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batch_norm_kernel.cpp
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batch_norm_kernel.cpp
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#define TORCH_ASSERT_ONLY_METHOD_OPERATORS
#include <ATen/native/batch_norm.h>
#include <ATen/core/Tensor.h>
#include <ATen/AccumulateType.h>
#include <ATen/Dispatch.h>
#include <ATen/Parallel.h>
#include <ATen/native/TensorIterator.h>
#include <ATen/native/cpu/Loops.h>
#include <ATen/native/cpu/utils.h>
#include <ATen/native/cpu/mixed_data_type.h>
#include <ATen/cpu/vec/functional.h>
#include <ATen/cpu/vec/vec.h>
#include <c10/util/irange.h>
#include <ATen/OpMathType.h>
#ifndef AT_PER_OPERATOR_HEADERS
#include <ATen/Functions.h>
#else
#include <ATen/ops/empty.h>
#include <ATen/ops/ones.h>
#include <ATen/ops/zeros.h>
#endif
namespace at::native {
namespace {
using namespace vec;
template<typename param_t, typename opmath_t>
void batch_norm_cpu_collect_linear_and_constant_terms(
opmath_t* alpha, opmath_t* beta, int64_t n_channel,
const Tensor& weight /* optional */, const Tensor& bias /* optional */,
const Tensor& save_mean, const Tensor& save_invstd,
const Tensor& running_mean, const Tensor& running_var, bool train, double eps) {
const param_t* weight_data = weight.defined() ? weight.const_data_ptr<param_t>() : nullptr;
const param_t* bias_data = bias.defined() ? bias.const_data_ptr<param_t>() : nullptr;
auto save_mean_a = conditional_accessor_1d<const param_t>(save_mean);
auto save_invstd_a = conditional_accessor_1d<const param_t>(save_invstd);
auto running_mean_a = conditional_accessor_1d<const param_t>(running_mean);
auto running_var_a = conditional_accessor_1d<const param_t>(running_var);
/// Collect the linear and constant terms regarding the input.
/// output(n, c, h, w)
/// = (input(n, c, h, w) - mean(c)) / sqrt(var(c) + eps) * weight(c)
/// + bias(c)
/// = input(n, c, h, w) * inv_var(c) * weight(c)
/// - mean(c) * inv_var(c) * weight(c) + bias(c),
/// where inv_var(c) = 1 / sqrt(var(c) + eps).
/// So the linear term, alpha(c) = inv_var(c) * weight(c),
/// the constant term beta(c) = bias(c) - mean(c) * inv_var(c) * weight(c)
/// Note that this is only a good idea if (input_size >> c), in degenerate
/// cases where image_size == 1 && batch_size == 1, it is slow.
for (const auto c : c10::irange(n_channel)) {
opmath_t mean, invstd;
if (train) {
mean = save_mean_a[c];
invstd = save_invstd_a[c];
} else {
mean = running_mean_a[c];
invstd = 1 / std::sqrt(running_var_a[c] + static_cast<opmath_t>(eps));
}
param_t weight_v = weight_data ? weight_data[c] : param_t(1);
param_t bias_v = bias_data ? bias_data[c] : param_t(0);
alpha[c] = invstd * weight_v;
beta[c] = bias_v - mean * alpha[c];
}
}
/// A fast path for CPU inference and training forward when all tensors are contiguous.
template<typename scalar_t>
typename std::enable_if_t<std::is_same_v<scalar_t, at::opmath_type<scalar_t>>, void>
batch_norm_cpu_contiguous_impl(Tensor& output, const Tensor& input,
const Tensor& weight, const Tensor& bias, const Tensor& save_mean, const Tensor& save_invstd,
const Tensor& running_mean, const Tensor& running_var, bool train, double eps) {
using Vec = Vectorized<scalar_t>;
int64_t n_batch = input.size(0);
int64_t n_channel = input.size(1);
int64_t image_size = input.numel() / n_batch / n_channel;
Tensor alpha = at::empty({n_channel}, input.options());
Tensor beta = at::empty({n_channel}, input.options());
scalar_t* alpha_data = alpha.mutable_data_ptr<scalar_t>();
scalar_t* beta_data = beta.data_ptr<scalar_t>();
batch_norm_cpu_collect_linear_and_constant_terms<scalar_t, scalar_t>(
alpha_data, beta_data, n_channel, weight, bias,
save_mean, save_invstd, running_mean, running_var, train, eps);
scalar_t* output_data = output.data_ptr<scalar_t>();
const scalar_t* input_data = input.const_data_ptr<scalar_t>();
// Apply the linear terms to the input,
// output(n, c, h, w) = input(n, c, h, w) * alpha(c) + beta(c)
const int64_t loop_size = image_size - (image_size % Vec::size());
at::parallel_for(0, n_batch * n_channel, 1, [&](int64_t begin, int64_t end) {
int64_t n = 0;
int64_t c = 0;
data_index_init(begin, n, n_batch, c, n_channel);
for (const auto i : c10::irange(begin, end)) {
const Vec alpha_vec(alpha_data[c]);
const Vec beta_vec(beta_data[c]);
int64_t offset = i * image_size;
int64_t d = 0;
for (; d < loop_size; d += Vec::size()) {
Vec data_vec = Vec::loadu(input_data + offset + d);
Vec output_vec = data_vec * alpha_vec + beta_vec;
output_vec.store(output_data + offset + d);
}
if (image_size - d > 0) {
Vec data_vec = Vec::loadu(input_data + offset + d, image_size - d);
Vec output_vec = data_vec * alpha_vec + beta_vec;
output_vec.store(output_data + offset + d, image_size - d);
