This section contains the passes defined by HEIR.

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# Passes

- 1: ApplyFoldersPasses
- 2: BGVToLWE
- 3: BGVToOpenfhe
- 4: CGGIPasses
- 5: CGGIToJaxite
- 6: CGGIToTfheRust
- 7: CGGIToTfheRustBool
- 8: CKKSToOpenfhe
- 9: CombToCGGI
- 10: ConvertIfToSelectPasses
- 11: ConvertSecretExtractToStaticExtractPasses
- 12: ConvertSecretForToStaticForPasses
- 13: ConvertSecretInsertToStaticInsertPasses
- 14: ConvertSecretWhileToStaticForPasses
- 15: ElementwiseToAffinePasses
- 16: ForwardInsertToExtractPasses
- 17: ForwardStoreToLoadPasses
- 18: FullLoopUnrollPasses
- 19: LinalgCanonicalizationsPasses
- 20: LinalgToTensorExt
- 21: LWEPasses
- 22: LWEToPolynomial
- 23: OpenfhePasses
- 24: OperationBalancerPasses
- 25: PolynomialPasses
- 26: PolynomialToStandard
- 27: SecretizePasses
- 28: SecretPasses
- 29: SecretToBGV
- 30: SecretToCKKS
- 31: StraightLineVectorizerPasses
- 32: TensorExtPasses
- 33: TensorToScalarsPasses
- 34: TosaToSecretArith
- 35: UnusedMemRefPasses
- 36: YosysOptimizerPasses

# 1 - ApplyFoldersPasses

`-apply-folders`

*Apply all folding patterns from canonicalize*

This pass applies all registered folding patterns greedily to the input IR. This is useful when running a full canonicalize is too slow, but applying folders before canonicalize is sufficient to simplify the IR for later passes, or even sufficient to then subsequently run a full canonicalize pass.

This is used to prepare an IR for `insert-rotate`

after fully unrolling
loops.

# 2 - BGVToLWE

`-bgv-to-lwe`

*Lower bgv to lwe dialect.*

This pass lowers the `bgv`

dialect to `lwe`

dialect.

# 3 - BGVToOpenfhe

`-bgv-to-openfhe`

*Lower bgv to openfhe dialect.*

This pass lowers the `bgv`

dialect to `Openfhe`

dialect.

# 4 - CGGIPasses

`-cggi-boolean-vectorize`

*Group different logic gates with the packed API*

This pass groups independent logic gates into a single call of the packed operations. Pass is based on the straight-line-vectorizer, but is fundamentally different. This pass combines any type of boolean gates and is not restricted to combining the same type of gate operand.

Pass is intended for the `FPT`

tfhe-rs API, where `packed_gates`

function get a
the boolean gates are passed as a string vector and a left and right vector of ciphertexts.
Each boolean gates specified in `gates`

is then applied element wise.

```
let outputs_ct = fpga_key.packed_gates(&gates, &ref_to_ct_lefts, &ref_to_ct_rights);
```

`-cggi-set-default-parameters`

*Set default parameters for CGGI ops*

This pass adds default parameters to all CGGI ops as `cggi_params`

named
attributes, overriding any existing attribute set with that name.

This pass is primarily for testing purposes, and as a parameter provider before a proper parameter selection mechanism is added. This pass should not be used in production.

The specific parameters are hard-coded in
`lib/Dialect/CGGI/Transforms/SetDefaultParameters.cpp`

.

# 5 - CGGIToJaxite

`-cggi-to-jaxite`

*Lower cggi to jaxite dialect.*

# 6 - CGGIToTfheRust

`-cggi-to-tfhe-rust`

*Lower cggi to tfhe_rust dialect.*

# 7 - CGGIToTfheRustBool

`-cggi-to-tfhe-rust-bool`

*Lower cggi to tfhe_rust_bool dialect.*

# 8 - CKKSToOpenfhe

`-ckks-to-openfhe`

*Lower ckks to openfhe dialect.*

This pass lowers the `ckks`

dialect to `Openfhe`

dialect.

# 9 - CombToCGGI

`-comb-to-cggi`

*Lower comb to cggi dialect.*

This pass lowers the `comb`

dialect to `cggi`

dialect.

