code/flash-linear-attention/fla/modules/fused_norm_gate.py

# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang

from __future__ import annotations

import math

import torch
import torch.nn as nn
import torch.nn.functional as F
import triton
import triton.language as tl

from fla.utils import autotune_cache_kwargs, get_multiprocessor_count, input_guard


@triton.heuristics({
    'STORE_RESIDUAL_OUT': lambda args: args['residual_out'] is not None,
    'HAS_RESIDUAL': lambda args: args['residual'] is not None,
    'HAS_WEIGHT': lambda args: args['w'] is not None,
    'HAS_BIAS': lambda args: args['b'] is not None,
})
@triton.autotune(
    configs=[
        triton.Config({'BT': BT}, num_warps=num_warps)
        for BT in [16, 32, 64]
        for num_warps in [4, 8, 16]
    ],
    key=['D', 'NB', 'IS_RMS_NORM', 'STORE_RESIDUAL_OUT', 'HAS_RESIDUAL', 'HAS_WEIGHT'],
    **autotune_cache_kwargs,
)
@triton.jit
def layer_norm_gated_fwd_kernel(
    x,  # pointer to the input
    g,  # pointer to the gate
    y,  # pointer to the output
    w,  # pointer to the weights
    b,  # pointer to the biases
    residual,  # pointer to the residual
    residual_out,  # pointer to the residual
    mean,  # pointer to the mean
    rstd,  # pointer to the 1/std
    eps,  # epsilon to avoid division by zero
    T,  # number of rows in x
    D: tl.constexpr,  # number of columns in x
    BT: tl.constexpr,
    BD: tl.constexpr,
    NB: tl.constexpr,
    ACTIVATION: tl.constexpr,
    IS_RMS_NORM: tl.constexpr,
    STORE_RESIDUAL_OUT: tl.constexpr,
    HAS_RESIDUAL: tl.constexpr,
    HAS_WEIGHT: tl.constexpr,
    HAS_BIAS: tl.constexpr,
):
    i_t = tl.program_id(0)

    o_d = tl.arange(0, BD)
    m_d = o_d < D

    p_x = tl.make_block_ptr(x, (T, D), (D, 1), (i_t * BT, 0), (BT, BD), (1, 0))
    b_x = tl.load(p_x, boundary_check=(0, 1)).to(tl.float32)
    if HAS_RESIDUAL:
        p_res = tl.make_block_ptr(residual, (T, D), (D, 1), (i_t * BT, 0), (BT, BD), (1, 0))
        b_x += tl.load(p_res, boundary_check=(0, 1)).to(tl.float32)
    if STORE_RESIDUAL_OUT:
        p_res_out = tl.make_block_ptr(residual_out, (T, D), (D, 1), (i_t * BT, 0), (BT, BD), (1, 0))
        tl.store(p_res_out, b_x.to(p_res_out.dtype.element_ty), boundary_check=(0, 1))
    if not IS_RMS_NORM:
        b_mean = tl.sum(b_x, axis=1) / D
        p_mean = tl.make_block_ptr(mean, (T,), (1,), (i_t * BT,), (BT,), (0,))
        tl.store(p_mean, b_mean.to(p_mean.dtype.element_ty), boundary_check=(0,))
        b_xbar = tl.where(m_d[None, :], b_x - b_mean[:, None], 0.0)
        b_var = tl.sum(b_xbar * b_xbar, axis=1) / D
    else:
        b_xbar = tl.where(m_d[None, :], b_x, 0.0)
        b_var = tl.sum(b_xbar * b_xbar, axis=1) / D
    b_rstd = 1 / tl.sqrt(b_var + eps)

    p_rstd = tl.make_block_ptr(rstd, (T,), (1,), (i_t * BT,), (BT,), (0,))
    tl.store(p_rstd, b_rstd.to(p_rstd.dtype.element_ty), boundary_check=(0,))

    if HAS_WEIGHT:
        b_w = tl.load(w + o_d, mask=m_d).to(tl.float32)
    if HAS_BIAS:
        b_b = tl.load(b + o_d, mask=m_d).to(tl.float32)
    b_x_hat = (b_x - b_mean[:, None]) * b_rstd[:, None] if not IS_RMS_NORM else b_x * b_rstd[:, None]
    b_y = b_x_hat * b_w[None, :] if HAS_WEIGHT else b_x_hat
    if HAS_BIAS:
        b_y = b_y + b_b[None, :]

    # swish/sigmoid output gate
    p_g = tl.make_block_ptr(g, (T, D), (D, 1), (i_t * BT, 0), (BT, BD), (1, 0))
    b_g = tl.load(p_g, boundary_check=(0, 1)).to(tl.float32)
    if ACTIVATION == 'swish' or ACTIVATION == 'silu':
        b_y = b_y * b_g * tl.sigmoid(b_g)
    elif ACTIVATION == 'sigmoid':
        b_y = b_y * tl.sigmoid(b_g)

    # Write output
    p_y = tl.make_block_ptr(y, (T, D), (D, 1), (i_t * BT, 0), (BT, BD), (1, 0))
    tl.store(p_y, b_y.to(p_y.dtype.element_ty), boundary_check=(0, 1))


