prompt: You will be provided with a partial code base and an issue statement explaining a problem to resolve.
  <issue>
  tf.sign(0) = 0
  
  
  </issue>
  <code>
  [start of xquant/quantizers.py]
  1 import tensorflow as tf
  2 from xquant import utils
  3 
  4 
  5 @utils.register_keras_custom_object
  6 @tf.custom_gradient
  7 def ste_sign(x):
  8     r"""
  9     Sign binarization function.
  10     \\[q(x) = \mathrm{Sign}(x)\\]
  11 
  12     The gradient is estimated using the Straight-Through Estimator.
  13     \\[\frac{\partial q(x)}{\partial x} = x\\]
  14 
  15     # Arguments
  16     x: Input tensor.
  17 
  18     # Returns
  19     Binarized tensor.
  20 
  21     # References
  22     - [Binarized Neural Networks: Training Deep Neural Networks with Weights and
  23       Activations Constrained to +1 or -1](http://arxiv.org/abs/1602.02830)
  24     """
  25 
  26     def grad(dy):
  27         return dy
  28 
  29     return tf.sign(x), grad
  30 
  31 
  32 @utils.register_keras_custom_object
  33 @tf.custom_gradient
  34 def approx_sign(x):
  35     r"""
  36     Sign binarization function.
  37     \\[q(x) = \mathrm{Sign}(x)\\]
  38 
  39     The gradient is estimated using the ApproxSign method.
  40     \\[\frac{\partial q(x)}{\partial x} = (2 - 2 \left|x\right|))\\]
  41 
  42     # Arguments
  43     x: Input tensor.
  44 
  45     # Returns
  46     Binarized tensor.
  47 
  48     # References
  49     - [Bi-Real Net: Enhancing the Performance of 1-bit CNNs With Improved
  50       Representational Capability and Advanced
  51       Training Algorithm](http://arxiv.org/abs/1808.00278)
  52     """
  53 
  54     def grad(dy):
  55         return (1 - tf.abs(x)) * 2 * dy
  56 
  57     return tf.sign(x), grad
  58 
  59 
  60 def serialize(initializer):
  61     return tf.keras.utils.serialize_keras_object(initializer)
  62 
  63 
  64 def deserialize(name, custom_objects=None):
  65     return tf.keras.utils.deserialize_keras_object(
  66         name,
  67         module_objects=globals(),
  68         custom_objects=custom_objects,
  69         printable_module_name="quantization function",
  70     )
  71 
  72 
  73 def get(identifier):
  74     if identifier is None:
  75         return None
  76     if isinstance(identifier, str):
  77         return deserialize(str(identifier))
  78     if callable(identifier):
  79         return identifier
  80     raise ValueError(
  81         "Could not interpret quantization function identifier:", identifier
  82     )
  83
  [end of xquant/quantizers.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/xquant/quantizers.py b/xquant/quantizers.py
  --- a/xquant/quantizers.py
  +++ b/xquant/quantizers.py
  @@ -2,12 +2,22 @@
   from xquant import utils
   
   
  +def sign(x):
  +    """A sign function that will never be zero"""
  +    return tf.sign(tf.sign(x) + 1e-10)
  +
  +
   @utils.register_keras_custom_object
   @tf.custom_gradient
   def ste_sign(x):
       r"""
       Sign binarization function.
  -    \\[q(x) = \mathrm{Sign}(x)\\]
  +    \\[
  +    q(x) = \begin{cases}
  +      -1 & x < 0 \\\
  +      1 & x \geq 0
  +   \end{cases}
  +   \\]
   
       The gradient is estimated using the Straight-Through Estimator.
       \\[\frac{\partial q(x)}{\partial x} = x\\]
  @@ -26,7 +36,7 @@
       def grad(dy):
           return dy
   
  -    return tf.sign(x), grad
  +    return sign(x), grad
   
   
   @utils.register_keras_custom_object
  @@ -34,7 +44,12 @@
   def approx_sign(x):
       r"""
       Sign binarization function.
  -    \\[q(x) = \mathrm{Sign}(x)\\]
  +    \\[
  +    q(x) = \begin{cases}
  +      -1 & x < 0 \\\
  +      1 & x \geq 0
  +   \end{cases}
  +   \\]
   
       The gradient is estimated using the ApproxSign method.
       \\[\frac{\partial q(x)}{\partial x} = (2 - 2 \left|x\right|))\\]
  @@ -54,7 +69,7 @@
       def grad(dy):
           return (1 - tf.abs(x)) * 2 * dy
   
