// *** Tensor Expressions ***
//
// This tutorial covers basics of NNC's tensor expressions, shows basic APIs to
// work with them, and outlines how they are used in the overall TorchScript
// compilation pipeline. This doc is permanently a "work in progress" since NNC
// is under active development and things change fast.
//
// This Tutorial's code is compiled in the standard pytorch build, and the
// executable can be found in `build/bin/tutorial_tensorexpr`.
//
// *** What is NNC ***
//
// NNC stands for Neural Net Compiler. It is a component of TorchScript JIT
// and it performs on-the-fly code generation for kernels, which are often a
// combination of multiple aten (torch) operators.
//
// When the JIT interpreter executes a torchscript model, it automatically
// extracts subgraphs from the torchscript IR graph for which specialized code
// can be JIT generated. This usually improves performance as the 'combined'
// kernel created from the subgraph could avoid unnecessary memory traffic that
// is unavoidable when the subgraph is interpreted as-is, operator by operator.
// This optimization is often referred to as 'fusion'. Relatedly, the process of
// finding and extracting subgraphs suitable for NNC code generation is done by
// a JIT pass called 'fuser'.
//
// *** What is TE ***
//
// TE stands for Tensor Expressions. TE is a commonly used approach for
// compiling kernels performing tensor (~matrix) computation. The idea behind it
// is that operators are represented as a mathematical formula describing what
// computation they do (as TEs) and then the TE engine can perform mathematical
// simplification and other optimizations using those formulas and eventually
// generate executable code that would produce the same results as the original
// sequence of operators, but more efficiently.
//
// NNC's design and implementation of TE was heavily inspired by Halide and TVM
// projects.
#include <iostream>
#include <string>
#include <c10/util/irange.h>
#include <torch/csrc/jit/ir/ir.h>
#include <torch/csrc/jit/ir/irparser.h>
#include <torch/csrc/jit/tensorexpr/eval.h>
#include <torch/csrc/jit/tensorexpr/expr.h>
#include <torch/csrc/jit/tensorexpr/ir.h>
#include <torch/csrc/jit/tensorexpr/ir_printer.h>
#include <torch/csrc/jit/tensorexpr/ir_simplifier.h>
#include <torch/csrc/jit/tensorexpr/kernel.h>
#include <torch/csrc/jit/tensorexpr/loopnest.h>
#include <torch/csrc/jit/tensorexpr/stmt.h>
#include <torch/csrc/jit/tensorexpr/tensor.h>
#include <torch/torch.h>
using namespace torch::jit::tensorexpr;
#ifdef TORCH_ENABLE_LLVM
// Helper function to print a snippet from a big multi-line string
static void printLinesToFrom(const std::string& input_str, int from, int to);
#endif
int main(int argc, char* argv[]) {
std::cout << "*** Structure of tensor expressions and statements ***"
<< std::endl;
{
// A tensor expression is a tree of expressions. Each expression has a type,
// and that type defines what sub-expressions the current expression has.
// For instance, an expression of type 'Mul' would have a type 'kMul' and
// two subexpressions: LHS and RHS. Each of these two sub-expressions could
// also be a 'Mul' or some other expression.
//
// Let's construct a simple TE:
ExprPtr lhs = alloc<IntImm>(5);
ExprPtr rhs = alloc<Var>("x", kInt);
ExprPtr mul = alloc<Mul>(lhs, rhs);
std::cout << "Tensor expression: " << *mul << std::endl;
// Prints: Tensor expression: 5 * x
// Here we created an expression representing a 5*x computation, where x is
// an int variable.
// Another, probably a more convenient, way to construct tensor expressions
// is to use so called expression handles (as opposed to raw expressions
// like we did in the previous example). Expression handles overload common
// operations and allow us to express the same semantics in a more natural
// way:
ExprHandle l = 5;
ExprHandle r = Var::make("x", kInt);
ExprHandle m = l * r;
std::cout << "Tensor expression: " << *m.node() << std::endl;
// Prints: Tensor expression: 5 * x
// Converting from handles to raw expressions and back is easy:
ExprHandle handle = Var::make("x", kInt);
ExprPtr raw_expr_from_handle = handle.node();
ExprPtr raw_expr = alloc<Var>("x", kInt);
ExprHandle handle_from_raw_expr = ExprHandle(raw_expr);
// We could construct arbitrarily complex expressions using mathematical
// and logical operations, casts between various data types, and a bunch of
// intrinsics.