# 10 - ConvertIfToSelectPasses

`-convert-if-to-select`

*Convert scf.if operations on secret conditions to arith.select operations.*

Conversion for If-operations that evaluate secret condition to alternative select operations.

# 11 - ConvertSecretExtractToStaticExtractPasses

`-convert-secret-extract-to-static-extract`

*Convert tensor.extract operations on secret index to static extract operations.*

Converts `tensor.extract`

operations that read value at secret index to alternative static `tensor.extract`

operations that extracts value at each index and conditionally selects the value extracted at the secret index.

Note: Running this pass alone does not result in a data-oblivious program; we have to run the `--convert-if-to-select`

pass to the resulting program to convert the secret-dependent If-operation to a Select-operation.

Example input:
`mlir func.func @main(%secretTensor: !secret.secret<tensor<32xi16>>, %secretIndex: !secret.secret<index>)) -> !secret.secret<i16> { ... %0 = secret.generic ins(%secretTensor, %secretIndex : !secret.secret<tensor<32xi16>>, !secret.secret<index>) { ^bb0(%tensor: tensor<32xi16>, %index: index): // Violation: tensor.extract loads value at secret index %extractedValue = tensor.extract %tensor[%index] : tensor<16xi32> ... }`

```
Output:
```mlir
func.func @main(%secretTensor: !secret.secret<tensor<32xi16>>, %secretIndex: !secret.secret<index>)) -> !secret.secret<i16> {
...
%0 = secret.generic ins(%secretTensor, %secretIndex : !secret.secret<tensor<32xi16>>, !secret.secret<index>) {
^bb0(%tensor: tensor<32xi16>, %index: index):
%extractedValue = affine.for %i=0 to 16 iter_args(%arg= %dummyValue) -> (i32) {
// 1. Check if %i matches %index
%cond = arith.cmpi eq, %i, %index : index
// 2. Extract value at %i
%value = tensor.extract %tensor[%i] : tensor<16xi32>
// 3. If %i matches %index, yield %value extracted in (2), else yield %dummyValue
%result = scf.if %cond -> (i32) {
scf.yield %value : i32
} else{
scf.yield %arg : i32
}
// 4. Yield result from (3)
affine.yield %result : i32
```

} … }

```
```
```

# 12 - ConvertSecretForToStaticForPasses

`-convert-secret-for-to-static-for`

*Convert secret scf.for ops to affine.for ops with constant bounds.*

Conversion for For-operation that evaluate secret bound(s) to alternative affine For-operation with constant bound(s).

It replaces data-dependent bounds with an If-operation to check the bounds, and conditionally execute and yield values from the For-operation’s body.
Note: Running this pass alone does not result in a data-oblivious program; we have to run the `--convert-if-to-select`

pass to the resulting program to convert the secret-dependent If-operation to a Select-operation.

Example input:

```
func.func @main(%secretTensor: !secret.secret<tensor<16xi32>>, %secretLower: !secret.secret<index>, %secretUpper: !secret.secret<index>) -> !secret.secret<i32> {
...
%0 = secret.generic ins(%secretTensor, %secretLower, %secretUpper : !secret.secret<tensor<16xi32>>, !secret.secret<index>, !secret.secret<index>){
^bb0(%tensor: tensor<16xi32>, %lower : index, %upper : index ):
...
%1 = scf.for %i = %lower to %upper step %step iter_args(%arg = %val) -> (i32) {
%extracted = tensor.extract %input[%i] : tensor<16xi32>
%sum = arith.addi %extracted, %arg : i32
scf.yield %sum : i32
} {lower = 0, upper = 16}
secret.yield %1 : i32
} -> !secret.secret<i32>
return %0 : !secret.secret<i32>
```

Output:

```
func.func @main(%secretTensor: !secret.secret<tensor<16xi32>>, %secretIndex: !secret.secret<index> {secret.secret}) -> !secret.secret<i32> {
...
%0 = secret.generic ins(%secretTensor, %secretLower, %secretUpper : !secret.secret<tensor<16xi32>>, !secret.secret<index>, !secret.secret<index>){
^bb0(%tensor: tensor<16xi32>, %lower : index, %upper : index ):
...
%1 = affine.for %i = 0 to 16 step %step iter_args(%arg = %val) -> (i32) {
%lowerCond = arith.cmpi sge, %i, %index : index
%upperCond = arith.cmpi slt, %i, %index : index
%cond = arith.andi %lowerCond, %upperCond : i1
%result = scf.if(%cond) -> (i32) {
%extracted = tensor.extract %input[%i] : tensor<16xi32>
%sum = arith.addi %extracted, %arg : i32
scf.yield %sum : i32
} else {
scf.yield %arg : i32
}
affine.yield %result : i32
} {lower = 0, upper = 16}
secret.yield %1 : i32
} -> !secret.secret<i32>
return %0 : !secret.secret<i32>
```

