import torch
import triton
import triton.language as tl
from torch._inductor.runtime.triton_heuristics import grid
from torch._C import _cuda_getCurrentRawStream as get_raw_stream
from torch._inductor.runtime import triton_helpers
from torch._inductor.runtime.triton_helpers import libdevice
from torch.autograd import Function
import torch.nn as nn
assert_size_stride = torch._C._dynamo.guards.assert_size_stride
empty_strided_cuda = torch._C._dynamo.guards._empty_strided_cuda


@triton.jit
def _triton_helper_fn_add0(arg0_0, arg1_0):
    tmp0 = arg0_0 + arg1_0
    return tmp0


@triton.jit
def triton_per_fused_cumsum_div_max_pow_sort_sub_0(in_ptr0, out_ptr0,
    out_ptr1, out_ptr2, out_ptr3, xnumel, rnumel, XBLOCK: tl.constexpr):
    xnumel = 64
    RBLOCK: tl.constexpr = 4
    xoffset = tl.program_id(0) * XBLOCK
    xindex = xoffset + tl.arange(0, XBLOCK)[:, None]
    xmask = xindex < xnumel
    rindex = tl.arange(0, RBLOCK)[None, :]
    tl.full([XBLOCK, RBLOCK], True, tl.int1)
    r1 = rindex
    x0 = xindex
    tmp0 = tl.load(in_ptr0 + (r1 + 4 * x0), xmask, other=0.0)
    tmp1 = tl.load(in_ptr0 + 4 * x0, xmask, eviction_policy='evict_last')
    tmp2 = tl.load(in_ptr0 + (1 + 4 * x0), xmask, eviction_policy='evict_last')
    tmp4 = tl.load(in_ptr0 + (2 + 4 * x0), xmask, eviction_policy='evict_last')
    tmp6 = tl.load(in_ptr0 + (3 + 4 * x0), xmask, eviction_policy='evict_last')
    tmp3 = triton_helpers.maximum(tmp1, tmp2)
    tmp5 = triton_helpers.maximum(tmp3, tmp4)
    tmp7 = triton_helpers.maximum(tmp5, tmp6)
    tmp8 = tmp0 - tmp7
    tmp9 = 0.5
    tmp10 = tmp8 * tmp9
    tmp11 = r1
    tmp12 = tmp11.to(tl.int16)
    tmp13 = tl.broadcast_to(tmp10, [XBLOCK, RBLOCK])
    tmp14 = tl.broadcast_to(tmp12, [XBLOCK, RBLOCK])
    tmp15, _tmp16 = triton_helpers.sort_with_index(tmp13, tmp14, None, 1,
        stable=False, descending=True)
    tmp17 = tmp15 * tmp15
    tmp18 = tmp17.to(tl.float32)
    tmp19 = tl.broadcast_to(tmp18, [XBLOCK, RBLOCK])
    tmp20, = tl.associative_scan((tmp19,), 1, _triton_helper_fn_add0)
    tmp21 = tmp15.to(tl.float32)
    tmp22 = tl.broadcast_to(tmp21, [XBLOCK, RBLOCK])
    tmp23, = tl.associative_scan((tmp22,), 1, _triton_helper_fn_add0)
    tl.store(out_ptr0 + (r1 + 4 * x0), tmp10, xmask)
    tl.store(out_ptr1 + (r1 + 4 * x0), tmp15, xmask)
    tl.store(out_ptr2 + (r1 + 4 * x0), tmp20, xmask)
    tl.store(out_ptr3 + (r1 + 4 * x0), tmp23, xmask)


