# Copyright (c) Facebook, Inc. and its affiliates.
#
# This source code is licensed under the MIT license found in the
# LICENSE file in the root directory of this source tree.

import math

from typing import List, Optional

import torch
import torch.nn as nn
from fairseq.token_generation_constraints import (
    ConstraintState,
    OrderedConstraintState,
    UnorderedConstraintState,
)
from torch import Tensor


class Search(nn.Module):
    def __init__(self, tgt_dict):
        super().__init__()
        self.pad = tgt_dict.pad()
        self.unk = tgt_dict.unk()
        self.eos = tgt_dict.eos()
        self.vocab_size = len(tgt_dict)
        self.src_lengths = torch.tensor(-1)
        self.supports_constraints = False
        self.stop_on_max_len = False

    def step(
        self, step, lprobs, scores, prev_output_tokens=None, original_batch_idxs=None
    ):
        """Take a single search step.

        Args:
            step: the current search step, starting at 0
            lprobs: (bsz x input_beam_size x vocab_size)
                the model's log-probabilities over the vocabulary at the current step
            scores: (bsz x input_beam_size x step)
                the historical model scores of each hypothesis up to this point
            prev_output_tokens: (bsz x step)
                the previously generated oputput tokens
            original_batch_idxs: (bsz)
                the tensor with the batch indices, in the range [0, bsz)
                this is useful in case there has been applied a re-ordering
                and we need to know the orignal indices

        Return: A tuple of (scores, indices, beams) where:
            scores: (bsz x output_beam_size)
                the scores of the chosen elements; output_beam_size can be
                larger than input_beam_size, e.g., we may return
                2*input_beam_size to account for EOS
            indices: (bsz x output_beam_size)
                the indices of the chosen elements
            beams: (bsz x output_beam_size)
                the hypothesis ids of the chosen elements, in the range [0, input_beam_size)
        """
        raise NotImplementedError

    @torch.jit.export
    def set_src_lengths(self, src_lengths):
        self.src_lengths = src_lengths

    @torch.jit.export
    def init_constraints(self, batch_constraints: Optional[Tensor], beam_size: int):
        """Initialize constraint states for constrained decoding (if supported).

        Args:
            batch_constraints: (torch.Tensor, optional)
                the list of constraints, in packed form
            beam_size: (int)
                the beam size
        Returns:
            *encoder_out* rearranged according to *new_order*
        """
        pass

    def prune_sentences(self, batch_idxs: Tensor):
        """
        Removes constraint states for completed sentences (if supported).
        This is called from sequence_generator._generate() when sentences are
        deleted from the batch.

        Args:
            batch_idxs: Indices of *sentences* whose constraint state should be *kept*.
        """
        pass

    def update_constraints(self, active_hypos: Tensor):
        """
        Updates the constraint states by selecting the beam items that are retained.
        This is called at each time step of sequence_generator._generate() when
        the set of 2 * {beam_size} candidate hypotheses are reduced to the beam size.

        Args:
            active_hypos: (batch size, beam size)
              list of integers denoting, for each sentence, which beam candidate items
              should be kept.
        """
        pass


class BeamSearch(Search):
    def __init__(self, tgt_dict):
        super().__init__(tgt_dict)
        self.constraint_states = None

    @torch.jit.export
    def step(
        self,
        step: int,
        lprobs,
        scores: Optional[Tensor],
        prev_output_tokens: Optional[Tensor] = None,
        original_batch_idxs: Optional[Tensor] = None,
        candidate_multiple: int = 2,
    ):
        bsz, beam_size, vocab_size = lprobs.size()

        if step == 0:
            # at the first step all hypotheses are equally likely, so use
            # only the first beam
            lprobs = lprobs[:, ::beam_size, :].contiguous()
        else:
            # make probs contain cumulative scores for each hypothesis
            assert scores is not None
            lprobs = lprobs + scores[:, :, step - 1].unsqueeze(-1)

        top_prediction = torch.topk(
            lprobs.view(bsz, -1),
            k=min(
                # Take the best `candidate_muliple`(default 2) x beam_size predictions. We'll choose the first
                # beam_size of these which don't predict eos to continue with.
                candidate_multiple * beam_size,
                lprobs.view(bsz, -1).size(1) - 1,  # -1 so we never select pad
            ),
        )
        scores_buf = top_prediction[0]
        indices_buf = top_prediction[1]
        # Project back into relative indices and beams
        beams_buf = torch.div(indices_buf, vocab_size, rounding_mode="trunc")
        indices_buf = indices_buf.fmod(vocab_size)