}
// move on to next index
data_index_step(n, n_batch, c, n_channel);
}
});
}
template <typename scalar_t>
typename std::enable_if_t<std::is_same_v<scalar_t, at::opmath_type<scalar_t>>, void>
batch_norm_cpu_channels_last_impl(Tensor& output, const Tensor& input,
const Tensor& weight, const Tensor& bias, const Tensor& save_mean, const Tensor& save_invstd,
const Tensor& running_mean, const Tensor& running_var, bool train, double eps) {
using Vec = Vectorized<scalar_t>;
int64_t n_batch = input.size(0);
int64_t n_channel = input.size(1);
int64_t image_size = input.numel() / n_batch / n_channel;
Tensor alpha = at::empty({n_channel}, input.options());
Tensor beta = at::empty({n_channel}, input.options());
scalar_t* alpha_data = alpha.mutable_data_ptr<scalar_t>();
scalar_t* beta_data = beta.data_ptr<scalar_t>();
batch_norm_cpu_collect_linear_and_constant_terms<scalar_t, scalar_t>(
alpha_data, beta_data, n_channel, weight, bias,
save_mean, save_invstd, running_mean, running_var, train, eps);
scalar_t* output_data = output.data_ptr<scalar_t>();
const scalar_t* input_data = input.const_data_ptr<scalar_t>();
// Apply the linear terms to the input,
// output(n, c, h, w) = input(n, c, h, w) * alpha(c) + beta(c)
const int64_t loop_size = n_channel - (n_channel % Vec::size());
at::parallel_for(0, n_batch * image_size, 1, [&](int64_t begin, int64_t end) {
for (const auto i : c10::irange(begin, end)) {
int64_t offset = i * n_channel;
int64_t d = 0;
// vectorize on channel dimension, for normal batch_norm input size,
// alpha/beta should fit in L1 cache, otherwise consider blocking.
for (; d < loop_size; d += Vec::size()) {
Vec alpha_vec = Vec::loadu(alpha_data + d);
Vec beta_vec = Vec::loadu(beta_data + d);
Vec data_vec = Vec::loadu(input_data + offset + d);
Vec output_vec = data_vec * alpha_vec + beta_vec;
output_vec.store(output_data + offset + d);
}
if (n_channel - d > 0) {
Vec alpha_vec = Vec::loadu(alpha_data + d, n_channel - d);
Vec beta_vec = Vec::loadu(beta_data + d, n_channel - d);
Vec data_vec = Vec::loadu(input_data + offset + d, n_channel - d);
Vec output_vec = data_vec * alpha_vec + beta_vec;
output_vec.store(output_data + offset + d, n_channel - d);
}
}
});
}
template <typename scalar_t>
typename std::enable_if_t<std::is_same_v<scalar_t, at::opmath_type<scalar_t>>, void>
batch_norm_cpu_collect_stats_contiguous_impl(
Tensor& mean, Tensor& var_sum, const Tensor& input) {
// keep acc_type as opmath_type will use float type when scalar_t==float
// while acc_type uses double for float.
using accscalar_t = at::acc_type<scalar_t, false>;
int64_t n_batch = input.size(0);
int64_t n_channel = input.size(1);
int64_t image_size = input.numel() / n_batch / n_channel;
int64_t N = input.numel() / n_channel;
const scalar_t* input_data = input.const_data_ptr<scalar_t>();
scalar_t* mean_data = mean.data_ptr<scalar_t>();
scalar_t* var_sum_data = var_sum.data_ptr<scalar_t>();
// parallel dim reduce on 'channel'
at::parallel_for(0, n_channel, 1, [&](int64_t begin, int64_t end) {
for (const auto c : c10::irange(begin, end)) {
// compute mean per input
accscalar_t sum = 0;
for (const auto n : c10::irange(n_batch)) {
for (const auto i : c10::irange(image_size)) {
auto offset = n * n_channel * image_size + c * image_size + i;
sum += input_data[offset];
}
}
scalar_t mean = sum / N;
mean_data[c] = mean;
// compute variance per input
accscalar_t _var_sum = 0;
for (const auto n : c10::irange(n_batch)) {
for (const auto i : c10::irange(image_size)) {
auto offset = n * n_channel * image_size + c * image_size + i;
auto x = input_data[offset];
_var_sum += (x - mean) * (x - mean);
}
}
var_sum_data[c] = _var_sum;
}
});
}
template <typename scalar_t>
typename std::enable_if_t<std::is_same_v<scalar_t, at::opmath_type<scalar_t>>, void>
batch_norm_cpu_collect_stats_channels_last_impl(
Tensor& mean, Tensor& var_sum, const Tensor& input) {
using Vec = Vectorized<scalar_t>;
// keep acc_type as opmath_type will use float type when scalar_t==float
// while acc_type uses double for float.
using accscalar_t = at::acc_type<scalar_t, false>;
int64_t n_channel = input.size(1);
int64_t N = input.numel() / n_channel;
const scalar_t* input_data = input.const_data_ptr<scalar_t>();
scalar_t* mean_data = mean.data_ptr<scalar_t>();
scalar_t* var_sum_data = var_sum.data_ptr<scalar_t>();
// Typical vertical reduce from shape of {NHW, C} to {C}.
// Apply two path parallel reduction when NHW > max_threads:
// First path: allocate an immediate buffer of size {max_threads, C}, parallel along dim0,
// {NHW, C} => {max_threads, C}
//
// Second path: parallel along dim1 of the immediate buffer,
// {max_threads, C} => {C}
//
// Normal size of C should fit in L1, otherwise consider blocking on C.
