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main
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Halide
/
src
/
ExtractTileOperations.cpp
Halide
/
src
/
ExtractTileOperations.cpp
ExtractTileOperations.cpp 23.00 KB
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#include "ExtractTileOperations.h"
#include "IRMatch.h"
#include "IRMutator.h"
#include "IROperator.h"
#include "Util.h"
/** \file Support extraction of AMX instructions. */
/**
* https://asciiflow.com/#/share/eJyVUkFugzAQ%2FMrKxwoRhdAkza23SmlySHvogQsBp7FkbGSbAoryiz6nr%2BlLugZDk6ghKvJhbXZmd2b3QEScUbIQBece4XFNFVmQQ0SqiCwegtCLSI1RMBtjZGhl8BIRAHh%2BeoFVbBSr4Pq36ZOiSOBpX5cDCEikSGhuipjzun0pmdnD4%2BqtwX9%2Ffg2cLmUcTML76WyO4VAtWJ%2Ff7kIkWMEJ6gbBae2%2F3q53OHBuFBz3TS1HodPqfvUO3%2F4wO7gQag07IXqVkCuZU4VzyApuWI5BAJkdZ0K1B2ZP2%2BwJ%2FEs%2BjhKY0EYViWFSaMAaO6kypBY1hLCtDRIvMTvsekmlsc2kiGgKMw2cxqkGIyEGjn%2FlzonoIMjPUibeQX5Q1bHGisbav%2FBh2kHW2ESzdlaZkqUltaFd9UZ25TnIrIOg%2Bb7vQykLnv661GysRSaSF1k78HkHcaSbntSReLAtTL%2FscOlaI9rxYaRzzgwUOTrZeOCokLzN0TDqRYvUqtFwB6Fvqco9S5r%2BBCiqsWmNLHabzny2Y7E4PyJHcvwBx0t%2BJw%3D%3D)
*
* LHS Matrix RHS Matrix
*
* K conceptually with AMX
* ┌────────┐
* │12345678│ N N*4
*M │ │ ┌──┐ ┌────────┐
* └────────┘ │1 │ K/4│1234 │
* │2 │ │5678 │
* To properly multiply 2 matrices, the │3 │ └────────┘
* AMX instructions perform many 4 byte K│4 │
* dot products, this leads to a lot of │5 │
* striding over 4 byte areas. │6 │
* Normally the row of the LHS matrix, │7 │
* 123... would multiply with the column │8 │
* of the RHS matrix 123..., but with AMX └──┘
* this column is split up into a matrix of columns / 4 byte and rows * 4.
* which then results in K/4 dot products per row.
*
*/
namespace Halide {
namespace Internal {
using std::string;
using std::vector;
namespace {
template<int Dim>
struct Tile {
bool result;
Expr base;
Expr stride[Dim];
int extent[Dim];
};
enum class AMXOpType {
Int8,
Bfloat16,
};
/// returns the appropriate `Halide::Type` for the given operation type
Type amx_op_type_result_type(AMXOpType op_ty) {
switch (op_ty) {
case AMXOpType::Int8:
return Int(32, 256);
case AMXOpType::Bfloat16:
return Float(32, 256);
default:
internal_error << "Unexpected";
return Type();
}
}
int amx_op_type_size(AMXOpType op_ty) {
switch (op_ty) {
case AMXOpType::Int8:
return 1;
case AMXOpType::Bfloat16:
return 2;
default:
internal_error << "Unexpected";
return -1;
}
}
const auto wild_i32 = Variable::make(Int(32), "*");
const auto wild_i32x = Variable::make(Int(32, 0), "*");
Tile<1> get_1d_tile_index(const Expr &e) {
if (const auto *r1 = e.as<Ramp>()) {
const auto stride_var = Variable::make(Int(32), "stride");
const auto v1 = Variable::make(Int(32), "v1");
const auto v2 = Variable::make(Int(32), "v2");
const auto v3 = Variable::make(Int(32), "v3");
Expr patterns[] = {
((v1 * stride_var) + v2) * v3,
v3 * ((v1 * stride_var) + v2),
(v2 + (v1 * stride_var)) * v3,
v3 * (v2 + (v1 * stride_var)),
};
std::map<std::string, Expr> matches;
for (const auto &pattern : patterns) {
if (expr_match(pattern, r1->base, matches)) {
auto stride = std::move(matches["stride"]);
// stride must be a constant in order to not be confused with v1
if (stride.as<IntImm>()) {
return {true, r1->base, {std::move(stride)}, {r1->lanes}};
