pyfwht 2.0.1

Fast Walsh-Hadamard Transform with CPU, OpenMP, and CUDA backends

pyfwht - Fast Walsh-Hadamard Transform for Python

Python bindings for the high-performance libfwht library, providing Fast Walsh-Hadamard Transform with NumPy integration and support for CPU (SIMD), OpenMP, and CUDA backends.

Features

• Zero-copy NumPy integration: Direct operation on NumPy arrays without data copying
• Multiple backends: Automatic selection or explicit choice of CPU (SIMD), OpenMP, or GPU (CUDA)
• Multi-precision GPU: fp64 (cryptographic), fp32 (balanced), fp16 (maximum speed, up to 54× faster with PyTorch DLPack)
• All data types: Support for int8, int32, and float64 with overflow protection
• Boolean function analysis: Convenience functions for cryptographic applications
• Bit-packed Boolean WHT: Compute WHT directly from uint64-packed truth tables via fwht.boolean_packed() (set backend=fwht.Backend.GPU to expand on the device for n ≤ 65536)
• GPU-resident Boolean contexts: repeated fwht.boolean_packed(..., backend=fwht.Backend.GPU) calls automatically reuse the CUDA buffers via fwht_gpu_boolean_context_*, eliminating per-call allocations on S-box workloads
• High performance:
  • GPU fp16: Up to 1115 GOps/s on RTX 4090 with PyTorch DLPack (zero-copy, exceeds Meta by 38%)
  • GPU fp32: Up to 625 GOps/s with perfect accuracy
  • Tensor Core kernels: n=256, 512, 1024, 2048, 4096, 8192, 16384, 32768 (Meta-inspired implementation)
  • DLPack support: 81× faster than NumPy for fp16 batch operations
  • Recursive cache-efficient algorithm (512-element L1-optimized base case)
  • Task-based OpenMP parallelism (2-3× speedup on 4-8 cores)
  • Software prefetching and cache-aligned memory allocation
  • SIMD optimization (AVX2/SSE2/NEON auto-detection)
• Easy to use: Pythonic API with comprehensive error handling and numerical documentation

Installation

Requirements

• Python 3.8+
• NumPy >= 1.20.0
• C99 compiler (gcc, clang, msvc)
• Optional: OpenMP-capable compiler for multi-threading
• Optional: CUDA toolkit (nvcc) for GPU support

From PyPI

# Install (automatically enables CUDA if nvcc is found)
pip install pyfwht

# On Linux, you may need to build from source for CUDA support
pip install pyfwht --no-binary :all:

# Disable CUDA even if available
USE_CUDA=0 pip install pyfwht --no-binary :all:

From Source

git clone https://github.com/hadipourh/fwht
cd fwht/python
pip install -e .  # Auto-detects CUDA if nvcc is available

# To enable GPU features with PyTorch (required for GPU DLPack API):
pip install -e ".[gpu]"  # Installs torch for DLPack GPU support

# Force CUDA on/off
USE_CUDA=1 pip install -e .  # Force enable (fails if nvcc not found)
USE_CUDA=0 pip install -e .  # Force disable

Quick Start

Basic Transform

import numpy as np
import pyfwht as fwht

# Create data (must be power of 2 length)
data = np.array([1, -1, -1, 1, -1, 1, 1, -1], dtype=np.int32)

# In-place transform
fwht.transform(data)
print(data)  # Transformed coefficients

Boolean Function Analysis

## Performance & Precision Reference

Detailed benchmark tables, GPU multi-precision comparisons, and FP16 precision guidelines live in the top-level `README.md`. The Python README focuses on installation and API usage—consult the root documentation whenever you need:

- GOps/s numbers for each backend or hardware platform
- Tensor Core coverage, runtime warnings, and accuracy graphs for fp16/fp32/fp64
- End-to-end benchmarking instructions (CLI, C harnesses, and Python runners)

All measurements and architectural notes are kept in a single place to avoid divergence between the C and Python docs.

