# -*- coding: utf-8 -*-

from typing import Optional, Tuple

import torch
import triton
import triton.language as tl
from einops import rearrange

from fla.utils import autocast_custom_bwd, autocast_custom_fwd, contiguous


# Inspired by "THE WY REPRESENTATION FOR PRODUCTS OF HOUSEHOLDER MATRICES" https://epubs.siam.org/doi/pdf/10.1137/0908009
@triton.autotune(
    configs=[
        triton.Config({}, num_warps=1),
        triton.Config({}, num_warps=2),
        triton.Config({}, num_warps=4),
        triton.Config({}, num_warps=8),
        triton.Config({}, num_warps=16)
    ],
    key=["BK"]
)
@triton.heuristics({'USE_OFFSETS': lambda args: args['offsets'] is not None})
@triton.jit
def fwd_prepare_wy_repr_kernel_chunk32(
    k,
    beta,
    A,
    offsets,
    indices,
    T: tl.constexpr,
    H: tl.constexpr,
    K: tl.constexpr,
    BT: tl.constexpr,
    BK: tl.constexpr,
    BC: tl.constexpr,
    USE_OFFSETS: tl.constexpr,
    HEAD_FIRST: tl.constexpr,
):
    i_t, i_bh = tl.program_id(0), tl.program_id(1)
    i_b, i_h = i_bh // H, i_bh % H
    if USE_OFFSETS:
        i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32)
        bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32)
        T = eos - bos
    else:
        bos, eos = i_b * T, i_b * T + T

    if HEAD_FIRST:
        p_beta = tl.make_block_ptr(beta + i_bh * T, (T,), (1,), (i_t * BT,), (BT,), (0,))
    else:
        p_beta = tl.make_block_ptr(beta + bos * H + i_h, (T,), (H,), (i_t * BT,), (BT,), (0,))
    b_beta = tl.load(p_beta, boundary_check=(0,))

    b_A = tl.zeros([BT, BT], dtype=tl.float32)
    for i_k in range(tl.cdiv(K, BK)):
        if HEAD_FIRST:
            p_k = tl.make_block_ptr(k + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
        else:
            p_k = tl.make_block_ptr(k + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
        b_k = tl.load(p_k, boundary_check=(0, 1))
        b_kb = (b_k * b_beta[:, None]).to(b_k.dtype)
        b_A += tl.dot(b_kb, tl.trans(b_k), allow_tf32=False)

    b_A = -tl.where(tl.arange(0, BT)[:, None] > tl.arange(0, BT)[None, :], b_A, 0)
    for i in range(1, BT):
        mask = tl.arange(0, BT) == i
        b_a = tl.sum(tl.where(mask[:, None], b_A, 0), 0)
        b_a = b_a + tl.sum(b_a[:, None] * b_A, 0) * (tl.arange(0, BT) < i)
        b_A = tl.where(mask[:, None], b_a, b_A)
    b_A += tl.arange(0, BT)[:, None] == tl.arange(0, BT)[None, :]

    if HEAD_FIRST:
        p_A = tl.make_block_ptr(A + i_bh * T * BT, (T, BT), (BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
    else:
        p_A = tl.make_block_ptr(A + (bos*H + i_h) * BT, (T, BT), (H*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
    tl.store(p_A, (b_A).to(p_A.dtype.element_ty), boundary_check=(0, 1))
    b_A = b_A.to(k.dtype.element_ty)


@triton.autotune(
    configs=[
        triton.Config({}, num_warps=1),
        triton.Config({}, num_warps=2),
        triton.Config({}, num_warps=4),
        triton.Config({}, num_warps=8),
        triton.Config({}, num_warps=16)
    ],
    key=["BK"],
)
@triton.heuristics({'USE_OFFSETS': lambda args: args['offsets'] is not None})
@triton.jit
def fwd_prepare_wy_repr_kernel_chunk64(
    k,
    beta,
    A,
    offsets,
    indices,
    T: tl.constexpr,
    H: tl.constexpr,
    K: tl.constexpr,
    BT: tl.constexpr,
    BK: tl.constexpr,
    BC: tl.constexpr,
    USE_OFFSETS: tl.constexpr,
    HEAD_FIRST: tl.constexpr
):
    i_t, i_bh = tl.program_id(0), tl.program_id(1)
    i_b, i_h = i_bh // H, i_bh % H
    if USE_OFFSETS:
        i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32)
        bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32)
        T = eos - bos
    else:
        bos, eos = i_b * T, i_b * T + T

