"""
PHI-SCAN: Physics-informed multi-directional token scanners.
Alternates between scan patterns per layer with zero extra parameters.
"""
import torch

SCAN_PATTERNS = ["row_major", "col_major", "hilbert", "zigzag_diag"]


def _hilbert_index(n, x, y):
    d = 0
    s = n // 2
    while s > 0:
        rx = 1 if (x & s) > 0 else 0
        ry = 1 if (y & s) > 0 else 0
        d += s * s * ((3 * rx) ^ ry)
        if ry == 0:
            if rx == 1:
                x = n - 1 - x
                y = n - 1 - y
            x, y = y, x
        s //= 2
    return d


def build_hilbert_permutation(h: int, w: int, device='cpu'):
    n = max(h, w)
    n = 1 << (n - 1).bit_length()
    indices = [-1] * (h * w)
    for y in range(h):
        for x in range(w):
            idx = _hilbert_index(n, x, y)
            indices[y * w + x] = idx
    sorted_pairs = sorted(enumerate(indices), key=lambda kv: kv[1])
    perm = torch.tensor([i for i, _ in sorted_pairs], dtype=torch.long, device=device)
    inv = torch.empty_like(perm)
    inv[perm] = torch.arange(h * w, device=device)
    return perm, inv


def build_zigzag_diag_permutation(h: int, w: int, device='cpu'):
    diag = {}
    for y in range(h):
        for x in range(w):
            s = x + y
            if s not in diag:
                diag[s] = []
            diag[s].append((y, x))
    order = []
    flip = False
    for s in sorted(diag.keys()):
        cells = diag[s]
        if flip:
            cells = cells[::-1]
        order.extend(cells)
        flip = not flip
    perm = torch.tensor([y * w + x for y, x in order], dtype=torch.long, device=device)
    inv = torch.empty_like(perm)
    inv[perm] = torch.arange(h * w, device=device)
    return perm, inv


def build_scan_permutations(h: int, w: int, device='cpu'):
    row_perm = torch.arange(h * w, device=device)
    row_inv = torch.arange(h * w, device=device)
    col_perm = torch.arange(h * w, device=device).reshape(h, w).t().reshape(-1)
    col_inv = torch.empty_like(col_perm)
    col_inv[col_perm] = torch.arange(h * w, device=device)
    hil_perm, hil_inv = build_hilbert_permutation(h, w, device)
    zig_perm, zig_inv = build_zigzag_diag_permutation(h, w, device)
    return {
        "row_major": (row_perm, row_inv),
        "col_major": (col_perm, col_inv),
        "hilbert": (hil_perm, hil_inv),
        "zigzag_diag": (zig_perm, zig_inv),
    }


def apply_scan(x: torch.Tensor, perm: torch.Tensor):
    B, L, C = x.shape
    return x[:, perm, :]


def unscan(x: torch.Tensor, inv: torch.Tensor):
    B, L, C = x.shape
    return x[:, inv, :]


def get_scan_pattern(layer_idx: int):
    return SCAN_PATTERNS[layer_idx % len(SCAN_PATTERNS)]