prompt: You will be provided with a partial code base and an issue statement explaining a problem to resolve.
  <issue>
  why MultiDiscrete  dtype=int8 
  MultiDiscrete  dtype is hardcoded as int8. 
  Is this a bug ? What happens when  we need more than 256 category  
  ```
  space = MultiDiscrete([7, 1024])
  space.sample()
  ```
  
  https://github.com/openai/gym/blob/e944885e3b31a10fb6973093b39ff7682ef3aa3d/gym/spaces/multi_discrete.py#L10
  
  </issue>
  <code>
  [start of gym/spaces/multi_discrete.py]
  1 import gym
  2 import numpy as np
  3 from .space import Space
  4 
  5 
  6 class MultiDiscrete(Space):
  7     """
  8     - The multi-discrete action space consists of a series of discrete action spaces with different number of actions in eachs
  9     - It is useful to represent game controllers or keyboards where each key can be represented as a discrete action space
  10     - It is parametrized by passing an array of positive integers specifying number of actions for each discrete action space
  11 
  12     Note: A value of 0 always need to represent the NOOP action.
  13 
  14     e.g. Nintendo Game Controller
  15     - Can be conceptualized as 3 discrete action spaces:
  16 
  17         1) Arrow Keys: Discrete 5  - NOOP[0], UP[1], RIGHT[2], DOWN[3], LEFT[4]  - params: min: 0, max: 4
  18         2) Button A:   Discrete 2  - NOOP[0], Pressed[1] - params: min: 0, max: 1
  19         3) Button B:   Discrete 2  - NOOP[0], Pressed[1] - params: min: 0, max: 1
  20 
  21     - Can be initialized as
  22 
  23         MultiDiscrete([ 5, 2, 2 ])
  24 
  25     """
  26     def __init__(self, nvec):
  27     
  28         """
  29         nvec: vector of counts of each categorical variable
  30         """
  31         assert (np.array(nvec) > 0).all(), 'nvec (counts) have to be positive'
  32         self.nvec = np.asarray(nvec, dtype=np.uint32)
  33 
  34         super(MultiDiscrete, self).__init__(self.nvec.shape, np.uint32)
  35         self.np_random = np.random.RandomState()
  36 
  37     def seed(self, seed):
  38         self.np_random.seed(seed)
  39 
  40     def sample(self):
  41         return (self.np_random.random_sample(self.nvec.shape) * self.nvec).astype(self.dtype)
  42 
  43     def contains(self, x):
  44         # if nvec is uint32 and space dtype is uint32, then 0 <= x < self.nvec guarantees that x
  45         # is within correct bounds for space dtype (even though x does not have to be unsigned)
  46         return (0 <= x).all() and (x < self.nvec).all()
  47 
  48     def to_jsonable(self, sample_n):
  49         return [sample.tolist() for sample in sample_n]
  50 
  51     def from_jsonable(self, sample_n):
  52         return np.array(sample_n)
  53 
  54     def __repr__(self):
  55         return "MultiDiscrete({})".format(self.nvec)
  56 
  57     def __eq__(self, other):
  58         return np.all(self.nvec == other.nvec)
  59
  [end of gym/spaces/multi_discrete.py]
  [start of gym/spaces/space.py]
  1 import numpy as np
  2 
  3 
  4 class Space(object):
  5     """Defines the observation and action spaces, so you can write generic
  6     code that applies to any Env. For example, you can choose a random
  7     action.
  8     """
  9     def __init__(self, shape=None, dtype=None):
  10         import numpy as np # takes about 300-400ms to import, so we load lazily
  11         self.shape = None if shape is None else tuple(shape)
  12         self.dtype = None if dtype is None else np.dtype(dtype)
  13 
  14     def sample(self):
  15         """
  16         Uniformly randomly sample a random element of this space
  17         """
  18         raise NotImplementedError
  19 
  20     def seed(self, seed):
  21         """Set the seed for this space's pseudo-random number generator. """
  22         raise NotImplementedError
  23 
  24     def contains(self, x):
  25         """
  26         Return boolean specifying if x is a valid
  27         member of this space
  28         """
  29         raise NotImplementedError
  30 
  31     def __contains__(self, x):
  32         return self.contains(x)
  33 
  34     def to_jsonable(self, sample_n):
  35         """Convert a batch of samples from this space to a JSONable data type."""
  36         # By default, assume identity is JSONable
  37         return sample_n
  38 
  39     def from_jsonable(self, sample_n):
  40         """Convert a JSONable data type to a batch of samples from this space."""
  41         # By default, assume identity is JSONable
  42         return sample_n
  43
  [end of gym/spaces/space.py]
  </code>
  