    b_A = tl.zeros([BC, BC], dtype=tl.float32)
    b_A2 = tl.zeros([BC, BC], dtype=tl.float32)
    b_A3 = tl.zeros([BC, BC], dtype=tl.float32)

    if HEAD_FIRST:
        p_beta = tl.make_block_ptr(beta + i_bh * T, (T,), (1,), (i_t * BT,), (BC,), (0,))
    else:
        p_beta = tl.make_block_ptr(beta + bos * H + i_h, (T,), (H,), (i_t * BT,), (BC,), (0,))
    b_beta = tl.load(p_beta, boundary_check=(0,))

    if HEAD_FIRST:
        p_beta2 = tl.make_block_ptr(beta + i_bh * T, (T,), (1,), (i_t * BT + BC,), (BC,), (0,))
    else:
        p_beta2 = tl.make_block_ptr(beta + bos * H + i_h, (T,), (H,), (i_t * BT + BC,), (BC,), (0,))
    b_beta2 = tl.load(p_beta2, boundary_check=(0,))

    for i_k in range(tl.cdiv(K, BK)):
        if HEAD_FIRST:
            p_k = tl.make_block_ptr(k + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BC, BK), (1, 0))
            p_k2 = tl.make_block_ptr(k + i_bh * T*K, (T, K), (K, 1), (i_t * BT + BC, i_k * BK), (BC, BK), (1, 0))
        else:
            p_k = tl.make_block_ptr(k + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BC, BK), (1, 0))
            p_k2 = tl.make_block_ptr(k + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT + BC, i_k * BK), (BC, BK), (1, 0))
        b_k = tl.load(p_k, boundary_check=(0, 1))
        b_kb = (b_k * b_beta[:, None]).to(b_k.dtype)
        b_k2 = tl.load(p_k2, boundary_check=(0, 1))
        b_kb2 = (b_k2 * b_beta2[:, None]).to(b_k2.dtype)
        b_A += tl.dot(b_kb, tl.trans(b_k), allow_tf32=False)
        b_A2 += tl.dot(b_kb2, tl.trans(b_k2), allow_tf32=False)
        b_A3 += tl.dot(b_kb2, tl.trans(b_k), allow_tf32=False)

    b_A = -tl.where(tl.arange(0, BC)[:, None] > tl.arange(0, BC)[None, :], b_A, 0)
    b_A2 = -tl.where(tl.arange(0, BC)[:, None] > tl.arange(0, BC)[None, :], b_A2, 0)
    for i in range(1, BC):
        mask = tl.arange(0, BC) == i
        b_a = tl.sum(tl.where(mask[:, None], b_A, 0), 0)
        b_a2 = tl.sum(tl.where(mask[:, None], b_A2, 0), 0)
        b_a = b_a + tl.sum(b_a[:, None] * b_A, 0) * (tl.arange(0, BC) < i)
        b_a2 = b_a2 + tl.sum(b_a2[:, None] * b_A2, 0) * (tl.arange(0, BC) < i)
        b_A = tl.where(mask[:, None], b_a, b_A)
        b_A2 = tl.where(mask[:, None], b_a2, b_A2)

    # blockwise computation of lower triangular matrix's inverse
    # i.e., [A11, 0; A21, A22]^-1 = [A11^-1, 0; -A22^-1 A21 A11^-1, A22^-1]
    b_A += tl.arange(0, BC)[:, None] == tl.arange(0, BC)[None, :]
    b_A2 += tl.arange(0, BC)[:, None] == tl.arange(0, BC)[None, :]
    b_A3 = -tl.dot(tl.dot(b_A2, b_A3, allow_tf32=False), b_A, allow_tf32=False)

