half atomic if
+// you would be.
+template <
+    typename scalar_t,
+    typename index_t,
+    typename std::enable_if<std::is_same<c10::Half, scalar_t>::value>::type* =
+        nullptr>
+__device__ __forceinline__ void fastSpecializedAtomicAdd(
+    scalar_t* tensor,
+    index_t index,
+    const index_t numel,
+    scalar_t value) {
+#if (                      \
+    (defined(USE_ROCM)) || \
+    (defined(__CUDA_ARCH__) && (__CUDA_ARCH__ < 700)))
+  gpuAtomicAddNoReturn(
+      reinterpret_cast<at::Half*>(tensor) + index,
+      static_cast<at::Half>(value));
+#else
+  // Accounts for the chance tensor falls on an odd 16 bit alignment (ie, not 32 bit aligned)
+  __half* target_addr = reinterpret_cast<__half*>(tensor + index);
+  bool low_byte = (reinterpret_cast<std::uintptr_t>(target_addr) % sizeof(__half2) == 0);
+
+  if (low_byte && index < (numel - 1)) {
+    __half2 value2;
+    value2.x = static_cast<__half>(value);
+    value2.y = __int2half_rz(0);
+    atomicAdd(reinterpret_cast<__half2*>(target_addr), value2);
+
+  } else if (!low_byte && index > 0) {
+    __half2 value2;
+    value2.x = __int2half_rz(0);
+    value2.y = static_cast<__half>(value);
+    atomicAdd(reinterpret_cast<__half2*>(target_addr - 1), value2);
+
+  } else {
+    atomicAdd(
+        reinterpret_cast<__half*>(tensor) + index, static_cast<__half>(value));
+  }
+#endif
+}
+
+template <
+    typename scalar_t,
+    typename index_t,
+    typename std::enable_if<std::is_same<c10::BFloat16, scalar_t>::value>::type* =
+        nullptr>
+__device__ __forceinline__ void fastSpecializedAtomicAdd(
+    scalar_t* tensor,
+    index_t index,
+    const index_t numel,
+    scalar_t value) {
+#if (                      \
+    (defined(USE_ROCM)) || \
+    (defined(__CUDA_ARCH__) && (__CUDA_ARCH__ < 800)))
+  gpuAtomicAddNoReturn(
+      reinterpret_cast<at::BFloat16*>(tensor) + index,
+      static_cast<at::BFloat16>(value));
+#else
+  // Accounts for the chance tensor falls on an odd 16 bit alignment (ie, not 32 bit aligned)
+  __nv_bfloat16* target_addr = reinterpret_cast<__nv_bfloat16*>(tensor + index);
+  bool low_byte = (reinterpret_cast<std::uintptr_t>(target_addr) % sizeof(__nv_bfloat162) == 0);
+
+  if (low_byte && index < (numel - 1)) {
+    __nv_bfloat162 value2;
+    value2.x = *reinterpret_cast<__nv_bfloat16*>(&value);
+    value2.y = __int2bfloat16_rz(0);
+    atomicAdd(reinterpret_cast<__nv_bfloat162*>(target_addr), value2);
+
+  } else if (!low_byte && index > 0) {
+    __nv_bfloat162 value2;
+    value2.x = __int2bfloat16_rz(0);
+    value2.y = *reinterpret_cast<__nv_bfloat16*>(&value);
+    atomicAdd(reinterpret_cast<__nv_bfloat162*>(target_addr - 1), value2);
+
+  } else {
+    atomicAdd(
+        reinterpret_cast<__nv_bfloat16*>(tensor) + index, *reinterpret_cast<__nv_bfloat16*>(&value));
+  }
+#endif
+}
+
+
+template <
+    typename scalar_t,
+    typename index_t,
+    typename std::enable_if<!std::is_same<c10::Half, scalar_t>::value && !std::is_same<c10::BFloat16, scalar_t>::value >::type* =
+        nullptr>
+__device__ __forceinline__ void fastSpecializedAtomicAdd(
+    scalar_t* tensor,
+    index_t index,
+    const index_t numel,
+    scalar_t value) {
+  gpuAtomicAddNoReturn(tensor + index, value);
+}
+
+template <class scalar_t, class index_t>
+__device__ __forceinline__ void fastAtomicAdd(
+    scalar_t* tensor,
+    index_t index,
+    const index_t numel,
+    scalar_t value,
+    bool fast_atomics) {
+  if (fast_atomics) {
+    fastSpecializedAtomicAdd(tensor, index, numel, value);
+  } else {
+    gpuAtomicAddNoReturn(tensor + index, value);
+  }
+}
+
+} // namespace native
+} // namespace at

venv/lib/python3.10/site-packages/torch/include/ATen/native/cuda/LaunchUtils.h

@@ -0,0 +1,18 @@
+#pragma once
+#include<algorithm>
+
+namespace at {
+namespace native {
+
+// returns 2**floor(log2(n))
+static int lastPow2(unsigned int n) {
+  n |= (n >> 1);
+  n |= (n >> 2);
+  n |= (n >> 4);
+  n |= (n >> 8);
+  n |= (n >> 16);
+  return std::max<int>(1, n - (n >> 1));
+}
+
+} // namespace native
+} // namespace at

venv/lib/python3.10/site-packages/torch/include/ATen/native/cuda/Loops.cuh

@@ -0,0 +1,326 @@
+#pragma once
+
+#include <ATen/detail/FunctionTraits.h>
+#include <ATen/native/TensorIterator.h>
+#include <ATen/native/TensorIteratorDynamicCasting.h>
+#include <ATen/cuda/detail/OffsetCalculator.cuh>
+#include <ATen/OpMathType.h>
+#include <ATen/native/cuda/thread_constants.h>
+
+#include <thrust/tuple.h>
+
+#include <ATen/native/cuda/MemoryAccess.cuh>
+
+
+namespace at { namespace native {
+
+template<int N>
+static OffsetCalculator<N> make_input_offset_calculator(const TensorIteratorBase& iter) {
+  // array size can not be 0, this happens when N == 0
+  constexpr int array_size = std::max<int>(N, 1);
+  TORCH_INTERNAL_ASSERT(N == iter.ntensors() - iter.noutputs());
+  std::array<const int64_t*, array_size> strides;
+  int64_t element_sizes[array_size];
+  for (int i = 0; i < N; i++) {
+    strides[i] = iter.strides(i + iter.noutputs()).data();
+    element_sizes[i] = iter.element_size(i + iter.noutputs());
+  }
+  return OffsetCalculator<N>(iter.ndim(), iter.shape().data(), strides.data(), element_sizes);
+}
+
+template <int num_outputs = 1>
+static OffsetCalculator<num_outputs> make_output_offset_calculator(const TensorIteratorBase& iter) {
+  TORCH_INTERNAL_ASSERT(num_outputs == iter.noutputs());
+  std::array<const int64_t*, num_outputs> strides;
+  int64_t element_sizes[num_outputs];
+  for (int i = 0; i < num_outputs; i++) {
+    strides[i] = iter.strides(i).data();
+    element_sizes[i] = iter.element_size(i);
+  }
+  return OffsetCalculator<num_outputs>(iter.ndim(), iter.shape().data(), strides.data(), element_sizes);
+}
+
+template<typename func_t, typename policy_t>
+__device__ inline void elementwise_kernel_helper(func_t f, policy_t policy) {
+  using traits = function_traits<func_t>;
+  using return_t = typename traits::result_type;
+  using args_t = typename traits::ArgsTuple;
+
+  int idx = blockIdx.x;
+
+  return_t results[thread_work_size()];
+  args_t args[thread_work_size()];
+
+  // load
+  policy.load(args, idx);
+
+  // compute
+  #pragma unroll
+  for (int i = 0; i < thread_work_size(); i++) {
+    if (policy.check_inbounds(i)) {
+      results[i] = c10::guts::apply(f, args[i]);
+    }
+  }
+
+  // store
+  policy.store(results, idx);
+}
+
+}}  // namespace at::native
+
+#include <ATen/native/cuda/CUDALoops.cuh>
+
+namespace at:: native {
+
+template <typename func_t>
+void gpu_kernel_nocast(TensorIteratorBase& iter, const func_t& f) {
+
+  for (int arg = 0; arg < iter.ntensors(); arg++) {
+    TORCH_INTERNAL_ASSERT(
+      iter.device(arg).is_cuda(),
+      "argument ", arg, ": expected a CUDA device but found ", iter.device(arg));
+  }
+
+  if (iter.numel() == 0) {
+    return;
+  }
+
+  if (!iter.can_use_32bit_indexing()) {
+    for (auto& sub_iter : iter.with_32bit_indexing()) {
+      gpu_kernel_nocast(sub_iter, f);
+    }
+    return;
+  }
+
+  gpu_kernel_impl_nocast(iter, f);
+}
+
+template <typename func_t>
+void gpu_kernel(TensorIteratorBase& iter, const func_t& f) {
+
+  for (int arg = 0; arg < iter.ntensors(); arg++) {
+    TORCH_INTERNAL_ASSERT(
+      iter.device(arg).is_cuda(),
+      "argument ", arg, ": expected a CUDA device but found ", iter.device(arg));
+  }
+
+  if (iter.numel() == 0) {
+    return;
+  }
+
+  if (!iter.can_use_32bit_indexing()) {
+    for (auto& sub_iter : iter.with_32bit_indexing()) {
+      gpu_kernel(sub_iter, f);
+    }
+    return;
+  }
+
+  gpu_kernel_impl(iter, f);
+}
+
+template<typename arg1_t, typename arg2_t, typename return_t, typename func_t>
+struct AUnaryFunctor {
+  using traits = function_traits<func_t>;
+  using opmath_arg1_t = typename traits::template arg<0>::type;
+  __device__ return_t operator()(arg2_t b) const {
+    return f(a, b);
+  }
+  // NB: scalar is stored in higher precision!
+  AUnaryFunctor(func_t f_, opmath_arg1_t a_): f(f_), a(a_) {}
+  private:
+    func_t f;
+    opmath_arg1_t a;
+};
+
+template<typename arg1_t, typename arg2_t, typename return_t, typename func_t>
+struct BUnaryFunctor {
+  using traits = function_traits<func_t>;
+  using opmath_arg2_t = typename traits::template arg<1>::type;
+  __device__ return_t operator()(arg1_t a) const {
+    return f(a, b);
+  }
+  // NB: scalar is stored in higher precision!
+  BUnaryFunctor(func_t f_, opmath_arg2_t b_): f(f_), b(b_) {}
+  private:
+    func_t f;
+    opmath_arg2_t b;
+};
+
+// Though seemingly noop, this inserts casts from arg1_t to func_t's type
+// (which may be higher precision), as well as casts to return_t
+template <typename arg1_t, typename arg2_t, typename return_t, typename func_t>
+struct BinaryFunctor {
+  __device__ return_t operator()(arg1_t a, arg2_t b) const {
+    return f(a, b);
+  }
+  BinaryFunctor(func_t f_): f(f_) {}
+  private:
+    func_t f;
+};
+
+// Unlike gpu_kernel_with_scalars, this allows you to pass a func_t which
+// accepts inputs at higher precision (typically opmath_t), but then
+// ensure that we load from memory at the correct precision (scalar_t)
+// to avoid expensive loads.  For the whole sordid story see
+// https://dev-discuss.pytorch.org/t/cuda-loops-case-study-code-generation-vs-templates/302
+template <typename arg1_t, typename arg2_t = arg1_t, typename return_t = arg1_t, typename func_t>
+void opmath_gpu_kernel_with_scalars(TensorIteratorBase& iter, const func_t& f) {
+  TORCH_INTERNAL_ASSERT(iter.ntensors() == 3);
+
+  using traits = function_traits<func_t>;
+  using opmath_arg1_t = typename traits::template arg<0>::type;
+  using opmath_arg2_t = typename traits::template arg<1>::type;
+  static_assert(
+      traits::arity == 2,
+      "gpu_kernel_with_scalars only supports two input arguments");
+
+  if (iter.is_cpu_scalar(1)) {
+    AUnaryFunctor<arg1_t, arg2_t, return_t, func_t> af(f, iter.scalar_value<opmath_arg1_t>(1));
+    iter.remove_operand(1);
+    // TODO: When all kernels that use gpu_kernel_with_scalars are
+    // ported to structured, this device guard can be deleted.  This
+    // works around incorrect device guard generation for pre-structured
+    // kernels device guards, but structured kernels do it right and
+    // we can assume the device is already set correctly
+    const OptionalDeviceGuard device_guard(iter.device(1));
+    gpu_kernel(iter, af);
+  } else if (iter.is_cpu_scalar(2)) {
+    BUnaryFunctor<arg1_t, arg2_t, return_t, func_t> bf(f, iter.scalar_value<opmath_arg2_t>(2));
+    iter.remove_operand(2);
+    gpu_kernel(iter, bf);
+  } else {
+    gpu_kernel(iter, BinaryFunctor<arg1_t, arg2_t, return_t, func_t>(f));
+  }
+}
+
+template <typename scalar_t, typename return_t = scalar_t, typename func_t>
+void opmath_symmetric_gpu_kernel_with_scalars(TensorIteratorBase& iter, const func_t& f) {
+  // Use symmetric property of the functor to reduce number of kernels,
+  // requires f(a, b) == f(b, a)
+  TORCH_INTERNAL_ASSERT(iter.ntensors() == 3);
+
+  using traits = function_traits<func_t>;
+  using opmath_arg_t = typename traits::template arg<0>::type;
+  static_assert(
+      traits::arity == 2,
+      "gpu_kernel_with_scalars only supports two input arguments");
+  static_assert(std::is_same<opmath_arg_t, typename traits::template arg<1>::type>::value,
+                "f is not symmetric");
+
+  OptionalDeviceGuard device_guard;
+  opmath_arg_t scalar_val{};
+
+  if (iter.is_cpu_scalar(1)) {
+    scalar_val = iter.scalar_value<opmath_arg_t>(1);
+    iter.remove_operand(1);
+
+    // TODO: When all kernels that use gpu_kernel_with_scalars are
+    // ported to structured, this device guard can be deleted.  This
+    // works around incorrect device guard generation for pre-structured
+    // kernels device guards, but structured kernels do it right and
+    // we can assume the device is already set correctly
+    device_guard.reset_device(iter.device(1));
+  } else if (iter.is_cpu_scalar(2)) {
+    scalar_val = iter.scalar_value<opmath_arg_t>(2);
+    iter.remove_operand(2);
+  }
+
+  if (iter.ninputs() == 2) {
+    gpu_kernel(iter, BinaryFunctor<scalar_t, scalar_t, return_t, func_t>(f));
+  } else {
+    AUnaryFunctor<scalar_t, scalar_t, return_t, func_t> unary_f(f, scalar_val);
+    gpu_kernel(iter, unary_f);
+  }
+}
+
+// Legacy variant that assumes that func_t has the correct types
+// that we expect to load from memory
+template <typename func_t>
+void gpu_kernel_with_scalars(TensorIteratorBase& iter, const func_t& f) {
+  using traits = function_traits<func_t>;
+  static_assert(
+      traits::arity == 2,
+      "gpu_kernel_with_scalars only supports two input arguments");
+  using arg1_t = typename traits::template arg<0>::type;
+  using arg2_t = typename traits::template arg<1>::type;
+  using return_t = typename traits::result_type;
+  opmath_gpu_kernel_with_scalars<arg1_t, arg2_t, return_t, func_t>(iter, f);
+}
+
+namespace { // functions for `gpu_kernel_multiple_outputs`.
+
+// check the return type is `thrust::tuple`, not `std::tuple`.
+template <typename T> struct is_tuple: std::false_type {};
+
+template <typename ...T> struct is_tuple<thrust::tuple<T...>>: std::true_type {};
+
+template <int num_outputs, typename func_t, typename array_t, typename inp_calc_t, typename out_calc_t>
+C10_LAUNCH_BOUNDS_1(num_threads())
+__global__ void unrolled_elementwise_kernel_for_multi_outputs(int N, func_t f, array_t data, inp_calc_t ic, out_calc_t oc) {
+  int remaining = N - block_work_size() * blockIdx.x;
+  elementwise_kernel_helper(f, memory::policies::multi_outputs_unroll<array_t, inp_calc_t, out_calc_t, num_outputs>(data, remaining, ic, oc));
+}
+
+template <int num_outputs, typename func_t, typename array_t, typename inp_calc_t, typename out_calc_t>
+static inline void launch_unrolled_kernel_for_multi_outputs(int64_t N, const func_t& f, array_t data, inp_calc_t ic, out_calc_t oc) {
+  TORCH_INTERNAL_ASSERT(N > 0 && N <= std::numeric_limits<int32_t>::max());
+  int64_t grid = (N + block_work_size() - 1) / block_work_size();
+  auto stream = at::cuda::getCurrentCUDAStream();
+  unrolled_elementwise_kernel_for_multi_outputs<num_outputs, func_t, array_t><<<grid, num_threads(), 0, stream>>>(N, f, data, ic, oc);
+  C10_CUDA_KERNEL_LAUNCH_CHECK();
+}
+
+template <typename func_t>
+void gpu_kernel_multiple_outputs_impl(TensorIteratorBase& iter, const func_t& f) {
+  using traits = function_traits<func_t>;
+  using output_t = typename traits::result_type;
+  static_assert(is_tuple<output_t>::value, "f's return type must be `thrust::tuple`");
+  constexpr int num_outputs = thrust::tuple_size<output_t>::value;
+  constexpr int num_inputs = traits::arity;
+  constexpr int ntensors = num_outputs + num_inputs;
+
+  TORCH_INTERNAL_ASSERT(iter.can_use_32bit_indexing());
+  TORCH_INTERNAL_ASSERT(iter.ntensors() == ntensors);
+
+  at::detail::Array<char*, ntensors> data;
+  for (int i = 0; i < ntensors; i++) {
+    data[i] = (char*)iter.data_ptr(i);
+  }
+
+  int64_t numel = iter.numel();
+
+  if (iter.is_contiguous()) {
+    auto input_calc = TrivialOffsetCalculator<num_inputs>();
+    auto output_calc = TrivialOffsetCalculator<num_outputs>();
+    launch_unrolled_kernel_for_multi_outputs<num_outputs>(numel, f, data, input_calc, output_calc);
+  } else {
+    auto input_calc = make_input_offset_calculator<num_inputs>(iter);
+    auto output_calc = make_output_offset_calculator<num_outputs>(iter);
+    launch_unrolled_kernel_for_multi_outputs<num_outputs>(numel, f, data, input_calc, output_calc);
+  }
+}
+} // namespace
+
+template <typename func_t>
+void gpu_kernel_multiple_outputs(TensorIteratorBase& iter, const func_t& f) {
+  ASSERT_HOST_DEVICE_LAMBDA(func_t);
+
+  for (int arg = 0; arg < iter.ntensors(); arg++) {
+    TORCH_INTERNAL_ASSERT(iter.device(arg).is_cuda());
+  }
+
+  if (iter.numel() == 0) {
+    return;
+  }
+
+  if (!iter.can_use_32bit_indexing()) {
+    for (auto& sub_iter : iter.with_32bit_indexing()) {
+      gpu_kernel_multiple_outputs(sub_iter, f);
+    }
+    return;
+  }
+
+  gpu_kernel_multiple_outputs_impl(iter, f);
+}
+
+} //namespace at::native

venv/lib/python3.10/site-packages/torch/include/ATen/native/cuda/MemoryAccess.cuh

@@ -0,0 +1,384 @@
+#pragma once
+
+#include <cstdint>
+#include <type_traits>
+#include <c10/core/DynamicCast.h>
+#include <c10/util/Exception.h>
+#include <c10/util/TypeCast.h>
+#include <c10/macros/Macros.h>
+#include <ATen/core/Array.h>
+#include <ATen/detail/FunctionTraits.h>
+#include <ATen/cuda/detail/OffsetCalculator.cuh>
+#include <ATen/native/cuda/thread_constants.h>
+
+#include <thrust/tuple.h>
+
+// References:
+// https://devblogs.nvidia.com/cuda-pro-tip-increase-performance-with-vectorized-memory-access/
+
+namespace at { namespace native { namespace memory {
+
+namespace detail {
+
+// What does the `static_unroll` do?