@triton.heuristics({
    'STORE_RESIDUAL_OUT': lambda args: args['residual_out'] is not None,
    'HAS_RESIDUAL': lambda args: args['residual'] is not None,
    'HAS_WEIGHT': lambda args: args['w'] is not None,
    'HAS_BIAS': lambda args: args['b'] is not None,
})
@triton.autotune(
    configs=[
        triton.Config({}, num_warps=num_warps)
        for num_warps in [2, 4, 8, 16]
    ],
    key=['D', 'IS_RMS_NORM', 'STORE_RESIDUAL_OUT', 'HAS_RESIDUAL', 'HAS_WEIGHT'],
    **autotune_cache_kwargs,
)
@triton.jit
def layer_norm_gated_fwd_kernel1(
    x,  # pointer to the input
    g,  # pointer to the gate
    y,  # pointer to the output
    w,  # pointer to the weights
    b,  # pointer to the biases
    residual,  # pointer to the residual
    residual_out,  # pointer to the residual
    mean,  # pointer to the mean
    rstd,  # pointer to the 1/std
    eps,  # epsilon to avoid division by zero
    D: tl.constexpr,  # number of columns in x
    BD: tl.constexpr,
    ACTIVATION: tl.constexpr,
    IS_RMS_NORM: tl.constexpr,
    STORE_RESIDUAL_OUT: tl.constexpr,
    HAS_RESIDUAL: tl.constexpr,
    HAS_WEIGHT: tl.constexpr,
    HAS_BIAS: tl.constexpr,
):
    i_t = tl.program_id(0)
    x += i_t * D
    y += i_t * D
    g += i_t * D
    if HAS_RESIDUAL:
        residual += i_t * D
    if STORE_RESIDUAL_OUT:
        residual_out += i_t * D

    o_d = tl.arange(0, BD)
    m_d = o_d < D
    b_x = tl.load(x + o_d, mask=m_d, other=0.0).to(tl.float32)
    if HAS_RESIDUAL:
        b_x += tl.load(residual + o_d, mask=m_d, other=0.0).to(tl.float32)
    if STORE_RESIDUAL_OUT:
        tl.store(residual_out + o_d, b_x, mask=m_d)
    if not IS_RMS_NORM:
        b_mean = tl.sum(b_x, axis=0) / D
        tl.store(mean + i_t, b_mean)
        b_xbar = tl.where(m_d, b_x - b_mean, 0.0)
        b_var = tl.sum(b_xbar * b_xbar, axis=0) / D
    else:
        b_xbar = tl.where(m_d, b_x, 0.0)
        b_var = tl.sum(b_xbar * b_xbar, axis=0) / D
    b_rstd = 1 / tl.sqrt(b_var + eps)
    tl.store(rstd + i_t, b_rstd)

    if HAS_WEIGHT:
        b_w = tl.load(w + o_d, mask=m_d).to(tl.float32)
    if HAS_BIAS:
        b_b = tl.load(b + o_d, mask=m_d).to(tl.float32)
    b_x_hat = (b_x - b_mean) * b_rstd if not IS_RMS_NORM else b_x * b_rstd
    b_y = b_x_hat * b_w if HAS_WEIGHT else b_x_hat
    if HAS_BIAS:
        b_y = b_y + b_b

    # swish/sigmoid output gate
    b_g = tl.load(g + o_d, mask=m_d, other=0.0).to(tl.float32)
    if ACTIVATION == 'swish' or ACTIVATION == 'silu':
        b_y = b_y * b_g * tl.sigmoid(b_g)
    elif ACTIVATION == 'sigmoid':
        b_y = b_y * tl.sigmoid(b_g)

    # Write output
    tl.store(y + o_d, b_y, mask=m_d)


@triton.heuristics({
    'HAS_DRESIDUAL': lambda args: args['dresidual'] is not None,
    'HAS_WEIGHT': lambda args: args['w'] is not None,
    'HAS_BIAS': lambda args: args['b'] is not None,
    'RECOMPUTE_OUTPUT': lambda args: args['y'] is not None,
})
@triton.autotune(
    configs=[
        triton.Config({'BT': BT}, num_warps=num_warps)
        for BT in [16, 32, 64]
        for num_warps in [4, 8, 16]
    ],
    key=['D', 'NB', 'IS_RMS_NORM', 'HAS_DRESIDUAL', 'HAS_WEIGHT'],
    **autotune_cache_kwargs,
)
@triton.jit
def layer_norm_gated_bwd_kernel(
    x,  # pointer to the input
    g,  # pointer to the gate
    w,  # pointer to the weights
    b,  # pointer to the biases
    y,  # pointer to the output to be recomputed
    dy,  # pointer to the output gradient
    dx,  # pointer to the input gradient
    dg,  # pointer to the gate gradient
    dw,  # pointer to the partial sum of weights gradient
    db,  # pointer to the partial sum of biases gradient
    dresidual,
    dresidual_in,
    mean,
    rstd,
    T,
    BS,
    D: tl.constexpr,
    BT: tl.constexpr,
    BD: tl.constexpr,
    NB: tl.constexpr,
    ACTIVATION: tl.constexpr,
    IS_RMS_NORM: tl.constexpr,
    STORE_DRESIDUAL: tl.constexpr,
    HAS_DRESIDUAL: tl.constexpr,
    HAS_WEIGHT: tl.constexpr,
    HAS_BIAS: tl.constexpr,
    RECOMPUTE_OUTPUT: tl.constexpr,
):
    i_s = tl.program_id(0)
    o_d = tl.arange(0, BD)
    m_d = o_d < D
    if HAS_WEIGHT:
        b_w = tl.load(w + o_d, mask=m_d).to(tl.float32)
        b_dw = tl.zeros((BT, BD), dtype=tl.float32)
    if HAS_BIAS:
        b_b = tl.load(b + o_d, mask=m_d, other=0.0).to(tl.float32)
        b_db = tl.zeros((BT, BD), dtype=tl.float32)

