#!/usr/bin/env python
# -*- coding: utf-8 -*-

#  Scour
#
#  Copyright 2010 Jeff Schiller
#  Copyright 2010 Louis Simard
#  Copyright 2013-2014 Tavendo GmbH
#
#  This file is part of Scour, http://www.codedread.com/scour/
#
#   Licensed under the Apache License, Version 2.0 (the "License");
#   you may not use this file except in compliance with the License.
#   You may obtain a copy of the License at
#
#       http://www.apache.org/licenses/LICENSE-2.0
#
#   Unless required by applicable law or agreed to in writing, software
#   distributed under the License is distributed on an "AS IS" BASIS,
#   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
#   See the License for the specific language governing permissions and
#   limitations under the License.

# Notes:

# rubys' path-crunching ideas here: http://intertwingly.net/code/svgtidy/spec.rb
# (and implemented here: http://intertwingly.net/code/svgtidy/svgtidy.rb )

# Yet more ideas here: http://wiki.inkscape.org/wiki/index.php/Save_Cleaned_SVG
#
# * Process Transformations
#  * Collapse all group based transformations

# Even more ideas here: http://esw.w3.org/topic/SvgTidy
#  * analysis of path elements to see if rect can be used instead? (must also need to look
#    at rounded corners)

# Next Up:
# - why are marker-start, -end not removed from the style attribute?
# - why are only overflow style properties considered and not attributes?
# - only remove unreferenced elements if they are not children of a referenced element
# - add an option to remove ids if they match the Inkscape-style of IDs
# - investigate point-reducing algorithms
# - parse transform attribute
# - if a <g> has only one element in it, collapse the <g> (ensure transform, etc are carried down)

# necessary to get true division
from __future__ import division

# Needed for Python 2/3 compatible print function.
from __future__ import print_function
from __future__ import absolute_import

import os
import sys
import xml.dom.minidom
import re
import math
import time
from collections import namedtuple
from scour.svg_regex import svg_parser
from scour.svg_transform import svg_transform_parser
import optparse
from scour.yocto_css import parseCssString
import six
from six.moves import range
from decimal import Context, Decimal, InvalidOperation, getcontext

# select the most precise walltime measurement function available on the platform
if sys.platform.startswith('win'):
   walltime = time.clock
else:
   walltime = time.time

from scour import __version__

APP = u'scour'
VER = __version__
COPYRIGHT = u'Copyright Jeff Schiller, Louis Simard, 2010'

NS = {'SVG':      'http://www.w3.org/2000/svg',
      'XLINK':    'http://www.w3.org/1999/xlink',
      'SODIPODI': 'http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd',
      'INKSCAPE': 'http://www.inkscape.org/namespaces/inkscape',
      'ADOBE_ILLUSTRATOR': 'http://ns.adobe.com/AdobeIllustrator/10.0/',
      'ADOBE_GRAPHS': 'http://ns.adobe.com/Graphs/1.0/',
      'ADOBE_SVG_VIEWER': 'http://ns.adobe.com/AdobeSVGViewerExtensions/3.0/',
      'ADOBE_VARIABLES': 'http://ns.adobe.com/Variables/1.0/',
      'ADOBE_SFW': 'http://ns.adobe.com/SaveForWeb/1.0/',
      'ADOBE_EXTENSIBILITY': 'http://ns.adobe.com/Extensibility/1.0/',
      'ADOBE_FLOWS': 'http://ns.adobe.com/Flows/1.0/',
      'ADOBE_IMAGE_REPLACEMENT': 'http://ns.adobe.com/ImageReplacement/1.0/',
      'ADOBE_CUSTOM': 'http://ns.adobe.com/GenericCustomNamespace/1.0/',
      'ADOBE_XPATH': 'http://ns.adobe.com/XPath/1.0/',
      'SKETCH': 'http://www.bohemiancoding.com/sketch/ns'
      }

unwanted_ns = [ NS['SODIPODI'], NS['INKSCAPE'], NS['ADOBE_ILLUSTRATOR'],
            NS['ADOBE_GRAPHS'], NS['ADOBE_SVG_VIEWER'], NS['ADOBE_VARIABLES'],
            NS['ADOBE_SFW'], NS['ADOBE_EXTENSIBILITY'], NS['ADOBE_FLOWS'],
            NS['ADOBE_IMAGE_REPLACEMENT'], NS['ADOBE_CUSTOM'],
            NS['ADOBE_XPATH'], NS['SKETCH'] ]

# A list of all SVG presentation properties
#
# Sources for this list:
#    https://www.w3.org/TR/SVG/propidx.html              (implemented)
#    https://www.w3.org/TR/SVGTiny12/attributeTable.html (implemented)
#    https://www.w3.org/TR/SVG2/propidx.html             (not yet implemented)
#
svgAttributes = [
            # SVG 1.1
            'alignment-baseline',
            'baseline-shift',
            'clip',
            'clip-path',
            'clip-rule',
            'color',
            'color-interpolation',
            'color-interpolation-filters',
            'color-profile',
            'color-rendering',
            'cursor',
            'direction',
            'display',
            'dominant-baseline',
            'enable-background',
            'fill',
            'fill-opacity',
            'fill-rule',
            'filter',
            'flood-color',
            'flood-opacity',
            'font',
            'font-family',
            'font-size',
            'font-size-adjust',
            'font-stretch',
            'font-style',
            'font-variant',
            'font-weight',
            'glyph-orientation-horizontal',
            'glyph-orientation-vertical',
            'image-rendering',
            'kerning',
            'letter-spacing',
            'lighting-color',
            'marker',
            'marker-end',
            'marker-mid',
            'marker-start',
            'mask',
            'opacity',
            'overflow',
            'pointer-events',
            'shape-rendering',
            'stop-color',
            'stop-opacity',
            'stroke',
            'stroke-dasharray',
            'stroke-dashoffset',
            'stroke-linecap',
            'stroke-linejoin',
            'stroke-miterlimit',
            'stroke-opacity',
            'stroke-width',
            'text-anchor',
            'text-decoration',
            'text-rendering',
            'unicode-bidi',
            'visibility',
            'word-spacing',
            'writing-mode',
            # SVG 1.2 Tiny
            'audio-level',
            'buffered-rendering',
            'display-align',
            'line-increment',
            'solid-color',
            'solid-opacity',
            'text-align',
            'vector-effect',
            'viewport-fill',
            'viewport-fill-opacity',
            ]

