You write custom CUDA kernels to replace the pytorch operators in the given architecture to get speedups. 

    You have complete freedom to choose the set of operators you want to replace. You may make the decision to replace some operators with custom CUDA kernels and leave others unchanged. You may replace multiple operators with custom implementations, consider operator fusion opportunities (combining multiple operators into a single kernel, for example, combining matmul+relu), or algorithmic changes (such as online softmax). You are only limited by your imagination.


        Here's an example to show you the syntax of inline embedding custom CUDA operators in torch: The example given architecture is: 

        ``` 

        # Copyright (c) Meta Platforms, Inc. and affiliates.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.

import torch
import torch.nn as nn
import torch.nn.functional as F


class Model(nn.Module):
    def __init__(self) -> None:
        super().__init__()

    def forward(self, a, b):
        return a + b


def get_inputs():
    # randomly generate input tensors based on the model architecture
    a = torch.randn(1, 128).cuda()
    b = torch.randn(1, 128).cuda()
    return [a, b]


def get_init_inputs():
    # randomly generate tensors required for initialization based on the model architecture
    return []

        ``` 

        The example new arch with custom CUDA kernels looks like this:
        ```
        # Copyright (c) Meta Platforms, Inc. and affiliates.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.

import torch
import torch.nn as nn
import torch.nn.functional as F
from torch.utils.cpp_extension import load_inline

# Define the custom CUDA kernel for element-wise addition
elementwise_add_source = """
#include <torch/extension.h>
#include <cuda_runtime.h>

__global__ void elementwise_add_kernel(const float* a, const float* b, float* out, int size) {
    int idx = blockIdx.x * blockDim.x + threadIdx.x;
    if (idx < size) {
        out[idx] = a[idx] + b[idx];
    }
}

torch::Tensor elementwise_add_cuda(torch::Tensor a, torch::Tensor b) {
    auto size = a.numel();
    auto out = torch::zeros_like(a);

    const int block_size = 256;
    const int num_blocks = (size + block_size - 1) / block_size;

    elementwise_add_kernel<<<num_blocks, block_size>>>(a.data_ptr<float>(), b.data_ptr<float>(), out.data_ptr<float>(), size);

    return out;
}
"""

elementwise_add_cpp_source = (
    "torch::Tensor elementwise_add_cuda(torch::Tensor a, torch::Tensor b);"
)

# Compile the inline CUDA code for element-wise addition
elementwise_add = load_inline(
    name="elementwise_add",
    cpp_sources=elementwise_add_cpp_source,
    cuda_sources=elementwise_add_source,
    functions=["elementwise_add_cuda"],
    verbose=True,
    extra_cflags=[""],
    extra_ldflags=[""],
)


class ModelNew(nn.Module):
    def __init__(self) -> None:
        super().__init__()
        self.elementwise_add = elementwise_add

    def forward(self, a, b):
        return self.elementwise_add.elementwise_add_cuda(a, b)

        ``` 

        
    You are given the following architecture: 

    ```
    # Copyright (c) Meta Platforms, Inc. and affiliates.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.

import torch
import torch.nn as nn

class Model(nn.Module):
    """
    Simple model that performs matrix-vector multiplication (C = A * B).
    """
    def __init__(self):
        super(Model, self).__init__()
    
    def forward(self, A: torch.Tensor, B: torch.Tensor) -> torch.Tensor:
        """
        Performs matrix-vector multiplication.

        Args:
            A: Input matrix of shape (M, K).
            B: Input vector of shape (K, 1).

        Returns:
            Output vector of shape (M, 1).
        """
        return torch.matmul(A, B)

M = 256 * 8 # 2048
K = 131072 * 8 # 1048576

def get_inputs():
    A = torch.rand(M, K)
    B = torch.rand(K, 1)
    return [A, B]

def get_init_inputs():
    return []  # No special initialization inputs needed
    ```
    
Optimize the architecture named Model with custom CUDA operators! Name your optimized output architecture ModelNew. Output the new code in codeblocks. Please generate real code, NOT pseudocode, make sure the code compiles and is fully functional. Just output the new model code, no other text, and NO testing code! 