    T = min(i_s * BS + BS, T)
    for i_t in range(i_s * BS, T, BT):
        p_x = tl.make_block_ptr(x, (T, D), (D, 1), (i_t, 0), (BT, BD), (1, 0))
        p_g = tl.make_block_ptr(g, (T, D), (D, 1), (i_t, 0), (BT, BD), (1, 0))
        p_dy = tl.make_block_ptr(dy, (T, D), (D, 1), (i_t, 0), (BT, BD), (1, 0))
        p_dx = tl.make_block_ptr(dx, (T, D), (D, 1), (i_t, 0), (BT, BD), (1, 0))
        p_dg = tl.make_block_ptr(dg, (T, D), (D, 1), (i_t, 0), (BT, BD), (1, 0))
        # [BT, BD]
        b_x = tl.load(p_x, boundary_check=(0, 1)).to(tl.float32)
        b_g = tl.load(p_g, boundary_check=(0, 1)).to(tl.float32)
        b_dy = tl.load(p_dy, boundary_check=(0, 1)).to(tl.float32)

        if not IS_RMS_NORM:
            p_mean = tl.make_block_ptr(mean, (T,), (1,), (i_t,), (BT,), (0,))
            b_mean = tl.load(p_mean, boundary_check=(0,))
        p_rstd = tl.make_block_ptr(rstd, (T,), (1,), (i_t,), (BT,), (0,))
        b_rstd = tl.load(p_rstd, boundary_check=(0,))
        # Compute dx
        b_xhat = (b_x - b_mean[:, None]) * b_rstd[:, None] if not IS_RMS_NORM else b_x * b_rstd[:, None]
        b_xhat = tl.where(m_d[None, :], b_xhat, 0.0)

        b_y = b_xhat * b_w[None, :] if HAS_WEIGHT else b_xhat
        if HAS_BIAS:
            b_y = b_y + b_b[None, :]
        if RECOMPUTE_OUTPUT:
            p_y = tl.make_block_ptr(y, (T, D), (D, 1), (i_t, 0), (BT, BD), (1, 0))
            tl.store(p_y, b_y.to(p_y.dtype.element_ty), boundary_check=(0, 1))

        b_sigmoid_g = tl.sigmoid(b_g)
        if ACTIVATION == 'swish' or ACTIVATION == 'silu':
            b_dg = b_dy * b_y * (b_sigmoid_g + b_g * b_sigmoid_g * (1 - b_sigmoid_g))
            b_dy = b_dy * b_g * b_sigmoid_g
        elif ACTIVATION == 'sigmoid':
            b_dg = b_dy * b_y * b_sigmoid_g * (1 - b_sigmoid_g)
            b_dy = b_dy * b_sigmoid_g
        b_wdy = b_dy

        if HAS_WEIGHT or HAS_BIAS:
            m_t = (i_t + tl.arange(0, BT)) < T
        if HAS_WEIGHT:
            b_wdy = b_dy * b_w
            b_dw += tl.where(m_t[:, None], b_dy * b_xhat, 0.0)
        if HAS_BIAS:
            b_db += tl.where(m_t[:, None], b_dy, 0.0)
        if not IS_RMS_NORM:
            b_c1 = tl.sum(b_xhat * b_wdy, axis=1) / D
            b_c2 = tl.sum(b_wdy, axis=1) / D
            b_dx = (b_wdy - (b_xhat * b_c1[:, None] + b_c2[:, None])) * b_rstd[:, None]
        else:
            b_c1 = tl.sum(b_xhat * b_wdy, axis=1) / D
            b_dx = (b_wdy - b_xhat * b_c1[:, None]) * b_rstd[:, None]
        if HAS_DRESIDUAL:
            p_dres = tl.make_block_ptr(dresidual, (T, D), (D, 1), (i_t, 0), (BT, BD), (1, 0))
            b_dres = tl.load(p_dres, boundary_check=(0, 1)).to(tl.float32)
            b_dx += b_dres
        # Write dx
        if STORE_DRESIDUAL:
            p_dres_in = tl.make_block_ptr(dresidual_in, (T, D), (D, 1), (i_t, 0), (BT, BD), (1, 0))
            tl.store(p_dres_in, b_dx.to(p_dres_in.dtype.element_ty), boundary_check=(0, 1))

        tl.store(p_dx, b_dx.to(p_dx.dtype.element_ty), boundary_check=(0, 1))
        tl.store(p_dg, b_dg.to(p_dg.dtype.element_ty), boundary_check=(0, 1))

    if HAS_WEIGHT:
        tl.store(dw + i_s * D + o_d, tl.sum(b_dw, axis=0), mask=m_d)
    if HAS_BIAS:
        tl.store(db + i_s * D + o_d, tl.sum(b_db, axis=0), mask=m_d)