colors = {
   'aliceblue': 'rgb(240, 248, 255)',
   'antiquewhite': 'rgb(250, 235, 215)',
   'aqua': 'rgb( 0, 255, 255)',
   'aquamarine': 'rgb(127, 255, 212)',
   'azure': 'rgb(240, 255, 255)',
   'beige': 'rgb(245, 245, 220)',
   'bisque': 'rgb(255, 228, 196)',
   'black': 'rgb( 0, 0, 0)',
   'blanchedalmond': 'rgb(255, 235, 205)',
   'blue': 'rgb( 0, 0, 255)',
   'blueviolet': 'rgb(138, 43, 226)',
   'brown': 'rgb(165, 42, 42)',
   'burlywood': 'rgb(222, 184, 135)',
   'cadetblue': 'rgb( 95, 158, 160)',
   'chartreuse': 'rgb(127, 255, 0)',
   'chocolate': 'rgb(210, 105, 30)',
   'coral': 'rgb(255, 127, 80)',
   'cornflowerblue': 'rgb(100, 149, 237)',
   'cornsilk': 'rgb(255, 248, 220)',
   'crimson': 'rgb(220, 20, 60)',
   'cyan': 'rgb( 0, 255, 255)',
   'darkblue': 'rgb( 0, 0, 139)',
   'darkcyan': 'rgb( 0, 139, 139)',
   'darkgoldenrod': 'rgb(184, 134, 11)',
   'darkgray': 'rgb(169, 169, 169)',
   'darkgreen': 'rgb( 0, 100, 0)',
   'darkgrey': 'rgb(169, 169, 169)',
   'darkkhaki': 'rgb(189, 183, 107)',
   'darkmagenta': 'rgb(139, 0, 139)',
   'darkolivegreen': 'rgb( 85, 107, 47)',
   'darkorange': 'rgb(255, 140, 0)',
   'darkorchid': 'rgb(153, 50, 204)',
   'darkred': 'rgb(139, 0, 0)',
   'darksalmon': 'rgb(233, 150, 122)',
   'darkseagreen': 'rgb(143, 188, 143)',
   'darkslateblue': 'rgb( 72, 61, 139)',
   'darkslategray': 'rgb( 47, 79, 79)',
   'darkslategrey': 'rgb( 47, 79, 79)',
   'darkturquoise': 'rgb( 0, 206, 209)',
   'darkviolet': 'rgb(148, 0, 211)',
   'deeppink': 'rgb(255, 20, 147)',
   'deepskyblue': 'rgb( 0, 191, 255)',
   'dimgray': 'rgb(105, 105, 105)',
   'dimgrey': 'rgb(105, 105, 105)',
   'dodgerblue': 'rgb( 30, 144, 255)',
   'firebrick': 'rgb(178, 34, 34)',
   'floralwhite': 'rgb(255, 250, 240)',
   'forestgreen': 'rgb( 34, 139, 34)',
   'fuchsia': 'rgb(255, 0, 255)',
   'gainsboro': 'rgb(220, 220, 220)',
   'ghostwhite': 'rgb(248, 248, 255)',
   'gold': 'rgb(255, 215, 0)',
   'goldenrod': 'rgb(218, 165, 32)',
   'gray': 'rgb(128, 128, 128)',
   'grey': 'rgb(128, 128, 128)',
   'green': 'rgb( 0, 128, 0)',
   'greenyellow': 'rgb(173, 255, 47)',
   'honeydew': 'rgb(240, 255, 240)',
   'hotpink': 'rgb(255, 105, 180)',
   'indianred': 'rgb(205, 92, 92)',
   'indigo': 'rgb( 75, 0, 130)',
   'ivory': 'rgb(255, 255, 240)',
   'khaki': 'rgb(240, 230, 140)',
   'lavender': 'rgb(230, 230, 250)',
   'lavenderblush': 'rgb(255, 240, 245)',
   'lawngreen': 'rgb(124, 252, 0)',
   'lemonchiffon': 'rgb(255, 250, 205)',
   'lightblue': 'rgb(173, 216, 230)',
   'lightcoral': 'rgb(240, 128, 128)',
   'lightcyan': 'rgb(224, 255, 255)',
   'lightgoldenrodyellow': 'rgb(250, 250, 210)',
   'lightgray': 'rgb(211, 211, 211)',
   'lightgreen': 'rgb(144, 238, 144)',
   'lightgrey': 'rgb(211, 211, 211)',
   'lightpink': 'rgb(255, 182, 193)',
   'lightsalmon': 'rgb(255, 160, 122)',
   'lightseagreen': 'rgb( 32, 178, 170)',
   'lightskyblue': 'rgb(135, 206, 250)',
   'lightslategray': 'rgb(119, 136, 153)',
   'lightslategrey': 'rgb(119, 136, 153)',
   'lightsteelblue': 'rgb(176, 196, 222)',
   'lightyellow': 'rgb(255, 255, 224)',
   'lime': 'rgb( 0, 255, 0)',
   'limegreen': 'rgb( 50, 205, 50)',
   'linen': 'rgb(250, 240, 230)',
   'magenta': 'rgb(255, 0, 255)',
   'maroon': 'rgb(128, 0, 0)',
   'mediumaquamarine': 'rgb(102, 205, 170)',
   'mediumblue': 'rgb( 0, 0, 205)',
   'mediumorchid': 'rgb(186, 85, 211)',
   'mediumpurple': 'rgb(147, 112, 219)',
   'mediumseagreen': 'rgb( 60, 179, 113)',
   'mediumslateblue': 'rgb(123, 104, 238)',
   'mediumspringgreen': 'rgb( 0, 250, 154)',
   'mediumturquoise': 'rgb( 72, 209, 204)',
   'mediumvioletred': 'rgb(199, 21, 133)',
   'midnightblue': 'rgb( 25, 25, 112)',
   'mintcream': 'rgb(245, 255, 250)',
   'mistyrose': 'rgb(255, 228, 225)',
   'moccasin': 'rgb(255, 228, 181)',
   'navajowhite': 'rgb(255, 222, 173)',
   'navy': 'rgb( 0, 0, 128)',
   'oldlace': 'rgb(253, 245, 230)',
   'olive': 'rgb(128, 128, 0)',
   'olivedrab': 'rgb(107, 142, 35)',
   'orange': 'rgb(255, 165, 0)',
   'orangered': 'rgb(255, 69, 0)',
   'orchid': 'rgb(218, 112, 214)',
   'palegoldenrod': 'rgb(238, 232, 170)',
   'palegreen': 'rgb(152, 251, 152)',
   'paleturquoise': 'rgb(175, 238, 238)',
   'palevioletred': 'rgb(219, 112, 147)',
   'papayawhip': 'rgb(255, 239, 213)',
   'peachpuff': 'rgb(255, 218, 185)',
   'peru': 'rgb(205, 133, 63)',
   'pink': 'rgb(255, 192, 203)',
   'plum': 'rgb(221, 160, 221)',
   'powderblue': 'rgb(176, 224, 230)',
   'purple': 'rgb(128, 0, 128)',
   'red': 'rgb(255, 0, 0)',
   'rosybrown': 'rgb(188, 143, 143)',
   'royalblue': 'rgb( 65, 105, 225)',
   'saddlebrown': 'rgb(139, 69, 19)',
   'salmon': 'rgb(250, 128, 114)',
   'sandybrown': 'rgb(244, 164, 96)',
   'seagreen': 'rgb( 46, 139, 87)',
   'seashell': 'rgb(255, 245, 238)',
   'sienna': 'rgb(160, 82, 45)',
   'silver': 'rgb(192, 192, 192)',
   'skyblue': 'rgb(135, 206, 235)',
   'slateblue': 'rgb(106, 90, 205)',
   'slategray': 'rgb(112, 128, 144)',
   'slategrey': 'rgb(112, 128, 144)',
   'snow': 'rgb(255, 250, 250)',
   'springgreen': 'rgb( 0, 255, 127)',
   'steelblue': 'rgb( 70, 130, 180)',
   'tan': 'rgb(210, 180, 140)',
   'teal': 'rgb( 0, 128, 128)',
   'thistle': 'rgb(216, 191, 216)',
   'tomato': 'rgb(255, 99, 71)',
   'turquoise': 'rgb( 64, 224, 208)',
   'violet': 'rgb(238, 130, 238)',
   'wheat': 'rgb(245, 222, 179)',
   'white': 'rgb(255, 255, 255)',
   'whitesmoke': 'rgb(245, 245, 245)',
   'yellow': 'rgb(255, 255, 0)',
   'yellowgreen': 'rgb(154, 205, 50)',
   }