This is turn 5 of 6 for this task. Your previous solution (turn 4) was:
```python
# Copyright (c) Meta Platforms, Inc. and affiliates.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.

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

# Custom matrix-vector multiplication kernel (C = A @ B).
# A is (M, K) row-major, B is (K, 1), C is (M, 1).
#
# The operation is purely DRAM-bandwidth bound (A, 8 GiB, is streamed
# exactly once), so the kernel is organized to make the DRAM access pattern
# as close to a linear sweep as possible:
#   * NO split-K: each thread block owns TWO full consecutive rows, so the
#     whole grid performs a perfectly sequential, forward-sliding read of A
#     (blocks are scheduled in ascending blockIdx order). Compared to the
#     previous split-K version this cuts the number of concurrent memory
#     streams ~4x (fewer open HBM pages -> higher row-buffer hit rate) and
#     lengthens each sequential burst from 512 KiB to 8 MiB.
#   * 128-bit (float4) loads; A uses the evict-first streaming cache hint
#     (__ldcs) so it does not evict the heavily reused, L2-resident B.
#   * Two rows per block: B is loaded once per iteration and reused for both
#     rows, halving B load instructions and L2 traffic while doubling the
#     A bytes in flight per thread (8 outstanding 16B loads per thread).
#   * 4-way unrolled main loop with 8 independent accumulators for deep
#     memory-level parallelism; because the kernel is bandwidth bound, the
#     modest block count still fully saturates DRAM even in the tail wave.
#   * No atomics and no separate fill kernel: each block owns its rows and
#     writes C directly (output allocated with torch::empty).
_matvec_cuda_src = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <c10/cuda/CUDAGuard.h>
#include <cuda_runtime.h>

#define MV_THREADS 256
#define MV_UNROLL 4

__global__ void __launch_bounds__(MV_THREADS) matvec_rows_kernel(
    const float4* __restrict__ A4,
    const float4* __restrict__ B4,
    const float*  __restrict__ As,
    const float*  __restrict__ Bs,
    float* __restrict__ C,
    const int K4,
    const int K,
    const int M)
{
    const int row0 = blockIdx.x * 2;
    int row1 = row0 + 1;
    if (row1 >= M) row1 = M - 1;  // odd M: duplicate row, result discarded

    const float4* a0 = A4 + (size_t)row0 * (size_t)K4;
    const float4* a1 = A4 + (size_t)row1 * (size_t)K4;

    const int stride = MV_THREADS;
    int i = threadIdx.x;

    float s00 = 0.f, s01 = 0.f, s02 = 0.f, s03 = 0.f;  // row0 partials
    float s10 = 0.f, s11 = 0.f, s12 = 0.f, s13 = 0.f;  // row1 partials

    // Main vectorized loop: 4-way unrolled, B reused across both rows.
    // Each iteration covers 16 KiB contiguous per row.
    for (; i + 3 * stride < K4; i += 4 * stride) {
        float4 b0 = __ldg(B4 + i);
        float4 b1 = __ldg(B4 + i + stride);
        float4 b2 = __ldg(B4 + i + 2 * stride);
        float4 b3 = __ldg(B4 + i + 3 * stride);

        float4 a00 = __ldcs(a0 + i);
        float4 a01 = __ldcs(a0 + i + stride);
        float4 a02 = __ldcs(a0 + i + 2 * stride);
        float4 a03 = __ldcs(a0 + i + 3 * stride);
        float4 a10 = __ldcs(a1 + i);
        float4 a11 = __ldcs(a1 + i + stride);
        float4 a12 = __ldcs(a1 + i + 2 * stride);
        float4 a13 = __ldcs(a1 + i + 3 * stride);

        s00 += a00.x * b0.x + a00.y * b0.y + a00.z * b0.z + a00.w * b0.w;
        s01 += a01.x * b1.x + a01.y * b1.y + a01.z * b1.z + a01.w * b1.w;
        s02 += a02.x * b2.x + a02.y * b2.y + a02.z * b2.z + a02.w * b2.w;
        s03 += a03.x * b3.x + a03.y * b3.y + a03.z * b3.z + a03.w * b3.w;
        s10 += a10.x * b0.x + a10.y * b0.y + a10.z * b0.z + a10.w * b0.w;
        s11 += a11.x * b1.x + a11.y * b1.y + a11.z * b1.z + a11.w * b1.w;
        s12 += a12.x * b2.x + a12.y * b2.y + a12.z * b2.z + a12.w * b2.w;
        s13 += a13.x * b3.x + a13.y * b3.y + a13.z * b3.z + a13.w * b3.w;
    }
    for (; i < K4; i += stride) {
        float4 bv  = __ldg(B4 + i);
        float4 av0 = __ldcs(a0 + i);
        float4 av1 = __ldcs(a1 + i);
        s00 += av0.x * bv.x + av0.y * bv.y + av0.z * bv.z + av0.w * bv.w;
        s10 += av1.x * bv.x + av1.y * bv.y + av1.z * bv.z + av1.w * bv.w;
    }

    float sum0 = (s00 + s01) + (s02 + s03);
    float sum1 = (s10 + s11) + (s12 + s13);

    // Scalar tail when K is not divisible by 4.
    {
        const int base = K4 * 4;
        if (base < K) {
            const float* ar0 = As + (size_t)row0 * (size_t)K;
