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


_cpp_source = r"""
#include <torch/extension.h>
torch::Tensor exclusive_scan_cuda(torch::Tensor x);
"""

_cuda_source = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <c10/cuda/CUDAGuard.h>
#include <c10/cuda/CUDAException.h>
#include <cuda_runtime.h>

constexpr int THREADS = 1024;
constexpr int WARPS = THREADS / 32;
constexpr unsigned MASK = 0xffffffffu;

__device__ __forceinline__ float warp_scan(float value) {
    #pragma unroll
    for (int delta = 1; delta < 32; delta <<= 1) {
        asm volatile(
            "{\n"
            "  .reg .pred p;\n"
            "  .reg .f32 other;\n"
            "  shfl.sync.up.b32 other|p, %0, %1, 0, %2;\n"
            "  @p add.f32 %0, %0, other;\n"
            "}\n"
            : "+f"(value)
            : "r"(delta), "r"(MASK));
    }
    return value;
}

template<int ROUNDS, int VECTORS>
__global__ __launch_bounds__(THREADS, 1)
void row_scan_kernel(
    const float* __restrict__ input,
    float* __restrict__ output)
{
    constexpr int COLUMNS = THREADS * ROUNDS * VECTORS * 4;
    constexpr int WARP_COLUMNS = 32 * ROUNDS * VECTORS * 4;
    constexpr int OUTPUT_STRIDE = COLUMNS + 4;

    const int lane = threadIdx.x & 31;
    const int warp = threadIdx.x >> 5;
    const int64_t row = static_cast<int64_t>(blockIdx.x);

    const float4* src = reinterpret_cast<const float4*>(
        input + row * COLUMNS + warp * WARP_COLUMNS);

    float4 prefixes[ROUNDS * VECTORS];
    float warp_total = 0.0f;

    #pragma unroll
    for (int round = 0; round < ROUNDS; ++round) {
        float4 local[VECTORS];
        float local_total = 0.0f;

        #pragma unroll
        for (int j = 0; j < VECTORS; ++j) {
            const float4 v =
                src[(round * 32 + lane) * VECTORS + j];
            const float xy = v.x + v.y;
            const float xyz = xy + v.z;

            local[j] = make_float4(
                local_total,
                local_total + v.x,
                local_total + xy,
                local_total + xyz);

            local_total += xyz + v.w;
        }

        const float inclusive = warp_scan(local_total);
        const float preceding = __shfl_up_sync(MASK, inclusive, 1);
        const float base =
            warp_total + (lane == 0 ? 0.0f : preceding);

        #pragma unroll
        for (int j = 0; j < VECTORS; ++j) {
            const float4 p = local[j];
            prefixes[round * VECTORS + j] = make_float4(
                base + p.x,
                base + p.y,
                base + p.z,
                base + p.w);
        }

        warp_total += __shfl_sync(MASK, inclusive, 31);
    }

    __shared__ float warp_offsets[WARPS];
    if (lane == 31)
        warp_offsets[warp] = warp_total;
    __syncthreads();

    float* output_row = output + row * OUTPUT_STRIDE;

    if (warp == 0) {
        const float inclusive = warp_scan(warp_offsets[lane]);
        const float preceding = __shfl_up_sync(MASK, inclusive, 1);
        warp_offsets[lane] = lane == 0 ? 0.0f : preceding;
        if (lane == 31)
            output_row[COLUMNS] = inclusive;
    }
    __syncthreads();

    const float offset = warp_offsets[warp];
    float4* dst = reinterpret_cast<float4*>(
        output_row + warp * WARP_COLUMNS);

    #pragma unroll
    for (int round = 0; round < ROUNDS; ++round) {
        #pragma unroll
        for (int j = 0; j < VECTORS; ++j) {
            const float4 p = prefixes[round * VECTORS + j];
            dst[(round * 32 + lane) * VECTORS + j] = make_float4(
                offset + p.x,
                offset + p.y,
                offset + p.z,
                offset + p.w);
        }
    }
}

torch::Tensor exclusive_scan_cuda(torch::Tensor x) {
    const c10::cuda::CUDAGuard guard(x.device());
    const int64_t rows = x.size(0) - 1;
    const int64_t columns = x.size(1);

    auto output = torch::empty_strided(
        {rows, columns + 1},
        {columns + 4, 1},
        x.options());

    if (rows == 0)
        return output;

    const auto stream = at::cuda::getCurrentCUDAStream();
    const dim3 grid(static_cast<unsigned int>(rows));

    switch (columns) {
        case 4096:
            row_scan_kernel<1, 1><<<grid, THREADS, 0, stream>>>(
                x.data_ptr<float>(), output.data_ptr<float>());
            break;
        case 8192:
            row_scan_kernel<1, 2><<<grid, THREADS, 0, stream>>>(
                x.data_ptr<float>(), output.data_ptr<float>());
            break;
        case 16384:
            row_scan_kernel<2, 2><<<grid, THREADS, 0, stream>>>(
                x.data_ptr<float>(), output.data_ptr<float>());
            break;
        case 32768:
            row_scan_kernel<4, 2><<<grid, THREADS, 0, stream>>>(
                x.data_ptr<float>(), output.data_ptr<float>());
            break;
        default:
            TORCH_CHECK(false, "Unsupported row length");
    }

    C10_CUDA_KERNEL_LAUNCH_CHECK();
    return output;
}
"""

_extension = load_inline(
    name="exclusive_cumsum_paired_scan_v6",
    cpp_sources=_cpp_source,
    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.is_contiguous()
            and x.data_ptr() % 16 == 0
            and 0 < x.size(0) <= 2147483647
            and x.size(1) in (4096, 8192, 16384, 32768)
            and not (torch.is_grad_enabled() and x.requires_grad)
        ):
            return _extension.exclusive_scan_cuda(x)

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