# A list of default poperties that are safe to remove
#
# Sources for this list:
#    https://www.w3.org/TR/SVG/propidx.html              (implemented)
#    https://www.w3.org/TR/SVGTiny12/attributeTable.html (implemented)
#    https://www.w3.org/TR/SVG2/propidx.html             (not yet implemented)
#
default_properties = { # excluded all properties with 'auto' as default
   # SVG 1.1 presentation attributes
   'baseline-shift': 'baseline',
   'clip-path': 'none',
   'clip-rule': 'nonzero',
   'color': '#000',
   'color-interpolation-filters': 'linearRGB',
   'color-interpolation': 'sRGB',
   'direction': 'ltr',
   'display': 'inline',
   'enable-background': 'accumulate',
   'fill': '#000',
   'fill-opacity': '1',
   'fill-rule': 'nonzero',
   'filter': 'none',
   'flood-color': '#000',
   'flood-opacity': '1',
   'font-size-adjust': 'none',
   'font-size': 'medium',
   'font-stretch': 'normal',
   'font-style': 'normal',
   'font-variant': 'normal',
   'font-weight': 'normal',
   'glyph-orientation-horizontal': '0deg',
   'letter-spacing': 'normal',
   'lighting-color': '#fff',
   'marker': 'none',
   'marker-start': 'none',
   'marker-mid': 'none',
   'marker-end': 'none',
   'mask': 'none',
   'opacity': '1',
   'pointer-events': 'visiblePainted',
   'stop-color': '#000',
   'stop-opacity': '1',
   'stroke': 'none',
   'stroke-dasharray': 'none',
   'stroke-dashoffset': '0',
   'stroke-linecap': 'butt',
   'stroke-linejoin': 'miter',
   'stroke-miterlimit': '4',
   'stroke-opacity': '1',
   'stroke-width': '1',
   'text-anchor': 'start',
   'text-decoration': 'none',
   'unicode-bidi': 'normal',
   'visibility': 'visible',
   'word-spacing': 'normal',
   'writing-mode': 'lr-tb',
   # SVG 1.2 tiny properties
   'audio-level': '1',
   'solid-color': '#000',
   'solid-opacity': '1',
   'text-align': 'start',
   'vector-effect': 'none',
   'viewport-fill': 'none',
   'viewport-fill-opacity': '1',
   }

def isSameSign(a,b): return (a <= 0 and b <= 0) or (a >= 0 and b >= 0)

scinumber = re.compile(r"[-+]?(\d*\.?)?\d+[eE][-+]?\d+")
number = re.compile(r"[-+]?(\d*\.?)?\d+")
sciExponent = re.compile(r"[eE]([-+]?\d+)")
unit = re.compile("(em|ex|px|pt|pc|cm|mm|in|%){1,1}$")

class Unit(object):
   # Integer constants for units.
   INVALID = -1
   NONE = 0
   PCT = 1
   PX = 2
   PT = 3
   PC = 4
   EM = 5
   EX = 6
   CM = 7
   MM = 8
   IN = 9