}
// if stride wasn't a constant then v1 could possibly be the stride if constant
auto v1_expr = std::move(matches["v1"]);
if (v1_expr.as<IntImm>()) {
return {true, r1->base, {std::move(v1_expr)}, {r1->lanes}};
}
}
}
}
return {};
}
Tile<2> get_2d_tile_index(const Expr &e) {
// ramp(ramp(base, 1, 4), x4(stride), 4)
vector<Expr> matches;
if (const auto *r1 = e.as<Ramp>()) {
if (const auto *r2 = r1->base.as<Ramp>()) {
auto ramp_2d_pattern = Ramp::make(Ramp::make(wild_i32, wild_i32, r2->lanes), Broadcast::make(wild_i32, r2->lanes), r1->lanes);
if (expr_match(ramp_2d_pattern, e, matches)) {
return {true, std::move(matches[0]), {std::move(matches[2]), std::move(matches[1])}, {r1->lanes, r2->lanes}};
}
}
}
return {};
}
Tile<3> get_3d_tile_index(const Expr &e) {
vector<Expr> matches;
// there could be a sub node
const Sub *sub = e.as<Sub>();
const Add *add = nullptr;
if (sub) {
add = sub->a.as<Add>();
} else {
add = e.as<Add>();
}
if (!add) {
return {};
}
const auto &first = add->a;
const auto &second = add->b;
// ramp(x[x*r](base), x[x*r](stride), x) + x[x*y](ramp(idx, 1, r))
const auto *r1 = first.as<Ramp>();
const auto *b2 = second.as<Broadcast>();
if (!r1 && !b2) {
// Try switching the order
r1 = second.as<Ramp>();
b2 = first.as<Broadcast>();
}
if (!r1 || !b2) {
return {};
}
const auto *b1 = r1->base.as<Broadcast>();
const auto *r2 = b2->value.as<Ramp>();
if (!b1 || !r2) {
return {};
}
int x_tile = r1->lanes;
int r_tile = r2->lanes;
int y_tile = b1->lanes / r_tile;
if (y_tile != b2->lanes / x_tile) {
return {};
}
auto pattern1 = Ramp::make(Broadcast::make(wild_i32, b1->lanes), Broadcast::make(wild_i32, b1->lanes), r1->lanes);
if (!expr_match(pattern1, first, matches)) {
return {};
}
Expr base = std::move(matches[0]);
Expr x_stride = std::move(matches[1]);
auto pattern2 = Broadcast::make(Ramp::make(wild_i32, wild_i32, r2->lanes), b2->lanes);
if (!expr_match(pattern2, second, matches)) {
return {};
}
base += std::move(matches[0]);
Expr r_stride = std::move(matches[1]);
if (sub) {
Expr adj = sub->b;
const Broadcast *bcast = adj.as<Broadcast>();
if (!bcast) {
return {};
}
if (bcast->lanes != b1->lanes * r1->lanes) {
return {};
}
base -= bcast->value;
}
return {true, base, {x_stride, 0, r_stride}, {x_tile, y_tile, r_tile}};
}
/**
* \brief Get the 3d rhs tile index configuration
*
* \param e index expression
* \param element_width the width of the elements, 1 for u8/i8, 2 for bf16
* \return Tile<3> the tile configuration found
*
* The pattern which is getting matched looks roughly like
* `broadcast(ramp(0, 1, r), x*y) / broadcast(4, x*y*r) + optional(broadcast(base, x*y*r)) * broadcast(8, x*y*r) +
* broadcast(ramp(0, 1, r), x*y) % broadcast(4, x*y*r) +
* broadcast(ramp(broadcast(_, r), broadcast(4, r), x) , y)`
*/
Tile<3> get_3d_rhs_tile_index(const Expr &e, int element_width) {
const auto *sub = e.as<Sub>();
const Add *add_lhs = nullptr;
// there's not always a sub pattern
// This depends on whether we have an ImageParam or a Buffer
if (!sub) {
add_lhs = e.as<Add>();
} else {
add_lhs = sub->a.as<Add>();
}
if (!add_lhs) {
return {};
}
// The right hand side of the add expression is used for retrieving the dimensions of the matrix.
