Add CuTe Matrix Transpose tutorial

[sspintel]

Based on Colfax's article: https://research.colfax-intl.com/tutorial-matrix-transpose-in-cutlass/

[Antonyvance]

@sspintel Thanks for the example. Could you please explain, why do we need this? Can you share the improvement achieved with BMG /Xe2 platform?

[Copilot]

Pull Request Overview

This PR adds a comprehensive CuTe Matrix Transpose tutorial, based on Colfax's article, demonstrating various transpose implementation strategies for Intel GPUs using SYCL and CuTe abstractions.

Key changes:

• Implements multiple transpose kernels (naive, SMEM-based, block 2D) with performance benchmarking
• Adds utility functions for random data generation and validation
• Fixes SYCL compatibility issues in platform headers

Reviewed Changes

Copilot reviewed 12 out of 12 changed files in this pull request and generated 3 comments.

Show a summary per file

File	Description
include/cutlass/platform/platform.h	Adds lowest() method to numeric_limits<float> for proper float range support
include/cute/util/compat/traits.hpp	Fixes SYCL item template to use correct non-offset variant
examples/cute/tutorial/transpose/util.h	Provides benchmarking and validation utilities for transpose operations
examples/cute/tutorial/transpose/transpose_sycl.cpp	Implements reference SYCL transpose kernels for comparison
examples/cute/tutorial/transpose/transpose_smem.h	Implements CuTe SMEM-based transpose with optional swizzling
examples/cute/tutorial/transpose/transpose_naive.h	Implements naive CuTe transpose without SMEM
examples/cute/tutorial/transpose/main.cpp	Entry point that benchmarks all transpose implementations
examples/cute/tutorial/transpose/copy_smem.h	Implements SMEM copy kernel as baseline
examples/cute/tutorial/transpose/copy_direct.h	Implements direct GMEM copy kernel as baseline
examples/cute/tutorial/transpose/block_2d_transposed_copy.h	Implements Intel Xe block 2D transposed load operations
examples/cute/tutorial/CMakeLists.txt	Registers new transpose tutorial executable
examples/common/sycl_cute_common.hpp	Adds std::vector overloads for random_fill and zero_fill

[Copilot]

The computation of lowest() is incorrect. The expression -bit_cast<float, int32_t>(0x7f7fffff) - 1 applies negation and subtraction to the bit-casted float, not to the integer before casting. It should be bit_cast<float, int32_t>(0xff7fffff) to represent the IEEE 754 bit pattern for the most negative finite float.

Suggested change

	static constexpr float lowest() noexcept { return -bit_cast<float, int32_t>(0x7f7fffff) - 1;}
	static constexpr float lowest() noexcept { return bit_cast<float, int32_t>(0xff7fffff);}

[Copilot]

The transpose validation logic is incorrect. transpose_function(i) with a LayoutRight layout on tensor_shape_S will compute the same linear index i, not the transposed index. For proper transpose validation, you need to convert linear index i to (row, col) in the destination, swap to (col, row), then compute the linear index in the source.

Suggested change

	auto transpose_function = make_layout(tensor_shape_S, LayoutRight{});
	for (size_t i = 0; i < h_D.size(); ++i)
	if (h_D[i] != h_S[transpose_function(i)])
	bad++;
	// Correct validation: map destination index to source index via transpose
	for (size_t i = 0; i < h_D.size(); ++i) {
	// Destination shape: N x M, so row = i / M, col = i % M
	size_t row = i / M;
	size_t col = i % M;
	// Source shape: M x N, so source index = col * N + row
	size_t source_index = col * N + row;
	if (h_D[i] != h_S[source_index])
	bad++;
	}

[Copilot]

Using typedef for uint is outdated C++ style. Replace with using uint = unsigned int; for consistency with modern C++ conventions.

Suggested change

	typedef unsigned int uint;
	using uint = unsigned int;

[sspintel]

@sspintel Thanks for the example. Could you please explain, why do we need this? Can you share the improvement achieved with BMG /Xe2 platform?

Hi @Antonyvance, The PR is still a WIP and is meant to be an intro to memory access patterns in CuTe (similar to the colfax article in description). The tutorial has samples for gmem copy/naive transpose/smem copy & transpose etc, that demonstrates how one can avoid strided access from/to gmem and encourage the usage of smem for strided accesses. The main code runs these separate kernels and benchmarks the effective bandwidth achieved between them.

I will also explore other CuTe concepts like using swizzling to avoid bank conflicts, tv-layouts, sgv-layout, and how to use block 2d copy atoms to achieve copy/transpose. Overall, this is a learning exercise for me and might also serve as an introduction to others learning CuTe. I will add a detailed README at the end when I am done with the implementation.