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