prompt: You will be provided with a partial code base and an issue statement explaining a problem to resolve.
  <issue>
  grid_axis_alignment_no_toolbar is broken in Windows (32-bit)
  `examples/integration/layout/grid_axis_alignment_no_toolbar`:
  
  ![image](https://user-images.githubusercontent.com/27475/52644650-81191480-2edf-11e9-9905-eb5b000448f1.png)
  
  All axes should be in 0 to 10, 10^3, 10^6, 10^9 ranges. All major browsers are affected the same way. I suspect this may be due to 32-bit system architecture. It would be good if someone with 64-bit windows could run this example for comparison.
  
  </issue>
  <code>
  [start of examples/integration/layout/grid_axis_alignment_no_toolbar.py]
  1 from __future__ import absolute_import
  2 
  3 import numpy as np
  4 
  5 from bokeh.plotting import figure, save
  6 from bokeh.layouts import gridplot
  7 
  8 coeffs = [10**0, 10**3, 10**6, 10**9]
  9 V = np.arange(10)
  10 
  11 figs = []
  12 
  13 for ycoeff in coeffs:
  14     row = []
  15     for xcoeff in coeffs:
  16         fig = figure(plot_height=200, plot_width=200)
  17         fig.xaxis[0].formatter.use_scientific = False
  18         fig.yaxis[0].formatter.use_scientific = False
  19         fig.xaxis[0].major_label_orientation = "vertical"
  20         fig.yaxis[0].major_label_orientation = "horizontal"
  21         fig.scatter(V*xcoeff, V*ycoeff)
  22         row.append(fig)
  23     figs.append(row)
  24 
  25 grid = gridplot(figs, toolbar_location=None)
  26 
  27 save(grid)
  28
  [end of examples/integration/layout/grid_axis_alignment_no_toolbar.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/examples/integration/layout/grid_axis_alignment_no_toolbar.py b/examples/integration/layout/grid_axis_alignment_no_toolbar.py
  --- a/examples/integration/layout/grid_axis_alignment_no_toolbar.py
  +++ b/examples/integration/layout/grid_axis_alignment_no_toolbar.py
  @@ -6,7 +6,7 @@
   from bokeh.layouts import gridplot
   
   coeffs = [10**0, 10**3, 10**6, 10**9]
  -V = np.arange(10)
  +V = np.arange(10, dtype="int64")
   
   figs = []
  
verification_info: {"golden_diff": "diff --git a/examples/integration/layout/grid_axis_alignment_no_toolbar.py b/examples/integration/layout/grid_axis_alignment_no_toolbar.py\n--- a/examples/integration/layout/grid_axis_alignment_no_toolbar.py\n+++ b/examples/integration/layout/grid_axis_alignment_no_toolbar.py\n@@ -6,7 +6,7 @@\n from bokeh.layouts import gridplot\n \n coeffs = [10**0, 10**3, 10**6, 10**9]\n-V = np.arange(10)\n+V = np.arange(10, dtype=\"int64\")\n \n figs = []\n", "issue": "grid_axis_alignment_no_toolbar is broken in Windows (32-bit)\n`examples/integration/layout/grid_axis_alignment_no_toolbar`:\r\n\r\n![image](https://user-images.githubusercontent.com/27475/52644650-81191480-2edf-11e9-9905-eb5b000448f1.png)\r\n\r\nAll axes should be in 0 to 10, 10^3, 10^6, 10^9 ranges. All major browsers are affected the same way. I suspect this may be due to 32-bit system architecture. It would be good if someone with 64-bit windows could run this example for comparison.\n", "before_files": [{"content": "from __future__ import absolute_import\n\nimport numpy as np\n\nfrom bokeh.plotting import figure, save\nfrom bokeh.layouts import gridplot\n\ncoeffs = [10**0, 10**3, 10**6, 10**9]\nV = np.arange(10)\n\nfigs = []\n\nfor ycoeff in coeffs:\n    row = []\n    for xcoeff in coeffs:\n        fig = figure(plot_height=200, plot_width=200)\n        fig.xaxis[0].formatter.use_scientific = False\n        fig.yaxis[0].formatter.use_scientific = False\n        fig.xaxis[0].major_label_orientation = \"vertical\"\n        fig.yaxis[0].major_label_orientation = \"horizontal\"\n        fig.scatter(V*xcoeff, V*ycoeff)\n        row.append(fig)\n    figs.append(row)\n\ngrid = gridplot(figs, toolbar_location=None)\n\nsave(grid)\n", "path": "examples/integration/layout/grid_axis_alignment_no_toolbar.py"}]}