        # At this point, beams_buf and indices_buf are single-dim and contain relative indices
        return scores_buf, indices_buf, beams_buf


class PrefixConstrainedBeamSearch(Search):
    def __init__(self, tgt_dict, prefix_allowed_tokens_fn):
        super().__init__(tgt_dict)
        self.prefix_allowed_tokens_fn = prefix_allowed_tokens_fn
        self.stop_on_max_len = True

    @torch.jit.export
    def apply_mask(self, x, prev_output_tokens, original_batch_idxs):
        beam_size = x.shape[0] // original_batch_idxs.shape[0]
        original_batch_idxs = (
            original_batch_idxs.unsqueeze(-1).repeat((1, beam_size)).flatten().tolist()
        )

        mask = torch.full_like(x, -math.inf)
        for sent_i, (sent, batch_i) in enumerate(
            zip(prev_output_tokens, original_batch_idxs)
        ):
            mask[sent_i, :, self.prefix_allowed_tokens_fn(batch_i, sent)] = 0

        return mask

    @torch.jit.export
    def step(
        self,
        step: int,
        lprobs: Tensor,
        scores: Tensor,
        prev_output_tokens: Tensor,
        original_batch_idxs: Tensor,
    ):
        bsz, beam_size, vocab_size = lprobs.size()

        lprobs += self.apply_mask(
            lprobs.view(bsz * beam_size, 1, vocab_size),
            prev_output_tokens,
            original_batch_idxs,
        ).view(bsz, beam_size, vocab_size)

        if step == 0:
            # at the first step all hypotheses are equally likely, so use
            # only the first beam
            lprobs = lprobs[:, ::beam_size, :].contiguous()
        else:
            # make probs contain cumulative scores for each hypothesis
            assert scores is not None
            lprobs = lprobs + scores[:, :, step - 1].unsqueeze(-1)

        top_prediction = torch.topk(
            lprobs.view(bsz, -1),
            k=min(
                # Take the best beam_size predictions. We'll choose the first
                # beam_size of these which don't predict eos to continue with.
                beam_size,
                lprobs.view(bsz, -1).size(1) - 1,  # -1 so we never select pad
            ),
        )
        scores_buf = top_prediction[0]
        indices_buf = top_prediction[1]
        beams_buf = indices_buf // vocab_size
        indices_buf = indices_buf.fmod(vocab_size)
        return scores_buf, indices_buf, beams_buf


class LexicallyConstrainedBeamSearch(Search):
    """Implements lexically constrained beam search as described in

        Fast Lexically Constrained Decoding with Dynamic Beam
        Allocation for Neural Machine Translation.  Post & Vilar,
        NAACL 2018.  https://www.aclweb.org/anthology/N18-1119/

    and

        Improved Lexically Constrained Decoding for Translation and
        Monolingual Rewriting. Hu et al, NAACL
        2019. https://www.aclweb.org/anthology/N19-1090/

    This is accomplished by maintaining, for each beam hypothesis, a
    ConstraintState object (see constraints.py) that tracks which
    constraints have been generated and using this information to
    shape the beam for each input sentence.
    """

    def __init__(self, tgt_dict, representation):
        super().__init__(tgt_dict)
        self.representation = representation
        self.vocab_size = len(tgt_dict)
        self.num_cands = 0
        self.supports_constraints = True

    @torch.jit.export
    def init_constraints(self, batch_constraints: Optional[Tensor], beam_size: int):
        self.constraint_states = []
        for constraint_tensor in batch_constraints:
            if self.representation == "ordered":
                constraint_state = OrderedConstraintState.create(constraint_tensor)
            elif self.representation == "unordered":
                constraint_state = UnorderedConstraintState.create(constraint_tensor)

            self.constraint_states.append([constraint_state for i in range(beam_size)])