# 13 - ConvertSecretInsertToStaticInsertPasses

`-convert-secret-insert-to-static-insert`

*Convert tensor.insert operations on secret index to static insert operations.*

Converts `tensor.insert`

operations that write to secret index to alternative static `tensor.insert`

operations that inserts the inserted value at each index and conditionally selects the newly produced tensor that contains the value at the secret index.

Note: Running this pass alone does not result in a data-oblivious program; we have to run the `--convert-if-to-select`

pass to the resulting program to convert the secret-dependent If-operation to a Select-operation.

Example input:

```
func.func @main(%secretTensor: !secret.secret<tensor<32xi16>>, %secretIndex: !secret.secret<index>)) -> !secret.secret<i16> {
...
%0 = secret.generic ins(%secretTensor, %secretIndex : !secret.secret<tensor<32xi16>>, !secret.secret<index>) {
^bb0(%tensor: tensor<32xi16>, %index: index):
// Violation: tensor.insert writes value at secret index
%inserted = tensor.insert %newValue into %tensor[%index] : tensor<16xi32>
...
}
```

Output:

```
func.func @main(%secretTensor: !secret.secret<tensor<32xi16>>, %secretIndex: !secret.secret<index>)) -> !secret.secret<i16> {
...
%0 = secret.generic ins(%secretTensor, %secretIndex : !secret.secret<tensor<32xi16>>, !secret.secret<index>) {
^bb0(%tensor: tensor<32xi16>, %index: index):
%inserted = affine.for %i=0 to 16 iter_args(%inputArg = %tensor) -> tensor<16xi32> {
// 1. Check if %i matches the %index
%cond = arith.cmpi eq, %i, %index : index
// 2. Insert %newValue and produce %newTensor
%newTensor = tensor.insert %value into %inputArg[%i] : tensor<16xi32>
// 3. If %i matches %inputIndex, yield %newTensor, else yield unchanged input tensor
%finalTensor = scf.if %cond -> (i32) {
scf.yield %newTensor : tensor<16xi32>
} else{
scf.yield %inputArg : tensor<16xi32>
}
// 4. Yield final tensor
affine.yield %finalTensor : tensor<16xi32>
}
...
}
```

# 14 - ConvertSecretWhileToStaticForPasses

`-convert-secret-while-to-static-for`

*Convert secret scf.while ops to affine.for ops that have constant bounds.*

Convert scf.while with a secret condition to affine.for with constant bounds. It replaces the scf.condition operation found in the scf.while loop with an scf.if operation that conditionally executes operations in the while operation’s body and yields values.

A “max_iter” attribute should be specified as part of the secret-dependent scf.while operation to successfully transform to a secret-independent affine.for operation. This attribute determines the maximum number of iterations for the new affine.for operation.

Note: Running this pass alone does not result in a data-oblivious program; we have to run the `--convert-if-to-select`

pass to the resulting program to convert the secret-dependent If-operation to a Select-operation.

Example input:

```
// C-like code
int main(int secretInput) {
while (secretInput > 100) {
secretInput = secretInput * secretInput;
}
return secretInput;
}
// MLIR
func.func @main(%secretInput: !secret.secret<i16>) -> !secret.secret<i16> {
%c100 = arith.constant 100 : i16
%0 = secret.generic ins(%secretInput : !secret.secret<i16>) {
^bb0(%input: i16):
%1 = scf.while (%arg1 = %input) : (i16) -> i16 {
%2 = arith.cmpi sgt, %arg1, %c100 : i16
scf.condition(%2) %arg1 : i16
} do {
^bb0(%arg1: i16):
%3 = arith.muli %arg1, %arg1 : i16
scf.yield %3 : i16
} attributes {max_iter = 16 : i64}
secret.yield %1 : i16
} -> !secret.secret<i16>
return %0 : !secret.secret<i16>
}
```