  I need you to solve this issue by generating a single patch file that I can apply directly to this repository using git apply. Please respond with a single patch file in the following format.
  <patch>
  diff --git a/file.py b/file.py
  --- a/file.py
  +++ b/file.py
  @@ -1,27 +1,35 @@
   def euclidean(a, b):
  -    while b:
  -        a, b = b, a % b
  -    return a
  +    if b == 0:
  +        return a
  +    return euclidean(b, a % b)
   
   
   def bresenham(x0, y0, x1, y1):
       points = []
       dx = abs(x1 - x0)
       dy = abs(y1 - y0)
  -    sx = 1 if x0 < x1 else -1
  -    sy = 1 if y0 < y1 else -1
  -    err = dx - dy
  +    x, y = x0, y0
  +    sx = -1 if x0 > x1 else 1
  +    sy = -1 if y0 > y1 else 1
   
  -    while True:
  -        points.append((x0, y0))
  -        if x0 == x1 and y0 == y1:
  -            break
  -        e2 = 2 * err
  -        if e2 > -dy:
  -            err -= dy
  -            x0 += sx
  -        if e2 < dx:
  -            err += dx
  -            y0 += sy
  +    if dx > dy:
  +        err = dx / 2.0
  +        while x != x1:
  +            points.append((x, y))
  +            err -= dy
  +            if err < 0:
  +                y += sy
  +                err += dx
  +            x += sx
  +    else:
  +        err = dy / 2.0
  +        while y != y1:
  +            points.append((x, y))
  +            err -= dx
  +            if err < 0:
  +                x += sx
  +                err += dy
  +            y += sy
  +
  +    points.append((x, y))
       return points
  
  </patch>
golden_diff: diff --git a/gym/spaces/multi_discrete.py b/gym/spaces/multi_discrete.py
  --- a/gym/spaces/multi_discrete.py
  +++ b/gym/spaces/multi_discrete.py
  @@ -1,4 +1,3 @@
  -import gym
   import numpy as np
   from .space import Space
   
  @@ -29,9 +28,9 @@
           nvec: vector of counts of each categorical variable
           """
           assert (np.array(nvec) > 0).all(), 'nvec (counts) have to be positive'
  -        self.nvec = np.asarray(nvec, dtype=np.uint32)
  +        self.nvec = np.asarray(nvec, dtype=np.int64)
   
  -        super(MultiDiscrete, self).__init__(self.nvec.shape, np.uint32)
  +        super(MultiDiscrete, self).__init__(self.nvec.shape, np.int64)
           self.np_random = np.random.RandomState()
   
       def seed(self, seed):
  diff --git a/gym/spaces/space.py b/gym/spaces/space.py
  --- a/gym/spaces/space.py
  +++ b/gym/spaces/space.py
  @@ -1,6 +1,3 @@
  -import numpy as np
  -
  -
   class Space(object):
       """Defines the observation and action spaces, so you can write generic
       code that applies to any Env. For example, you can choose a random
  
