code/flash-linear-attention/fla/modules/l2norm.py

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


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

from fla.utils import autotune_cache_kwargs, input_guard, is_amd

BT_LIST = [8, 16, 32, 64, 128]
NUM_WARPS_AUTOTUNE = [1, 2, 4, 8, 16] if is_amd else [1, 2, 4, 8, 16, 32]


@triton.autotune(
    configs=[
        triton.Config({}, num_warps=num_warps)
        for num_warps in NUM_WARPS_AUTOTUNE
    ],
    key=['D'],
    **autotune_cache_kwargs,
)
@triton.jit
def l2norm_fwd_kernel1(
    x,
    y,
    rstd,
    eps,
    D,
    BD: tl.constexpr,
):
    i_t = tl.program_id(0)
    x += i_t * D
    y += i_t * D
    # Compute mean and variance
    cols = tl.arange(0, BD)
    mask = cols < D

    b_x = tl.load(x + cols, mask=mask, other=0.0).to(tl.float32)
    b_rstd = 1 / tl.sqrt(tl.sum(b_x * b_x) + eps)
    b_y = b_x * b_rstd
    tl.store(y + cols, b_y, mask=mask)
    tl.store(rstd + i_t, b_rstd)


@triton.autotune(
    configs=[
        triton.Config({}, num_warps=num_warps)
        for num_warps in NUM_WARPS_AUTOTUNE
    ],
    key=['D'],
    **autotune_cache_kwargs,
)
@triton.jit
def l2norm_bwd_kernel1(
    y,
    rstd,
    dy,
    dx,
    eps,
    D,
    BD: tl.constexpr,
):
    i_t = tl.program_id(0)
    y += i_t * D
    dx += i_t * D
    dy += i_t * D

    cols = tl.arange(0, BD)
    mask = cols < D
    b_y = tl.load(y + cols, mask=mask, other=0.0).to(tl.float32)
    b_rstd = tl.load(rstd + i_t).to(tl.float32)
    b_dy = tl.load(dy + cols, mask=mask, other=0.0).to(tl.float32)
    b_dx = b_dy * b_rstd - tl.sum(b_dy * b_y) * b_y * b_rstd
    tl.store(dx + cols, b_dx, mask=mask)


@triton.autotune(
    configs=[
        triton.Config({'BT': BT}, num_warps=num_warps)
        for num_warps in [1, 2, 4, 8, 16]
        for BT in BT_LIST
    ],
    key=['D', 'NB'],
    **autotune_cache_kwargs,
)
@triton.jit
def l2norm_fwd_kernel(
    x,
    y,
    rstd,
    eps,
    T: tl.constexpr,
    D: tl.constexpr,
    BD: tl.constexpr,
    NB: tl.constexpr,
    BT: tl.constexpr,
):
    i_t = tl.program_id(0)
    p_x = tl.make_block_ptr(x, (T, D), (D, 1), (i_t * BT, 0), (BT, BD), (1, 0))
    p_y = tl.make_block_ptr(y, (T, D), (D, 1), (i_t * BT, 0), (BT, BD), (1, 0))
    p_rstd = tl.make_block_ptr(rstd, (T,), (1,), (i_t * BT,), (BT,), (0,))

    b_x = tl.load(p_x, boundary_check=(0, 1)).to(tl.float32)
    b_rstd = 1 / tl.sqrt(tl.sum(b_x * b_x, 1) + eps)
    b_y = b_x * b_rstd[:, None]

    tl.store(p_y, b_y.to(p_y.dtype.element_ty), boundary_check=(0, 1))
    tl.store(p_rstd, b_rstd.to(p_rstd.dtype.element_ty), boundary_check=(0,))


@triton.autotune(
    configs=[
        triton.Config({'BT': BT}, num_warps=num_warps)
        for num_warps in [1, 2, 4, 8, 16]
        for BT in BT_LIST
    ],
    key=['D', 'NB'],
    **autotune_cache_kwargs,
)
@triton.jit
def l2norm_bwd_kernel(
    y,
    rstd,
    dy,
    dx,
    eps,
    T: tl.constexpr,
    D: tl.constexpr,
    BD: tl.constexpr,
    NB: tl.constexpr,
    BT: tl.constexpr,
):
    i_t = tl.program_id(0)
    p_y = tl.make_block_ptr(y, (T, D), (D, 1), (i_t * BT, 0), (BT, BD), (1, 0))
    p_rstd = tl.make_block_ptr(rstd, (T,), (1,), (i_t * BT,), (BT,), (0,))
    p_dy = tl.make_block_ptr(dy, (T, D), (D, 1), (i_t * BT, 0), (BT, BD), (1, 0))
    p_dx = tl.make_block_ptr(dx, (T, D), (D, 1), (i_t * BT, 0), (BT, BD), (1, 0))