Output:

```
func.func @main(%secretInput: !secret.secret<i16>) -> !secret.secret<i16> {
%c100 = arith.constant 100 : i16
%0 = secret.generic ins(%secretInput : !secret.secret<i16>) {
^bb0(%input: i16):
%1 = affine.for 0 to 16 iter_args(%arg1 = %input) -> (i16) {
%2 = arith.cmpi sgt, %arg1, %c100 : i16
%3 = scf.if (%2) -> i16{
%4 = arith.muli %arg1, %arg1 : i16
scf.yield %4 : i16
} else {
scf.yield %arg1 : i16
}
affine.yield %3 : i16
} attributes {max_iter = 16 : i64}
secret.yield %1 : i16
} -> !secret.secret<i16>
return %0 : !secret.secret<i16>
}
```

# 15 - ElementwiseToAffinePasses

`-convert-elementwise-to-affine`

*This pass lowers ElementwiseMappable operations to Affine loops.*

This pass lowers ElementwiseMappable operations over tensors to affine loop nests that instead apply the operation to the underlying scalar values.

Usage: ‘–convert-elementwise-to-affine=convert-ops=arith.mulf ' restrict conversion to mulf op from arith dialect.

‘–convert-elementwise-to-affine=convert-ops=arith.addf,arith.divf convert-dialects=bgv’ restrict conversion to addf and divf ops from arith dialect and all of the ops in bgv dialect.

–convert-elementwise-to-affine=convert-dialects=arith restrict conversion to arith dialect so ops only from arith dialect is processed.

–convert-elementwise-to-affine=convert-ops=arith.addf,arith.mulf restrict conversion only to these two ops - addf and mulf - from arith dialect.

#### Options

```
-convert-ops : comma-separated list of ops to run this pass on
-convert-dialects : comma-separated list of dialects to run this pass on
```

# 16 - ForwardInsertToExtractPasses

`-forward-insert-to-extract`

*Forward inserts to extracts within a single block*

This pass is similar to forward-store-to-load pass where store ops are forwarded load ops; here instead tensor.insert ops are forwarded to tensor.extract ops.

Does not support complex control flow within a block, nor ops with arbitrary subregions.

# 17 - ForwardStoreToLoadPasses

`-forward-store-to-load`

*Forward stores to loads within a single block*

This pass is a simplified version of mem2reg and similar passes. It analyzes an operation, finding all basic blocks within that op that have memrefs whose stores can be forwarded to loads.

Does not support complex control flow within a block, nor ops with arbitrary subregions.

# 18 - FullLoopUnrollPasses

`-full-loop-unroll`

*Fully unroll all loops*

Scan the IR for affine.for loops and unroll them all.

# 19 - LinalgCanonicalizationsPasses

`-linalg-canonicalizations`

*This pass canonicalizes the linalg.transpose operation of a constant into a transposed constant.*

This pass canonicalizes the linalg.transpose operation of a constant into a transposed constant.

# 20 - LinalgToTensorExt

`-linalg-to-tensor-ext`

*Lower linalg.matmul to arith and tensor_ext dialects.*

This pass lowers the `linalg.matmul`

to a mixture of affine, tensor, and
via the Halevi-Shoup and squat matrix multiplication algorithms.

# 21 - LWEPasses

`-lwe-add-client-interface`

*Add client interfaces to (R)LWE encrypted functions*

This pass adds encrypt and decrypt functions for each compiled function in the IR. These functions maintain the same interface as the original function, while the compiled function may lose some of this information by the lowerings to ciphertext types (e.g., a scalar ciphertext, when lowered through RLWE schemes, must be encoded as a tensor).

#### Options

```
-use-public-key : If true, generate a client interface that uses a public key for encryption.
-one-value-per-helper-fn : If true, split encryption helpers into separate functions for each SSA value.
```

`-lwe-set-default-parameters`

*Set default parameters for LWE ops*

This pass adds default parameters to all `lwe`

types as the `lwe_params`

attribute, and for `lwe`

ops as the `params`

attribute, overriding any
existing attributes set with those names.

This pass is primarily for testing purposes, and as a parameter provider before a proper parameter selection mechanism is added. This pass should not be used in production.

The specific parameters are hard-coded in
`lib/Dialect/LWE/Transforms/SetDefaultParameters.cpp`

.