@triton.heuristics({
    'HAS_DRESIDUAL': lambda args: args['dresidual'] is not None,
    'HAS_WEIGHT': lambda args: args['w'] is not None,
    'HAS_BIAS': lambda args: args['b'] is not None,
    'RECOMPUTE_OUTPUT': lambda args: args['y'] is not None,
})
@triton.autotune(
    configs=[
        triton.Config({}, num_warps=num_warps)
        for num_warps in [2, 4, 8, 16]
    ],
    key=['D', 'IS_RMS_NORM', 'STORE_DRESIDUAL', 'HAS_DRESIDUAL', 'HAS_WEIGHT'],
    **autotune_cache_kwargs,
)
@triton.jit
def layer_norm_gated_bwd_kernel1(
    x,  # pointer to the input
    g,  # pointer to the gate
    w,  # pointer to the weights
    b,  # pointer to the biases
    y,  # pointer to the output to be recomputed
    dy,  # pointer to the output gradient
    dx,  # pointer to the input gradient
    dg,  # pointer to the gate gradient
    dw,  # pointer to the partial sum of weights gradient
    db,  # pointer to the partial sum of biases gradient
    dresidual,
    dresidual_in,
    mean,
    rstd,
    T,
    BS,
    D: tl.constexpr,
    BD: tl.constexpr,
    ACTIVATION: tl.constexpr,
    IS_RMS_NORM: tl.constexpr,
    STORE_DRESIDUAL: tl.constexpr,
    HAS_DRESIDUAL: tl.constexpr,
    HAS_WEIGHT: tl.constexpr,
    HAS_BIAS: tl.constexpr,
    RECOMPUTE_OUTPUT: tl.constexpr,
):
    i_s = tl.program_id(0)
    o_d = tl.arange(0, BD)
    mask = o_d < D
    x += i_s * BS * D
    g += i_s * BS * D
    if HAS_DRESIDUAL:
        dresidual += i_s * BS * D
    if STORE_DRESIDUAL:
        dresidual_in += i_s * BS * D
    dy += i_s * BS * D
    dx += i_s * BS * D
    dg += i_s * BS * D
    if RECOMPUTE_OUTPUT:
        y += i_s * BS * D
    if HAS_WEIGHT:
        b_w = tl.load(w + o_d, mask=mask).to(tl.float32)
        b_dw = tl.zeros((BD,), dtype=tl.float32)
    if HAS_BIAS:
        b_b = tl.load(b + o_d, mask=mask, other=0.0).to(tl.float32)
        b_db = tl.zeros((BD,), dtype=tl.float32)

    for i_t in range(i_s * BS, min(i_s * BS + BS, T)):
        # Load data to SRAM
        b_x = tl.load(x + o_d, mask=mask, other=0).to(tl.float32)
        b_g = tl.load(g + o_d, mask=mask, other=0).to(tl.float32)
        b_dy = tl.load(dy + o_d, mask=mask, other=0).to(tl.float32)

        if not IS_RMS_NORM:
            b_mean = tl.load(mean + i_t)
        b_rstd = tl.load(rstd + i_t)
        # Compute dx
        b_xhat = (b_x - b_mean) * b_rstd if not IS_RMS_NORM else b_x * b_rstd
        b_xhat = tl.where(mask, b_xhat, 0.0)

        b_y = b_xhat * b_w if HAS_WEIGHT else b_xhat
        if HAS_BIAS:
            b_y = b_y + b_b
        if RECOMPUTE_OUTPUT:
            tl.store(y + o_d, b_y, mask=mask)

        b_sigmoid_g = tl.sigmoid(b_g)
        if ACTIVATION == 'swish' or ACTIVATION == 'silu':
            b_dg = b_dy * b_y * (b_sigmoid_g + b_g * b_sigmoid_g * (1 - b_sigmoid_g))
            b_dy = b_dy * b_g * b_sigmoid_g
        elif ACTIVATION == 'sigmoid':
            b_dg = b_dy * b_y * b_sigmoid_g * (1 - b_sigmoid_g)
            b_dy = b_dy * b_sigmoid_g
        b_wdy = b_dy
        if HAS_WEIGHT:
            b_wdy = b_dy * b_w
            b_dw += b_dy * b_xhat
        if HAS_BIAS:
            b_db += b_dy
        if not IS_RMS_NORM:
            b_c1 = tl.sum(b_xhat * b_wdy, axis=0) / D
            b_c2 = tl.sum(b_wdy, axis=0) / D
            b_dx = (b_wdy - (b_xhat * b_c1 + b_c2)) * b_rstd
        else:
            b_c1 = tl.sum(b_xhat * b_wdy, axis=0) / D
            b_dx = (b_wdy - b_xhat * b_c1) * b_rstd
        if HAS_DRESIDUAL:
            b_dres = tl.load(dresidual + o_d, mask=mask, other=0).to(tl.float32)
            b_dx += b_dres
        # Write dx
        if STORE_DRESIDUAL:
            tl.store(dresidual_in + o_d, b_dx, mask=mask)
        tl.store(dx + o_d, b_dx, mask=mask)
        tl.store(dg + o_d, b_dg, mask=mask)

        x += D
        g += D
        if HAS_DRESIDUAL:
            dresidual += D
        if STORE_DRESIDUAL:
            dresidual_in += D
        if RECOMPUTE_OUTPUT:
            y += D
        dy += D
        dx += D
        dg += D
    if HAS_WEIGHT:
        tl.store(dw + i_s * D + o_d, b_dw, mask=mask)
    if HAS_BIAS:
        tl.store(db + i_s * D + o_d, b_db, mask=mask)


def layer_norm_gated_fwd(
    x: torch.Tensor,
    g: torch.Tensor,
    weight: torch.Tensor,
    bias: torch.Tensor,
    activation: str = 'swish',
    eps: float = 1e-5,
    residual: torch.Tensor = None,
    out_dtype: torch.dtype = None,
    residual_dtype: torch.dtype = None,
    is_rms_norm: bool = False,
):
    if residual is not None:
        residual_dtype = residual.dtype
    T, D = x.shape
    if residual is not None:
        assert residual.shape == (T, D)
    if weight is not None:
        assert weight.shape == (D,)
    if bias is not None:
        assert bias.shape == (D,)
    # allocate output
    y = torch.empty_like(x, dtype=x.dtype if out_dtype is None else out_dtype)
    if residual is not None or (residual_dtype is not None and residual_dtype != x.dtype):
        residual_out = torch.empty(T, D, device=x.device, dtype=residual_dtype)
    else:
        residual_out = None
    mean = torch.empty((T,), dtype=torch.float, device=x.device) if not is_rms_norm else None
    rstd = torch.empty((T,), dtype=torch.float, device=x.device)
    # Less than 64KB per feature: enqueue fused kernel
    MAX_FUSED_SIZE = 65536 // x.element_size()
    BD = min(MAX_FUSED_SIZE, triton.next_power_of_2(D))
    if D > BD:
        raise RuntimeError("This layer norm doesn't support feature dim >= 64KB.")
    # heuristics for number of warps