ExprHandle a = Var::make("a", kInt);
ExprHandle b = Var::make("b", kFloat);
ExprHandle c = Var::make("c", kFloat);
ExprHandle x = ExprHandle(5) * a + b / (sigmoid(c) - 3.0f);
std::cout << "Tensor expression: " << *x.node() << std::endl;
// Prints: Tensor expression: float(5 * a) + b / ((sigmoid(c)) - 3.f)
// An ultimate purpose of tensor expressions is to optimize tensor
// computations, and in order to represent accesses to tensors data, there
// is a special kind of expression - a load.
// To construct a load we need two pieces: the base and the indices. The
// base of a load is a Buf expression, which could be thought of as a
// placeholder similar to Var, but with dimensions info.
//
// Let's construct a simple load:
BufHandle A("A", {64, 32}, kInt);
VarPtr i_var = alloc<Var>("i", kInt), j_var = alloc<Var>("j", kInt);
ExprHandle i(i_var), j(j_var);
ExprHandle load = Load::make(A.dtype(), A, {i, j});
std::cout << "Tensor expression: " << *load.node() << std::endl;
// Prints: Tensor expression: A[i, j]
// Tensor Expressions constitute Tensor Statements, which are used to
// represent computation of a given operator or a group of operators from a
// fusion group.
//
// There are three main kinds of tensor statements:
// - block
// - store
// - loop
//
// A Store represents a store to a single element of a tensor (or to a
// group of elements if it's a vectorized store). Store statements,
// similarly to Load expressions, have a base and indices, but on top of
// that they also include a value - an expression representing what needs
// to be stored at the given memory location. Let's create a Store stmt:
StmtPtr store_a = Store::make(A, {i, j}, i + j);
std::cout << "Store statement: " << *store_a << std::endl;
// Prints: Store statement: A[i, j] = i + j;
// An operator fills the entire tensor, not just a single element, and to
// represent this we need to use For stmt: let's wrap our store stmt with
// two nested loops to represent that variables i and j need to iterate
// over some ranges.
ForPtr loop_j_a = For::make(VarHandle(j_var), 0, 32, store_a);
ForPtr loop_i_a = For::make(VarHandle(i_var), 0, 64, loop_j_a);
std::cout << "Nested for loops: " << std::endl << *loop_i_a << std::endl;
// Prints:
// Nested for loops:
// for (const auto i : c10::irange(64)) {
// for (const auto j : c10::irange(32)) {
// A[i, j] = i + j;
// }
// }
// A Block statement is used when we need a sequence of other statements.
// E.g. if a fusion group contains several operators, we initially define
// separate loopnest for each of them and put them all into a common block:
BufHandle B("B", {64, 32}, kInt);
StmtPtr store_b = Store::make(B, {i, j}, A.load(i, j));
ForPtr loop_j_b = For::make(VarHandle(j_var), 0, 32, store_b);
ForPtr loop_i_b = For::make(VarHandle(i_var), 0, 64, loop_j_b);
BlockPtr block = Block::make({loop_i_a, loop_i_b});
std::cout << "Compound Block statement: " << std::endl
<< *block << std::endl;
// Prints:
// Compound Block statement:
// {
// for (const auto i : c10::irange(64)) {
// for (const auto j : c10::irange(32)) {
// A[i, j] = i + j;
// }
// }
// for (const auto i : c10::irange(64)) {
// for (const auto j : c10::irange(32)) {
// B[i, j] = A[i, j];
// }
// }
// }
// Manually constructing nested loops and blocks to represent a computation
// might be laborious, and instead we can use a 'Compute' API. This API
// requires us to specify dimensions and a lambda to compute a single
// element of the resulting tensor and returns a `Tensor` structure. This
// structure is simply a pair of a buffer that was created to represent the
// result of the computation (BufPtr) and a statement representing the
// computation itself (StmtPtr).