+//
+// We want to do something like:
+//
+//    using args_t = typename traits::ArgsTuple;
+//    args_t args;
+//    #pragma unroll
+//    for (int i = 0; i < traits::arity; i++) {
+//      std::get<i>(args) = ....
+//    }
+//
+// but unfortunately the above code does not work because
+// the template argument has to be a compile time constant
+// so `static_unroll` is created to simulate `#pragma unroll`
+// using template metaprogramming.
+
+template<template<int i> typename func, int end, int current=0>
+struct static_unroll {
+  template<typename... Args>
+  static inline C10_HOST_DEVICE void with_args(Args&&... args) {
+    func<current>::apply(std::forward<Args>(args)...);
+    static_unroll<func, end, current+1>::with_args(args...);
+  }
+};
+
+template<template<int i> typename func, int end>
+struct static_unroll<func, end, end> {
+  template<typename... Args>
+  static inline C10_HOST_DEVICE void with_args(Args... args) {}
+};
+
+// helper structs to be used with static_unroll to load arguments
+// one by one
+
+template<int arg_index>
+struct vectorized_load_helper {
+  template <typename args_t, typename policy_t>
+  static __device__ void apply(policy_t &self, args_t *args, int idx) {
+    using arg_t = std::tuple_element_t<arg_index, args_t>;
+    // `data` hold the data_ptr for tensors [output, input0, input1, ...], so we
+    // need a +1 offset to get the input
+    auto ptr = reinterpret_cast<arg_t *>(self.data[arg_index + 1]) + block_work_size() * idx;
+    auto args_accessor = [&args] __device__ (int thread_unroll_idx) -> arg_t & { return std::get<arg_index>(args[thread_unroll_idx]); };
+    self.load_single_arg(args_accessor, ptr);
+  }
+};
+
+template<int arg_index>
+struct unroll_load_helper {
+  template <typename args_t, typename policy_t, typename offset_t, typename loader_t>
+  static __device__ void apply(policy_t &self, args_t *args, offset_t offset, loader_t loader, int j, int num_outputs) {
+    using arg_t = std::tuple_element_t<arg_index, args_t>;
+    // `data` hold the data_ptr for tensors [output, input0, input1, ...], so we
+    // need a +1 offset to get the input
+    std::get<arg_index>(args[j]) = loader.template load<arg_t>(self.data[arg_index + num_outputs], offset[arg_index], arg_index);
+  }
+};
+
+template <int current>
+struct multi_outputs_store_helper {
+  template<int ntensors, int num_outputs, typename ...Args>
+  C10_HOST_DEVICE static void apply(
+      at::detail::Array<char*, ntensors> data,
+      at::detail::Array<uint32_t, num_outputs> offsets,
+      thrust::tuple<Args...> ret) {
+    using T = typename thrust::tuple_element<current, thrust::tuple<Args...>>::type;
+    T *to = reinterpret_cast<T *>(data[current]) + offsets[current];
+    *to = thrust::get<current>(ret);
+  }
+};
+
+}  // namespace detail
+
+struct LoadWithoutCast {
+  template<typename scalar_t>
+  __device__ scalar_t load(char *base_ptr, uint32_t offset, int arg) {
+    return c10::load(reinterpret_cast<scalar_t *>(base_ptr) + offset);
+  }
+};
+
+template <int N>
+struct LoadWithCast {
+  using array_t = at::detail::Array<at::ScalarType, std::max<int>(N, 1)>;
+  using size_array_t = at::detail::Array<uint32_t, std::max<int>(N, 1)>;
+
+  array_t dtypes;
+  size_array_t element_sizes;
+
+  LoadWithCast(const TensorIteratorBase& iter) {
+    CUDA_KERNEL_ASSERT(iter.ninputs() == N);
+    #pragma unroll
+    for (auto i = 0; i < N; ++i) {
+      this->dtypes[i] = iter.dtype(i + iter.noutputs());
+      element_sizes[i] = c10::elementSize(iter.dtype(i + iter.noutputs()));
+    }
+  }
+
+  template<typename scalar_t>
+  __device__ scalar_t load(char *base_ptr, uint32_t offset, int arg) {
+    void *ptr = base_ptr + element_sizes[arg] * offset;
+    return c10::fetch_and_cast<scalar_t>(dtypes[arg], ptr);
+  }
+};
+
+struct StoreWithoutCast {
+  template<typename scalar_t>
+  __device__ void store(scalar_t value, char *base_ptr, uint32_t offset, int arg = 0) {
+    *(reinterpret_cast<scalar_t *>(base_ptr) + offset) = value;
+  }
+};
+
+template <int N = 1>
+struct StoreWithCast {
+  using array_t = at::detail::Array<at::ScalarType, std::max<int>(N, 1)>;
+  using size_array_t = at::detail::Array<uint32_t, std::max<int>(N, 1)>;
+
+  array_t dtypes;
+  size_array_t element_sizes;
+
+  StoreWithCast(const TensorIteratorBase& iter) {
+    CUDA_KERNEL_ASSERT(iter.noutputs() == N);
+    #pragma unroll
+    for (auto i = 0; i < N; ++i) {
+      this->dtypes[i] = iter.dtype(i);
+      element_sizes[i] = c10::elementSize(iter.dtype(i));
+    }
+  }
+
+  template<typename scalar_t>
+  __device__ void store(scalar_t value, char *base_ptr, uint32_t offset, int arg = 0) {
+    void *ptr = base_ptr + element_sizes[arg] * offset;
+    c10::cast_and_store<scalar_t>(dtypes[arg], ptr, value);
+  }
+};
+
+// aligned vector generates vectorized load/store on CUDA
+template<typename scalar_t, int vec_size>
+struct alignas(sizeof(scalar_t) * vec_size) aligned_vector {
+  scalar_t val[vec_size];
+};
+
+template <int vec_size, typename scalar_t>
+__device__ aligned_vector<scalar_t, vec_size> load_vector(const scalar_t *base_ptr, uint32_t offset) {
+  using vec_t = aligned_vector<scalar_t, vec_size>;
+  auto *from = reinterpret_cast<const vec_t *>(base_ptr);
+  return from[offset];
+}
+
+template <int vec_size>
+__device__ aligned_vector<bool, vec_size> load_vector(const bool *base_ptr, uint32_t offset) {
+  // See NOTE [Loading boolean values]
+  auto tmp = load_vector<vec_size>(reinterpret_cast<const uint8_t*>(base_ptr), offset);
+  aligned_vector<bool, vec_size> ret;
+  for (int i = 0; i < vec_size; ++i) {
+    ret.val[i] = bool(tmp.val[i]);
+  }
+  return ret;
+}
+
+namespace policies {
+
+// Assumption:
+// all tensors are contiguous, that is: stride == sizeof(type) for all tensors
+template<typename data_t, typename inp_calc_t, typename out_calc_t, typename loader_t, typename storer_t, int num_outputs = 1>
+struct unroll {
+
+  data_t data;
+  int remaining;
+  inp_calc_t input_offset_calculator;
+  out_calc_t output_offset_calculator;
+  loader_t loader;
+  storer_t storer;
+
+  __device__ unroll(data_t data, int remaining, inp_calc_t ic, out_calc_t oc, loader_t l, storer_t s):
+    data(data), remaining(remaining), input_offset_calculator(ic), output_offset_calculator(oc), loader(l), storer(s) {}
+
+  __device__ inline bool check_inbounds(int thread_work_elem) {
+    return ((int)(threadIdx.x  + thread_work_elem*num_threads()) < remaining);
+  }
+
+  template<typename args_t>
+  __device__ inline void load(args_t *args, int idx) {
+    constexpr int arity = std::tuple_size<args_t>::value;
+    int thread_idx = threadIdx.x;
+    #pragma unroll
+    for (int i = 0; i < thread_work_size(); i++) {
+      if (thread_idx >= remaining) {
+        return;
+      }
+      int linear_idx = thread_idx + block_work_size() * idx;
+      auto offset = input_offset_calculator.get(linear_idx);
+      detail::static_unroll<detail::unroll_load_helper, arity>::with_args(*this, args, offset, loader, i, num_outputs);
+      thread_idx += num_threads();
+    }
+  }
+
+  template<typename scalar_t>
+  __device__ inline void store(scalar_t *from, int idx) {
+    int thread_idx = threadIdx.x;
+    #pragma unroll
+    for (int i = 0; i < thread_work_size(); i++) {
+      if (thread_idx >= remaining) {
+        return;
+      }
+      int linear_idx = thread_idx + block_work_size() * idx;
+      int offset = output_offset_calculator.get(linear_idx)[0];
+      storer.store(from[i], data[0], offset);
+      thread_idx += num_threads();
+    }
+  }
+};
+
+// Assumption:
+// all tensors are contiguous, that is: stride == sizeof(type) for all tensors
+// Note:
+// Functions in vectorized policy does not do boundary check. It assumes the whole block
+// has its job to do. So the reminders should be handled by the caller manually.
+template <int vec_size, typename data_t>  // vec_size: number of scalars, can be 1, 2, or 4.
+struct vectorized {
+
+  static_assert(thread_work_size() % vec_size == 0, "The workload per thread must be a multiple of vec_size");
+  static constexpr int loop_size = thread_work_size() / vec_size;
+
+  data_t data;
+
+  __device__ vectorized(data_t data) : data(data) {}
+
+  __device__ inline constexpr bool check_inbounds(int thread_work_elem) {
+    return true;
+  }
+
+  template<typename accessor_t, typename scalar_t>
+  __device__ inline void load_single_arg(accessor_t to, scalar_t *from) {
+    int thread_idx = threadIdx.x;
+    #pragma unroll
+    for (int i = 0; i < loop_size; i++) {
+      int index = thread_idx + i * num_threads();
+      auto v = load_vector<vec_size>(from, index);
+      #pragma unroll
+      for (int j = 0; j < vec_size; j++) {
+        to(vec_size * i + j) = v.val[j];
+      }
+    }
+  }
+
+  template<typename args_t>
+  __device__ inline void load(args_t *args, int idx) {
+    constexpr int arity = std::tuple_size<args_t>::value;
+    detail::static_unroll<detail::vectorized_load_helper, arity>::with_args(*this, args, idx);
+  }
+
+  template<typename scalar_t>
+  __device__ inline void store(scalar_t *from, int idx) {
+    using vec_t = aligned_vector<scalar_t, vec_size>;
+    scalar_t *to = reinterpret_cast<scalar_t *>(data[0]) + block_work_size() * idx;
+    vec_t *to_ = reinterpret_cast<vec_t *>(to);
+    int thread_idx = threadIdx.x;
+    #pragma unroll
+    for (int i = 0; i < loop_size; i++) {
+      int index = thread_idx + i * num_threads();
+      vec_t v;
+      for (int j = 0; j < vec_size; j++) {
+        v.val[j] = from[vec_size * i + j];
+      }
+      to_[index] = v;
+    }
+  }
+};
+
+template <typename data_t, typename inp_calc_t, typename out_calc_t, int num_outputs>
+struct multi_outputs_unroll {
+  //multi_outputs_unroll struct members and check_inbounds and load methods are copypasted from unroll struct
+  //we don't use inheritance because of compiler bug in cuda 10.2+
+  data_t data;
+  int remaining;
+  inp_calc_t input_offset_calculator;
+  out_calc_t output_offset_calculator;
+  LoadWithoutCast loader;
+  StoreWithoutCast storer;
+
+  __device__ multi_outputs_unroll(data_t data, int remaining, inp_calc_t ic, out_calc_t oc):
+  data(data), remaining(remaining), input_offset_calculator(ic), output_offset_calculator(oc) {}
+
+  __device__ inline bool check_inbounds(int thread_work_elem) {
+    return ((int)(threadIdx.x  + thread_work_elem*num_threads()) < remaining);
+  }
+
+  template<typename args_t>
+  __device__ inline void load(args_t *args, int idx) {
+    constexpr int arity = std::tuple_size<args_t>::value;
+    int thread_idx = threadIdx.x;
+    #pragma unroll
+    for (int i = 0; i < thread_work_size(); i++) {
+      if (thread_idx >= remaining) {
+        return;
+      }
+      int linear_idx = thread_idx + block_work_size() * idx;
+      auto offset = input_offset_calculator.get(linear_idx);
+      detail::static_unroll<detail::unroll_load_helper, arity>::with_args(*this, args, offset, loader, i, num_outputs);
+      thread_idx += num_threads();
+    }
+  }
+
+
+  template <typename return_t>
+  __device__ inline void store(return_t *from, int idx) {
+    int thread_idx = threadIdx.x;
+    #pragma unroll
+    for (int i = 0; i < thread_work_size(); i++) {
+      if (thread_idx >= this->remaining) {
+        return;
+      }
+      int linear_idx = thread_idx + block_work_size() * idx;
+      auto offsets = this->output_offset_calculator.get(linear_idx);
+      memory::detail::static_unroll<detail::multi_outputs_store_helper, num_outputs>::with_args(this->data, offsets, from[i]);
+      thread_idx += num_threads();
+    }
+  }
+};
+
+}  // namespace policies
+
+// This is only used in host, but we will wrap this into some templates
+// which is C10_HOST_DEVICE, so we have to make this C10_HOST_DEVICE
+// in order to compile
+template<typename scalar_t>
+inline C10_HOST_DEVICE int can_vectorize_up_to(char *pointer) {
+  uint64_t address = reinterpret_cast<uint64_t>(pointer);
+  constexpr int vec2_alignment = std::alignment_of<aligned_vector<scalar_t, 2>>::value;
+  constexpr int vec4_alignment = std::alignment_of<aligned_vector<scalar_t, 4>>::value;
+  if (address % vec4_alignment == 0) {
+    return 4;
+  } else if (address % vec2_alignment == 0) {
+    return 2;
+  }
+  return 1;
+}
+
+template<int i>
+struct can_vectorize_up_to_helper {
+  template <typename array_t, typename traits>
+  static C10_HOST_DEVICE void apply(int &result, array_t pointers, traits _) {
+    using arg_t = typename traits::template arg<i>::type;
+    // `pointers` hold the data_ptr for tensors [output, input0, input1, ...], so we
+    // need a +1 offset to get the input
+    result = std::min<int>(result, can_vectorize_up_to<arg_t>(pointers[i + 1]));
+  }
+};
+
+template<typename func_t, typename array_t>
+inline int can_vectorize_up_to(array_t pointers) {
+  using traits = function_traits<func_t>;
+  using return_t = typename traits::result_type;
+  constexpr int arity = traits::arity;
+  int result = can_vectorize_up_to<return_t>(pointers[0]);
+  // We need to get the type for each argument of `func_t`, this can only
+  // be done at compile time.
+  detail::static_unroll<can_vectorize_up_to_helper, arity>::with_args(result, pointers, traits());
+  return result;
+}
+
+}}} // namespace at::native::memory

venv/lib/python3.10/site-packages/torch/include/ATen/native/cuda/Normalization.cuh

@@ -0,0 +1,1742 @@
+#pragma once
+
+#include <ATen/core/Tensor.h>
+#include <ATen/Dispatch.h>
+#include <ATen/AccumulateType.h>
+#include <ATen/ceil_div.h>
+#include <ATen/cuda/CUDAContext.h>
+#include <ATen/cuda/DeviceUtils.cuh>
+#include <ATen/native/cuda/block_reduce.cuh>
+#include <ATen/native/cuda/DeviceSqrt.cuh>
+#include <ATen/native/cuda/LaunchUtils.h>
+#include <c10/macros/Macros.h>
+
+#ifndef AT_PER_OPERATOR_HEADERS
+#include <ATen/Functions.h>
+#else
+#include <ATen/ops/empty.h>
+#include <ATen/ops/empty_like.h>
+#include <ATen/ops/zeros.h>
+#endif
+
+namespace at { namespace native {
+
+// The maximum number of threads in a block
+#if defined(USE_ROCM)
+constexpr int MAX_BLOCK_SIZE = 256;
+#else
+constexpr int MAX_BLOCK_SIZE = 512;
+#endif
+
+constexpr unsigned MAX_GRID_SIZE = 65535u;
+
+// Number of threads in a block given an input size up to MAX_BLOCK_SIZE
+static int getNumThreads(int nElem) {
+#if defined(USE_ROCM)
+  int threadSizes[5] = { 16, 32, 64, 128, MAX_BLOCK_SIZE };
+#else
+  int threadSizes[5] = { 32, 64, 128, 256, MAX_BLOCK_SIZE };
+#endif
+  for (int i = 0; i != 5; ++i) {
+    if (nElem <= threadSizes[i]) {
+      return threadSizes[i];
+    }
+  }
+  return MAX_BLOCK_SIZE;
+}
+
+// Returns the index of the most significant 1 bit in `val`.