            const float* ar1 = As + (size_t)row1 * (size_t)K;
            for (int j = base + threadIdx.x; j < K; j += stride) {
                const float bj = __ldg(Bs + j);
                sum0 += ar0[j] * bj;
                sum1 += ar1[j] * bj;
            }
        }
    }

    // Warp-level reduction of both row sums.
    #pragma unroll
    for (int off = 16; off > 0; off >>= 1) {
        sum0 += __shfl_down_sync(0xffffffffu, sum0, off);
        sum1 += __shfl_down_sync(0xffffffffu, sum1, off);
    }

    __shared__ float w0[MV_THREADS / 32];
    __shared__ float w1[MV_THREADS / 32];
    const int lane = threadIdx.x & 31;
    const int warp = threadIdx.x >> 5;
    if (lane == 0) {
        w0[warp] = sum0;
        w1[warp] = sum1;
    }
    __syncthreads();

    if (warp == 0) {
        float v0 = (lane < MV_THREADS / 32) ? w0[lane] : 0.f;
        float v1 = (lane < MV_THREADS / 32) ? w1[lane] : 0.f;
        #pragma unroll
        for (int off = MV_THREADS / 64; off > 0; off >>= 1) {
            v0 += __shfl_down_sync(0xffffffffu, v0, off);
            v1 += __shfl_down_sync(0xffffffffu, v1, off);
        }
        if (lane == 0) {
            C[row0] = v0;                    // block owns its rows: direct store
            if (row1 != row0) C[row1] = v1;
        }
    }
}

torch::Tensor matvec_cuda(torch::Tensor A, torch::Tensor B) {
    TORCH_CHECK(A.is_cuda() && B.is_cuda(), "A and B must be CUDA tensors");
    TORCH_CHECK(A.scalar_type() == at::kFloat && B.scalar_type() == at::kFloat,
                "A and B must be float32");
    TORCH_CHECK(A.dim() == 2, "A must be 2-D");
    TORCH_CHECK(B.numel() == A.size(1), "B must have A.size(1) elements");

    const c10::cuda::CUDAGuard device_guard(A.device());

    auto Ac = A.contiguous();
    auto Bc = B.contiguous();

    const int64_t M = Ac.size(0);
    const int64_t K = Ac.size(1);

    if (M == 0) return torch::empty({M, 1}, Ac.options());
    if (K == 0) return torch::zeros({M, 1}, Ac.options());

    // The vectorized kernel requires 16-byte alignment (true for fresh
    // allocations) and 32-bit-indexable operands; otherwise use cuBLAS.
    if ((reinterpret_cast<uintptr_t>(Ac.data_ptr<float>()) & 0xF) != 0 ||
        (reinterpret_cast<uintptr_t>(Bc.data_ptr<float>()) & 0xF) != 0 ||
        K > (int64_t)1 << 30 || M > (int64_t)1 << 30) {
        return torch::matmul(A, B);
    }

    auto C = torch::empty({M, 1}, Ac.options());  // fully overwritten, no fill

    const int K4 = (int)(K >> 2);
    const int row_blocks = (int)((M + 1) >> 1);

    dim3 grid((unsigned)row_blocks);
    dim3 block(MV_THREADS);

    auto stream = at::cuda::getCurrentCUDAStream();
    matvec_rows_kernel<<<grid, block, 0, stream>>>(
        reinterpret_cast<const float4*>(Ac.data_ptr<float>()),
        reinterpret_cast<const float4*>(Bc.data_ptr<float>()),
        Ac.data_ptr<float>(),
        Bc.data_ptr<float>(),
        C.data_ptr<float>(),
        K4, (int)K, (int)M);

    return C;
}
"""

_matvec_cpp_src = "torch::Tensor matvec_cuda(torch::Tensor A, torch::Tensor B);"

_matvec_ext = load_inline(
    name="matvec_stream_ext_v4",
    cpp_sources=_matvec_cpp_src,
    cuda_sources=_matvec_cuda_src,
    functions=["matvec_cuda"],
    verbose=False,
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
)


class ModelNew(nn.Module):
    """
    Matrix-vector multiplication (C = A * B) accelerated with a custom
    streaming CUDA kernel: each block owns two full rows (a perfectly
    sequential DRAM sweep with no split-K, no atomics, and no output
    pre-fill), float4 streaming loads for A (__ldcs), and cached float4
    loads for the L2-resident B.
    """
    def __init__(self):
        super(ModelNew, self).__init__()
        self._op = _matvec_ext

    def forward(self, A: torch.Tensor, B: torch.Tensor) -> torch.Tensor:
        if (A.is_cuda and B.is_cuda and A.dim() == 2
                and A.dtype == torch.float32 and B.dtype == torch.float32):
            return self._op.matvec_cuda(A, B)
        return torch.matmul(A, B)
```
Result of evaluating it:
The solution is correct on the test inputs. Mean runtime 5.83 ms; the PyTorch reference (with TF32 enabled) takes 6.1 ms; speedup 1.046x.
Profiler, top device kernels of one forward pass of your solution:
| device kernel | total device time (us) | calls |
|---|---|---|
| matvec_rows_kernel(float4 const*, float4 const*, float const*, float const*, float*, int,  | 5842.2 | 1 |