@triton.jit
def triton_poi_fused_clamp_div_le_mul_pow_rsub_sqrt_sub_sum_1(in_ptr0,
    in_ptr1, in_ptr2, out_ptr0, xnumel, XBLOCK: tl.constexpr):
    xnumel = 64
    xoffset = tl.program_id(0) * XBLOCK
    xindex = xoffset + tl.arange(0, XBLOCK)[:]
    xmask = xindex < xnumel
    x0 = xindex
    tmp0 = tl.load(in_ptr0 + 4 * x0, xmask, eviction_policy='evict_last')
    tmp3 = tl.load(in_ptr1 + 4 * x0, xmask, eviction_policy='evict_last')
    tmp14 = tl.load(in_ptr2 + 4 * x0, xmask, eviction_policy='evict_last')
    tmp17 = tl.load(in_ptr0 + (1 + 4 * x0), xmask, eviction_policy='evict_last'
        )
    tmp20 = tl.load(in_ptr1 + (1 + 4 * x0), xmask, eviction_policy='evict_last'
        )
    tmp30 = tl.load(in_ptr2 + (1 + 4 * x0), xmask, eviction_policy='evict_last'
        )
    tmp34 = tl.load(in_ptr0 + (2 + 4 * x0), xmask, eviction_policy='evict_last'
        )
    tmp37 = tl.load(in_ptr1 + (2 + 4 * x0), xmask, eviction_policy='evict_last'
        )
    tmp47 = tl.load(in_ptr2 + (2 + 4 * x0), xmask, eviction_policy='evict_last'
        )
    tmp51 = tl.load(in_ptr0 + (3 + 4 * x0), xmask, eviction_policy='evict_last'
        )
    tmp54 = tl.load(in_ptr1 + (3 + 4 * x0), xmask, eviction_policy='evict_last'
        )
    tmp64 = tl.load(in_ptr2 + (3 + 4 * x0), xmask, eviction_policy='evict_last'
        )
    tmp1 = 1.0
    tmp2 = tmp0 / tmp1
    tmp4 = tmp3 / tmp1
    tmp5 = tmp2 * tmp2
    tmp6 = tmp4 - tmp5
    tmp7 = tmp1 * tmp6
    tmp8 = tmp1 - tmp7
    tmp9 = tmp8 / tmp1
    tmp10 = 0.0
    tmp11 = triton_helpers.maximum(tmp9, tmp10)
    tmp12 = libdevice.sqrt(tmp11)
    tmp13 = tmp2 - tmp12
    tmp15 = tmp13 <= tmp14
    tmp16 = tmp15.to(tl.int64)
    tmp18 = 2.0
    tmp19 = tmp17 / tmp18
    tmp21 = tmp20 / tmp18
    tmp22 = tmp19 * tmp19
    tmp23 = tmp21 - tmp22
    tmp24 = tmp18 * tmp23
    tmp25 = tmp1 - tmp24
    tmp26 = tmp25 / tmp18
    tmp27 = triton_helpers.maximum(tmp26, tmp10)
    tmp28 = libdevice.sqrt(tmp27)
    tmp29 = tmp19 - tmp28
    tmp31 = tmp29 <= tmp30
    tmp32 = tmp31.to(tl.int64)
    tmp33 = tmp16 + tmp32
    tmp35 = 3.0
    tmp36 = tmp34 / tmp35
    tmp38 = tmp37 / tmp35
    tmp39 = tmp36 * tmp36
    tmp40 = tmp38 - tmp39
    tmp41 = tmp35 * tmp40
    tmp42 = tmp1 - tmp41
    tmp43 = tmp42 / tmp35
    tmp44 = triton_helpers.maximum(tmp43, tmp10)
    tmp45 = libdevice.sqrt(tmp44)
    tmp46 = tmp36 - tmp45
    tmp48 = tmp46 <= tmp47
    tmp49 = tmp48.to(tl.int64)
    tmp50 = tmp33 + tmp49
    tmp52 = 4.0
    tmp53 = tmp51 / tmp52
    tmp55 = tmp54 / tmp52
    tmp56 = tmp53 * tmp53
    tmp57 = tmp55 - tmp56
    tmp58 = tmp52 * tmp57
    tmp59 = tmp1 - tmp58
    tmp60 = tmp59 / tmp52
    tmp61 = triton_helpers.maximum(tmp60, tmp10)
    tmp62 = libdevice.sqrt(tmp61)
    tmp63 = tmp53 - tmp62
    tmp65 = tmp63 <= tmp64
    tmp66 = tmp65.to(tl.int64)
    tmp67 = tmp50 + tmp66
    tl.store(out_ptr0 + x0, tmp67, xmask)


