Math optimizations

cairosvg/bounding_box.py

@@ -5,7 +5,9 @@
 
 """
 
-from math import acos, atan, cos, fmod, isinf, pi, radians, sin, sqrt, tan
+from math import (
+ acos, atan, copysign, cos, fmod, hypot, isinf, pi, radians, sin, sqrt, tan,
+ tau)
 
 from .features import match_features
 from .helpers import PATH_LETTERS, normalize, point, size
@@ -220,9 +222,7 @@ def bounding_box_text(surface, node):
 
 def angle(bx, by):
  """Get the angle between vector (1,0) and vector (bx,by)."""
- return fmod(
- 2 * pi + (1 if by > 0 else -1) * acos(bx / sqrt(bx * bx + by * by)),
- 2 * pi)
+ return fmod(tau + copysign(acos(bx / hypot(bx, by)), by), tau)
 
 
 def bounding_box_elliptical_arc(x1, y1, rx, ry, phi, large, sweep, x, y):
@@ -260,7 +260,7 @@ def bounding_box_elliptical_arc(x1, y1, rx, ry, phi, large, sweep, x, y):
  cx = cxprime * cos(phi) - cyprime * sin(phi) + (x1 + x) / 2
  cy = cxprime * sin(phi) + cyprime * cos(phi) + (y1 + y) / 2
 
- if phi == 0 or phi == pi:
+ if phi in (0, pi):
  minx = cx - rx
  tminx = angle(-rx, 0)
  maxx = cx + rx
@@ -269,7 +269,7 @@ def bounding_box_elliptical_arc(x1, y1, rx, ry, phi, large, sweep, x, y):
  tminy = angle(0, -ry)
  maxy = cy + ry
  tmaxy = angle(0, ry)
- elif phi == pi / 2 or phi == 3 * pi / 2:
+ elif phi in (pi / 2, 3 * pi / 2):
  minx = cx - ry
  tminx = angle(-ry, 0)
  maxx = cx + ry
@@ -314,17 +314,13 @@ def bounding_box_elliptical_arc(x1, y1, rx, ry, phi, large, sweep, x, y):
  angle1, angle2 = angle2, angle1
  other_arc = True
 
- if ((not other_arc and (angle1 > tminx or angle2 < tminx)) or
- (other_arc and not (angle1 > tminx or angle2 < tminx))):
+ if other_arc == (angle1 <= tminx <= angle2):
  minx = min(x, x1)
- if ((not other_arc and (angle1 > tmaxx or angle2 < tmaxx)) or
- (other_arc and not (angle1 > tmaxx or angle2 < tmaxx))):
+ if other_arc == (angle1 <= tmaxx <= angle2):
  maxx = max(x, x1)
- if ((not other_arc and (angle1 > tminy or angle2 < tminy)) or
- (other_arc and not (angle1 > tminy or angle2 < tminy))):
+ if other_arc == (angle1 <= tminy <= angle2):
  miny = min(y, y1)
- if ((not other_arc and (angle1 > tmaxy or angle2 < tmaxy)) or
- (other_arc and not (angle1 > tmaxy or angle2 < tmaxy))):
+ if other_arc == (angle1 <= tmaxy <= angle2):
  maxy = max(y, y1)
 
  return minx, miny, maxx - minx, maxy - miny

cairosvg/helpers.py

@@ -4,7 +4,7 @@
 """
 
 import re
-from math import atan2, cos, radians, sin, tan
+from math import atan2, cos, hypot, radians, sin, tan
 
 from .surface import cairo
 from .url import parse_url
@@ -13,8 +13,8 @@
  'mm': 1 / 25.4,
  'cm': 1 / 2.54,
  'in': 1,
- 'pt': 1 / 72.,
- 'pc': 1 / 6.,
+ 'pt': 1 / 72,
+ 'pc': 1 / 6,
  'px': None,
 }
 
@@ -29,7 +29,7 @@ class PointError(Exception):
 
 def distance(x1, y1, x2, y2):
  """Get the distance between two points."""
- return ((x2 - x1) ** 2 + (y2 - y1) ** 2) ** 0.5
+ return hypot(x2 - x1, y2 - y1)
 
 
 def paint(value):
@@ -345,8 +345,7 @@ def size(surface, string, reference='xy'):
  If ``reference`` is a float, it is used as reference for percentages. If it
  is ``'x'``, we use the viewport width as reference. If it is ``'y'``, we
  use the viewport height as reference. If it is ``'xy'``, we use
- ``(viewport_width ** 2 + viewport_height ** 2) ** .5 / 2 ** .5`` as
- reference.
+ ``hypot(viewport_width, viewport_height) / 2 ** .5`` as reference.
 