# 22 - LWEToPolynomial

`-lwe-to-polynomial`

*Lower lwe to polynomial dialect.*

This pass lowers the `lwe`

dialect to `polynomial`

dialect.

# 23 - OpenfhePasses

`-openfhe-configure-crypto-context`

*Configure the crypto context in OpenFHE*

This pass generates helper functions to generate and configure the OpenFHE crypto context for the given function. Generating the crypto context sets the appropriate encryption parameters, while the configuration generates the necessary evaluation keys (relinearization and rotation keys).

For example, for an MLIR function `@my_func`

, the generated helpers have the following signatures

```
func.func @my_func__generate_crypto_context() -> !openfhe.crypto_context
func.func @my_func__configure_crypto_context(!openfhe.crypto_context, !openfhe.private_key) -> !openfhe.crypto_context
```

#### Options

```
-entry-function : Default entry function name of entry function.
```

# 24 - OperationBalancerPasses

`-operation-balancer`

*This pass balances addition and multiplication operations.*

This pass examines a tree or graph of add and multiplication operations and balances them to minimize the depth of the tree. This exposes better parallelization and reducing the multiplication depth can decrease the parameters used in FHE, which improves performance. This pass is not necessarily optimal, as there may be intermediate computations that this pass does not optimally minimize the depth for.

The algorithm is to analyze a graph of addition operations and do a depth-first search for the operands (from the last computed values in the graph). If there are intermediate computations that are used more than once, then the pass treats that computation as its own tree to balance instead of trying to minimize the global depth of the tree.

This pass only runs on addition and multiplication operations on the arithmetic dialect that are encapsulated inside a secret.generic.

This pass was inspired by section 2.6 of ‘EVA Improved: Compiler and Extension Library for CKKS’ by Chowdhary et al.

# 25 - PolynomialPasses

`-convert-polynomial-mul-to-ntt`

*Rewrites polynomial operations to their NTT equivalents*

Applies a rewrite pattern to convert polynomial multiplication to the equivalent using the number-theoretic transforms (NTT) when possible.

Polynomial multiplication can be rewritten as polynomial.NTT on each operand, followed by modulo elementwise multiplication of the point-value representation and then the inverse-NTT back to coefficient representation.

# 26 - PolynomialToStandard

`-polynomial-to-standard`

*Lower polynomial to standard MLIR dialects.*

This pass lowers the `polynomial`

dialect to standard MLIR, a mixture of
affine, tensor, and arith.

# 27 - SecretizePasses

`-secretize`

*Adds secret argument attributes to entry function*

Adds a secret.secret attribute argument to each argument in the entry
function of an MLIR module. By default, the function is `main`

. This may be
overridden with the option -entry-function=top_level_func.

#### Options

```
-entry-function : entry function of the module
```

`-wrap-generic`

*Wraps regions using secret args in secret.generic bodies*

This pass wraps function regions of `func.func`

that use secret arguments in
`secret.generic`

bodies.

Secret arguments are annotated using a `secret.secret`

argument attribute.
This pass converts these to secret types and then inserts a `secret.generic`

body to hold the functions region. The output type is also converted to a
secret.

Example input:

```
func.func @main(%arg0: i32 {secret.secret}) -> i32 {
%0 = arith.constant 100 : i32
%1 = arith.addi %0, %arg0 : i32
return %1 : i32
}
```

Output:

```
func.func @main(%arg0: !secret.secret<i32>) -> !secret.secret<i32> {
%0 = secret.generic ins(%arg0 : !secret.secret<i32>) {
^bb0(%arg1: i32):
%1 = arith.constant 100 : i32
%2 = arith.addi %0, %arg1 : i32
secret.yield %2 : i32
} -> !secret.secret<i32>
return %0 : !secret.secret<i32>
}
```

# 28 - SecretPasses

`-secret-capture-generic-ambient-scope`

*Capture the ambient scope used in a secret.generic*

For each value used in the body of a `secret.generic`

op, which is defined
in the ambient scope outside the `generic`

, add it to the argument list of
the `generic`

.

`-secret-distribute-generic`

*Distribute generic ops through their bodies.*

Converts `generic`

ops whose region contains many ops into smaller
sequences of generic ops whose regions contain a single op, dropping the
`generic`

part from any resulting `generic`

ops that have no
`secret.secret`

inputs. If the op has associated regions, and the operands
are not secret, then the generic is distributed recursively through the
op’s regions as well.