   # String to Unit. Basically, converts unit strings to their integer constants.
   s2u = {
      '': NONE,
      '%': PCT,
      'px': PX,
      'pt': PT,
      'pc': PC,
      'em': EM,
      'ex': EX,
      'cm': CM,
      'mm': MM,
      'in': IN,
   }

   # Unit to String. Basically, converts unit integer constants to their corresponding strings.
   u2s = {
      NONE: '',
      PCT: '%',
      PX: 'px',
      PT: 'pt',
      PC: 'pc',
      EM: 'em',
      EX: 'ex',
      CM: 'cm',
      MM: 'mm',
      IN: 'in',
   }

#  @staticmethod
   def get(unitstr):
      if unitstr is None: return Unit.NONE
      try:
         return Unit.s2u[unitstr]
      except KeyError:
         return Unit.INVALID

#  @staticmethod
   def str(unitint):
      try:
         return Unit.u2s[unitint]
      except KeyError:
         return 'INVALID'

   get = staticmethod(get)
   str = staticmethod(str)

class SVGLength(object):
   def __init__(self, str):
      try: # simple unitless and no scientific notation
         self.value = float(str)
         if int(self.value) == self.value:
            self.value = int(self.value)
         self.units = Unit.NONE
      except ValueError:
         # we know that the length string has an exponent, a unit, both or is invalid

         # parse out number, exponent and unit
         self.value = 0
         unitBegin = 0
         scinum = scinumber.match(str)
         if scinum != None:
            # this will always match, no need to check it
            numMatch = number.match(str)
            expMatch = sciExponent.search(str, numMatch.start(0))
            self.value = (float(numMatch.group(0)) *
               10 ** float(expMatch.group(1)))
            unitBegin = expMatch.end(1)
         else:
            # unit or invalid
            numMatch = number.match(str)
            if numMatch != None:
               self.value = float(numMatch.group(0))
               unitBegin = numMatch.end(0)

         if int(self.value) == self.value:
            self.value = int(self.value)

         if unitBegin != 0:
            unitMatch = unit.search(str, unitBegin)
            if unitMatch != None:
               self.units = Unit.get(unitMatch.group(0))

         # invalid
         else:
            # TODO: this needs to set the default for the given attribute (how?)
            self.value = 0
            self.units = Unit.INVALID

def findElementsWithId(node, elems=None):
   """
   Returns all elements with id attributes
   """
   if elems is None:
      elems = {}
   id = node.getAttribute('id')
   if id != '':
      elems[id] = node
   if node.hasChildNodes():
      for child in node.childNodes:
         # from http://www.w3.org/TR/DOM-Level-2-Core/idl-definitions.html
         # we are only really interested in nodes of type Element (1)
         if child.nodeType == 1:
            findElementsWithId(child, elems)
   return elems

referencingProps = ['fill', 'stroke', 'filter', 'clip-path', 'mask',  'marker-start',
               'marker-end', 'marker-mid']

def findReferencedElements(node, ids=None):
   """
   Returns the number of times an ID is referenced as well as all elements
   that reference it.  node is the node at which to start the search.  The
   return value is a map which has the id as key and each value is an array
   where the first value is a count and the second value is a list of nodes
   that referenced it.

   Currently looks at fill, stroke, clip-path, mask, marker, and
   xlink:href attributes.
   """
   global referencingProps
   if ids is None:
      ids = {}
   # TODO: input argument ids is clunky here (see below how it is called)
   # GZ: alternative to passing dict, use **kwargs

   # if this node is a style element, parse its text into CSS
   if node.nodeName == 'style' and node.namespaceURI == NS['SVG']:
      # one stretch of text, please! (we could use node.normalize(), but
      # this actually modifies the node, and we don't want to keep
      # whitespace around if there's any)
      stylesheet = "".join([child.nodeValue for child in node.childNodes])
      if stylesheet != '':
         cssRules = parseCssString(stylesheet)
         for rule in cssRules:
            for propname in rule['properties']:
               propval = rule['properties'][propname]
               findReferencingProperty(node, propname, propval, ids)
      return ids

   # else if xlink:href is set, then grab the id
   href = node.getAttributeNS(NS['XLINK'],'href')
   if href != '' and len(href) > 1 and href[0] == '#':
      # we remove the hash mark from the beginning of the id
      id = href[1:]
      if id in ids:
         ids[id][0] += 1
         ids[id][1].append(node)
      else:
         ids[id] = [1,[node]]

   # now get all style properties and the fill, stroke, filter attributes
   styles = node.getAttribute('style').split(';')
   for attr in referencingProps:
      styles.append(':'.join([attr, node.getAttribute(attr)]))

   for style in styles:
      propval = style.split(':')
      if len(propval) == 2:
         prop = propval[0].strip()
         val = propval[1].strip()
         findReferencingProperty(node, prop, val, ids)

   if node.hasChildNodes():
      for child in node.childNodes:
         if child.nodeType == 1:
            findReferencedElements(child, ids)
   return ids

def findReferencingProperty(node, prop, val, ids):
   global referencingProps
   if prop in referencingProps and val != '':
      if len(val) >= 7 and val[0:5] == 'url(#':
         id = val[5:val.find(')')]
         if id in ids:
            ids[id][0] += 1
            ids[id][1].append(node)
         else:
            ids[id] = [1,[node]]
      # if the url has a quote in it, we need to compensate
      elif len(val) >= 8:
         id = None
         # double-quote
         if val[0:6] == 'url("#':
            id = val[6:val.find('")')]
         # single-quote
         elif val[0:6] == "url('#":
            id = val[6:val.find("')")]
         if id != None:
            if id in ids:
               ids[id][0] += 1
               ids[id][1].append(node)
            else:
               ids[id] = [1,[node]]

numIDsRemoved = 0
numElemsRemoved = 0
numAttrsRemoved = 0
numRastersEmbedded = 0
numPathSegmentsReduced = 0
numCurvesStraightened = 0
numBytesSavedInPathData = 0
numBytesSavedInColors = 0
numBytesSavedInIDs = 0
numBytesSavedInLengths = 0
numBytesSavedInTransforms = 0
numPointsRemovedFromPolygon = 0
numCommentBytes = 0

def removeUnusedDefs(doc, defElem, elemsToRemove=None):
   if elemsToRemove is None:
      elemsToRemove = []

   identifiedElements = findElementsWithId(doc.documentElement)
   referencedIDs = findReferencedElements(doc.documentElement)

   keepTags = ['font', 'style', 'metadata', 'script', 'title', 'desc']
   for elem in defElem.childNodes:
      # only look at it if an element and not referenced anywhere else
      if elem.nodeType == 1 and (elem.getAttribute('id') == '' or \
            (not elem.getAttribute('id') in referencedIDs)):

