CPU C++ Kernels for x86 Processors

This skill provides patterns and guidance for developing optimized C++ kernels targeting x86 CPUs (Intel Xeon and compatible processors) with AVX2 and AVX512 intrinsics. Kernels are compiled via kernel-builder and distributed through the Hugging Face kernels ecosystem.

Who runs these commands? You, the agent — not a human. This is an autonomous loop: you write/edit the C++ kernel, build it, then run the scripts below as tools (via Bash) to check correctness, benchmark, and profile. You read each result, record it with trial_manager.py, decide the next change from the Phase 2 decision tree, and repeat until you hit early_stop_speedup or run all max_trials.

Supported Hardware

GEMM Acceleration: brgemm

For kernels that involve matrix multiplication (quantized GEMM, Flash Attention, MoE), large-M cases use at::native::cpublas::brgemm() — a PyTorch wrapper around oneDNN brgemm, which internally dispatches to AMX tile instructions on Intel Xeon (4th Gen+). Small-M cases (M ≤ 4 for bf16) fall back to hand-written tinygemm using AVX512 _mm512_dpbf16_ps. See brgemm_patterns.yaml for details.

Note: brgemm is NOT used in element-wise kernels (RMSNorm, activations, reductions). Those use AVX512 intrinsics directly.

When This Skill Applies

Use this skill when:

• Writing C++ CPU kernels with SIMD intrinsics for the HF kernels ecosystem
• Optimizing existing CPU kernels (e.g., adding AVX512 to a generic implementation)
• Implementing quantized GEMM kernels (INT4, NF4, FP4, FP8, MXFP4)
• Implementing Flash Attention or other attention kernels for CPU
• Building kernels with kernel-builder that target backend = "cpu"

Two-Phase Optimization Workflow

CPU kernel development has two distinct phases with different strategies.

Configuration — Read config.yaml first

At the start of every session, read scripts/config.yaml. It controls:

• max_trials — hard cap on Phase 2 optimization trials
• early_stop_speedup — speedup vs PyTorch baseline to trigger early stop (default: 3.0)
• perf_stat_enabled — if true, use perf stat for profiling (default)
• vtune_enabled — if true, use VTune for detailed microarchitecture analysis
• build_command — command to build the kernel package

Rules — Never Violate

1. ONLY modify C++ kernel files (.cpp, .hpp), torch_binding.cpp, and build.toml. Do NOT create benchmark or test scripts.
2. NEVER write custom timing code — ONLY use scripts/benchmark_cpu.py.
3. If a tool fails, STOP and report the error. Do NOT work around it with custom scripts.
4. Generated kernels must follow the runtime dispatch pattern with cpu_features.hpp — see references/runtime_dispatch.yaml.
5. Every kernel should have a generic ATen fallback that works on any CPU. If a specific path cannot have a meaningful fallback, use TORCH_CHECK(false, ...) with a clear error message.
6. Each SIMD tier (AVX2, AVX512) must be in a separate translation unit (.cpp file) with its own compiler flags in build.toml. Do NOT mix intrinsics from different ISA levels in the same file.
7. All SIMD implementations must handle edge cases (hidden_size not divisible by vector width).
8. AVX2 tier is optional — most CPU kernels go directly from generic fallback to AVX512. Only add AVX2 when it provides meaningful benefit for element-wise ops.
9. You MUST run all max_trials trials in Phase 2. Do NOT stop early due to plateau — the only valid early stop is speedup > early_stop_speedup.

Mandatory Tools

Benchmark discipline: Pin to a single NUMA node — numactl --cpunodebind=0 --membind=0 python scripts/benchmark_cpu.py .... See threading_patterns.yaml.

Phase 1: Correctness (Linear, No Branching)

Build the kernel tier by tier. Each tier must be correct before moving on.

Tier 0: Generic Fallback

• Implement using PyTorch ATen ops only (no intrinsics).
• This serves as the portable baseline that runs on any CPU.
• Must produce results matching the PyTorch reference within tolerance.
• File: <kernel>_cpu/<kernel>_cpu.cpp

# Validate + build
python scripts/validate_cpu_kernel.py .
kernel-builder build --release
pip install dist/*.whl --force-reinstall

# Benchmark (this also establishes the PyTorch baseline time)
python scripts/benchmark_cpu.py baseline.py --kernel-package my_kernel --op my_kernel.rms_norm

Tier 1: AVX2 (Optional)

• Add AVX2 implementation using _mm256_* intrinsics.
• Compile with -mavx2 -mfma -mf16c -fopenmp.
• Must be correct; performance improvement is a bonus.
• File: <kernel>_cpu/<kernel>_avx2.cpp

Tier 2: AVX512

• Add AVX512 implementation using _mm512_* intrinsics.
• Compile with -mavx512f -mavx512bf16 -mavx512vl -mavx512dq -mavx512bw -mavx512vbmi -mfma -mf16c -fopenmp.
• For GEMM kernels using brgemm, additionally add -mamx-tile -mamx-bf16 -mamx-int8.
• This is the entry point to Phase 2 — performance optimization starts here.
• File: <kernel>_cpu/<kernel>_avx512.cpp

Phase 2: Performance Exploration (Branching, With Backtracking)

Once AVX512 is correct, optimize for peak performance. This phase uses the trial manager with branching.

