diff --git a/array_api_tests/__init__.py b/array_api_tests/__init__.py
index b4c0e8ba..27b6fe1e 100644
--- a/array_api_tests/__init__.py
+++ b/array_api_tests/__init__.py
@@ -1,14 +1,12 @@
 from functools import wraps
 
 from hypothesis import strategies as st
-from hypothesis.extra.array_api import make_strategies_namespace
+from hypothesis.extra import array_api
 
 from ._array_module import mod as _xp
 
 __all__ = ["xps"]
 
-xps = make_strategies_namespace(_xp)
-
 
 # We monkey patch floats() to always disable subnormals as they are out-of-scope
 
@@ -23,5 +21,29 @@ def floats(*a, **kw):
 
 st.floats = floats
 
+
+# We do the same with xps.from_dtype() - this is not strictly necessary, as
+# the underlying floats() will never generate subnormals. We only do this
+# because internal logic in xps.from_dtype() assumes xp.finfo() has its
+# attributes as scalar floats, which is expected behaviour but disrupts many
+# unrelated tests.
+try:
+    __from_dtype = array_api._from_dtype
+
+    @wraps(__from_dtype)
+    def _from_dtype(*a, **kw):
+        kw["allow_subnormal"] = False
+        return __from_dtype(*a, **kw)
+
+    array_api._from_dtype = _from_dtype
+except AttributeError:
+    # Ignore monkey patching if Hypothesis changes the private API
+    pass
+
+
+xps = array_api.make_strategies_namespace(_xp)
+
+
 from . import _version
-__version__ = _version.get_versions()['version']
+
+__version__ = _version.get_versions()["version"]
diff --git a/array_api_tests/dtype_helpers.py b/array_api_tests/dtype_helpers.py
index 29d87216..c8e76a90 100644
--- a/array_api_tests/dtype_helpers.py
+++ b/array_api_tests/dtype_helpers.py
@@ -1,5 +1,6 @@
+from collections.abc import Mapping
 from functools import lru_cache
-from typing import NamedTuple, Tuple, Union
+from typing import Any, NamedTuple, Sequence, Tuple, Union
 from warnings import warn
 
 from . import _array_module as xp
@@ -36,6 +37,49 @@
 ]
 
 
+class EqualityMapping(Mapping):
+    """
+    Mapping that uses equality for indexing
+
+    Typical mappings (e.g. the built-in dict) use hashing for indexing. This
+    isn't ideal for the Array API, as no __hash__() method is specified for
+    dtype objects - but __eq__() is!
+
+    See https://data-apis.org/array-api/latest/API_specification/data_types.html#data-type-objects
+    """
+
+    def __init__(self, key_value_pairs: Sequence[Tuple[Any, Any]]):
+        keys = [k for k, _ in key_value_pairs]
+        for i, key in enumerate(keys):
+            if not (key == key):  # specifically checking __eq__, not __neq__
+                raise ValueError("Key {key!r} does not have equality with itself")
+            other_keys = keys[:]
+            other_keys.pop(i)
+            for other_key in other_keys:
+                if key == other_key:
+                    raise ValueError("Key {key!r} has equality with key {other_key!r}")
+        self._key_value_pairs = key_value_pairs
+
+    def __getitem__(self, key):
+        for k, v in self._key_value_pairs:
+            if key == k:
+                return v
+        else:
+            raise KeyError(f"{key!r} not found")
+
+    def __iter__(self):
+        return (k for k, _ in self._key_value_pairs)
+
+    def __len__(self):
+        return len(self._key_value_pairs)
+
+    def __str__(self):
+        return "{" + ", ".join(f"{k!r}: {v!r}" for k, v in self._key_value_pairs) + "}"
+
+    def __repr__(self):
+        return f"EqualityMapping({self})"
+
+
 _uint_names = ("uint8", "uint16", "uint32", "uint64")
 _int_names = ("int8", "int16", "int32", "int64")
 _float_names = ("float32", "float64")
@@ -51,14 +95,16 @@
 bool_and_all_int_dtypes = (xp.bool,) + all_int_dtypes
 
 
-dtype_to_name = {getattr(xp, name): name for name in _dtype_names}
+dtype_to_name = EqualityMapping([(getattr(xp, name), name) for name in _dtype_names])
 
 
-dtype_to_scalars = {
-    xp.bool: [bool],
-    **{d: [int] for d in all_int_dtypes},
-    **{d: [int, float] for d in float_dtypes},
-}
+dtype_to_scalars = EqualityMapping(
+    [
+        (xp.bool, [bool]),
+        *[(d, [int]) for d in all_int_dtypes],
+        *[(d, [int, float]) for d in float_dtypes],
+    ]
+)
 
 
 def is_int_dtype(dtype):
@@ -90,31 +136,32 @@ class MinMax(NamedTuple):
     max: Union[int, float]
 