Tensor C =
Compute("C", {64, 32}, [&](const VarHandle& i, const VarHandle& j) {
return i * j;
});
std::cout << "Stmt produced by 'Compute' API: " << std::endl
<< *C.stmt() << std::endl;
// Prints:
// Stmt produced by 'Compute' API:
// for (const auto i : c10::irange(64)) {
// for (const auto j : c10::irange(32)) {
// C[i, j] = i * j;
// }
// }
// To construct statements to represent computations with reductions, we
// can use a 'Reduce' API - it is similar to 'Compute' but takes a couple
// of extra arguments defining how to perform the reduction. Let's define a
// simple 2D sum of C using that:
Tensor D = Reduce(
"D",
{},
Sum(),
[&](const VarHandle& i, const VarHandle& j) { return C.load(i, j); },
{64, 32});
std::cout << "Stmt produced by 'Reduce' API: " << std::endl
<< *D.stmt() << std::endl;
}
std::cout << "*** Loopnests transformations ***" << std::endl;
{
// When a statement for the computation is generated, we might want to
// apply some optimizations to it. These transformations allow us to end up
// with a statement producing the same results, but more efficiently.
//
// Let's look at a couple of transformations that are used in NNC. We will
// begin with constructing a Block statement like we did before.
Tensor C =
Compute("C", {64, 32}, [&](const VarHandle& i, const VarHandle& j) {
return i * (j + 1);
});
BufHandle c_buf(C.buf());
Tensor D =
Compute("D", {64, 32}, [&](const VarHandle& i, const VarHandle& j) {
return c_buf.load(i, j) - i;
});
StmtPtr block = Block::make({C.stmt(), D.stmt()});
std::cout << "Stmt produced by 'Compute' API: " << std::endl
<< *block << std::endl;
// Prints:
// Stmt produced by 'Compute' API:
// {
// for (const auto i : c10::irange(64)) {
// for (const auto j : c10::irange(32)) {
// C[i, j] = i * (j + 1);
// }
// }
// for (const auto i_1 : c10::irange(64)) {
// for (const auto j_1 : c10::irange(32)) {
// D[i_1, j_1] = (C[i_1, j_1]) - i_1;
// }
// }
// }
// One transformation we can apply to this computation is inlining: i.e.
// taking the expression that defines values of C and substituting a load
// from C with it.
// To do that, we first need to create a special object called LoopNest -
// all transformations are methods of this class. To create a loopnest we
// need to provide a list of output buffers and the root statement:
LoopNest nest(block, {D.buf()});
// We can always retrieve the Stmt back from LoopNest:
std::cout << "LoopNest root stmt: " << std::endl
<< *nest.root_stmt() << std::endl;
// Prints:
// LoopNest root stmt:
// {
// for (const auto i : c10::irange(64)) {
// for (const auto j : c10::irange(32)) {
// C[i, j] = i * (j + 1);
// }
// }
// for (const auto i_1 : c10::irange(64)) {
// for (const auto j_1 : c10::irange(32)) {
// D[i_1, j_1] = (C[i_1, j_1]) - i_1;
// }
// }
// }
// Now we can apply the inlining transformation:
nest.computeInline(C.buf());
std::cout << "Stmt after inlining:" << std::endl
<< *nest.root_stmt() << std::endl;
// Prints:
// Stmt after inlining:
// {
// for (const auto i : c10::irange(64)) {
// for (const auto j : c10::irange(32)) {
// D[i, j] = i * (j + 1) - i;
// }
// }
// }
// We can also apply algebraic simplification to a statement:
StmtPtr simplified = IRSimplifier::simplify(nest.root_stmt());
std::cout << "Stmt after simplification:" << std::endl
<< *simplified << std::endl;
// Prints:
// Stmt after simplification:
// {
// for (const auto i : c10::irange(64)) {
// for (const auto j : c10::irange(32)) {
// D[i, j] = i * j;
// }
// }
// }
// Many loopnest transformations are stateless and can be applied without
// creating a LoopNest object. In fact, we plan to make all transformations
// stateless.
// splitWithTail is one such transformation: it splits an iteration space
// of a given loop into two with a given factor.