    if D <= 512:
        NB = triton.cdiv(T, 2048)
        def grid(meta): return (triton.cdiv(T, meta['BT']),)
        layer_norm_gated_fwd_kernel[grid](
            x=x,
            g=g,
            y=y,
            w=weight,
            b=bias,
            residual=residual,
            residual_out=residual_out,
            mean=mean,
            rstd=rstd,
            eps=eps,
            T=T,
            D=D,
            BD=BD,
            NB=NB,
            ACTIVATION=activation,
            IS_RMS_NORM=is_rms_norm,
        )
    else:
        layer_norm_gated_fwd_kernel1[(T,)](
            x=x,
            g=g,
            y=y,
            w=weight,
            b=bias,
            residual=residual,
            residual_out=residual_out,
            mean=mean,
            rstd=rstd,
            eps=eps,
            D=D,
            BD=BD,
            ACTIVATION=activation,
            IS_RMS_NORM=is_rms_norm,
        )
    # residual_out is None if residual is None and residual_dtype == input_dtype
    return y, mean, rstd, residual_out if residual_out is not None else x


def layer_norm_gated_bwd(
    dy: torch.Tensor,
    x: torch.Tensor,
    g: torch.Tensor,
    weight: torch.Tensor,
    bias: torch.Tensor,
    activation: str = 'swish',
    eps: float = 1e-5,
    mean: torch.Tensor = None,
    rstd: torch.Tensor = None,
    dresidual: torch.Tensor = None,
    has_residual: bool = False,
    is_rms_norm: bool = False,
    x_dtype: torch.dtype = None,
    recompute_output: bool = False,
):
    T, D = x.shape
    assert dy.shape == (T, D)
    if dresidual is not None:
        assert dresidual.shape == (T, D)
    if weight is not None:
        assert weight.shape == (D,)
    if bias is not None:
        assert bias.shape == (D,)
    # allocate output
    dx = torch.empty_like(x) if x_dtype is None else torch.empty(T, D, dtype=x_dtype, device=x.device)
    dg = torch.empty_like(g) if x_dtype is None else torch.empty(T, D, dtype=x_dtype, device=x.device)
    dresidual_in = torch.empty_like(x) if has_residual and dx.dtype != x.dtype else None
    y = torch.empty(T, D, dtype=dy.dtype, device=dy.device) if recompute_output else None

    # Less than 64KB per feature: enqueue fused kernel
    MAX_FUSED_SIZE = 65536 // x.element_size()
    BD = min(MAX_FUSED_SIZE, triton.next_power_of_2(D))
    if D > BD:
        raise RuntimeError("This layer norm doesn't support feature dim >= 64KB.")
    NS = get_multiprocessor_count(x.device.index)
    BS = math.ceil(T / NS)

    dw = torch.empty((NS, D), dtype=torch.float, device=weight.device) if weight is not None else None
    db = torch.empty((NS, D), dtype=torch.float, device=bias.device) if bias is not None else None
    grid = (NS,)

    if D <= 512:
        NB = triton.cdiv(T, 2048)
        layer_norm_gated_bwd_kernel[grid](
            x=x,
            g=g,
            w=weight,
            b=bias,
            y=y,
            dy=dy,
            dx=dx,
            dg=dg,
            dw=dw,
            db=db,
            dresidual=dresidual,
            dresidual_in=dresidual_in,
            mean=mean,
            rstd=rstd,
            T=T,
            D=D,
            BS=BS,
            BD=BD,
            NB=NB,
            ACTIVATION=activation,
            IS_RMS_NORM=is_rms_norm,
            STORE_DRESIDUAL=dresidual_in is not None,
        )
    else:
        layer_norm_gated_bwd_kernel1[grid](
            x=x,
            g=g,
            w=weight,
            b=bias,
            y=y,
            dy=dy,
            dx=dx,
            dg=dg,
            dw=dw,
            db=db,
            dresidual=dresidual,
            dresidual_in=dresidual_in,
            mean=mean,
            rstd=rstd,
            T=T,
            D=D,
            BS=BS,
            BD=BD,
            ACTIVATION=activation,
            IS_RMS_NORM=is_rms_norm,
            STORE_DRESIDUAL=dresidual_in is not None,
        )
    dw = dw.sum(0).to(weight.dtype) if weight is not None else None
    db = db.sum(0).to(bias.dtype) if bias is not None else None
    # Don't need to compute dresidual_in separately in this case
    if has_residual and dx.dtype == x.dtype:
        dresidual_in = dx
    return (dx, dg, dw, db, dresidual_in) if not recompute_output else (dx, dg, dw, db, dresidual_in, y)


class LayerNormGatedFunction(torch.autograd.Function):

    @staticmethod
    @input_guard
    def forward(
        ctx,
        x: torch.Tensor,
        g: torch.Tensor,
        weight: torch.Tensor,
        bias: torch.Tensor,
        activation: str,
        residual: torch.Tensor | None = None,
        eps: float = 1e-6,
        prenorm: bool = False,
        residual_in_fp32: bool = False,
        is_rms_norm: bool = False,
    ):
        x_shape_og = x.shape
        g_shape_og = g.shape
        # reshape input data into 2D tensor
        x = x.reshape(-1, x.shape[-1])
        g = g.reshape(-1, g.shape[-1])
        if residual is not None:
            assert residual.shape == x_shape_og
            residual = residual.reshape(-1, residual.shape[-1])
        residual_dtype = (
            residual.dtype
            if residual is not None
            else (torch.float if residual_in_fp32 else None)
        )
        y, mean, rstd, residual_out = layer_norm_gated_fwd(
            x=x,
            g=g,
            weight=weight,
            bias=bias,
            activation=activation,
            eps=eps,
            residual=residual,
            residual_dtype=residual_dtype,
            is_rms_norm=is_rms_norm,
        )
        ctx.save_for_backward(residual_out, g, weight, bias, mean, rstd)
        ctx.x_shape_og = x_shape_og
        ctx.g_shape_og = g_shape_og
        ctx.activation = activation
        ctx.eps = eps
        ctx.is_rms_norm = is_rms_norm
        ctx.has_residual = residual is not None
        ctx.prenorm = prenorm
        ctx.x_dtype = x.dtype
        y = y.reshape(x_shape_og)
        return y if not prenorm else (y, residual_out.reshape(x_shape_og))