// obtain the x, y, r dimensions
// this expr looks like below, the shape of `add_lhs->a` can be seen further down below
// broadcast(ramp(0, 1, r), x*y) % broadcast(4, x*y*r) + broadcast(ramp(broadcast(base, r), broadcast(4, r), x) , y)
const Add *dim_expr = add_lhs->b.as<Add>();
if (!dim_expr) {
return {};
}
// broadcast(ramp(broadcast(_, r), broadcast(4, r), x), y)
const Broadcast *base_stride_bc = dim_expr->b.as<Broadcast>();
if (!base_stride_bc) {
return {};
}
int tile_y = base_stride_bc->lanes;
// broadcast(ramp(0, 1, r), x*y) % broadcast(4, x*y*r)
const Mod *mod = dim_expr->a.as<Mod>();
if (!mod) {
return {};
}
// broadcast(ramp(0, 1, r), x*y)
const Broadcast *bc_ramp = mod->a.as<Broadcast>();
if (!bc_ramp) {
return {};
}
int tile_xy = bc_ramp->lanes;
int tile_x = tile_xy / tile_y;
// ramp(0, 1, r)
const Ramp *r_ramp = bc_ramp->value.as<Ramp>();
if (!r_ramp) {
return {};
}
int tile_r = r_ramp->lanes;
// get the base and stride
// ramp(broadcast(_, r), broadcast(4, r), x)
const Ramp *base_stride_ramp = base_stride_bc->value.as<Ramp>();
if (!base_stride_ramp) {
return {};
}
// broadcast(_, r)
const Broadcast *base_bc = base_stride_ramp->base.as<Broadcast>();
if (!base_bc) {
return {};
}
Expr base = base_bc->value;
Expr stride;
bool found_stride = false;
// the following pattern will match the following shape
// broadcast(ramp(0, 1, k), x*y) / broadcast(4, x*y*k) * broadcast(_, x*y*k)
// where the stride is marked by _.
// this stride pattern can occur if `tile_r` is the same size as `acc`
auto stride_pattern = Broadcast::make(Ramp::make(0, 1, tile_r), tile_x * tile_y) / Broadcast::make((4 / element_width), tile_x * tile_y * tile_r) * Broadcast::make(wild_i32, tile_x * tile_y * tile_r);
std::vector<Expr> results{};
if (expr_match(stride_pattern, add_lhs->a, results)) {
found_stride = true;
stride = std::move(results[0]);
}
// This pattern is similar to the above except with an additional offset to iterate over the tiles in the k dimension
// (broadcast(ramp(0, 1, k), m * n) / broadcast(4, m*n*k) + _) * broadcast(_, m*n*k)
// here the first _ marks the base and the second _ the stride.
if (!found_stride) {
stride_pattern = (Broadcast::make(Ramp::make(0, 1, tile_r), tile_x * tile_y) / Broadcast::make((4 / element_width), tile_x * tile_y * tile_r) + wild_i32) * Broadcast::make(wild_i32, tile_x * tile_y * tile_r);
if (expr_match(stride_pattern, add_lhs->a, results)) {
found_stride = true;
stride = std::move(results[1]);
base = std::move(results[0]) * stride + base;
}
}
if (!found_stride) {
return {};
}
return {true, base, {stride, 0, 0}, {tile_x, tile_y, tile_r}};
}
struct BaseStride {
bool result{false};
Expr base{};
Expr stride{};
};
BaseStride get_rhs_tile_index(const Expr &index, int element_width, int tile_x, int tile_y, int tile_r) {
const auto rhs_tile2 = get_2d_tile_index(index);
if (!rhs_tile2.result) {
const auto rhs_tile1 = get_1d_tile_index(index);
if (!rhs_tile1.result) {
auto rhs_tile3 = get_3d_rhs_tile_index(index, element_width);
if (rhs_tile3.extent[0] != tile_x || rhs_tile3.extent[1] != tile_y || rhs_tile3.extent[2] != tile_r) {
return {};
}
return {true, rhs_tile3.base, rhs_tile3.stride[0] * element_width};
} else {
if (rhs_tile1.extent[0] != tile_y * tile_r) {
return {};
}
// times 4 because of the rhs layout, each vector used by AMX is 4 bytes in size.