         # we only inspect the children of a group in a defs if the group
         # is not referenced anywhere else
         if elem.nodeName == 'g' and elem.namespaceURI == NS['SVG']:
            elemsToRemove = removeUnusedDefs(doc, elem, elemsToRemove)
         # we only remove if it is not one of our tags we always keep (see above)
         elif not elem.nodeName in keepTags:
            elemsToRemove.append(elem)
   return elemsToRemove

def removeUnreferencedElements(doc, keepDefs):
   """
   Removes all unreferenced elements except for <svg>, <font>, <metadata>, <title>, and <desc>.
   Also vacuums the defs of any non-referenced renderable elements.

   Returns the number of unreferenced elements removed from the document.
   """
   global numElemsRemoved
   num = 0

   # Remove certain unreferenced elements outside of defs
   removeTags = ['linearGradient', 'radialGradient', 'pattern']
   identifiedElements = findElementsWithId(doc.documentElement)
   referencedIDs = findReferencedElements(doc.documentElement)

   for id in identifiedElements:
      if not id in referencedIDs:
         goner = identifiedElements[id]
         if (goner != None and goner.nodeName in removeTags
                           and goner.parentNode != None
                           and goner.parentNode.tagName != 'defs'):
            goner.parentNode.removeChild(goner)
            num += 1
            numElemsRemoved += 1

   if not keepDefs:
      # Remove most unreferenced elements inside defs
      defs = doc.documentElement.getElementsByTagName('defs')
      for aDef in defs:
         elemsToRemove = removeUnusedDefs(doc, aDef)
         for elem in elemsToRemove:
            elem.parentNode.removeChild(elem)
            numElemsRemoved += 1
            num += 1
   return num

def shortenIDs(doc, prefix, unprotectedElements=None):
   """
   Shortens ID names used in the document. ID names referenced the most often are assigned the
   shortest ID names.
   If the list unprotectedElements is provided, only IDs from this list will be shortened.

   Returns the number of bytes saved by shortening ID names in the document.
   """
   num = 0

   identifiedElements = findElementsWithId(doc.documentElement)
   if unprotectedElements is None:
      unprotectedElements = identifiedElements
   referencedIDs = findReferencedElements(doc.documentElement)

   # Make idList (list of idnames) sorted by reference count
   # descending, so the highest reference count is first.
   # First check that there's actually a defining element for the current ID name.
   # (Cyn: I've seen documents with #id references but no element with that ID!)
   idList = [(referencedIDs[rid][0], rid) for rid in referencedIDs
            if rid in unprotectedElements]
   idList.sort(reverse=True)
   idList = [rid for count, rid in idList]

   # Add unreferenced IDs to end of idList in arbitrary order
   idList.extend([rid for rid in unprotectedElements if not rid in idList])

   curIdNum = 1

   for rid in idList:
      curId = intToID(curIdNum, prefix)
      # First make sure that *this* element isn't already using
      # the ID name we want to give it.
      if curId != rid:
         # Then, skip ahead if the new ID is already in identifiedElement.
         while curId in identifiedElements:
            curIdNum += 1
            curId = intToID(curIdNum, prefix)
         # Then go rename it.
         num += renameID(doc, rid, curId, identifiedElements, referencedIDs)
      curIdNum += 1

   return num

def intToID(idnum, prefix):
   """
   Returns the ID name for the given ID number, spreadsheet-style, i.e. from a to z,
   then from aa to az, ba to bz, etc., until zz.
   """
   rid = ''

   while idnum > 0:
      idnum -= 1
      rid = chr((idnum % 26) + ord('a')) + rid
      idnum = int(idnum / 26)

   return prefix + rid

def renameID(doc, idFrom, idTo, identifiedElements, referencedIDs):
   """
   Changes the ID name from idFrom to idTo, on the declaring element
   as well as all references in the document doc.

   Updates identifiedElements and referencedIDs.
   Does not handle the case where idTo is already the ID name
   of another element in doc.

   Returns the number of bytes saved by this replacement.
   """

   num = 0

   definingNode = identifiedElements[idFrom]
   definingNode.setAttribute("id", idTo)
   del identifiedElements[idFrom]
   identifiedElements[idTo] = definingNode
   num += len(idFrom) - len(idTo)

   # Update references to renamed node
   referringNodes = referencedIDs.get(idFrom)
   if referringNodes is not None:

      # Look for the idFrom ID name in each of the referencing elements,
      # exactly like findReferencedElements would.
      # Cyn: Duplicated processing!

      for node in referringNodes[1]:
         # if this node is a style element, parse its text into CSS
         if node.nodeName == 'style' and node.namespaceURI == NS['SVG']:
            # node.firstChild will be either a CDATA or a Text node now
            if node.firstChild != None:
               # concatenate the value of all children, in case
               # there's a CDATASection node surrounded by whitespace
               # nodes
               # (node.normalize() will NOT work here, it only acts on Text nodes)
               oldValue = "".join([child.nodeValue for child in node.childNodes])
               # not going to reparse the whole thing
               newValue = oldValue.replace('url(#' + idFrom + ')', 'url(#' + idTo + ')')
               newValue = newValue.replace("url(#'" + idFrom + "')", 'url(#' + idTo + ')')
               newValue = newValue.replace('url(#"' + idFrom + '")', 'url(#' + idTo + ')')
               # and now replace all the children with this new stylesheet.
               # again, this is in case the stylesheet was a CDATASection
               node.childNodes[:] = [node.ownerDocument.createTextNode(newValue)]
               num += len(oldValue) - len(newValue)