# Example: f(x) for x in {0,1}^4
truth_table = np.array([0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0], dtype=np.uint8)

# Compute Walsh-Hadamard coefficients
# For signed convention: 0 → +1, 1 → -1
wht = fwht.from_bool(truth_table, signed=True)

# Find best linear approximation
n = int(np.log2(len(truth_table)))  # Number of input bits
best_idx = np.argmax(np.abs(wht))
best_wht = wht[best_idx]

# Compute correlation: cor(f, ℓ_u) = W_f(u) / 2^n
correlation = best_wht / (2**n)

# Compute bias: ε = W_f(u) / 2^(n+1)
bias = best_wht / (2**(n+1))

print(f"Best linear mask u: {best_idx:0{n}b}")
print(f"WHT coefficient: {best_wht}")
print(f"Correlation: {correlation:.4f}")
print(f"Bias: {bias:.4f}")
print(f"Linear probability: {0.5 + bias:.4f}")

Batch Processing: Computing Nonlinearity

Analyze cryptographic properties of Boolean functions:

import numpy as np
import pyfwht as fwht

# Generate 1000 random Boolean functions
num_vars = 8  # Number of input variables
num_functions = 1000
functions = np.random.randint(0, 2, size=(num_functions, 2**num_vars), dtype=np.uint8)

# Compute nonlinearity for all functions
nonlinearities = []
for func in functions:
    # from_bool computes WHT coefficients with signed convention
    wht = fwht.from_bool(func, signed=True)
    
    # Nonlinearity: NL(f) = 2^(n-1) - (1/2)·max|W_f(u)|
    # For n-variable function, length of truth table is 2^n
    max_abs_wht = np.max(np.abs(wht))
    nl = 2**(num_vars - 1) - max_abs_wht // 2
    nonlinearities.append(nl)

print(f"Average nonlinearity: {np.mean(nonlinearities):.2f}")
print(f"Max nonlinearity: {max(nonlinearities)}")
print(f"Min nonlinearity: {min(nonlinearities)}")
print(f"Theoretical max for {num_vars}-bit functions: {2**(num_vars-1) - 2**(num_vars//2 - 1)}")

Vectorial S-box Analysis

Use the high-level helper to compute Boolean component spectra and full LAT metrics:

import numpy as np
import pyfwht as fwht

# 3-bit identity S-box
table = np.arange(8, dtype=np.uint32)

analysis = fwht.analyze_sbox(
  table,
  backend=fwht.Backend.CPU,
  profile_timings=True,
  return_spectra=True,
  return_lat=True,
)

print("m_bits", analysis.components.m_bits)
print("n_bits", analysis.components.n_bits)
print("max_walsh", analysis.components.max_walsh)
print("lat_max", analysis.lat.lat_max if analysis.lat else None)

# Spectra shape: (n_bits, 2^m)
spectra = analysis.components.spectra
# LAT matrix shape: (2^m, 2^n)
lat_matrix = analysis.lat.lat if analysis.lat else None

Performance Comparison: Backend Selection

import numpy as np
import pyfwht as fwht
import time

def benchmark_backends(size, num_repeats=10, num_warmup=2):
    """Compare performance across different backends with statistical rigor."""
    data = np.random.randn(size).astype(np.float64)
    results = {}
    
    backends = [
        (fwht.Backend.CPU, "CPU (SIMD)"),
        (fwht.Backend.OPENMP, "OpenMP"),
    ]
    
    if fwht.has_gpu():
        backends.append((fwht.Backend.GPU, "GPU (CUDA)"))
    
    for backend, name in backends:
        timings = []
        
        # Warmup runs to stabilize cache and CPU frequency
        for _ in range(num_warmup):
            test_data = data.copy()
            fwht.transform(test_data, backend=backend)
        
        # Benchmark runs
        for _ in range(num_repeats):
            test_data = data.copy()
            start = time.perf_counter()
            fwht.transform(test_data, backend=backend)
            elapsed = time.perf_counter() - start
            timings.append(elapsed * 1000)  # Convert to ms
        
        # Statistical analysis
        timings_array = np.array(timings)
        mean_time = np.mean(timings_array)
        std_time = np.std(timings_array)
        median_time = np.median(timings_array)
        min_time = np.min(timings_array)
        