    b_y = tl.load(p_y, boundary_check=(0, 1)).to(tl.float32)
    b_rstd = tl.load(p_rstd, boundary_check=(0,)).to(tl.float32)
    b_dy = tl.load(p_dy, boundary_check=(0, 1)).to(tl.float32)
    b_dx = b_dy * b_rstd[:, None] - tl.sum(b_dy * b_y, 1)[:, None] * b_y * b_rstd[:, None]
    tl.store(p_dx, b_dx.to(p_dx.dtype.element_ty), boundary_check=(0, 1))


def l2norm_fwd(
    x: torch.Tensor,
    eps: float = 1e-6,
    output_dtype: torch.dtype | None = None,
):
    x_shape_og = x.shape
    x = x.view(-1, x.shape[-1])
    # allocate output
    if output_dtype is None:
        y = torch.empty_like(x)
    else:
        y = torch.empty_like(x, dtype=output_dtype)
    assert y.stride(-1) == 1
    T, D = x.shape[0], x.shape[-1]
    # 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 doesn't support feature dim >= 64KB.")

    rstd = torch.empty((T,), dtype=torch.float32, device=x.device)
    if D <= 512:
        NB = triton.cdiv(T, 2048)
        def grid(meta): return (triton.cdiv(T, meta['BT']), )
        l2norm_fwd_kernel[grid](
            x=x,
            y=y,
            rstd=rstd,
            eps=eps,
            T=T,
            D=D,
            BD=BD,
            NB=NB,
        )
    else:
        l2norm_fwd_kernel1[(T,)](
            x=x,
            y=y,
            rstd=rstd,
            eps=eps,
            D=D,
            BD=BD,
        )
    return y.view(x_shape_og), rstd.view(x_shape_og[:-1])


def l2norm_bwd(
    y: torch.Tensor,
    rstd: torch.Tensor,
    dy: torch.Tensor,
    eps: float = 1e-6,
):
    y_shape_og = y.shape
    y = y.view(-1, dy.shape[-1])
    dy = dy.view(-1, dy.shape[-1])
    assert dy.shape == y.shape
    # allocate output
    dx = torch.empty_like(y)
    T, D = y.shape[0], y.shape[-1]
    # Less than 64KB per feature: enqueue fused kernel
    MAX_FUSED_SIZE = 65536 // y.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.")

    if D <= 512:
        NB = triton.cdiv(T, 2048)
        def grid(meta): return (triton.cdiv(T, meta['BT']), )
        l2norm_bwd_kernel[grid](
            y=y,
            rstd=rstd,
            dy=dy,
            dx=dx,
            eps=eps,
            T=T,
            D=D,
            BD=BD,
            NB=NB,
        )
    else:
        l2norm_bwd_kernel1[(T,)](
            y=y,
            rstd=rstd,
            dy=dy,
            dx=dx,
            eps=eps,
            D=D,
            BD=BD,
        )

    return dx.view(y_shape_og)


class L2NormFunction(torch.autograd.Function):

    @staticmethod
    @input_guard
    def forward(
        ctx,
        x,
        eps=1e-6,
        output_dtype=None,
    ):
        y, rstd = l2norm_fwd(x, eps, output_dtype)
        ctx.eps = eps
        ctx.x_dtype = x.dtype
        ctx.save_for_backward(y, rstd)
        return y

    @staticmethod
    @input_guard
    def backward(ctx, dy):
        y, rstd = ctx.saved_tensors
        dx = l2norm_bwd(y, rstd, dy, ctx.eps)
        return dx, None, None


def l2norm(
    x: torch.Tensor,
    eps: float = 1e-6,
    output_dtype: torch.dtype | None = None,
) -> torch.Tensor:
    return L2NormFunction.apply(x, eps, output_dtype)


l2_norm = l2norm


class L2Norm(nn.Module):

    def __init__(
        self,
        eps: float = 1e-6,
        output_dtype: torch.dtype | None = None,
    ):
        super().__init__()
        self.eps = eps
        self.output_dtype = output_dtype

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        return l2norm(x, self.eps, self.output_dtype)