The fastest correct solution so far (1.050x speedup) is:
```python
# Copyright (c) Meta Platforms, Inc. and affiliates.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.

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

# Custom split-K matrix-vector multiplication kernel (C = A @ B).
# A is (M, K) row-major, B is (K, 1), C is (M, 1).
#
# The operation is purely DRAM-bandwidth bound (A is streamed exactly once),
# so the kernel is engineered for maximum sustainable read throughput:
#   * 128-bit (float4) loads; A uses the evict-first streaming cache hint
#     (__ldcs) so it does not evict the much smaller, heavily reused B.
#   * Each thread block reduces TWO rows at once: B is loaded once per
#     iteration and reused for both rows, halving B load instructions and
#     L1/L2 traffic while doubling A bytes in flight per thread.
#   * split-K across the (small) M dimension sized from the SM count so the
#     whole device stays saturated; grid is ordered row-fastest so all
#     resident blocks share the same B slice (excellent L1/L2 locality).
#   * 4-way unrolled main loop with 8 independent accumulators for deep
#     memory-level parallelism; warp-shuffle + tiny shared second stage
#     reduction; partials combined with atomicAdd into a zero-filled output.
_matvec_cuda_src = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <c10/cuda/CUDAGuard.h>
#include <cuda_runtime.h>

#define MV_THREADS 256
#define MV_UNROLL 4

__global__ void __launch_bounds__(MV_THREADS) matvec2row_kernel(
    const float4* __restrict__ A4,
    const float4* __restrict__ B4,
    const float*  __restrict__ As,
    const float*  __restrict__ Bs,
    float* __restrict__ C,
    const int K4,
    const int K,
    const int chunk,
    const int M)
{
    const int row0 = blockIdx.x * 2;
    int row1 = row0 + 1;
    if (row1 >= M) row1 = M - 1;  // odd M: duplicate row, result discarded

    const int part  = blockIdx.y;
    const int start = part * chunk;
    int end = start + chunk;
    if (end > K4) end = K4;

    const float4* a0 = A4 + (size_t)row0 * (size_t)K4;
    const float4* a1 = A4 + (size_t)row1 * (size_t)K4;

    const int stride = MV_THREADS;
    int i = start + threadIdx.x;

    float s00 = 0.f, s01 = 0.f, s02 = 0.f, s03 = 0.f;  // row0 partials
    float s10 = 0.f, s11 = 0.f, s12 = 0.f, s13 = 0.f;  // row1 partials

    // Main vectorized loop: 4-way unrolled, B reused across both rows.
    for (; i + 3 * stride < end; i += 4 * stride) {
        float4 b0 = __ldg(B4 + i);
        float4 b1 = __ldg(B4 + i + stride);
        float4 b2 = __ldg(B4 + i + 2 * stride);
        float4 b3 = __ldg(B4 + i + 3 * stride);

        float4 a00 = __ldcs(a0 + i);
        float4 a01 = __ldcs(a0 + i + stride);
        float4 a02 = __ldcs(a0 + i + 2 * stride);
        float4 a03 = __ldcs(a0 + i + 3 * stride);
        float4 a10 = __ldcs(a1 + i);
        float4 a11 = __ldcs(a1 + i + stride);
        float4 a12 = __ldcs(a1 + i + 2 * stride);
        float4 a13 = __ldcs(a1 + i + 3 * stride);

