prompt: We are currently solving the following issue within our repository. Here is the issue text:
  --- BEGIN ISSUE ---
  [Bug, Enhancement] array_equal returns False on identical arrays with NaN values
  * Conditions (you can just paste the output of `python -c 'import cupy; cupy.show_config()'`)
    - CuPy Version          : 8.0.0
    - OS/Platform : Pop OS
    - CUDA Version    : 10000
    - cuDNN Version         : 7605
    - NCCL Version    : 2604
  
  * Code to reproduce
  ```python
  import cupy as cp
  a = cp.array([0, 1, cp.nan])
  print(cp.array_equal(a, a))         # False
  ```
  This relates exactly with https://github.com/numpy/numpy/issues/9229
  This could be resolved by following the same procedure, resolved by https://github.com/numpy/numpy/pull/16128, which would essentially add an `equal_nan` kwarg to let user decide if NaN values should be considered equal or not, which is consistent with: https://github.com/cupy/cupy/blob/0dc6bbafb0cf75bb873531cbf69c6995a72c61a3/cupy/_logic/comparison.py#L60
  https://github.com/cupy/cupy/blob/0dc6bbafb0cf75bb873531cbf69c6995a72c61a3/cupy/_logic/comparison.py#L89
  
  * Error messages, stack traces, or logs
  `<null>`
  
  --- END ISSUE ---
  
  Below are some code segments, each from a relevant file. One or more of these files may contain bugs.
  --- BEGIN FILES ---
  Path: `cupy/_logic/comparison.py`
  Content:
  ```
  1 import numpy
  2 
  3 import cupy
  4 from cupy import core
  5 
  6 
  7 _is_close = core.create_ufunc(
  8     'cupy_is_close',
  9     ('eeee?->?', 'ffff?->?', 'dddd?->?'),
  10     '''
  11     bool equal_nan = in4;
  12     if (isfinite(in0) && isfinite(in1)) {
  13       out0 = fabs(in0 - in1) <= in3 + in2 * fabs(in1);
  14     } else if (equal_nan) {
  15       out0 = (in0 == in1) || (isnan(in0) && isnan(in1));
  16     } else {
  17       out0 = (in0 == in1);
  18     }
  19     '''
  20 )
  21 
  22 # Note that in cupy/core/include/cupy/complex.cuh, we already got isfinite and
  23 # isnan working for complex numbers, so just replace fabs above by abs (from
  24 # thrust) and we are ready to go
  25 _is_close_complex = core.create_ufunc(
  26     'cupy_is_close_complex',
  27     ('FFff?->?', 'DDdd?->?'),
  28     '''
  29     bool equal_nan = in4;
  30     if (isfinite(in0) && isfinite(in1)) {
  31       out0 = abs(in0 - in1) <= in3 + in2 * abs(in1);
  32     } else if (equal_nan) {
  33       out0 = (in0 == in1) || (isnan(in0) && isnan(in1));
  34     } else {
  35       out0 = (in0 == in1);
  36     }
  37     '''
  38 )
  39 
  40 
  41 def array_equal(a1, a2):
  42     """Returns ``True`` if two arrays are element-wise exactly equal.
  43 
  44     Args:
  45         a1 (cupy.ndarray): Input array to compare.
  46         a2 (cupy.ndarray): Input array to compare.
  47 
  48     Returns:
  49         cupy.ndarray: A boolean 0-dim array.
  50             If its value is ``True``, two arrays are element-wise equal.
  51 
  52     .. seealso:: :func:`numpy.array_equal`
  53 
  54     """
  55     if a1.shape != a2.shape:
  56         return cupy.array(False)
  57     return (a1 == a2).all()
  58 
  59 
  60 def allclose(a, b, rtol=1.e-5, atol=1.e-8, equal_nan=False):
  61     """Returns True if two arrays are element-wise equal within a tolerance.
  62 
  63     Two values in ``a`` and ``b`` are  considiered equal when the following
  64     equation is satisfied.
  65 
  66     .. math::
  67 
  68        |a - b| \\le \\mathrm{atol} + \\mathrm{rtol} |b|
  69 
  70     Args:
  71         a (cupy.ndarray): Input array to compare.
  72         b (cupy.ndarray): Input array to compare.
  73         rtol (float): The relative tolerance.
  74         atol (float): The absolute tolerance.
  75         equal_nan (bool): If ``True``, NaN's in ``a`` will be considered equal
  76             to NaN's in ``b``.
  77 
  78     Returns:
  79         cupy.ndarray: A boolean 0-dim array.
  80             If its value is ``True``, two arrays are element-wise equal within
  81             a tolerance.
  82 
  83     .. seealso:: :func:`numpy.allclose`
  84 
  85     """
  86     return isclose(a, b, rtol=rtol, atol=atol, equal_nan=equal_nan).all()
  87 
  88 
  89 def isclose(a, b, rtol=1.e-5, atol=1.e-8, equal_nan=False):
  90     """Returns a boolean array where two arrays are equal within a tolerance.
  91 
  92     Two values in ``a`` and ``b`` are  considiered equal when the following
  93     equation is satisfied.
  94 
  95     .. math::
  96 
  97        |a - b| \\le \\mathrm{atol} + \\mathrm{rtol} |b|
  98 
  99     Args:
  100         a (cupy.ndarray): Input array to compare.
  101         b (cupy.ndarray): Input array to compare.
  102         rtol (float): The relative tolerance.
  103         atol (float): The absolute tolerance.
  104         equal_nan (bool): If ``True``, NaN's in ``a`` will be considered equal
  105             to NaN's in ``b``.
  106 
  107     Returns:
  108         cupy.ndarray: A boolean array storing where ``a`` and ``b`` are equal.
  109 
  110     .. seealso:: :func:`numpy.isclose`
  111 
  112     """
  113     a = cupy.asanyarray(a)
  114     b = cupy.asanyarray(b)
  115     if (a.dtype in [numpy.complex64, numpy.complex128]) or \
  116        (b.dtype in [numpy.complex64, numpy.complex128]):
  117         return _is_close_complex(a, b, rtol, atol, equal_nan)
  118     else:
  119         return _is_close(a, b, rtol, atol, equal_nan)
  120 
  121 
  122 # TODO(okuta): Implement array_equal
  123 
  124 
  125 # TODO(okuta): Implement array_equiv
  126 
  127 
  128 greater = core.greater
  129 
  130 
  131 greater_equal = core.greater_equal
  132 
  133 
  134 less = core.less
  135 
  136 
  137 less_equal = core.less_equal
  138 
  139 
  140 equal = core.equal
  141 
  142 
  143 not_equal = core.not_equal
  144
  ```
  --- END FILES ---
  