         # if xlink:href is set to #idFrom, then change the id
         href = node.getAttributeNS(NS['XLINK'],'href')
         if href == '#' + idFrom:
            node.setAttributeNS(NS['XLINK'],'href', '#' + idTo)
            num += len(idFrom) - len(idTo)

         # if the style has url(#idFrom), then change the id
         styles = node.getAttribute('style')
         if styles != '':
            newValue = styles.replace('url(#' + idFrom + ')', 'url(#' + idTo + ')')
            newValue = newValue.replace("url('#" + idFrom + "')", 'url(#' + idTo + ')')
            newValue = newValue.replace('url("#' + idFrom + '")', 'url(#' + idTo + ')')
            node.setAttribute('style', newValue)
            num += len(styles) - len(newValue)

         # now try the fill, stroke, filter attributes
         for attr in referencingProps:
            oldValue = node.getAttribute(attr)
            if oldValue != '':
               newValue = oldValue.replace('url(#' + idFrom + ')', 'url(#' + idTo + ')')
               newValue = newValue.replace("url('#" + idFrom + "')", 'url(#' + idTo + ')')
               newValue = newValue.replace('url("#' + idFrom + '")', 'url(#' + idTo + ')')
               node.setAttribute(attr, newValue)
               num += len(oldValue) - len(newValue)

      del referencedIDs[idFrom]
      referencedIDs[idTo] = referringNodes

   return num

def unprotected_ids(doc, options):
   u"""Returns a list of unprotected IDs within the document doc."""
   identifiedElements = findElementsWithId(doc.documentElement)
   if not (options.protect_ids_noninkscape or
         options.protect_ids_list or
         options.protect_ids_prefix):
      return identifiedElements
   if options.protect_ids_list:
      protect_ids_list = options.protect_ids_list.split(",")
   if options.protect_ids_prefix:
      protect_ids_prefixes = options.protect_ids_prefix.split(",")
   for id in list(identifiedElements.keys()):
      protected = False
      if options.protect_ids_noninkscape and not id[-1].isdigit():
         protected = True
      if options.protect_ids_list and id in protect_ids_list:
         protected = True
      if options.protect_ids_prefix:
         for prefix in protect_ids_prefixes:
            if id.startswith(prefix):
               protected = True
      if protected:
         del identifiedElements[id]
   return identifiedElements

def removeUnreferencedIDs(referencedIDs, identifiedElements):
   """
   Removes the unreferenced ID attributes.

   Returns the number of ID attributes removed
   """
   global numIDsRemoved
   keepTags = ['font']
   num = 0;
   for id in list(identifiedElements.keys()):
      node = identifiedElements[id]
      if (id in referencedIDs) == False and not node.nodeName in keepTags:
         node.removeAttribute('id')
         numIDsRemoved += 1
         num += 1
   return num

def removeNamespacedAttributes(node, namespaces):
   global numAttrsRemoved
   num = 0
   if node.nodeType == 1:
      # remove all namespace'd attributes from this element
      attrList = node.attributes
      attrsToRemove = []
      for attrNum in range(attrList.length):
         attr = attrList.item(attrNum)
         if attr != None and attr.namespaceURI in namespaces:
            attrsToRemove.append(attr.nodeName)
      for attrName in attrsToRemove:
         num += 1
         numAttrsRemoved += 1
         node.removeAttribute(attrName)

      # now recurse for children
      for child in node.childNodes:
         num += removeNamespacedAttributes(child, namespaces)
   return num

def removeNamespacedElements(node, namespaces):
   global numElemsRemoved
   num = 0
   if node.nodeType == 1:
      # remove all namespace'd child nodes from this element
      childList = node.childNodes
      childrenToRemove = []
      for child in childList:
         if child != None and child.namespaceURI in namespaces:
            childrenToRemove.append(child)
      for child in childrenToRemove:
         num += 1
         numElemsRemoved += 1
         node.removeChild(child)

      # now recurse for children
      for child in node.childNodes:
         num += removeNamespacedElements(child, namespaces)
   return num

def removeDescriptiveElements(doc, options):
   elementTypes = []
   if options.remove_descriptive_elements:
      elementTypes.extend(("title", "desc", "metadata"))
   else:
      if options.remove_titles:
         elementTypes.append("title")
      if options.remove_descriptions:
         elementTypes.append("desc")
      if options.remove_metadata:
         elementTypes.append("metadata")
   if not elementTypes:
      return

   global numElemsRemoved
   num = 0
   elementsToRemove = []
   for elementType in elementTypes:
      elementsToRemove.extend(doc.documentElement.getElementsByTagName(elementType))

   for element in elementsToRemove:
      element.parentNode.removeChild(element)
      num += 1
      numElemsRemoved += 1

   return num

def removeNestedGroups(node):
   """
   This walks further and further down the tree, removing groups
   which do not have any attributes or a title/desc child and
   promoting their children up one level
   """
   global numElemsRemoved
   num = 0

   groupsToRemove = []
   # Only consider <g> elements for promotion if this element isn't a <switch>.
   # (partial fix for bug 594930, required by the SVG spec however)
   if not (node.nodeType == 1 and node.nodeName == 'switch'):
      for child in node.childNodes:
         if child.nodeName == 'g' and child.namespaceURI == NS['SVG'] and len(child.attributes) == 0:
            # only collapse group if it does not have a title or desc as a direct descendant,
            for grandchild in child.childNodes:
               if grandchild.nodeType == 1 and grandchild.namespaceURI == NS['SVG'] and \
                     grandchild.nodeName in ['title','desc']:
                  break
            else:
               groupsToRemove.append(child)

   for g in groupsToRemove:
      while g.childNodes.length > 0:
         g.parentNode.insertBefore(g.firstChild, g)
      g.parentNode.removeChild(g)
      numElemsRemoved += 1
      num += 1