// For the 4 gets divided by the element width which means each vector has 4 elements in u8/i8 and
// 2 elements for bf16.
return {true, rhs_tile1.base, rhs_tile1.stride[0] * (4 / element_width)};
}
} else {
if (tile_y != rhs_tile2.extent[0] || tile_r != rhs_tile2.extent[1]) {
return {};
}
return {true, rhs_tile2.base, rhs_tile2.stride[0]};
}
}
struct Matmul {
bool result = false;
Stmt stmt;
int tile_x;
int tile_y;
int tile_r;
};
Matmul convert_to_matmul(const Store *op, const string &new_name, AMXOpType op_type) {
// m[ramp(0, 1, S)] = VectorAdd(lhs[{XYR tile}] * xX(rhs[{YR tile}])) + m[ramp(0, 1, S)]
const auto wild_i8x = Variable::make(Int(8, 0), "*");
const auto wild_u8x = Variable::make(UInt(8, 0), "*");
const auto wild_bf16x = Variable::make(BFloat(16, 0), "*");
const auto wild_f32x = Variable::make(Float(32, 0), "*");
vector<Expr> matches;
if (op_type == AMXOpType::Int8) {
const auto pattern1 = wild_i32x + wild_i32x;
if (!expr_match(pattern1, op->value, matches)) {
return {};
}
} else { // AMXOpType::Bfloat16
const auto pattern1 = wild_f32x + wild_f32x;
if (!expr_match(pattern1, op->value, matches)) {
return {};
}
}
const auto *reduce = matches[0].as<VectorReduce>();
const auto *load = matches[1].as<Load>();
if (!reduce || reduce->op != VectorReduce::Add) {
return {};
}
if (!load || load->name != op->name || !equal(load->index, op->index)) {
return {};
}
if (op_type == AMXOpType::Int8) {
auto pattern2 = cast(Int(32, 0), cast(Int(32, 0), wild_i8x) * wild_i32x);
auto pattern2_unsigned = cast(Int(32, 0), cast(Int(32, 0), wild_u8x) * wild_i32x);
if (!(expr_match(pattern2, reduce->value, matches) || expr_match(pattern2_unsigned, reduce->value, matches))) {
return {};
}
} else {
auto pattern2 = cast(Float(32, 0), cast(Float(32, 0), wild_bf16x) * wild_f32x);
if (!expr_match(pattern2, reduce->value, matches)) {
return {};
}
}
const auto *lhs_load = matches[0].as<Load>();
const auto *rhs_broadcast = matches[1].as<Broadcast>();
const Cast *rhs_cast = nullptr;
if (lhs_load && !rhs_broadcast) {
// now working on a larger k dimension
// with a K dimension of 4 (or 2) with bf16 all the elements in the right-hand matrix are
// layed out in a way that multiplying with a column can be done in a single dot product.
// Therefore the indexing can be reused with a broadcast,
// with higher K dimensions this can no longer be done and the broadcast won't exist.