ForPtr outer_loop = to<For>(to<Block>(simplified)->stmts().front());
LoopNest::splitWithTail(outer_loop, 13);
// Call simplifier once more to fold some arithmetic.
simplified = IRSimplifier::simplify(simplified);
std::cout << "Stmt after splitWithTail:" << std::endl
<< *simplified << std::endl;
// Prints:
// Stmt after splitWithTail:
// {
// for (const auto i_outer : c10::irange(4)) {
// for (const auto i_inner : c10::irange(13)) {
// for (const auto j : c10::irange(32)) {
// D[i_inner + 13 * i_outer, j] = i_inner * j + 13 * (i_outer * j);
// }
// }
// }
// for (const auto i_tail : c10::irange(12)) {
// for (const auto j : c10::irange(32)) {
// D[i_tail + 52, j] = i_tail * j + 52 * j;
// }
// }
// }
// NNC supports a wide range of loop nest transformations, which we are not
// listing here. Please refer to documentation in
// https://github.com/pytorch/pytorch/blob/master/torch/csrc/jit/tensorexpr/loopnest.h
// for more details.
}
std::cout << "*** Codegen ***" << std::endl;
{
// An ultimate goal of tensor expressions is to be provide a mechanism to
// execute a given computation in the fastest possible way. So far we've
// looked at how we could describe what computation we're interested in, but
// we haven't looked at how to actually execute it.
//
// All we've been dealing with was just symbols with no actual data
// associated, in this section we would look at how we can bridge that gap.
// Let's start by constructing a simple computation for us to work with:
BufHandle A("A", {64, 32}, kInt);
BufHandle B("B", {64, 32}, kInt);
Tensor X =
Compute("X", {64, 32}, [&](const VarHandle& i, const VarHandle& j) {
return A.load(i, j) + B.load(i, j);
});
// And let's lower it to a loop nest, as we did in the previous section. We
// can pass Tensor object directly:
LoopNest loopnest({X});
std::cout << *loopnest.root_stmt() << std::endl;
// Prints:
// {
// for (const auto i : c10::irange(64)) {
// for (const auto j : c10::irange(32)) {
// X[i, j] = (A[i, j]) + (B[i, j]);
// }
// }
// Now imagine that we have two actual tensors 64x32 that we want sum
// together, how do we pass those tensors to the computation and how do we
// carry it out?
//
// Codegen object is aimed at providing exactly that functionality. Codegen
// is an abstract class and concrete codegens are derived from it.
// Currently, we have three codegens:
// 1) Simple Evaluator,
// 2) LLVM Codegen for CPU,
// 3) CUDA Codegen.
// In this example we will be using Simple Evaluator, since it's available
// everywhere.
// To create a codegen, we need to provide the statement - it specifies the
// computation we want to perform - and a list of placeholders and tensors
// used in the computation. The latter part is crucial since that's the only
// way the codegen could use to correlate symbols in the statement to actual
// data arrays that we will be passing when we will actually be performing
// the computation.
//
// Let's create a Simple IR Evaluator codegen for our computation:
SimpleIREvaluator ir_eval(loopnest.root_stmt(), {A, B, X});
// We are using the simplest codegen and in it almost no work is done at the
// construction step. Real codegens such as CUDA and LLVM perform
// compilation during that stage so that when we're about to run the
// computation everything is ready.
// Let's now create some inputs and run our computation with them:
std::vector<int> data_A(64 * 32, 3); // This will be the input A
std::vector<int> data_B(64 * 32, 5); // This will be the input B
std::vector<int> data_X(64 * 32, 0); // This will be used for the result
// Now let's invoke our codegen to perform the computation on our data. We
// need to provide as many arguments as how many placeholders and tensors we
// passed at the codegen construction time. A position in these lists would
// define how real data arrays from the latter call (these arguments are
// referred to as 'CallArg's in our codebase) correspond to symbols
// (placeholders and tensors) used in the tensor expressions we constructed
// (these are referred to as 'BufferArg').
// Thus, we will provide three arguments: data_A, data_B, and data_X. data_A
// contains data for the placeholder A, data_B - for the placeholder B, and
// data_X would be used for contents of tensor X.
ir_eval(data_A, data_B, data_X);
// Let's print one of the elements from each array to verify that the
// computation did happen:
std::cout << "A[10] = " << data_A[10] << std::endl
<< "B[10] = " << data_B[10] << std::endl
<< "X[10] = A[10] + B[10] = " << data_X[10] << std::endl;
// Prints:
// A[10] = 3
// B[10] = 5
// X[10] = A[10] + B[10] = 8
}
std::cout << "*** Lowering TorchScript IR to TensorExpr IR ***" << std::endl;
{
// This section requires a LLVM-enabled PyTorch build, so we have to use a
// guard:
#ifdef TORCH_ENABLE_LLVM
// Often we would like to convert a TorchScript IR to TE rather than
// construct TE IR from scratch. NNC provides an API to perform such
// lowering: it takes a TorchScript graph and returns an object that can be
// used to invoke the generated kernel.