    if HEAD_FIRST:
        p_A1 = tl.make_block_ptr(A + i_bh * T * BT, (T, BT), (BT, 1), (i_t * BT, 0), (BC, BC), (1, 0))
        p_A2 = tl.make_block_ptr(A + i_bh * T * BT, (T, BT), (BT, 1), (i_t * BT + BC, BC), (BC, BC), (1, 0))
        p_A3 = tl.make_block_ptr(A + i_bh * T * BT, (T, BT), (BT, 1), (i_t * BT + BC, 0), (BC, BC), (1, 0))
        p_A4 = tl.make_block_ptr(A + i_bh * T * BT, (T, BT), (BT, 1), (i_t * BT, BC), (BC, BC), (1, 0))
    else:
        p_A1 = tl.make_block_ptr(A + (bos*H + i_h) * BT, (T, BT), (H*BT, 1), (i_t * BT, 0), (BC, BC), (1, 0))
        p_A2 = tl.make_block_ptr(A + (bos*H + i_h) * BT, (T, BT), (H*BT, 1), (i_t * BT + BC, BC), (BC, BC), (1, 0))
        p_A3 = tl.make_block_ptr(A + (bos*H + i_h) * BT, (T, BT), (H*BT, 1), (i_t * BT + BC, 0), (BC, BC), (1, 0))
        p_A4 = tl.make_block_ptr(A + (bos*H + i_h) * BT, (T, BT), (H*BT, 1), (i_t * BT, BC), (BC, BC), (1, 0))
    tl.store(p_A1, b_A.to(p_A1.dtype.element_ty), boundary_check=(0, 1))
    tl.store(p_A2, b_A2.to(p_A2.dtype.element_ty), boundary_check=(0, 1))
    tl.store(p_A3, b_A3.to(p_A3.dtype.element_ty), boundary_check=(0, 1))
    # causal mask
    tl.store(p_A4, tl.zeros([BC, BC], dtype=tl.float32).to(p_A4.dtype.element_ty), boundary_check=(0, 1))


@triton.autotune(
    configs=[
        triton.Config({}, num_warps=1),
        triton.Config({}, num_warps=2),
        triton.Config({}, num_warps=4),
        triton.Config({}, num_warps=8)
    ],
    key=["BT", "BK", "BV"],
)
@triton.heuristics({'USE_OFFSETS': lambda args: args['offsets'] is not None})
@triton.jit
def fwd_recompute_w_u_kernel(
    k,
    v,
    beta,
    w,
    u,
    A,
    offsets,
    indices,
    T: tl.constexpr,
    H: tl.constexpr,
    K: tl.constexpr,
    V: tl.constexpr,
    BT: tl.constexpr,
    BK: tl.constexpr,
    BV: tl.constexpr,
    USE_OFFSETS: tl.constexpr,
    HEAD_FIRST: tl.constexpr
):
    i_t, i_bh = tl.program_id(0), tl.program_id(1)
    i_b, i_h = i_bh // H, i_bh % H
    if USE_OFFSETS:
        i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32)
        bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32)
        T = eos - bos
    else:
        bos, eos = i_b * T, i_b * T + T

    if HEAD_FIRST:
        p_beta = tl.make_block_ptr(beta + i_bh * T, (T,), (1,), (i_t * BT,), (BT,), (0,))
        p_A = tl.make_block_ptr(A + i_bh * T * BT, (T, BT), (BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
    else:
        p_beta = tl.make_block_ptr(beta + bos * H + i_h, (T,), (H,), (i_t * BT,), (BT,), (0,))
        p_A = tl.make_block_ptr(A + (bos*H + i_h) * BT, (T, BT), (H*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
    b_beta = tl.load(p_beta, boundary_check=(0,))
    b_A = tl.load(p_A, boundary_check=(0, 1))

    for i_v in range(tl.cdiv(V, BV)):
        if HEAD_FIRST:
            p_v = tl.make_block_ptr(v + i_bh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
            p_u = tl.make_block_ptr(u + i_bh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
        else:
            p_v = tl.make_block_ptr(v + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
            p_u = tl.make_block_ptr(u + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
        b_v = tl.load(p_v, boundary_check=(0, 1))
        b_vb = (b_v * b_beta[:, None]).to(b_v.dtype)
        b_u = tl.dot(b_A.to(b_vb.dtype), b_vb, allow_tf32=False)
        tl.store(p_u, (b_u).to(p_u.dtype.element_ty), boundary_check=(0, 1))

    for i_k in range(tl.cdiv(K, BK)):
        if HEAD_FIRST:
            p_k = tl.make_block_ptr(k + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
            p_w = tl.make_block_ptr(w + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
        else:
            p_k = tl.make_block_ptr(k + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
            p_w = tl.make_block_ptr(w + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
        b_k = tl.load(p_k, boundary_check=(0, 1))
        b_kb = (b_k * b_beta[:, None]).to(b_k.dtype)
        b_w = tl.dot(b_A.to(b_kb.dtype), b_kb, allow_tf32=False)
        tl.store(p_w, b_w.to(p_w.dtype.element_ty), boundary_check=(0, 1))