verification_info: {"golden_diff": "diff --git a/gym/spaces/multi_discrete.py b/gym/spaces/multi_discrete.py\n--- a/gym/spaces/multi_discrete.py\n+++ b/gym/spaces/multi_discrete.py\n@@ -1,4 +1,3 @@\n-import gym\n import numpy as np\n from .space import Space\n \n@@ -29,9 +28,9 @@\n         nvec: vector of counts of each categorical variable\n         \"\"\"\n         assert (np.array(nvec) > 0).all(), 'nvec (counts) have to be positive'\n-        self.nvec = np.asarray(nvec, dtype=np.uint32)\n+        self.nvec = np.asarray(nvec, dtype=np.int64)\n \n-        super(MultiDiscrete, self).__init__(self.nvec.shape, np.uint32)\n+        super(MultiDiscrete, self).__init__(self.nvec.shape, np.int64)\n         self.np_random = np.random.RandomState()\n \n     def seed(self, seed):\ndiff --git a/gym/spaces/space.py b/gym/spaces/space.py\n--- a/gym/spaces/space.py\n+++ b/gym/spaces/space.py\n@@ -1,6 +1,3 @@\n-import numpy as np\n-\n-\n class Space(object):\n     \"\"\"Defines the observation and action spaces, so you can write generic\n     code that applies to any Env. For example, you can choose a random\n", "issue": "why MultiDiscrete  dtype=int8 \nMultiDiscrete  dtype is hardcoded as int8. \r\nIs this a bug ? What happens when  we need more than 256 category  \r\n```\r\nspace = MultiDiscrete([7, 1024])\r\nspace.sample()\r\n```\r\n\r\nhttps://github.com/openai/gym/blob/e944885e3b31a10fb6973093b39ff7682ef3aa3d/gym/spaces/multi_discrete.py#L10\n", "before_files": [{"content": "import gym\nimport numpy as np\nfrom .space import Space\n\n\nclass MultiDiscrete(Space):\n    \"\"\"\n    - The multi-discrete action space consists of a series of discrete action spaces with different number of actions in eachs\n    - It is useful to represent game controllers or keyboards where each key can be represented as a discrete action space\n    - It is parametrized by passing an array of positive integers specifying number of actions for each discrete action space\n\n    Note: A value of 0 always need to represent the NOOP action.\n\n    e.g. Nintendo Game Controller\n    - Can be conceptualized as 3 discrete action spaces:\n\n        1) Arrow Keys: Discrete 5  - NOOP[0], UP[1], RIGHT[2], DOWN[3], LEFT[4]  - params: min: 0, max: 4\n        2) Button A:   Discrete 2  - NOOP[0], Pressed[1] - params: min: 0, max: 1\n        3) Button B:   Discrete 2  - NOOP[0], Pressed[1] - params: min: 0, max: 1\n\n    - Can be initialized as\n\n        MultiDiscrete([ 5, 2, 2 ])\n\n    \"\"\"\n    def __init__(self, nvec):\n    \n        \"\"\"\n        nvec: vector of counts of each categorical variable\n        \"\"\"\n        assert (np.array(nvec) > 0).all(), 'nvec (counts) have to be positive'\n        self.nvec = np.asarray(nvec, dtype=np.uint32)\n\n        super(MultiDiscrete, self).__init__(self.nvec.shape, np.uint32)\n        self.np_random = np.random.RandomState()\n\n    def seed(self, seed):\n        self.np_random.seed(seed)\n\n    def sample(self):\n        return (self.np_random.random_sample(self.nvec.shape) * self.nvec).astype(self.dtype)\n\n    def contains(self, x):\n        # if nvec is uint32 and space dtype is uint32, then 0 <= x < self.nvec guarantees that x\n        # is within correct bounds for space dtype (even though x does not have to be unsigned)\n        return (0 <= x).all() and (x < self.nvec).all()\n\n    def to_jsonable(self, sample_n):\n        return [sample.tolist() for sample in sample_n]\n\n    def from_jsonable(self, sample_n):\n        return np.array(sample_n)\n\n    def __repr__(self):\n        return \"MultiDiscrete({})\".format(self.nvec)\n\n    def __eq__(self, other):\n        return np.all(self.nvec == other.nvec)\n", "path": "gym/spaces/multi_discrete.py"}, {"content": "import numpy as np\n\n\nclass Space(object):\n    \"\"\"Defines the observation and action spaces, so you can write generic\n    code that applies to any Env. For example, you can choose a random\n    action.\n    \"\"\"\n    def __init__(self, shape=None, dtype=None):\n        import numpy as np # takes about 300-400ms to import, so we load lazily\n        self.shape = None if shape is None else tuple(shape)\n        self.dtype = None if dtype is None else np.dtype(dtype)\n\n    def sample(self):\n        \"\"\"\n        Uniformly randomly sample a random element of this space\n        \"\"\"\n        raise NotImplementedError\n\n    def seed(self, seed):\n        \"\"\"Set the seed for this space's pseudo-random number generator. \"\"\"\n        raise NotImplementedError\n\n    def contains(self, x):\n        \"\"\"\n        Return boolean specifying if x is a valid\n        member of this space\n        \"\"\"\n        raise NotImplementedError\n\n    def __contains__(self, x):\n        return self.contains(x)\n\n    def to_jsonable(self, sample_n):\n        \"\"\"Convert a batch of samples from this space to a JSONable data type.\"\"\"\n        # By default, assume identity is JSONable\n        return sample_n\n\n    def from_jsonable(self, sample_n):\n        \"\"\"Convert a JSONable data type to a batch of samples from this space.\"\"\"\n        # By default, assume identity is JSONable\n        return sample_n\n", "path": "gym/spaces/space.py"}]}