# Initialize Phase 2 trials
python scripts/trial_manager.py init <kernel_name> baseline.py

# For each trial:
# 1. Modify kernel code (AVX512 intrinsics, or brgemm for GEMM kernels)
# 2. Build
kernel-builder build --release && pip install dist/*.whl --force-reinstall
# 3. Benchmark
python scripts/benchmark_cpu.py baseline.py --kernel-package <pkg> --op <func>
# 4. Save trial
python scripts/trial_manager.py save <kernel_name> <dir> --parent <parent_id> --strategy "description"
# 5. Record result
python scripts/trial_manager.py result <kernel_name> <trial_id> --correctness pass --speedup <float> --baseline_us <float> --kernel_us <float>
# 6. Profile (after t1, or when plateaued)
python scripts/cpu_profiler.py --kernel-package <pkg> --op <func>

Phase 2 Decision Tree

Optimization Search Space (Phase 2)

These tables are a starting menu of values seen in existing kernels, not an exhaustive recipe. Use them to seed trials, but when a branch plateaus, prefer a structurally different idea (algorithm, fusion, memory strategy) over sweeping these knobs further. See the try-harder tree in optimization_levels.yaml.

GEMM kernels (quantized GEMM, Flash Attention, MoE):

Element-wise kernels (RMSNorm, activations):

Phase 2 Finalization

python scripts/trial_manager.py finalize <kernel_name> output/
# Re-run benchmark without cached baseline for final accurate comparison
python scripts/benchmark_cpu.py baseline.py --kernel-package <pkg> --op <func>

Reference Docs — Read During Phase 1

Reference Docs — Read During Phase 2

Core CPU Kernel Patterns

Runtime Dispatch (Required for All Kernels)

Every CPU kernel has its own cpu_features.hpp (in its own namespace) and dispatches at runtime. Most kernels dispatch as AVX512 → fallback (no AVX2 tier):

// my_kernel_cpu/cpu_features.hpp — each kernel has its OWN copy
namespace my_kernel_cpu {
class CPUFeatures {
public:
    static bool hasAVX512BF16() { /* CPUID + XCR0 checks */ }
    static bool hasAVX2() { /* CPUID check */ }
    // GEMM kernels also check: static bool hasAMX() { ... }
};
}

// my_kernel_cpu/my_kernel_cpu.cpp — dispatcher
#include "cpu_features.hpp"
#include "my_kernel_avx512.hpp"

void my_kernel(torch::Tensor& out, const torch::Tensor& input, ...) {
    if (CPUFeatures::hasAVX512BF16()) {
        avx512::my_kernel_impl(out, input, ...);
    } else {
        // ATen fallback — inline or in a separate _fallback.cpp
        out = torch::some_aten_op(input, ...);
    }
}

Note: Only rmsnorm has a three-tier dispatch (AVX512 → AVX2 → ATen). GEMM kernels skip AVX2. Flash-attn2 additionally requires AMX via hasAllRequiredFeatures().

Full pattern: runtime_dispatch.yaml

build.toml Multi-Target Compilation

Each SIMD tier is a separate [kernel.*] section with its own compiler flags. The include directive is required for header resolution:

[kernel.my_kernel_cpu]
backend = "cpu"
depends = ["torch"]
include = ["my_kernel_cpu"]
src = [
    "my_kernel_cpu/my_kernel_cpu.cpp",
    "my_kernel_cpu/my_kernel_cpu_torch.cpp",
    "my_kernel_cpu/my_kernel_cpu.hpp",
    "my_kernel_cpu/cpu_features.hpp",
]

[kernel.my_kernel_cpu_avx512]
backend = "cpu"
# Note: For GEMM kernels (e.g., flash-attn2, megablocks), you must also include "-mamx-tile", "-mamx-bf16", "-mamx-int8"
cxx-flags = ["-mavx512f", "-mavx512bf16", "-mavx512vl", "-mavx512dq", "-mavx512bw", "-mavx512vbmi", "-mfma", "-mf16c", "-fopenmp"]
depends = ["torch"]
include = ["my_kernel_cpu"]
src = [
    "my_kernel_cpu/my_kernel_avx512.cpp",
    "my_kernel_cpu/my_kernel_avx512.hpp",
]

Note: Every section needs include = ["<kernel_dir>"] for header resolution. The _torch.cpp file bridges Python-facing declarations to the C++ dispatcher. AVX2 section is optional (only rmsnorm has one).