    @torch.jit.export
    def prune_sentences(self, batch_idxs: Tensor):
        self.constraint_states = [
            self.constraint_states[i] for i in batch_idxs.tolist()
        ]

    @torch.jit.export
    def update_constraints(self, active_hypos: Tensor):
        if self.constraint_states:
            batch_size = active_hypos.size(0)
            for sentid in range(batch_size):
                self.constraint_states[sentid] = [
                    self.constraint_states[sentid][i] for i in active_hypos[sentid]
                ]

    @torch.jit.export
    def step(
        self,
        step: int,
        lprobs: Tensor,
        scores: Optional[Tensor],
        prev_output_tokens: Optional[Tensor] = None,
        original_batch_idxs: Optional[Tensor] = None,
    ):
        """
        A constrained step builds a large candidates list from the following:
        - the top 2 * {beam_size} items over the whole beam
        - for each item in the beam
          - the top {each_k} (default 1)
          - all next constraints
        We then compute the constrained state of each beam item, and assign
        stripe codes: 0 to the best in each bank, 1 to the 2nd-best, and so
        on. We then sort by (stripe, score), and truncate the list at
        2 * beam size.

        Args:
            step: the decoder step
            lprobs: (batch size, beam size, target vocab)
                the target-vocab distributions for each item in the beam.
        Retrun: A tuple of (scores, indices, beams, constraints) where:
            scores: (batch, output beam size)
                the scores of the chosen elements
            indices: (batch, output beam size)
                the target vocab indices of the chosen elements
            beams: (batch, output beam size)
                the 0-indexed hypothesis ids of the chosen elements
            constraints: (batch, output beam size)
                the new constraint states
        """
        each_k = 1
        device = lprobs.device

        batch_size, beam_size, vocab_size = lprobs.size()

        self.num_cands = min(
            # Just take the k-best. We'll get another k from the 1-best from each
            # row, plus more from the constraints
            beam_size * 2,
            lprobs.view(batch_size, -1).size(1) - 1,  # -1 so we never select pad
        )

        # STEP 0: Preliminary. Prevent EOS for unfinished hyps across all batch items
        constraint_states = self.constraint_states
        if constraint_states and step > 0:
            not_finished_indices = []
            for sentno, sent_constraints in enumerate(constraint_states):
                for beamno, state in enumerate(sent_constraints):
                    index = sentno * beam_size + beamno
                    if not state.finished:
                        not_finished_indices.append(index)
            not_finished_indices = torch.tensor(not_finished_indices)
            if not_finished_indices.numel() > 0:
                lprobs.view(batch_size * beam_size, -1)[
                    not_finished_indices, self.eos
                ] = -math.inf

        if step == 0:
            # at the first step all hypotheses are equally likely, so use
            # only the first beam entry for each batch item
            lprobs = lprobs[:, ::beam_size, :].contiguous()
        else:
            # make probs contain cumulative scores for each hypothesis
            assert scores is not None
            lprobs = lprobs + scores[:, :, step - 1].unsqueeze(-1)

        top_prediction = torch.topk(
            lprobs.view(batch_size, -1),
            self.num_cands,
        )
        scores_buf, indices_buf = top_prediction
        # Project back into relative indices and beams
        beams_buf = indices_buf // vocab_size
        indices_buf = indices_buf.fmod(vocab_size)

        # Short circuit if there are no constraints in this batch
        if not constraint_states:
            return scores_buf, indices_buf, beams_buf

        # STEP 1: get top-1 from each hypothesis across all sentences in the batch
        if step > 0:
            top_scores, top_indices = torch.topk(
                lprobs.view(batch_size * beam_size, -1),
                k=each_k,
                dim=1,
            )
            top_scores = top_scores.view(batch_size, -1)
            top_indices = top_indices.view(batch_size, -1)
            scores_buf = torch.cat((scores_buf, top_scores), dim=1)
            indices_buf = torch.cat((indices_buf, top_indices), dim=1)
            new_beams = torch.arange(0, beam_size, device=device).repeat(batch_size, 1)
            beams_buf = torch.cat((beams_buf, new_beams), dim=1)