  Please first localize the bug based on the issue statement, and then generate a patch according to the `git diff` format fenced by three backticks.
  
  Here is an example:
  
  ```diff
  diff --git a/examples/server_async.py b/examples/server_async.py
  --- a/examples/server_async.py
  +++ b/examples/server_async.py
  @@ -313,4 +313,4 @@
   
   
   if __name__ == "__main__":
  -    asyncio.run(run_async_server("."), debug=True)
  +    asyncio.run(run_async_server(), debug=True)
  diff --git a/examples/server_sync.py b/examples/server_sync.py
  --- a/examples/server_sync.py
  +++ b/examples/server_sync.py
  @@ -313,5 +313,5 @@
   
   
   if __name__ == "__main__":
  -    server = run_sync_server(".")
  +    server = run_sync_server()
       server.shutdown()
  
  ```
  
golden_diff: diff --git a/cupy/_logic/comparison.py b/cupy/_logic/comparison.py
  --- a/cupy/_logic/comparison.py
  +++ b/cupy/_logic/comparison.py
  @@ -2,6 +2,7 @@
   
   import cupy
   from cupy import core
  +from cupy._logic import content
   
   
   _is_close = core.create_ufunc(
  @@ -38,12 +39,14 @@
   )
   
   
  -def array_equal(a1, a2):
  +def array_equal(a1, a2, equal_nan=False):
       """Returns ``True`` if two arrays are element-wise exactly equal.
   
       Args:
           a1 (cupy.ndarray): Input array to compare.
           a2 (cupy.ndarray): Input array to compare.
  +        equal_nan (bool): If ``True``, NaN's in ``a1`` will be considered equal
  +            to NaN's in ``a2``.
   
