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group_norm_kernel.cpp
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#define TORCH_ASSERT_ONLY_METHOD_OPERATORS
#include <ATen/native/group_norm.h>
#include <algorithm>
#include <array>
#include <numeric>
#include <ATen/core/Tensor.h>
#include <ATen/Dispatch.h>
#include <ATen/cpu/vec/vec.h>
#include <ATen/cpu/vec/functional.h>
#include <ATen/native/cpu/utils.h>
#include <ATen/native/cpu/moments_utils.h>
#include <ATen/native/cpu/mixed_data_type.h>
#include <ATen/OpMathType.h>
#include <c10/util/irange.h>
#ifndef AT_PER_OPERATOR_HEADERS
#include <ATen/Functions.h>
#else
#include <ATen/ops/empty.h>
#endif
namespace at::native {
namespace {
template <typename T, typename PT>
void GroupNormKernelImplInternal(
const Tensor& X,
const Tensor& gamma,
const Tensor& beta,
int64_t N,
int64_t C,
int64_t HxW,
int64_t group,
double eps,
Tensor& Y,
Tensor& mean,
Tensor& rstd) {
TORCH_CHECK(X.numel() == N * C * HxW);
TORCH_CHECK(!gamma.defined() || gamma.numel() == C);
TORCH_CHECK(!beta.defined() || beta.numel() == C);
const int64_t G = group;
const int64_t D = C / G;
const T* X_data = X.data_ptr<T>();
const PT* gamma_data = gamma.defined() ? gamma.data_ptr<PT>() : nullptr;
const PT* beta_data = beta.defined() ? beta.data_ptr<PT>() : nullptr;
T* Y_data = Y.data_ptr<T>();
PT* mean_data = mean.data_ptr<PT>();
PT* rstd_data = rstd.data_ptr<PT>();
const bool gamma_null = (gamma_data == nullptr);
const bool beta_null = beta_data == nullptr;
const int64_t inner_size = D * HxW;
using T_ACC = at::opmath_type<T>;
at::parallel_for(0, N * G, 1, [&](int64_t start, int64_t end) {
for (const auto i : c10::irange(start, end)) {
const T* X_ptr = X_data + i * inner_size;
T_ACC mean_val;
T_ACC rstd_val;
std::tie(mean_val, rstd_val) = RowwiseMoments(X_ptr, inner_size);
rstd_val = T_ACC(1) / std::sqrt(std::max(rstd_val, T_ACC(0)) + eps);
if (gamma_null && beta_null) {
T* Y_ptr = Y_data + i * inner_size;
for (const auto j : c10::irange(inner_size)) {
Y_ptr[j] = (X_ptr[j] - mean_val) * rstd_val;
}
} else {
const int64_t g = i % G;
for (const auto j : c10::irange(D)) {
const int64_t c = g * D + j;
const T_ACC scale = rstd_val * (gamma_null ? T_ACC(1) : T_ACC(gamma_data[c]));
const T_ACC bias = -scale * mean_val + (beta_null ? T_ACC(0) : T_ACC(beta_data[c]));
X_ptr = X_data + (i * D + j) * HxW;
T* Y_ptr = Y_data + (i * D + j) * HxW;
for (const auto k : c10::irange(HxW)) {
Y_ptr[k] = scale * X_ptr[k] + bias;
}
}
}
mean_data[i] = mean_val;
rstd_data[i] = rstd_val;
}
});
}
template <typename T>
std::tuple<T, T> ColumnwiseMoments(
const T* X_data,
int64_t HxW,
int64_t C,
int64_t D) {
using Vec = vec::Vectorized<T>;
constexpr int64_t K = Vec::size();
const int64_t inner_size = D / K * K;
Vec acc0_vec{0}, acc1_vec{0};
for (const auto m : c10::irange(HxW)) {
const T* X_ptr = X_data + m * C;
int64_t d = 0;
for (; d < inner_size; d += K) {
Vec x_vec = Vec::loadu(X_ptr + d);
acc0_vec += x_vec;
acc1_vec += x_vec * x_vec;
}
if (D - d > 0) {
Vec x_vec = Vec::loadu(X_ptr + d, D - d);
acc0_vec += x_vec;
acc1_vec += x_vec * x_vec;
}
}
T mean_val = vec::vec_reduce_all([](Vec& x, Vec& y) { return x + y; }, acc0_vec);
T rstd_val = vec::vec_reduce_all([](Vec& x, Vec& y) { return x + y; }, acc1_vec);
return std::tuple<T, T>(mean_val, rstd_val);
}
template <typename T = BFloat16>
std::tuple<float, float> ColumnwiseMoments(
const BFloat16* X_data,
int64_t HxW,
int64_t C,
int64_t D) {
using bVec = vec::Vectorized<BFloat16>;
using fVec = vec::Vectorized<float>;
constexpr int64_t K = bVec::size();
const int64_t inner_size = D / K * K;
fVec acc0_fvec{0}, acc1_fvec{0}, zero{0};
for (const auto m : c10::irange(HxW)) {
const BFloat16* X_ptr = X_data + m * C;
int64_t d = 0;
for (; d < inner_size; d += K) {
bVec x_bvec = bVec::loadu(X_ptr + d);
fVec x_fvec0, x_fvec1;
std::tie(x_fvec0, x_fvec1) = convert_bfloat16_float(x_bvec);
acc0_fvec += x_fvec0 + x_fvec1;
acc1_fvec += x_fvec0 * x_fvec0 + x_fvec1 * x_fvec1;
}
if (D - d > 0) {
bVec x_bvec = bVec::loadu(X_ptr + d, D - d);
fVec x_fvec0, x_fvec1;
std::tie(x_fvec0, x_fvec1) = convert_bfloat16_float(x_bvec);