+__device__ __forceinline__ int getMSB(int val) {
+  return 31 - __clz(val);
+}
+
+template <typename scalar_t, typename accscalar_t>
+struct Float2 {
+  accscalar_t v1, v2;
+  __device__ Float2() {}
+  __device__ Float2(scalar_t v1, scalar_t v2) : v1(static_cast<accscalar_t>(v1)), v2(static_cast<accscalar_t>(v2)) {}
+  __device__ Float2(int v) : v1(static_cast<accscalar_t>(v)), v2(static_cast<accscalar_t>(v)) {}
+  __device__ Float2& operator+=(const Float2& a) {
+    v1 += a.v1;
+    v2 += a.v2;
+    return *this;
+  }
+  __device__ friend Float2 operator+(Float2 a, const Float2& b) {
+    a += b;
+    return a;
+  }
+};
+
+template <typename scalar_t, typename accscalar_t, typename PTA>
+struct GradOp {
+  __device__ GradOp(accscalar_t m, const PTA& i, const PTA& g)
+    : mean(m), input(i), grad_output(g) {}
+  __device__ __forceinline__ Float2<scalar_t, accscalar_t> operator()(int batch, int plane, int n) {
+    accscalar_t g = grad_output[batch][plane][n];
+    accscalar_t c = static_cast<accscalar_t>(input[batch][plane][n]) - mean;
+    return Float2<scalar_t, accscalar_t>(g, g * c);
+  }
+  const accscalar_t mean;
+  const PTA& input;
+  const PTA& grad_output;
+};
+
+template <typename acc_t>
+struct SumReduceOp {
+    __device__ __forceinline__ acc_t combine(acc_t a, acc_t b) const { return a + b; }
+
+    __device__ __forceinline__ acc_t warp_shfl_down(acc_t data, int offset) const {
+        return WARP_SHFL_DOWN(data, offset);
+    }
+};
+
+template <typename scalar_t, typename accscalar_t>
+struct SumReduceOp<Float2<scalar_t, accscalar_t>> {
+    using acc_t = Float2<scalar_t, accscalar_t>;
+
+    __device__ __forceinline__ acc_t combine(acc_t a, acc_t b) const { return a + b; }
+
+    __device__ __forceinline__ acc_t warp_shfl_down(acc_t data, int offset) const {
+        return {WARP_SHFL_DOWN(data.v1, offset), WARP_SHFL_DOWN(data.v2, offset)};
+    }
+};
+
+// Sum across (batch, x/y/z) applying Op() pointwise
+// this works by first having each thread sum it's part
+// of the data. Then there is a double-shuffling reduction.
+// First each warp (of C10_WARP_SIZE threads) uses warpSum to reduce its
+// data to the "warp leader", who writes its value into shared memory.
+// Then a single warp reads the remaining (at most C10_WARP_SIZE) items
+// and reduces them using another warpSum.
+// The implicit assumption is that there are no more
+// than C10_WARP_SIZE**2 threads.
+template<typename scalar_t, typename Op, typename PTA>
+__device__ scalar_t reduce(Op op, PTA tensor, int plane) {
+  // first the reductions each thread does separately
+  scalar_t sum = static_cast<scalar_t>(0);
+  for (int batch = threadIdx.y; batch < tensor.size(0); batch += blockDim.y) {
+    for (int x = threadIdx.x; x < tensor.size(2); x += blockDim.x) {
+      sum += op(batch, plane, x);
+    }
+  }
+  __shared__ scalar_t shared[C10_WARP_SIZE];
+  SumReduceOp<scalar_t> reduce_op;
+  sum = cuda_utils::BlockReduce<scalar_t, SumReduceOp<scalar_t>, cuda_utils::Block2D>(sum, reduce_op, 0, shared);
+  if (threadIdx.x == 0 && threadIdx.y == 0) {
+      shared[0] = sum;
+  }
+  __syncthreads();
+  // Everyone picks it up, should be broadcast into the whole grad_input
+  return shared[0];
+}
+
+constexpr int ELEMENTS_PER_ITER = 4; // enables concurrency within each thread to hide latency
+constexpr int ELEMENTS_PER_THREAD = 16;
+constexpr int OPTIMAL_TILE_W = 32;
+constexpr int MAX_H_BLOCK = 128;
+
+__host__ void flexible_launch_configs(
+      const int reduction,
+      const int stride,
+      dim3 &block,
+      dim3 &grid,
+      const bool coop_flag = false) {
+  int block_x = std::min(lastPow2(stride), OPTIMAL_TILE_W);
+  int block_y = std::min(lastPow2(at::ceil_div(reduction , ELEMENTS_PER_THREAD)),
+                         MAX_BLOCK_SIZE / block_x);
+  if (block_x * block_y != MAX_BLOCK_SIZE) {
+    block_x = std::min(lastPow2(stride), MAX_BLOCK_SIZE / block_y);
+  }
+
+  int grid_x = at::ceil_div(stride, block_x);
+  int grid_y = std::min(at::ceil_div(reduction, block_y * ELEMENTS_PER_THREAD), MAX_H_BLOCK);
+  if (coop_flag) {
+    // it's not worth having a grid reduction if the reduction dimension is not big enough
+    grid_y = grid_y < 8 ? 1 : grid_y;
+  }
+
+  block.x = block_x;
+  block.y = block_y;
+  block.z = 1;
+  grid.x = grid_x;
+  grid.y = grid_y;
+  grid.z = 1;
+}
+
+template<typename T, typename C>
+__device__ __forceinline__ void welford_merge_element(C& count,
+                                                      T& mean,
+                                                      T& m2n,
+                                                      const C& count_new,
+                                                      const T& mean_new,
+                                                      const T& m2n_new) {
+      T factor = T(1.0) / ::max(1, (count + count_new));
+      T delta0 = mean - mean_new;
+      mean = (mean_new * count_new + mean * count) * factor;
+      m2n += m2n_new + delta0 * delta0 * count_new * count * factor;
+      count += count_new;
+}
+
+// merge mean/m2n among threadIdx.y within block
+template<typename T, typename C>
+__device__ __forceinline__ void welford_merge_block_vertical(C& count,
+                                                             T& mean,
+                                                             T& m2n,
+                                                             C* shmem_count,
+                                                             T* shmem_mean,
+                                                             T* shmem_m2n) {
+  // write to shared memory
+  auto address_base = threadIdx.x + threadIdx.y * blockDim.x;
+
+#pragma unroll
+  for (int offset = blockDim.y/2; offset > 0; offset >>= 1) {
+    if (threadIdx.y < offset*2) {
+      shmem_mean[address_base] = mean;
+      shmem_m2n[address_base] = m2n;
+      shmem_count[address_base] = count;
+    }
+    __syncthreads();
+    if (threadIdx.y < offset && threadIdx.y + offset < blockDim.y) {
+      auto address = address_base + offset * blockDim.x;
+      // read shared memory back to register for reduction
+      auto count_new = shmem_count[address];
+      auto mean_new = shmem_mean[address];
+      auto m2n_new = shmem_m2n[address];
+
+      welford_merge_element(count, mean, m2n, count_new, mean_new, m2n_new);
+    }
+  }
+}
+
+template <typename input_scalar_t, typename stat_scalar_t, typename stat_accscalar_t, bool train, typename index_t>
+__global__ void batch_norm_transform_input_kernel(
+    const GenericPackedTensorAccessor<input_scalar_t, 3, RestrictPtrTraits, index_t> input,
+    GenericPackedTensorAccessor<input_scalar_t, 3, RestrictPtrTraits, index_t> output,
+    const GenericPackedTensorAccessor<typename std::conditional<train, stat_accscalar_t, stat_scalar_t>::type, 1, RestrictPtrTraits, index_t> mean_,
+    const GenericPackedTensorAccessor<typename std::conditional<train, stat_accscalar_t, stat_scalar_t>::type, 1, RestrictPtrTraits, index_t> var_or_invstd,
+    const GenericPackedTensorAccessor<stat_scalar_t, 1, RestrictPtrTraits, index_t> weight,
+    const GenericPackedTensorAccessor<stat_scalar_t, 1, RestrictPtrTraits, index_t> bias,
+    stat_accscalar_t epsilon) {
+
+  index_t plane = blockIdx.x;
+
+  if (plane >= input.size(1)) {
+    return;
+  }
+
+  stat_accscalar_t gamma = weight.size(0) > 0 ? static_cast<stat_accscalar_t>(weight[plane]) : static_cast<stat_accscalar_t>(1);
+  stat_accscalar_t beta = bias.size(0) > 0 ? static_cast<stat_accscalar_t>(bias[plane]) : static_cast<stat_accscalar_t>(0);
+  stat_accscalar_t mean = static_cast<stat_accscalar_t>(mean_[plane]);
+  stat_accscalar_t invstd;
+  if (train) {
+    invstd = var_or_invstd[plane];
+  } else {
+    invstd = static_cast<stat_accscalar_t>(1) / device_sqrt(static_cast<stat_accscalar_t>(var_or_invstd[plane]) + epsilon);
+  }
+
+  index_t bs = input.size(0);
+  index_t fs = input.size(2);
+
+  index_t bstep  = blockDim.y * gridDim.y;
+  for (index_t batch = threadIdx.y + blockIdx.y * blockDim.y; batch < bs; batch += bstep) {
+    auto o = output[batch][plane];
+    auto i = input[batch][plane];
+    for (index_t feature = threadIdx.x; feature < fs; feature += blockDim.x) {
+      o[feature] = static_cast<input_scalar_t>(gamma * (i[feature] - mean) * invstd + beta);
+    }
+  }
+}
+
+struct InvStd {
+  template <typename T>
+  __device__ __forceinline__ T operator()(T var, double epsilon) const {
+    T invstd = 0;
+    if (var != static_cast<T>(0) || epsilon != static_cast<T>(0)) {
+      invstd = static_cast<T>(1) / device_sqrt(var + epsilon);
+    }
+    return invstd;
+  }
+};
+
+struct Var {
+  template <typename T>
+  __device__ __forceinline__ T operator()(T var, double epsilon) const {
+    return var;
+  }
+};
+
+template <typename VarTransform, typename input_scalar_t, typename stat_scalar_t, typename stat_accscalar_t, typename index_t>
+__global__ void batch_norm_collect_statistics_kernel(
+    const GenericPackedTensorAccessor<input_scalar_t, 3, RestrictPtrTraits, index_t> input,
+    const stat_accscalar_t epsilon,
+    const stat_accscalar_t momentum,
+    GenericPackedTensorAccessor<stat_accscalar_t, 1, RestrictPtrTraits, index_t> save_mean,
+    GenericPackedTensorAccessor<stat_accscalar_t, 1, RestrictPtrTraits, index_t> save_transformed_var) {
+
+  __shared__ int shared_n[2 * 2 * C10_WARP_SIZE + C10_WARP_SIZE];
+
+  int plane = blockIdx.x;
+  int N = input.size(0) * input.size(2);
+  int tid = threadIdx.x + threadIdx.y * blockDim.x;
+
+  // Compute the mean and variance across (batch, x/y/z)
+  // this uses the Welford (in the for loop)/parallel algorithm (to sum across the block)
+  // https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Welford's_Online_algorithm
+  // and the parallel algorithm on the same page.
+  // We use two shuffles to reduce across the entire block.
+  // https://devblogs.nvidia.com/faster-parallel-reductions-kepler/ has a description.
+  stat_accscalar_t* shared_avg_var = (stat_accscalar_t*) &shared_n[C10_WARP_SIZE];
+
+  // first the reductions each thread does separately
+  stat_accscalar_t avg = 0;
+  stat_accscalar_t var_n = 0;
+  int n = 0;
+  for (int batch = threadIdx.y; batch < input.size(0); batch += blockDim.y) {
+    for (int x = threadIdx.x; x < input.size(2); x += blockDim.x) {
+      stat_accscalar_t v = input[batch][plane][x];
+      stat_accscalar_t d1 = v - avg;
+      n++;
+      avg += d1 / n;
+      var_n += d1 * (v - avg);
+    }
+  }
+
+  // first warpSum to get one value per thread to
+  // one value per warp
+  for (int i = 0; i < getMSB(C10_WARP_SIZE); ++i) {
+    stat_accscalar_t o_avg = WARP_SHFL_XOR(avg, 1 << i, C10_WARP_SIZE);
+    int o_n = WARP_SHFL_XOR(n, 1 << i, C10_WARP_SIZE);
+    stat_accscalar_t factor = 1.0 / fmaxf(1.0, n+o_n);
+    var_n += WARP_SHFL_XOR(var_n, 1 << i, C10_WARP_SIZE) + (avg - o_avg) * (avg - o_avg) * n * o_n * factor;
+    avg = (n * avg + o_n * o_avg) * factor;
+    n += o_n;
+  }
+
+  // this writes each warps  item into shared memory
+  // there are at most C10_WARP_SIZE items left because
+  // there are at most C10_WARP_SIZE**2 threads at the beginning
+  __syncthreads();
+  if (tid % C10_WARP_SIZE == 0) {
+    shared_n[tid / C10_WARP_SIZE] = n;
+    shared_avg_var[tid / C10_WARP_SIZE * 2] = avg;
+    shared_avg_var[tid / C10_WARP_SIZE * 2 + 1] = var_n;
+  }
+  __syncthreads();
+  // now have a second warpSum to reduce the intermediate values
+  // from shared memory to a single number. The very first
+  // thread writes it to shared memory.
+
+  if (tid < C10_WARP_SIZE) {
+    n = (tid < blockDim.x * blockDim.y / C10_WARP_SIZE ? shared_n[tid] : 0);
+    avg = (tid < blockDim.x * blockDim.y  / C10_WARP_SIZE ? shared_avg_var[2 * tid] : stat_accscalar_t(0));
+    var_n = (tid < blockDim.x * blockDim.y  / C10_WARP_SIZE ? shared_avg_var[2 * tid + 1] : stat_accscalar_t(0));
+  }
+  for (int i = 0; i < getMSB(C10_WARP_SIZE); ++i) {
+    stat_accscalar_t o_avg = WARP_SHFL_XOR(avg, 1 << i, C10_WARP_SIZE);
+    int o_n = WARP_SHFL_XOR(n, 1 << i, C10_WARP_SIZE);
+    stat_accscalar_t factor = 1.0 / fmaxf(1.0, n+o_n);
+    var_n += WARP_SHFL_XOR(var_n, 1 << i, C10_WARP_SIZE) + (avg - o_avg) * (avg - o_avg) * n * o_n * factor;
+    avg = (n * avg + o_n * o_avg) * factor;
+    n += o_n;
+  }
+
+  // Save the mean, variance, and moving averages
+  if (tid == 0) {
+    if (save_mean.data() != NULL) {
+      save_mean[plane] = avg;
+    }
+    if (save_transformed_var.data() != NULL) {
+      save_transformed_var[plane] = VarTransform{}(var_n / N, epsilon);
+    }
+  }
+
+}
+
+template <typename input_scalar_t, typename stat_scalar_t, typename stat_accscalar_t, typename index_t>
+__global__ void batch_norm_backward_kernel(
+    const GenericPackedTensorAccessor<input_scalar_t, 3, DefaultPtrTraits, index_t> input,
+    const GenericPackedTensorAccessor<input_scalar_t, 3, DefaultPtrTraits, index_t> grad_output,
+    GenericPackedTensorAccessor<input_scalar_t, 3, DefaultPtrTraits, index_t> grad_input,
+    GenericPackedTensorAccessor<stat_scalar_t, 1, DefaultPtrTraits, index_t> grad_weight,
+    GenericPackedTensorAccessor<stat_scalar_t, 1, DefaultPtrTraits, index_t> grad_bias,
+    const GenericPackedTensorAccessor<stat_scalar_t, 1, DefaultPtrTraits, index_t> weight,
+    const GenericPackedTensorAccessor<stat_scalar_t, 1, DefaultPtrTraits, index_t> running_mean,
+    const GenericPackedTensorAccessor<stat_scalar_t, 1, DefaultPtrTraits, index_t> running_var,
+    const GenericPackedTensorAccessor<stat_accscalar_t, 1, DefaultPtrTraits, index_t> save_mean,
+    const GenericPackedTensorAccessor<stat_accscalar_t, 1, DefaultPtrTraits, index_t> save_invstd,
+    bool train,
+    stat_accscalar_t epsilon) {
+
+  index_t plane = blockIdx.x;
+  index_t N = grad_output.size(0) * grad_output.size(2);
+
+  stat_accscalar_t mean, invstd;
+  if (train) {
+    mean = save_mean[plane];
+    invstd = save_invstd[plane];
+  } else {
+    mean = static_cast<stat_accscalar_t>(running_mean[plane]);
+    invstd = static_cast<stat_accscalar_t>(1) / device_sqrt(static_cast<stat_accscalar_t>(running_var[plane]) + epsilon);
+  }
+
+  stat_accscalar_t weight_val = weight.size(0) > 0 ? static_cast<stat_accscalar_t>(weight[plane]) : stat_accscalar_t(1);
+  stat_accscalar_t norm = stat_accscalar_t(1) / N;
+
+  // Compute two values across (batch, x/y/z) in one pass:
+  // 1. Sum(grad_output)
+  // 2. DotProduct(input - mean, grad_output)
+  GradOp<input_scalar_t, stat_accscalar_t, GenericPackedTensorAccessor<input_scalar_t, 3, DefaultPtrTraits, index_t>> g(mean, input, grad_output);
+  auto res = reduce<Float2<input_scalar_t, stat_accscalar_t>>(g, grad_output, plane);
+
+  stat_accscalar_t grad_output_sum = res.v1;
+  stat_accscalar_t dot_p = res.v2;
+
+  stat_accscalar_t grad_mean = grad_output_sum * norm;
+  stat_accscalar_t proj_scale = dot_p * norm * invstd * invstd;
+  stat_accscalar_t grad_scale = invstd * weight_val;
+
+  if (grad_input.data() != NULL) {
+    for (int batch = threadIdx.y; batch < grad_output.size(0); batch += blockDim.y) {
+      for (int x = threadIdx.x; x < grad_output.size(2); x += blockDim.x) {
+        input_scalar_t go = grad_output[batch][plane][x];
+        if (train) {
+          stat_accscalar_t inp = input[batch][plane][x];
+          stat_accscalar_t proj = (inp - mean) * proj_scale;
+          grad_input[batch][plane][x] = static_cast<input_scalar_t>((go - proj - grad_mean) * grad_scale);
+        } else {
+          grad_input[batch][plane][x] = static_cast<input_scalar_t>(go * grad_scale);
+        }
+      }
+    }
+  }
+
+  if (grad_weight.size(0) > 0) {
+    if (threadIdx.x == 0) {
+      grad_weight[plane] = static_cast<stat_scalar_t>(dot_p * invstd);
+    }
+  }
+
+  if (grad_bias.size(0) > 0) {