//
int num_threads = at::get_num_threads();
if (N > num_threads) {
Tensor buffer = at::zeros({num_threads, n_channel}, input.options());
scalar_t* buffer_data = buffer.data_ptr<scalar_t>();
// compute mean per input
at::parallel_for(0, N, 1, [&](int64_t begin, int64_t end) {
int tid = at::get_thread_num();
TORCH_CHECK(tid < num_threads,
"expect thread id smaller than ", num_threads, ", got thread id ", tid);
scalar_t* buffer_ptr = buffer_data + tid * n_channel;
for (const auto i : c10::irange(begin, end)) {
const scalar_t* x_ptr = input_data + i * n_channel;
vec::map2<scalar_t>(
[](Vec x, Vec y) { return x + y; },
buffer_ptr,
x_ptr,
buffer_ptr,
n_channel);
}
});
at::parallel_for(0, n_channel, 1, [&](int64_t begin, int64_t end) {
for (const auto c : c10::irange(begin, end)) {
accscalar_t sum = 0;
for (const auto t : c10::irange(num_threads)) {
sum += buffer_data[t * n_channel + c];
}
scalar_t mean = sum / N;
mean_data[c] = mean;
}
});
// compute variance per input, reuse the immediate buffer
buffer.zero_();
at::parallel_for(0, N, 1, [&](int64_t begin, int64_t end) {
int tid = at::get_thread_num();
TORCH_CHECK(tid < num_threads, "expect thread id smaller than ", num_threads, ", got thread id ", tid);
scalar_t* buffer_ptr = buffer_data + tid * n_channel;
for (const auto i : c10::irange(begin, end)) {
const scalar_t* x_ptr = input_data + i * n_channel;
vec::map3<scalar_t>(
[](Vec x, Vec y, Vec mean) { return y + (x - mean) * (x - mean); },
buffer_ptr,
x_ptr,
buffer_ptr,
mean_data,
n_channel);
}
});
at::parallel_for(0, n_channel, 1, [&](int64_t begin, int64_t end) {
for (const auto c : c10::irange(begin, end)) {
accscalar_t _var_sum = 0;
for (const auto t : c10::irange(num_threads)) {
_var_sum += buffer_data[t * n_channel + c];
}
var_sum_data[c] = _var_sum;
}
});
} else {
// Vertical reduce from shape of {NHW, C} to {C} when NHW <= max_threads.
// We'll use two methods, Method 1 and Method 2.
//
// Method 1: when TILE_SIZE < C <= THRESHOLD, parallel on C
// {NHW, C} => {C}
//
// Method 2: when C <= TILE_SIZE or C > THRESHOLD, tile and vectorize on C, C is tiled as:
// C: {TILE_SIZE, TILE_SIZE, ..., Remainder}
// parallel on tiles, vectorized vertical reduce on each tile
// {NHW, TILE_SIZE} => {TILE_SIZE}
//
// The optimal THRESHOLD to tile was found empirically.
// When C > THRESHOLD, C is large enough that the benefit from tiling and vectorization outweigh the synchronization overhead.
// Wehn C <= TILE_SIZE, the problem size is small enough (C <= TILE_SIZE && NHW <= max_threads) that it's better to launch single thread with vectorization than C threads without vectorization.
//
// When num_threads == 1, always use Method 2 as there is no synchronization overhead.
//
int64_t TILE_SIZE = 16;
int64_t THRESHOLD = 2048;
// Method 2: parallel on tiles of C, vectorized vertical reduce on each tile
if (num_threads == 1 || (n_channel <= TILE_SIZE || n_channel > THRESHOLD)) {
// compute mean per input
mean.zero_();
at::parallel_for(0, (n_channel + TILE_SIZE - 1) / TILE_SIZE, 1, [&](int64_t tile_idx_begin, int64_t tile_idx_end) {
for (int64_t tile_idx = tile_idx_begin; tile_idx < tile_idx_end; tile_idx++) {
int64_t jj_begin = tile_idx * TILE_SIZE;
int64_t jj_end = std::min(jj_begin + TILE_SIZE, n_channel);
scalar_t* mean_ptr = mean_data + jj_begin;
for (const auto i : c10::irange(N)) {
const scalar_t* x_ptr = input_data + (i * n_channel + jj_begin);
vec::map2<scalar_t>(
[](Vec x, Vec y) { return x + y; },
mean_ptr,
x_ptr,
mean_ptr,
jj_end - jj_begin);
}
vec::map<scalar_t>(
[N](Vec x) { return x / Vec(N); },
mean_ptr,
mean_ptr,
jj_end - jj_begin);
}
});
// compute variance per input
var_sum.zero_();
at::parallel_for(0, (n_channel + TILE_SIZE - 1) / TILE_SIZE, 1, [&](int64_t tile_idx_begin, int64_t tile_idx_end) {
for (int64_t tile_idx = tile_idx_begin; tile_idx < tile_idx_end; tile_idx++) {
int64_t jj_begin = tile_idx * TILE_SIZE;
int64_t jj_end = std::min(jj_begin + TILE_SIZE, n_channel);
scalar_t* var_sum_ptr = var_sum_data + jj_begin;
scalar_t* mean_ptr = mean_data + jj_begin;
for (const auto i : c10::irange(N)) {
const scalar_t* x_ptr = input_data + (i * n_channel + jj_begin);
vec::map3<scalar_t>(
[](Vec x, Vec y, Vec mean) { return y + (x - mean) * (x - mean); },
var_sum_ptr,
x_ptr,
var_sum_ptr,
mean_ptr,
jj_end - jj_begin);
}
}
});
}
// Method 1: parallel on C, vertical reduce
else {
// compute mean per input
at::parallel_for(0, n_channel, 1, [&](int64_t begin, int64_t end) {
for (const auto c : c10::irange(begin, end)) {
accscalar_t sum = 0;
for (const auto t : c10::irange(N)) {
sum += input_data[t * n_channel + c];
}
scalar_t mean = sum / N;
mean_data[c] = mean;
}
});
// compute variance per input
at::parallel_for(0, n_channel, 1, [&](int64_t begin, int64_t end) {
for (const auto c : c10::irange(begin, end)) {
accscalar_t _var_sum = 0;
for (const auto t : c10::irange(N)) {
_var_sum += (input_data[t * n_channel + c] - mean_data[c]) * (input_data[t * n_channel + c] - mean_data[c]);
}
var_sum_data[c] = _var_sum;
}
});
}
}
}
template <typename scalar_t>
typename std::enable_if_t<std::is_same_v<scalar_t, at::opmath_type<scalar_t>>, void>
batch_norm_cpu_backward_contiguous_impl(Tensor& grad_input, Tensor& grad_weight, Tensor& grad_bias,
const Tensor& grad_output, 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 eps) {
using Vec = Vectorized<scalar_t>;
// keep acc_type as opmath_type will use float type when scalar_t==float
// while acc_type uses double for float.