        # Now, process sentences in the batch one by one.
        new_scores_buf = torch.zeros((batch_size, 2 * beam_size), device=device)
        new_indices_buf = torch.zeros((batch_size, 2 * beam_size), device=device).long()
        new_beams_buf = torch.zeros((batch_size, 2 * beam_size), device=device).long()
        for sentno, states in enumerate(constraint_states):
            scores, indices, beams, new_states = self.step_sentence(
                step,
                sentno,
                lprobs[sentno],
                constraint_states[sentno],
                beams_buf[sentno].clone(),
                indices_buf[sentno].clone(),
                scores_buf[sentno].clone(),
            )
            new_scores_buf[sentno] = scores
            new_indices_buf[sentno] = indices
            new_beams_buf[sentno] = beams
            self.constraint_states[sentno] = new_states

        return new_scores_buf, new_indices_buf, new_beams_buf

    @torch.jit.export
    def step_sentence(
        self,
        step: int,
        sentno: int,
        lprobs: Tensor,
        constraint_states: List[List[ConstraintState]],
        beams_buf: Tensor,
        indices_buf: Tensor,
        scores_buf: Tensor,
    ):
        """Does per-sentence processing. Adds all constraints for each
        hypothesis to the list of candidates; then removes duplicates,
        sorts, and dynamically stripes across the banks. All tensor inputs
        are collapsed to those pertaining to a single input sentence.
        """
        device = lprobs.device

        # STEP 2: Add all constraints for each beam item
        for beamno, state in enumerate(constraint_states):
            next_tokens = torch.tensor(list(state.next_tokens()), device=device).long()
            if next_tokens.numel() != 0:
                indices_buf = torch.cat((indices_buf, next_tokens))
                next_beams = (
                    torch.tensor(beamno, device=device)
                    .repeat(next_tokens.size(0))
                    .long()
                )
                beams_buf = torch.cat((beams_buf, next_beams))
                next_values = lprobs[beamno].take(next_tokens.view(-1))
                scores_buf = torch.cat((scores_buf, next_values))

            # At the 0th time step, there is just one beam item
            if step == 0:
                break

        # STEP 3: Compute the "bank" for each candidate. This is the
        # number of constraints it's generated. We need this so that
        # we can do round-robin allocation of the beam across these
        # banks. If C is the number of constraints, we select the best
        # item in bank C, then the best in bank C-1, etc, followed by
        # the 2nd-best in bank C, the 2nd-best in bank C-1, etc, and so
        # on, until the maximum beam size. We accomplish this by
        # creating a sort key and striping across the banks.

        # Compute the new states for all candidates
        cands_size = indices_buf.size(0)
        constraint_states = [
            constraint_states[beams_buf[i]].advance(indices_buf[i])
            for i in range(cands_size)
        ]

        banks = torch.tensor([state.bank for state in constraint_states], device=device)

        # STEP 4: Sort
        num_constraint_tokens = len(state.tokens)

        # Sort by keys (bank, score) (i.e., sort banks together, and scores
        # within banks). AFAIK pytorch doesn't support either stable sort or
        # multi-key sorting, so we have to hack this.
        MAX_SCORE = -100
        sort_key = (num_constraint_tokens - banks) * MAX_SCORE + scores_buf
        sort_values, sort_indices = sort_key.sort(dim=0, descending=True)
        scores_buf = scores_buf[sort_indices]
        indices_buf = indices_buf[sort_indices]
        beams_buf = beams_buf[sort_indices]
        banks = banks[sort_indices]

        # Sort the constraints to follow suit
        constraint_states = [constraint_states[i] for i in sort_indices]

        # STEP 5: Remove duplicates. The topk calls (overall and
        # per-row) plus the per-row generation of constraints will
        # produce duplicates. Here we remove them.

        def roll(t):
            """Rolls a 1d tensor left by 1.