This pass is intended to be used as part of a front-end pipeline, where a
program that operates on a secret type annotates the input to a region as
`secret`

, and then wraps the contents of the region in a single large
`secret.generic`

, then uses this pass to simplify it.

The `distribute-through`

option allows one to specify a comma-separated
list of op names (e.g., `distribute-thorugh="affine.for,scf.if"`

), which
limits the distribution to only pass through those ops. If unset, all ops
are distributed through when possible.

#### Options

```
-distribute-through : comma-separated list of ops that should be distributed through
```

`-secret-extract-generic-body`

*Extract the bodies of all generic ops into functions*

This pass extracts the body of all generic ops into functions, and replaces the generic bodies with call ops. Used as a sub-operation in some passes, and extracted into its own pass for testing purposes.

This pass works best when `--secret-generic-absorb-constants`

is run
before it so that the extracted function contains any constants used
in the generic op’s body.

`-secret-forget-secrets`

*Convert secret types to standard types*

Drop the `secret<...>`

type from the IR, replacing it with the contained
type and the corresponding cleartext computation.

`-secret-generic-absorb-constants`

*Copy constants into a secret.generic body*

For each constant value used in the body of a `secret.generic`

op, which is
defined in the ambient scope outside the `generic`

, add it’s definition into
the `generic`

body.

`-secret-generic-absorb-dealloc`

*Copy deallocs of internal memrefs into a secret.generic body*

For each memref allocated and used only within a body of a `secret.generic`

op, add it’s dealloc of the memref into its `generic`

body.

`-secret-merge-adjacent-generics`

*Merge two adjacent generics into a single generic*

This pass merges two immedaitely sequential generics into a single generic. Useful as a sub-operation in some passes, and extracted into its own pass for testing purposes.

# 29 - SecretToBGV

`-secret-to-bgv`

*Lower secret to bgv dialect.*

This pass lowers an IR with `secret.generic`

blocks containing arithmetic
operations to operations on ciphertexts with the BGV dialect.

The pass assumes that the `secret.generic`

regions have been distributed
through arithmetic operations so that only one ciphertext operation appears
per generic block. It also requires that `canonicalize`

was run so that
non-secret values used are removed from the `secret.generic`

’s block
arguments.

The pass requires that all types are tensors of a uniform shape matching the
dimension of the ciphertext space specified my `poly-mod-degree`

.

#### Options

```
-poly-mod-degree : Default degree of the cyclotomic polynomial modulus to use for ciphertext space.
-coefficient-mod-bits : Default number of bits of the prime coefficient modulus to use for the ciphertext space.
```

# 30 - SecretToCKKS

`-secret-to-ckks`

*Lower secret to ckks dialect.*

This pass lowers an IR with `secret.generic`

blocks containing arithmetic
operations to operations on ciphertexts with the CKKS dialect.

The pass assumes that the `secret.generic`

regions have been distributed
through arithmetic operations so that only one ciphertext operation appears
per generic block. It also requires that `canonicalize`

was run so that
non-secret values used are removed from the `secret.generic`

’s block
arguments.

The pass requires that all types are tensors of a uniform shape matching the
dimension of the ciphertext space specified my `poly-mod-degree`

.

#### Options

```
-poly-mod-degree : Default degree of the cyclotomic polynomial modulus to use for ciphertext space.
-coefficient-mod-bits : Default number of bits of the prime coefficient modulus to use for the ciphertext space.
```

# 31 - StraightLineVectorizerPasses

`-straight-line-vectorize`

*A vectorizer for straight line programs.*

This pass ignores control flow and only vectorizes straight-line programs within a given region.

#### Options

```
-dialect : Use this to restrict the dialect whose ops should be vectorized.
```

# 32 - TensorExtPasses

`-align-tensor-sizes`

*Resize tensors into tensors with a fixed size final dimension*

This pass resizes input tensors with arbitrary sizes into
tensors with whose final dimensions has a fixed size. All input tensors are
required to be one-dimensional. The `--size`

option specifies the size of the
final dimension of the output tensors, and is required to be a power of two.