// ┌──┐
// │1 │
// │2 │
// │3 │ ┌────────┐
// │4 │ │1234 │
// │5 │ │5678 │
// │6 │ └────────┘
// │7 │
// │8 │
// └──┘
rhs_cast = matches[1].as<Cast>();
} else {
rhs_cast = rhs_broadcast->value.as<Cast>();
}
if (!lhs_load || !rhs_cast) {
return {};
}
if (rhs_cast) {
bool is_i8_u8 = rhs_cast->value.type().element_of() == Int(8) || rhs_cast->value.type().element_of() == UInt(8);
bool is_bf16 = rhs_cast->value.type().element_of() == BFloat(16);
if ((op_type == AMXOpType::Int8 && !is_i8_u8) || (op_type == AMXOpType::Bfloat16 && !is_bf16)) {
user_error << "Expected rhs type of " << (op_type == AMXOpType::Int8 ? "i8/u8" : "bf16")
<< ", got " << rhs_cast->value.type() << " instead.\nIn Expression: " << Expr(rhs_cast);
}
} else {
return {};
}
const auto *rhs_load = rhs_cast->value.as<Load>();
if (!rhs_load) {
return {};
}
const auto lhs_tile = get_3d_tile_index(lhs_load->index);
if (!lhs_tile.result) {
return {};
}
const int tile_x = lhs_tile.extent[0];
const int tile_y = lhs_tile.extent[1];
const int tile_r = lhs_tile.extent[2];
const int factor = reduce->value.type().lanes() / reduce->type.lanes();
Expr rhs_base;
Expr rhs_stride;
auto opt_base_stride = get_rhs_tile_index(rhs_load->index, amx_op_type_size(op_type), tile_x, tile_y, tile_r);
if (!opt_base_stride.result) {
return {};
}
rhs_base = opt_base_stride.base;
rhs_stride = opt_base_stride.stride;
if (op->index.type().lanes() != tile_x * tile_y ||
factor != tile_r) {
return {};
}
// {rows, colbytes, var, index}
auto lhs_var = Variable::make(Handle(), lhs_load->name);
const auto &lhs_load_type = lhs_load->type;
int element_width = lhs_load_type.bytes();
auto lhs_type = lhs_load_type.with_lanes(1024 / element_width);
auto lhs = Call::make(lhs_type, "tile_load", {tile_x, tile_r * element_width, lhs_var, lhs_tile.base * element_width, lhs_tile.stride[0] * element_width}, Call::Intrinsic);
auto rhs_var = Variable::make(Handle(), rhs_load->name);
const auto &rhs_load_type = rhs_load->type;
auto rhs_type = rhs_load_type.with_lanes(1024 / element_width);
auto rhs = Call::make(rhs_type, "tile_load", {tile_r / (4 / element_width), tile_y * 4, rhs_var, rhs_base * element_width, rhs_stride}, Call::Intrinsic);
auto res_type = amx_op_type_result_type(op_type);
// {rows, colbytes, acc, out, lhs, rhs}
auto out = Load::make(res_type, new_name, Ramp::make(0, 1, 256), {}, {}, const_true(256), {});
// 4 bytes for i32, f32
auto colbytes = tile_y * 4;
auto matmul = Call::make(res_type, "tile_matmul", {tile_x, colbytes, tile_r, out, lhs, rhs}, Call::Intrinsic);
auto store = Store::make(new_name, matmul, Ramp::make(0, 1, 256), Parameter(), const_true(256), ModulusRemainder());
return {true, std::move(store), tile_x, tile_y, tile_r};
}
Stmt convert_to_zero(const Store *op, int tile_x, int tile_y, const string &new_name) {
if (const auto *ramp = op->index.as<Ramp>()) {
if (const auto *bcast = op->value.as<Broadcast>()) {
if (is_const_one(ramp->stride) &&
is_const_zero(bcast->value) &&
(bcast->lanes == tile_x * tile_y)) {
auto rows = Cast::make(Int(16), tile_x);
auto bytes = op->value.type().bytes();
auto colbytes = Cast::make(Int(16), tile_y * bytes);
const auto &store_type = op->value.type();
// will be f32 or i32
auto tile_zero_type = store_type.with_lanes(1024 / store_type.bytes());
auto val = Call::make(tile_zero_type, "tile_zero", {rows, colbytes}, Call::Intrinsic);
auto store = Store::make(new_name, std::move(val), Ramp::make(0, 1, 256), Parameter(), const_true(256), ModulusRemainder());
return store;
}
}
}
return {};
}
Stmt convert_to_tile_store(const Store *op, const string &amx_name, int tile_x, int tile_y) {
auto tile = get_2d_tile_index(op->index);
if (tile.result && tile.extent[0] == tile_x && tile.extent[1] == tile_y) {
auto out = Variable::make(Handle(), op->name);
auto tile_type = op->value.type().with_lanes(256);
auto tile_val = Load::make(tile_type, amx_name, Ramp::make(0, 1, 256), {}, {}, const_true(256), {});