Full pattern: build_system.yaml

torch_binding.cpp Registration

All kernels use registration.h macros for op registration:

#include "registration.h"

// Forward declarations
#if defined(CPU_KERNEL)
torch::Tensor my_kernel_cpu_forward(torch::Tensor input, torch::Tensor weight, float eps);
#endif

TORCH_LIBRARY_EXPAND(TORCH_EXTENSION_NAME, ops) {
    ops.def("forward(Tensor input, Tensor weight, float eps) -> Tensor");
    ops.impl("forward", torch::kCPU, &my_kernel_cpu_forward);
}

REGISTER_EXTENSION(TORCH_EXTENSION_NAME)

Note: registration.h is provided by kernel-builder. Multi-device kernels (rmsnorm, megablocks) use #if defined(CPU_KERNEL) / #elif defined(CUDA_KERNEL) guards.

Vector Type Abstractions (AVX512)

Wrap raw intrinsics in typed vector classes for readability:

// cpu_types_avx512.hpp
struct FP32Vec16 {
    __m512 reg;
    FP32Vec16(float v) : reg(_mm512_set1_ps(v)) {}
    FP32Vec16(__m512 r) : reg(r) {}
    FP32Vec16 operator*(const FP32Vec16& other) const {
        return FP32Vec16(_mm512_mul_ps(reg, other.reg));
    }
    float reduce_sum() const { return _mm512_reduce_add_ps(reg); }
};

Full pattern: simd_optimization_patterns.yaml

Quantized GEMM Template (INT4/NF4/FP4)

All 4-bit quantized GEMM kernels share the same skeleton — only the LUT and zero-point handling differ:

nibble split → zero subtract → LUT lookup → _mm512_dpbf16_ps accumulate → scale fmadd (per group) → bf16 output

The parameterized components:

• LUT: GPTQ (linear INT4), BnB (NF4/FP4), MegaBlocks (FP8/MXFP4)
• Zero-point: per-group (GPTQ), none/encoded in LUT (BnB), per-block (FP8)
• Algorithm: tinygemm (small M, fused) vs brgemm (large M, unpack+BLAS)
• Weight conversion: The C++ kernel expects a specific block-interleaved format, NOT raw checkpoint format. Each framework converts in its own repo:
  • GPTQ: transform_cpu() unpacks int32→uint8, reorders by g_idx, transposes to [N,K]; then convert_weight_packed_zp() repacks to [N,K/2] block-interleaved (BLOCK_N=32). Zeros unpacked to [groups,N] uint8. Scales to bf16. Done at first forward in GPTQModel repo.
  • BnB: _convert_weight_packed_for_cpu() unpacks uint8 nibbles→[N,K], repacks to [N,K/2] block-interleaved (same algo as GPTQ). Denests nested absmax. Transposes scales to [K/blocksize,N] bf16. Done at first forward in bitsandbytes repo.
  • Megablocks MoE: ops.convert_weight_packed() does transpose+VNNI pack. ops.convert_scale_packed() reorders scales. Cached via packed_weight=True.
• VNNI Conversion (K/V Activations):
  • Flash Attention: pack_vnni() per tile per forward (K/V change every call, so caching is not possible).
• Element-wise (RMSNorm): No conversion needed.

Full pattern: quantized_gemm_patterns.yaml, weight conversion: brgemm_patterns.yaml

Critical CPU Constraints

• Always use unaligned loads: All existing kernels use _mm512_loadu_* exclusively. Never use _mm512_load_*.
• Edge cases: When hidden_size % VEC_ELEM_NUM != 0, handle the tail with scalar or masked SIMD ops.
• FTZ/DAZ: Flush-to-zero and denormals-as-zero may be set by PyTorch. Do NOT assume IEEE 754 denormal behavior.
• OpenMP overhead: For small tensors, use adjust_num_threads(m) to reduce thread count. GEMM kernels use parallel_2d for 2D thread decomposition.
• bf16 precision: _mm512_dpbf16_ps accumulates in fp32 but inputs are bf16 — precision loss is expected. Use atol=1e-2 for correctness checks.
• Data alignment: Use alignas(64) for stack-allocated tile buffers to optimize cache-line access.