        # Use minimum time for throughput (best-case scenario, least noise)
        throughput = (size * fwht.log2(size)) / (min_time / 1000) / 1e9
        
        results[name] = {
            'mean': mean_time,
            'std': std_time,
            'median': median_time,
            'min': min_time,
            'throughput': throughput  # GOps/s based on minimum time
        }
    
    return results

# Test different sizes with sufficient repetitions
print("FWHT Performance Benchmark (Python)")
print("=" * 80)
print(f"Warmup runs: 2, Benchmark runs: 10 per configuration")
print(f"GPU available: {fwht.has_gpu()}")
print(f"OpenMP available: {fwht.has_openmp()}")
print(f"Version: {fwht.version()}")
print()

for k in range(20, 30, 2):
    size = 2**k
    print(f"\nSize: {size:,} (2^{k})")
    print("-" * 80)
    results = benchmark_backends(size, num_repeats=10, num_warmup=2)
    
    for name, metrics in results.items():
        print(f"  {name:15s}: {metrics['min']:7.2f} ms (min)  "
              f"{metrics['mean']:7.2f} ± {metrics['std']:5.2f} ms (mean±std)  "
              f"[{metrics['throughput']:5.2f} GOps/s]")

Numerical Accuracy Validation

import numpy as np
import pyfwht as fwht

def test_orthogonality(n):
    """
    Verify WHT orthogonality: WHT(WHT(x)) = n * x
    """
    x = np.random.randn(n)
    
    # Forward transform
    y = fwht.compute(x)
    
    # Inverse transform (forward again, then divide by n)
    x_reconstructed = fwht.compute(y) / n
    
    # Check reconstruction error
    error = np.linalg.norm(x - x_reconstructed)
    rel_error = error / np.linalg.norm(x)
    
    print(f"Size {n}: Relative error = {rel_error:.2e}")
    return rel_error < 1e-10

# Test for various sizes
for k in range(4, 16):
    assert test_orthogonality(2**k), f"Failed for size 2^{k}"

print("All orthogonality tests passed!")

Benchmark Results

Performance Comparison: CPU vs OpenMP vs GPU

Benchmark performed on GPU server with statistical rigor (10 runs per configuration, 2 warmup runs).

System Configuration:

• GPU: NVIDIA GeForce RTX 5090 (32 GB GDDR7)
• CPU: AMD EPYC 9334 32-Core Processor (64 threads with SMT)
• System RAM: 377 GB
• CUDA: Version 13.0 (driver 580.95.05, nvcc V13.0.88)
• Library Version: pyfwht 1.1.4

FWHT Performance Benchmark (Python)
================================================================================
Warmup runs: 2, Benchmark runs: 10 per configuration
GPU available: True
OpenMP available: True
Version: 1.1.4


Size: 1,048,576 (2^20)
--------------------------------------------------------------------------------
  CPU (SIMD)     :    4.11 ms (min)     4.15 ±  0.03 ms (mean±std)  [ 5.11 GOps/s]
  OpenMP         :    1.60 ms (min)    21.53 ± 31.49 ms (mean±std)  [13.09 GOps/s]
  GPU (CUDA)     :    0.86 ms (min)     0.87 ±  0.01 ms (mean±std)  [24.45 GOps/s]

Size: 4,194,304 (2^22)
--------------------------------------------------------------------------------
  CPU (SIMD)     :   20.78 ms (min)    21.50 ±  0.24 ms (mean±std)  [ 4.44 GOps/s]
  OpenMP         :    6.02 ms (min)    45.35 ± 38.26 ms (mean±std)  [15.32 GOps/s]
  GPU (CUDA)     :    3.55 ms (min)     3.58 ±  0.02 ms (mean±std)  [26.00 GOps/s]

Size: 16,777,216 (2^24)
--------------------------------------------------------------------------------
  CPU (SIMD)     :   90.52 ms (min)    90.68 ±  0.16 ms (mean±std)  [ 4.45 GOps/s]
  OpenMP         :   23.61 ms (min)    26.43 ±  2.96 ms (mean±std)  [17.06 GOps/s]
  GPU (CUDA)     :   16.32 ms (min)    16.35 ±  0.02 ms (mean±std)  [24.67 GOps/s]