@triton.autotune(
    configs=[
        triton.Config({}, num_warps=1),
        triton.Config({}, num_warps=2),
        triton.Config({}, num_warps=4),
        triton.Config({}, num_warps=8)
    ],
    key=["BT", "BK"],
)
@triton.heuristics({'USE_OFFSETS': lambda args: args['offsets'] is not None})
@triton.jit
def fwd_recompute_w_kernel(
    k,
    beta,
    w,
    A,
    offsets,
    indices,
    T: tl.constexpr,
    H: tl.constexpr,
    K: tl.constexpr,
    BT: tl.constexpr,
    BK: tl.constexpr,
    USE_OFFSETS: tl.constexpr,
    HEAD_FIRST: tl.constexpr
):
    i_t, i_bh = tl.program_id(0), tl.program_id(1)
    i_b, i_h = i_bh // H, i_bh % H
    if USE_OFFSETS:
        i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32)
        bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32)
        T = eos - bos
    else:
        bos, eos = i_b * T, i_b * T + T

    if HEAD_FIRST:
        p_beta = tl.make_block_ptr(beta + i_bh * T, (T,), (1,), (i_t * BT,), (BT,), (0,))
        p_A = tl.make_block_ptr(A + i_bh * T * BT, (T, BT), (BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
    else:
        p_beta = tl.make_block_ptr(beta + bos * H + i_h, (T,), (H,), (i_t * BT,), (BT,), (0,))
        p_A = tl.make_block_ptr(A + (bos*H + i_h) * BT, (T, BT), (H*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0))
    b_beta = tl.load(p_beta, boundary_check=(0,))
    b_A = tl.load(p_A, boundary_check=(0, 1)).to(k.dtype.element_ty)

    for i_k in range(tl.cdiv(K, BK)):
        if HEAD_FIRST:
            p_k = tl.make_block_ptr(k + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
            p_w = tl.make_block_ptr(w + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
        else:
            p_k = tl.make_block_ptr(k + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
            p_w = tl.make_block_ptr(w + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
        b_k = tl.load(p_k, boundary_check=(0, 1))
        b_kb = (b_k * b_beta[:, None]).to(b_k.dtype)
        b_w = tl.dot(b_A, b_kb, allow_tf32=False)

        tl.store(p_w, b_w.to(p_w.dtype.element_ty), boundary_check=(0, 1))


@triton.autotune(
    configs=[
        triton.Config({}, num_warps=1),
        triton.Config({}, num_warps=2),
        triton.Config({}, num_warps=4),
        triton.Config({}, num_warps=8),
        triton.Config({}, num_warps=16)
    ],
    key=["BT", "BK", "BV"],
)
@triton.heuristics({'USE_OFFSETS': lambda args: args['offsets'] is not None})
@triton.jit
def bwd_prepare_wy_repr_kernel(
    k,
    v,
    beta,
    A,
    dw,
    du,
    dk,
    dv,
    dbeta,
    offsets,
    indices,
    T: tl.constexpr,
    H: tl.constexpr,
    K: tl.constexpr,
    V: tl.constexpr,
    BT: tl.constexpr,
    BK: tl.constexpr,
    BV: tl.constexpr,
    USE_OFFSETS: tl.constexpr,
    HEAD_FIRST: tl.constexpr
):
    i_t, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
    i_b, i_h = i_bh // H, i_bh % H
    if USE_OFFSETS:
        i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32)
        bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32)
        T = eos - bos
    else:
        bos, eos = i_b * T, i_b * T + T

    if HEAD_FIRST:
        p_beta = tl.make_block_ptr(beta + i_bh * T, (T,), (1,), (i_t * BT,), (BT,), (0,))
        p_A = tl.make_block_ptr(A + i_bh * T * BT, (BT, T), (1, BT), (0, i_t * BT), (BT, BT), (0, 1))
    else:
        p_beta = tl.make_block_ptr(beta + bos * H + i_h, (T,), (H,), (i_t * BT,), (BT,), (0,))
        p_A = tl.make_block_ptr(A + (bos*H + i_h) * BT, (BT, T), (1, H*BT), (0, i_t * BT), (BT, BT), (0, 1))