   # now recurse for children
   for child in node.childNodes:
      if child.nodeType == 1:
         num += removeNestedGroups(child)
   return num

def moveCommonAttributesToParentGroup(elem, referencedElements):
   """
   This recursively calls this function on all children of the passed in element
   and then iterates over all child elements and removes common inheritable attributes
   from the children and places them in the parent group.  But only if the parent contains
   nothing but element children and whitespace.  The attributes are only removed from the
   children if the children are not referenced by other elements in the document.
   """
   num = 0

   childElements = []
   # recurse first into the children (depth-first)
   for child in elem.childNodes:
      if child.nodeType == 1:
         # only add and recurse if the child is not referenced elsewhere
         if not child.getAttribute('id') in referencedElements:
            childElements.append(child)
            num += moveCommonAttributesToParentGroup(child, referencedElements)
      # else if the parent has non-whitespace text children, do not
      # try to move common attributes
      elif child.nodeType == 3 and child.nodeValue.strip():
         return num

   # only process the children if there are more than one element
   if len(childElements) <= 1: return num

   commonAttrs = {}
   # add all inheritable properties of the first child element
   # FIXME: Note there is a chance that the first child is a set/animate in which case
   # its fill attribute is not what we want to look at, we should look for the first
   # non-animate/set element
   attrList = childElements[0].attributes
   for index in range(attrList.length):
      attr = attrList.item(index)
      # this is most of the inheritable properties from http://www.w3.org/TR/SVG11/propidx.html
      # and http://www.w3.org/TR/SVGTiny12/attributeTable.html
      if attr.nodeName in ['clip-rule',
               'display-align',
               'fill', 'fill-opacity', 'fill-rule',
               'font', 'font-family', 'font-size', 'font-size-adjust', 'font-stretch',
               'font-style', 'font-variant', 'font-weight',
               'letter-spacing',
               'pointer-events', 'shape-rendering',
               'stroke', 'stroke-dasharray', 'stroke-dashoffset', 'stroke-linecap', 'stroke-linejoin',
               'stroke-miterlimit', 'stroke-opacity', 'stroke-width',
               'text-anchor', 'text-decoration', 'text-rendering', 'visibility',
               'word-spacing', 'writing-mode']:
         # we just add all the attributes from the first child
         commonAttrs[attr.nodeName] = attr.nodeValue

   # for each subsequent child element
   for childNum in range(len(childElements)):
      # skip first child
      if childNum == 0:
         continue

      child = childElements[childNum]
      # if we are on an animateXXX/set element, ignore it (due to the 'fill' attribute)
      if child.localName in ['set', 'animate', 'animateColor', 'animateTransform', 'animateMotion']:
         continue

      distinctAttrs = []
      # loop through all current 'common' attributes
      for name in list(commonAttrs.keys()):
         # if this child doesn't match that attribute, schedule it for removal
         if child.getAttribute(name) != commonAttrs[name]:
            distinctAttrs.append(name)
      # remove those attributes which are not common
      for name in distinctAttrs:
         del commonAttrs[name]

   # commonAttrs now has all the inheritable attributes which are common among all child elements
   for name in list(commonAttrs.keys()):
      for child in childElements:
         child.removeAttribute(name)
      elem.setAttribute(name, commonAttrs[name])

   # update our statistic (we remove N*M attributes and add back in M attributes)
   num += (len(childElements)-1) * len(commonAttrs)
   return num

def createGroupsForCommonAttributes(elem):
   """
   Creates <g> elements to contain runs of 3 or more
   consecutive child elements having at least one common attribute.

   Common attributes are not promoted to the <g> by this function.
   This is handled by moveCommonAttributesToParentGroup.

   If all children have a common attribute, an extra <g> is not created.

   This function acts recursively on the given element.
   """
   num = 0
   global numElemsRemoved

   # TODO perhaps all of the Presentation attributes in http://www.w3.org/TR/SVG/struct.html#GElement
   # could be added here
   # Cyn: These attributes are the same as in moveAttributesToParentGroup, and must always be
   for curAttr in ['clip-rule',
            'display-align',
            'fill', 'fill-opacity', 'fill-rule',
            'font', 'font-family', 'font-size', 'font-size-adjust', 'font-stretch',
            'font-style', 'font-variant', 'font-weight',
            'letter-spacing',
            'pointer-events', 'shape-rendering',
            'stroke', 'stroke-dasharray', 'stroke-dashoffset', 'stroke-linecap', 'stroke-linejoin',
            'stroke-miterlimit', 'stroke-opacity', 'stroke-width',
            'text-anchor', 'text-decoration', 'text-rendering', 'visibility',
            'word-spacing', 'writing-mode']:
      # Iterate through the children in reverse order, so item(i) for
      # items we have yet to visit still returns the correct nodes.
      curChild = elem.childNodes.length - 1
      while curChild >= 0:
         childNode = elem.childNodes.item(curChild)

         if childNode.nodeType == 1 and childNode.getAttribute(curAttr) != '' and \
               childNode.nodeName in [
                  # only attempt to group elements that the content model allows to be children of a <g>

                  # SVG 1.1 (see https://www.w3.org/TR/SVG/struct.html#GElement)
                  'animate', 'animateColor', 'animateMotion', 'animateTransform', 'set', # animation elements
                  'desc', 'metadata', 'title',                                           # descriptive elements
                  'circle', 'ellipse', 'line', 'path', 'polygon', 'polyline', 'rect',    # shape elements
                  'defs', 'g', 'svg', 'symbol', 'use',                                   # structural elements
                  'linearGradient', 'radialGradient',                                    # gradient elements
                  'a', 'altGlyphDef', 'clipPath', 'color-profile', 'cursor', 'filter',
                  'font', 'font-face', 'foreignObject', 'image', 'marker', 'mask',
                  'pattern', 'script', 'style', 'switch', 'text', 'view',