Size: 67,108,864 (2^26)
--------------------------------------------------------------------------------
  CPU (SIMD)     :  447.80 ms (min)   448.15 ±  0.17 ms (mean±std)  [ 3.90 GOps/s]
  OpenMP         :  178.32 ms (min)   219.37 ± 19.93 ms (mean±std)  [ 9.78 GOps/s]
  GPU (CUDA)     :   66.09 ms (min)    66.15 ±  0.04 ms (mean±std)  [26.40 GOps/s]

Size: 268,435,456 (2^28)
--------------------------------------------------------------------------------
  CPU (SIMD)     : 2348.43 ms (min)  2350.81 ±  1.95 ms (mean±std)  [ 3.20 GOps/s]
  OpenMP         : 1178.15 ms (min)  1220.09 ± 26.66 ms (mean±std)  [ 6.38 GOps/s]
  GPU (CUDA)     :  268.10 ms (min)   268.44 ±  0.19 ms (mean±std)  [28.03 GOps/s]

Key Observations:

• GPU Performance: Achieves 24-28 GOps/s consistently, with extremely low variance (std < 0.2 ms even for large transforms)
• RTX 5090 Advantage: Latest generation GPU with GDDR7 memory provides excellent bandwidth for this memory-bound algorithm
• OpenMP Scaling: 2-4x speedup over single-threaded CPU on 32-core system
• CPU SIMD: Consistent ~4-5 GOps/s throughput with NEON/AVX2 optimizations
• Speedup Summary:
  • GPU vs CPU: 5.9x for small sizes (2^20), up to 8.8x for large sizes (2^28)
  • GPU vs OpenMP: 2.8x for small sizes, up to 4.4x for large sizes
• Python Overhead: Negligible - performance matches C library within measurement variance

Run your own benchmark:

cd python
# Use the improved benchmark from README examples section
python3 -c "$(sed -n '/def benchmark_backends/,/GOps\/s\]\")$/p' README.md)"

Multi-Precision GPU Performance (fp64/fp32/fp16)

The pyfwht GPU backend now supports multiple precision modes for different speed/accuracy trade-offs. Benchmark on NVIDIA RTX 4090:

System Configuration:

• GPU: NVIDIA GeForce RTX 4090 (SM 8.9, 128 SMs, 24 GB GDDR6X)
• CUDA: Version 12.x
• Library Version: pyfwht 1.2.0+

Correctness Results (with precision-matched references)

Kernel               Max Error       Status              
-------------------------------------------------------
pyfwht fp64          0.00e+00        PASS               
pyfwht fp32          0.00e+00        PASS               
pyfwht fp16          1.25e-01        PASS               

Boolean ±1 test vectors now match CPU exactly for fp16, fp32, and fp64. The fp16 number above comes from a Gaussian floating-point workload (benchmark_all_precisions_fixed.py) and reflects intrinsic fp16 rounding.

Performance Results

Single Transform (batch=1, dtype=float16):

Size	pyfwht GPU fp16 (ms / GOps/s)	Meta GPU fp16 (ms / GOps/s)	pyfwht Speedup
1024	0.032 ms / 0.64 GOps/s	0.051 ms / 0.40 GOps/s	1.6×
2048	0.034 ms / 1.31 GOps/s	0.054 ms / 0.84 GOps/s	1.6×
4096	0.036 ms / 2.76 GOps/s	0.049 ms / 2.02 GOps/s	1.4×

Batched Transforms (batch=100, dtype=float16):

Size	pyfwht GPU fp16 (ms / GOps/s)	Meta GPU fp16 (ms / GOps/s)	pyfwht Speedup
1024	0.030 ms / 68.01 GOps/s	0.049 ms / 41.65 GOps/s	1.6×
2048	0.030 ms / 148.59 GOps/s	0.049 ms / 91.59 GOps/s	1.6×
4096	0.031 ms / 314.83 GOps/s	0.049 ms / 199.43 GOps/s	1.6×

Key Highlights:

• Tests run on NVIDIA RTX 4090 (driver 560.35.03, CUDA 12.6.85) using PyTorch tensors (zero-copy DLPack path).
• pyfwht beats Meta's CUDA kernel by 1.4–1.6× at every measured size and batch depth.
• Boolean workloads are now bit-exact on fp16; Gaussian floats exhibit max error ≈1.3e-1 (mean ≈2.5e-2, relative <6e-4).
• fp32 stays the balanced option (~1e-6 error) if you do not need fp16's throughput.
• Tensor Core kernels cover power-of-two sizes 256–32768; larger sizes fall back to the general CUDA backend.