    b_beta = tl.load(p_beta, boundary_check=(0,))
    b_A = tl.load(p_A, boundary_check=(0, 1))

    b_dbeta = tl.zeros([BT], dtype=tl.float32)
    b_dA = tl.zeros([BT, BT], dtype=tl.float32)
    for i_v in range(tl.cdiv(V, BV)):
        if HEAD_FIRST:
            p_v = tl.make_block_ptr(v + i_bh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
            p_dv = tl.make_block_ptr(dv + i_bh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
            p_du = tl.make_block_ptr(du + i_bh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
        else:
            p_v = tl.make_block_ptr(v + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
            p_dv = tl.make_block_ptr(dv + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
            p_du = tl.make_block_ptr(du + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0))

        b_v = tl.load(p_v, boundary_check=(0, 1))
        b_v_beta = (b_v * b_beta[:, None]).to(b_v.dtype)
        b_du = tl.load(p_du, boundary_check=(0, 1))
        b_dA += tl.dot(b_du, tl.trans(b_v_beta), allow_tf32=False)
        b_dv_beta = tl.dot(b_A, b_du, allow_tf32=False)
        b_dv = b_dv_beta * b_beta[:, None]
        b_dbeta += tl.sum(b_dv_beta * b_v, 1)

        tl.store(p_dv, b_dv.to(p_dv.dtype.element_ty), boundary_check=(0, 1))

    for i_k in range(tl.cdiv(K, BK)):
        if HEAD_FIRST:
            p_k = tl.make_block_ptr(k + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
            p_dk = tl.make_block_ptr(dk + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
            p_dw = tl.make_block_ptr(dw + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
        else:
            p_k = tl.make_block_ptr(k + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
            p_dk = tl.make_block_ptr(dk + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
            p_dw = tl.make_block_ptr(dw + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
        b_k = tl.load(p_k, boundary_check=(0, 1))
        b_k_beta = (b_k * b_beta[:, None]).to(b_k.dtype)
        b_dw = tl.load(p_dw, boundary_check=(0, 1))
        b_dA += tl.dot(b_dw, tl.trans(b_k_beta), allow_tf32=False)
        b_dk_beta = tl.dot(b_A, b_dw, allow_tf32=False)
        b_dk = b_dk_beta * b_beta[:, None]
        b_dbeta += tl.sum(b_dk_beta * b_k, 1)

        tl.store(p_dk, b_dk.to(p_dk.dtype.element_ty), boundary_check=(0, 1))

    b_dA = tl.where(tl.arange(0, BT)[:, None] > tl.arange(0, BT)[None, :], b_dA, 0)
    b_dA = tl.dot(b_dA.to(b_A.dtype), b_A)
    b_dA = tl.dot(b_A, b_dA.to(b_A.dtype))
    b_dA = tl.where(tl.arange(0, BT)[:, None] > tl.arange(0, BT)[None, :], -b_dA, 0).to(k.dtype.element_ty)

    for i_k in range(tl.cdiv(K, BK)):
        if HEAD_FIRST:
            p_k = tl.make_block_ptr(k + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
            p_dk = tl.make_block_ptr(dk + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
        else:
            p_k = tl.make_block_ptr(k + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
            p_dk = tl.make_block_ptr(dk + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
        b_k = tl.load(p_k, boundary_check=(0, 1))
        b_dk = tl.load(p_dk, boundary_check=(0, 1))
        b_k_beta = (b_k * b_beta[:, None]).to(b_k.dtype)

        b_dk_beta = tl.dot(b_dA, b_k, allow_tf32=False)
        b_dbeta += tl.sum(b_dk_beta * b_k, 1)
        b_dk += tl.dot(tl.trans(b_dA), b_k_beta, allow_tf32=False)
        b_dk += b_dk_beta * b_beta[:, None]
        tl.store(p_dk, b_dk.to(p_dk.dtype.element_ty), boundary_check=(0, 1))

    if HEAD_FIRST:
        p_dbeta = tl.make_block_ptr(dbeta + i_bh * T, (T,), (1,), (i_t * BT,), (BT,), (0,))
    else:
        p_dbeta = tl.make_block_ptr(dbeta + bos * H + i_h, (T,), (H,), (i_t * BT,), (BT,), (0,))
    tl.store(p_dbeta, b_dbeta.to(p_dbeta.dtype.element_ty), boundary_check=(0,))