 
-dtype_ranges = {
-    xp.int8: MinMax(-128, +127),
-    xp.int16: MinMax(-32_768, +32_767),
-    xp.int32: MinMax(-2_147_483_648, +2_147_483_647),
-    xp.int64: MinMax(-9_223_372_036_854_775_808, +9_223_372_036_854_775_807),
-    xp.uint8: MinMax(0, +255),
-    xp.uint16: MinMax(0, +65_535),
-    xp.uint32: MinMax(0, +4_294_967_295),
-    xp.uint64: MinMax(0, +18_446_744_073_709_551_615),
-    xp.float32: MinMax(-3.4028234663852886e+38, 3.4028234663852886e+38),
-    xp.float64: MinMax(-1.7976931348623157e+308, 1.7976931348623157e+308),
-}
+dtype_ranges = EqualityMapping(
+    [
+        (xp.int8, MinMax(-128, +127)),
+        (xp.int16, MinMax(-32_768, +32_767)),
+        (xp.int32, MinMax(-2_147_483_648, +2_147_483_647)),
+        (xp.int64, MinMax(-9_223_372_036_854_775_808, +9_223_372_036_854_775_807)),
+        (xp.uint8, MinMax(0, +255)),
+        (xp.uint16, MinMax(0, +65_535)),
+        (xp.uint32, MinMax(0, +4_294_967_295)),
+        (xp.uint64, MinMax(0, +18_446_744_073_709_551_615)),
+        (xp.float32, MinMax(-3.4028234663852886e38, 3.4028234663852886e38)),
+        (xp.float64, MinMax(-1.7976931348623157e308, 1.7976931348623157e308)),
+    ]
+)
 
-dtype_nbits = {
-    **{d: 8 for d in [xp.int8, xp.uint8]},
-    **{d: 16 for d in [xp.int16, xp.uint16]},
-    **{d: 32 for d in [xp.int32, xp.uint32, xp.float32]},
-    **{d: 64 for d in [xp.int64, xp.uint64, xp.float64]},
-}
+dtype_nbits = EqualityMapping(
+    [(d, 8) for d in [xp.int8, xp.uint8]]
+    + [(d, 16) for d in [xp.int16, xp.uint16]]
+    + [(d, 32) for d in [xp.int32, xp.uint32, xp.float32]]
+    + [(d, 64) for d in [xp.int64, xp.uint64, xp.float64]]
+)
 
 
-dtype_signed = {
-    **{d: True for d in int_dtypes},
-    **{d: False for d in uint_dtypes},
-}
+dtype_signed = EqualityMapping(
+    [(d, True) for d in int_dtypes] + [(d, False) for d in uint_dtypes]
+)
 
 
 if isinstance(xp.asarray, _UndefinedStub):
@@ -137,52 +184,51 @@ class MinMax(NamedTuple):
     default_uint = xp.uint64
 