if (D - d > fVec::size()) {
x_fvec1 = fVec::set(zero, x_fvec1, D - d - fVec::size());
acc0_fvec += x_fvec0 + x_fvec1;
acc1_fvec += x_fvec0 * x_fvec0 + x_fvec1 * x_fvec1;
} else {
x_fvec0 = fVec::set(zero, x_fvec0, D - d);
acc0_fvec += x_fvec0;
acc1_fvec += x_fvec0 * x_fvec0;
}
}
}
float mean_val = vec::vec_reduce_all([](fVec& x, fVec& y) { return x + y; }, acc0_fvec);
float rstd_val = vec::vec_reduce_all([](fVec& x, fVec& y) { return x + y; }, acc1_fvec);
return std::tuple<float, float>(mean_val, rstd_val);
}
template <typename scalar_t, typename param_t>
inline void CalcMeanVar(
const scalar_t* X_ptr,
param_t* mean_ptr,
param_t* rstd_ptr,
int64_t C) {
using Vec = vec::Vectorized<scalar_t>;
vec::map2<scalar_t>(
[](Vec x, Vec y) { return x + y; },
mean_ptr,
X_ptr,
mean_ptr,
C);
vec::map2<scalar_t>(
[](Vec x, Vec y) { return x * x + y; },
rstd_ptr,
X_ptr,
rstd_ptr,
C);
}
template <>
inline void CalcMeanVar(
const BFloat16* X_ptr,
float* mean_ptr,
float* rstd_ptr,
int64_t C) {
using fVec = vec::Vectorized<float>;
using bVec = vec::Vectorized<BFloat16>;
int64_t d = 0;
for (; d < C - (C % bVec::size()); d += bVec::size()) {
bVec data_bvec = bVec::loadu(X_ptr + d);
fVec mean_fvec0 = fVec::loadu(mean_ptr + d);
fVec mean_fvec1 = fVec::loadu(mean_ptr + d + fVec::size());
fVec rstd_fvec0 = fVec::loadu(rstd_ptr + d);
fVec rstd_fvec1 = fVec::loadu(rstd_ptr + d + fVec::size());
fVec data_fvec0, data_fvec1;
std::tie(data_fvec0, data_fvec1) = convert_bfloat16_float(data_bvec);
mean_fvec0 = data_fvec0 + mean_fvec0;
mean_fvec1 = data_fvec1 + mean_fvec1;
rstd_fvec0 = data_fvec0 * data_fvec0 + rstd_fvec0;
rstd_fvec1 = data_fvec1 * data_fvec1 + rstd_fvec1;
mean_fvec0.store(mean_ptr + d);
mean_fvec1.store(mean_ptr + d + fVec::size());
rstd_fvec0.store(rstd_ptr + d);
rstd_fvec1.store(rstd_ptr + d + fVec::size());
}
if (C - d > 0) {
bVec data_bvec = bVec::loadu(X_ptr + d, C - d);
fVec mean_fvec0 = fVec::loadu(mean_ptr + d, (C - d) > fVec::size() ? fVec::size() : (C - d));
fVec mean_fvec1 = fVec::loadu(mean_ptr + d + fVec::size(), (C - d) > fVec::size() ? (C - d - fVec::size()) : 0);
fVec rstd_fvec0 = fVec::loadu(rstd_ptr + d, (C - d) > fVec::size() ? fVec::size() : (C - d));
fVec rstd_fvec1 = fVec::loadu(rstd_ptr + d + fVec::size(), (C - d) > fVec::size() ? (C - d - fVec::size()) : 0);
fVec data_fvec0, data_fvec1;
std::tie(data_fvec0, data_fvec1) = convert_bfloat16_float(data_bvec);
mean_fvec0 = data_fvec0 + mean_fvec0;
mean_fvec1 = data_fvec1 + mean_fvec1;
rstd_fvec0 = data_fvec0 * data_fvec0 + rstd_fvec0;
rstd_fvec1 = data_fvec1 * data_fvec1 + rstd_fvec1;
mean_fvec0.store(mean_ptr + d, (C - d) > fVec::size() ? fVec::size() : (C - d));
mean_fvec1.store(mean_ptr + d + fVec::size(), (C - d) > fVec::size() ? (C - d - fVec::size()) : 0);
rstd_fvec0.store(rstd_ptr + d, (C - d) > fVec::size() ? fVec::size() : (C - d));
rstd_fvec1.store(rstd_ptr + d + fVec::size(), (C - d) > fVec::size() ? (C - d - fVec::size()) : 0);
}
}
template <typename scalar_t, typename param_t>
inline void ApplyScaleBias(
scalar_t* Y_ptr,
const scalar_t* X_ptr,
const param_t* scale_ptr,
const param_t* bias_ptr,
int64_t C) {
using Vec = vec::Vectorized<scalar_t>;
vec::map3<scalar_t>(
[](Vec x, Vec scale, Vec bias) { return x * scale + bias; },
Y_ptr,
X_ptr,
scale_ptr,
bias_ptr,
C);
}
template <>
inline void ApplyScaleBias(
BFloat16* Y_ptr,
const BFloat16* X_ptr,
const float* scale_ptr,
const float* bias_ptr,
int64_t C) {
using fVec = vec::Vectorized<float>;
using bVec = vec::Vectorized<BFloat16>;
int64_t d = 0;
for (; d < C - (C % bVec::size()); d += bVec::size()) {
bVec data_bvec = bVec::loadu(X_ptr + d);
fVec scale_fvec0 = fVec::loadu(scale_ptr + d);
fVec scale_fvec1 = fVec::loadu(scale_ptr + d + fVec::size());
fVec bias_fvec0 = fVec::loadu(bias_ptr + d);
fVec bias_fvec1 = fVec::loadu(bias_ptr + d + fVec::size());
fVec data_fvec0, data_fvec1, out0, out1;
std::tie(data_fvec0, data_fvec1) = convert_bfloat16_float(data_bvec);
out0 = data_fvec0 * scale_fvec0 + bias_fvec0;
out1 = data_fvec1 * scale_fvec1 + bias_fvec1;
convert_float_bfloat16(out0, out1).store(Y_ptr + d);
