scikit-learn
diff --git a/‎azure-pipelines.yml
+1 b/‎azure-pipelines.yml
+1
diff --git a/‎doc/computing/parallelism.rst
+8 b/‎doc/computing/parallelism.rst
+8
diff --git a/‎doc/developers/develop.rst
+16 b/‎doc/developers/develop.rst
+16
diff --git a/‎sklearn/conftest.py
+12 b/‎sklearn/conftest.py
+12
diff --git a/‎sklearn/feature_selection/tests/test_mutual_info.py
+10-6 b/‎sklearn/feature_selection/tests/test_mutual_info.py
+10-6
diff --git a/‎sklearn/utils/_testing.py
+75-1 b/‎sklearn/utils/_testing.py
+75-1
diff --git a/‎sklearn/utils/tests/test_testing.py
+19 b/‎sklearn/utils/tests/test_testing.py
+19
@@ -204,6 +204,7 @@ jobs:
         MATPLOTLIB_VERSION: 'min'
         THREADPOOLCTL_VERSION: '2.2.0'
         SKLEARN_ENABLE_DEBUG_CYTHON_DIRECTIVES: '1'
+        SKLEARN_RUN_FLOAT32_TESTS: '1'
         SKLEARN_TESTS_GLOBAL_RANDOM_SEED: '2'  # non-default seed
       # Linux environment to test the latest available dependencies.
       # It runs tests requiring lightgbm, pandas and PyAMG.
 
@@ -263,6 +263,14 @@ When this environment variable is set to a non zero value, the tests that need
 network access are skipped. When this environment variable is not set then
 network tests are skipped.
 
+`SKLEARN_RUN_FLOAT32_TESTS`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+When this environment variable is set to '1', the tests using the
+`global_dtype` fixture are also run on float32 data.
+When this environment variable is not set, the tests are only run on
+float64 data.
+
 `SKLEARN_ENABLE_DEBUG_CYTHON_DIRECTIVES`
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
 
@@ -774,3 +774,19 @@ The reason for this setup is reproducibility:
 when an estimator is ``fit`` twice to the same data,
 it should produce an identical model both times,
 hence the validation in ``fit``, not ``__init__``.
+
+Numerical assertions in tests
+-----------------------------
+
+When asserting the quasi-equality of arrays of continuous values,
+do use :func:`sklearn.utils._testing.assert_allclose`.
+
+The relative tolerance is automatically inferred from the provided arrays
+dtypes (for float32 and float64 dtypes in particular) but you can override
+via ``rtol``.
+
+When comparing arrays of zero-elements, please do provide a non-zero value for
+the absolute tolerance via ``atol``.
+
+For more information, please refer to the docstring of
+:func:`sklearn.utils._testing.assert_allclose`.
@@ -4,6 +4,7 @@
 import sys
 
 import pytest
+import numpy as np
 from threadpoolctl import threadpool_limits
 from _pytest.doctest import DoctestItem
 
@@ -41,6 +42,17 @@
     "fetch_rcv1_fxt": fetch_rcv1,
 }
 
+_SKIP32_MARK = pytest.mark.skipif(
+    environ.get("SKLEARN_RUN_FLOAT32_TESTS", "0") != "1",
+    reason="Set SKLEARN_RUN_FLOAT32_TESTS=1 to run float32 dtype tests",
+)
+
+
+# Global fixtures
+@pytest.fixture(params=[pytest.param(np.float32, marks=_SKIP32_MARK), np.float64])
+def global_dtype(request):
+    yield request.param
+
 
 def _fetch_fixture(f):
     """Fetch dataset (download if missing and requested by environment)."""
 
@@ -3,7 +3,11 @@
 from scipy.sparse import csr_matrix
 
 from sklearn.utils import check_random_state
-from sklearn.utils._testing import assert_array_equal, assert_almost_equal
+from sklearn.utils._testing import (
+    assert_array_equal,
+    assert_almost_equal,
+    assert_allclose,
+)
 from sklearn.feature_selection._mutual_info import _compute_mi
 from sklearn.feature_selection import mutual_info_regression, mutual_info_classif
 
@@ -21,7 +25,7 @@ def test_compute_mi_dd():
     assert_almost_equal(_compute_mi(x, y, True, True), I_xy)
 
 
-def test_compute_mi_cc():
+def test_compute_mi_cc(global_dtype):
     # For two continuous variables a good approach is to test on bivariate
     # normal distribution, where mutual information is known.
 
