code: def test_normalize_integer():
      a = Integer(2, 30, transform="normalize")
      for i in range(50):
          check_limits(a.rvs(random_state=i), 2, 30)
      assert_array_equal(a.transformed_bounds, (0, 1))
      rng = np.random.RandomState(0)
      X = rng.randint(2, 31, dtype=np.int64)
      # Check transformed values are in [0, 1]
      assert np.all(a.transform(X) <= np.ones_like(X))
      assert np.all(np.zeros_like(X) <= a.transform(X))
  
      # Check inverse transform
      X_orig = a.inverse_transform(a.transform(X))
      assert isinstance(X_orig, np.int64)
      assert_array_equal(X_orig, X)
  
      a = Integer(2, 30, transform="normalize", dtype=int)
      X = rng.randint(2, 31, dtype=int)
      # Check inverse transform
      X_orig = a.inverse_transform(a.transform(X))
      assert isinstance(X_orig, int)
  
      a = Integer(2, 30, transform="normalize", dtype="int")
      X = rng.randint(2, 31, dtype=int)
      # Check inverse transform
      X_orig = a.inverse_transform(a.transform(X))
      assert isinstance(X_orig, int)
  
      a = Integer(
          2,
          30,
          prior="log-uniform",
          base=2,
          transform="normalize",
          dtype=int,
      )
      for i in range(50):
          check_limits(a.rvs(random_state=i), 2, 30)
      assert_array_equal(a.transformed_bounds, (0, 1))
  
      X = rng.randint(2, 31, dtype=int)
      # Check transformed values are in [0, 1]
      assert np.all(a.transform(X) <= np.ones_like(X))
      assert np.all(np.zeros_like(X) <= a.transform(X))
  
      # Check inverse transform
      X_orig = a.inverse_transform(a.transform(X))
      assert isinstance(X_orig, int)
      assert_array_equal(X_orig, X)
  
imports: import pytest
  import numbers
  import numpy
  import os
  import yaml
  from tempfile import NamedTemporaryFile
  from numpy.testing import assert_array_almost_equal
  from numpy.testing import assert_array_equal
  from numpy.testing import assert_equal
  from numpy.testing import assert_raises_regex
  from skopt import Optimizer
  from skopt.space import Space
  from skopt.space import Real
  from skopt.space import Integer
  from skopt.space import Categorical
  from skopt.space import check_dimension
  from skopt.utils import normalize_dimensions
label_desc: Use image node_id 20 for calling a global function with example usage: test_normalize_integer() without return types