To align the tensors in the input IR, the pass first zero pads the input to
the nearest power of two before replicating or splitting it into the output
shape determined by `size`

. The resulting transformation is described in a
`SIMDPackingAttr`

encoding attribute on the final tensor.

For example, with `size=16`

,a tensor with 7 elements will be zero-padded to 8
elements, and then replicated twice to fill a tensor with size 16. The
`SIMDPackingAttr`

will encode the input shape, the number of elements that
were zero-padded, and the output shape.

Input:

```
%0 = tensor.empty() : tensor<7xi32>
```

Output:

```
%0 = tensor.empty() : tensor<16xi32, #tensor_ext.simd_packing<in = [7], padding = [1], out = [16]>>
```

A tensor with 30 elements will be zero padded with 2 elements and split into two tensors of size 16.

Input:

```
%0 = tensor.empty() : tensor<30xi32>
```

Output:

```
%0 = tensor.empty() : tensor<2x16xi32, #tensor_ext.simd_packing<in = [30], padding = [2], out = [16]>>
```

Note that this pass does not insert any new operations like `reshape`

, but
rather transforms the IR to use tensors with a fixed dimension. This pass may
be used to align the sizes of tensors that represent plaintexts and
ciphertexts in RLWE schemes that support SIMD slots and operations.

#### Options

```
-size : Power of two size of the final dimension of the output tensors.
```

`-collapse-insertion-chains`

*Collapse chains of extract/insert ops into rotate ops when possible*

This pass is a cleanup pass for `insert-rotate`

. That pass sometimes leaves
behind a chain of insertion operations like this:

```
%extracted = tensor.extract %14[%c5] : tensor<16xi16>
%inserted = tensor.insert %extracted into %dest[%c0] : tensor<16xi16>
%extracted_0 = tensor.extract %14[%c6] : tensor<16xi16>
%inserted_1 = tensor.insert %extracted_0 into %inserted[%c1] : tensor<16xi16>
%extracted_2 = tensor.extract %14[%c7] : tensor<16xi16>
%inserted_3 = tensor.insert %extracted_2 into %inserted_1[%c2] : tensor<16xi16>
...
%extracted_28 = tensor.extract %14[%c4] : tensor<16xi16>
%inserted_29 = tensor.insert %extracted_28 into %inserted_27[%c15] : tensor<16xi16>
yield %inserted_29 : tensor<16xi16>
```

In many cases, this chain will insert into every index of the `dest`

tensor,
and the extracted values all come from consistently aligned indices of the same
source tensor. In this case, the chain can be collapsed into a single `rotate`

.

Each index used for insertion or extraction must be constant; this may
require running `--canonicalize`

or `--sccp`

before this pass to apply
folding rules (use `--sccp`

if you need to fold constant through control flow).

`-insert-rotate`

*Vectorize arithmetic FHE operations using HECO-style heuristics*

This pass implements the SIMD-vectorization passes from the HECO paper.

The pass operates by identifying arithmetic operations that can be suitably combined into a combination of cyclic rotations and vectorized operations on tensors. It further identifies a suitable “slot target” for each operation and heuristically aligns the operations to reduce unnecessary rotations.

This pass by itself does not eliminate any operations, but instead inserts
well-chosen rotations so that, for well-structured code (like unrolled affine loops),
a subsequent `--cse`

and `--canonicalize`

pass will dramatically reduce the IR.
As such, the pass is designed to be paired with the canonicalization patterns
in `tensor_ext`

, as well as the `collapse-insertion-chains`

pass, which
cleans up remaining insertion and extraction ops after the main simplifications
are applied.

Unlike HECO, this pass operates on plaintext types and tensors, along with
the HEIR-specific `tensor_ext`

dialect for its cyclic `rotate`

op. It is intended
to be run before lowering to a scheme dialect like `bgv`

.

`-rotate-and-reduce`

*Use a logarithmic number of rotations to reduce a tensor.*

This pass identifies when a commutative, associative binary operation is used to reduce all of the entries of a tensor to a single value, and optimizes the operations by using a logarithmic number of reduction operations.