}
if (C - d > 0) {
bVec data_bvec = bVec::loadu(X_ptr + d, C - d);
fVec scale_fvec0 = fVec::loadu(scale_ptr + d, (C - d) > fVec::size() ? fVec::size() : (C - d));
fVec scale_fvec1 = fVec::loadu(scale_ptr + d + fVec::size(), (C - d) > fVec::size() ? (C - d - fVec::size()) : 0);
fVec bias_fvec0 = fVec::loadu(bias_ptr + d, (C - d) > fVec::size() ? fVec::size() : (C - d));
fVec bias_fvec1 = fVec::loadu(bias_ptr + d + fVec::size(), (C - d) > fVec::size() ? (C - d - fVec::size()) : 0);
fVec data_fvec0, data_fvec1, out0, out1;
std::tie(data_fvec0, data_fvec1) = convert_bfloat16_float(data_bvec);
out0 = data_fvec0 * scale_fvec0 + bias_fvec0;
out1 = data_fvec1 * scale_fvec1 + bias_fvec1;
convert_float_bfloat16(out0, out1).store(Y_ptr + d, C - d);
}
}
template <typename T, typename PT>
void GroupNormKernelImplChannelsLastInternal(
const Tensor& X,
const Tensor& gamma,
const Tensor& beta,
int64_t N,
int64_t C,
int64_t HxW,
int64_t group,
double eps,
Tensor& Y,
Tensor& mean,
Tensor& rstd) {
TORCH_CHECK(X.numel() == N * C * HxW);
TORCH_CHECK(!gamma.defined() || gamma.numel() == C);
TORCH_CHECK(!beta.defined() || beta.numel() == C);
const int64_t G = group;
const int64_t D = C / G;
const T* X_data = X.data_ptr<T>();
const PT* gamma_data = gamma.defined() ? gamma.data_ptr<PT>() : nullptr;
const PT* beta_data = beta.defined() ? beta.data_ptr<PT>() : nullptr;
T* Y_data = Y.data_ptr<T>();
PT* mean_data = mean.data_ptr<PT>();
PT* rstd_data = rstd.data_ptr<PT>();
using T_ACC = at::opmath_type<T>;
const T_ACC s = T_ACC(1) / static_cast<T_ACC>(D * HxW);
const bool gamma_null = (gamma_data == nullptr);
const bool beta_null = beta_data == nullptr;
// NB: About algorithm choosen:
//
// On channels last, GroupNorm has a input shape of {N, H, W, GD},
// Mean and rstd are collected per each n and g, which involves reduction
// on non-adjacent dimensions. We can parallel in the following 2 impls:
//
// impl-1: parallel on N * G. Only need one omp session but memory access
// per thread is non-contiguous.
//
// impl-2: parallel on N * HxW. Memory access per thread is contiguous,
// but requires help of extra temp buffer of size {T, N, 2C}.
//
// Generally impl-2 has better performance when HxW is large enough, so that
// data per thread {NHWC / T} is much larger then temp buffer per thread {2NC}
//
constexpr int64_t feature_map_threshold = 1024;
if (HxW < feature_map_threshold) {
// impl-1: parallel on N * G.
//
// for each plain of HxW, scale and bias is calculated only once
Tensor buffer = at::empty({N * G, 2 * D}, X.options().dtype(c10::CppTypeToScalarType<T_ACC>::value));
T_ACC* buffer_data = buffer.mutable_data_ptr<T_ACC>();
at::parallel_for(0, N * G, 1, [&](int64_t begin, int64_t end) {
int64_t n{0}, g{0};
data_index_init(begin, n, N, g, G);
for (const auto i : c10::irange(begin, end)) {
// step-1: for each n and g, collect sum of x and x2
//
// Note that using vec::map_reduce_all here is simpler to write
// but it is slower since horizontal reduce from vec to scalar is slow.
// So it is better to reduce with a vec across all HxW plain,
// and do a horizontal add just once for each {n, g}.
//
T_ACC mean_val, rstd_val;
std::tie(mean_val, rstd_val) = ColumnwiseMoments(
X_data + n * HxW * C + g * D,
HxW,
C,
D);
mean_val *= s;
rstd_val = std::max(rstd_val * s - mean_val * mean_val, T_ACC(0));
rstd_val = T_ACC(1) / std::sqrt(rstd_val + eps);
mean_data[i] = mean_val;
rstd_data[i] = rstd_val;
// step-2: calculate scale and bias
T_ACC* scale_ptr = buffer_data + i * 2 * D;
T_ACC* bias_ptr = scale_ptr + D;
for (const auto d : c10::irange(D)) {
const int64_t c = g * D + d;
scale_ptr[d] = rstd_val * (gamma_null ? T_ACC(1) : T_ACC(gamma_data[c]));
bias_ptr[d] = -scale_ptr[d] * mean_val + (beta_null ? T_ACC(0) : T_ACC(beta_data[c]));
}
// step-3: apply scale and bias
for (const auto m : c10::irange(HxW)) {
const T* X_ptr = X_data + n * HxW * C + m * C + g * D;
T* Y_ptr = Y_data + n * HxW * C + m * C + g * D;
ApplyScaleBias<T, T_ACC>(Y_ptr, X_ptr, scale_ptr, bias_ptr, D);
}
data_index_step(n, N, g, G);
}
});
} else {
// impl-2: parallel on N * HxW.