+    if (threadIdx.x == 0) {
+      grad_bias[plane] = static_cast<stat_scalar_t>(grad_output_sum);
+    }
+  }
+}
+
+template <typename scalar_t, typename accscalar_t, typename index_t>
+__global__ void batch_norm_reduce_statistics_kernel(
+    const GenericPackedTensorAccessor<accscalar_t, 2, RestrictPtrTraits, index_t> vec_mean,
+    const GenericPackedTensorAccessor<accscalar_t, 2, RestrictPtrTraits, index_t> vec_invstd,
+    GenericPackedTensorAccessor<accscalar_t, 1, RestrictPtrTraits, index_t> mean,
+    GenericPackedTensorAccessor<accscalar_t, 1, RestrictPtrTraits, index_t> invstd,
+    GenericPackedTensorAccessor<scalar_t, 1, RestrictPtrTraits, index_t> running_mean,
+    GenericPackedTensorAccessor<scalar_t, 1, RestrictPtrTraits, index_t> running_var,
+    const accscalar_t epsilon,
+    const accscalar_t momentum,
+    const GenericPackedTensorAccessor<scalar_t, 1, RestrictPtrTraits, index_t> counts) {
+
+  int feature_size = vec_mean.size(1);
+  int world_size = vec_mean.size(0);
+
+  int bid = blockIdx.x;
+  int tid = threadIdx.x;
+
+  // first the reductions each thread does separately
+  for (int i = bid*blockDim.x+tid; i < feature_size; i += gridDim.x*blockDim.x) {
+    accscalar_t avg = 0;
+    accscalar_t var_n = 0;
+    index_t n = 0;
+    for (int j = 0; j < world_size; j++) {
+      scalar_t count = counts[j];
+      accscalar_t m = vec_mean[j][i];
+      accscalar_t v = accscalar_t(1.0) / (vec_invstd[j][i]);
+      v = (v * v - epsilon) * count;
+      accscalar_t factor = 1.0 / (n + count);
+      var_n += v + (avg - m) * (avg - m) * n * count * factor;
+      avg = n * factor * avg + count * factor * m;
+      n += count;
+    }
+    mean[i] = avg;
+    invstd[i] = static_cast<accscalar_t>(1) / device_sqrt(var_n / n + epsilon);
+    if (running_mean.data() != NULL) {
+      running_mean[i] = static_cast<scalar_t>((1 - momentum) * running_mean[i] + momentum * avg);
+    }
+    accscalar_t unbiasedVar = var_n / (n - 1);
+    if (running_var.data() != NULL) {
+      running_var[i] = static_cast<scalar_t>((1 - momentum) * running_var[i] + momentum * unbiasedVar);
+    }
+  }
+
+}
+
+template <typename input_scalar_t, typename stat_scalar_t, typename stat_accscalar_t, typename index_t>
+__global__ void batch_norm_backward_reduce_kernel(
+    const GenericPackedTensorAccessor<input_scalar_t, 3, DefaultPtrTraits, index_t> input,
+    const GenericPackedTensorAccessor<input_scalar_t, 3, DefaultPtrTraits, index_t> grad_output,
+    GenericPackedTensorAccessor<stat_accscalar_t, 1, DefaultPtrTraits, index_t> mean,
+    GenericPackedTensorAccessor<stat_accscalar_t, 1, DefaultPtrTraits, index_t> invstd,
+    GenericPackedTensorAccessor<stat_accscalar_t, 1, DefaultPtrTraits, index_t> sum_dy,
+    GenericPackedTensorAccessor<stat_accscalar_t, 1, DefaultPtrTraits, index_t> sum_dy_xmu,
+    GenericPackedTensorAccessor<stat_scalar_t, 1, DefaultPtrTraits, index_t> grad_weight,
+    GenericPackedTensorAccessor<stat_scalar_t, 1, DefaultPtrTraits, index_t> grad_bias) {
+
+  index_t plane = blockIdx.x;
+
+  stat_accscalar_t r_mean = mean[plane];
+  stat_accscalar_t factor = invstd[plane];
+
+  GradOp<input_scalar_t, stat_accscalar_t, GenericPackedTensorAccessor<input_scalar_t, 3, DefaultPtrTraits, index_t>> g(r_mean, input, grad_output);
+  auto res = reduce<Float2<input_scalar_t, stat_accscalar_t>>(g, grad_output, plane);
+
+  if (threadIdx.x == 0) {
+    if (grad_weight.size(0) > 0) {
+      grad_weight[plane] = static_cast<stat_scalar_t>(res.v2 * factor);
+    }
+    if (grad_bias.size(0) > 0) {
+      grad_bias[plane] = static_cast<stat_scalar_t>(res.v1);
+    }
+    if (sum_dy.size(0) > 0) {
+      sum_dy[plane] = static_cast<stat_accscalar_t>(res.v1);
+    }
+    if (sum_dy_xmu.size(0) > 0) {
+      sum_dy_xmu[plane] = static_cast<stat_accscalar_t>(res.v2);
+    }
+  }
+}
+
+template <typename input_scalar_t, typename stat_scalar_t, typename stat_accscalar_t, typename index_t>
+__device__ __forceinline__ void batch_norm_backward_elemt_kernel_impl(
+    const GenericPackedTensorAccessor<input_scalar_t, 3, DefaultPtrTraits, index_t> input,
+    const GenericPackedTensorAccessor<input_scalar_t, 3, DefaultPtrTraits, index_t> grad_output,
+    const GenericPackedTensorAccessor<stat_accscalar_t, 1, DefaultPtrTraits, index_t> mean,
+    const GenericPackedTensorAccessor<stat_accscalar_t, 1, DefaultPtrTraits, index_t> invstd,
+    const GenericPackedTensorAccessor<stat_scalar_t, 1, DefaultPtrTraits, index_t> weight,
+    const GenericPackedTensorAccessor<stat_accscalar_t, 1, DefaultPtrTraits, index_t> sum_dy,
+    const GenericPackedTensorAccessor<stat_accscalar_t, 1, DefaultPtrTraits, index_t> sum_dy_xmu,
+    GenericPackedTensorAccessor<input_scalar_t, 3, DefaultPtrTraits, index_t> grad_input,
+    const stat_accscalar_t norm_fct) {
+  index_t plane = blockIdx.x;
+
+  if (plane >= input.size(1)) {
+    return;
+  }
+
+  stat_accscalar_t m_c = mean[plane];
+  stat_accscalar_t m_dy_c = sum_dy[plane] * norm_fct;
+  stat_accscalar_t factor_1_c = invstd[plane];
+  stat_accscalar_t factor_2_c = weight.size(0) > 0 ? static_cast<stat_accscalar_t>(weight[plane]) : stat_accscalar_t(1);
+  factor_2_c *= factor_1_c;
+  factor_1_c = factor_1_c * factor_1_c * sum_dy_xmu[plane] * norm_fct;
+
+  index_t bs = input.size(0);
+  index_t fs = input.size(2);
+
+  index_t bstep  = blockDim.y * gridDim.y;
+  for (index_t batch = threadIdx.y + blockIdx.y * blockDim.y; batch < bs; batch += bstep) {
+    auto g_i = grad_input[batch][plane];
+    auto g_o = grad_output[batch][plane];
+    auto i = input[batch][plane];
+    for (index_t feature = threadIdx.x; feature < fs; feature += blockDim.x) {
+      g_i[feature] = static_cast<input_scalar_t>((g_o[feature] - m_dy_c - (i[feature] - m_c) * factor_1_c) * factor_2_c);
+    }
+  }
+}
+
+template <typename input_scalar_t, typename stat_scalar_t, typename stat_accscalar_t, typename index_t>
+__global__ void batch_norm_backward_elemt_kernel(
+    const GenericPackedTensorAccessor<input_scalar_t, 3, DefaultPtrTraits, index_t> input,
+    const GenericPackedTensorAccessor<input_scalar_t, 3, DefaultPtrTraits, index_t> grad_output,
+    const GenericPackedTensorAccessor<stat_accscalar_t, 1, DefaultPtrTraits, index_t> mean,
+    const GenericPackedTensorAccessor<stat_accscalar_t, 1, DefaultPtrTraits, index_t> invstd,
+    const GenericPackedTensorAccessor<stat_scalar_t, 1, DefaultPtrTraits, index_t> weight,
+    const GenericPackedTensorAccessor<stat_accscalar_t, 1, DefaultPtrTraits, index_t> sum_dy,
+    const GenericPackedTensorAccessor<stat_accscalar_t, 1, DefaultPtrTraits, index_t> sum_dy_xmu,
+    GenericPackedTensorAccessor<input_scalar_t, 3, DefaultPtrTraits, index_t> grad_input,
+    const int* __restrict__ numel, const int world_size) {
+  int64_t total_numel = 0;
+  for (int i = 0; i < world_size; i ++) {
+    total_numel += numel[i];
+  }
+
+  const stat_accscalar_t norm_fct =
+      static_cast<stat_accscalar_t>(1) / static_cast<stat_accscalar_t>(total_numel);
+  batch_norm_backward_elemt_kernel_impl(
+      input, grad_output, mean, invstd, weight, sum_dy, sum_dy_xmu, grad_input, norm_fct);
+}
+
+template <typename input_scalar_t, typename stat_scalar_t, typename stat_accscalar_t, typename index_t>
+__global__ void batch_norm_backward_elemt_kernel(
+    const GenericPackedTensorAccessor<input_scalar_t, 3, DefaultPtrTraits, index_t> input,
+    const GenericPackedTensorAccessor<input_scalar_t, 3, DefaultPtrTraits, index_t> grad_output,
+    const GenericPackedTensorAccessor<stat_accscalar_t, 1, DefaultPtrTraits, index_t> mean,
+    const GenericPackedTensorAccessor<stat_accscalar_t, 1, DefaultPtrTraits, index_t> invstd,
+    const GenericPackedTensorAccessor<stat_scalar_t, 1, DefaultPtrTraits, index_t> weight,
+    const GenericPackedTensorAccessor<stat_accscalar_t, 1, DefaultPtrTraits, index_t> sum_dy,
+    const GenericPackedTensorAccessor<stat_accscalar_t, 1, DefaultPtrTraits, index_t> sum_dy_xmu,
+    GenericPackedTensorAccessor<input_scalar_t, 3, DefaultPtrTraits, index_t> grad_input,
+    const stat_accscalar_t norm_fct) {
+  batch_norm_backward_elemt_kernel_impl(
+      input, grad_output, mean, invstd, weight, sum_dy, sum_dy_xmu, grad_input, norm_fct);
+}
+
+template <typename scalar_t, int64_t dim, template <typename U> class PtrTraits = DefaultPtrTraits, typename index_t = int64_t>
+static GenericPackedTensorAccessor<scalar_t, dim, PtrTraits, index_t> get_packed_accessor(
+    const Tensor& t, c10::string_view var_name) {
+  constexpr auto expect_type = c10::CppTypeToScalarType<scalar_t>::value;
+  const auto actual_type = t.scalar_type();
+  TORCH_CHECK(actual_type == expect_type, "Expected ", var_name,
+              " to have type ", expect_type, " but got ", actual_type);
+  return t.generic_packed_accessor<scalar_t, dim, PtrTraits, index_t>();
+}
+
+template <typename scalar_t, int64_t dim, template <typename U> class PtrTraits = DefaultPtrTraits, typename index_t = int64_t>
+static GenericPackedTensorAccessor<scalar_t, dim, PtrTraits, index_t> packed_accessor_or_dummy(
+    const Tensor& t, c10::string_view var_name) {
+  if (!t.defined()) {
+    const std::array<index_t, dim> zeros{{0}};
+    return GenericPackedTensorAccessor<scalar_t, dim, PtrTraits, index_t>(nullptr, zeros.data(), zeros.data());
+  }
+  return get_packed_accessor<scalar_t, dim, PtrTraits, index_t>(t, var_name);
+}
+
+template<typename input_scalar_t, typename stat_scalar_t, typename index_t>
+std::tuple<Tensor, Tensor, Tensor> batch_norm_backward_cuda_template(const Tensor& grad_out_, const Tensor& input_, const Tensor& weight_,
+                                                                     const Tensor& running_mean_, const Tensor& running_var_, const Tensor& save_mean_, const Tensor& save_invstd_,
+                                                                     bool train, double epsilon, std::array<bool,3> grad_input_mask) {
+
+  using accscalar_t = at::acc_type<stat_scalar_t, true>;
+  Tensor grad_input_;
+  Tensor grad_input_reshaped;
+  Tensor grad_weight_;
+  Tensor grad_bias_;
+  auto input_reshaped = input_.reshape({input_.size(0), input_.size(1), -1});
+  auto grad_output_reshaped = grad_out_.reshape(input_reshaped.sizes());
+
+  if (grad_input_mask[0]) {
+    grad_input_ = at::empty_like(input_, LEGACY_CONTIGUOUS_MEMORY_FORMAT);
+    grad_input_reshaped = grad_input_.view(input_reshaped.sizes());
+  }
+  if (grad_input_mask[1]) {
+    grad_weight_ = at::empty_like(weight_, LEGACY_CONTIGUOUS_MEMORY_FORMAT);
+  }
+  if (grad_input_mask[2]) {
+    grad_bias_ = at::empty_like(weight_, LEGACY_CONTIGUOUS_MEMORY_FORMAT);
+  }
+
+  auto input = get_packed_accessor<
+      input_scalar_t, 3, DefaultPtrTraits, index_t>(input_reshaped, "input");
+  auto grad_output = get_packed_accessor<
+      input_scalar_t, 3, DefaultPtrTraits, index_t>(grad_output_reshaped, "grad_output");
+  auto grad_input = packed_accessor_or_dummy<
+      input_scalar_t, 3, DefaultPtrTraits, index_t>(grad_input_reshaped, "grad_input");
+  auto weight = packed_accessor_or_dummy<
+      stat_scalar_t, 1, DefaultPtrTraits, index_t>(weight_, "weight");
+  auto grad_weight = packed_accessor_or_dummy<
+      stat_scalar_t, 1, DefaultPtrTraits, index_t>(grad_weight_, "grad_weight");
+  auto grad_bias = packed_accessor_or_dummy<
+      stat_scalar_t, 1, DefaultPtrTraits, index_t>(grad_bias_, "grad_bias");
+  auto running_mean = packed_accessor_or_dummy<
+      stat_scalar_t, 1, DefaultPtrTraits, index_t>(running_mean_, "running_mean");
+  auto running_var = packed_accessor_or_dummy<
+      stat_scalar_t, 1, DefaultPtrTraits, index_t>(running_var_, "running_var");
+  auto save_mean = packed_accessor_or_dummy<
+      accscalar_t, 1, DefaultPtrTraits, index_t>(save_mean_, "save_mean");
+  auto save_invstd = packed_accessor_or_dummy<
+      accscalar_t, 1, DefaultPtrTraits, index_t>(save_invstd_, "save_invstd");
+
+  auto stream = at::cuda::getCurrentCUDAStream();
+  dim3 blocks(input.size(1));
+  int tf = getNumThreads(input.size(2));
+  dim3 threads(tf, std::max<int>(1, MAX_BLOCK_SIZE/tf));
+
+  batch_norm_backward_kernel<input_scalar_t, stat_scalar_t, accscalar_t, index_t> <<<blocks, threads, 0, stream>>>
+    (input, grad_output, grad_input, grad_weight, grad_bias, weight, running_mean, running_var,
+     save_mean, save_invstd, train, epsilon);
+  C10_CUDA_KERNEL_LAUNCH_CHECK();
+
+  return std::make_tuple(grad_input_, grad_weight_, grad_bias_);
+}
+
+template<typename scalar_t, typename index_t, typename VarTransform>
+void batch_norm_stats_cuda_template(
+    const Tensor& out_mean, const Tensor& out_invstd, const Tensor& input_, double epsilon) {
+
+  using accscalar_t = at::acc_type<scalar_t, true>;
+  int64_t n_input = input_.size(1);
+  Tensor dummy_mean_;
+  Tensor dummy_var_;
+  auto input_reshaped = input_.reshape({input_.size(0), input_.size(1), -1}); // internally we merge the feature dimensions
+
+  resize_output(out_mean, {n_input});
+  resize_output(out_invstd, {n_input});
+  auto input = get_packed_accessor<
+      scalar_t, 3, RestrictPtrTraits, index_t>(input_reshaped, "input");
+  TORCH_INTERNAL_ASSERT(out_invstd.dim() == 1 && out_invstd.is_contiguous() &&
+                        out_invstd.sizes()[0]);
+  TORCH_INTERNAL_ASSERT(out_mean.dim() == 1 && out_mean.is_contiguous() &&
+                        out_mean.sizes()[0]);
+
+  auto mean = packed_accessor_or_dummy<
+      accscalar_t, 1, RestrictPtrTraits, index_t>(out_mean, "out_mean");
+  auto invstd = packed_accessor_or_dummy<
+      accscalar_t, 1, RestrictPtrTraits, index_t>(out_invstd, "out_invstd");
+  auto stream = at::cuda::getCurrentCUDAStream();
+
+  dim3 blocks(input.size(1));
+  int tf = getNumThreads(input.size(2));
+  dim3 threads(tf, std::max<int>(1, MAX_BLOCK_SIZE/tf));
+  batch_norm_collect_statistics_kernel<VarTransform, scalar_t, scalar_t, accscalar_t, index_t> <<<blocks, threads, 0, stream>>>
+    (input, epsilon, 0.0, mean, invstd);
+  C10_CUDA_KERNEL_LAUNCH_CHECK();
+}
+
+template<typename input_scalar_t, typename stat_scalar_t, typename index_t>
+void batch_norm_elemt_cuda_template(const Tensor& output_, const Tensor& input_, const Tensor& weight_,
+                                    const Tensor& bias_, const Tensor& mean_, const Tensor& invstd_) {
+
+  using stat_accscalar_t = at::acc_type<stat_scalar_t, true>;
+  int64_t n_input = input_.size(1);
+  auto input_reshaped = input_.reshape({input_.size(0), input_.size(1), -1}); // internally we merge the feature dimensions
+  auto output_reshaped = output_.view({input_.size(0), input_.size(1), -1});
+
+  auto input = get_packed_accessor<
+      input_scalar_t, 3, RestrictPtrTraits, index_t>(input_reshaped, "input");
+  auto output = get_packed_accessor<
+      input_scalar_t, 3, RestrictPtrTraits, index_t>(output_reshaped, "output");
+  auto weight = packed_accessor_or_dummy<
+    stat_scalar_t, 1, RestrictPtrTraits, index_t>(weight_, "weight");
+  auto bias = packed_accessor_or_dummy<
+      stat_scalar_t, 1, RestrictPtrTraits, index_t>(bias_, "bias");
+  auto mean = packed_accessor_or_dummy<
+      stat_accscalar_t, 1, RestrictPtrTraits, index_t>(mean_, "mean");
+  auto invstd = packed_accessor_or_dummy<
+      stat_accscalar_t, 1, RestrictPtrTraits, index_t>(invstd_, "invstd");
+  auto stream = at::cuda::getCurrentCUDAStream();
+
+  // NOTE: We use transform_input_kernel in training mode, which ignores epsilon
+  const double dummy_epsilon = 1e-5;
+
+  // The input_transform kernel is pointwise, but we need to balance reading parameters (save_var/mean,
+  // weight/bias) - which we only do once and have a for loop afterwards - with having many threads and blocks
+  // and good occupancy. Quiet likely, we could go with even more blocks than 1024.