            [0, 1, 2, 3, 4] becomes [4, 0, 1, 2, 3]
            """
            return torch.cat((t[-1].unsqueeze(0), t[0:-1]), dim=0)

        # We map candidates (beam, token_id) to a single dimension.
        # This is then shifted by 1. We can then easily identify
        # duplicates and create a mask that identifies unique
        # extensions.
        uniques_mask = beams_buf * (self.vocab_size + 1) + indices_buf
        uniques_mask = roll(uniques_mask) != uniques_mask

        # Use the mask to pare down the data structures
        scores_buf = torch.masked_select(scores_buf, uniques_mask)
        indices_buf = torch.masked_select(indices_buf, uniques_mask)
        beams_buf = torch.masked_select(beams_buf, uniques_mask)
        banks = torch.masked_select(banks, uniques_mask)
        i = 1
        for mask in uniques_mask[1:]:
            if not mask:
                constraint_states.pop(i)
            i += mask

        # STEP 6: Assign IDs round-robin across banks, sort, and
        # truncate. Now that the candidates are sorted by (bank,
        # score) and uniqed, we dynamically allocate the {beam_size}
        # beam by striping across the candidates. These stripes will
        # be used as sort keys to do round-robin selection. This is
        # accomplished in a single pass with offsets. Sorting by
        # highest-banks (furthest-along hypotheses) first ensures
        # progress through the constraints.
        #
        # e.g., BANKS: 3 3 3 2 2 2 2 1 1 1 0 0
        # OLD STRIPES: 0 1 2 0 1 2 3 0 1 2 0 1
        # NEW STRIPES: 0 1+4 2+8 0+1 1+5 2+9 3+11 0+2 1+6 2+10 0+3 1+7
        #            = 0 5 10 1 6 11 13 2 7 12 3 8
        #
        # Sorting by this then gives the following banks:
        #
        #             3 2 1 0 3 2 1 0 3 2 1 2
        #
        # We'll take the top {beam_size} of these.
        stripe_offsets = [offset * (len(banks) + 1) for offset in range(len(banks) + 1)]
        stripes = torch.zeros_like(banks)
        cur_bank_count = -1
        cur_bank = banks[0]
        for i, bank in enumerate(banks):
            if bank != cur_bank:
                cur_bank_count = 0
                cur_bank = bank
            else:
                cur_bank_count += 1
            stripes[i] = num_constraint_tokens - bank + stripe_offsets[cur_bank_count]

        # STEP 7: Sort by the stripes values
        sort_values, sort_indices = stripes.sort(dim=0)
        scores_buf = scores_buf[sort_indices]
        indices_buf = indices_buf[sort_indices]
        beams_buf = beams_buf[sort_indices]
        constraint_states = [constraint_states[i] for i in sort_indices]

        # STEP 8: Truncate to the candidates size!
        scores_buf = scores_buf[: self.num_cands]
        indices_buf = indices_buf[: self.num_cands]
        beams_buf = beams_buf[: self.num_cands]

        return scores_buf, indices_buf, beams_buf, constraint_states


class LengthConstrainedBeamSearch(Search):
    def __init__(self, tgt_dict, min_len_a, min_len_b, max_len_a, max_len_b):
        super().__init__(tgt_dict)
        self.min_len_a = min_len_a
        self.min_len_b = min_len_b
        self.max_len_a = max_len_a
        self.max_len_b = max_len_b
        self.beam = BeamSearch(tgt_dict)
        self.needs_src_lengths = True

    def step(
        self,
        step: int,
        lprobs,
        scores,
        prev_output_tokens: Optional[Tensor] = None,
        original_batch_idxs: Optional[Tensor] = None,
    ):
        min_lens = self.min_len_a * self.src_lengths + self.min_len_b
        max_lens = self.max_len_a * self.src_lengths + self.max_len_b
        lprobs[step < min_lens, :, self.eos] = -math.inf
        lprobs[step >= max_lens, :, self.eos] = 0
        return self.beam.step(step, lprobs, scores)


class DiverseBeamSearch(Search):
    """Diverse Beam Search.

    See "Diverse Beam Search: Decoding Diverse Solutions from Neural Sequence
    Models" for details.

    We implement cumulative diversity penalty here as default, optionally provide Hamming diversity described
    in the original paper, and a way to interpolate between the two through diversity_discount.