  """
  if not string:
@@ -370,9 +369,8 @@ def size(surface, string, reference='xy'):
  reference = surface.context_height or 0
  elif reference == 'xy':
  reference = (
- (surface.context_width ** 2 +
- surface.context_height ** 2) ** .5 /
- 2 ** .5)
+ hypot(surface.context_width, surface.context_height) / 2 ** .5
+ )
  return float(string[:-1]) * reference / 100
  elif string.endswith('em'):
  return surface.font_size * float(string[:-2])

cairosvg/image.py

@@ -34,10 +34,12 @@ def image(surface, node):
  width = size(surface, node.get('width'), 'x')
  height = size(surface, node.get('height'), 'y')
 
- if image_bytes[:4] == b'\x89PNG' and not surface.map_image:
+ if image_bytes.startswith(b'\x89PNG') and not surface.map_image:
  png_file = BytesIO(image_bytes)
- elif (image_bytes[:5] in (b'<svg ', b'<?xml', b'<!DOC') or
- image_bytes[:2] == b'\x1f\x8b') or b'<svg' in image_bytes:
+ elif (
+ image_bytes.startswith((b'<svg ', b'<?xml', b'<!DOC', b'\x1f\x8b'))
+ or b'<svg' in image_bytes
+ ):
  if 'x' in node:
  del node['x']
  if 'y' in node:

cairosvg/parser.py

@@ -385,7 +385,7 @@ def __init__(self, **kwargs):
  if not bytestring:
  bytestring = self.fetch_url(
  parse_url(self.url), 'image/svg+xml')
- if len(bytestring) >= 2 and bytestring[:2] == b'\x1f\x8b':
+ if bytestring.startswith(b'\x1f\x8b'):
  bytestring = gzip.decompress(bytestring)
  tree = ElementTree.fromstring(
  bytestring, forbid_entities=not unsafe,

cairosvg/path.py

@@ -3,7 +3,7 @@
 
 """
 
-from math import pi, radians
+from math import copysign, hypot, pi, radians
 
 from .bounding_box import calculate_bounding_box
 from .helpers import (
@@ -206,7 +206,7 @@ def path(surface, node):
  angle = point_angle(0, 0, xe, ye)
 
  # Put the second point onto the x axis
- xe = (xe ** 2 + ye ** 2) ** .5
+ xe = hypot(xe, ye)
  ye = 0
 
  # Update the x radius if it is too small
@@ -423,7 +423,7 @@ def path(surface, node):
  # Relative vertical line
  y, string = (string + ' ').split(' ', 1)
  old_x, old_y = current_point
- angle = pi / 2 if size(surface, y, 'y') > 0 else -pi / 2
+ angle = copysign(pi / 2, size(surface, y, 'y'))
  node.vertices.append((-angle, angle))
  y = size(surface, y, 'y')
  surface.context.rel_line_to(0, y)
@@ -433,7 +433,7 @@ def path(surface, node):
  # Vertical line
  y, string = (string + ' ').split(' ', 1)
  old_x, old_y = current_point
- angle = pi / 2 if size(surface, y, 'y') > old_y else -pi / 2
+ angle = copysign(pi / 2, size(surface, y, 'y') - old_y)
  node.vertices.append((-angle, angle))
  y = size(surface, y, 'y')
  surface.context.line_to(old_x, y)

cairosvg/shapes.py

@@ -87,10 +87,8 @@ def rect(surface, node):
  if rx == 0 or ry == 0:
  surface.context.rectangle(x, y, width, height)
  else:
- if rx > width / 2:
- rx = width / 2
- if ry > height / 2:
- ry = height / 2
+ rx = min(rx, width / 2)
+ ry = min(ry, height / 2)
 
  # Inspired by Cairo Cookbook
  # http://cairographics.org/cookbook/roundedrectangles/

cairosvg/text.py

@@ -101,7 +101,7 @@ def text(surface, node, draw_as_text=False):
 
  text_anchor = node.get('text-anchor')
  if text_anchor == 'middle':
- x_align = - (width / 2. + x_bearing)
+ x_align = - (width / 2 + x_bearing)
  if letter_spacing and node.text:
  x_align -= (len(node.text) - 1) * letter_spacing / 2
  elif text_anchor == 'end':
@@ -121,7 +121,7 @@ def text(surface, node, draw_as_text=False):
  alignment_baseline = (node.get('dominant-baseline') or
  node.get('alignment-baseline'))
  if display_anchor == 'middle':
- y_align = -height / 2.0 - y_bearing
+ y_align = -height / 2 - y_bearing
  elif display_anchor == 'top':
  y_align = -y_bearing
  elif display_anchor == 'bottom':
@@ -130,7 +130,7 @@ def text(surface, node, draw_as_text=False):
  alignment_baseline == 'middle'):
  # TODO: This is wrong, Cairo gives no reasonable access to x-height
  # information, so we use font top-to-bottom
- y_align = (ascent + descent) / 2.0 - descent
+ y_align = (ascent + descent) / 2 - descent
  elif (alignment_baseline == 'text-before-edge' or
  alignment_baseline == 'before_edge' or
  alignment_baseline == 'top' or