def fwd_prepare_wy_repr(
    k: torch.Tensor,
    v: torch.Tensor,
    beta: torch.Tensor,
    offsets: Optional[torch.LongTensor],
    indices: Optional[torch.LongTensor],
    head_first: bool = True,
    chunk_size: int = 64
) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
    if head_first:
        B, H, T, K = k.shape
    else:
        B, T, H, K = k.shape
    BT = min(chunk_size, max(triton.next_power_of_2(T), 16))
    if offsets is None:
        NT = triton.cdiv(T, BT)
    else:
        if indices is None:
            indices = torch.cat([torch.arange(n) for n in triton.cdiv(offsets[1:] - offsets[:-1], BT).tolist()])
            indices = torch.stack([indices.eq(0).cumsum(0) - 1, indices], 1).to(offsets)
        NT = len(indices)
    BC = min(BT, 32)
    BK = min(triton.next_power_of_2(K), 64)

    u = torch.empty_like(v)
    w = torch.empty_like(k)
    A = torch.empty(B, *((H, T) if head_first else (T, H)), BT, device=k.device, dtype=k.dtype)
    fwd_fn = fwd_prepare_wy_repr_kernel_chunk64 if BT == 64 else fwd_prepare_wy_repr_kernel_chunk32
    fwd_fn[(NT, B * H)](
        k=k,
        beta=beta,
        A=A,
        offsets=offsets,
        indices=indices,
        T=T,
        H=H,
        K=K,
        BT=BT,
        BK=BK,
        BC=BC,
        HEAD_FIRST=head_first
    )
    w, u = fwd_recompute_w_u(
        k=k,
        v=v,
        beta=beta,
        A=A,
        offsets=offsets,
        indices=indices,
        head_first=head_first,
        chunk_size=chunk_size
    )
    return w, u, A


def fwd_prepare_T(
    k: torch.Tensor,
    beta: torch.Tensor,
    offsets: Optional[torch.LongTensor],
    indices: Optional[torch.LongTensor],
    head_first: bool,
    chunk_size: int
) -> Tuple[torch.Tensor, torch.Tensor]:
    if head_first:
        B, H, T, K = k.shape
    else:
        B, T, H, K = k.shape
    BT = min(chunk_size, max(triton.next_power_of_2(T), 16))
    assert BT in [16, 32, 64]
    if offsets is None:
        NT = triton.cdiv(T, BT)
    else:
        if indices is None:
            indices = torch.cat([torch.arange(n) for n in triton.cdiv(offsets[1:] - offsets[:-1], BT).tolist()])
            indices = torch.stack([indices.eq(0).cumsum(0) - 1, indices], 1).to(offsets)
        NT = len(indices)
    BC = min(BT, 32)

    BK = min(triton.next_power_of_2(K), 64)
    A = torch.empty(B, *((H, T) if head_first else (T, H)), BT, device=k.device, dtype=k.dtype)
    fwd_fn = fwd_prepare_wy_repr_kernel_chunk64 if BT == 64 else fwd_prepare_wy_repr_kernel_chunk32
    fwd_fn[(NT, B * H)](
        k=k,
        beta=beta,
        A=A,
        offsets=offsets,
        indices=indices,
        T=T,
        H=H,
        K=K,
        BT=BT,
        BK=BK,
        BC=BC,
        HEAD_FIRST=head_first
    )
    return A


def fwd_recompute_w_u(
    k: torch.Tensor,
    v: torch.Tensor,
    beta: torch.Tensor,
    A: torch.Tensor,
    offsets: Optional[torch.LongTensor],
    indices: Optional[torch.LongTensor],
    head_first: bool,
    chunk_size: int
) -> Tuple[torch.Tensor, torch.Tensor]:
    if head_first:
        B, H, T, K, V = *k.shape, v.shape[-1]
    else:
        B, T, H, K, V = *k.shape, v.shape[-1]
    BT = min(chunk_size, max(triton.next_power_of_2(T), 16))
    if offsets is None:
        NT = triton.cdiv(T, BT)
    else:
        if indices is None:
            indices = torch.cat([torch.arange(n) for n in triton.cdiv(offsets[1:] - offsets[:-1], BT).tolist()])
            indices = torch.stack([indices.eq(0).cumsum(0) - 1, indices], 1).to(offsets)
        NT = len(indices)
    BK = min(triton.next_power_of_2(K), 64)
    BV = min(triton.next_power_of_2(V), 64)