+  // The various planes are independent, so we use blocks for them.
+  int tf = std::max<int>(getNumThreads(input.size(2)/4),
+                         std::min<int>(getNumThreads(input.size(2)), 64));
+  int tb = std::max<int>(64/tf, 1);
+  dim3 blocks_trans(input.size(1), std::max<int>(1, std::min<int>((256*1024)/input.size(1),
+                                                                  (input.size(0)+tb-1)/tb)));
+  blocks_trans.y = std::min(blocks_trans.y, MAX_GRID_SIZE);
+  dim3 threads_trans(tf, tb);
+  batch_norm_transform_input_kernel<input_scalar_t, stat_scalar_t, stat_accscalar_t, true, index_t> <<<blocks_trans, threads_trans, 0, stream>>>
+    (input, output, mean, invstd, weight, bias, dummy_epsilon);
+  C10_CUDA_KERNEL_LAUNCH_CHECK();
+}
+
+template<typename scalar_t, typename accscalar_t, typename index_t>
+std::tuple<Tensor, Tensor> batch_norm_gather_stats_cuda_template(const Tensor& mean_, const Tensor& invstd_,
+                                                                 const Tensor& running_mean_, const Tensor& running_var_,
+                                                                 double momentum, double epsilon, const Tensor& counts_) {
+
+  Tensor save_mean_;
+  Tensor save_invstd_;
+
+  auto features = mean_.size(1);
+  auto input_options = mean_.options();
+  if (mean_.scalar_type() == at::ScalarType::Half || mean_.scalar_type() == at::ScalarType::BFloat16) {
+    input_options = input_options.dtype(ScalarType::Float);
+  }
+  save_mean_ = at::empty({features}, input_options);
+  save_invstd_ = at::empty({features}, input_options);
+
+  auto mean = packed_accessor_or_dummy<
+      accscalar_t, 2, RestrictPtrTraits, index_t>(mean_, "mean");
+  auto invstd = packed_accessor_or_dummy<
+      accscalar_t, 2, RestrictPtrTraits, index_t>(invstd_, "invstd");
+  auto running_mean = packed_accessor_or_dummy<
+      scalar_t, 1, RestrictPtrTraits, index_t>(running_mean_, "running_mean");
+  auto running_var = packed_accessor_or_dummy<
+      scalar_t, 1, RestrictPtrTraits, index_t>(running_var_, "running_mean");
+  auto counts = packed_accessor_or_dummy<
+      scalar_t, 1, RestrictPtrTraits, index_t>(counts_, "counts");
+
+  auto save_mean = get_packed_accessor<
+      accscalar_t, 1, RestrictPtrTraits, index_t>(save_mean_, "save_mean");
+  auto save_invstd = get_packed_accessor<
+      accscalar_t, 1, RestrictPtrTraits, index_t>(save_invstd_, "save_invstd");
+  auto stream = at::cuda::getCurrentCUDAStream();
+
+  int block = getNumThreads(features);
+  int grid = std::max<int>(1, features/block);
+  batch_norm_reduce_statistics_kernel<scalar_t, accscalar_t, index_t> <<<grid, block, 0, stream>>>
+      (mean, invstd, save_mean, save_invstd, running_mean, running_var, epsilon, momentum, counts);
+  C10_CUDA_KERNEL_LAUNCH_CHECK();
+
+  return std::make_tuple(save_mean_, save_invstd_);
+}
+
+template<typename input_scalar_t, typename stat_scalar_t, typename index_t>
+std::tuple<Tensor, Tensor, Tensor, Tensor> batch_norm_backward_reduce_cuda_template(const Tensor& grad_out_, const Tensor& input_,
+                                                                                    const Tensor& mean_, const Tensor& invstd_, const Tensor& weight_,
+                                                                                    const bool input_g, const bool weight_g, const bool bias_g) {
+
+  using stat_accscalar_t = at::acc_type<stat_scalar_t, true>;
+  int64_t n_input = input_.size(1);
+  Tensor sum_dy_;
+  Tensor sum_dy_xmu_;
+  Tensor grad_weight_;
+  Tensor grad_bias_;
+  auto input_reshaped = input_.reshape({input_.size(0), input_.size(1), -1}); // internally we merge the feature dimensions
+  auto grad_output_reshaped = grad_out_.reshape(input_reshaped.sizes());
+
+  if (input_g) {
+    sum_dy_ = at::empty_like(mean_, LEGACY_CONTIGUOUS_MEMORY_FORMAT);
+    sum_dy_xmu_ = at::empty_like(mean_, LEGACY_CONTIGUOUS_MEMORY_FORMAT);
+  }
+  if (weight_g) {
+    grad_weight_ = at::empty({n_input}, weight_.options());
+  }
+  if (bias_g) {
+    grad_bias_ = at::empty({n_input}, weight_.options());
+  }
+
+  auto input = get_packed_accessor<
+      input_scalar_t, 3, DefaultPtrTraits, index_t>(input_reshaped, "input");
+  auto grad_output = get_packed_accessor<
+      input_scalar_t, 3, DefaultPtrTraits, index_t>(grad_output_reshaped, "grad_output");
+  auto grad_weight = packed_accessor_or_dummy<
+      stat_scalar_t, 1, DefaultPtrTraits, index_t>(grad_weight_, "grad_weight");
+  auto grad_bias = packed_accessor_or_dummy<
+      stat_scalar_t, 1, DefaultPtrTraits, index_t>(grad_bias_, "grad_bias");
+  auto mean = packed_accessor_or_dummy<
+      stat_accscalar_t, 1, DefaultPtrTraits, index_t>(mean_, "mean");
+  auto invstd = packed_accessor_or_dummy<
+      stat_accscalar_t, 1, DefaultPtrTraits, index_t>(invstd_, "invstd");
+  auto sum_dy = packed_accessor_or_dummy<
+      stat_accscalar_t, 1, DefaultPtrTraits, index_t>(sum_dy_, "sum_dy");
+  auto sum_dy_xmu = packed_accessor_or_dummy<
+      stat_accscalar_t, 1, DefaultPtrTraits, index_t>(sum_dy_xmu_, "sum_dy_xmu");
+
+  auto batch_size = input_reshaped.size(0);
+  auto feature_size = input_reshaped.size(2);
+  auto stream = at::cuda::getCurrentCUDAStream();
+
+  int warp_size = at::cuda::warp_size();
+  int block_y = std::min<int>(lastPow2(batch_size), MAX_BLOCK_SIZE/warp_size);
+  // We want block_x to be at least a warp width
+  int block_x = std::min<int>(std::max<int>(getNumThreads(feature_size), warp_size), MAX_BLOCK_SIZE/block_y);
+  const dim3 block(block_x, block_y);
+  const dim3 grid(n_input);
+
+  batch_norm_backward_reduce_kernel<input_scalar_t, stat_scalar_t, stat_accscalar_t, index_t> <<<grid, block, 0, stream>>>
+    (input, grad_output, mean, invstd, sum_dy, sum_dy_xmu, grad_weight, grad_bias);
+  C10_CUDA_KERNEL_LAUNCH_CHECK();
+
+  return std::make_tuple(sum_dy_, sum_dy_xmu_, grad_weight_, grad_bias_);
+}
+
+template<typename input_scalar_t, typename stat_scalar_t, typename index_t>
+Tensor batch_norm_backward_elemt_cuda_template(const Tensor& grad_out_, const Tensor& input_,
+                                               const Tensor& mean_, const Tensor& invstd_,
+                                               const Tensor& weight_, const Tensor& sum_dy_, const Tensor& sum_dy_xmu_) {
+
+  using stat_accscalar_t = at::acc_type<stat_scalar_t, true>;
+  int64_t n_input = input_.size(1);
+  auto input_reshaped = input_.reshape({input_.size(0), input_.size(1), -1}); // internally we merge the feature dimensions
+  auto grad_output_reshaped = grad_out_.reshape(input_reshaped.sizes());
+  auto grad_input_reshaped = at::empty_like(input_reshaped, LEGACY_CONTIGUOUS_MEMORY_FORMAT);
+
+  auto input = get_packed_accessor<
+      input_scalar_t, 3, DefaultPtrTraits, index_t>(input_reshaped, "input");
+  auto grad_input = get_packed_accessor<
+      input_scalar_t, 3, DefaultPtrTraits, index_t>(grad_input_reshaped, "grad_input");
+  auto grad_output = get_packed_accessor<
+      input_scalar_t, 3, DefaultPtrTraits, index_t>(grad_output_reshaped, "grad_output");
+  auto mean = packed_accessor_or_dummy<
+      stat_accscalar_t, 1, DefaultPtrTraits, index_t>(mean_, "mean");
+  auto invstd = packed_accessor_or_dummy<
+      stat_accscalar_t, 1, DefaultPtrTraits, index_t>(invstd_, "invstd");
+  auto weight = packed_accessor_or_dummy<
+      stat_scalar_t, 1, DefaultPtrTraits, index_t>(weight_, "weight");
+  auto sum_dy = packed_accessor_or_dummy<
+      stat_accscalar_t, 1, DefaultPtrTraits, index_t>(sum_dy_, "sum_dy");
+  auto sum_dy_xmu = packed_accessor_or_dummy<
+      stat_accscalar_t, 1, DefaultPtrTraits, index_t>(sum_dy_xmu_, "sum_dy_xmu");
+
+  auto stream = at::cuda::getCurrentCUDAStream();
+
+  // The kernel is pointwise, but we need to balance reading parameters (save_var/mean,
+  // weight/bias) - which we only do once and have a for loop afterwards - with having many threads and blocks
+  // and good occupancy. Quiet likely, we could go with even more blocks than 1024.
+  // The various planes are independent, so we use blocks for them.
+  int tf = std::max<int>(getNumThreads(input.size(2)/4),
+                         std::min<int>(getNumThreads(input.size(2)), 64));
+  int tb = std::max<int>(64/tf, 1);
+  dim3 blocks_trans(input.size(1), std::max<int>(1, std::min<int>((256*1024)/input.size(1),
+                                                                  (input.size(0)+tb-1)/tb)));
+  blocks_trans.y = std::min(blocks_trans.y, MAX_GRID_SIZE);
+  dim3 threads_trans(tf, tb);
+  auto reduction_size = input_.numel() / n_input;
+  auto norm_fct = static_cast<stat_accscalar_t>(1.0 / reduction_size);
+  batch_norm_backward_elemt_kernel<input_scalar_t, stat_scalar_t, stat_accscalar_t, index_t>
+      <<<blocks_trans, threads_trans, 0, stream>>>
+      (input, grad_output, mean, invstd, weight, sum_dy, sum_dy_xmu, grad_input, norm_fct);
+  C10_CUDA_KERNEL_LAUNCH_CHECK();
+
+  return grad_input_reshaped.view(input_.sizes());
+}
+
+template<typename input_scalar_t, typename stat_scalar_t, typename index_t>
+Tensor batch_norm_backward_elemt_cuda_template(const Tensor& grad_out_, const Tensor& input_,
+                                               const Tensor& mean_, const Tensor& invstd_,
+                                               const Tensor& weight_, const Tensor& sum_dy_, const Tensor& sum_dy_xmu_, const Tensor& count) {
+
+  using stat_accscalar_t = at::acc_type<stat_scalar_t, true>;
+  int64_t n_input = input_.size(1);
+  auto input_reshaped = input_.reshape({input_.size(0), input_.size(1), -1}); // internally we merge the feature dimensions
+  auto grad_output_reshaped = grad_out_.reshape(input_reshaped.sizes());
+  auto grad_input_reshaped = at::empty_like(input_reshaped, LEGACY_CONTIGUOUS_MEMORY_FORMAT);
+
+  auto input = get_packed_accessor<
+      input_scalar_t, 3, DefaultPtrTraits, index_t>(input_reshaped, "input");
+  auto grad_input = get_packed_accessor<
+      input_scalar_t, 3, DefaultPtrTraits, index_t>(grad_input_reshaped, "grad_input");
+  auto grad_output = get_packed_accessor<
+      input_scalar_t, 3, DefaultPtrTraits, index_t>(grad_output_reshaped, "grad_output");
+  auto mean = packed_accessor_or_dummy<
+      stat_accscalar_t, 1, DefaultPtrTraits, index_t>(mean_, "mean");
+  auto invstd = packed_accessor_or_dummy<
+      stat_accscalar_t, 1, DefaultPtrTraits, index_t>(invstd_, "invstd");
+  auto weight = packed_accessor_or_dummy<
+      stat_scalar_t, 1, DefaultPtrTraits, index_t>(weight_, "weight");
+  auto sum_dy = packed_accessor_or_dummy<
+      stat_accscalar_t, 1, DefaultPtrTraits, index_t>(sum_dy_, "sum_dy");
+  auto sum_dy_xmu = packed_accessor_or_dummy<
+      stat_accscalar_t, 1, DefaultPtrTraits, index_t>(sum_dy_xmu_, "sum_dy_xmu");
+
+  auto stream = at::cuda::getCurrentCUDAStream();
+
+  // The kernel is pointwise, but we need to balance reading parameters (save_var/mean,
+  // weight/bias) - which we only do once and have a for loop afterwards - with having many threads and blocks
+  // and good occupancy. Quiet likely, we could go with even more blocks than 1024.
+  // The various planes are independent, so we use blocks for them.