//
// temp buffer holding x and x2
int num_threads = at::get_num_threads();
Tensor buffer = at::empty({num_threads, N, 2 * C},
X.options().dtype(c10::CppTypeToScalarType<T_ACC>::value)).zero_();
T_ACC* buffer_data = buffer.data_ptr<T_ACC>();
Tensor tmp_buffer = at::empty({N, 2 * G},
X.options().dtype(c10::CppTypeToScalarType<T_ACC>::value));
T_ACC* tmp_buffer_data = tmp_buffer.data_ptr<T_ACC>();
// step-1: accumulate on dimension of C
//
// In order to improve multi-core performance when N=1,
// we parallel on the all the outer dimensions of N and HxW,
// leaving the most inner dimension C for vectorization.
//
// Note that parallel on {N, HxW, G} is not feasible for some common configs,
// e.g. say input shape is {1, 32, h, w} and G = 8,
// this will give D = 4 which is unable to take full SIMD length.
//
// To avoid thread conflict, we make use of a temp buffer of {T, N, 2C},
// firstly, reduce from {N, HxW, C} to {T, N, 2C}
//
at::parallel_for(0, N * HxW, 1, [&](int64_t begin, int64_t end) {
int tid = at::get_thread_num();
T_ACC* buffer_ptr = buffer_data + tid * N * 2 * C;
int64_t n{0}, m{0};
data_index_init(begin, n, N, m, HxW);
for (const auto i : c10::irange(begin, end)) {
T_ACC* mean_ptr = buffer_ptr + n * 2 * C;
T_ACC* rstd_ptr = mean_ptr + C;
const T* X_ptr = X_data + i * C;
CalcMeanVar<T, T_ACC>(X_ptr, mean_ptr, rstd_ptr, C);
data_index_step(n, N, m, HxW);
}
});
// step-2: compute mean and rstd
for (const auto n : c10::irange(N)) {
for (const auto g : c10::irange(G)) {
T_ACC mean_val{0}, rstd_val{0};
for (const auto d : c10::irange(D)) {
for (const auto t : c10::irange(num_threads)) {
T_ACC* buffer_ptr = buffer_data + t * N * 2 * C + n * 2 * C;
mean_val += buffer_ptr[g * D + d];
rstd_val += buffer_ptr[g * D + d + C];
}
}
mean_val *= s;
rstd_val = std::max(rstd_val * s - mean_val * mean_val, T_ACC(0));
rstd_val = T_ACC(1) / std::sqrt(rstd_val + eps);
tmp_buffer_data[n * 2 * G + 2 * g] = mean_val;
tmp_buffer_data[n * 2 * G + 2 * g + 1] = rstd_val;
}
}
// step-3: compute scale and bias
//
// mean/rstd have shape of {N, G}, gamma/beta have shape of {G, D}.
// And scale/bias have shape of {N, C} so that we can directly vectorize on
// dimension of C in the final step.
//
// We could fuse step 3 and 4 into a single session but this way is better:
// a. D might be too small for vectorization;
// b. Avoid duplicate caculation of scale/bias, each HxW plain share the same scale/bias
//
for (const auto n : c10::irange(N)) {
for (const auto g : c10::irange(G)) {
T_ACC* scale_ptr = buffer_data + n * 2 * C;
T_ACC* bias_ptr = scale_ptr + C;
T_ACC mean_val = tmp_buffer_data[n * 2 * G + 2 * g];
T_ACC rstd_val = tmp_buffer_data[n * 2 * G + 2 * g + 1];
mean_data[n * G + g] = mean_val;
rstd_data[n * G + g] = rstd_val;
for (const auto d : c10::irange(D)) {
const int64_t c = g * D + d;
scale_ptr[c] = rstd_val * (gamma_null ? T_ACC(1) : T_ACC(gamma_data[c]));
bias_ptr[c] = -scale_ptr[c] * mean_val + (beta_null ? T_ACC(0) : T_ACC(beta_data[c]));
}
}
}
// step-4: apply scale and bias
//
// Parallel on on the all the outer dimensions of N and HxW
// and vectorize on C.