using accscalar_t = at::acc_type<scalar_t, false>;
int64_t n_batch = input.size(0);
int64_t n_channel = input.size(1);
int64_t image_size = input.numel() / n_batch / n_channel;
int64_t N = input.numel() / n_channel;
const scalar_t* grad_output_data = grad_output.const_data_ptr<scalar_t>();
const scalar_t* input_data = input.const_data_ptr<scalar_t>();
scalar_t* grad_input_data = grad_input.defined() ? grad_input.mutable_data_ptr<scalar_t>() : nullptr;
scalar_t* grad_weight_data = grad_weight.defined() ? grad_weight.data_ptr<scalar_t>() : nullptr;
scalar_t* grad_bias_data = grad_bias.defined() ? grad_bias.data_ptr<scalar_t>() : nullptr;
const bool grad_input_null = grad_input_data == nullptr;
const bool grad_weight_null = grad_weight_data == nullptr;
const bool grad_bias_null = grad_bias_data == nullptr;
auto weight_a = conditional_accessor_1d<const scalar_t>(weight);
auto save_mean_a = conditional_accessor_1d<const scalar_t>(save_mean);
auto save_invstd_a = conditional_accessor_1d<const scalar_t>(save_invstd);
auto running_mean_a = conditional_accessor_1d<const scalar_t>(running_mean);
auto running_var_a = conditional_accessor_1d<const scalar_t>(running_var);
// parallel dim reduce on 'channel'
at::parallel_for(0, n_channel, 1, [&](int64_t begin, int64_t end) {
for (const auto c : c10::irange(begin, end)) {
scalar_t w = weight.defined() ? weight_a[c] : 1;
scalar_t mean, invstd;
if (train) {
mean = save_mean_a[c];
invstd = save_invstd_a[c];
} else {
mean = running_mean_a[c];
invstd = 1 / std::sqrt(running_var_a[c] + eps);
}
// reduce over grad_output in feature plane
// compute 1) sum; 2) dot product of Q(X) and dY.
// fuse into a single loop to reuse dY
//
accscalar_t sum = 0;
accscalar_t dotp = 0;
for (const auto n : c10::irange(n_batch)) {
const scalar_t* x_ptr = input_data + n * n_channel * image_size + c * image_size;
const scalar_t* dy_ptr = grad_output_data + n * n_channel * image_size + c * image_size;
sum += vec::reduce_all<scalar_t>(
[](Vec& x, Vec& y) { return x + y; },
dy_ptr,
image_size);
dotp += vec::map2_reduce_all<scalar_t>(
[mean](Vec x, Vec dy) { return (x - Vec(mean)) * dy; },
[](Vec x, Vec y) { return x + y; },
x_ptr,
dy_ptr,
image_size);
}
if (!grad_input_null) {
if (train) {
scalar_t k = (scalar_t) dotp * invstd * invstd / N;
scalar_t grad_mean = sum / N;
for (const auto n : c10::irange(n_batch)) {
const scalar_t* x_ptr = input_data + n * n_channel * image_size + c * image_size;
scalar_t* dx_ptr = grad_input_data + n * n_channel * image_size + c * image_size;
const scalar_t* dy_ptr = grad_output_data + n * n_channel * image_size + c * image_size;
// Scalar math:
// for (const auto j : c10::irange(image_size)) {
// scalar_t dx = (x_ptr[j] - mean) * k;
// dx_ptr[j] = (dy_ptr[j] - grad_mean - dx) * invstd * w;
// }
vec::map2<scalar_t>(
[=](Vec x, Vec dy) {
Vec dx = (x - Vec(mean)) * Vec(k);
return (dy - Vec(grad_mean) - dx) * Vec(invstd) * Vec(w);
},
dx_ptr,
x_ptr,
dy_ptr,
image_size);
}
} else { // evaluation mode
for (const auto n : c10::irange(n_batch)) {
scalar_t* dx_ptr = grad_input_data + n * n_channel * image_size + c * image_size;
const scalar_t* dy_ptr = grad_output_data + n * n_channel * image_size + c * image_size;
// Scalar math:
// for (const auto j : c10::irange(image_size)) {
// dx_ptr[j] = dy_ptr[j] * invstd * w;
// }
vec::map<scalar_t>(
[=](Vec dy) { return dy * Vec(invstd) * Vec(w); },
dx_ptr,
dy_ptr,
image_size);
}
}
}
if (!grad_weight_null) {
grad_weight_data[c] = dotp * invstd;
}
if (!grad_bias_null) {
grad_bias_data[c] = sum;
}
}
});
}
template <typename scalar_t>
typename std::enable_if_t<std::is_same_v<scalar_t, at::opmath_type<scalar_t>>, void>
batch_norm_cpu_backward_channels_last_impl(Tensor& grad_input, Tensor& grad_weight, Tensor& grad_bias,
const Tensor& grad_output, 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 eps) {
using Vec = Vectorized<scalar_t>;
// keep acc_type as opmath_type will use float type when scalar_t==float
// while acc_type uses double for float.