@@ -43,15 +47,15 @@ def test_compute_mi_cc():
     I_theory = np.log(sigma_1) + np.log(sigma_2) - 0.5 * np.log(np.linalg.det(cov))
 
     rng = check_random_state(0)
-    Z = rng.multivariate_normal(mean, cov, size=1000)
+    Z = rng.multivariate_normal(mean, cov, size=1000).astype(global_dtype, copy=False)
 
     x, y = Z[:, 0], Z[:, 1]
 
-    # Theory and computed values won't be very close, assert that the
-    # first figures after decimal point match.
+    # Theory and computed values won't be very close
+    # We here check with a large relative tolerance
     for n_neighbors in [3, 5, 7]:
         I_computed = _compute_mi(x, y, False, False, n_neighbors)
-        assert_almost_equal(I_computed, I_theory, 1)
+        assert_allclose(I_computed, I_theory, rtol=1e-1)
 
 
 def test_compute_mi_cd():
 
@@ -38,7 +38,7 @@
 except NameError:
     WindowsError = None
 
-from numpy.testing import assert_allclose
+from numpy.testing import assert_allclose as np_assert_allclose
 from numpy.testing import assert_almost_equal
 from numpy.testing import assert_approx_equal
 from numpy.testing import assert_array_equal
@@ -387,6 +387,80 @@ def assert_raise_message(exceptions, message, function, *args, **kwargs):
         raise AssertionError("%s not raised by %s" % (names, function.__name__))
 
 
+def assert_allclose(
+    actual, desired, rtol=None, atol=0.0, equal_nan=True, err_msg="", verbose=True
+):
+    """dtype-aware variant of numpy.testing.assert_allclose
+
+    This variant introspects the least precise floating point dtype
+    in the input argument and automatically sets the relative tolerance
+    parameter to 1e-4 float32 and use 1e-7 otherwise (typically float64
+    in scikit-learn).
+
+    `atol` is always left to 0. by default. It should be adjusted manually
+    to an assertion-specific value in case there are null values expected
+    in `desired`.
+
+    The aggregate tolerance is `atol + rtol * abs(desired)`.
+
+    Parameters
+    ----------
+    actual : array_like
+        Array obtained.
+    desired : array_like
+        Array desired.
+    rtol : float, optional, default=None
+        Relative tolerance.
+        If None, it is set based on the provided arrays' dtypes.
+    atol : float, optional, default=0.
+        Absolute tolerance.
+        If None, it is set based on the provided arrays' dtypes.
+    equal_nan : bool, optional, default=True
+        If True, NaNs will compare equal.
+    err_msg : str, optional, default=''
+        The error message to be printed in case of failure.
+    verbose : bool, optional, default=True
+        If True, the conflicting values are appended to the error message.
+
+    Raises
+    ------
+    AssertionError
+        If actual and desired are not equal up to specified precision.
+
+    See Also
+    --------
+    numpy.testing.assert_allclose
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from sklearn.utils._testing import assert_allclose
+    >>> x = [1e-5, 1e-3, 1e-1]
+    >>> y = np.arccos(np.cos(x))
+    >>> assert_allclose(x, y, rtol=1e-5, atol=0)
+    >>> a = np.full(shape=10, fill_value=1e-5, dtype=np.float32)
+    >>> assert_allclose(a, 1e-5)
+    """
+    dtypes = []
+
+    actual, desired = np.asanyarray(actual), np.asanyarray(desired)
+    dtypes = [actual.dtype, desired.dtype]
+
+    if rtol is None:
+        rtols = [1e-4 if dtype == np.float32 else 1e-7 for dtype in dtypes]
+        rtol = max(rtols)
+
+    np_assert_allclose(
+        actual,
+        desired,
+        rtol=rtol,
+        atol=atol,
+        equal_nan=equal_nan,
+        err_msg=err_msg,
+        verbose=verbose,
+    )
+
+
 def assert_allclose_dense_sparse(x, y, rtol=1e-07, atol=1e-9, err_msg=""):
     """Assert allclose for sparse and dense data.
 
 
@@ -28,6 +28,7 @@
     _delete_folder,
     _convert_container,
     raises,
+    assert_allclose,
 )
 
 from sklearn.tree import DecisionTreeClassifier
@@ -854,3 +855,21 @@ def test_raises():
     with pytest.raises(AssertionError):
         with raises((TypeError, ValueError)):
             pass
+
+
+def test_float32_aware_assert_allclose():
+    # The relative tolerance for float32 inputs is 1e-4
+    assert_allclose(np.array([1.0 + 2e-5], dtype=np.float32), 1.0)
+    with pytest.raises(AssertionError):
+        assert_allclose(np.array([1.0 + 2e-4], dtype=np.float32), 1.0)
+
+    # The relative tolerance for other inputs is left to 1e-7 as in
+    # the original numpy version.
+    assert_allclose(np.array([1.0 + 2e-8], dtype=np.float64), 1.0)
+    with pytest.raises(AssertionError):
+        assert_allclose(np.array([1.0 + 2e-7], dtype=np.float64), 1.0)
+
+    # atol is left to 0.0 by default, even for float32
+    with pytest.raises(AssertionError):
+        assert_allclose(np.array([1e-5], dtype=np.float32), 0.0)
+    assert_allclose(np.array([1e-5], dtype=np.float32), 0.0, atol=2e-5)