    @staticmethod
    @input_guard
    def backward(ctx, dy, *args):
        x, g, weight, bias, mean, rstd = ctx.saved_tensors
        dy = dy.reshape(-1, dy.shape[-1])
        assert dy.shape == x.shape
        if ctx.prenorm:
            dresidual = args[0]
            dresidual = dresidual.reshape(-1, dresidual.shape[-1])
            assert dresidual.shape == x.shape
        else:
            dresidual = None
        dx, dg, dw, db, dres_in = layer_norm_gated_bwd(
            dy=dy,
            x=x,
            g=g,
            weight=weight,
            bias=bias,
            activation=ctx.activation,
            eps=ctx.eps,
            mean=mean,
            rstd=rstd,
            dresidual=dresidual,
            has_residual=ctx.has_residual,
            is_rms_norm=ctx.is_rms_norm,
            x_dtype=ctx.x_dtype,
        )
        return (
            dx.reshape(ctx.x_shape_og),
            dg.reshape(ctx.g_shape_og),
            dw,
            db,
            None,
            dres_in.reshape(ctx.x_shape_og) if ctx.has_residual else None,
            None,
            None,
            None,
            None,
        )


class LayerNormGatedLinearFunction(torch.autograd.Function):

    @staticmethod
    @input_guard
    def forward(
        ctx,
        x: torch.Tensor,
        g: torch.Tensor,
        norm_weight: torch.Tensor,
        norm_bias: torch.Tensor,
        linear_weight: torch.Tensor,
        linear_bias: torch.Tensor,
        residual: torch.Tensor | None = None,
        eps: float = 1e-6,
        prenorm: bool = False,
        residual_in_fp32: bool = False,
        is_rms_norm: bool = False,
    ):
        x_shape_og = x.shape
        g_shape_og = g.shape
        # reshape input data into 2D tensor
        x = x.reshape(-1, x.shape[-1])
        g = g.reshape(-1, g.shape[-1])
        if residual is not None:
            assert residual.shape == x_shape_og
            residual = residual.reshape(-1, residual.shape[-1])
        residual_dtype = (
            residual.dtype
            if residual is not None
            else (torch.float if residual_in_fp32 else None)
        )
        y, mean, rstd, residual_out = layer_norm_gated_fwd(
            x=x,
            g=g,
            weight=norm_weight,
            bias=norm_bias,
            eps=eps,
            residual=residual,
            residual_dtype=residual_dtype,
            is_rms_norm=is_rms_norm,
        )
        y = y.reshape(x_shape_og)
        dtype = torch.get_autocast_gpu_dtype() if torch.is_autocast_enabled() else y.dtype
        linear_weight = linear_weight.to(dtype)
        linear_bias = linear_bias.to(dtype) if linear_bias is not None else None
        out = F.linear(y.to(linear_weight.dtype), linear_weight, linear_bias)
        # We don't store y, will be recomputed in the backward pass to save memory
        ctx.save_for_backward(residual_out, g, norm_weight, norm_bias, linear_weight, mean, rstd)
        ctx.x_shape_og = x_shape_og
        ctx.g_shape_og = g_shape_og
        ctx.eps = eps
        ctx.is_rms_norm = is_rms_norm
        ctx.has_residual = residual is not None
        ctx.prenorm = prenorm
        ctx.x_dtype = x.dtype
        ctx.linear_bias_is_none = linear_bias is None
        return out if not prenorm else (out, residual_out.reshape(x_shape_og))

    @staticmethod
    @input_guard
    def backward(ctx, dout, *args):
        x, g, norm_weight, norm_bias, linear_weight, mean, rstd = ctx.saved_tensors
        dout = dout.reshape(-1, dout.shape[-1])
        dy = F.linear(dout, linear_weight.t())
        dlinear_bias = None if ctx.linear_bias_is_none else dout.sum(0)
        assert dy.shape == x.shape
        if ctx.prenorm:
            dresidual = args[0]
            dresidual = dresidual.reshape(-1, dresidual.shape[-1])
            assert dresidual.shape == x.shape
        else:
            dresidual = None
        dx, dg, dnorm_weight, dnorm_bias, dres_in, y = layer_norm_gated_bwd(
            dy=dy,
            x=x,
            g=g,
            weight=norm_weight,
            bias=norm_bias,
            eps=ctx.eps,
            mean=mean,
            rstd=rstd,
            dresidual=dresidual,
            has_residual=ctx.has_residual,
            is_rms_norm=ctx.is_rms_norm,
            x_dtype=ctx.x_dtype,
            recompute_output=True,
        )
        dlinear_weight = torch.einsum("bo,bi->oi", dout, y)
        return (
            dx.reshape(ctx.x_shape_og),
            dg.reshape(ctx.g_shape_og),
            dnorm_weight,
            dnorm_bias,
            dlinear_weight,
            dlinear_bias,
            dres_in.reshape(ctx.x_shape_og) if ctx.has_residual else None,
            None,
            None,
            None,
            None,
        )


