"""Sparse, smoothed trigram corrections and exact second-order chain decoding."""

from pathlib import Path
import math

import torch

MAX_TRIGRAM_LOOKUP_ELEMENTS = 2_000_000


class TrigramScorer(torch.nn.Module):
    """Correction log P(c|a,b) - log P(c|b), with bigram backoff.

    All context totals precede singleton filtering during training. Unseen or
    low-count triples give zero correction; clipping limits corpus preferences.
    """

    def __init__(
        self,
        vocab_size,
        triple_keys,
        triple_counts,
        prefix_keys,
        prefix_counts,
        *,
        alpha=50.0,
        metadata=None,
    ):
        super().__init__()
        if (
            vocab_size < 1
            or vocab_size**3 >= 2**63
            or not math.isfinite(alpha)
            or alpha <= 0
        ):
            raise ValueError("Invalid trigram vocabulary or smoothing")
        self.vocab_size = int(vocab_size)
        self.alpha = float(alpha)
        self.metadata = metadata or {}
        for name, keys, counts, limit in [
            ("triple", triple_keys, triple_counts, vocab_size**3),
            ("prefix", prefix_keys, prefix_counts, vocab_size**2),
        ]:
            keys = torch.as_tensor(keys, dtype=torch.long)
            counts = torch.as_tensor(counts, dtype=torch.float32)
            if (
                keys.ndim != 1
                or counts.shape != keys.shape
                or (keys < 0).any()
                or (keys >= limit).any()
                or (keys[1:] <= keys[:-1]).any()
            ):
                raise ValueError("Invalid sorted sparse trigram keys")
            if not torch.isfinite(counts).all() or (counts <= 0).any():
                raise ValueError("Invalid trigram counts")
            self.register_buffer(name + "_keys", keys)
            self.register_buffer(name + "_counts", counts)

    @staticmethod
    def _lookup(keys, counts, query):
        if not keys.numel():
            return torch.zeros_like(query, dtype=torch.float32)
        index = torch.searchsorted(keys, query.contiguous())
        safe = index.clamp_max(len(keys) - 1)
        return torch.where(
            (index < len(keys)) & (keys[safe] == query), counts[safe], 0.0
        )

    def correction(self, a, b, c, bigram, *, min_count=2, clip=2.0):
        if bigram.vocab_size != self.vocab_size:
            raise ValueError("Bigram/trigram vocabulary mismatch")
        if (
            not isinstance(min_count, int)
            or min_count < 1
            or not math.isfinite(clip)
            or clip < 0
        ):
            raise ValueError("Invalid trigram minimum count or clipping")
        if min_count < self.metadata.get("storage_min_count", 1):
            raise ValueError(
                "Requested count threshold is below checkpoint storage threshold"
            )
        a, b, c = torch.broadcast_tensors(a, b, c)
        for ids in (a, b, c):
            if ids.device != self.triple_keys.device:
                raise ValueError("Move trigram scorer to candidate device")
            if ((ids < 0) | (ids >= self.vocab_size)).any():
                raise ValueError("Token outside trigram vocabulary")
        context = a * self.vocab_size + b
        counts = self._lookup(
            self.triple_keys, self.triple_counts, context * self.vocab_size + c
        )
        totals = self._lookup(self.prefix_keys, self.prefix_counts, context)
        base = bigram.log_prob(b, c)
        smoothed = (
            torch.logaddexp(counts.log(), math.log(self.alpha) + base)
            - (totals + self.alpha).log()
        )
        return torch.where(
            counts >= min_count, (smoothed - base).clamp(-clip, clip), 0.0
        )