Usage Example:

import torch
import pyfwht

# For maximum performance: use PyTorch tensors with DLPack (zero-copy)
data_fp64 = torch.randn(100, 4096, dtype=torch.float64, device='cuda')  # Max precision
data_fp32 = torch.randn(100, 4096, dtype=torch.float32, device='cuda')  # Balanced
data_fp16 = torch.randn(100, 4096, dtype=torch.float16, device='cuda')  # Max speed

# DLPack API (recommended): zero-copy, eliminates H2D/D2H overhead
pyfwht.gpu.batch_transform_dlpack(data_fp64)  # Uses fp64 kernel
pyfwht.gpu.batch_transform_dlpack(data_fp32)  # Uses fp32 kernel (balanced speed/accuracy)
pyfwht.gpu.batch_transform_dlpack(data_fp16)  # Uses fp16 kernel (maximum Tensor Core throughput)

# NumPy API (convenience): includes H2D/D2H transfers
import numpy as np
data_np = np.random.randn(100, 4096).astype(np.float16)
result = pyfwht.fwht(data_np, backend='cuda')  # Transfers to GPU, computes, transfers back

Performance Comparison:

• DLPack (PyTorch): Keeps tensors on the GPU (see tables above for up to 315 GOps/s at n=4096, batch=100)
• NumPy: Includes H2D/D2H transfers and is typically 10–100× slower for fp16 workloads
• Recommendation: Use DLPack for any high-throughput batch job; reserve NumPy for convenience scripts

Run the multi-precision benchmark:

cd python/tests
python benchmark_all_precisions_fixed.py

FP16 Precision Characteristics (Important!)

FP16 provides up to ~35× speedup (with PyTorch DLPack) but uses limited precision (11-bit mantissa). This is the expected tradeoff for Tensor Core acceleration.

Measured Accuracy (RTX 4090, CUDA 12.6):

• Boolean truth tables (±1 inputs): max|error| = 0 (fp16 == CPU)
• Gaussian fp32 inputs (n=1024, batch=10): max|error| = 1.25e-01, mean = 2.47e-02, relative < 6e-4

FP16 roundoff is therefore inconsequential for Boolean cryptanalysis yet still bounded and predictable for ML workloads.

When to Use Each Precision:

Precision	Speed (relative)	Accuracy snapshot	Best For
fp64	1× (baseline)	Bit-exact	Cryptanalysis, validation
fp32	~30× faster	~1e-6 error	Balanced workloads
fp16	~35× faster	Boolean exact, ≤1.3e-1 abs. err on floats	ML/AI with PyTorch DLPack

Important: For fp16 throughput, keep data on the GPU (PyTorch DLPack). The NumPy path includes H2D/D2H copies and is orders of magnitude slower.

Supported Tensor Core Sizes:

All power-of-2 sizes from 256 to 32768 use optimized Tensor Core kernels:

• n=256: Meta-inspired kernel (chunks_per_warp=1, 8 warps/block)
• n=512: Meta-inspired kernel (chunks_per_warp=1, 8 warps/block)
• n=1024: Meta-inspired kernel (chunks_per_warp=1, 8 warps/block)
• n=2048: Meta-inspired kernel (chunks_per_warp=1, 8 warps/block)
• n=4096: Meta-inspired kernel (chunks_per_warp=2, 8 warps/block)
• n=8192: Meta-inspired kernel (chunks_per_warp=2, 8 warps/block)
• n=16384: Meta-inspired kernel (chunks_per_warp=4, 8 warps/block)
• n=32768: Meta-inspired kernel (chunks_per_warp=8, 8 warps/block)

Sizes outside this range fall back to standard GPU kernels (slower but still faster than CPU).

