feat: LPC CUDA kernel

[yoyolicoris]

import torch
import torchlpc
from torchlpc.core import lpc_cuda
from numba import cuda

from timeit import timeit
from time import sleep

batch_size = 64
samples = 2**14
order = 2

lpc_A = torch.zeros(batch_size, samples, order).cuda() + 0j
lpc_zi = torch.randn(batch_size, order).cuda() + 0j
lpc_x = torch.randn(batch_size, samples).cuda() + 0j

lpc_cuda(lpc_x, lpc_A, lpc_zi)
t_numba_lpc = timeit(
    "lpc_cuda(lpc_x, lpc_A, lpc_zi)",
    globals=globals(),
    number=100,
)
print(f"Numba LPC time: {t_numba_lpc:.4f} seconds")

sleep(1)  # Ensure the GPU is ready for the next operation

t_torch_lpc = timeit(
    "torch.ops.torchlpc.lpc(lpc_x, lpc_A, lpc_zi)",
    globals=globals(),
    number=100,
)
print(f"Torch LPC time: {t_torch_lpc:.4f} seconds")
print(f"Torch LPC is {t_numba_lpc / t_torch_lpc:.2f}x faster than Numba")

The results on a 5060 ti GPU with linux machine:

Numba LPC time: 0.8524 seconds
Torch LPC time: 0.0152 seconds
Torch LPC is 56.07x faster than Numba

Don't know why, but the .cu version is significantly faster.

[Copilot]

Pull Request Overview

This PR introduces a new LPC CUDA kernel implementation and updates related recurrence functions to leverage both CUDA and CPU runners. Key changes include refactoring the recurrence functions to use lambdas for kernel dispatching, adding CUDA kernel implementations in C++ under torchlpc/csrc/cuda/lpc.cu, and extending test coverage to include additional sample sizes and device options.

Reviewed Changes

Copilot reviewed 4 out of 4 changed files in this pull request and generated 2 comments.

File	Description
torchlpc/recurrence.py	Updated recurrence functions to choose between CUDA and CPU runners via lambdas.
torchlpc/csrc/cuda/lpc.cu	Added new CUDA kernels for LPC computation including support for complex types.
torchlpc/core.py	Adjusted LPC forward logic to conditionally dispatch based on EXTENSION_LOADED.
tests/test_extension.py	Expanded test parameters for sample sizes and devices (CPU/CUDA) for LPC equivalence.