auto bytes = op->value.type().bytes();
internal_assert(bytes == 4) << "AMX store only supported for int32 and float32 output, not for " << op->value.type() << "\n";
// {tile_x, tile_y, var, base, stride}
auto store = Call::make(Int(32), "tile_store", {tile_x, tile_y * bytes, std::move(out), tile.base * bytes, tile.stride[0] * bytes, std::move(tile_val)}, Call::Intrinsic);
return Evaluate::make(std::move(store));
}
return {};
}
class ExtractTileOperations : public IRMutator {
using IRMutator::visit;
string tile_name;
string amx_name;
vector<Stmt> pending_stores;
bool in_allocate = false;
int found_tile_x = -1;
int found_tile_y = -1;
int found_tile_r = -1;
AMXOpType op_type;
Stmt visit(const Allocate *op) override {
if (op->memory_type == MemoryType::AMXTile) {
user_assert(
(op->type.is_int() && op->type.bits() == 32) ||
(op->type.is_float() && op->type.bits() == 32))
<< "scheduled tile operations must yield 32-bit integers or 32-bit floats";
if (op->type.is_int() && op->type.bits() == 32) {
op_type = AMXOpType::Int8;
} else {
op_type = AMXOpType::Bfloat16;
}
user_assert(!in_allocate) << "Already in AMX allocation: " << amx_name;
ScopedValue<string> old_amx_name(amx_name, op->name + ".amx");
ScopedValue<string> old_tile_name(tile_name, op->name);
ScopedValue<bool> old_in_alloc(in_allocate, true);
Stmt body = op->body;
pending_stores.clear();
body = mutate(body);
if (found_tile_x < 0 || found_tile_y < 0 || found_tile_r < 0) {
return op;
}
if (!pending_stores.empty()) {
// Really only need to go over the pending stores
body = mutate(body);
}
auto alloc_type = amx_op_type_result_type(op_type);
return Allocate::make(amx_name, alloc_type, MemoryType::AMXTile, {1}, const_true(), body);
}
return IRMutator::visit(op);
}
Stmt visit(const Free *op) override {
if (op->name != tile_name) {
return op;
}
return Free::make(amx_name);
}
Stmt visit(const ProducerConsumer *op) override {
if (op->name != tile_name) {
return IRMutator::visit(op);
}
auto body = mutate(op->body);
return ProducerConsumer::make(amx_name, op->is_producer, std::move(body));
}
Expr visit(const Load *op) override {
// Any tile load will be matched elsewhere, so a load here means that
// the AMX tile is used outside of a tile instruction.
user_assert(op->name != tile_name) << "AMX tile allocation used outside a tile instruction";
return IRMutator::visit(op);
}
Stmt visit(const Store *op) override {
if (op->name != tile_name) {
const auto *load = op->value.as<Load>();
if (!load || load->name != tile_name) {
return op;
}
auto store = convert_to_tile_store(op, amx_name, found_tile_x, found_tile_y);
user_assert(store.defined()) << "Store to AMX tile allocation of a non-tile value";
return store;
}
auto matmul = convert_to_matmul(op, amx_name, op_type);
if (matmul.result) {
user_assert(
(found_tile_x < 0 || matmul.tile_x == found_tile_x) &&
(found_tile_y < 0 || matmul.tile_y == found_tile_y) &&
(found_tile_r < 0 || matmul.tile_r == found_tile_r))
<< "Found different tile sizes for AMX tile allocation";
found_tile_x = matmul.tile_x;
found_tile_y = matmul.tile_y;
found_tile_r = matmul.tile_r;
return matmul.stmt;
}
if (found_tile_x < 0 || found_tile_y < 0) {
pending_stores.emplace_back(op);
return op;
}
auto zero = convert_to_zero(op, found_tile_x, found_tile_y, amx_name);
if (zero.defined()) {
return zero;
}
// Otherwise there is some other operation using the allocation, so we cannot use the AMX instructions
user_error << "Found non-tile operations for AMX tile allocation";
return op;
}
};
} // namespace
Stmt extract_tile_operations(const Stmt &s) {
return ExtractTileOperations().mutate(s);
}
} // namespace Internal
} // namespace Halide
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简介

MIT计算机科学和人工智能实验室的研究人员创造出一种专门设计简化图像处理的程序语言Halide,源代码托管在GitHub上,目前二进制程序只支持Mac OS X和Ubuntu 12
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