<!-- Autogenerated by mlir-tblgen; don't manually edit -->
# 'symbol' Dialect Passes

## `-encoding-to-symbol`

_Convert tensor encoding to bind_symbolic_shape._

## `-erase-symbol`

_Erase symbols._

Remove symbols from the function, used to clean up symbolic shape annotations when symbol analysis is not needed

## `-propagate-symbol`

_Propagate symbols through operations._

Propagate symbols bound for argument by replacing the usage of 
`tensor.dim`, to make the relationships between tensor dynamic 
dims more explicit.

1. bind `symbolic_int` to func arguments (if not already bound)
   ensures each dynamic dim is represented by a symbol
2. use `reifyResultShapes` to bind each op's tensor result with 
   `bind_symbolic_shape`, with dynamic output dims represented
   by `tensor.dim`, or `affine.apply` with `tensor.dim` operands
3. propagate symbol by replacing `tensor.dim` with `symbolic_int`.
   ensures that all dynamic dims are symbolic

Example:

```mlir
%dim0 = tensor.dim %arg0, %c0 : tensor<?x640xf16>
%out0 = tensor.empty(%dim0) : tensor<?x640xf16>
%add0 = linalg.elemwise_binary ins(%arg0, %arg0) outs(%out0)
%concat = tensor.concat dim(0) %add0, %add0 : tensor<?x640xf16>
%dim1 = tensor.dim %concat, %c0 : tensor<?x640xf16>
%out1 = tensor.empty(%dim1) : tensor<?x640xf16>
%add1 = linalg.elemwise_binary ins(%concat, %concat) outs(%out1)
```

will be transformed into:

```mlir
%S0 = symbol.symbolic_int @S0 : index
%S1 = symbol.symbolic_int @S1 [%S0, %S0], affine_map<()[s0, s1] -> (s0 + s1)>
symbol.bind_symbolic_shape %arg0, [%S0]

%out0 = tensor.empty(%S0) : tensor<?x640xf16>
symbol.bind_symbolic_shape %0, [%S0]
%add0 = linalg.elemwise_binary ins(%arg0, %arg0) outs(%out0)
symbol.bind_symbolic_shape %add0, [%S0]

// result dim for concat will be reified to an `affine.apply` op.
// this pass keeps the affine map in `%S1`
%concat = tensor.concat dim(0) %add0, %add0 : tensor<?x640xf16>
symbol.bind_symbolic_shape %concat, [%S1]

%out1 = tensor.empty(%S1) : tensor<?x640xf16>
symbol.bind_symbolic_shape %out1, [%S1]
%add1 = linalg.elemwise_binary ins(%concat, %concat) outs(%out1)
symbol.bind_symbolic_shape %add1, [%S1]
```

## `-symbol-to-encoding`

_Convert bind_symbolic_shape to tensor encoding._

## `-unfold-symbolic-int`

_Replace symbol.symbolic_int op by concrete values_

Replace all symbol.symbolic_int based on bind_symbolic_shape.
All symbol.symbolic_int should be replaceable by the first use
in bind_symbolic_shape. This pass doesn't do any reifying symbols.
Check propagate-symbol pass to do the reifying.

Constraints:

1. symbolic_int should be replaceable by the first bind_symbolic_shape that it's binded to.
2. first bind_symbolic_shape that a symbolic_int's binded, should have indentity affine map
e.g. symbol.bind_symbolic_shape %arg0, [%S0, %S1], affine_map<()[s0, s1] -> (s0, 640, s1)> : tensor<?x640x?xf16>
3. first bind_symbolic_shape that a symbolic_int's binded, shouldn't bind to a tensor.empty

Example of invalid bind_symbolic_shape ops:

```mlir
symbol.bind_symbolic_shape %arg0, [%S0, %S1], affine_map<()[s0, s1] -> (s0/2, s0/s1, s1+1)> : tensor<?x640x?xf16>
%empty = tensor.empty(%S2, %S3) : tensor<?x?xf16>
symbol.bind_symbolic_shape %empty, [%S2, %S3], affine_map<()[s0, s1] -> (s0, s1)> : tensor<?x?xf16>
```

Example before and after the pass:

```mlir
func.func @test_already_bind_symbol_0(%arg0: tensor<?x640x?xf16>) -> tensor<?x640x?xf16> {
  %S0 = symbol.symbolic_int @S0 {max_val = 9223372036854775807 : i64, min_val = 0 : i64} : index
  %S1 = symbol.symbolic_int @S1 {max_val = 9223372036854775807 : i64, min_val = 0 : i64} : index
  symbol.bind_symbolic_shape %arg0, [%S0, %S1], affine_map<()[s0, s1] -> (s0, 640, s1)> : tensor<?x640x?xf16>
}
```

will be transformed into:

```mlir
func.func @test_already_bind_symbol_0(%arg0: tensor<?x640x?xf16>) -> tensor<?x640x?xf16> {
  %c0 = arith.constant 0 : index
  %dim = tensor.dim %arg0, %c0 : tensor<?x640x?xf16>
  %c2 = arith.constant 2 : index
  %dim_0 = tensor.dim %arg0, %c2 : tensor<?x640x?xf16>
}
```