using accscalar_t = at::acc_type<scalar_t, false>;
int64_t n_channel = input.size(1);
int64_t N = input.numel() / n_channel;
const scalar_t* grad_output_data = grad_output.const_data_ptr<scalar_t>();
const scalar_t* input_data = input.const_data_ptr<scalar_t>();
scalar_t* grad_input_data = grad_input.defined() ? grad_input.mutable_data_ptr<scalar_t>() : nullptr;
scalar_t* grad_weight_data = grad_weight.defined() ? grad_weight.data_ptr<scalar_t>() : nullptr;
scalar_t* grad_bias_data = grad_bias.defined() ? grad_bias.data_ptr<scalar_t>() : nullptr;
const scalar_t* save_mean_data = conditional_data_ptr<const scalar_t>(save_mean);
scalar_t* save_invstd_data = conditional_data_ptr<scalar_t>(save_invstd);
const scalar_t* running_mean_data = conditional_data_ptr<const scalar_t>(running_mean);
const scalar_t* running_var_data = conditional_data_ptr<const scalar_t>(running_var);
Tensor weight_ = weight.defined() ? weight : at::ones({n_channel}, input.options());
const scalar_t* weight_data = weight_.const_data_ptr<scalar_t>();
const scalar_t* mean_ptr = nullptr;
scalar_t* invstd_ptr = nullptr;
Tensor invstd = at::empty({0}, input.options());
if (train) {
mean_ptr = save_mean_data;
invstd_ptr = save_invstd_data;
} else {
mean_ptr = running_mean_data;
invstd.resize_({n_channel});
invstd_ptr = invstd.data_ptr<scalar_t>();
for (const auto c : c10::irange(n_channel)) {
invstd_ptr[c] = 1 / std::sqrt(running_var_data[c] + eps);
}
}
// Typical vertical reduce from shape of {NHW, C} to {C}.
// Apply two path parallel reduction:
// First path: allocate an immediate buffer of size {2, max_threads, C}, parallel along dim0,
// sum = buffer[0], dotp = buffer[2]
//
// Second path: parallel along dim1 of the immediate buffer.
//
int num_threads = at::get_num_threads();
Tensor buffer = at::zeros({2, num_threads, n_channel}, input.options());
scalar_t* sum_data = buffer.data_ptr<scalar_t>();
scalar_t* dotp_data = sum_data + num_threads * n_channel;
// compute sum and dotp per feature plain,
// fuse into a single loop to reuse grad_output in L1.
at::parallel_for(0, N, 1, [&](int64_t begin, int64_t end) {
int tid = at::get_thread_num();
TORCH_CHECK(tid < num_threads, "expect thread id smaller than ", num_threads, ", got thread id ", tid);
scalar_t* sum_ptr = sum_data + tid * n_channel;
scalar_t* dotp_ptr = dotp_data + tid * n_channel;
for (const auto i : c10::irange(begin, end)) {
const scalar_t* x_ptr = input_data + i * n_channel;
const scalar_t* dy_ptr = grad_output_data + i * n_channel;
vec::map2<scalar_t>(
[](Vec sum, Vec dy) { return sum + dy; },
sum_ptr,
sum_ptr,
dy_ptr,
n_channel);
vec::map4<scalar_t>(
[](Vec dotp, Vec x, Vec mean, Vec dy) { return dotp + (x - mean) * dy; },
dotp_ptr,
dotp_ptr,
x_ptr,
mean_ptr,
dy_ptr,
n_channel);
}
});
at::parallel_for(0, n_channel, 1, [&](int64_t begin, int64_t end) {
for (const auto c : c10::irange(begin, end)) {
// store the final result of sum and dotp in the 1st lane of immediate buffer,
// so that we won't need to allocate anther buffer to store the temp values.