 
-_numeric_promotions = {
+_numeric_promotions = [
     # ints
-    (xp.int8, xp.int8): xp.int8,
-    (xp.int8, xp.int16): xp.int16,
-    (xp.int8, xp.int32): xp.int32,
-    (xp.int8, xp.int64): xp.int64,
-    (xp.int16, xp.int16): xp.int16,
-    (xp.int16, xp.int32): xp.int32,
-    (xp.int16, xp.int64): xp.int64,
-    (xp.int32, xp.int32): xp.int32,
-    (xp.int32, xp.int64): xp.int64,
-    (xp.int64, xp.int64): xp.int64,
+    ((xp.int8, xp.int8), xp.int8),
+    ((xp.int8, xp.int16), xp.int16),
+    ((xp.int8, xp.int32), xp.int32),
+    ((xp.int8, xp.int64), xp.int64),
+    ((xp.int16, xp.int16), xp.int16),
+    ((xp.int16, xp.int32), xp.int32),
+    ((xp.int16, xp.int64), xp.int64),
+    ((xp.int32, xp.int32), xp.int32),
+    ((xp.int32, xp.int64), xp.int64),
+    ((xp.int64, xp.int64), xp.int64),
     # uints
-    (xp.uint8, xp.uint8): xp.uint8,
-    (xp.uint8, xp.uint16): xp.uint16,
-    (xp.uint8, xp.uint32): xp.uint32,
-    (xp.uint8, xp.uint64): xp.uint64,
-    (xp.uint16, xp.uint16): xp.uint16,
-    (xp.uint16, xp.uint32): xp.uint32,
-    (xp.uint16, xp.uint64): xp.uint64,
-    (xp.uint32, xp.uint32): xp.uint32,
-    (xp.uint32, xp.uint64): xp.uint64,
-    (xp.uint64, xp.uint64): xp.uint64,
+    ((xp.uint8, xp.uint8), xp.uint8),
+    ((xp.uint8, xp.uint16), xp.uint16),
+    ((xp.uint8, xp.uint32), xp.uint32),
+    ((xp.uint8, xp.uint64), xp.uint64),
+    ((xp.uint16, xp.uint16), xp.uint16),
+    ((xp.uint16, xp.uint32), xp.uint32),
+    ((xp.uint16, xp.uint64), xp.uint64),
+    ((xp.uint32, xp.uint32), xp.uint32),
+    ((xp.uint32, xp.uint64), xp.uint64),
+    ((xp.uint64, xp.uint64), xp.uint64),
     # ints and uints (mixed sign)
-    (xp.int8, xp.uint8): xp.int16,
-    (xp.int8, xp.uint16): xp.int32,
-    (xp.int8, xp.uint32): xp.int64,
-    (xp.int16, xp.uint8): xp.int16,
-    (xp.int16, xp.uint16): xp.int32,
-    (xp.int16, xp.uint32): xp.int64,
-    (xp.int32, xp.uint8): xp.int32,
-    (xp.int32, xp.uint16): xp.int32,
-    (xp.int32, xp.uint32): xp.int64,
-    (xp.int64, xp.uint8): xp.int64,
-    (xp.int64, xp.uint16): xp.int64,
-    (xp.int64, xp.uint32): xp.int64,
+    ((xp.int8, xp.uint8), xp.int16),
+    ((xp.int8, xp.uint16), xp.int32),
+    ((xp.int8, xp.uint32), xp.int64),
+    ((xp.int16, xp.uint8), xp.int16),
+    ((xp.int16, xp.uint16), xp.int32),
+    ((xp.int16, xp.uint32), xp.int64),
+    ((xp.int32, xp.uint8), xp.int32),
+    ((xp.int32, xp.uint16), xp.int32),
+    ((xp.int32, xp.uint32), xp.int64),
+    ((xp.int64, xp.uint8), xp.int64),
+    ((xp.int64, xp.uint16), xp.int64),
+    ((xp.int64, xp.uint32), xp.int64),
     # floats
-    (xp.float32, xp.float32): xp.float32,
-    (xp.float32, xp.float64): xp.float64,
-    (xp.float64, xp.float64): xp.float64,
-}
-promotion_table = {
-    (xp.bool, xp.bool): xp.bool,
-    **_numeric_promotions,
-    **{(d2, d1): res for (d1, d2), res in _numeric_promotions.items()},
-}
+    ((xp.float32, xp.float32), xp.float32),
+    ((xp.float32, xp.float64), xp.float64),
+    ((xp.float64, xp.float64), xp.float64),
+]
+_numeric_promotions += [((d2, d1), res) for (d1, d2), res in _numeric_promotions]
+_promotion_table = list(set(_numeric_promotions))
+_promotion_table.insert(0, ((xp.bool, xp.bool), xp.bool))
+promotion_table = EqualityMapping(_promotion_table)
 
 
 def result_type(*dtypes: DataType):
diff --git a/array_api_tests/meta/test_equality_mapping.py b/array_api_tests/meta/test_equality_mapping.py
new file mode 100644
index 00000000..86fa7e14
--- /dev/null
+++ b/array_api_tests/meta/test_equality_mapping.py
@@ -0,0 +1,37 @@
+import pytest
+
+from ..dtype_helpers import EqualityMapping
+
+
+def test_raises_on_distinct_eq_key():
+    with pytest.raises(ValueError):
+        EqualityMapping([(float("nan"), "value")])
+
+
+def test_raises_on_indistinct_eq_keys():
+    class AlwaysEq:
+        def __init__(self, hash):
+            self._hash = hash
+
+        def __eq__(self, other):
+            return True
+
+        def __hash__(self):
+            return self._hash
+
+    with pytest.raises(ValueError):
+        EqualityMapping([(AlwaysEq(0), "value1"), (AlwaysEq(1), "value2")])
+
+
+def test_key_error():
+    mapping = EqualityMapping([("key", "value")])
+    with pytest.raises(KeyError):
+        mapping["nonexistent key"]
+
+
+def test_iter():
+    mapping = EqualityMapping([("key", "value")])
+    it = iter(mapping)
+    assert next(it) == "key"
+    with pytest.raises(StopIteration):
+        next(it)