ExtractTileOperations.cpp
#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