//
at::parallel_for(0, N * HxW, 1, [&](int64_t begin, int64_t end) {
int64_t n{0}, m{0};
data_index_init(begin, n, N, m, HxW);
for (const auto i : c10::irange(begin, end)) {
const T* X_ptr = X_data + i * C;
T* Y_ptr = Y_data + i * C;
T_ACC* scale_ptr = buffer_data + n * 2 * C;
T_ACC* bias_ptr = scale_ptr + C;
ApplyScaleBias<T, T_ACC>(Y_ptr, X_ptr, scale_ptr, bias_ptr, C);
data_index_step(n, N, m, HxW);
}
});
}
}
void GroupNormKernelImpl(
const Tensor& X,
const Tensor& gamma,
const Tensor& beta,
int64_t N,
int64_t C,
int64_t HxW,
int64_t group,
double eps,
Tensor& Y,
Tensor& mean,
Tensor& rstd) {
const bool mixed_type = is_mixed_type(X, gamma, beta);
switch (X.suggest_memory_format()) {
case at::MemoryFormat::Contiguous: {
AT_DISPATCH_FLOATING_TYPES_AND(ScalarType::BFloat16, X.scalar_type(), "GroupNormKernelImpl", [&]() {
using param_t = at::opmath_type<scalar_t>;
if (mixed_type) {
GroupNormKernelImplInternal<scalar_t, param_t>(
X, gamma, beta, N, C, HxW, group, eps, Y, mean, rstd);
} else {
GroupNormKernelImplInternal<scalar_t, scalar_t>(
X, gamma, beta, N, C, HxW, group, eps, Y, mean, rstd);
}
});
break;
}
case at::MemoryFormat::ChannelsLast:
case at::MemoryFormat::ChannelsLast3d: {
AT_DISPATCH_FLOATING_TYPES_AND(ScalarType::BFloat16, X.scalar_type(), "GroupNormKernelImpl", [&]() {
using param_t = at::opmath_type<scalar_t>;
if (mixed_type) {
GroupNormKernelImplChannelsLastInternal<scalar_t, param_t>(
X, gamma, beta, N, C, HxW, group, eps, Y, mean, rstd);
} else {
GroupNormKernelImplChannelsLastInternal<scalar_t, scalar_t>(
X, gamma, beta, N, C, HxW, group, eps, Y, mean, rstd);
}
});
break;
}
default:
TORCH_CHECK(false, "Unsupported memory format. Supports only ChannelsLast, ChannelsLast3d, Contiguous");
}
}
template <typename T, typename T_ACC>
void ComputeInternalGradients(
int64_t N,
int64_t C,
int64_t HxW,
const T* dY,
const T* X,
T_ACC* ds,
T_ACC* db) {
using Vec = at::vec::Vectorized<T_ACC>;
at::parallel_for(0, N * C, 1, [=](int64_t start, int64_t end) {
for (const auto i : c10::irange(start, end)) {
const T* dY_ptr = dY + i * HxW;
const T* X_ptr = X + i * HxW;
ds[i] = at::vec::map2_reduce_all<T>(
[](Vec x, Vec y) { return x * y; },
[](Vec x, Vec y) { return x + y; },
dY_ptr,
X_ptr,
HxW);
db[i] = at::vec::reduce_all<T>(
[](Vec& x, Vec& y) { return x + y; }, dY_ptr, HxW);
}
});
}
template <>
void ComputeInternalGradients(
int64_t N,
int64_t C,
int64_t HxW,
const BFloat16* dY,
const BFloat16* X,
float* ds,
float* db) {
using bVec = vec::Vectorized<BFloat16>;
using fVec = vec::Vectorized<float>;
at::parallel_for(0, N * C, 1, [=](int64_t start, int64_t end) {
constexpr int64_t K = bVec::size();
const int64_t inner_size = HxW / K * K;
// NOLINTNEXTLINE(cppcoreguidelines-pro-type-member-init)
std::array<float, K / 2> ds_arr;
// NOLINTNEXTLINE(cppcoreguidelines-pro-type-member-init)
std::array<float, K / 2> db_arr;
for (const auto i : c10::irange(start, end)) {
const BFloat16* dY_ptr = dY + i * HxW;
const BFloat16* X_ptr = X + i * HxW;
fVec ds_vec(0);
fVec db_vec(0);
for (int64_t j = 0; j < inner_size; j += K) {
const bVec dy_bvec = bVec::loadu(dY_ptr + j);
const bVec x_bvec = bVec::loadu(X_ptr + j);
fVec x_fvec0, x_fvec1, dy_fvec0, dy_fvec1;
std::tie(x_fvec0, x_fvec1) = convert_bfloat16_float(x_bvec);
std::tie(dy_fvec0, dy_fvec1) = convert_bfloat16_float(dy_bvec);
ds_vec = ds_vec + dy_fvec0 * x_fvec0;
ds_vec = ds_vec + dy_fvec1 * x_fvec1;
db_vec = db_vec + dy_fvec0 + dy_fvec1;
}
ds_vec.store(ds_arr.data());
db_vec.store(db_arr.data());
float ds_val = std::accumulate(ds_arr.cbegin(), ds_arr.cend(), float(0));
float db_val = std::accumulate(db_arr.cbegin(), db_arr.cend(), float(0));
for (const auto j : c10::irange(inner_size, HxW)) {
ds_val += float(dY_ptr[j]) * float(X_ptr[j]);
db_val += float(dY_ptr[j]);
}
ds[i] = ds_val;
db[i] = db_val;
}
});
}
template <typename PT, typename T_ACC>
inline void CalcDsDb(
const T_ACC* ds_ptr,
const T_ACC* db_ptr,
bool gamma_null,
const PT* gamma_ptr,
const int64_t d,
const int64_t K,