def layer_norm_gated(
    x: torch.Tensor,
    g: torch.Tensor,
    weight: torch.Tensor,
    bias: torch.Tensor,
    activation: str = 'swish',
    residual: torch.Tensor | None = None,
    prenorm: bool = False,
    residual_in_fp32: bool = False,
    eps: float = 1e-6,
):
    return LayerNormGatedFunction.apply(
        x,
        g,
        weight,
        bias,
        activation,
        residual,
        eps,
        prenorm,
        residual_in_fp32,
        False,
    )


def rms_norm_gated(
    x: torch.Tensor,
    g: torch.Tensor,
    weight: torch.Tensor,
    bias: torch.Tensor,
    activation: str = 'swish',
    residual: torch.Tensor | None = None,
    prenorm: bool = False,
    residual_in_fp32: bool = False,
    eps: float = 1e-6,
):
    return LayerNormGatedFunction.apply(
        x,
        g,
        weight,
        bias,
        activation,
        residual,
        eps,
        prenorm,
        residual_in_fp32,
        True,
    )


def layer_norm_swish_gate_linear(
    x: torch.Tensor,
    g: torch.Tensor,
    norm_weight: torch.Tensor,
    norm_bias: torch.Tensor,
    linear_weight: torch.Tensor,
    linear_bias: torch.Tensor,
    residual: torch.Tensor | None = None,
    prenorm: bool = False,
    residual_in_fp32: bool = False,
    eps: float = 1e-6,
):
    return LayerNormGatedLinearFunction.apply(
        x,
        g,
        norm_weight,
        norm_bias,
        linear_weight,
        linear_bias,
        residual,
        eps,
        prenorm,
        residual_in_fp32,
        False,
    )


def rms_norm_swish_gate_linear(
    x,
    g: torch.Tensor,
    norm_weight: torch.Tensor,
    norm_bias: torch.Tensor,
    linear_weight: torch.Tensor,
    linear_bias: torch.Tensor,
    residual: torch.Tensor | None = None,
    prenorm: bool = False,
    residual_in_fp32: bool = False,
    eps: float = 1e-6,
):
    return LayerNormGatedLinearFunction.apply(
        x,
        g,
        norm_weight,
        norm_bias,
        linear_weight,
        linear_bias,
        residual,
        eps,
        prenorm,
        residual_in_fp32,
        True,
    )


class FusedLayerNormGated(nn.Module):

    def __init__(
        self,
        hidden_size: int,
        elementwise_affine: bool = True,
        bias: bool = False,
        activation: str = 'swish',
        eps: float = 1e-5,
        device: torch.device | None = None,
        dtype: torch.dtype | None = None,
    ) -> FusedLayerNormGated:
        factory_kwargs = {"device": device, "dtype": dtype}
        super().__init__()

        self.hidden_size = hidden_size
        self.elementwise_affine = elementwise_affine
        self.eps = eps
        self.activation = activation

        if self.activation not in ['swish', 'silu', 'sigmoid']:
            raise ValueError(f"Unsupported activation: {self.activation}")

        self.register_parameter("weight", None)
        self.register_parameter("bias", None)
        if elementwise_affine:
            self.weight = nn.Parameter(torch.empty(hidden_size, **factory_kwargs))
            if bias:
                self.bias = nn.Parameter(torch.empty(hidden_size, **factory_kwargs))

        self.reset_parameters()

    def reset_parameters(self):
        if self.elementwise_affine:
            nn.init.ones_(self.weight)
            if self.bias is not None:
                nn.init.zeros_(self.bias)

    def __repr__(self) -> str:
        s = f"{self.__class__.__name__}({self.hidden_size}"
        if not self.elementwise_affine:
            s += f", elementwise_affine={self.elementwise_affine}"
        s += f", eps={self.eps}"
        s += f", activation={self.activation}"
        s += ")"
        return s

    def forward(
        self,
        x: torch.Tensor,
        g: torch.Tensor,
        residual: torch.Tensor | None = None,
        prenorm: bool = False,
        residual_in_fp32: bool = False,
    ) -> torch.Tensor:
        return layer_norm_gated(
            x,
            g,
            self.weight,
            self.bias,
            self.activation,
            residual=residual,
            eps=self.eps,
            prenorm=prenorm,
            residual_in_fp32=residual_in_fp32,
        )


class FusedRMSNormGated(nn.Module):

    def __init__(
        self,
        hidden_size: int,
        elementwise_affine: bool = True,
        eps: float = 1e-5,
        activation: str = 'swish',
        device: torch.device | None = None,
        dtype: torch.dtype | None = None,
    ) -> FusedRMSNormGated:
        factory_kwargs = {"device": device, "dtype": dtype}
        super().__init__()

        self.hidden_size = hidden_size
        self.elementwise_affine = elementwise_affine
        self.eps = eps
        self.activation = activation

        if self.activation not in ['swish', 'silu', 'sigmoid']:
            raise ValueError(f"Unsupported activation: {self.activation}")

        if elementwise_affine:
            self.weight = nn.Parameter(torch.empty(hidden_size, **factory_kwargs))
        else:
            self.register_parameter("weight", None)
        self.register_parameter("bias", None)

        self.reset_parameters()

    def reset_parameters(self):
        if self.elementwise_affine:
            nn.init.ones_(self.weight)

    def __repr__(self) -> str:
        s = f"{self.__class__.__name__}({self.hidden_size}"
        if not self.elementwise_affine:
            s += f", elementwise_affine={self.elementwise_affine}"
        s += f", eps={self.eps}"
        s += f", activation={self.activation}"
        s += ")"
        return s

