feat: add complex root finding and dynamic CUDA shared memory optimization

Major update extending the library to solve for complex roots and optimizing GPU performance using Shared Memory.

Complex Number Support:
- Implemented `_solve_complex_cuda` and `_solve_complex_numpy` to find roots in the complex plane.
- Added specialized CUDA kernels (`_FITNESS_KERNEL_COMPLEX`, `_FITNESS_KERNEL_COMPLEX_DYNAMIC`) handling complex arithmetic (multiplication/addition) directly on the GPU.
- Updated `Function` class and `set_coeffs` to handle `np.complex128` data types.
- Updated `quadratic_solve` to return complex roots using `cmath`.

CUDA Performance & Optimization:
- Implemented Dynamic Shared Memory kernels (`extern __shared__`) to cache polynomial coefficients on the GPU block, significantly reducing global memory latency.
- Added intelligent fallback logic: The solver checks `MaxSharedMemoryPerBlock`. If the polynomial is too large for Shared Memory, it falls back to the standard Global Memory kernel to prevent crashes.
- Split complex coefficients into separate Real and Imaginary arrays for CUDA kernel efficiency.

Polynomial Logic:
- Added `_strip_leading_zeros` helper to ensure polynomial degree is correctly maintained after arithmetic operations (e.g., preventing `0x^2 + x` from being treated as degree 2).
- Updated `__init__` to allow direct coefficient injection.

GA Algorithm:
- Updated crossover logic to support 2D search space (Real + Imaginary) for complex solutions.
- Refined fitness function to explicitly handle `isinf`/`isnan` for numerical stability.

pyproject.toml

@@ -5,7 +5,7 @@ build-backend = "setuptools.build_meta"
 [project]
 # --- Core Metadata ---
 name = "polysolve"
-version = "0.6.3"
+version = "0.7.0"
 authors = [
   { name="Jonathan Rampersad", email="jonathan@jono-rams.work" },
 ]

tests/test_polysolve.py

@@ -43,6 +43,11 @@ def base_func():
     f.set_coeffs([1, 2, 3])
     return f
 
+@pytest.fixture
+def complex_func():
+    f = Function(2, [1, 2, 2])
+    return f
+
 # --- Core Functionality Tests ---
 
 def test_solve_y(quadratic_func):
@@ -162,3 +167,36 @@ def test_get_real_roots_cuda(quadratic_func):
     # Verify that the CUDA implementation also finds the correct roots within tolerance.
     npt.assert_allclose(np.sort(roots), np.sort(expected_roots), atol=1e-2)
 
+def test_get_roots_numpy(complex_func):
+    """
+    Tests that the NumPy-based genetic algorithm approximates the roots correctly.
+    """
+    # Using more generations for higher accuracy in testing
+    ga_opts = GA_Options(num_of_generations=50, data_size=200000, selection_percentile=0.66, root_precision=3)
+    
+    roots = complex_func.get_roots(ga_opts, use_cuda=False)
+    
+    # Check if the algorithm found values close to the two known roots.
+    # We don't know which order they'll be in, so we check for presence.
+    expected_roots = np.array([-1.0-1.j, -1.0+1.j])
+    
+    npt.assert_allclose(np.sort(roots), np.sort(expected_roots), atol=1e-2)
+
+
+@pytest.mark.skipif(not _CUPY_AVAILABLE, reason="CuPy is not installed, skipping CUDA test.")
+def test_get_roots_cuda(complex_func):
+    """
+    Tests that the CUDA-based genetic algorithm approximates the roots correctly.
+    This test implicitly verifies that the CUDA kernel is functioning.
+    It will be skipped automatically if CuPy is not available.
+    """
+    
+    ga_opts = GA_Options(num_of_generations=50, data_size=200000, selection_percentile=0.66, root_precision=3)
+    
+    roots = complex_func.get_roots(ga_opts, use_cuda=True)
+    
+    expected_roots = np.array([-1.0-1.j, -1+1.j])
+    
+    # Verify that the CUDA implementation also finds the correct roots within tolerance.
+    npt.assert_allclose(np.sort(roots), np.sort(expected_roots), atol=1e-2)
+