diff --git a/tests/conftest.py b/tests/conftest.py
index 681274b..9911468 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -1,5 +1,6 @@
 from __future__ import annotations
 
+import logging
 from typing import TYPE_CHECKING
 
 import jax.numpy
@@ -8,9 +9,18 @@
 
 import array_api_strict
 
+import glass._array_api_utils
+
 if TYPE_CHECKING:
     from types import ModuleType
 
+    from glass._types import UnifiedGenerator
+
+
+# Change jax logger to only log ERROR or worse
+logging.getLogger("jax").setLevel(logging.ERROR)
+
+
 xp_available_backends: dict[str, ModuleType] = {
     "array_api_strict": array_api_strict,
     "numpy": numpy,
@@ -26,3 +36,15 @@ def xp(request: pytest.FixtureRequest) -> ModuleType:
     Access array library functions using `xp.` in tests.
     """
     return request.param  # type: ignore[no-any-return]
+
+
+@pytest.fixture(scope="session")
+def urng(xp: ModuleType) -> UnifiedGenerator:
+    """
+    Fixture for a unified RNG interface.
+
+    Access the relevant RNG using `urng.` in tests.
+
+    Must be used with the `xp` fixture. Use `rng` for non array API tests.
+    """
+    return glass._array_api_utils.rng_dispatcher(xp=xp)  # noqa: SLF001
diff --git a/tests/test_algorithm.py b/tests/test_algorithm.py
index 52b5762..6ad8225 100644
--- a/tests/test_algorithm.py
+++ b/tests/test_algorithm.py
@@ -4,6 +4,7 @@
 
 from typing import TYPE_CHECKING
 
+import numpy as np
 import pytest
 
 import glass.algorithm
@@ -13,6 +14,8 @@
 
     from pytest_benchmark.fixture import BenchmarkFixture
 
+    from glass._types import UnifiedGenerator
+
 
 def test_nnls(xp: ModuleType, benchmark: BenchmarkFixture) -> None:
     """
@@ -31,3 +34,82 @@ def test_nnls(xp: ModuleType, benchmark: BenchmarkFixture) -> None:
     y = a @ b
     res = benchmark(glass.algorithm.nnls, a, y)
     assert xp.linalg.vector_norm((a @ res) - y) < 1e-7
+
+
+@pytest.mark.parametrize("rtol", [None, 1.0])
+def test_cov_clip(
+    xp: ModuleType,
+    urng: UnifiedGenerator,
+    benchmark: BenchmarkFixture,
+    rtol: float | None,
+) -> None:
+    """
+    Benchmark test for glass.algorithm.cov_clip.
+
+    Parameterize over rtol to ensure the most coverage possible.
+    """
+    # prepare a random matrix
+    m = urng.random((4, 4))
+
+    # symmetric matrix
+    a = (m + m.T) / 2
+
+    # fix by clipping negative eigenvalues
+    cov = benchmark(glass.algorithm.cov_clip, a, rtol=rtol)
+
+    # make sure all eigenvalues are positive
+    assert xp.all(xp.linalg.eigvalsh(cov) >= 0)
+
+    if rtol is not None:
+        h = xp.max(xp.linalg.eigvalsh(a))
+        np.testing.assert_allclose(xp.linalg.eigvalsh(cov), h, rtol=1e-6)
+
+
+@pytest.mark.parametrize("tol", [None, 0.0001])
+def test_nearcorr(
+    xp: ModuleType,
+    benchmark: BenchmarkFixture,
+    tol: float | None,
+) -> None:
+    """
+    Benchmark test for glass.algorithm.nearcorr.
+
+    Parameterize over tol to ensure the most coverage possible.
+    """
+    # from Higham (2002)
+    a = xp.asarray(
+        [
+            [1.0, 1.0, 0.0],
+            [1.0, 1.0, 1.0],
+            [0.0, 1.0, 1.0],
+        ],
+    )
+    b = xp.asarray(
+        [
+            [1.0000, 0.7607, 0.1573],
+            [0.7607, 1.0000, 0.7607],
+            [0.1573, 0.7607, 1.0000],
+        ],
+    )
+
+    x = benchmark(glass.algorithm.nearcorr, a, tol=tol)
+    np.testing.assert_allclose(x, b, atol=0.0001)
+
+
+def test_cov_nearest(
+    xp: ModuleType,
+    urng: UnifiedGenerator,
+    benchmark: BenchmarkFixture,
+) -> None:
+    """Benchmark test for glass.algorithm.cov_nearest."""
+    # prepare a random matrix
+    m = urng.random((4, 4))
+
+    # symmetric matrix
+    a = xp.eye(4) + (m + m.T) / 2
+
+    # compute covariance
+    cov = benchmark(glass.algorithm.cov_nearest, a)
+
+    # make sure all eigenvalues are positive
+    assert xp.all(xp.linalg.eigvalsh(cov) >= 0)