Description: On mips, 1**np.nan and np.nan**0 may be NaN not 1

Done this way not a plain xfail to allow only this difference,
not clearly wrong answers

(The same hardware's "invalid value encountered" warnings,
probably from sNaN/qNaN being reversed, are ignored elsewhere:
d/rules and xfail_tests_nonintel_io.patch)

https://en.wikipedia.org/wiki/NaN#Encoding

Author: Rebecca N. Palmer <rebecca_palmer@zoho.com>
Forwarded: no

--- a/pandas/tests/arrays/floating/test_arithmetic.py
+++ b/pandas/tests/arrays/floating/test_arithmetic.py
@@ -1,4 +1,5 @@
 import operator
+import platform
 
 import numpy as np
 import pytest
@@ -69,6 +70,11 @@ def test_pow_scalar(dtype):
         np.array([np.nan, np.nan, 1, np.nan, np.nan], dtype=dtype.numpy_dtype),
         mask=a._mask,
     )
+    if 'mips' in platform.uname()[4] and np.isnan(result[2]):
+        expected = FloatingArray(
+            np.array([np.nan, np.nan, np.nan, np.nan, np.nan], dtype=dtype.numpy_dtype),
+            mask=a._mask,
+        )
     tm.assert_extension_array_equal(result, expected)
 
     # reversed
@@ -80,6 +86,12 @@ def test_pow_scalar(dtype):
 
     result = 1**a
     expected = pd.array([1, 1, 1, 1], dtype=dtype)
+    if 'mips' in platform.uname()[4] and np.isnan(result[2]):
+        expected = FloatingArray(
+            np.array([1, 1, np.nan, 1], dtype=dtype.numpy_dtype),
+            mask=expected._mask,
+        )
+
     tm.assert_extension_array_equal(result, expected)
 
     result = pd.NA**a
@@ -90,6 +102,11 @@ def test_pow_scalar(dtype):
     expected = FloatingArray(
         np.array([1, np.nan, np.nan, np.nan], dtype=dtype.numpy_dtype), mask=a._mask
     )
+    if 'mips' in platform.uname()[4] and np.isnan(result[0]):
+        expected = FloatingArray(
+            np.array([np.nan, np.nan, np.nan, np.nan], dtype=dtype.numpy_dtype),
+            mask=a._mask,
+        )
     tm.assert_extension_array_equal(result, expected)
 
 
@@ -98,6 +115,8 @@ def test_pow_array(dtype):
     b = pd.array([0, 1, None, 0, 1, None, 0, 1, None], dtype=dtype)
     result = a**b
     expected = pd.array([1, 0, None, 1, 1, 1, 1, None, None], dtype=dtype)
+    if 'mips' in platform.uname()[4] and np.isnan(result[5]):
+        expected = FloatingArray(np.array([1, 0, np.nan, 1, 1, np.nan, np.nan, np.nan, np.nan], dtype=dtype.numpy_dtype), mask=expected._mask)
     tm.assert_extension_array_equal(result, expected)
 
 
--- a/pandas/tests/arrays/sparse/test_arithmetics.py
+++ b/pandas/tests/arrays/sparse/test_arithmetics.py
@@ -1,4 +1,5 @@
 import operator
+import platform
 
 import numpy as np
 import pytest
@@ -44,6 +45,8 @@ class TestSparseArrayArithmetics:
                 result = op(a, b_dense).to_dense()
             else:
                 result = op(a, b).to_dense()
+        if 'mips' in platform.uname()[4] and op==operator.pow and a[1]==1 and np.isnan(b if np.isscalar(b) else b[1]) and np.isnan(expected[1]) and result[1]==1:
+            expected[1]=1
 
         self._assert(result, expected)