void* ds_arr,
void* db_arr) {
vec::Vectorized<T_ACC> ds_vec(0);
vec::Vectorized<T_ACC> db_vec(0);
for (int64_t j = 0; j < d; j += K) {
const vec::Vectorized<PT> gamma_vec = gamma_null
? vec::Vectorized<PT>(1)
: vec::Vectorized<PT>::loadu(gamma_ptr + j);
ds_vec = ds_vec + vec::Vectorized<PT>::loadu(ds_ptr + j) * gamma_vec;
db_vec = db_vec + vec::Vectorized<PT>::loadu(db_ptr + j) * gamma_vec;
}
ds_vec.store(ds_arr);
db_vec.store(db_arr);
}
template <>
inline void CalcDsDb(
const float* ds_ptr,
const float* db_ptr,
bool gamma_null,
const BFloat16* gamma_ptr,
const int64_t d,
const int64_t K,
void* ds_arr,
void* db_arr) {
using fVec = at::vec::Vectorized<float>;
using bVec = at::vec::Vectorized<BFloat16>;
fVec ds_acc(0);
fVec db_acc(0);
for (int64_t j = 0; j < d; j += K) {
const bVec gamma_vec = gamma_null ? bVec(1) : bVec::loadu(gamma_ptr + j);
fVec gamma_vec0, gamma_vec1;
std::tie(gamma_vec0, gamma_vec1) = convert_bfloat16_float(gamma_vec);
ds_acc += fVec::loadu(ds_ptr + j) * gamma_vec0;
ds_acc += fVec::loadu(ds_ptr + j + fVec::size()) * gamma_vec1;
db_acc += fVec::loadu(db_ptr + j) * gamma_vec0;
db_acc += fVec::loadu(db_ptr + j + fVec::size()) * gamma_vec1;
}
ds_acc.store(ds_arr);
db_acc.store(db_arr);
}
template <typename T, typename PT, typename T_ACC>
void GroupNormInputBackward(
int64_t N,
int64_t C,
int64_t HxW,
int64_t group,
const T* dY,
const T* X,
const PT* mean,
const PT* rstd,
const PT* gamma,
const T_ACC* ds,
const T_ACC* db,
T* dX) {
const int64_t G = group;
const int64_t D = C / G;
const T_ACC s = T_ACC(1) / static_cast<T_ACC>(D * HxW);
const bool gamma_null = (gamma == nullptr);
at::parallel_for(0, N * G, 1, [=](int64_t start, int64_t end) {
constexpr int64_t K = vec::Vectorized<PT>::size();
const int64_t d = D / K * K;
// NOLINTNEXTLINE(cppcoreguidelines-pro-type-member-init)
std::array<T_ACC, at::vec::Vectorized<T_ACC>::size()> ds_arr;
// NOLINTNEXTLINE(cppcoreguidelines-pro-type-member-init)
std::array<T_ACC, at::vec::Vectorized<T_ACC>::size()> db_arr;
for (const auto i : c10::irange(start, end)) {
const int64_t g = i % G;
const T_ACC* ds_ptr = ds + i * D;
const T_ACC* db_ptr = db + i * D;
const PT* gamma_ptr = gamma + g * D;
CalcDsDb(ds_ptr, db_ptr, gamma_null, gamma_ptr, d, K, ds_arr.data(), db_arr.data());
T_ACC ds_val = std::accumulate(ds_arr.cbegin(), ds_arr.cend(), T_ACC(0));
T_ACC db_val = std::accumulate(db_arr.cbegin(), db_arr.cend(), T_ACC(0));
for (const auto j : c10::irange(d, D)) {
const T_ACC gamma_v = gamma_null ? T_ACC(1) : T_ACC(gamma[g * D + j]);
ds_val += ds_ptr[j] * gamma_v;
db_val += db_ptr[j] * gamma_v;
}
const T_ACC c2 =
(db_val * T_ACC(mean[i]) - ds_val) * T_ACC(rstd[i]) * T_ACC(rstd[i]) * T_ACC(rstd[i]) * s;
const T_ACC c3 = -c2 * T_ACC(mean[i]) - db_val * T_ACC(rstd[i]) * s;
for (const auto j : c10::irange(D)) {
const int64_t c = g * D + j;
const T* dY_ptr = dY + (i * D + j) * HxW;
const T* X_ptr = X + (i * D + j) * HxW;
T* dX_ptr = dX + (i * D + j) * HxW;
const T_ACC c1 = T_ACC(rstd[i]) * (gamma_null ? T_ACC(1) : T_ACC(gamma[c]));
for (const auto k : c10::irange(HxW)) {
dX_ptr[k] = c1 * T_ACC(dY_ptr[k]) + c2 * T_ACC(X_ptr[k]) + c3;
}
}
}
});
}
template <typename PT, typename T_ACC>
void GammaBackward(
int64_t N,
int64_t C,
int64_t group,
const PT* mean,
const PT* rstd,
const T_ACC* ds,
const T_ACC* db,
PT* dgamma) {
const int64_t G = group;
const int64_t D = C / G;
constexpr int64_t K = at::vec::Vectorized<PT>::size();
using Vec = at::vec::Vectorized<PT>;
const int64_t inner_size = D / K * K;
for (const auto g : c10::irange(G)) {
int64_t i = 0;
for (; i < inner_size; i += K) {
Vec acc_vec{0};
for (const auto n : c10::irange(N)) {
const PT* ds_ptr = ds + n * C + g * D + i;
const PT* db_ptr = db + n * C + g * D + i;
auto ds_vec = Vec::loadu(ds_ptr);
auto db_vec = Vec::loadu(db_ptr);
auto mean_vec = Vec(mean[n * G + g]);
auto rstd_vec = Vec(rstd[n * G + g]);
acc_vec += (ds_vec - db_vec * mean_vec) * rstd_vec;
}
acc_vec.store(dgamma + g * D + i);
}
if (D - i > 0) {
Vec acc_vec{0};