    def lattice_corrections(self, ids, bigram, *, min_count=2, clip=2.0):
        k = ids.shape[1]
        if len(ids) < 3:
            return torch.zeros((0, k, k, k), device=ids.device)
        if bigram.vocab_size != self.vocab_size:
            raise ValueError("Bigram/trigram vocabulary mismatch")
        if (
            not isinstance(min_count, int)
            or min_count < 1
            or not math.isfinite(clip)
            or clip < 0
        ):
            raise ValueError("Invalid trigram minimum count or clipping")
        if min_count < self.metadata.get("storage_min_count", 1):
            raise ValueError(
                "Requested count threshold is below checkpoint storage threshold"
            )
        if ids.device != self.triple_keys.device:
            raise ValueError("Move trigram scorer to candidate device")
        if ((ids < 0) | (ids >= self.vocab_size)).any():
            raise ValueError("Token outside trigram vocabulary")
        # At ordinary K=16 this is one vectorized lookup across all positions.
        # Large K uses window chunks so sparse-lookup temporaries do not grow
        # into multiple gigabytes beyond the required K^3 potential table.
        chunk = max(1, MAX_TRIGRAM_LOOKUP_ELEMENTS // (k**3))
        output = torch.empty(
            (len(ids) - 2, k, k, k), device=ids.device, dtype=torch.float32
        )
        for start in range(0, len(ids) - 2, chunk):
            end = min(len(ids) - 2, start + chunk)
            # Prefix totals depend on (a,b), and backoff on (b,c). Looking them
            # up on the full K^3 broadcast repeats each sparse search K times.
            a, b, c = ids[start:end], ids[start + 1 : end + 1], ids[start + 2 : end + 2]
            context = a[:, :, None] * self.vocab_size + b[:, None, :]
            totals = self._lookup(self.prefix_keys, self.prefix_counts, context)[
                :, :, :, None
            ]
            base = bigram.log_prob(b[:, :, None], c[:, None, :])[:, None, :, :]
            counts = self._lookup(
                self.triple_keys,
                self.triple_counts,
                context[:, :, :, None] * self.vocab_size + c[:, None, None, :],
            )
            smoothed = (
                torch.logaddexp(counts.log(), math.log(self.alpha) + base)
                - (totals + self.alpha).log()
            )
            output[start:end] = torch.where(
                counts >= min_count, (smoothed - base).clamp(-clip, clip), 0.0
            )
        return output

    @classmethod
    def load(cls, path, *, bigram, device="cpu"):
        state = torch.load(Path(path), map_location="cpu", weights_only=True)
        if state.pop("version", None) != 1:
            raise ValueError("Unsupported trigram checkpoint")
        scorer = cls(**state)
        if scorer.vocab_size != bigram.vocab_size or scorer.metadata.get(
            "tokenizer_sha256"
        ) != bigram.metadata.get("tokenizer_sha256"):
            raise ValueError("Bigram and trigram tokenizer mismatch")
        if scorer.metadata.get("tokens") != bigram.metadata.get("tokens"):
            raise ValueError("Bigram and trigram training corpora mismatch")
        return scorer.to(device)


def _potentials(emissions, edges, triples, temperature=1.0):
    length, k = emissions.shape
    if edges.shape != (length - 1, k, k) or triples.shape != (
        max(0, length - 2),
        k,
        k,
        k,
    ):
        raise ValueError("Invalid second-order lattice shapes")
    if length < 1 or k < 1:
        raise ValueError("Empty second-order lattice")
    temperature = float(temperature)
    if not math.isfinite(temperature) or temperature <= 0:
        raise ValueError("Temperature must be positive")
    scale = max(temperature, 1e-6)
    unary = emissions.float()
    unary = (unary - unary.amax(-1, keepdim=True)) / scale
    edges = edges.float()
    triples = triples.float()
    if edges.numel():
        edges = (edges - edges.amax((1, 2), keepdim=True)) / scale
    if triples.numel():
        triples = (triples - triples.amax((1, 2, 3), keepdim=True)) / scale
    return unary, edges, triples


def _forward(unary, edges, triples, *, maximum=False):
    length, k = unary.shape
    rows = []
    back = []
    if length < 2:
        return rows, back
    row = unary[0, :, None] + unary[1, None, :] + edges[0]
    rows.append(row - row.max())
    for t in range(2, length):
        score = rows[-1][:, :, None] + triples[t - 2]
        if maximum:
            row, index = score.max(0)
            back.append(index)
        else:
            row = torch.logsumexp(score, 0)
        row = row + edges[t - 1] + unary[t, None, :]
        rows.append(row - row.max())
    return rows, back


def decode_second_order(ids, emissions, edges, triples):
    # A small chain launches hundreds of tiny GPU reductions. A single host
    # transfer and vectorized CPU reductions can cost less than those launches.
    # Keep the GPU route for large lattices, and sampling on its existing route.
    if ids.device.type == "cuda" and len(ids) <= 256 and ids.shape[1] <= 16:
        return _decode_second_order_host(ids, emissions, edges, triples)
    unary, edges, triples = _potentials(emissions, edges, triples)
    if len(ids) == 1:
        return ids.gather(1, unary.argmax(-1, keepdim=True)).squeeze(1)
    forward, back = _forward(unary, edges, triples, maximum=True)
    k = ids.shape[1]
    if ids.device.type != "cuda":
        # Scalar indexing is inexpensive on CPU; retain its lean traceback.
        path = torch.empty(len(ids), device=ids.device, dtype=torch.long)
        last = forward[-1].reshape(-1).argmax()
        path[-2] = last // k
        path[-1] = last % k
        for t in range(len(ids) - 3, -1, -1):
            path[t] = back[t][path[t + 1], path[t + 2]]
    else:
        path = _traceback_device(back, forward[-1].reshape(-1).argmax(), k)
    return ids.gather(1, path[:, None]).squeeze(1)


def _decode_second_order_host(ids, emissions, edges, triples):
    """Exact MAP recurrence on CPU, preserving float32 operations/tie order."""
    import numpy as np