        s00 += a00.x * b0.x + a00.y * b0.y + a00.z * b0.z + a00.w * b0.w;
        s01 += a01.x * b1.x + a01.y * b1.y + a01.z * b1.z + a01.w * b1.w;
        s02 += a02.x * b2.x + a02.y * b2.y + a02.z * b2.z + a02.w * b2.w;
        s03 += a03.x * b3.x + a03.y * b3.y + a03.z * b3.z + a03.w * b3.w;
        s10 += a10.x * b0.x + a10.y * b0.y + a10.z * b0.z + a10.w * b0.w;
        s11 += a11.x * b1.x + a11.y * b1.y + a11.z * b1.z + a11.w * b1.w;
        s12 += a12.x * b2.x + a12.y * b2.y + a12.z * b2.z + a12.w * b2.w;
        s13 += a13.x * b3.x + a13.y * b3.y + a13.z * b3.z + a13.w * b3.w;
    }
    for (; i < end; i += stride) {
        float4 bv  = __ldg(B4 + i);
        float4 av0 = __ldcs(a0 + i);
        float4 av1 = __ldcs(a1 + i);
        s00 += av0.x * bv.x + av0.y * bv.y + av0.z * bv.z + av0.w * bv.w;
        s10 += av1.x * bv.x + av1.y * bv.y + av1.z * bv.z + av1.w * bv.w;
    }

    float sum0 = (s00 + s01) + (s02 + s03);
    float sum1 = (s10 + s11) + (s12 + s13);

    // Scalar tail when K is not divisible by 4 (handled by slice 0).
    if (part == 0) {
        const int base = K4 * 4;
        const float* ar0 = As + (size_t)row0 * (size_t)K;
        const float* ar1 = As + (size_t)row1 * (size_t)K;
        for (int j = base + threadIdx.x; j < K; j += stride) {
            const float bj = __ldg(Bs + j);
            sum0 += ar0[j] * bj;
            sum1 += ar1[j] * bj;
        }
    }

    // Warp-level reduction of both row sums.
    #pragma unroll
    for (int off = 16; off > 0; off >>= 1) {
        sum0 += __shfl_down_sync(0xffffffffu, sum0, off);
        sum1 += __shfl_down_sync(0xffffffffu, sum1, off);
    }

    __shared__ float w0[MV_THREADS / 32];
    __shared__ float w1[MV_THREADS / 32];
    const int lane = threadIdx.x & 31;
    const int warp = threadIdx.x >> 5;
    if (lane == 0) {
        w0[warp] = sum0;
        w1[warp] = sum1;
    }
    __syncthreads();

    if (warp == 0) {
        float v0 = (lane < MV_THREADS / 32) ? w0[lane] : 0.f;
        float v1 = (lane < MV_THREADS / 32) ? w1[lane] : 0.f;
        #pragma unroll
        for (int off = MV_THREADS / 64; off > 0; off >>= 1) {
            v0 += __shfl_down_sync(0xffffffffu, v0, off);
            v1 += __shfl_down_sync(0xffffffffu, v1, off);
        }
        if (lane == 0) {
            atomicAdd(C + row0, v0);
            if (row1 != row0) atomicAdd(C + row1, v1);
        }
    }
}

torch::Tensor matvec_cuda(torch::Tensor A, torch::Tensor B) {
    TORCH_CHECK(A.is_cuda() && B.is_cuda(), "A and B must be CUDA tensors");
    TORCH_CHECK(A.scalar_type() == at::kFloat && B.scalar_type() == at::kFloat,
                "A and B must be float32");
    TORCH_CHECK(A.dim() == 2, "A must be 2-D");
    TORCH_CHECK(B.numel() == A.size(1), "B must have A.size(1) elements");

    const c10::cuda::CUDAGuard device_guard(A.device());

    auto Ac = A.contiguous();
    auto Bc = B.contiguous();

    const int64_t M = Ac.size(0);
    const int64_t K = Ac.size(1);

    auto C = torch::zeros({M, 1}, Ac.options());