Runtime Warning:

When you first use fp16, you'll see a one-time warning:

╔═══════════════════════════════════════════════════════════════════════════╗
║ FP16 Tensor Core Precision Notice                                         ║
╠═══════════════════════════════════════════════════════════════════════════╣
║ Using float16 Tensor Cores provides 25-36× speedup                        ║
║                                                                           ║
║ Observed behavior (RTX 4090, CUDA 12.6):                                  ║
║   • Boolean {-1,+1} inputs remain bit-exact                               ║
║   • Random fp32/fp64 data: max|error| ≈ 1.3e-1, mean ≈ 2.5e-2             ║
║   • Relative error stays < 6e-4 for values in the ±4k range               ║
║                                                                           ║
║ Recommended use cases:                                                    ║
║   • Machine learning / signal processing (PyTorch DLPack)                 ║
║   • Boolean cryptanalysis                                                 ║
║   • High-precision floating workloads (use fp32/fp64 instead)             ║
║                                                                           ║
║ To suppress this warning: set FWHT_SILENCE_FP16_WARNING=1                 ║
╚═══════════════════════════════════════════════════════════════════════════╝

To suppress:

import os
os.environ['FWHT_SILENCE_FP16_WARNING'] = '1'
import pyfwht

Or in bash:

export FWHT_SILENCE_FP16_WARNING=1
python your_script.py

Verification:

GPU fp32 results are always bit-exact with CPU int32, proving the differences are purely from FP16 quantization, not algorithmic bugs.

Examples

The examples/ directory contains comprehensive demonstrations:

• basic_usage.py - Core API: transforms, backends, Boolean functions, utilities
• boolean_packed.py - Bit-packed Boolean WHT for memory-efficient cryptanalysis
• gpu_batch.py - GPU batch transforms, profiling, and persistent contexts
• gpu_multi_precision.py - fp16/fp32/fp64 with PyTorch DLPack integration
• compare_fast_hadamard.py - Benchmarks vs. Dao-AILab's fast-hadamard-transform
• sbox_analysis.py - S-box cryptanalysis with LAT computation (includes 16-bit GPU example)

Run any example:

cd examples
python basic_usage.py
python sbox_analysis.py  # Shows AES S-box analysis, LAT computation, and 16-bit GPU demo

Development

Running Tests

The tests/ directory contains comprehensive Python test suites and benchmarks:

# Install package in development mode
pip install -e .

# Install testing dependencies
pip install pytest pytest-cov

# Run all tests
pytest tests/ -v

# Run with coverage report
pytest tests/ --cov=pyfwht --cov-report=html

# Run specific test files
pytest tests/test_correctness.py -v          # Core correctness tests
pytest tests/test_gpu.py -v                  # GPU tests (requires CUDA)

# Run benchmarks (not part of pytest suite)
python tests/benchmark_all_precisions_fixed.py     # Multi-precision GPU benchmarks
python tests/benchmark_compare_meta.py             # Compare vs Dao-AILab implementation

Available test files:

• test_correctness.py - Core API validation (transforms, Boolean functions, backends, batch processing)
• test_gpu.py - GPU-specific tests (Tensor Cores, fp16/fp32/fp64, batch operations, DLPack)
• benchmark_all_precisions_fixed.py - Multi-precision performance benchmarks
• benchmark_compare_meta.py - Comparative benchmarks against fast-hadamard-transform

GPU Tests: Tests in test_gpu.py automatically skip if CUDA is not available. Build with USE_CUDA=1 pip install -e . to enable GPU support.

Building Distribution Packages

pip install build
python -m build  # Creates both sdist and wheel in dist/

Relation to C Library

This package wraps the libfwht C library. All computation happens in highly-optimized C/CUDA code; Python provides only a thin interface layer.

For C/C++ projects, use the C library directly. For Python workflows, this package provides seamless NumPy integration.

License

GNU General Public License v3.0 or later (GPL-3.0-or-later)

See LICENSE file for full text.

Citation

If you use this library in your research, please cite:

@software{libfwht,
  author = {Hadipour, Hosein},
  title = {libfwht: Fast Walsh-Hadamard Transform Library},
  year = {2025},
  url = {https://github.com/hadipourh/fwht}
}

Support

• Issues: https://github.com/hadipourh/fwht/issues
• Email: [e-mail]
• Documentation: https://github.com/hadipourh/fwht

Contributing

Contributions welcome! Please open an issue or pull request on GitHub.