for (const auto n : c10::irange(N)) {
const PT* ds_ptr = ds + n * C + g * D + i;
const PT* db_ptr = db + n * C + g * D + i;
auto ds_vec = Vec::loadu(ds_ptr, D - i);
auto db_vec = Vec::loadu(db_ptr, D - i);
auto mean_vec = Vec(mean[n * G + g]);
auto rstd_vec = Vec(rstd[n * G + g]);
acc_vec += (ds_vec - db_vec * mean_vec) * rstd_vec;
}
acc_vec.store(dgamma + g * D + i, D - i);
}
}
}
template <>
void GammaBackward(
int64_t N,
int64_t C,
int64_t group,
const BFloat16* mean,
const BFloat16* rstd,
const float* ds,
const float* db,
BFloat16* dgamma) {
const int64_t G = group;
const int64_t D = C / G;
using Vec = at::vec::Vectorized<BFloat16>;
using fVec = at::vec::Vectorized<float>;
constexpr int64_t K = Vec::size();
const int64_t inner_size = D / K * K;
for (const auto g : c10::irange(G)) {
int64_t i = 0;
for (; i < inner_size; i += K) {
fVec acc0_vec{0}, acc1_vec{0};
for (const auto n : c10::irange(N)) {
const float* ds_ptr = ds + n * C + g * D + i;
const float* db_ptr = db + n * C + g * D + i;
fVec ds_vec0, ds_vec1, db_vec0, db_vec1;
ds_vec0 = fVec::loadu(ds_ptr);
ds_vec1 = fVec::loadu(ds_ptr + fVec::size());
db_vec0 = fVec::loadu(db_ptr);
db_vec1 = fVec::loadu(db_ptr + fVec::size());
fVec mean_vec = fVec(float(mean[n * G + g]));
fVec rstd_vec = fVec(float(rstd[n * G + g]));
acc0_vec += (ds_vec0 - db_vec0 * mean_vec) * rstd_vec;
acc1_vec += (ds_vec1 - db_vec1 * mean_vec) * rstd_vec;
}
convert_float_bfloat16(acc0_vec, acc1_vec).store(dgamma + g * D + i);
}
if (D - i > 0) {
fVec acc0_vec{0}, acc1_vec{0};
for (const auto n : c10::irange(N)) {
const float* ds_ptr = ds + n * C + g * D + i;
const float* db_ptr = db + n * C + g * D + i;
fVec ds_vec0, ds_vec1, db_vec0, db_vec1;
ds_vec0 = fVec::loadu(
ds_ptr, (D - i) > fVec::size() ? fVec::size() : (D - i));
ds_vec1 = fVec::loadu(
ds_ptr + fVec::size(),
(D - i) > fVec::size() ? (D - i - fVec::size()) : 0);
db_vec0 = fVec::loadu(
db_ptr, (D - i) > fVec::size() ? fVec::size() : (D - i));
db_vec1 = fVec::loadu(
db_ptr + fVec::size(),
(D - i) > fVec::size() ? (D - i - fVec::size()) : 0);
fVec mean_vec = fVec(float(mean[n * G + g]));
fVec rstd_vec = fVec(float(rstd[n * G + g]));
acc0_vec += (ds_vec0 - db_vec0 * mean_vec) * rstd_vec;
acc1_vec += (ds_vec1 - db_vec1 * mean_vec) * rstd_vec;
}
convert_float_bfloat16(acc0_vec, acc1_vec)
.store(dgamma + g * D + i, D - i);
}
}
}
template <typename PT, typename T_ACC>
void BetaBackward(int64_t N, int64_t C, const T_ACC* db, PT* dbeta) {
using Vec = at::vec::Vectorized<PT>;
constexpr int64_t K = Vec::size();
Vec acc_vec{0}, zero{0};
const int64_t inner_size = C / K * K;
int64_t i = 0;
for (; i < inner_size; i += K) {
for (const auto n : c10::irange(N)) {
acc_vec += Vec::loadu(db + n * C + i);
}
acc_vec.store(dbeta + i);
acc_vec = Vec::set(acc_vec, zero);
}
if (C - i > 0) {
for (const auto n : c10::irange(N)) {
acc_vec += Vec::loadu(db + n * C + i, C - i);
}
acc_vec.store(dbeta + i, C - i);
acc_vec = Vec::set(acc_vec, zero, C - i);
}
}
template <>
void BetaBackward(int64_t N, int64_t C, const float* db, BFloat16* dbeta) {
using Vec = at::vec::Vectorized<BFloat16>;
using fVec = at::vec::Vectorized<float>;
constexpr int64_t K = Vec::size();
fVec acc0_vec{0}, acc1_vec{0}, zero{0};
const int64_t inner_size = C / K * K;
int64_t i = 0;
for (; i < inner_size; i += K) {
for (const auto n : c10::irange(N)) {
fVec db_vec0, db_vec1;
db_vec0 = fVec::loadu(db + n * C + i);
db_vec1 = fVec::loadu(db + n * C + i + fVec::size());
acc0_vec += db_vec0;
acc1_vec += db_vec1;
}
convert_float_bfloat16(acc0_vec, acc1_vec).store(dbeta + i);
acc0_vec = fVec::set(acc0_vec, zero);
acc1_vec = fVec::set(acc1_vec, zero);
}
if (C - i > 0) {
for (const auto n : c10::irange(N)) {
fVec db_vec0, db_vec1;
db_vec0 = fVec::loadu(
db + n * C + i, (C - i) > fVec::size() ? fVec::size() : (C - i));
db_vec1 = fVec::loadu(
db + n * C + i + fVec::size(),
(C - i) > fVec::size() ? (C - i - fVec::size()) : 0);
acc0_vec += db_vec0;
acc1_vec += db_vec1;
}
convert_float_bfloat16(acc0_vec, acc1_vec).store(dbeta + i, C - i);
