```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline


_cuda_source = r"""
#include <torch/extension.h>
#include <c10/cuda/CUDAGuard.h>
#include <c10/cuda/CUDAStream.h>
#include <c10/cuda/CUDAException.h>
#include <cuda_runtime.h>
#include <cub/cub.cuh>

constexpr int THREADS = 256;
constexpr int ITEMS = 8;
constexpr int TILE = THREADS * ITEMS;

__global__ void tile_sums_kernel(
    const float* __restrict__ x,
    float* __restrict__ sums,
    int64_t columns,
    int64_t tiles)
{
    const int64_t block = blockIdx.x;
    const int64_t row = block / tiles;
    const int64_t tile = block % tiles;
    const int64_t start = tile * TILE;

    float value = 0.0f;
    #pragma unroll
    for (int i = 0; i < ITEMS; ++i) {
        const int64_t column = start + threadIdx.x + i * THREADS;
        if (column < columns)
            value += x[row * columns + column];
    }

    using Reduce = cub::BlockReduce<float, THREADS>;
    __shared__ typename Reduce::TempStorage storage;
    const float total = Reduce(storage).Sum(value);

    if (threadIdx.x == 0)
        sums[block] = total;
}

__global__ void scan_tile_sums_kernel(
    float* __restrict__ sums,
    int64_t rows,
    int64_t tiles)
{
    const int lane = threadIdx.x & 31;
    const int64_t row =
        static_cast<int64_t>(blockIdx.x) * 8 + (threadIdx.x >> 5);

    if (row >= rows)
        return;

    float carry = 0.0f;
    for (int64_t base = 0; base < tiles; base += 32) {
        const int64_t tile = base + lane;
        float value = tile < tiles ? sums[row * tiles + tile] : 0.0f;

        #pragma unroll
        for (int distance = 1; distance < 32; distance <<= 1) {
            const float previous =
                __shfl_up_sync(0xffffffffu, value, distance);
            if (lane >= distance)
                value += previous;
        }

        const float previous = __shfl_up_sync(0xffffffffu, value, 1);
        const float offset = carry + (lane == 0 ? 0.0f : previous);

        if (tile < tiles)
            sums[row * tiles + tile] = offset;

        carry += __shfl_sync(0xffffffffu, value, 31);
    }
}

__global__ void output_scan_kernel(
    const float* __restrict__ x,
    const float* __restrict__ offsets,
    float* __restrict__ output,
    int64_t columns,
    int64_t tiles)
{
    using Load = cub::BlockLoad<
        float, THREADS, ITEMS, cub::BLOCK_LOAD_WARP_TRANSPOSE>;
    using Scan = cub::BlockScan<float, THREADS>;
    using Store = cub::BlockStore<
        float, THREADS, ITEMS, cub::BLOCK_STORE_WARP_TRANSPOSE>;

    __shared__ union {
        typename Load::TempStorage load;
        typename Scan::TempStorage scan;
        typename Store::TempStorage store;
    } storage;

    const int64_t block = blockIdx.x;
    const int64_t row = block / tiles;
    const int64_t tile = block % tiles;
    const int64_t start = tile * TILE;
    const int valid = static_cast<int>(
        columns - start < TILE ? columns - start : TILE);

    float values[ITEMS];
    Load(storage.load).Load(
        x + row * columns + start, values, valid, 0.0f);
    __syncthreads();

    Scan(storage.scan).InclusiveSum(values, values);
    __syncthreads();

    const float offset = offsets[block];
    #pragma unroll
    for (int i = 0; i < ITEMS; ++i)
        values[i] += offset;

    Store(storage.store).Store(
        output + row * (columns + 1) + start + 1, values, valid);

    if (tile == 0 && threadIdx.x == 0)
        output[row * (columns + 1)] = 0.0f;
}

torch::Tensor exclusive_scan_cuda(torch::Tensor x)
{
    TORCH_CHECK(x.is_cuda(), "Expected a CUDA tensor");
    TORCH_CHECK(x.scalar_type() == at::kFloat, "Expected float32");
    TORCH_CHECK(x.dim() == 2 && x.is_contiguous(),
                "Expected a contiguous matrix");
    TORCH_CHECK(x.size(1) > 0, "Expected a nonempty scan dimension");

    const c10::cuda::CUDAGuard guard(x.device());

    // The reference's [:-1] slices dimension zero after concatenation.
    const int64_t rows = x.size(0) > 0 ? x.size(0) - 1 : 0;
    const int64_t columns = x.size(1);
    auto output = torch::empty({rows, columns + 1}, x.options());

    if (rows == 0)
        return output;

    const int64_t tiles = (columns + TILE - 1) / TILE;
    const int64_t blocks = rows * tiles;
    TORCH_CHECK(blocks <= 2147483647LL, "Input exceeds launch capacity");

    auto offsets = torch::empty({rows, tiles}, x.options());
    const auto stream = c10::cuda::getCurrentCUDAStream();

    tile_sums_kernel<<<static_cast<unsigned int>(blocks), THREADS, 0, stream>>>(
        x.data_ptr<float>(), offsets.data_ptr<float>(), columns, tiles);
    C10_CUDA_KERNEL_LAUNCH_CHECK();

    scan_tile_sums_kernel<<<
        static_cast<unsigned int>((rows + 7) / 8), 256, 0, stream>>>(
        offsets.data_ptr<float>(), rows, tiles);
    C10_CUDA_KERNEL_LAUNCH_CHECK();

    output_scan_kernel<<<static_cast<unsigned int>(blocks), THREADS, 0, stream>>>(
        x.data_ptr<float>(), offsets.data_ptr<float>(),
        output.data_ptr<float>(), columns, tiles);
    C10_CUDA_KERNEL_LAUNCH_CHECK();

    return output;
}
"""

_extension = load_inline(
    name="exclusive_cumsum_tiled_cuda_v1",
    cpp_sources="torch::Tensor exclusive_scan_cuda(torch::Tensor x);",
    cuda_sources=_cuda_source,
    functions=["exclusive_scan_cuda"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
    verbose=False,
)


class ModelNew(nn.Module):
    def __init__(self, dim):
        super().__init__()
        self.dim = dim

    def forward(self, x):
        if (
            x.is_cuda
            and x.dtype == torch.float32
            and x.ndim == 2
            and self.dim in (1, -1)
            and x.shape[1] > 0
            and x.is_contiguous()
            and not (torch.is_grad_enabled() and x.requires_grad)
        ):
            return _extension.exclusive_scan_cuda(x)

        exclusive_cumsum = torch.cat(
            (
                torch.zeros_like(
                    x.select(self.dim, 0).unsqueeze(self.dim)
                ),
                x,
            ),
            dim=self.dim,
        )[:-1]
        return torch.cumsum(exclusive_cumsum, dim=self.dim)
```