@triton.jit
def triton_poi_fused_clamp_div_gather_mul_pow_rsub_sqrt_sub_2(in_ptr0,
    in_ptr1, in_ptr2, in_ptr3, out_ptr0, xnumel, XBLOCK: tl.constexpr):
    xnumel = 256
    xoffset = tl.program_id(0) * XBLOCK
    xindex = xoffset + tl.arange(0, XBLOCK)[:]
    xmask = xindex < xnumel
    x2 = xindex
    x1 = xindex // 4
    tmp0 = tl.load(in_ptr0 + x2, xmask)
    tmp1 = tl.load(in_ptr1 + x1, xmask, eviction_policy='evict_last')
    tmp2 = tl.full([1], 1, tl.int64)
    tmp3 = tmp1 - tmp2
    tmp4 = tl.full([XBLOCK], 4, tl.int32)
    tmp5 = tmp3 + tmp4
    tmp6 = tmp3 < 0
    tmp7 = tl.where(tmp6, tmp5, tmp3)
    tl.device_assert((0 <= tmp7) & (tmp7 < 4) | ~xmask,
        'index out of bounds: 0 <= tmp7 < 4')
    tmp9 = tl.load(in_ptr2 + (tmp7 + 4 * x1), xmask, eviction_policy=
        'evict_last')
    tmp10 = 1 + tmp7
    tmp11 = tmp10.to(tl.float32)
    tmp12 = tmp9 / tmp11
    tmp13 = tl.load(in_ptr3 + (tmp7 + 4 * x1), xmask, eviction_policy=
        'evict_last')
    tmp14 = tmp13 / tmp11
    tmp15 = tmp12 * tmp12
    tmp16 = tmp14 - tmp15
    tmp17 = tmp11 * tmp16
    tmp18 = 1.0
    tmp19 = tmp18 - tmp17
    tmp20 = tmp19 / tmp11
    tmp21 = 0.0
    tmp22 = triton_helpers.maximum(tmp20, tmp21)
    tmp23 = libdevice.sqrt(tmp22)
    tmp24 = tmp12 - tmp23
    tmp25 = tmp0 - tmp24
    tmp26 = triton_helpers.maximum(tmp25, tmp21)
    tmp27 = tmp26 * tmp26
    tl.store(out_ptr0 + x2, tmp27, xmask)


def call(args):
    arg0_1, = args
    args.clear()
    assert_size_stride(arg0_1, (4, 4, 4, 4), (64, 16, 4, 1))
    with torch.cuda._DeviceGuard(0):
        torch.cuda.set_device(0)
        buf0 = empty_strided_cuda((4, 4, 4, 4), (64, 16, 4, 1), torch.float32)
        buf1 = empty_strided_cuda((4, 4, 4, 4), (64, 16, 4, 1), torch.float32)
        buf3 = empty_strided_cuda((4, 4, 4, 4), (64, 16, 4, 1), torch.float32)
        buf4 = empty_strided_cuda((4, 4, 4, 4), (64, 16, 4, 1), torch.float32)
        get_raw_stream(0)
        triton_per_fused_cumsum_div_max_pow_sort_sub_0[grid(64)](arg0_1,
            buf0, buf1, buf3, buf4, 64, 4, XBLOCK=1, num_warps=2, num_stages=1)
        del arg0_1
        buf5 = empty_strided_cuda((4, 4, 4), (16, 4, 1), torch.int64)
        triton_poi_fused_clamp_div_le_mul_pow_rsub_sqrt_sub_sum_1[grid(64)](
            buf4, buf3, buf1, buf5, 64, XBLOCK=64, num_warps=1, num_stages=1)
        buf6 = buf1
        del buf1
        triton_poi_fused_clamp_div_gather_mul_pow_rsub_sqrt_sub_2[grid(256)](
            buf0, buf5, buf4, buf3, buf6, 256, XBLOCK=128, num_warps=4,
            num_stages=1)
        del buf0
        del buf3
        del buf4
        del buf5
    return buf6,


def _make_ix_like(X, dim):
    d = X.size(dim)
    rho = torch.arange(1, d + 1, device=X.device, dtype=X.dtype)
    view = [1] * X.dim()
    view[0] = -1
    return rho.view(view).transpose(0, dim)


def _roll_last(X, dim):
    if dim == -1:
        return X
    elif dim < 0:
        dim = X.dim() - dim
    perm = [i for i in range(X.dim()) if i != dim] + [dim]
    return X.permute(perm)


def _entmax_threshold_and_support(X, dim=-1, k=None):
    """Core computation for 1.5-entmax: optimal threshold and support size.