+  int tf = std::max<int>(getNumThreads(input.size(2)/4),
+                         std::min<int>(getNumThreads(input.size(2)), 64));
+  int tb = std::max<int>(64/tf, 1);
+  dim3 blocks_trans(input.size(1), std::max<int>(1, std::min<int>((256*1024)/input.size(1),
+                                                                  (input.size(0)+tb-1)/tb)));
+  blocks_trans.y = std::min(blocks_trans.y, MAX_GRID_SIZE);
+  dim3 threads_trans(tf, tb);
+  batch_norm_backward_elemt_kernel<input_scalar_t, stat_scalar_t, stat_accscalar_t, index_t> <<<blocks_trans, threads_trans, 0, stream>>>
+    (input, grad_output, mean, invstd, weight, sum_dy, sum_dy_xmu, grad_input, count.const_data_ptr<int>(), count.numel());
+  C10_CUDA_KERNEL_LAUNCH_CHECK();
+
+  return grad_input_reshaped.view(input_.sizes());
+}
+
+// welford kernel for c last tensor calculating mean/biased_variance/unbiased_variance
+// original apex name: welford_kernel_c_last
+template
+   <typename VarTransform,
+    typename scalar_t,
+    typename accscalar_t,
+    int PARALLEL_LOADS>
+__global__ void
+batch_norm_collect_statistics_channels_last_kernel(
+      const scalar_t* __restrict__ input,
+      accscalar_t* __restrict__ out_mean,
+      accscalar_t* __restrict__ out_invstd,
+      volatile accscalar_t* staging_data,
+      int* semaphores,
+      const int reduction_size,
+      const int stride,
+      accscalar_t epsilon) {
+  // hide latency with concurrency
+  accscalar_t x_mean[PARALLEL_LOADS];
+  accscalar_t m_2_n[PARALLEL_LOADS];
+  int count[PARALLEL_LOADS];
+
+#pragma unroll
+  for (int i = 0; i < PARALLEL_LOADS; i++) {
+    x_mean[i] = accscalar_t(0);
+    m_2_n[i] = accscalar_t(0);
+    count[i] = accscalar_t(0);
+  }
+  // tensor dimension (m,c)
+
+  // loop along m dimension
+  int inner_loop_stride = blockDim.y * gridDim.y;
+
+  // offset along m dimension
+  int m_offset = blockIdx.y * blockDim.y + threadIdx.y;
+  int c_offset = blockIdx.x * blockDim.x + threadIdx.x;
+
+  int loop_count = 1 + (reduction_size - 1) / (inner_loop_stride * PARALLEL_LOADS);
+  int address_base = m_offset * stride + c_offset;
+  int address_increment = inner_loop_stride * stride;
+
+  for (int i = 0; i < loop_count; i++) {
+    accscalar_t x_math[PARALLEL_LOADS];
+    accscalar_t x_count_inv[PARALLEL_LOADS];
+    accscalar_t is_valid[PARALLEL_LOADS];
+
+    // load multiple data in
+#pragma unroll
+    for (int j = 0; j < PARALLEL_LOADS; j++) {
+      if (c_offset < stride && m_offset < reduction_size) {
+        x_math[j] = input[address_base];
+        count[j]++;
+        x_count_inv[j] = accscalar_t(1) / count[j];
+        is_valid[j] = accscalar_t(1);
+      } else {
+        x_math[j] = accscalar_t(0);
+        x_count_inv[j] = accscalar_t(0);
+        is_valid[j] = accscalar_t(0);
+      }
+      m_offset += inner_loop_stride;
+      address_base += address_increment;
+    }
+
+    // calculate mean/m2n with welford
+#pragma unroll
+    for (int j = 0; j < PARALLEL_LOADS; j++) {
+      accscalar_t delta0 = x_math[j] - x_mean[j];
+      x_mean[j] += delta0 * x_count_inv[j];
+      accscalar_t delta1 = x_math[j] - x_mean[j];
+      m_2_n[j] += delta0 * delta1 * is_valid[j];
+    }
+  }
+
+  // thread reduction to accumulate mean/m_2_n/count between PARALLEL_LOADS
+#pragma unroll
+  for (int j = 1; j < PARALLEL_LOADS; j++) {
+    welford_merge_element(count[0], x_mean[0], m_2_n[0], count[j], x_mean[j], m_2_n[j]);
+  }
+
+  // release x_mean / m_2_n
+  auto mean_th = x_mean[0];
+  auto m2_th = m_2_n[0];
+  auto count_th = count[0];
+
+  // block-wise reduction with shared memory (since reduction cannot be done within a warp)
+  static __shared__ accscalar_t shmem_mean[MAX_BLOCK_SIZE];
+  static __shared__ accscalar_t shmem_m2n[MAX_BLOCK_SIZE];
+  static __shared__ int shmem_count[MAX_BLOCK_SIZE];
+
+  welford_merge_block_vertical(count_th, mean_th, m2_th, shmem_count, shmem_mean, shmem_m2n);
+
+  if (gridDim.y > 1) {
+    volatile accscalar_t* staging_mean = staging_data;
+    volatile accscalar_t* staging_m2n = &staging_data[stride*gridDim.y];
+    volatile int* staging_count = reinterpret_cast<volatile int*>(&staging_m2n[stride*gridDim.y]);
+
+    address_base = c_offset + blockIdx.y * stride;
+    // write data to staging_data;
+    if (threadIdx.y == 0 && c_offset < stride) {
+      staging_mean[address_base] = mean_th;
+      staging_m2n[address_base] = m2_th;
+      staging_count[address_base] = count_th;
+    }
+
+    __threadfence();
+    __syncthreads(); // ensuring writes to staging_ is visible to all blocks
+
+    __shared__ bool is_last_block_done;
+    // mark block done
+    if (threadIdx.x == 0 && threadIdx.y == 0) {
+      int old = atomicAdd(&semaphores[blockIdx.x], 1);
+      is_last_block_done = (old == (gridDim.y-1));
+    }
+
+    __syncthreads();
+
+    // check that all data is now available in global memory
+    if (is_last_block_done) {
+      count_th = 0;
+      mean_th = accscalar_t(0.0);
+      m2_th = accscalar_t(0.0);
+
+      for (int y = threadIdx.y; y < gridDim.y; y += blockDim.y) {
+        address_base = c_offset + y * stride;
+        int count_new = c_offset < stride ? staging_count[address_base] : 0;
+        accscalar_t mean_new = c_offset < stride ? staging_mean[address_base] : accscalar_t(0.0);
+        accscalar_t m2n_new = c_offset < stride ? staging_m2n[address_base] : accscalar_t(0.0);
+
+        welford_merge_element(count_th, mean_th, m2_th, count_new, mean_new, m2n_new);
+      }
+
+      welford_merge_block_vertical(count_th, mean_th, m2_th, shmem_count, shmem_mean, shmem_m2n);
+      if (threadIdx.y == 0 && c_offset < stride) {
+        out_mean[c_offset] = static_cast<accscalar_t>(mean_th);
+        out_invstd[c_offset] = VarTransform{}(m2_th/count_th, epsilon);
+      }
+    }
+  } else {
+    if (blockIdx.y == 0 && threadIdx.y == 0 && c_offset < stride) {
+      out_mean[c_offset] = static_cast<accscalar_t>(mean_th);
+      out_invstd[c_offset] = VarTransform{}(m2_th/count_th, epsilon);
+    }
+  }
+}
+
+// elementwise BN kernel
+// original apex name: batchnorm_forward_c_last_kernel
+template <
+    typename scalar_t,
+    typename accscalar_t,
+    typename layerscalar_t,
+    int PARALLEL_LOADS>
+__global__ void batch_norm_transform_input_channels_last_kernel(
+      const scalar_t* __restrict__ input,
+      const scalar_t* __restrict__ z,
+      const accscalar_t* __restrict__ mean,
+      const accscalar_t* __restrict__ inv_std,
+      const layerscalar_t* __restrict__ weight,
+      const layerscalar_t* __restrict__ shift,
+      scalar_t* __restrict__ out,
+      const int reduction_size,
+      const int stride,
+      const bool fuse_relu) {
+  // tensor dimension (m,c)
+  // loop along m dimension
+  int inner_loop_stride = blockDim.y * gridDim.y;
+
+  // offset along m dimension
+  int m_offset = blockIdx.y * blockDim.y + threadIdx.y;
+  int c_offset = blockIdx.x * blockDim.x + threadIdx.x;
+
+  if (c_offset >= stride || m_offset >= reduction_size) {
+    return;
+  }
+
+  auto m_c = mean[c_offset];
+  auto inv_std_c = static_cast<accscalar_t>(inv_std[c_offset]);
+  auto w_c = weight == nullptr ? accscalar_t(1.0) : static_cast<accscalar_t>(weight[c_offset]);
+  auto s_c = shift == nullptr ? accscalar_t(0.0) : static_cast<accscalar_t>(shift[c_offset]);
+
+  int loop_count = 1 + (reduction_size - 1) / (inner_loop_stride * PARALLEL_LOADS);
+  int address_base = m_offset * stride + c_offset;
+  int address_increment = inner_loop_stride * stride;
+
+  for (int i = 0; i < loop_count; i++) {
+#pragma unroll
+    for (int j = 0; j < PARALLEL_LOADS; j++) {
+      if (c_offset < stride && m_offset < reduction_size) {
+        auto tmp = w_c * (static_cast<accscalar_t>(input[address_base]) - m_c ) * inv_std_c + s_c;
+        if (z != nullptr) {
+          tmp += z[address_base];
+        }
+        out[address_base] = (fuse_relu && tmp <= accscalar_t(0.0) ? scalar_t(0.0) : static_cast<scalar_t>(tmp));
+      }
+      m_offset += inner_loop_stride;
+      address_base += address_increment;
+    }
+  }
+}
+
+template<typename T>
+__device__ __forceinline__ void merge_block_vertical_backward(T& sum_dy,
+    T& sum_dy_xmu,
+    T* shmem_sum_dy,
+    T* shmem_sum_dy_xmu) {
+  // write to shared memory
+  auto address_base = threadIdx.x + threadIdx.y * blockDim.x;
+
+#pragma unroll
+  for (int offset = blockDim.y/2; offset > 0; offset >>= 1) {
+    if (threadIdx.y < offset*2) {
+      shmem_sum_dy[address_base] = sum_dy;
+      shmem_sum_dy_xmu[address_base] = sum_dy_xmu;
+    }
+    __syncthreads();
+    if (threadIdx.y < offset && threadIdx.y + offset < blockDim.y) {
+      auto address = address_base + offset * blockDim.x;
+
+      sum_dy += shmem_sum_dy[address];
+      sum_dy_xmu += shmem_sum_dy_xmu[address];
+    }
+  }
+}
+
+// batchnorm backward kernel for c last tensor
+// original apex name: reduce_bn_c_last_kernel
+template <
+    int PARALLEL_LOADS,
+    typename scalar_t,
+    typename accscalar_t,
+    typename layerscalar_t>
+__global__ void batch_norm_backward_reduce_channels_last_kernel(
+      const scalar_t* __restrict__ input,
+      const scalar_t* __restrict__ grad_output,
+      const accscalar_t* __restrict__ mean,
+      const accscalar_t* __restrict__ inv_std,
+      accscalar_t* __restrict__ sum_dy_o,
+      accscalar_t* __restrict__ sum_dy_xmu_o,
+      layerscalar_t* __restrict__ grad_weight,
+      layerscalar_t* __restrict__ grad_bias,
+      volatile accscalar_t* staging_data,
+      int* semaphores,
+      const int reduction_size,
+      const int stride) {
+
+  // hide latency with concurrency
+  accscalar_t sum_dy[PARALLEL_LOADS];
+  accscalar_t sum_dy_xmu[PARALLEL_LOADS];
+
+#pragma unroll
+  for (int i = 0; i < PARALLEL_LOADS; i++) {
+    sum_dy[i] = accscalar_t(0);
+    sum_dy_xmu[i] = accscalar_t(0);
+  }
+  // tensor dimension (m,c)
+
+  // loop along m dimension
+  int inner_loop_stride = blockDim.y * gridDim.y;
+
+  // offset along m dimension
+  int m_offset = blockIdx.y * blockDim.y + threadIdx.y;
+  int c_offset = blockIdx.x * blockDim.x + threadIdx.x;
+
+  if (c_offset >= stride || m_offset >= reduction_size) {
+    return;
+  }
+
+  int loop_count = 1 + (reduction_size - 1) / (inner_loop_stride * PARALLEL_LOADS);
+  int address_base = m_offset * stride + c_offset;
+  int address_increment = inner_loop_stride * stride;
+
+  auto r_mean = mean[c_offset];
+  auto factor = inv_std[c_offset];
+
+  for (int i = 0; i < loop_count; i++) {
+    accscalar_t x_input[PARALLEL_LOADS];
+    accscalar_t x_grad_output[PARALLEL_LOADS];
+
+    // load multiple data in
+#pragma unroll
+    for (int j = 0; j < PARALLEL_LOADS; j++) {
+      if (c_offset < stride && m_offset < reduction_size) {
+        x_input[j] = input[address_base];
+        x_grad_output[j] = grad_output[address_base];
+      } else {
+        x_input[j] = accscalar_t(0);
+        x_grad_output[j] = accscalar_t(0);
+      }
+      m_offset += inner_loop_stride;
+      address_base += address_increment;
+    }
+
+    // calculate sum_dy / sum_dy_xmu
+#pragma unroll
+    for (int j = 0; j < PARALLEL_LOADS; j++) {
+      sum_dy[j] += x_grad_output[j];
+      sum_dy_xmu[j] += x_grad_output[j] * (x_input[j] - r_mean);
+    }
+  }
+
+  // thread reduction to accumulate sum_dy / sum_dy_xmu between PARALLEL_LOADS
+#pragma unroll
+  for (int j = 1; j < PARALLEL_LOADS; j++) {
+    sum_dy[0] += sum_dy[j];
+    sum_dy_xmu[0] += sum_dy_xmu[j];
+  }
+
+  // release array of registers
+  auto sum_dy_th = sum_dy[0];
+  auto sum_dy_xmu_th = sum_dy_xmu[0];
+
+  // block-wise reduction with shared memory (since reduction cannot be done within a warp)
+  static __shared__ accscalar_t shmem_sum_dy[MAX_BLOCK_SIZE];
+  static __shared__ accscalar_t shmem_sum_dy_xmu[MAX_BLOCK_SIZE];
+
+  merge_block_vertical_backward(sum_dy_th, sum_dy_xmu_th, shmem_sum_dy, shmem_sum_dy_xmu);
+
+  if (gridDim.y > 1) {
+    volatile accscalar_t* staging_sum_dy = staging_data;
+    volatile accscalar_t* staging_sum_dy_xmu = &staging_data[stride*gridDim.y];
+
+    address_base = c_offset + blockIdx.y * stride;
+    // write data to staging_data;
+    if (threadIdx.y == 0 && c_offset < stride) {
+      staging_sum_dy[address_base] = sum_dy_th;
+      staging_sum_dy_xmu[address_base] = sum_dy_xmu_th;
+    }
+
+    __threadfence();
+    __syncthreads(); // ensuring writes to staging_ is visible to all blocks
+
+    __shared__ bool is_last_block_done;
+    // mark block done
+    if (threadIdx.x == 0 && threadIdx.y == 0) {
+      int old = atomicAdd(&semaphores[blockIdx.x], 1);
+      is_last_block_done = (old == (gridDim.y-1));
+    }
+
+    __syncthreads();
+
+    // check that all data is now available in global memory
+    if (is_last_block_done) {
+      sum_dy_th = accscalar_t(0.0);
+      sum_dy_xmu_th = accscalar_t(0.0);
+
+      for (int y = threadIdx.y; y < gridDim.y; y += blockDim.y) {
+        address_base = c_offset + y * stride;
+        sum_dy_th += (c_offset < stride ? staging_sum_dy[address_base] : accscalar_t(0.0));
+        sum_dy_xmu_th += (c_offset < stride ? staging_sum_dy_xmu[address_base] : accscalar_t(0.0));
+      }
+
+      merge_block_vertical_backward(sum_dy_th, sum_dy_xmu_th, shmem_sum_dy, shmem_sum_dy_xmu);
+      if (threadIdx.y == 0 && c_offset < stride) {
+        if (grad_bias != nullptr) {
+          grad_bias[c_offset] = static_cast<layerscalar_t>(sum_dy_th);
+        }
+        if (grad_weight != nullptr) {
+          grad_weight[c_offset] = static_cast<layerscalar_t>(sum_dy_xmu_th * factor);
+        }
+        //mean_dy[c_offset] = sum_dy_th / reduction_size;
+        //mean_dy_xmu[c_offset] = sum_dy_xmu_th / reduction_size;
+        sum_dy_o[c_offset] = sum_dy_th;
+        sum_dy_xmu_o[c_offset] = sum_dy_xmu_th;
+      }
+    }
+  } else {
+    if (blockIdx.y == 0 && threadIdx.y == 0 && c_offset < stride) {
+      if (grad_bias != nullptr) {
+        grad_bias[c_offset] = static_cast<layerscalar_t>(sum_dy_th);
+      }
+      if (grad_weight != nullptr) {
+        grad_weight[c_offset] = static_cast<layerscalar_t>(sum_dy_xmu_th * factor);
+      }
+      //mean_dy[c_offset] = sum_dy_th / reduction_size;
+      //mean_dy_xmu[c_offset] = sum_dy_xmu_th / reduction_size;
+      sum_dy_o[c_offset] = sum_dy_th;
+      sum_dy_xmu_o[c_offset] = sum_dy_xmu_th;
+    }
+  }
+}
+
+// elementwise BN kernel
+// original apex name: batchnorm_backward_c_last_kernel
+template <
+    int PARALLEL_LOADS,
+    typename scalar_t,
+    typename accscalar_t,
+    typename layerscalar_t>
+__device__ __forceinline__ void batch_norm_backward_elemt_channels_last_kernel_impl(
+      const scalar_t* __restrict__ grad_output,
+      const scalar_t* __restrict__ input,
+      const accscalar_t* __restrict__ mean,
+      const accscalar_t* __restrict__ inv_std,
+      const layerscalar_t* __restrict__ weight,
+      const accscalar_t* __restrict__ sum_dy,
+      const accscalar_t* __restrict__ sum_dy_xmu,
+      scalar_t* __restrict__ grad_input,
+      const accscalar_t norm_fct,
+      const int reduction_size,
+      const int stride) {
+  // tensor dimension (m,c)
+  // loop along m dimension
+  int inner_loop_stride = blockDim.y * gridDim.y;
+
+  // offset along m dimension
+  int m_offset = blockIdx.y * blockDim.y + threadIdx.y;
+  int c_offset = blockIdx.x * blockDim.x + threadIdx.x;
+
+  if (c_offset >= stride || m_offset >= reduction_size) {
+    return;
+  }
+
+  auto m_c = mean[c_offset];
+  auto m_dy_c = sum_dy[c_offset] * norm_fct;
+  auto factor_1_c = inv_std[c_offset];
+  auto factor_2_c = (weight == nullptr? accscalar_t(1.0) : static_cast<accscalar_t>(weight[c_offset])) * factor_1_c;
+  factor_1_c = factor_1_c * factor_1_c * sum_dy_xmu[c_offset] * norm_fct;
+
+  int loop_count = 1 + (reduction_size - 1) / (inner_loop_stride * PARALLEL_LOADS);
+  int address_base = m_offset * stride + c_offset;
+  int address_increment = inner_loop_stride * stride;
+
+  for (int i = 0; i < loop_count; i++) {
+#pragma unroll
+    for (int j = 0; j < PARALLEL_LOADS; j++) {
+      if (c_offset < stride && m_offset < reduction_size) {
+        grad_input[address_base] = static_cast<scalar_t>(
+            (static_cast<accscalar_t>(grad_output[address_base]) - m_dy_c -
+            (static_cast<accscalar_t>(input[address_base]) - m_c) * factor_1_c)
+            * factor_2_c);
+      }
+      m_offset += inner_loop_stride;
+      address_base += address_increment;
+    }
+  }
+}
+
+template <
+    int PARALLEL_LOADS,
+    typename scalar_t,
+    typename accscalar_t,
+    typename layerscalar_t>
+__global__ void batch_norm_backward_elemt_channels_last_kernel(
+      const scalar_t* __restrict__ grad_output,
+      const scalar_t* __restrict__ input,
+      const accscalar_t* __restrict__ mean,
+      const accscalar_t* __restrict__ inv_std,
+      const layerscalar_t* __restrict__ weight,
+      const accscalar_t* __restrict__ sum_dy,
+      const accscalar_t* __restrict__ sum_dy_xmu,
+      const int* __restrict__ numel,
+      scalar_t* __restrict__ grad_input,
+      const int64_t world_size,
+      const int reduction_size,
+      const int stride) {
+
+  int64_t total_numel = 0;
+  for (int i = 0; i < world_size; i++) {
+    total_numel += numel[i];
+  }
+
+  auto norm_fct = static_cast<accscalar_t>(1) / static_cast<accscalar_t>(total_numel);
+  batch_norm_backward_elemt_channels_last_kernel_impl<PARALLEL_LOADS>(
+      grad_output, input, mean, inv_std, weight, sum_dy, sum_dy_xmu,
+      grad_input, norm_fct, reduction_size, stride);
+}
+
+template <
+    int PARALLEL_LOADS,
+    typename scalar_t,
+    typename accscalar_t,