    Take the example below for illustration of cumulative diversity implemented.
    A) I like dogs.
    B) I like ____.
    C) There are ___.
    And we are at step=2, trying to fill in the blank:

    Hamming diversity:
    Penalty for B from A is 1 for "dogs" and 0 for any other words like "cats".
    Penalty for C from A is 1 for "dogs" and 0 for any other words like "cats".

    Cumulative diversity (default):
    Penalty for B from A is 3 for "dogs" and 0 for any other words like "cats".
    Penalty for C from A is 1 for "dogs" and 0 for any other words like "cats".
    B and C differ because B matches with A for "I" and "like" at respective steps incurring 2 cumulative penalty.

    Using divesrity_discount to interpolate between the two:
    if diverstiy_discount = 0.5, then
    Penalty for B from A is 1.75 (1 + 0.5 + 0.25) for "dogs" and 0 for any other words like "cats".
    Penalty for C from A is 1 for "dogs" and 0 for any other words like "cats".
    "I" and "like" matched for B and A at step 0 and 1 respectively. Since "I" is two steps away and "like" is one step away, they are discounted by (0.5)^2 and 0.5 respectively.
    When diversity_discount = 0, we recover Hammning diversity and when diversity_discount = 1, we recover cumulative diversity.

    NB: During beam search for each diversity group, `candidate_mutiple` is set to 1 rather than BeamSearch default(2).
    This is to ensure we have final `beam_size` candidates so that no diversity groups would be dropped during final token selection in sequence generation.
    For full backwards compatibility, use diversity_discount=0 and candidate_multiple=2.

    """

    def __init__(
        self,
        tgt_dict,
        num_groups,
        diversity_strength,
        diversity_discount=1.0,
        candidate_multiple=1,
    ):
        super().__init__(tgt_dict)
        self.num_groups = num_groups
        self.diversity_strength = -diversity_strength
        self.beam = BeamSearch(tgt_dict)
        self.diversity_discount = diversity_discount
        self.candidate_multiple = candidate_multiple

        # Float tensor to keep track of overlap between groups.
        # Each token shared at the same step between two groups is counted as one.
        # Then token counts are discounted by `diversity_discount` for every next timestep.
        # Once initialized, dimension is batch_size * num_groups * num_groups.
        self.group_overlap = torch.empty(0)

    @torch.jit.export
    def step(
        self,
        step: int,
        lprobs,
        scores,
        prev_output_tokens: Optional[Tensor] = None,
        original_batch_idxs: Optional[Tensor] = None,
    ):
        bsz, beam_size, vocab_size = lprobs.size()
        if beam_size % self.num_groups != 0:
            raise ValueError(
                "DiverseBeamSearch requires --beam to be divisible by the number of groups"
            )

        # initialize diversity penalty
        diversity_buf = torch.zeros(lprobs[:, 0, :].size()).to(lprobs)

        scores_G, beams_G = [], []

        # pre-allocating tensor for indices for all groups
        indices_G_stacked = torch.empty(
            bsz,
            int(beam_size / self.num_groups) * self.candidate_multiple,
            self.num_groups,
            dtype=torch.long,
            device=lprobs.device,
        )

        for g in range(self.num_groups):
            lprobs_g = lprobs[:, g :: self.num_groups, :]
            scores_g = scores[:, g :: self.num_groups, :] if step > 0 else None

            diversity_buf.zero_()
            # apply diversity penalty
            if g > 0:
                indices_ = indices_G_stacked[:, :, :g]
                if step > 0:
                    penalty_val = 1 + self.group_overlap[original_batch_idxs, g, :g]
                    penalty_val = penalty_val.unsqueeze(1)
                else:
                    penalty_val = torch.ones(bsz, 1, 1)
                diversity_buf.scatter_add_(
                    1,
                    indices_.reshape(bsz, -1),
                    penalty_val.expand(indices_.size())
                    .reshape(bsz, -1)
                    .to(diversity_buf),
                )

                lprobs_g = torch.add(
                    lprobs_g,
                    other=diversity_buf.unsqueeze(1),
                    alpha=self.diversity_strength,
                )
            else:
                lprobs_g = lprobs_g.contiguous()