       Returns:
           cupy.ndarray: A boolean 0-dim array.
  @@ -54,7 +57,15 @@
       """
       if a1.shape != a2.shape:
           return cupy.array(False)
  -    return (a1 == a2).all()
  +    if not equal_nan:
  +        return (a1 == a2).all()
  +    # Handling NaN values if equal_nan is True
  +    a1nan, a2nan = content.isnan(a1), content.isnan(a2)
  +    # NaN's occur at different locations
  +    if not (a1nan == a2nan).all():
  +        return cupy.array(False)
  +    # Shapes of a1, a2 and masks are guaranteed to be consistent by this point
  +    return (a1[~a1nan] == a2[~a1nan]).all()
   
   
   def allclose(a, b, rtol=1.e-5, atol=1.e-8, equal_nan=False):
  
verification_info: {"golden_diff": "diff --git a/cupy/_logic/comparison.py b/cupy/_logic/comparison.py\n--- a/cupy/_logic/comparison.py\n+++ b/cupy/_logic/comparison.py\n@@ -2,6 +2,7 @@\n \n import cupy\n from cupy import core\n+from cupy._logic import content\n \n \n _is_close = core.create_ufunc(\n@@ -38,12 +39,14 @@\n )\n \n \n-def array_equal(a1, a2):\n+def array_equal(a1, a2, equal_nan=False):\n     \"\"\"Returns ``True`` if two arrays are element-wise exactly equal.\n \n     Args:\n         a1 (cupy.ndarray): Input array to compare.\n         a2 (cupy.ndarray): Input array to compare.\n+        equal_nan (bool): If ``True``, NaN's in ``a1`` will be considered equal\n+            to NaN's in ``a2``.\n \n     Returns:\n         cupy.ndarray: A boolean 0-dim array.\n@@ -54,7 +57,15 @@\n     \"\"\"\n     if a1.shape != a2.shape:\n         return cupy.array(False)\n-    return (a1 == a2).all()\n+    if not equal_nan:\n+        return (a1 == a2).all()\n+    # Handling NaN values if equal_nan is True\n+    a1nan, a2nan = content.isnan(a1), content.isnan(a2)\n+    # NaN's occur at different locations\n+    if not (a1nan == a2nan).all():\n+        return cupy.array(False)\n+    # Shapes of a1, a2 and masks are guaranteed to be consistent by this point\n+    return (a1[~a1nan] == a2[~a1nan]).all()\n \n \n def allclose(a, b, rtol=1.e-5, atol=1.e-8, equal_nan=False):\n", "issue": "[Bug, Enhancement] array_equal returns False on identical arrays with NaN values\n* Conditions (you can just paste the output of `python -c 'import cupy; cupy.show_config()'`)\r\n  - CuPy Version          : 8.0.0\r\n  - OS/Platform : Pop OS\r\n  - CUDA Version    : 10000\r\n  - cuDNN Version         : 7605\r\n  - NCCL Version    : 2604\r\n\r\n* Code to reproduce\r\n```python\r\nimport cupy as cp\r\na = cp.array([0, 1, cp.nan])\r\nprint(cp.array_equal(a, a))         # False\r\n```\r\nThis relates exactly with https://github.com/numpy/numpy/issues/9229\r\nThis could be resolved by following the same procedure, resolved by https://github.com/numpy/numpy/pull/16128, which would essentially add an `equal_nan` kwarg to let user decide if NaN values should be considered equal or not, which is consistent with: https://github.com/cupy/cupy/blob/0dc6bbafb0cf75bb873531cbf69c6995a72c61a3/cupy/_logic/comparison.py#L60\r\nhttps://github.com/cupy/cupy/blob/0dc6bbafb0cf75bb873531cbf69c6995a72c61a3/cupy/_logic/comparison.py#L89\r\n\r\n* Error messages, stack traces, or logs\r\n`<null>`\n", "before_files": [{"content": "import numpy\n\nimport cupy\nfrom cupy import core\n\n\n_is_close = core.create_ufunc(\n    'cupy_is_close',\n    ('eeee?->?', 'ffff?->?', 'dddd?->?'),\n    '''\n    bool equal_nan = in4;\n    if (isfinite(in0) && isfinite(in1)) {\n      out0 = fabs(in0 - in1) <= in3 + in2 * fabs(in1);\n    } else if (equal_nan) {\n      out0 = (in0 == in1) || (isnan(in0) && isnan(in1));\n    } else {\n      out0 = (in0 == in1);\n    }\n    '''\n)\n\n# Note that in cupy/core/include/cupy/complex.cuh, we already got isfinite and\n# isnan working for complex numbers, so just replace fabs above by abs (from\n# thrust) and we are ready to go\n_is_close_complex = core.create_ufunc(\n    'cupy_is_close_complex',\n    ('FFff?