Full constraint list: correctness.yaml

Project Structure

cpu-kernels/
├── SKILL.md                                    # This file (skill definition + workflow)
├── manifest.txt                                # Files included in this skill
│
├── scripts/                                    # Standalone CLI tools
│   ├── analyze_op.py                           # PyTorch op → compute/memory analysis
│   ├── validate_cpu_kernel.py                  # Static checks on C++ kernel code
│   ├── benchmark_cpu.py                        # Correctness + performance via torch.utils.benchmark
│   ├── cpu_profiler.py                         # perf stat hardware counters + recommendations
│   ├── trial_manager.py                        # Tree-structured trial management
│   ├── config.yaml                             # Session config (max_trials, profiler, build)
│   └── config.py                               # Shared configuration loader
│
└── references/                                 # Knowledge base
    ├── correctness.yaml                        # Critical constraints for CPU kernels
    ├── runtime_dispatch.yaml                   # cpu_features.hpp + dispatch pattern
    ├── build_system.yaml                       # build.toml multi-target CPU compilation
    ├── simd_optimization_patterns.yaml         # AVX2/AVX512 vector abstractions and patterns
    ├── quantized_gemm_patterns.yaml            # LUT + tinygemm/brgemm template
    ├── brgemm_patterns.yaml                     # brgemm API, VNNI packing, tinygemm fallback (GEMM kernels only)
    ├── memory_patterns.yaml                    # Prefetch, alignment, cache blocking
    ├── threading_patterns.yaml                 # OpenMP parallel patterns
    ├── dtype_optimizations.yaml                # bf16/fp8/int8 handling on CPU
    ├── optimization_levels.yaml                # Progressive L1→L5 optimization checklist
    ├── implementation_reference.md             # C++ kernel templates and examples
    ├── optimization_strategies.md              # Strategy reference + decision tree
    ├── workflow_details.md                     # Detailed workflow reference
    └── huggingface-kernels-integration.md      # HF kernels ecosystem integration guide

See Also

Tools

• analyze_op.py — Analyze PyTorch op characteristics
• validate_cpu_kernel.py — Static kernel validation
• benchmark_cpu.py — Correctness + performance measurement
• cpu_profiler.py — perf stat hardware counters
• trial_manager.py — Trial tree management

CPU Optimization References

• correctness.yaml — Critical constraints
• simd_optimization_patterns.yaml — SIMD patterns
• quantized_gemm_patterns.yaml — Quantized GEMM template
• optimization_levels.yaml — Progressive optimization
• implementation_reference.md — Code templates

External Resources

• Hugging Face Kernels — Kernel hub and builder CLI
• Intel Intrinsics Guide
• kernel-builder Documentation
• xpu-kernels skill — the Intel XPU Triton skill this workflow was adapted from
• Xe-Forge — the LLM-driven optimization framework the skill methodology originates from

Key Concepts (read before the Quick Start)

The commands use a few names that mean different things. They are not interchangeable:

⚠️ --op means two different things depending on the script. In analyze_op.py, --op is a plain operation name (e.g. "rms_norm") used to look up compute/memory characteristics. In benchmark_cpu.py and cpu_profiler.py, --op is a package.function path (e.g. my_kernel.rms_norm) used to import and call your kernel. Same flag, different meaning — read each command below carefully.

Quick Start

Write a New CPU Kernel

The example below optimizes an RMSNorm kernel. The trial label is my_rmsnorm, the built package is my_kernel, and its function is my_kernel.rms_norm — keep these consistent across all six steps.

# 1. Analyze the target op. Here --op is an OPERATION NAME (looked up in the
#    knowledge base), not a package path.
python scripts/analyze_op.py --op "rms_norm" --shapes "1024x4096,2048x8192"

# 2. Initialize trial tracking. Args: <trial-label> <baseline-file>.
#    Creates trials/my_rmsnorm/ and records baseline.py as the reference.
python scripts/trial_manager.py init my_rmsnorm baseline.py

# 3. Build the kernel package (produces the installable 'my_kernel' wheel).
cd /path/to/my-kernel && kernel-builder build --release && pip install dist/*.whl --force-reinstall

# 4. Benchmark correctness + performance. Here --op is a PACKAGE.FUNCTION path.
#    Compares my_kernel.rms_norm against baseline.py (correctness + speedup).
python scripts/benchmark_cpu.py baseline.py --kernel-package my_kernel --op my_kernel.rms_norm

# 5. Profile with perf stat (same package.function path as step 4).
python scripts/cpu_profiler.py --kernel-package my_kernel --op my_kernel.rms_norm

# 6. Finalize: promote the best trial in trials/my_rmsnorm/ into output/.
python scripts/trial_manager.py finalize my_rmsnorm output/

Common Issues