            scores_buf, indices_buf, beams_buf = self.beam.step(
                step, lprobs_g, scores_g, candidate_multiple=self.candidate_multiple
            )
            beams_buf.mul_(self.num_groups).add_(g)

            scores_G.append(scores_buf.clone())
            beams_G.append(beams_buf.clone())

            indices_G_stacked[:, :, g] = indices_buf

        # interleave results from different groups
        scores_buf = torch.stack(scores_G, dim=2).view(bsz, -1)
        indices_buf = indices_G_stacked.view(bsz, -1)
        beams_buf = torch.stack(beams_G, dim=2).view(bsz, -1)
        # find num of overlapped tokens for each group pair
        # then discount it for next timestamp
        overlap = self.diversity_discount * torch.sum(
            indices_G_stacked.unsqueeze(2).eq(indices_G_stacked.unsqueeze(3)), dim=1
        )
        if step == 0:
            self.group_overlap = overlap
        else:
            self.group_overlap[original_batch_idxs] = (
                self.group_overlap[original_batch_idxs] * self.diversity_discount
                + overlap
            )

        return scores_buf, indices_buf, beams_buf


class Sampling(Search):
    sampling_topk: int
    sampling_topp: float

    def __init__(self, tgt_dict, sampling_topk=-1, sampling_topp=-1.0):
        super().__init__(tgt_dict)
        self.sampling_topk = sampling_topk
        self.sampling_topp = sampling_topp

    def _sample_topp(self, lprobs):
        """Sample among the smallest set of elements whose cumulative probability mass exceeds p.

        See `"The Curious Case of Neural Text Degeneration"
        (Holtzman et al., 2019) <https://arxiv.org/abs/1904.09751>`_.

        Args:
            lprobs: (bsz x input_beam_size x vocab_size)
                the model's log-probabilities over the vocabulary at the current step

        Return: A tuple of (trimed_probs, truncated_indices) where:
            trimed_probs: (bsz x input_beam_size x ?)
                the model's probabilities over the elements selected to sample from. The
                width of the third dimension is determined by top-P.
            truncated_indices: (bsz x input_beam_size x ?)
                the indices of the chosen elements.
        """
        probs = lprobs.exp_()

        # sort the last dimension (vocab dimension) in descending order
        sorted_probs, sorted_indices = probs.sort(descending=True)

        # compute a mask to indicate the words to be included in the top-P set.
        cumsum_probs = sorted_probs.cumsum(dim=2)
        mask = cumsum_probs.lt(self.sampling_topp)

        # note that mask was computed by 'lt'. One more word needs to be included
        # so that the cumulative probability mass can exceed p.
        cumsum_mask = mask.cumsum(dim=2)
        last_included = cumsum_mask[:, :, -1:]
        last_included.clamp_(0, mask.size()[2] - 1)
        mask = mask.scatter_(2, last_included, 1)

        # truncate unnecessary dims.
        max_dim = last_included.max()
        truncated_mask = mask[:, :, : max_dim + 1]
        truncated_probs = sorted_probs[:, :, : max_dim + 1]
        truncated_indices = sorted_indices[:, :, : max_dim + 1]

        # trim the words that are not in top-P by setting their probabilities
        # to 0, so that they would not be sampled later.
        trim_mask = ~truncated_mask
        trimed_probs = truncated_probs.masked_fill_(trim_mask, 0)
        return trimed_probs, truncated_indices

    @torch.jit.export
    def step(
        self,
        step: int,
        lprobs,
        scores,
        prev_output_tokens: Optional[Tensor] = None,
        original_batch_idxs: Optional[Tensor] = None,
    ):
        bsz, beam_size, vocab_size = lprobs.size()

        if step == 0:
            # at the first step all hypotheses are equally likely, so use
            # only the first beam
            lprobs = lprobs[:, ::beam_size, :].contiguous()

        if self.sampling_topp > 0:
            # only sample from the smallest set of words whose cumulative probability mass exceeds p
            probs, top_indices = self._sample_topp(lprobs)
        elif self.sampling_topk > 0:
            # only sample from top-k candidates
            lprobs, top_indices = lprobs.topk(self.sampling_topk)
            probs = lprobs.exp_()
        else:
            probs = lprobs.exp_()