    u = torch.empty_like(v)
    w = torch.empty_like(k)
    fwd_recompute_w_u_kernel[(NT, B*H)](
        k,
        v,
        beta,
        w,
        u,
        A,
        offsets=offsets,
        indices=indices,
        T=T,
        H=H,
        K=K,
        V=V,
        BT=BT,
        BK=BK,
        BV=BV,
        HEAD_FIRST=head_first
    )
    return w, u


def fwd_recompute_w(
    k: torch.Tensor,
    beta: torch.Tensor,
    A: torch.Tensor,
    offsets: Optional[torch.LongTensor],
    indices: Optional[torch.LongTensor],
    head_first: bool,
    chunk_size: int
) -> torch.Tensor:
    if head_first:
        B, H, T, K = k.shape
    else:
        B, T, H, K = k.shape
    BT = min(chunk_size, max(triton.next_power_of_2(T), 16))
    if offsets is None:
        NT = triton.cdiv(T, BT)
    else:
        if indices is None:
            indices = torch.cat([torch.arange(n) for n in triton.cdiv(offsets[1:] - offsets[:-1], BT).tolist()])
            indices = torch.stack([indices.eq(0).cumsum(0) - 1, indices], 1).to(offsets)
        NT = len(indices)
    BK = min(triton.next_power_of_2(K), 64)

    w = torch.empty_like(k)
    fwd_recompute_w_kernel[(NT, B*H)](
        k,
        beta,
        w,
        A,
        T=T,
        H=H,
        K=K,
        BT=BT,
        BK=BK,
        HEAD_FIRST=head_first
    )
    return w


def bwd_prepare_wy_repr(
    k: torch.Tensor,
    v: torch.Tensor,
    beta: torch.Tensor,
    A: torch.Tensor,
    dw: torch.Tensor,
    du: torch.Tensor,
    offsets: Optional[torch.LongTensor],
    indices: Optional[torch.LongTensor],
    head_first: bool,
    chunk_size: int
) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
    if head_first:
        B, H, T, K, V = *k.shape, v.shape[-1]
    else:
        B, T, H, K, V = *k.shape, v.shape[-1]
    BT = min(chunk_size, max(triton.next_power_of_2(T), 16))
    if offsets is None:
        NT = triton.cdiv(T, BT)
    else:
        if indices is None:
            indices = torch.cat([torch.arange(n) for n in triton.cdiv(offsets[1:] - offsets[:-1], BT).tolist()])
            indices = torch.stack([indices.eq(0).cumsum(0) - 1, indices], 1).to(offsets)
        NT = len(indices)
    BK = min(triton.next_power_of_2(K), 64)
    BV = min(triton.next_power_of_2(V), 64)

    dk = torch.empty_like(k)
    dv = torch.empty_like(v)
    dbeta = torch.empty_like(beta)
    bwd_prepare_wy_repr_kernel[(NT, B * H)](
        k,
        v,
        beta,
        A,
        dw,
        du,
        dk,
        dv,
        dbeta,
        offsets=offsets,
        indices=indices,
        T=T,
        H=H,
        K=K,
        V=V,
        BT=BT,
        BK=BK,
        BV=BV,
        HEAD_FIRST=head_first
    )
    return dk, dv, dbeta


class WYRepresentationPrepration(torch.autograd.Function):

    @staticmethod
    @contiguous
    @autocast_custom_fwd
    def forward(
        ctx,
        k: torch.Tensor,
        v: torch.Tensor,
        beta: torch.Tensor,
        offsets: Optional[torch.LongTensor] = None,
        head_first: bool = True,
        chunk_size: int = 64
    ):
        assert chunk_size in [16, 32, 64]
        # 2-d indices denoting the offsets of chunks in each sequence
        # for example, if the passed `offsets` is [0, 100, 356] and `chunk_size` is 64,
        # then there are 2 and 4 chunks in the 1st and 2nd sequences respectively, and `indices` will be
        # [[0, 0], [0, 1], [1, 0], [1, 1], [1, 2], [1, 3]]
        indices = None
        if offsets is not None:
            indices = torch.cat([torch.arange(n) for n in triton.cdiv(offsets[1:] - offsets[:-1], chunk_size).tolist()])
            indices = torch.stack([indices.eq(0).cumsum(0) - 1, indices], 1).to(offsets)

        w, u, A = fwd_prepare_wy_repr(
            k=k,
            v=v,
            beta=beta,
            offsets=offsets,
            indices=indices,
            head_first=head_first,
            chunk_size=chunk_size
        )
        ctx.offsets = offsets
        ctx.indices = indices
        ctx.head_first = head_first
        ctx.chunk_size = chunk_size
        ctx.save_for_backward(k, v, beta, A)
        return w, u