    def forward(
        self,
        x: torch.Tensor,
        g: torch.Tensor,
        residual: torch.Tensor | None = None,
        prenorm: bool = False,
        residual_in_fp32: bool = False,
    ) -> torch.Tensor:
        return rms_norm_gated(
            x,
            g,
            self.weight,
            self.bias,
            self.activation,
            residual=residual,
            eps=self.eps,
            prenorm=prenorm,
            residual_in_fp32=residual_in_fp32,
        )


class FusedLayerNormSwishGate(FusedLayerNormGated):

    def __init__(
        self,
        hidden_size: int,
        elementwise_affine: bool = True,
        bias: bool = False,
        eps: float = 1e-5,
        device: torch.device | None = None,
        dtype: torch.dtype | None = None,
    ) -> FusedLayerNormSwishGate:
        super().__init__(
            hidden_size=hidden_size,
            elementwise_affine=elementwise_affine,
            bias=bias,
            eps=eps,
            device=device,
            dtype=dtype,
        )


class FusedRMSNormSwishGate(FusedRMSNormGated):

    def __init__(
        self,
        hidden_size: int,
        elementwise_affine: bool = True,
        eps: float = 1e-5,
        device: torch.device | None = None,
        dtype: torch.dtype | None = None,
    ) -> FusedRMSNormSwishGate:
        super().__init__(
            hidden_size=hidden_size,
            elementwise_affine=elementwise_affine,
            eps=eps,
            device=device,
            dtype=dtype,
        )


class FusedLayerNormGatedLinear(nn.Module):

    def __init__(
        self,
        hidden_size: int,
        elementwise_affine: bool = True,
        eps: float = 1e-5,
        device: torch.device | None = None,
        dtype: torch.dtype | None = None,
    ) -> FusedLayerNormGatedLinear:
        factory_kwargs = {"device": device, "dtype": dtype}
        super().__init__()

        self.hidden_size = hidden_size
        self.elementwise_affine = elementwise_affine
        self.eps = eps

        if elementwise_affine:
            self.weight = nn.Parameter(torch.empty(hidden_size, **factory_kwargs))
        else:
            self.register_parameter("weight", None)
        self.register_parameter("bias", None)

        self.reset_parameters()

    def reset_parameters(self):
        if self.elementwise_affine:
            nn.init.ones_(self.weight)

    def __repr__(self) -> str:
        s = f"{self.__class__.__name__}({self.hidden_size}"
        if not self.elementwise_affine:
            s += f", elementwise_affine={self.elementwise_affine}"
        s += f", eps={self.eps}"
        s += ")"
        return s

    def forward(
        self,
        x: torch.Tensor,
        g: torch.Tensor,
        weight: torch.Tensor | None = None,
        bias: torch.Tensor | None = None,
        residual: torch.Tensor | None = None,
        prenorm: bool = False,
        residual_in_fp32: bool = False,
    ) -> torch.Tensor:
        return layer_norm_swish_gate_linear(
            x,
            g,
            self.weight,
            self.bias,
            weight,
            bias,
            residual=residual,
            eps=self.eps,
            prenorm=prenorm,
            residual_in_fp32=residual_in_fp32,
        )


class FusedLayerNormSwishGateLinear(FusedLayerNormGatedLinear):

    def __init__(
        self,
        hidden_size: int,
        elementwise_affine: bool = True,
        eps: float = 1e-5,
        device: torch.device | None = None,
        dtype: torch.dtype | None = None,
    ) -> FusedLayerNormSwishGateLinear:
        super().__init__(
            hidden_size=hidden_size,
            elementwise_affine=elementwise_affine,
            eps=eps,
            device=device,
            dtype=dtype,
        )


class FusedRMSNormGatedLinear(nn.Module):

    def __init__(
        self,
        hidden_size,
        elementwise_affine: bool = True,
        eps: float = 1e-5,
        device: torch.device | None = None,
        dtype: torch.dtype | None = None,
    ) -> FusedRMSNormGatedLinear:
        factory_kwargs = {"device": device, "dtype": dtype}
        super().__init__()

        self.hidden_size = hidden_size
        self.elementwise_affine = elementwise_affine
        self.eps = eps

        self.register_parameter("weight", None)
        self.register_parameter("bias", None)
        if elementwise_affine:
            self.weight = nn.Parameter(torch.empty(hidden_size, **factory_kwargs))

        self.reset_parameters()

    def reset_parameters(self):
        if self.elementwise_affine:
            nn.init.ones_(self.weight)

    def __repr__(self) -> str:
        s = f"{self.__class__.__name__}({self.hidden_size}"
        if not self.elementwise_affine:
            s += f", elementwise_affine={self.elementwise_affine}"
        s += f", eps={self.eps}"
        s += ")"
        return s

    def forward(
        self,
        x: torch.Tensor,
        g: torch.Tensor,
        weight: torch.Tensor | None = None,
        bias: torch.Tensor | None = None,
        residual: torch.Tensor | None = None,
        prenorm: bool = False,
        residual_in_fp32: bool = False,
    ) -> torch.Tensor:
        return rms_norm_swish_gate_linear(
            x,
            g,
            self.weight,
            self.bias,
            weight,
            bias,
            residual=residual,
            eps=self.eps,
            prenorm=prenorm,
            residual_in_fp32=residual_in_fp32,
        )


class FusedRMSNormSwishGateLinear(FusedRMSNormGatedLinear):

    def __init__(
        self,
        hidden_size: int,
        elementwise_affine: bool = True,
        eps: float = 1e-5,
        device: torch.device | None = None,
        dtype: torch.dtype | None = None,
    ) -> FusedRMSNormSwishGateLinear:
        super().__init__(
            hidden_size=hidden_size,
            elementwise_affine=elementwise_affine,
            eps=eps,
            device=device,
            dtype=dtype,
        )