code: def differenceFunctionTorch(
      xs: torch.Tensor, N, tau_max
  ) -> torch.Tensor:
      """pytorch backend batch-wise differenceFunction
      has 1e-4 level error with input shape of (32, 22050*1.5)
      Args:
          xs:
          N:
          tau_max:
  
      Returns:
  
      """
      xs = xs.double()
      w = xs.shape[-1]
      tau_max = min(tau_max, w)
      zeros = torch.zeros((xs.shape[0], 1))
      x_cumsum = torch.cat(
          (
              torch.zeros((xs.shape[0], 1), device=xs.device),
              (xs * xs).cumsum(dim=-1, dtype=torch.double),
          ),
          dim=-1,
      )  # B x w
      size = w + tau_max
      p2 = (size // 32).bit_length()
      nice_numbers = (16, 18, 20, 24, 25, 27, 30, 32)
      size_pad = min(
          x * 2**p2 for x in nice_numbers if x * 2**p2 >= size
      )
  
      fcs = torch.fft.rfft(xs, n=size_pad, dim=-1)
      convs = torch.fft.irfft(fcs * fcs.conj())[:, :tau_max]
      y1 = torch.flip(x_cumsum[:, w - tau_max + 1 : w + 1], dims=[-1])
      y = (
          y1
          + x_cumsum[:, w].unsqueeze(-1)
          - x_cumsum[:, :tau_max]
          - 2 * convs
      )
      return y
  
imports: import numpy
  import torch
  import torch.nn.functional
label_desc: Use image node_id 4 for calling a global function with example usage: differenceFunctionTorch(xs, N, tau_max) and returns: y