    Parameters
    ----------
    X : torch.Tensor
        The input tensor to compute thresholds over.

    dim : int
        The dimension along which to apply 1.5-entmax.

    k : int or None
        number of largest elements to partial-sort over. For optimal
        performance, should be slightly bigger than the expected number of
        nonzeros in the solution. If the solution is more than k-sparse,
        this function is recursively called with a 2*k schedule.
        If `None`, full sorting is performed from the beginning.

    Returns
    -------
    tau : torch.Tensor like `X`, with all but the `dim` dimension intact
        the threshold value for each vector
    support_size : torch LongTensor, shape like `tau`
        the number of nonzeros in each vector.
    """
    if k is None or k >= X.shape[dim]:
        Xsrt, _ = torch.sort(X, dim=dim, descending=True)
    else:
        Xsrt, _ = torch.topk(X, k=k, dim=dim)
    rho = _make_ix_like(Xsrt, dim)
    mean = Xsrt.cumsum(dim) / rho
    mean_sq = (Xsrt ** 2).cumsum(dim) / rho
    ss = rho * (mean_sq - mean ** 2)
    delta = (1 - ss) / rho
    delta_nz = torch.clamp(delta, 0)
    tau = mean - torch.sqrt(delta_nz)
    support_size = (tau <= Xsrt).sum(dim).unsqueeze(dim)
    tau_star = tau.gather(dim, support_size - 1)
    if k is not None and k < X.shape[dim]:
        unsolved = (support_size == k).squeeze(dim)
        if torch.any(unsolved):
            X_ = _roll_last(X, dim)[unsolved]
            tau_, ss_ = _entmax_threshold_and_support(X_, dim=-1, k=2 * k)
            _roll_last(tau_star, dim)[unsolved] = tau_
            _roll_last(support_size, dim)[unsolved] = ss_
    return tau_star, support_size


def entmax15(X, dim=-1, k=None):
    """1.5-entmax: normalizing sparse transform (a la softmax).

    Solves the optimization problem:

        max_p <x, p> - H_1.5(p)    s.t.    p >= 0, sum(p) == 1.

    where H_1.5(p) is the Tsallis alpha-entropy with alpha=1.5.

    Parameters
    ----------
    X : torch.Tensor
        The input tensor.

    dim : int
        The dimension along which to apply 1.5-entmax.

    k : int or None
        number of largest elements to partial-sort over. For optimal
        performance, should be slightly bigger than the expected number of
        nonzeros in the solution. If the solution is more than k-sparse,
        this function is recursively called with a 2*k schedule.
        If `None`, full sorting is performed from the beginning.

    Returns
    -------
    P : torch tensor, same shape as X
        The projection result, such that P.sum(dim=dim) == 1 elementwise.
    """
    return Entmax15Function.apply(X, dim, k)


class Entmax15Function(Function):

    @classmethod
    def forward(cls, ctx, X, dim=0, k=None):
        ctx.dim = dim
        max_val, _ = X.max(dim=dim, keepdim=True)
        X = X - max_val
        X = X / 2
        tau_star, _ = _entmax_threshold_and_support(X, dim=dim, k=k)
        Y = torch.clamp(X - tau_star, min=0) ** 2
        ctx.save_for_backward(Y)
        return Y

    @classmethod
    def backward(cls, ctx, dY):
        Y, = ctx.saved_tensors
        gppr = Y.sqrt()
        dX = dY * gppr
        q = dX.sum(ctx.dim) / gppr.sum(ctx.dim)
        q = q.unsqueeze(ctx.dim)
        dX -= q * gppr
        return dX, None, None


class Entmax15New(nn.Module):

    def __init__(self, dim=-1, k=None):
        """1.5-entmax: normalizing sparse transform (a la softmax).

        Solves the optimization problem:

            max_p <x, p> - H_1.5(p)    s.t.    p >= 0, sum(p) == 1.

        where H_1.5(p) is the Tsallis alpha-entropy with alpha=1.5.

        Parameters
        ----------
        dim : int
            The dimension along which to apply 1.5-entmax.

        k : int or None
            number of largest elements to partial-sort over. For optimal
            performance, should be slightly bigger than the expected number of
            nonzeros in the solution. If the solution is more than k-sparse,
            this function is recursively called with a 2*k schedule.
            If `None`, full sorting is performed from the beginning.
        """
        self.dim = dim
        self.k = k
        super(Entmax15New, self).__init__()

    def forward(self, input_0):
        arg0_1 = input_0
        output = call([arg0_1])
        return output[0]


Measured latency_ms: 0.043752