  -    return tf.sign(x), grad
  +    return sign(x), grad
   
   
   def serialize(initializer):
  
verification_info: {"golden_diff": "diff --git a/xquant/quantizers.py b/xquant/quantizers.py\n--- a/xquant/quantizers.py\n+++ b/xquant/quantizers.py\n@@ -2,12 +2,22 @@\n from xquant import utils\n \n \n+def sign(x):\n+    \"\"\"A sign function that will never be zero\"\"\"\n+    return tf.sign(tf.sign(x) + 1e-10)\n+\n+\n @utils.register_keras_custom_object\n @tf.custom_gradient\n def ste_sign(x):\n     r\"\"\"\n     Sign binarization function.\n-    \\\\[q(x) = \\mathrm{Sign}(x)\\\\]\n+    \\\\[\n+    q(x) = \\begin{cases}\n+      -1 & x < 0 \\\\\\\n+      1 & x \\geq 0\n+   \\end{cases}\n+   \\\\]\n \n     The gradient is estimated using the Straight-Through Estimator.\n     \\\\[\\frac{\\partial q(x)}{\\partial x} = x\\\\]\n@@ -26,7 +36,7 @@\n     def grad(dy):\n         return dy\n \n-    return tf.sign(x), grad\n+    return sign(x), grad\n \n \n @utils.register_keras_custom_object\n@@ -34,7 +44,12 @@\n def approx_sign(x):\n     r\"\"\"\n     Sign binarization function.\n-    \\\\[q(x) = \\mathrm{Sign}(x)\\\\]\n+    \\\\[\n+    q(x) = \\begin{cases}\n+      -1 & x < 0 \\\\\\\n+      1 & x \\geq 0\n+   \\end{cases}\n+   \\\\]\n \n     The gradient is estimated using the ApproxSign method.\n     \\\\[\\frac{\\partial q(x)}{\\partial x} = (2 - 2 \\left|x\\right|))\\\\]\n@@ -54,7 +69,7 @@\n     def grad(dy):\n         return (1 - tf.abs(x)) * 2 * dy\n \n-    return tf.sign(x), grad\n+    return sign(x), grad\n \n \n def serialize(initializer):\n", "issue": "tf.sign(0) = 0\n\n", "before_files": [{"content": "import tensorflow as tf\nfrom xquant import utils\n\n\n@utils.register_keras_custom_object\n@tf.custom_gradient\ndef ste_sign(x):\n    r\"\"\"\n    Sign binarization function.\n    \\\\[q(x) = \\mathrm{Sign}(x)\\\\]\n\n    The gradient is estimated using the Straight-Through Estimator.\n    \\\\[\\frac{\\partial q(x)}{\\partial x} = x\\\\]\n\n    # Arguments\n    x: Input tensor.\n\n    # Returns\n    Binarized tensor.\n\n    # References\n    - [Binarized Neural Networks: Training Deep Neural Networks with Weights and\n      Activations Constrained to +1 or -1](http://arxiv.org/abs/1602.02830)\n    \"\"\"\n\n    def grad(dy):\n        return dy\n\n    return tf.sign(x), grad\n\n\n@utils.register_keras_custom_object\n@tf.custom_gradient\ndef approx_sign(x):\n    r\"\"\"\n    Sign binarization function.\n    \\\\[q(x) = \\mathrm{Sign}(x)\\\\]\n\n    The gradient is estimated using the ApproxSign method.\n    \\\\[\\frac{\\partial q(x)}{\\partial x} = (2 - 2 \\left|x\\right|))\\\\]\n\n    # Arguments\n    x: Input tensor.\n\n    # Returns\n    Binarized tensor.\n\n    # References\n    - [Bi-Real Net: Enhancing the Performance of 1-bit CNNs With Improved\n      Representational Capability and Advanced\n      Training Algorithm](http://arxiv.org/abs/1808.00278)\n    \"\"\"\n\n    def grad(dy):\n        return (1 - tf.abs(x)) * 2 * dy\n\n    return tf.sign(x), grad\n\n\ndef serialize(initializer):\n    return tf.keras.utils.serialize_keras_object(initializer)\n\n\ndef deserialize(name, custom_objects=None):\n    return tf.keras.utils.deserialize_keras_object(\n        name,\n        module_objects=globals(),\n        custom_objects=custom_objects,\n        printable_module_name=\"quantization function\",\n    )\n\n\ndef get(identifier):\n    if identifier is None:\n        return None\n    if isinstance(identifier, str):\n        return deserialize(str(identifier))\n    if callable(identifier):\n        return identifier\n    raise ValueError(\n        \"Could not interpret quantization function identifier:\", identifier\n    )\n", "path": "xquant/quantizers.py"}]}