[FEA]: Efficient Intra-Tile Shift/Shuffle or Relaxed extract/cat Constraints

Issue には実装ファイルやテストが指定されていないため、まず ct.extract と ct.cat の Python tile API、およびそれらの 2 のべき乗形状の検証を追跡します。その経路を提案されている ct.shift API と比較し、適切なカバレッジを備えた、説明されているタイル内シフトまたは任意形状の代替案をサポートできれば完了と定義します。

Is this a new feature, an improvement, or a change to existing functionality?

New Feature

How would you describe the priority of this feature request?

Critical (currently preventing usage)

Please provide a clear description of problem this feature solves

I am implementing a wavefront-style parallel algorithm where each thread needs to access the value computed by its neighbor in the previous step. Mathematically, this represents a "Shift Right" operation on a 1D Tile residing in registers: new_vec[i] = old_vec[i-1].

Currently, cuTile enforces strict Power-of-2 shape constraints on extract and cat. This makes it impossible to implement a shift by extracting the first $N-1$ elements and concatenating a boundary value (e.g., splitting a size-128 tile into a size-1 boundary and a size-127 slice is forbidden).

Real usage example:
In stencil computations or dynamic programming wavefronts, data often flows diagonally or horizontally between threads. Without a register-level shift, developers are forced to use high-overhead workarounds:

1. Global Memory: Writing to global memory and reading back with an offset (scatter gather).
2. Matrix Multiplication: Constructing a shift matrix and using mma to perform the shift. This works but is computationally expensive (overkill) for a simple data movement operation.

Feature Description

As a high-performance kernel developer,
I want to efficiently shift or rotate elements within a Tile (intra-tile communication),
So that I can implement stencil and wavefront dependencies entirely within registers without incurring global memory latency or Tensor Core overhead.

Describe your ideal solution

I propose adding a dedicated primitive for intra-tile communication, which maps to efficient hardware instructions (like __shfl_up_sync or __shfl_down_sync in CUDA).

Proposed API:

# Shift elements to the right by 'shift_amount'.
# Elements shifted in are filled with 'fill_value'.
output_tile = ct.shift(input_tile, shift_amount=1, fill_value=0)

Alternative Solution:
Relax the Power-of-2 constraint for ct.extract and ct.cat. If the library allowed operations on arbitrary shapes (e.g., extracting a size-127 tile), users could manually implement shifts via slicing and concatenation:

# Ideally, this should be allowed:
slice = ct.extract(val, index=(0,), shape=(127,))
boundary = ct.full((1,), 0, dtype=ct.int32)
shifted = ct.cat(boundary, slice, axis=0)

Describe any alternatives you have considered

No response

Additional context

No response

Contributing Guidelines

• I agree to follow cuTile Python's contributing guidelines
• I have searched the open feature requests and have found no duplicates for this feature request