code: def _gen_func_defs_pxd(
      outfile, x_funcs, no_x_funcs, max_num_inputs=4
  ):
      """
      Cython does not support template parameter packs, so to keep it
      from freaking out, we'll manually produce all the different template
      expansions we need to call in the cython wrappers.
      """
  
      contents = (
          "# This file was generated by stats/_boost/include/"
          "_gen_func_defs_pxd.py\n"
      )
      contents += (
          "# All modifications to this file will be overwritten.\n"
      )
      hdr = str(
          (pathlib.Path(__file__).parent / "func_defs.hpp").as_posix()
      )
      contents += f'cdef extern from "{hdr}" namespace "" nogil:\n'
  
      for ii in range(1, max_num_inputs + 1):
          template_args = ", ".join(
              f"T{jj} arg{jj}" for jj in range(1, ii + 1)
          )
          template_types = ", ".join(
              f"T{jj}" for jj in range(1, ii + 1)
          )
  
          # for all the different "overloads", we need to produce a
          # distinct Cython reference;
          # assumes that all number template types are the same,
          # i.e. RealType == T1 == T2 == etc
          for func in x_funcs:
              fname = f"boost_{func}"
              tmpl = f"Dist, RealType, {template_types}"
              contents += (
                  f'    RealType {fname}{ii} "{fname}" '
                  f"[{tmpl}](RealType x, {template_args})\n"
              )
          for func in no_x_funcs:
              fname = f"boost_{func}"
              tmpl = f"Dist, RealType, {template_types}"
              contents += (
                  f'    RealType {fname}{ii} "{fname}" '
                  f"[{tmpl}]({template_args})\n"
              )
  
      # patch for boost::math::beta_distibution to handle x = 0 when a < 1
      # and x = 1 when beta < 1
      contents += (
          '    RealType boost_pdf_beta2 "boost_pdf_beta" '
          "[Dist, RealType, T1, T2](RealType x, T1 a, T2 b)"
      )
  
      with open(outfile, "w") as fp:
          fp.write(contents)
  
label_desc: Use image node_id 1 for calling a global function with example usage: _gen_func_defs_pxd(outfile, x_funcs, no_x_funcs, max_num_inputs) without return types