accscalar_t _sum = 0;
for (const auto t : c10::irange(num_threads)) {
_sum += sum_data[t * n_channel + c];
}
sum_data[/* 0 * n_channel + */c] = _sum;
accscalar_t _dotp = 0;
for (const auto t : c10::irange(num_threads)) {
_dotp += dotp_data[t * n_channel + c];
}
dotp_data[/* 0 * n_channel + */c] = _dotp;
}
});
// compute grad_input
const int64_t loop_size = n_channel - (n_channel % Vec::size());
if (grad_input.defined()) {
at::parallel_for(0, N, 1, [&](int64_t begin, int64_t end) {
for (const auto i : c10::irange(begin, end)) {
scalar_t* dx_ptr = grad_input_data + i * n_channel;
const scalar_t* x_ptr = input_data + i * n_channel;
const scalar_t* dy_ptr = grad_output_data + i * n_channel;
if (train) {
int64_t d = 0;
for (; d < loop_size; d += Vec::size()) {
Vec x = Vec::loadu(x_ptr + d);
Vec mean = Vec::loadu(mean_ptr + d);
Vec dotp = Vec::loadu(dotp_data + d);
Vec invstd = Vec::loadu(invstd_ptr + d);
Vec k = dotp * invstd * invstd / Vec(N);
Vec dx = (x - mean) * k;
Vec dy = Vec::loadu(dy_ptr + d);
Vec grad_mean = Vec::loadu(sum_data + d) / Vec(N);
Vec w = Vec::loadu(weight_data + d);
dx = (dy - grad_mean - dx) * invstd * w;
dx.store(dx_ptr + d);
}
if (n_channel - d > 0) {
Vec x = Vec::loadu(x_ptr + d, n_channel - d);
Vec mean = Vec::loadu(mean_ptr + d, n_channel - d);
Vec dotp = Vec::loadu(dotp_data + d, n_channel - d);
Vec invstd = Vec::loadu(invstd_ptr + d, n_channel - d);
Vec k = dotp * invstd * invstd / Vec(N);
Vec dx = (x - mean) * k;
Vec dy = Vec::loadu(dy_ptr + d, n_channel - d);
Vec grad_mean = Vec::loadu(sum_data + d, n_channel - d) / Vec(N);
Vec w = Vec::loadu(weight_data + d, n_channel - d);
dx = (dy - grad_mean - dx) * invstd * w;
dx.store(dx_ptr + d, n_channel - d);
}
} else { // evaluation mode
int64_t d = 0;
for (; d < loop_size; d += Vec::size()) {
Vec dy = Vec::loadu(dy_ptr + d);
Vec invstd = Vec::loadu(invstd_ptr + d);
Vec w = Vec::loadu(weight_data + d);
Vec dx = dy * invstd * w;
dx.store(dx_ptr + d);
}
if (n_channel - d > 0) {
Vec dy = Vec::loadu(dy_ptr + d, n_channel - d);
Vec invstd = Vec::loadu(invstd_ptr + d, n_channel - d);
Vec w = Vec::loadu(weight_data + d, n_channel - d);
Vec dx = dy * invstd * w;
dx.store(dx_ptr + d, n_channel - d);
}
}
}
});
}
if (grad_weight.defined()) {
// grad_weight = dotp * invstd
vec::map2<scalar_t>(
[](Vec dotp, Vec invstd) { return dotp * invstd; },
grad_weight_data,
dotp_data,
invstd_ptr,
n_channel);
}
// grad_bias = sum
if (grad_bias.defined()) {
vec::map<scalar_t>(
[](Vec sum) { return sum; },
grad_bias_data,
sum_data,
n_channel);
}
}
/// bfloat16/Half kernels
template<typename scalar_t>
typename std::enable_if_t<!std::is_same_v<scalar_t, at::opmath_type<scalar_t>>, void>
batch_norm_cpu_contiguous_impl(Tensor& output, const Tensor& input,
const Tensor& weight, const Tensor& bias, const Tensor& save_mean, const Tensor& save_invstd,
const Tensor& running_mean, const Tensor& running_var, bool train, double eps) {
using opmath_t = at::opmath_type<scalar_t>;
using bVec = Vectorized<scalar_t>;
using fVec = Vectorized<opmath_t>;
int64_t n_batch = input.size(0);
int64_t n_channel = input.size(1);
int64_t image_size = input.numel() / n_batch / n_channel;
// use float as acc type
Tensor alpha = at::empty({n_channel}, input.options().dtype(kFloat));
Tensor beta = at::empty({n_channel}, input.options().dtype(kFloat));
opmath_t* alpha_data = alpha.mutable_data_ptr<opmath_t>();
opmath_t* beta_data = beta.data_ptr<opmath_t>();
const bool mixed_type = is_mixed_type(input, weight, bias, save_mean, save_invstd, running_mean, running_var);
if (mixed_type) {
batch_norm_cpu_collect_linear_and_constant_terms<opmath_t, opmath_t>(
alpha_data, beta_data, n_channel, weight, bias,
save_mean, save_invstd, running_mean, running_var, train, eps);
} else {
batch_norm_cpu_collect_linear_and_constant_terms<scalar_t, opmath_t>(
alpha_data, beta_data, n_channel, weight, bias,
save_mean, save_invstd, running_mean, running_var, train, eps);
}
scalar_t* output_data = output.data_ptr<scalar_t>();
const scalar_t* input_data = input.const_data_ptr<scalar_t>();
const int64_t loop_size = image_size - (image_size % bVec::size());
at::parallel_for(0, n_batch * n_channel, 1, [&](int64_t begin, int64_t end) {
int64_t n = 0;
int64_t c = 0;
data_index_init(begin, n, n_batch, c, n_channel);
for (const auto i : c10::irange(begin, end)) {
const scalar_t* input_ptr = input_data + i * image_size;
scalar_t* output_ptr = output_data + i * image_size;
const opmath_t alpha_val = alpha_data[c];
const opmath_t beta_val = beta_data[c];
const fVec alpha_fvec(alpha_val);
const fVec beta_fvec(beta_val);
int64_t d = 0;
for (; d < loop_size; d += bVec::size()) {
bVec data_bvec = bVec::loadu(input_ptr + d);
auto [data_fvec0, data_fvec1] = convert_to_float<scalar_t>(data_bvec);