acc0_vec = fVec::set(acc0_vec, zero, C - i);
acc1_vec = fVec::set(acc1_vec, zero, C - i);
}
}
template <typename T, typename PT>
void GroupNormBackwardKernelImplInternal(
const Tensor& dY,
const Tensor& X,
const Tensor& mean,
const Tensor& rstd,
const Tensor& gamma,
int64_t N,
int64_t C,
int64_t HxW,
int64_t group,
Tensor& dX,
Tensor& dgamma,
Tensor& dbeta) {
TORCH_CHECK(dY.numel() == N * C * HxW);
TORCH_CHECK(X.numel() == N * C * HxW);
TORCH_CHECK(mean.numel() == N * group);
TORCH_CHECK(rstd.numel() == N * group);
TORCH_CHECK(!gamma.defined() || gamma.numel() == C);
const T* dY_data = dY.data_ptr<T>();
const T* X_data = X.data_ptr<T>();
const PT* mean_data = mean.data_ptr<PT>();
const PT* rstd_data = rstd.data_ptr<PT>();
const PT* gamma_data = gamma.defined() ? gamma.data_ptr<PT>() : nullptr;
T* dX_data = dX.defined() ? dX.data_ptr<T>() : nullptr;
PT* dgamma_data = dgamma.defined() ? dgamma.data_ptr<PT>() : nullptr;
PT* dbeta_data = dbeta.defined() ? dbeta.data_ptr<PT>() : nullptr;
using T_ACC = at::opmath_type<T>;
Tensor ds = at::empty({N, C}, X.options().dtype(c10::CppTypeToScalarType<T_ACC>::value));
Tensor db = at::empty({N, C}, X.options().dtype(c10::CppTypeToScalarType<T_ACC>::value));
T_ACC* ds_data = ds.data_ptr<T_ACC>();
T_ACC* db_data = db.data_ptr<T_ACC>();
ComputeInternalGradients<T, T_ACC>(N, C, HxW, dY_data, X_data, ds_data, db_data);
if (dX_data != nullptr) {
GroupNormInputBackward<T, PT, T_ACC>(
N,
C,
HxW,
group,
dY_data,
X_data,
mean_data,
rstd_data,
gamma_data,
ds_data,
db_data,
dX_data);
}
if (dgamma_data != nullptr) {
GammaBackward(
N, C, group, mean_data, rstd_data, ds_data, db_data, dgamma_data);
}
if (dbeta_data != nullptr) {
BetaBackward(N, C, db_data, dbeta_data);
}
}
template <typename T, typename T_ACC>
inline void DsDbRowwiseMomentsChannelsLast(
const T* dY_ptr,
const T* X_ptr,
T_ACC* ds_ptr,
T_ACC* db_ptr,
int64_t C) {
using Vec = vec::Vectorized<T>;
constexpr int64_t K = vec::Vectorized<T>::size();
const int64_t inner_size = C / K * K;
int64_t d = 0;
for (; d < inner_size; d += K) {
Vec ds_dev = Vec::loadu(ds_ptr + d);
Vec db_vec = Vec::loadu(db_ptr + d);
Vec x_vec = Vec::loadu(X_ptr + d);
Vec dy_vec = Vec::loadu(dY_ptr + d);
ds_dev += x_vec * dy_vec;
db_vec += dy_vec;
ds_dev.store(ds_ptr + d);
db_vec.store(db_ptr + d);
}
if (C - d > 0) {
Vec ds_dev = Vec::loadu(ds_ptr + d, C - d);
Vec db_vec = Vec::loadu(db_ptr + d, C - d);
Vec x_vec = Vec::loadu(X_ptr + d, C - d);
Vec dy_vec = Vec::loadu(dY_ptr + d, C - d);
ds_dev += x_vec * dy_vec;
db_vec += dy_vec;
ds_dev.store(ds_ptr + d, C - d);
db_vec.store(db_ptr + d, C - d);
}
}
template <>
inline void DsDbRowwiseMomentsChannelsLast(
const BFloat16* dY_ptr,
const BFloat16* X_ptr,
float* ds_ptr,
float* db_ptr,
int64_t C) {
using fVec = vec::Vectorized<float>;
using bVec = vec::Vectorized<BFloat16>;
int64_t d = 0;
for (; d < C - (C % bVec::size()); d += bVec::size()) {
fVec ds_dev0 = fVec::loadu(ds_ptr + d);
fVec ds_dev1 = fVec::loadu(ds_ptr + d + fVec::size());
fVec db_vec0 = fVec::loadu(db_ptr + d);
fVec db_vec1 = fVec::loadu(db_ptr + d + fVec::size());
bVec x_vec = bVec::loadu(X_ptr + d);
bVec dy_vec = bVec::loadu(dY_ptr + d);
fVec x_vec0, x_vec1, dy_vec0, dy_vec1;
std::tie(x_vec0, x_vec1) = convert_bfloat16_float(x_vec);
std::tie(dy_vec0, dy_vec1) = convert_bfloat16_float(dy_vec);
ds_dev0 += x_vec0 * dy_vec0;
ds_dev1 += x_vec1 * dy_vec1;
db_vec0 += dy_vec0;
db_vec1 += dy_vec1;
ds_dev0.store(ds_ptr + d);
ds_dev1.store(ds_ptr + d + fVec::size());
db_vec0.store(db_ptr + d);
db_vec1.store(db_ptr + d + fVec::size());
}
if (C - d > 0) {
fVec ds_dev0 = fVec::loadu(ds_ptr + d, (C - d) > fVec::size() ? fVec::size() : (C - d));
fVec ds_dev1 = fVec::loadu(ds_ptr + d + fVec::size(), (C - d) > fVec::size() ? (C - d - fVec::size()) : 0);
fVec db_vec0 = fVec::loadu(db_ptr + d, (C - d) > fVec::size() ? fVec::size() : (C - d));
fVec db_vec1 = fVec::loadu(db_ptr + d + fVec::size(), (C - d) > fVec::size() ? (C - d - fVec::size()) : 0);