+    typename layerscalar_t>
+__global__ void batch_norm_backward_elemt_channels_last_kernel(
+      const scalar_t* __restrict__ grad_output,
+      const scalar_t* __restrict__ input,
+      const accscalar_t* __restrict__ mean,
+      const accscalar_t* __restrict__ inv_std,
+      const layerscalar_t* __restrict__ weight,
+      const accscalar_t* __restrict__ sum_dy,
+      const accscalar_t* __restrict__ sum_dy_xmu,
+      scalar_t* __restrict__ grad_input,
+      const accscalar_t norm_fct,
+      const int reduction_size,
+      const int stride) {
+  batch_norm_backward_elemt_channels_last_kernel_impl<PARALLEL_LOADS>(
+      grad_output, input, mean, inv_std, weight, sum_dy, sum_dy_xmu,
+      grad_input, norm_fct, reduction_size, stride);
+}
+
+template<typename scalar_t, typename VarTransform>
+void batch_norm_stats_channels_last_cuda_template(
+    const Tensor& out_mean, const Tensor& out_invstd, const Tensor& input, double epsilon) {
+  using accscalar_t = at::acc_type<scalar_t, true>;
+
+  const auto stride = input.sizes()[1];
+  const auto reduction_size = input.numel() / stride;
+
+  resize_output(out_mean, {stride});
+  resize_output(out_invstd, {stride});
+  TORCH_INTERNAL_ASSERT(out_invstd.dim() == 1 && out_invstd.is_contiguous() &&
+                        out_invstd.sizes()[0]);
+  TORCH_INTERNAL_ASSERT(out_mean.dim() == 1 && out_mean.is_contiguous() &&
+                        out_mean.sizes()[0]);
+
+  dim3 block;
+  dim3 grid;
+  flexible_launch_configs(reduction_size, stride, block, grid, true);
+
+  at::Tensor staging_data;
+  at::Tensor semaphores;
+  if (grid.y > 1) {
+    staging_data = at::empty({4*stride*grid.y}, out_mean.options());
+    semaphores = at::zeros({grid.x}, input.options().dtype(at::kInt));
+  }
+
+  accscalar_t* staging_data_ptr = grid.y > 1 ? staging_data.mutable_data_ptr<accscalar_t>() : nullptr;
+  int* semaphores_ptr = grid.y > 1 ? semaphores.mutable_data_ptr<int>() : nullptr;
+  batch_norm_collect_statistics_channels_last_kernel<VarTransform, scalar_t, accscalar_t, ELEMENTS_PER_ITER>
+      <<<grid, block, 0, at::cuda::getCurrentCUDAStream()>>>(
+      input.const_data_ptr<scalar_t>(),
+      out_mean.mutable_data_ptr<accscalar_t>(),
+      out_invstd.mutable_data_ptr<accscalar_t>(),
+      staging_data_ptr,
+      semaphores_ptr,
+      reduction_size,
+      stride,
+      epsilon);
+  C10_CUDA_KERNEL_LAUNCH_CHECK();
+}
+
+void batch_norm_elemt_channels_last_cuda_template(
+    const at::Tensor& output,
+    const at::Tensor& input,
+    const at::Tensor& weight,
+    const at::Tensor& shift,  // bias of BN
+    const at::Tensor& mean,
+    const at::Tensor& inv_std,
+    const at::optional<at::Tensor>& z = c10::nullopt,  // bias after BN
+    const bool fuse_relu = false) {
+  const auto stride = input.sizes()[1];
+  const auto reduction_size = input.numel() / stride;
+
+  dim3 block;
+  dim3 grid;
+  flexible_launch_configs(reduction_size, stride, block, grid);
+
+  auto stream = at::cuda::getCurrentCUDAStream();
+  const auto second_dtype = weight.defined() ? weight.scalar_type() :
+      (shift.defined() ? shift.scalar_type() : input.scalar_type());
+
+  if (input.scalar_type() != second_dtype) {
+    AT_DISPATCH_FLOATING_TYPES_AND2(kHalf, kBFloat16, input.scalar_type(), "batchnorm_forward", [&] {
+      using accscalar_t = at::acc_type<scalar_t, true>;
+      batch_norm_transform_input_channels_last_kernel<scalar_t, accscalar_t, accscalar_t, ELEMENTS_PER_ITER>
+          <<<grid, block, 0, stream>>>(
+          input.const_data_ptr<scalar_t>(),
+          z.has_value() ? z.value().const_data_ptr<scalar_t>() : nullptr,
+          mean.const_data_ptr<accscalar_t>(),
+          inv_std.const_data_ptr<accscalar_t>(),
+          weight.defined() ? weight.const_data_ptr<accscalar_t>() : nullptr,
+          shift.defined() ? shift.const_data_ptr<accscalar_t>() : nullptr,
+          output.mutable_data_ptr<scalar_t>(),
+          reduction_size,
+          stride,
+          fuse_relu);
+      C10_CUDA_KERNEL_LAUNCH_CHECK();
+    });
+  } else {
+    if (weight.defined()){
+      TORCH_CHECK(input.scalar_type() == weight.scalar_type(), "batchnorm_forward: input.scalar_type() ", input.scalar_type(),
+        " is not supported with weight.scalar_type() ", weight.scalar_type());
+    }
+    AT_DISPATCH_FLOATING_TYPES_AND2(kHalf, kBFloat16, input.scalar_type(), "batchnorm_forward", [&] {
+      using accscalar_t = at::acc_type<scalar_t, true>;
+      batch_norm_transform_input_channels_last_kernel<scalar_t, accscalar_t, scalar_t, ELEMENTS_PER_ITER>
+          <<<grid, block, 0, stream>>>(
+          input.const_data_ptr<scalar_t>(),
+          z.has_value() ? z.value().const_data_ptr<scalar_t>() : nullptr,
+          mean.const_data_ptr<accscalar_t>(),
+          inv_std.const_data_ptr<accscalar_t>(),
+          weight.defined() ? weight.const_data_ptr<scalar_t>() : nullptr,
+          shift.defined() ? shift.const_data_ptr<scalar_t>(): nullptr,
+          output.mutable_data_ptr<scalar_t>(),
+          reduction_size,
+          stride,
+          fuse_relu);
+      C10_CUDA_KERNEL_LAUNCH_CHECK();
+    });
+  }
+}
+
+std::tuple<Tensor, Tensor, Tensor, Tensor>
+batch_norm_backward_reduce_cuda_channels_last_template(const at::Tensor& grad_output,
+    const at::Tensor& input,
+    const at::Tensor& mean,
+    const at::Tensor& inv_std,
+    const at::Tensor& weight,
+    const bool input_g, const bool weight_g, const bool bias_g) {
+  const auto stride = input.sizes()[1];
+  const auto reduction_size = input.numel() / stride;
+
+  at::Tensor sumn_dy = at::empty({stride}, mean.options());
+  at::Tensor sum_dy_xmu = at::empty({stride}, mean.options());
+
+  at::Tensor grad_weight;
+  at::Tensor grad_bias;
+  if (weight.defined()) {
+    grad_weight = at::empty({stride}, weight.options());
+    grad_bias = at::empty({stride}, weight.options());
+  } else {
+    // because I cannot return an uninitialized at::Tensor
+    grad_weight = at::empty({0}, mean.options());
+    grad_bias = at::empty({0}, mean.options());
+  }
+
+  dim3 block;
+  dim3 grid;
+  flexible_launch_configs(reduction_size, stride, block, grid, true);
+
+  at::Tensor staging_data;
+  at::Tensor semaphores;
+  if (grid.y > 1) {
+    staging_data = at::empty({2*stride*grid.y}, mean.options());
+    semaphores = at::zeros({grid.x}, input.options().dtype(at::kInt));
+  }
+  auto stream = at::cuda::getCurrentCUDAStream();
+
+  if (weight.defined() && input.scalar_type() != weight.scalar_type()) {
+    AT_DISPATCH_FLOATING_TYPES_AND2(kHalf, kBFloat16, input.scalar_type(), "batchnorm_backward_reduce", [&] {
+      using accscalar_t = at::acc_type<scalar_t, true>;
+      accscalar_t* staging_data_ptr = grid.y > 1 ? staging_data.mutable_data_ptr<accscalar_t>() : nullptr;
+      int* semaphores_ptr = grid.y > 1 ? semaphores.mutable_data_ptr<int>() : nullptr;
+      batch_norm_backward_reduce_channels_last_kernel<ELEMENTS_PER_ITER>
+          <<<grid, block, 0, stream>>>(
+          input.const_data_ptr<scalar_t>(),
+          grad_output.const_data_ptr<scalar_t>(),
+          mean.const_data_ptr<accscalar_t>(),
+          inv_std.const_data_ptr<accscalar_t>(),
+          sumn_dy.mutable_data_ptr<accscalar_t>(),
+          sum_dy_xmu.mutable_data_ptr<accscalar_t>(),
+          grad_weight.mutable_data_ptr<accscalar_t>(),
+          grad_bias.mutable_data_ptr<accscalar_t>(),
+          staging_data_ptr,
+          semaphores_ptr,
+          reduction_size,
+          stride);
+      C10_CUDA_KERNEL_LAUNCH_CHECK();
+    });
+  } else {
+    if (weight.defined()) {
+      TORCH_CHECK(input.scalar_type() == weight.scalar_type(), "batchnorm_backward_reduce: input.scalar_type() ", input.scalar_type(),
+        " is not supported with weight.scalar_type() ", weight.scalar_type());
+    }
+    AT_DISPATCH_FLOATING_TYPES_AND2(kHalf, kBFloat16, input.scalar_type(), "batchnorm_backward_reduce", [&] {
+      using accscalar_t = at::acc_type<scalar_t, true>;
+      accscalar_t* staging_data_ptr = grid.y > 1 ? staging_data.mutable_data_ptr<accscalar_t>() : nullptr;
+      int* semaphores_ptr = grid.y > 1 ? semaphores.mutable_data_ptr<int>() : nullptr;
+      batch_norm_backward_reduce_channels_last_kernel<ELEMENTS_PER_ITER>
+          <<<grid, block, 0, stream>>>(
+          input.const_data_ptr<scalar_t>(),
+          grad_output.const_data_ptr<scalar_t>(),
+          mean.const_data_ptr<accscalar_t>(),
+          inv_std.const_data_ptr<accscalar_t>(),
+          sumn_dy.mutable_data_ptr<accscalar_t>(),
+          sum_dy_xmu.mutable_data_ptr<accscalar_t>(),
+          weight.defined() ? grad_weight.mutable_data_ptr<scalar_t>() : nullptr,
+          weight.defined() ? grad_bias.mutable_data_ptr<scalar_t>() : nullptr,
+          staging_data_ptr,
+          semaphores_ptr,
+          reduction_size,
+          stride);
+      C10_CUDA_KERNEL_LAUNCH_CHECK();
+    });
+  }
+
+  return std::make_tuple(sumn_dy, sum_dy_xmu, grad_weight, grad_bias);
+}
+
+at::Tensor batch_norm_backward_elemt_channels_last_cuda_template(
+    const at::Tensor& grad_output,
+    const at::Tensor& input,
+    const at::Tensor& mean,
+    const at::Tensor& inv_std,
+    const at::Tensor& weight,
+    const at::Tensor& sum_dy,
+    const at::Tensor& sum_dy_xmu,
+    const at::Tensor& count) {
+  const auto stride = input.sizes()[1];
+  const auto reduction_size = input.numel() / stride;
+
+  // Input is guarunteed to be channels-last compatible
+  at::Tensor grad_input = at::empty_like(input);
+
+  dim3 block;
+  dim3 grid;
+  flexible_launch_configs(reduction_size, stride, block, grid);
+
+  auto stream = at::cuda::getCurrentCUDAStream();
+
+  if (weight.defined() && weight.scalar_type() != input.scalar_type()) {
+    AT_DISPATCH_FLOATING_TYPES_AND2(kHalf, kBFloat16, input.scalar_type(), "batchnorm_backward_element", [&] {
+      using accscalar_t = at::acc_type<scalar_t, true>;
+      batch_norm_backward_elemt_channels_last_kernel<ELEMENTS_PER_ITER>
+          <<<grid, block, 0, stream>>>(
+          grad_output.const_data_ptr<scalar_t>(),
+          input.const_data_ptr<scalar_t>(),
+          mean.const_data_ptr<accscalar_t>(),
+          inv_std.const_data_ptr<accscalar_t>(),
+          weight.const_data_ptr<accscalar_t>(),
+          sum_dy.const_data_ptr<accscalar_t>(),
+          sum_dy_xmu.const_data_ptr<accscalar_t>(),
+          count.const_data_ptr<int>(),
+          grad_input.mutable_data_ptr<scalar_t>(),
+          count.numel(),
+          reduction_size,
+          stride);
+      C10_CUDA_KERNEL_LAUNCH_CHECK();
+    });
+  } else {
+    if (weight.defined()) {
+      TORCH_CHECK(input.scalar_type() == weight.scalar_type(), "batchnorm_backward_element: input.scalar_type() ", input.scalar_type(),
+        " is not supported with weight.scalar_type() ", weight.scalar_type());
+    }
+    AT_DISPATCH_FLOATING_TYPES_AND2(at::ScalarType::Half, at::ScalarType::BFloat16, input.scalar_type(), "batchnorm_backward_element", [&] {
+      using accscalar_t = at::acc_type<scalar_t, true>;
+      batch_norm_backward_elemt_channels_last_kernel<ELEMENTS_PER_ITER>
+          <<<grid, block, 0, stream>>>(
+          grad_output.const_data_ptr<scalar_t>(),
+          input.const_data_ptr<scalar_t>(),
+          mean.const_data_ptr<accscalar_t>(),
+          inv_std.const_data_ptr<accscalar_t>(),
+          weight.defined() ? weight.const_data_ptr<scalar_t>() : nullptr,
+          sum_dy.const_data_ptr<accscalar_t>(),
+          sum_dy_xmu.const_data_ptr<accscalar_t>(),
+          count.const_data_ptr<int>(),
+          grad_input.mutable_data_ptr<scalar_t>(),
+          count.numel(),
+          reduction_size,
+          stride);
+      C10_CUDA_KERNEL_LAUNCH_CHECK();
+    });
+  }
+
+  return grad_input;
+}
+
+at::Tensor batch_norm_backward_elemt_channels_last_cuda_template(
+    const at::Tensor& grad_output,
+    const at::Tensor& input,
+    const at::Tensor& mean,
+    const at::Tensor& inv_std,
+    const at::Tensor& weight,
+    const at::Tensor& sum_dy,
+    const at::Tensor& sum_dy_xmu) {
+  const auto stride = input.sizes()[1];
+  const auto reduction_size = input.numel() / stride;
+  auto norm_fct = 1.0 / reduction_size;
+
+  // Input is guarunteed to be channels-last compatible
+  at::Tensor grad_input = at::empty_like(input);
+
+  dim3 block;
+  dim3 grid;
+  flexible_launch_configs(reduction_size, stride, block, grid);
+
+  auto stream = at::cuda::getCurrentCUDAStream();
+
+  AT_DISPATCH_FLOATING_TYPES_AND2(kHalf, kBFloat16, input.scalar_type(), "batchnorm_backward_element", [&] {
+    using accscalar_t = at::acc_type<scalar_t, true>;
+
+    if (weight.defined() && weight.scalar_type() != input.scalar_type()) {
+      batch_norm_backward_elemt_channels_last_kernel<ELEMENTS_PER_ITER>
+          <<<grid, block, 0, stream>>>(
+          grad_output.const_data_ptr<scalar_t>(),
+          input.const_data_ptr<scalar_t>(),
+          mean.const_data_ptr<accscalar_t>(),
+          inv_std.const_data_ptr<accscalar_t>(),
+          weight.const_data_ptr<accscalar_t>(),
+          sum_dy.const_data_ptr<accscalar_t>(),
+          sum_dy_xmu.const_data_ptr<accscalar_t>(),
+          grad_input.mutable_data_ptr<scalar_t>(),
+          static_cast<accscalar_t>(norm_fct),
+          reduction_size,
+          stride);
+          C10_CUDA_KERNEL_LAUNCH_CHECK();
+    } else {
+      batch_norm_backward_elemt_channels_last_kernel<ELEMENTS_PER_ITER>
+          <<<grid, block, 0, stream>>>(
+          grad_output.const_data_ptr<scalar_t>(),
+          input.const_data_ptr<scalar_t>(),
+          mean.const_data_ptr<accscalar_t>(),
+          inv_std.const_data_ptr<accscalar_t>(),
+          weight.defined() ? weight.const_data_ptr<scalar_t>() : nullptr,
+          sum_dy.const_data_ptr<accscalar_t>(),
+          sum_dy_xmu.const_data_ptr<accscalar_t>(),
+          grad_input.mutable_data_ptr<scalar_t>(),
+          static_cast<accscalar_t>(norm_fct),
+          reduction_size,
+          stride);
+          C10_CUDA_KERNEL_LAUNCH_CHECK();
+    }
+  });
+
+  return grad_input;
+}
+
+} } // namespace at::native

venv/lib/python3.10/site-packages/torch/include/ATen/native/cuda/PersistentSoftmax.cuh

@@ -0,0 +1,401 @@
+#pragma once
+
+#include <cfloat>
+#include <limits>
+#include <stdint.h>
+#include <cuda_fp16.h>
+#include <c10/macros/Macros.h>
+
+#include <ATen/cuda/DeviceUtils.cuh>
+
+namespace {
+
+int log2_ceil(int value) {
+    int log2_value = 0;
+    while ((1 << log2_value) < value) ++log2_value;
+    return log2_value;
+}
+
+template<typename T>
+struct Add {
+  __device__ __forceinline__ T operator()(T a, T b) const {
+    return a + b;
+  }
+};
+
+template<typename T>
+struct Max {
+  __device__ __forceinline__ T operator()(T a, T b) const {
+    return a < b ? b : a;
+  }
+};
+
+template <typename acc_t, int WARP_BATCH, int WARP_SIZE, template<typename> class ReduceOp>
+__device__ __forceinline__ void warp_reduce(acc_t* sum) {
+    ReduceOp<acc_t> r;
+    #pragma unroll
+    for (int offset = WARP_SIZE / 2; offset > 0; offset /= 2) {
+        #pragma unroll
+        for (int i = 0;  i < WARP_BATCH;  ++i) {
+            acc_t b = WARP_SHFL_XOR(sum[i], offset, WARP_SIZE);
+            sum[i] = r(sum[i], b);
+        }
+    }
+}
+
+// The softmax_warp_* methods perform softmax forward and backward propagation on samples spanning the fast dimension.
+// Each sample contains element_count scalar elements. element_count can be any integer value <= 1024.
+// The template arguments have the following meaning:
+// One "WARP" works on one "BATCH". One "BATCH" contains "WARP_BATCH" samples.
+// WARP_BATCH is equal to 1 when element_count is large, and > 1 when element_count is small.
+// A "WARP" contains "C10_WARPS_SIZE" threads, these treads are guaranteed to belong to the same warp.
+// This is important because it means only __shfl_ instructions are required for reductions.
+// Note that this means WARP_SIZE must be a power of two and <= architecture warp size.
+// CUDA warp size is 32 for all existing GPU architectures, but there is no guarantee this will not change for future arch.
+// ROCm warp size is 64 for all currently ROCm-supported GPU architectures, but this may change for future archs.
+// is_log_softmax is a flag indicating whether SoftMax or LogSoftMax should be computed.
+// is_masked is a flag indicating whether SoftMax or MaskedSoftMax should be computed.
+// The template can be instantiated with any floating point type for the type arguments input_t, output_t and acc_t.
+// This allows SoftMax to be fused with a cast immediately following the SoftMax.
+// The mask should have the same shape as input, with a boolean indicate if the value is masked.
+// The head_chunk_size is only used for transformer mask softmax, equals to H * D * D.
+// For instance:
+// input_t=half,  acc_t=float, output_t=half  => read half tensor, float accumulators, write half tensor.
+// input_t=half,  acc_t=float, output_t=float => read half tensor, float accumulators, write float tensor.
+// input_t_float, acc_t=float, output_t=half  => read float tensor, float accumulators, write half tensor.
+
+template <typename input_t, typename output_t, typename acc_t, int log2_elements, bool is_log_softmax, bool is_masked>
+__global__ void softmax_warp_forward(output_t *dst, const input_t *src, int batch_size, int stride, int element_count, const bool *mask = nullptr, const int head_chunk_size = -1, bool is_transformer_mask = false)
+{
+    // WARP_SIZE and WARP_BATCH must match the return values batches_per_warp and warp_size of method warp_softmax_forward_kernel.