fVec out_fvec0 = data_fvec0 * alpha_fvec + beta_fvec;
fVec out_fvec1 = data_fvec1 * alpha_fvec + beta_fvec;
bVec out_bvec = convert_from_float<scalar_t>(out_fvec0, out_fvec1);
out_bvec.store(output_ptr + d);
}
for (; d < image_size; d++) {
output_ptr[d] = scalar_t(opmath_t(input_ptr[d]) * alpha_val + beta_val);
}
// move on to next index
data_index_step(n, n_batch, c, n_channel);
}
});
}
template <typename scalar_t>
typename std::enable_if_t<!std::is_same_v<scalar_t, at::opmath_type<scalar_t>>, void>
batch_norm_cpu_channels_last_impl(Tensor& output, const Tensor& input,
const Tensor& weight, const Tensor& bias, const Tensor& save_mean, const Tensor& save_invstd,
const Tensor& running_mean, const Tensor& running_var, bool train, double eps) {
using opmath_t = at::opmath_type<scalar_t>;
using bVec = Vectorized<scalar_t>;
using fVec = Vectorized<opmath_t>;
int64_t n_batch = input.size(0);
int64_t n_channel = input.size(1);
int64_t image_size = input.numel() / n_batch / n_channel;
Tensor alpha = at::empty({n_channel}, input.options().dtype(kFloat));
Tensor beta = at::empty({n_channel}, input.options().dtype(kFloat));
opmath_t* alpha_data = alpha.mutable_data_ptr<opmath_t>();
opmath_t* beta_data = beta.data_ptr<opmath_t>();
const bool mixed_type = is_mixed_type(input, weight, bias, save_mean, save_invstd, running_mean, running_var);
if (mixed_type) {
batch_norm_cpu_collect_linear_and_constant_terms<opmath_t, opmath_t>(
alpha_data, beta_data, n_channel, weight, bias,
save_mean, save_invstd, running_mean, running_var, train, eps);
} else {
batch_norm_cpu_collect_linear_and_constant_terms<scalar_t, opmath_t>(
alpha_data, beta_data, n_channel, weight, bias,
save_mean, save_invstd, running_mean, running_var, train, eps);
}
scalar_t* output_data = output.data_ptr<scalar_t>();
const scalar_t* input_data = input.const_data_ptr<scalar_t>();
const int64_t loop_size = n_channel - (n_channel % bVec::size());
at::parallel_for(0, n_batch * image_size, 1, [&](int64_t begin, int64_t end) {
for (const auto i : c10::irange(begin, end)) {
const scalar_t* input_ptr = input_data + i * n_channel;
scalar_t* output_ptr = output_data + i * n_channel;
int64_t d = 0;
for (; d < loop_size; d += bVec::size()) {
fVec alpha_fvec0 = fVec::loadu(alpha_data + d);
fVec alpha_fvec1 = fVec::loadu(alpha_data + d + fVec::size());
fVec beta_fvec0 = fVec::loadu(beta_data + d);
fVec beta_fvec1 = fVec::loadu(beta_data + d + fVec::size());
bVec data_bvec = bVec::loadu(input_ptr + d);
auto [data_fvec0, data_fvec1] = convert_to_float<scalar_t>(data_bvec);
fVec out_fvec0 = data_fvec0 * alpha_fvec0 + beta_fvec0;
fVec out_fvec1 = data_fvec1 * alpha_fvec1 + beta_fvec1;
bVec out_bvec = convert_from_float<scalar_t>(out_fvec0, out_fvec1);
out_bvec.store(output_ptr + d);
}
for (; d < n_channel; d++) {
output_ptr[d] = scalar_t(opmath_t(input_ptr[d]) * alpha_data[d] + beta_data[d]);
}
}
});
}
template <typename scalar_t, typename param_t>
inline void batch_norm_cpu_collect_stats_contiguous_internal(
Tensor& mean, Tensor& var_sum, const Tensor& input) {
using opmath_t = at::opmath_type<scalar_t>;
using bVec = Vectorized<scalar_t>;
using fVec = Vectorized<opmath_t>;
int64_t n_batch = input.size(0);
int64_t n_channel = input.size(1);
int64_t image_size = input.numel() / n_batch / n_channel;
int64_t N = input.numel() / n_channel;
const scalar_t* input_data = input.const_data_ptr<scalar_t>();
param_t* mean_data = mean.data_ptr<param_t>();
param_t* var_sum_data = var_sum.data_ptr<param_t>();
at::parallel_for(0, n_channel, 1, [&](int64_t begin, int64_t end) {
for (const auto c : c10::irange(begin, end)) {
opmath_t sum_val = opmath_t(0);
fVec sum_fvec = fVec(opmath_t(0));
for (int64_t n = 0; n < n_batch; n++) {
const scalar_t* input_ptr = input_data + n * n_channel * image_size + c * image_size;
int64_t d = 0;
for (; d < image_size - (image_size % bVec::size()); d += bVec::size()) {
bVec data_bvec = bVec::loadu(input_ptr + d);
auto [data_fvec0, data_fvec1] = convert_to_float<scalar_t>(data_bvec);
sum_fvec += data_fvec0;
sum_fvec += data_fvec1;
}
for (; d < image_size; d++) {
sum_val += opmath_t(input_ptr[d]);
}
}
// TODO: use fast version
sum_val += vec_reduce_all([](fVec& x, fVec& y) { return x + y; }, sum_fvec, fVec::size());
opmath_t mean_val = sum_val / N;
mean_data[c] = param_t(mean_val);
opmath_t var_val = opmath_t(0);
fVec var_fvec = fVec(opmath_t(0));
fVec mean_fvec = fVec(mean_val);
for (int64_t n = 0; n < n_batch; n++) {
const scalar_t* input_ptr = input_data + n * n_channel * image_size + c * image_size;
int64_t d = 0;
for (; d < image_size - (image_size % bVec::size()); d += bVec::size()) {
bVec data_bvec = bVec::loadu(input_ptr + d);
auto [data_fvec0, data_fvec1] = convert_to_float<scalar_t>(data_bvec);