    if (M == 0 || K == 0) return C;

    // The vectorized path requires 16-byte alignment (true for fresh
    // allocations); fall back to cuBLAS for exotic views.
    if ((reinterpret_cast<uintptr_t>(Ac.data_ptr<float>()) & 0xF) != 0 ||
        (reinterpret_cast<uintptr_t>(Bc.data_ptr<float>()) & 0xF) != 0) {
        return torch::matmul(A, B);
    }

    const int K4 = (int)(K >> 2);
    const int row_blocks = (int)((M + 1) >> 1);

    // Choose a power-of-two split-K factor so that the grid has enough
    // blocks to keep every SM busy (and the slices stay balanced).
    const int sm_count =
        at::cuda::getCurrentDeviceProperties()->multiProcessorCount;
    const int64_t target = (int64_t)sm_count * 64;
    int split = 1;
    while (split < 32 && (int64_t)split * row_blocks < target) split <<= 1;

    int chunk = 0;
    if (K4 > 0) {
        const int unit = MV_THREADS * MV_UNROLL;
        chunk = (K4 + split - 1) / split;
        chunk = ((chunk + unit - 1) / unit) * unit;  // keep slices balanced
        split = (K4 + chunk - 1) / chunk;
    } else {
        split = 1;
        chunk = 0;
    }

    dim3 grid((unsigned)row_blocks, (unsigned)split);
    dim3 block(MV_THREADS);

    auto stream = at::cuda::getCurrentCUDAStream();
    matvec2row_kernel<<<grid, block, 0, stream>>>(
        reinterpret_cast<const float4*>(Ac.data_ptr<float>()),
        reinterpret_cast<const float4*>(Bc.data_ptr<float>()),
        Ac.data_ptr<float>(),
        Bc.data_ptr<float>(),
        C.data_ptr<float>(),
        K4, (int)K, chunk, (int)M);

    return C;
}
"""

_matvec_cpp_src = "torch::Tensor matvec_cuda(torch::Tensor A, torch::Tensor B);"

_matvec_ext = load_inline(
    name="matvec_splitk_ext_v2",
    cpp_sources=_matvec_cpp_src,
    cuda_sources=_matvec_cuda_src,
    functions=["matvec_cuda"],
    verbose=False,
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
)


class ModelNew(nn.Module):
    """
    Matrix-vector multiplication (C = A * B) accelerated with a custom
    split-K CUDA kernel: two rows per block, streaming float4 loads for A
    (__ldcs), cached float4 loads for B, and SM-count-adaptive split-K.
    """
    def __init__(self):
        super(ModelNew, self).__init__()
        self._op = _matvec_ext

    def forward(self, A: torch.Tensor, B: torch.Tensor) -> torch.Tensor:
        if (A.is_cuda and B.is_cuda and A.dim() == 2
                and A.dtype == torch.float32 and B.dtype == torch.float32):
            return self._op.matvec_cuda(A, B)
        return torch.matmul(A, B)
```

Write an improved complete ModelNew: fix any error, and if the solution is already correct, make it faster. Output the new code in one ```python codeblock. Just the model code, no other text, and NO testing code.


Precision rule: the timed forward must compute in FP32 (TF32 tensor-core math is allowed, as in the PyTorch reference). Do not cast inputs, weights or intermediate results to float16 or bfloat16 and do not call half-precision kernels in forward().
