yuanfz98 commented on issue #10211:
URL: https://github.com/apache/tvm/issues/10211#issuecomment-1057078163
Hello,
For semantic extension, I listed some items:
- commutativity (identifying for instance (x+y) with (y+x))
- associativity (identifying for instance (x+y)+z with x+(y+z))
- distributivity (x*(y+z) and x\*y+x\*z)
We may call tvm/arith library to do the job.
```cpp
bool EquivalentTerms(const PrimExpr& a, const PrimExpr& b) {
// For now, we just check the syntactic equality, but that could later
become a semantic test,
// for instance identifying computations modulo commutativity (like x+y
and y+x), or modulo
// associativity (like (x+y)+z and x+(y+z)), etc.
arith::Analyzer analyser;
PrimExpr a_simplified = analyser.Simplify(a);
PrimExpr b_simplified = analyser.Simplify(b);
return EqualTerms(a_simplified, b_simplified);
}
```
An example test :
```
def test_semantic_equiv_distributivity():
i1 = te.var("i1")
i2 = te.var("i2")
x = te.var("x")
y = te.var("y")
z = te.var("z")
dtype = "int32"
buffer = tvm.tir.decl_buffer((50,), dtype)
body = tvm.tir.SeqStmt(
[
tvm.tir.Store(buffer.data, x*(y+z), i1),
tvm.tir.Store(buffer.data, x*y+x*z, i2),
]
)
mod = tvm.IRModule.from_expr(tvm.tir.PrimFunc([i1, i2, x, y, z], body))
body = tvm.tir.transform.CommonSubexprElimTIR()(mod)
tvm.transform.PrintIR()(body)
```
And I got:
```
[15:10:03] /home/yuan/Coding/compiler/repos/tvm/src/ir/transform.cc:566:
PrintIR():
#[version = "0.0.5"]
@main = primfn(i1: int32, i2: int32, x: int32, y: int32, z: int32) -> () {
let cse_var_1: int32 = (x*(y + z))
{
buffer: Pointer(int32)[i1] = cse_var_1
buffer[i2] = cse_var_1
}
}
```
However I found that the arith system may not be able to do the
commutativity (x+y != y+x and x\*y != y\*x).
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