    @staticmethod
    @contiguous
    @autocast_custom_bwd
    def backward(
        ctx,
        dw: torch.Tensor,
        du: torch.Tensor
    ):
        k, v, beta, A = ctx.saved_tensors
        dk, dv, dbeta = bwd_prepare_wy_repr(
            k=k,
            v=v,
            beta=beta,
            A=A,
            dw=dw,
            du=du,
            offsets=ctx.offsets,
            indices=ctx.indices,
            head_first=ctx.head_first,
            chunk_size=ctx.chunk_size
        )
        return dk, dv, dbeta, None, None, None


prepare_wy_repr = WYRepresentationPrepration.apply


def naive(k, v, beta, chunk_size):
    l_org = k.shape[2]
    l_new = triton.next_power_of_2(l_org)
    # pad k, v, beta
    k = torch.cat([k, torch.zeros_like(k)[:, :, :l_new-l_org, :]], dim=2)
    v = torch.cat([v, torch.zeros_like(v)[:, :, :l_new-l_org, :]], dim=2)
    beta = torch.cat([beta, torch.zeros_like(beta)[:, :, :l_new-l_org]], dim=2)

    k, v = map(lambda x: rearrange(x, 'b h (n c) d -> b h n c d', c=chunk_size), (k, v))
    # k = torch.nn.functional.normalize(k, dim=-1, p=2)
    beta = rearrange(beta, 'b h (n c) -> b h n c', c=chunk_size)
    mask = torch.triu(torch.ones(chunk_size, chunk_size, dtype=torch.bool, device=k.device), diagonal=0)
    k_beta = k * beta[..., None]
    v = v * beta[..., None]
    attn = (k @ k.transpose(-1, -2)).masked_fill_(mask, 0)
    attn = attn * beta[..., None]
    x = attn @ v

    o = torch.zeros_like(k)
    o2 = torch.zeros_like(v)

    o[..., 0, :] = k_beta[..., 0, :].clone()
    o2[..., 0, :] = x[..., 0, :].clone()
    for i in range(1, chunk_size):
        o_i = (o[..., :i, :]).clone()
        o[..., i, :] = -(attn[..., i, :i, None] * o_i).sum(3) + k_beta[..., i, :]
        o2_i = (o2[..., :i, :]).clone()
        o2[..., i, :] = -(attn[..., i, :i, None] * o2_i).sum(3) + x[..., i, :]
    return map(lambda x: rearrange(x, 'b h n c d -> b h (n c) d')[:, :, :l_org], (o, v-o2))


if __name__ == "__main__":
    torch.set_default_dtype(torch.bfloat16)
    seq_len = 1024
    b = 4
    h = 4
    k = torch.nn.functional.normalize(torch.randn(b, h, seq_len, 128), dim=-1, p=2)
    v = torch.randn(b, h, seq_len, 128)
    beta = torch.rand(b, h, seq_len).sigmoid()
    # beta = torch.ones(b, h, seq_len)
    require_grad = True

    k, v, beta = map(lambda x: x.cuda().requires_grad_(require_grad), (k, v, beta))
    do = torch.rand_like(k)
    do2 = torch.rand_like(v)

    o1, o2 = naive(k.clone(), v.clone(), beta.clone(), 64)
    if require_grad:
        o1.backward(do, retain_graph=True)
        o2.backward(do2, retain_graph=True)
        k_grad2, v_grad2, beta_grad2 = k.grad, v.grad, beta.grad
        k.grad = v.grad = beta.grad = None
    o3, o4 = prepare_wy_repr(k.clone(), v.clone(), beta.clone(), 64)
    print((o1-o3).abs().max())
    print((o2-o4).abs().max())

    if require_grad:
        o3.backward(do, retain_graph=True)
        o4.backward(do2, retain_graph=True)
        k_grad, v_grad, beta_grad = k.grad, v.grad, beta.grad
        print((k_grad2-k_grad).abs().max())
        print((v_grad2-v_grad).abs().max())
        print((beta_grad2-beta_grad).abs().max())