            # dummy data to be consistent with true branch for type check
            top_indices = torch.empty(0).to(probs)
        # sample
        if step == 0:
            indices_buf = torch.multinomial(
                probs.view(bsz, -1),
                beam_size,
                replacement=True,
            ).view(bsz, beam_size)
        else:
            indices_buf = torch.multinomial(
                probs.view(bsz * beam_size, -1),
                1,
                replacement=True,
            ).view(bsz, beam_size)

        if step == 0:
            # expand to beam size
            probs = probs.expand(bsz, beam_size, -1)

        # gather scores
        scores_buf = torch.gather(probs, dim=2, index=indices_buf.unsqueeze(-1))
        scores_buf = scores_buf.log_().view(bsz, -1)

        # remap indices if using top-k or top-P sampling
        if self.sampling_topk > 0 or self.sampling_topp > 0:
            indices_buf = torch.gather(
                top_indices.expand(bsz, beam_size, -1),
                dim=2,
                index=indices_buf.unsqueeze(-1),
            ).squeeze(2)

        if step == 0:
            beams_buf = indices_buf.new_zeros(bsz, beam_size)
        else:
            beams_buf = torch.arange(0, beam_size).to(indices_buf).repeat(bsz, 1)
            # make scores cumulative
            scores_buf.add_(
                torch.gather(scores[:, :, step - 1], dim=1, index=beams_buf)
            )

        return scores_buf, indices_buf, beams_buf


class DiverseSiblingsSearch(Search):
    """
    Beam search with diverse siblings.

    See "A Simple, Fast Diverse Decoding Algorithm for Neural Generation" for details.
    https://arxiv.org/abs/1611.08562

    1/ Calculate hypotheses for each beam
    2/ Intra-sibling ordering
    3/ Rewrite scores
    4/ Choose top K hypotheses

    if diversity_rate == 0 is equivalent to BeamSearch
    """

    def __init__(self, tgt_dict, diversity_rate):
        super().__init__(tgt_dict)
        self.diversity_rate = diversity_rate
        self.beam = BeamSearch(tgt_dict)

    def step(
        self,
        step: int,
        lprobs,
        scores,
        prev_output_tokens: Optional[Tensor] = None,
        original_batch_idxs: Optional[Tensor] = None,
    ):
        bsz, beam_size, vocab_size = lprobs.size()
        k = min(
            # Take the best 2 x beam_size predictions. We'll choose the first
            # beam_size of these which don't predict eos to continue with.
            beam_size * 2,
            lprobs.view(bsz, -1).size(1) - 1,  # -1 so we never select pad
        )
        s_list: List[Tensor]
        i_list: List[Tensor]
        s_list = [torch.empty(0).to(lprobs) for i in range(beam_size)]
        i_list = [torch.LongTensor().to(device=lprobs.device) for i in range(beam_size)]
        sibling_score = torch.arange(1, k + 1).to(lprobs) * self.diversity_rate

        if step == 0:
            return self.beam.step(step, lprobs, scores)
        lprobs.add_(scores[:, :, step - 1].unsqueeze(-1))

        # 1/ Calculate hypotheses for each beam
        for i in range(beam_size):
            torch.topk(lprobs[:, i, :].view(bsz, -1), k, out=(s_list[i], i_list[i]))
            i_list[i].fmod_(vocab_size)

            # 2/ Intra-sibling ordering by default from topk + 3/ Rewrite scores
            s_list[i].sub_(sibling_score)

        # 4/ Choose top K hypotheses
        indices = torch.stack(i_list, dim=1).view(bsz, -1)

        final_scores = torch.empty(0).to(lprobs)
        final_indices = torch.LongTensor().to(device=lprobs.device)
        final_beams = torch.LongTensor().to(device=lprobs.device)
        (final_scores, final_indices) = torch.topk(
            torch.stack(s_list, dim=1).view(bsz, -1),
            k,
        )

        final_beams = final_indices // k

        for i in range(bsz):
            final_indices[i] = indices[i][final_indices[i]]

        return final_scores, final_indices, final_beams