+    constexpr int next_power_of_two = 1 << log2_elements;
+    constexpr int WARP_SIZE = (next_power_of_two < C10_WARP_SIZE) ? next_power_of_two : C10_WARP_SIZE;
+    constexpr int WARP_ITERATIONS = next_power_of_two / WARP_SIZE;
+    constexpr int WARP_BATCH = (next_power_of_two <= 128) ? 2 : 1;
+
+    int first_batch = (blockDim.y * blockIdx.x + threadIdx.y) * WARP_BATCH;
+
+    // batch_size might not be a multiple of WARP_BATCH. Check how
+    // many batches have to computed within this WARP.
+    int local_batches = batch_size - first_batch;
+    if (local_batches > WARP_BATCH)
+        local_batches = WARP_BATCH;
+
+    // there might be multiple batches per warp. compute the index within the batch
+    int local_idx = threadIdx.x;
+    int idx_offset = first_batch * stride + local_idx;
+
+    src += idx_offset;
+    dst += idx_offset;
+
+    if (is_transformer_mask) {
+        mask += ((first_batch * stride) / head_chunk_size) * stride + local_idx;
+    } else {
+        mask += idx_offset;
+    }
+    // The nested loops over WARP_BATCH and then WARP_ITERATIONS can be simplified to one loop,
+    // but I think doing so would obfuscate the logic of the algorithm, thus I chose to keep
+    // the nested loops.
+    // This should have no impact on performance because the loops are unrolled anyway.
+
+    // load data from global memory
+    acc_t elements[WARP_BATCH][WARP_ITERATIONS];
+    for (int i = 0;  i < WARP_BATCH;  ++i) {
+        int batch_element_count = (i >= local_batches) ? 0 : element_count;
+        for (int it = 0;  it < WARP_ITERATIONS;  ++it) {
+            int element_index = local_idx + it * WARP_SIZE;
+            if (element_index < batch_element_count) {
+                elements[i][it] = src[i*element_count+it*WARP_SIZE];
+            } else {
+                elements[i][it] = -std::numeric_limits<acc_t>::infinity();
+            }
+        }
+    }
+
+    // compute max_value
+    acc_t max_value[WARP_BATCH];
+    #pragma unroll
+    for (int i = 0;  i < WARP_BATCH;  ++i) {
+        int batch_element_count = (i >= local_batches) ? 0 : element_count;
+        bool is_meaningful_max = false;
+        max_value[i] = elements[i][0];
+        #pragma unroll
+        for (int it = 0;  it < WARP_ITERATIONS;  ++it) {
+            if (is_masked) {
+                int idx = it*WARP_SIZE;
+                if ((idx + local_idx) < batch_element_count) {
+                    if (!is_transformer_mask) {
+                        idx += i*element_count;
+                    }
+                    if (!mask[idx]) {
+                        max_value[i] = (is_meaningful_max && max_value[i] > elements[i][it]) ? max_value[i] : elements[i][it];
+                        is_meaningful_max = true;
+                    }
+                }
+            } else {
+                max_value[i] = max_value[i] > elements[i][it] ? max_value[i] : elements[i][it];
+            }
+        }
+        if (is_masked) {
+            if (!is_meaningful_max) {
+                max_value[i] = -std::numeric_limits<acc_t>::infinity();
+            }
+        }
+    }
+    warp_reduce<acc_t, WARP_BATCH, WARP_SIZE, Max>(max_value);
+
+    acc_t sum[WARP_BATCH] { 0.0f };
+    #pragma unroll
+    for (int i = 0;  i < WARP_BATCH;  ++i) {
+        int batch_element_count = (i >= local_batches) ? 0 : element_count;
+        #pragma unroll
+        for (int it = 0;  it < WARP_ITERATIONS;  ++it) {
+            if (!is_masked) {
+                if (is_log_softmax) {
+                    sum[i] += std::exp(elements[i][it] - max_value[i]);
+                } else {
+                    elements[i][it] = std::exp(elements[i][it] - max_value[i]);
+                    sum[i] += elements[i][it];
+                }
+            } else {
+                int idx = it*WARP_SIZE;
+                bool valid = (idx + local_idx) < batch_element_count;
+                if (!is_transformer_mask) {
+                    idx += i*element_count;
+                }
+                if (valid) {
+                    if (!mask[idx]) {
+                        if (is_log_softmax) {
+                            sum[i] += std::exp(elements[i][it] - max_value[i]);
+                        } else {
+                            elements[i][it] = std::exp(elements[i][it] - max_value[i]);
+                            sum[i] += elements[i][it];
+                        }
+                    } else {
+                        if (!is_log_softmax) {
+                            // Masked values are treated as -infinity, and std::exp(-infinity) is 0.
+                            elements[i][it] = 0;
+                        }
+                    }
+                } else {
+                    if (!is_log_softmax) {
+                        elements[i][it] = 0.;
+                    }
+                }
+            }
+        }
+    }
+    warp_reduce<acc_t, WARP_BATCH, WARP_SIZE, Add>(sum);
+
+    // store result
+    #pragma unroll
+    for (int i = 0;  i < WARP_BATCH;  ++i) {
+        if (i >= local_batches)
+            break;
+        if (is_log_softmax) sum[i] = std::log(sum[i]);
+        #pragma unroll
+        for (int it = 0;  it < WARP_ITERATIONS;  ++it) {
+            int element_index = local_idx + it * WARP_SIZE;
+            if (element_index < element_count) {
+                if (is_log_softmax) {
+                    dst[i*element_count+it*WARP_SIZE] = elements[i][it] - max_value[i] - sum[i];
+                } else if (sum[i] == 0) {
+                    dst[i*element_count+it*WARP_SIZE] = std::numeric_limits<acc_t>::quiet_NaN();
+                } else {
+                    dst[i*element_count+it*WARP_SIZE] = elements[i][it] / sum[i];
+                }
+            } else {
+                break;
+            }
+        }
+    }
+}
+
+template <typename input_t, typename output_t, typename acc_t, int log2_elements, bool is_log_softmax, bool is_masked>
+__global__ void softmax_warp_backward(output_t *gradInput, const input_t *grad, const input_t *output, int batch_size, int stride, int element_count, const bool *mask = nullptr)
+{
+    // WARP_SIZE and WARP_BATCH must match the return values batches_per_warp and warp_size of method warp_softmax_backward_kernel.
+    constexpr int next_power_of_two = 1 << log2_elements;
+    constexpr int WARP_SIZE = (next_power_of_two < C10_WARP_SIZE) ? next_power_of_two : C10_WARP_SIZE;
+    constexpr int WARP_ITERATIONS = next_power_of_two / WARP_SIZE;
+    constexpr int WARP_BATCH = (next_power_of_two <= 128) ? 2 : 1;
+
+    int first_batch = (blockDim.y * blockIdx.x + threadIdx.y) * WARP_BATCH;
+
+    // batch_size might not be a multiple of WARP_BATCH. Check how
+    // many batches have to computed within this WARP.
+    int local_batches = batch_size - first_batch;
+    if (local_batches > WARP_BATCH)
+        local_batches = WARP_BATCH;
+
+    // there might be multiple batches per warp. compute the index within the batch
+    int local_idx = threadIdx.x % WARP_SIZE;
+
+    // the first element to process by the current thread
+    int thread_offset = first_batch * stride + local_idx;
+    grad += thread_offset;
+    output += thread_offset;
+    gradInput += thread_offset;
+    if (is_masked) {
+        mask += thread_offset;
+    }
+
+    // The nested loops over WARP_BATCH and then WARP_ITERATIONS can be simplified to one loop,
+    // but I think doing so would obfuscate the logic of the algorithm, thus I chose to keep
+    // the nested loops.
+    // This should have no impact on performance because the loops are unrolled anyway.
+
+    // load data from global memory
+    acc_t grad_reg[WARP_BATCH][WARP_ITERATIONS];
+    acc_t output_reg[WARP_BATCH][WARP_ITERATIONS];
+    for (int i = 0;  i < WARP_BATCH;  ++i) {
+        int batch_element_count = (i >= local_batches) ? 0 : element_count;
+        for (int it = 0;  it < WARP_ITERATIONS;  ++it) {
+            int element_index = local_idx + it * WARP_SIZE;
+            if (element_index < batch_element_count) {
+                grad_reg[i][it] = grad[i*element_count+it*WARP_SIZE];
+                output_reg[i][it] = output[i*element_count+it*WARP_SIZE];
+            } else {
+                grad_reg[i][it] = acc_t(0);
+                output_reg[i][it] = acc_t(0);
+            }
+        }
+    }
+
+    acc_t sum[WARP_BATCH] { 0.0f };
+    #pragma unroll
+    for (int i = 0;  i < WARP_BATCH;  ++i) {
+        #pragma unroll
+        for (int it = 0;  it < WARP_ITERATIONS;  ++it) {
+            if (!is_masked || !mask[i*element_count+it*WARP_SIZE]) {
+                sum[i] += grad_reg[i][it];
+            }
+        }
+    }
+    warp_reduce<acc_t, WARP_BATCH, WARP_SIZE, Add>(sum);
+
+    // store result
+    #pragma unroll
+    for (int i = 0;  i < WARP_BATCH;  ++i) {
+        if (i >= local_batches)
+            break;
+        #pragma unroll
+        for (int it = 0;  it < WARP_ITERATIONS;  ++it) {
+            int element_index = local_idx + it * WARP_SIZE;
+            if (element_index < element_count) {
+                if (is_masked && mask[i*element_count+it*WARP_SIZE]) {
+                    gradInput[i*element_count+it*WARP_SIZE] = 0;
+                }
+                // compute gradients
+                else if (is_log_softmax) {
+                    gradInput[i*element_count+it*WARP_SIZE] = (grad_reg[i][it] - std::exp(output_reg[i][it]) * sum[i]);
+                } else {
+                    gradInput[i*element_count+it*WARP_SIZE] = (grad_reg[i][it] - output_reg[i][it] * sum[i]);
+                }
+            }
+        }
+    }
+}
+
+} // end of anonymous namespace
+
+template<typename input_t, typename output_t, typename acc_t, bool is_log_softmax, bool is_masked>
+void dispatch_softmax_forward(output_t *dst, const input_t *src, int softmax_elements, int softmax_elements_stride, int batch_count, const bool *mask = nullptr, int chunk_size = -1, bool is_transformer_mask = false)
+{
+    TORCH_INTERNAL_ASSERT( softmax_elements >= 0 && softmax_elements <= 1024 );
+    if (softmax_elements == 0) {
+        return;
+    } else {
+        int log2_elements = log2_ceil(softmax_elements);
+        const int next_power_of_two = 1 << log2_elements;
+
+        // This value must match the WARP_SIZE constexpr value computed inside softmax_warp_forward.
+        int warp_size = at::cuda::warp_size();
+        warp_size = (next_power_of_two < warp_size) ? next_power_of_two : warp_size;
+
+        // This value must match the WARP_BATCH constexpr value computed inside softmax_warp_forward.
+        int batches_per_warp = (next_power_of_two <= 128) ? 2 : 1;
+
+        // use 128 threads per block to maximize gpu utilization
+        constexpr int threads_per_block = 128;
+
+        int warps_per_block = (threads_per_block / warp_size);
+        int batches_per_block = warps_per_block * batches_per_warp;
+        int blocks = (batch_count + batches_per_block - 1) / batches_per_block;
+        dim3 threads(warp_size, warps_per_block, 1);
+        // Launch code would be more elegant if C++ supported FOR CONSTEXPR
+        switch (log2_elements) {
+            #define LAUNCH_SOFTMAX_WARP_FORWARD(L2E) case L2E:                    \
+            softmax_warp_forward<input_t, output_t, acc_t, L2E, is_log_softmax, is_masked>   \
+                <<<blocks, threads, 0, at::cuda::getCurrentCUDAStream()>>>(dst,   \
+                    src, batch_count, softmax_elements_stride, softmax_elements, mask, chunk_size, is_transformer_mask); \
+            C10_CUDA_KERNEL_LAUNCH_CHECK();                                       \
+            break;
+
+            LAUNCH_SOFTMAX_WARP_FORWARD(0);  // 1
+            LAUNCH_SOFTMAX_WARP_FORWARD(1);  // 2
+            LAUNCH_SOFTMAX_WARP_FORWARD(2);  // 4
+            LAUNCH_SOFTMAX_WARP_FORWARD(3);  // 8
+            LAUNCH_SOFTMAX_WARP_FORWARD(4);  // 16
+            LAUNCH_SOFTMAX_WARP_FORWARD(5);  // 32
+            LAUNCH_SOFTMAX_WARP_FORWARD(6);  // 64
+            LAUNCH_SOFTMAX_WARP_FORWARD(7);  // 128
+            LAUNCH_SOFTMAX_WARP_FORWARD(8);  // 256
+            LAUNCH_SOFTMAX_WARP_FORWARD(9);  // 512
+            LAUNCH_SOFTMAX_WARP_FORWARD(10); ; // 1024
+            default:
+                break;
+        }
+    }
+}
+
+template<typename input_t, typename output_t, typename acc_t, bool is_log_softmax, bool is_masked>
+void dispatch_softmax_backward(output_t *grad_input, const input_t *grad, const input_t *output, int softmax_elements, int softmax_elements_stride, int batch_count, const bool *mask = nullptr)
+{
+    TORCH_INTERNAL_ASSERT( softmax_elements >= 0 && softmax_elements <= 1024 );
+    if (softmax_elements == 0) {
+       return;
+    } else {
+        int log2_elements = log2_ceil(softmax_elements);
+        const int next_power_of_two = 1 << log2_elements;
+
+        // This value must match the WARP_SIZE constexpr value computed inside softmax_warp_backward.
+        int warp_size = at::cuda::warp_size();
+        warp_size = (next_power_of_two < warp_size) ? next_power_of_two : warp_size;
+
+        // This value must match the WARP_BATCH constexpr value computed inside softmax_warp_backward.
+        int batches_per_warp = (next_power_of_two <= 128) ? 2 : 1;
+
+        // use 128 threads per block to maximize gpu utilization
+        constexpr int threads_per_block = 128;
+
+        int warps_per_block = (threads_per_block / warp_size);
+        int batches_per_block = warps_per_block * batches_per_warp;
+        int blocks = (batch_count + batches_per_block - 1) / batches_per_block;
+        dim3 threads(warp_size, warps_per_block, 1);
+        // Launch code would be more elegant if C++ supported FOR CONSTEXPR
+        switch (log2_elements) {
+            #define LAUNCH_SOFTMAX_WARP_BACKWARD(L2E) case L2E:                      \
+            softmax_warp_backward<input_t, output_t, acc_t, L2E, is_log_softmax, is_masked> \
+                <<<blocks, threads, 0, at::cuda::getCurrentCUDAStream()>>>       \
+                (grad_input, grad, output, batch_count, softmax_elements_stride, \
+                softmax_elements, mask);                                              \
+            C10_CUDA_KERNEL_LAUNCH_CHECK();                                      \
+            break;
+
+            LAUNCH_SOFTMAX_WARP_BACKWARD(0); // 1
+            LAUNCH_SOFTMAX_WARP_BACKWARD(1); // 2
+            LAUNCH_SOFTMAX_WARP_BACKWARD(2); // 4
+            LAUNCH_SOFTMAX_WARP_BACKWARD(3); // 8
+            LAUNCH_SOFTMAX_WARP_BACKWARD(4); // 16
+            LAUNCH_SOFTMAX_WARP_BACKWARD(5); // 32
+            LAUNCH_SOFTMAX_WARP_BACKWARD(6); // 64
+            LAUNCH_SOFTMAX_WARP_BACKWARD(7); // 128
+            LAUNCH_SOFTMAX_WARP_BACKWARD(8); // 256
+            LAUNCH_SOFTMAX_WARP_BACKWARD(9); // 512
+            LAUNCH_SOFTMAX_WARP_BACKWARD(10); // 1024
+            default:
+                break;
+        }
+    }
+}

venv/lib/python3.10/site-packages/torch/include/ATen/native/cuda/Pow.cuh

@@ -0,0 +1,58 @@
+#pragma once
+#include <ATen/native/Pow.h>
+#include <c10/core/Scalar.h>
+
+namespace at { namespace native {
+
+namespace {
+
+
+// SFINAE doesn't work well with NVCC under Windows for math functions like pow and sqrt.
+// So we need to define the functions with the explicit function signatures.
+// As for pow, the following signatures are defined as the device function:
+//   pow(float, int)
+//   pow(double, int)
+//   pow(float, float)
+//   pow(double, double)
+#ifdef _MSC_VER
+// Functions for pow
+// pow for at::Half
+static inline __host__ __device__ at::Half pow_(at::Half base, at::Half exp) {
+  return static_cast<at::Half>(std::pow(static_cast<float>(base), static_cast<float>(exp)));
+}
+// pow for at::BFloat16
+static inline __host__ __device__ at::BFloat16 pow_(at::BFloat16 base, at::BFloat16 exp) {
+  return static_cast<at::BFloat16>(std::pow(static_cast<float>(base), static_cast<float>(exp)));
+}
+// pow (floating, floating/int)
+template <typename Base_type, typename Exp_type>
+static inline __host__ __device__ typename std::enable_if<std::is_floating_point<Base_type>::value && (std::is_same<Base_type, Exp_type>::value || std::is_same<Exp_type, int>::value), Base_type>::type
+  pow_(Base_type base, Exp_type exp) {
+  return std::pow(base, exp);
+}
+// pow (Otherwise)
+template <typename Base_type, typename Exp_type>
+static inline __host__ __device__ typename std::enable_if<!std::is_same<Base_type, Exp_type>::value && !std::is_same<Exp_type, int>::value, Base_type>::type
+  pow_(Base_type base, Exp_type exp) {
+  return static_cast<Base_type>(std::pow(static_cast<double>(base), static_cast<double>(exp)));
+}
+#else
+template <typename Base_type, typename Exp_type>
+static inline __host__ __device__ Base_type pow_(Base_type base, Exp_type exp) {
+  return ::pow(base, exp);
+}
+#endif
+
+template <typename T>
+static inline __host__ __device__ std::enable_if_t<std::is_integral<T>::value, T> pow_(
+    T base, T exp) {
+  return at::native::powi(base, exp);
+}
+
+template <typename T>
+static inline __host__ __device__ c10::complex<T> pow_(c10::complex<T> base, c10::complex<T> exp) {
+  return c10_complex_math::pow(base, exp);
+}
+
+} // namespace
+}} // namespace at::native