->?', 'DDdd?->?'),\n    '''\n    bool equal_nan = in4;\n    if (isfinite(in0) && isfinite(in1)) {\n      out0 = abs(in0 - in1) <= in3 + in2 * abs(in1);\n    } else if (equal_nan) {\n      out0 = (in0 == in1) || (isnan(in0) && isnan(in1));\n    } else {\n      out0 = (in0 == in1);\n    }\n    '''\n)\n\n\ndef array_equal(a1, a2):\n    \"\"\"Returns ``True`` if two arrays are element-wise exactly equal.\n\n    Args:\n        a1 (cupy.ndarray): Input array to compare.\n        a2 (cupy.ndarray): Input array to compare.\n\n    Returns:\n        cupy.ndarray: A boolean 0-dim array.\n            If its value is ``True``, two arrays are element-wise equal.\n\n    .. seealso:: :func:`numpy.array_equal`\n\n    \"\"\"\n    if a1.shape != a2.shape:\n        return cupy.array(False)\n    return (a1 == a2).all()\n\n\ndef allclose(a, b, rtol=1.e-5, atol=1.e-8, equal_nan=False):\n    \"\"\"Returns True if two arrays are element-wise equal within a tolerance.\n\n    Two values in ``a`` and ``b`` are  considiered equal when the following\n    equation is satisfied.\n\n    .. math::\n\n       |a - b| \\\\le \\\\mathrm{atol} + \\\\mathrm{rtol} |b|\n\n    Args:\n        a (cupy.ndarray): Input array to compare.\n        b (cupy.ndarray): Input array to compare.\n        rtol (float): The relative tolerance.\n        atol (float): The absolute tolerance.\n        equal_nan (bool): If ``True``, NaN's in ``a`` will be considered equal\n            to NaN's in ``b``.\n\n    Returns:\n        cupy.ndarray: A boolean 0-dim array.\n            If its value is ``True``, two arrays are element-wise equal within\n            a tolerance.\n\n    .. seealso:: :func:`numpy.allclose`\n\n    \"\"\"\n    return isclose(a, b, rtol=rtol, atol=atol, equal_nan=equal_nan).all()\n\n\ndef isclose(a, b, rtol=1.e-5, atol=1.e-8, equal_nan=False):\n    \"\"\"Returns a boolean array where two arrays are equal within a tolerance.\n\n    Two values in ``a`` and ``b`` are  considiered equal when the following\n    equation is satisfied.\n\n    .. math::\n\n       |a - b| \\\\le \\\\mathrm{atol} + \\\\mathrm{rtol} |b|\n\n    Args:\n        a (cupy.ndarray): Input array to compare.\n        b (cupy.ndarray): Input array to compare.\n        rtol (float): The relative tolerance.\n        atol (float): The absolute tolerance.\n        equal_nan (bool): If ``True``, NaN's in ``a`` will be considered equal\n            to NaN's in ``b``.\n\n    Returns:\n        cupy.ndarray: A boolean array storing where ``a`` and ``b`` are equal.\n\n    .. seealso:: :func:`numpy.isclose`\n\n    \"\"\"\n    a = cupy.asanyarray(a)\n    b = cupy.asanyarray(b)\n    if (a.dtype in [numpy.complex64, numpy.complex128]) or \\\n       (b.dtype in [numpy.complex64, numpy.complex128]):\n        return _is_close_complex(a, b, rtol, atol, equal_nan)\n    else:\n        return _is_close(a, b, rtol, atol, equal_nan)\n\n\n# TODO(okuta): Implement array_equal\n\n\n# TODO(okuta): Implement array_equiv\n\n\ngreater = core.greater\n\n\ngreater_equal = core.greater_equal\n\n\nless = core.less\n\n\nless_equal = core.less_equal\n\n\nequal = core.equal\n\n\nnot_equal = core.not_equal\n", "path": "cupy/_logic/comparison.py"}], "after_files": [{"content": "import numpy\n\nimport cupy\nfrom cupy import core\nfrom cupy._logic import content\n\n\n_is_close = core.create_ufunc(\n    'cupy_is_close',\n    ('eeee?->?', 'ffff?->?', 'dddd?->?'),\n    '''\n    bool equal_nan = in4;\n    if (isfinite(in0) && isfinite(in1)) {\n      out0 = fabs(in0 - in1) <= in3 + in2 * fabs(in1);\n    } else if (equal_nan) {\n      out0 = (in0 == in1) || (isnan(in0) && isnan(in1));\n    } else {\n      out0 = (in0 == in1);\n    }\n    '''\n)\n\n# Note that in cupy/core/include/cupy/complex.cuh, we already got isfinite and\n# isnan working for complex numbers, so just replace fabs above by abs (from\n# thrust) and we are ready to go\n_is_close_complex = core.create_ufunc(\n    'cupy_is_close_complex',\n    ('FFff?