In particular, this pass identifies an unrolled set of operations of the form (the binary ops may come in any order):

```
%0 = tensor.extract %t[0] : tensor<8xi32>
%1 = tensor.extract %t[1] : tensor<8xi32>
%2 = tensor.extract %t[2] : tensor<8xi32>
%3 = tensor.extract %t[3] : tensor<8xi32>
%4 = tensor.extract %t[4] : tensor<8xi32>
%5 = tensor.extract %t[5] : tensor<8xi32>
%6 = tensor.extract %t[6] : tensor<8xi32>
%7 = tensor.extract %t[7] : tensor<8xi32>
%8 = arith.addi %0, %1 : i32
%9 = arith.addi %8, %2 : i32
%10 = arith.addi %9, %3 : i32
%11 = arith.addi %10, %4 : i32
%12 = arith.addi %11, %5 : i32
%13 = arith.addi %12, %6 : i32
%14 = arith.addi %13, %7 : i32
```

and replaces it with a logarithmic number of `rotate`

and `addi`

operations:

```
%0 = tensor_ext.rotate %t, 4 : tensor<8xi32>
%1 = arith.addi %t, %0 : tensor<8xi32>
%2 = tensor_ext.rotate %1, 2 : tensor<8xi32>
%3 = arith.addi %1, %2 : tensor<8xi32>
%4 = tensor_ext.rotate %3, 1 : tensor<8xi32>
%5 = arith.addi %3, %4 : tensor<8xi32>
```

# 33 - TensorToScalarsPasses

`-convert-tensor-to-scalars`

*Effectively ‘unrolls’ tensors of static shape to scalars.*

This pass will convert a static-shaped tensor type to a TypeRange containing product(dim) copies of the element type of the tensor. This pass currently includes two patterns:

- It converts tensor.from_elements operations to the corresponding scalar inputs.
- It converts tensor.insert operations by updating the ValueRange corresponding to the converted input and updating it with the scalar to be inserted.

It also applies folders greedily to simplify, e.g., extract(from_elements).

Note: The pass is designed to be run on an IR, where the only operations
with tensor typed operands are tensor “management” operations such as insert/extract,
with all other operations (e.g., arith operations) already taking (extracted) scalar inputs.
For example, an IR where elementwise operations have been converted to scalar operations via
`--convert-elementwise-to-affine`

.

The pass might insert new tensor.from_elements operations or manually create the scalar ValueRange via inserting tensor.extract operations if any operations remain that operate on tensors. The pass currently applies irrespective of tensor size, i.e., might be very slow for large tensors.

TODO (#1023): Extend this pass to support more tensor operations, e.g., `tensor.slice`

#### Options

```
-max-size : Limits `unrolling` to tensors with at most max-size elements
```

# 34 - TosaToSecretArith

`-tosa-to-secret-arith`

*Lower tosa.sigmoid to secret arith dialects.*

This pass lowers the `tosa.sigmoid`

dialect to the polynomial approximation
-0.004 * x^3 + 0.197 * x + 0.5 (composed of arith, affine, and tensor operations).

This polynomial approximation of sigmoid only works over the range [-5, 5] and is taken from the paper ‘Logisitic regression over encrypted data from fully homomorphic encryption’ by Chen et al..

# 35 - UnusedMemRefPasses

`-remove-unused-memref`

*Cleanup any unused memrefs*

Scan the IR for unused memrefs and remove them.

This pass looks for locally allocated memrefs that are never used and deletes them. This pass can be used as a cleanup pass from other IR simplifications that forward stores to loads.

# 36 - YosysOptimizerPasses

`-yosys-optimizer`

*Invoke Yosys to perform circuit optimization.*

This pass invokes Yosys to convert an arithmetic circuit to an optimized boolean circuit that uses the arith and comb dialects.

Note that booleanization changes the function signature: multi-bit integers
are transformed to a tensor of booleans, for example, an `i8`

is converted
to `tensor<8xi1>`

.

The optimizer will be applied to each `secret.generic`

op containing
arithmetic ops that can be optimized.

Optional parameters:

`abc-fast`

: Run the abc optimizer in “fast” mode, getting faster compile time at the expense of a possibly larger output circuit.`unroll-factor`

: Before optimizing the circuit, unroll loops by a given factor. If unset, this pass will not unroll any loops.`print-stats`

: Prints statistics about the optimized circuits.`mode={Boolean,LUT}`

: Map gates to boolean gates or lookup table gates.

#### Statistics

```
total circuit size : The total circuit size for all optimized circuits, after optimization is done.
```