// This API is currently used by the TorchScript JIT fuser and can also be
// used ahead of time to pre-compile parts of a model.
//
// To get familiar with this API let's first start with defining a simple
// TorchScript graph:
const auto graph_string = R"IR(
graph(%A : Float(5, 3, strides=[3, 1], device=cpu),
%B : Float(5, 3, strides=[3, 1], device=cpu)):
%AB : Float(5, 3, strides=[3, 1]) = aten::mul(%A, %B)
%one : int = prim::Constant[value=1]()
%AAB : Float(5, 3, strides=[3, 1]) = aten::mul(%A, %AB)
%AAB_plus_B: Float(5, 3, strides=[3, 1]) = aten::add(%AAB, %B, %one)
return (%AAB_plus_B))IR";
auto graph = std::make_shared<torch::jit::Graph>();
parseIR(graph_string, &*graph);
// This graph defines a simple computation of A*A*B + B where A and B are
// input 5x3 tensors.
// To lower this TorchScript graph to TE, we just need to create a
// TensorExprKernel object. In its constructor it constructs the
// corresponding TE IR and compiles it for the given backend (in this
// example for CPU using LLVM compiler).
TensorExprKernel kernel(graph);
// We can retrieve the generated TE stmt from the kernel object:
StmtPtr kernel_stmt = kernel.getCodeGenStmt();
std::cout << "TE Stmt constructed from TorchScript: " << std::endl
<< *kernel_stmt << std::endl;
// Prints:
// TE Stmt constructed from TorchScript:
// {
// for (const auto v : c10::irange(5)) {
// for (const auto _tail_tail : c10::irange(3)) {
// aten_add[_tail_tail + 3 * v] = (tA[_tail_tail + 3 * v]) *
// ((tA[_tail_tail + 3 * v]) * (tB[_tail_tail + 3 * v])) +
// (tB[_tail_tail + 3 * v]);
// }
// }
// }
// We can also examine generated LLVM IR and assembly code:
std::cout << "Generated LLVM IR: " << std::endl;
auto ir_str = kernel.getCodeText("ir");
printLinesToFrom(ir_str, 15, 20);
// Prints:
// Generated LLVM IR:
// %9 = bitcast float* %2 to <8 x float>*
// %10 = load <8 x float>, <8 x float>* %9 ...
// %11 = bitcast float* %5 to <8 x float>*
// %12 = load <8 x float>, <8 x float>* %11 ...
// %13 = fmul <8 x float> %10, %12
// %14 = fmul <8 x float> %10, %13
std::cout << "Generated assembly: " << std::endl;
auto asm_str = kernel.getCodeText("asm");
printLinesToFrom(asm_str, 10, 15);
// Prints:
// Generated assembly:
// vmulps %ymm1, %ymm0, %ymm2
// vfmadd213ps %ymm1, %ymm0, %ymm2
// vmovups %ymm2, (%rax)
// vmovss 32(%rcx), %xmm0
// vmovss 32(%rdx), %xmm1
// vmulss %xmm1, %xmm0, %xmm2
// We can also execute the generated kernel:
auto A =
at::ones({5, 3}, torch::TensorOptions(torch::kCPU).dtype(at::kFloat)) *
2.0;
auto B =
at::ones({5, 3}, torch::TensorOptions(torch::kCPU).dtype(at::kFloat)) *
3.0;
std::vector<at::Tensor> inputs = {A, B};
std::vector<torch::IValue> stack = torch::fmap<torch::IValue>(inputs);
kernel.run(stack);
auto R = stack[0].toTensor();
// Let's print one of the elements from the result tensor to verify that the
// computation did happen and was correct:
std::cout << "R[2][2] = " << R[2][2] << std::endl;
// Prints:
// R[2][2] = 15
// [ CPUFloatType{} ]
#endif
}
return 0;
}
void printLinesToFrom(const std::string& input_str, int from, int to) {
std::istringstream f(input_str);
std::string s;
int idx = 0;
while (getline(f, s)) {
if (idx > from) {
std::cout << s << "\n";
}
if (idx++ > to) {
break;
}
}
}