var_fvec += (data_fvec0 - mean_fvec) * (data_fvec0 - mean_fvec);
var_fvec += (data_fvec1 - mean_fvec) * (data_fvec1 - mean_fvec);
}
for (; d < image_size; d++) {
opmath_t data_val = input_ptr[d];
var_val += (data_val - mean_val) * (data_val - mean_val);
}
}
// TODO: use fast version
var_val += vec_reduce_all([](fVec& x, fVec& y) { return x + y; }, var_fvec, fVec::size());
var_sum_data[c] = param_t(var_val);
}
});
}
template <typename scalar_t>
typename std::enable_if_t<!std::is_same_v<scalar_t, at::opmath_type<scalar_t>>, void>
batch_norm_cpu_collect_stats_contiguous_impl(
Tensor& mean, Tensor& var_sum, const Tensor& input) {
const bool mixed_type = is_mixed_type(input, mean, var_sum);
if (mixed_type) {
batch_norm_cpu_collect_stats_contiguous_internal<scalar_t, at::opmath_type<scalar_t>>(mean, var_sum, input);
} else {
batch_norm_cpu_collect_stats_contiguous_internal<scalar_t, scalar_t>(mean, var_sum, input);
}
}
template <typename scalar_t, typename param_t>
inline void batch_norm_cpu_collect_stats_channels_last_internal(
Tensor& mean, Tensor& var_sum, const Tensor& input) {
using opmath_t = at::opmath_type<scalar_t>;
using bVec = Vectorized<scalar_t>;
using fVec = Vectorized<opmath_t>;
int64_t n_channel = input.size(1);
int64_t N = input.numel() / n_channel;
const scalar_t* input_data = input.const_data_ptr<scalar_t>();
param_t* mean_data = mean.data_ptr<param_t>();
param_t* var_sum_data = var_sum.data_ptr<param_t>();
int num_threads = at::get_num_threads();
Tensor buffer = at::zeros({num_threads, n_channel}, input.options().dtype(kFloat));
opmath_t* buffer_data = buffer.data_ptr<opmath_t>();
at::parallel_for(0, N, 1, [&](int64_t begin, int64_t end) {
int tid = at::get_thread_num();
TORCH_CHECK(tid < num_threads, "expect thread id smaller than ", num_threads, ", got thread id ", tid);
opmath_t* buffer_ptr = buffer_data + tid * n_channel;
for (const auto i : c10::irange(begin, end)) {
const scalar_t* input_ptr = input_data + i * n_channel;
int64_t d = 0;
for (; d < n_channel - (n_channel % bVec::size()); d += bVec::size()) {
bVec data_bvec = bVec::loadu(input_ptr + d);
auto [data_fvec0, data_fvec1] = convert_to_float<scalar_t>(data_bvec);
fVec sum_fvec0 = fVec::loadu(buffer_ptr + d) + data_fvec0;
fVec sum_fvec1 = fVec::loadu(buffer_ptr + d + fVec::size()) + data_fvec1;
sum_fvec0.store(buffer_ptr + d);
sum_fvec1.store(buffer_ptr + d + fVec::size());
}
for (; d < n_channel; d++) {
buffer_ptr[d] += input_ptr[d];
}
}
});
for (const auto c : c10::irange(n_channel)) {
opmath_t sum = 0;
for (const auto t : c10::irange(num_threads)) {
sum += buffer_data[t * n_channel + c];
}
mean_data[c] = param_t(sum / N);
}
buffer.zero_();
at::parallel_for(0, N, 1, [&](int64_t begin, int64_t end) {
int tid = at::get_thread_num();
TORCH_CHECK(tid < num_threads, "expect thread id smaller than ", num_threads, ", got thread id ", tid);
opmath_t* buffer_ptr = buffer_data + tid * n_channel;
for (const auto i : c10::irange(begin, end)) {
const scalar_t* input_ptr = input_data + i * n_channel;
int64_t d = 0;
for (; d < n_channel - (n_channel % bVec::size()); d += bVec::size()) {
bVec data_bvec = bVec::loadu(input_ptr + d);
auto [data_fvec0, data_fvec1] = convert_to_float<scalar_t>(data_bvec);
auto [mean_fvec0, mean_fvec1] = load2f(mean_data + d);
fVec var_fvec0 = fVec::loadu(buffer_ptr + d);
fVec var_fvec1 = fVec::loadu(buffer_ptr + d + fVec::size());
var_fvec0 += (data_fvec0 - mean_fvec0) * (data_fvec0 - mean_fvec0);
var_fvec1 += (data_fvec1 - mean_fvec1) * (data_fvec1 - mean_fvec1);
var_fvec0.store(buffer_ptr + d);
var_fvec1.store(buffer_ptr + d + fVec::size());
}
for (; d < n_channel; d++) {
opmath_t data_val = opmath_t(input_ptr[d]);
opmath_t mean_val = opmath_t(mean_data[d]);
buffer_ptr[d] += (data_val - mean_val) * (data_val - mean_val);
}
}
});
for (const auto c : c10::irange(n_channel)) {
opmath_t _var_sum = 0;
for (const auto t : c10::irange(num_threads)) {
_var_sum += buffer_data[t * n_channel + c];
}
var_sum_data[c] = param_t(_var_sum);
}
}
template <typename scalar_t>
typename std::enable_if_t<!std::is_same_v<scalar_t, at::opmath_type<scalar_t>>, void>
batch_norm_cpu_collect_stats_channels_last_impl(
Tensor& mean, Tensor& var_sum, const Tensor& input) {
const bool mixed_type = is_mixed_type(input, mean, var_sum);
if (mixed_type) {
batch_norm_cpu_collect_stats_channels_last_internal<scalar_t, at::opmath_type<scalar_t>>(mean, var_sum, input);
} else {
batch_norm_cpu_collect_stats_channels_last_internal<scalar_t, scalar_t>(mean, var_sum, input);
}
}
template <typename scalar_t, typename param_t>
void batch_norm_cpu_backward_contiguous_internal(Tensor& grad_input, Tensor& grad_weight, Tensor& grad_bias,
const Tensor& grad_output, 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 eps) {