->?', 'DDdd?->?'),\n    '''\n    bool equal_nan = in4;\n    if (isfinite(in0) && isfinite(in1)) {\n      out0 = abs(in0 - in1) <= in3 + in2 * abs(in1);\n    } else if (equal_nan) {\n      out0 = (in0 == in1) || (isnan(in0) && isnan(in1));\n    } else {\n      out0 = (in0 == in1);\n    }\n    '''\n)\n\n\ndef array_equal(a1, a2, equal_nan=False):\n    \"\"\"Returns ``True`` if two arrays are element-wise exactly equal.\n\n    Args:\n        a1 (cupy.ndarray): Input array to compare.\n        a2 (cupy.ndarray): Input array to compare.\n        equal_nan (bool): If ``True``, NaN's in ``a1`` will be considered equal\n            to NaN's in ``a2``.\n\n    Returns:\n        cupy.ndarray: A boolean 0-dim array.\n            If its value is ``True``, two arrays are element-wise equal.\n\n    .. seealso:: :func:`numpy.array_equal`\n\n    \"\"\"\n    if a1.shape != a2.shape:\n        return cupy.array(False)\n    if not equal_nan:\n        return (a1 == a2).all()\n    # Handling NaN values if equal_nan is True\n    a1nan, a2nan = content.isnan(a1), content.isnan(a2)\n    # NaN's occur at different locations\n    if not (a1nan == a2nan).all():\n        return cupy.array(False)\n    # Shapes of a1, a2 and masks are guaranteed to be consistent by this point\n    return (a1[~a1nan] == a2[~a1nan]).all()\n\n\ndef allclose(a, b, rtol=1.e-5, atol=1.e-8, equal_nan=False):\n    \"\"\"Returns True if two arrays are element-wise equal within a tolerance.\n\n    Two values in ``a`` and ``b`` are  considiered equal when the following\n    equation is satisfied.\n\n    .. math::\n\n       |a - b| \\\\le \\\\mathrm{atol} + \\\\mathrm{rtol} |b|\n\n    Args:\n        a (cupy.ndarray): Input array to compare.\n        b (cupy.ndarray): Input array to compare.\n        rtol (float): The relative tolerance.\n        atol (float): The absolute tolerance.\n        equal_nan (bool): If ``True``, NaN's in ``a`` will be considered equal\n            to NaN's in ``b``.\n\n    Returns:\n        cupy.ndarray: A boolean 0-dim array.\n            If its value is ``True``, two arrays are element-wise equal within\n            a tolerance.\n\n    .. seealso:: :func:`numpy.allclose`\n\n    \"\"\"\n    return isclose(a, b, rtol=rtol, atol=atol, equal_nan=equal_nan).all()\n\n\ndef isclose(a, b, rtol=1.e-5, atol=1.e-8, equal_nan=False):\n    \"\"\"Returns a boolean array where two arrays are equal within a tolerance.\n\n    Two values in ``a`` and ``b`` are  considiered equal when the following\n    equation is satisfied.\n\n    .. math::\n\n       |a - b| \\\\le \\\\mathrm{atol} + \\\\mathrm{rtol} |b|\n\n    Args:\n        a (cupy.ndarray): Input array to compare.\n        b (cupy.ndarray): Input array to compare.\n        rtol (float): The relative tolerance.\n        atol (float): The absolute tolerance.\n        equal_nan (bool): If ``True``, NaN's in ``a`` will be considered equal\n            to NaN's in ``b``.\n\n    Returns:\n        cupy.ndarray: A boolean array storing where ``a`` and ``b`` are equal.\n\n    .. seealso:: :func:`numpy.isclose`\n\n    \"\"\"\n    a = cupy.asanyarray(a)\n    b = cupy.asanyarray(b)\n    if (a.dtype in [numpy.complex64, numpy.complex128]) or \\\n       (b.dtype in [numpy.complex64, numpy.complex128]):\n        return _is_close_complex(a, b, rtol, atol, equal_nan)\n    else:\n        return _is_close(a, b, rtol, atol, equal_nan)\n\n\n# TODO(okuta): Implement array_equal\n\n\n# TODO(okuta): Implement array_equiv\n\n\ngreater = core.greater\n\n\ngreater_equal = core.greater_equal\n\n\nless = core.less\n\n\nless_equal = core.less_equal\n\n\nequal = core.equal\n\n\nnot_equal = core.not_equal\n", "path": "cupy/_logic/comparison.py"}]}