    # Normalize on the original device to retain the original score arithmetic.
    unary, edges, triples = _potentials(emissions, edges, triples)
    length, k = unary.shape
    # One synchronous copy instead of one per predecessor or lattice row.
    packed = torch.cat((unary.reshape(-1), edges.reshape(-1), triples.reshape(-1)))
    host = packed.detach().cpu().numpy()
    cut = length * k
    end = cut + (length - 1) * k * k
    u = host[:cut].reshape(length, k)
    e = host[cut:end].reshape(length - 1, k, k)
    tri = host[end:].reshape(max(0, length - 2), k, k, k)
    if length == 1:
        path = np.array([u[0].argmax()], dtype=np.int64)
    else:
        row = u[0, :, None] + u[1, None, :] + e[0]
        row = row - row.max()
        back = []
        for t in range(2, length):
            score = row[:, :, None] + tri[t - 2]
            index = score.argmax(axis=0)
            row = score.max(axis=0) + e[t - 1] + u[t, None, :]
            row = row - row.max()
            back.append(index)
        path = np.empty(length, dtype=np.int64)
        last = row.reshape(-1).argmax()
        path[-2] = last // k
        path[-1] = last % k
        for t in range(length - 3, -1, -1):
            path[t] = back[t][path[t + 1], path[t + 2]]
    indices = torch.from_numpy(path).to(device=ids.device)
    return ids.gather(1, indices[:, None]).squeeze(1)


def _traceback_device(back, last, k):
    """Trace pair states without converting GPU indices to host scalars."""
    pair = last.reshape(1)
    reverse = [(pair % k).squeeze(0), (pair // k).squeeze(0)]
    for predecessors in reversed(back):
        # A one-element tensor gather keeps the index on the GPU. Scalar
        # tensor indexing can otherwise synchronize with the host each hop.
        previous = predecessors.reshape(-1).gather(0, pair)
        reverse.append(previous.squeeze(0))
        pair = previous * k + pair // k
    return torch.stack(reverse[::-1])


def sample_second_order(ids, emissions, edges, triples, temperature=1.0):
    if temperature == 0:
        return decode_second_order(ids, emissions, edges, triples)
    unary, edges, triples = _potentials(emissions, edges, triples, temperature)
    if len(ids) == 1:
        index = torch.multinomial(unary[0].softmax(-1), 1)
        return ids[0, index]
    forward, _ = _forward(unary, edges, triples)
    k = ids.shape[1]
    path = torch.empty(len(ids), device=ids.device, dtype=torch.long)
    last = torch.multinomial(forward[-1].reshape(-1).softmax(-1), 1).squeeze(0)
    path[-2] = last // k
    path[-1] = last % k
    for t in range(len(ids) - 3, -1, -1):
        scores = forward[t][:, path[t + 1]] + triples[t, :, path[t + 1], path[t + 2]]
        path[t] = torch.multinomial(scores.softmax(-1), 1).squeeze(0)
    return ids.gather(1, path[:, None]).squeeze(1)


def second_order_marginals(
    emissions, edges, triples, temperature=1.0, *, maximum=False
):
    """Return pair log-potentials (max) or normalized joint pair probabilities."""
    unary, edges, triples = _potentials(emissions, edges, triples, temperature or 1.0)
    if len(unary) < 2:
        return edges.clone()
    forward, _ = _forward(unary, edges, triples, maximum=maximum)
    backward = [None] * (len(unary) - 1)
    backward[-1] = torch.zeros_like(edges[-1])
    for t in range(len(unary) - 3, -1, -1):
        scores = (
            triples[t]
            + edges[t + 1][None, :, :]
            + unary[t + 2, None, None, :]
            + backward[t + 1][None, :, :]
        )
        row = scores.max(-1).values if maximum else torch.logsumexp(scores, -1)
        backward[t] = row - row.max()
    pair_scores = torch.stack([a + b for a, b in zip(forward, backward)])
    return (
        pair_scores
        if maximum
        else pair_scores.flatten(1).softmax(-1).reshape_as(pair_scores)
    )


def second_order_path_margins(ids, emissions, edges, triples, selected):
    if len(ids) == 1:
        from .bigram import BigramViterbiSelector

        return BigramViterbiSelector.path_margins(ids, emissions, edges, selected, 1.0)
    pairs = second_order_marginals(emissions, edges, triples, maximum=True)
    scores = torch.cat((pairs[0].max(1).values[None, :], pairs.max(1).values), 0)
    same = ids == selected[:, None]
    return (
        scores.masked_fill(~same, -torch.inf).max(-1).values
        - scores.masked_fill(same, -torch.inf).max(-1).values
    ).clamp_min(0.0)