feat: add optional GPU acceleration using backend abstraction

CUDA_SETUP_GUIDE.md

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+# CUDA Setup Guide
+
+## Quick Fix
+
+If you're getting `nvrtc64_*.dll` or `DLL load failed` errors, run:
+
+```powershell
+python fix_cuda_path.py
+```
+
+Or double-click: `fix_cuda.bat`
+
+## Diagnostic Tools
+
+### Check CUDA Setup
+```powershell
+python check_cuda_setup.py
+```
+This will show you:
+- CUDA installation status
+- PATH configuration
+- CuPy installation
+- GPU operation status
+
+### Fix CUDA PATH
+```powershell
+python fix_cuda_path.py
+```
+This script will:
+1. Find your CUDA installation
+2. Add CUDA bin directory to PATH
+3. Test if GPU operations work
+4. Provide troubleshooting steps if issues persist
+
+## Common Issues
+
+### Issue: "CuPy failed to load nvrtc64_120_0.dll"
+
+**Cause**: CUDA version mismatch between installed CUDA and CuPy package.
+
+**Solution**:
+1. Check your CUDA version: `nvcc --version`
+2. Reinstall CuPy matching your CUDA version:
+   ```powershell
+   pip uninstall cupy
+   pip install cupy-cuda12x  # For CUDA 12.x
+   # or
+   pip install cupy-cuda11x  # For CUDA 11.x
+   ```
+
+### Issue: "CUDA not in PATH"
+
+**Solution**: Run `python fix_cuda_path.py` - it will automatically add CUDA to PATH.
+
+### Issue: "GPU Usable: False"
+
+This means CuPy is installed but can't access CUDA DLLs. Usually caused by:
+- CUDA not in PATH → Run `fix_cuda_path.py`
+- Version mismatch → Reinstall matching CuPy version
+- Incomplete CUDA installation → Reinstall CUDA Toolkit
+
+## Automatic Fixes
+
+The `backend.py` now automatically tries to find and add CUDA to PATH when imported.
+
+The `run_gpu_demo.py` script will also attempt to fix PATH issues automatically before running benchmarks.
+
+## Manual PATH Setup
+
+If automatic fixes don't work:
+
+1. Find your CUDA installation (usually):
+   `C:\Program Files\NVIDIA GPU Computing Toolkit\CUDA\v12.x\bin`
+
+2. Add to System PATH:
+   - Win + X → System → Advanced system settings
+   - Environment Variables → System variables → Path → Edit
+   - Add: `C:\Program Files\NVIDIA GPU Computing Toolkit\CUDA\v12.x\bin`
+   - Replace `v12.x` with your actual version
+
+3. Restart PowerShell/terminal
+
+## Verification
+
+After setup, verify everything works:
+
+```powershell
+python check_cuda_setup.py
+python run_gpu_demo.py
+```
+
+You should see `GPU Usable: True` and successful GPU benchmarks.

backend.py

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+import os
+from pathlib import Path
+
+def find_and_add_cuda_to_path():
+    """Automatically find CUDA installation and add to PATH if not present"""
+    # Check if CUDA is already in PATH
+    path_dirs = os.environ.get("PATH", "").split(os.pathsep)
+    if any("CUDA" in d and "bin" in d for d in path_dirs):
+        return True  # Already in PATH
+
+    # Try to find CUDA installation
+    possible_paths = [
+        Path("C:/Program Files/NVIDIA GPU Computing Toolkit/CUDA"),
+        Path("C:/Program Files (x86)/NVIDIA GPU Computing Toolkit/CUDA"),
+    ]
+
+    for base_path in possible_paths:
+        if base_path.exists():
+            versions = [d for d in base_path.iterdir() if d.is_dir() and d.name.startswith('v')]
+            if versions:
+                # Use the latest version
+                latest = sorted(versions, key=lambda x: x.name, reverse=True)[0]
+                cuda_bin = latest / "bin"
+                if cuda_bin.exists():
+                    # Add to current session PATH
+                    current_path = os.environ.get("PATH", "")
+                    cuda_bin_str = str(cuda_bin)
+                    if cuda_bin_str not in current_path:
+                        os.environ["PATH"] = cuda_bin_str + os.pathsep + current_path
+                        return True
+    return False
+
+# Try to fix CUDA PATH automatically
+find_and_add_cuda_to_path()
+
+try:
+    import cupy as xp
+    GPU_AVAILABLE = True
+
+    def sync():
+        try:
+            xp.cuda.stream.get_current_stream().synchronize()
+        except Exception:
+            pass
+except Exception:
+    import numpy as xp
+    GPU_AVAILABLE = False
+
+    def sync():
+        return
+