                  # SVG 1.2 (see https://www.w3.org/TR/SVGTiny12/elementTable.html)
                  'animation', 'audio', 'discard', 'handler', 'listener',
                  'prefetch', 'solidColor', 'textArea', 'video'
               ]:
            # We're in a possible run! Track the value and run length.
            value = childNode.getAttribute(curAttr)
            runStart, runEnd = curChild, curChild
            # Run elements includes only element tags, no whitespace/comments/etc.
            # Later, we calculate a run length which includes these.
            runElements = 1

            # Backtrack to get all the nodes having the same
            # attribute value, preserving any nodes in-between.
            while runStart > 0:
               nextNode = elem.childNodes.item(runStart - 1)
               if nextNode.nodeType == 1:
                  if nextNode.getAttribute(curAttr) != value: break
                  else:
                     runElements += 1
                     runStart -= 1
               else: runStart -= 1

            if runElements >= 3:
               # Include whitespace/comment/etc. nodes in the run.
               while runEnd < elem.childNodes.length - 1:
                  if elem.childNodes.item(runEnd + 1).nodeType == 1: break
                  else: runEnd += 1

               runLength = runEnd - runStart + 1
               if runLength == elem.childNodes.length: # Every child has this
                  # If the current parent is a <g> already,
                  if elem.nodeName == 'g' and elem.namespaceURI == NS['SVG']:
                     # do not act altogether on this attribute; all the
                     # children have it in common.
                     # Let moveCommonAttributesToParentGroup do it.
                     curChild = -1
                     continue
                  # otherwise, it might be an <svg> element, and
                  # even if all children have the same attribute value,
                  # it's going to be worth making the <g> since
                  # <svg> doesn't support attributes like 'stroke'.
                  # Fall through.

               # Create a <g> element from scratch.
               # We need the Document for this.
               document = elem.ownerDocument
               group = document.createElementNS(NS['SVG'], 'g')
               # Move the run of elements to the group.
               # a) ADD the nodes to the new group.
               group.childNodes[:] = elem.childNodes[runStart:runEnd + 1]
               for child in group.childNodes:
                  child.parentNode = group
               # b) REMOVE the nodes from the element.
               elem.childNodes[runStart:runEnd + 1] = []
               # Include the group in elem's children.
               elem.childNodes.insert(runStart, group)
               group.parentNode = elem
               num += 1
               curChild = runStart - 1
               numElemsRemoved -= 1
            else:
               curChild -= 1
         else:
            curChild -= 1

   # each child gets the same treatment, recursively
   for childNode in elem.childNodes:
      if childNode.nodeType == 1:
         num += createGroupsForCommonAttributes(childNode)

   return num

def removeUnusedAttributesOnParent(elem):
   """
   This recursively calls this function on all children of the element passed in,
   then removes any unused attributes on this elem if none of the children inherit it
   """
   num = 0

   childElements = []
   # recurse first into the children (depth-first)
   for child in elem.childNodes:
      if child.nodeType == 1:
         childElements.append(child)
         num += removeUnusedAttributesOnParent(child)

   # only process the children if there are more than one element
   if len(childElements) <= 1: return num

   # get all attribute values on this parent
   attrList = elem.attributes
   unusedAttrs = {}
   for index in range(attrList.length):
      attr = attrList.item(index)
      if attr.nodeName in ['clip-rule',
               'display-align',
               'fill', 'fill-opacity', 'fill-rule',
               'font', 'font-family', 'font-size', 'font-size-adjust', 'font-stretch',
               'font-style', 'font-variant', 'font-weight',
               'letter-spacing',
               'pointer-events', 'shape-rendering',
               'stroke', 'stroke-dasharray', 'stroke-dashoffset', 'stroke-linecap', 'stroke-linejoin',
               'stroke-miterlimit', 'stroke-opacity', 'stroke-width',
               'text-anchor', 'text-decoration', 'text-rendering', 'visibility',
               'word-spacing', 'writing-mode']:
         unusedAttrs[attr.nodeName] = attr.nodeValue

   # for each child, if at least one child inherits the parent's attribute, then remove
   for childNum in range(len(childElements)):
      child = childElements[childNum]
      inheritedAttrs = []
      for name in list(unusedAttrs.keys()):
         val = child.getAttribute(name)
         if val == '' or val == None or val == 'inherit':
            inheritedAttrs.append(name)
      for a in inheritedAttrs:
         del unusedAttrs[a]

   # unusedAttrs now has all the parent attributes that are unused
   for name in list(unusedAttrs.keys()):
      elem.removeAttribute(name)
      num += 1

   return num

def removeDuplicateGradientStops(doc):
   global numElemsRemoved
   num = 0

   for gradType in ['linearGradient', 'radialGradient']:
      for grad in doc.getElementsByTagName(gradType):
         stops = {}
         stopsToRemove = []
         for stop in grad.getElementsByTagName('stop'):
            # convert percentages into a floating point number
            offsetU = SVGLength(stop.getAttribute('offset'))
            if offsetU.units == Unit.PCT:
               offset = offsetU.value / 100.0
            elif offsetU.units == Unit.NONE:
               offset = offsetU.value
            else:
               offset = 0
            # set the stop offset value to the integer or floating point equivalent
            if int(offset) == offset: stop.setAttribute('offset', str(int(offset)))
            else: stop.setAttribute('offset', str(offset))

            color = stop.getAttribute('stop-color')
            opacity = stop.getAttribute('stop-opacity')
            style = stop.getAttribute('style')
            if offset in stops:
               oldStop = stops[offset]
               if oldStop[0] == color and oldStop[1] == opacity and oldStop[2] == style:
                  stopsToRemove.append(stop)
            stops[offset] = [color, opacity, style]

         for stop in stopsToRemove:
            stop.parentNode.removeChild(stop)
            num += 1
            numElemsRemoved += 1

   # linear gradients
   return num

def collapseSinglyReferencedGradients(doc):
   global numElemsRemoved
   num = 0

   identifiedElements = findElementsWithId(doc.documentElement)

   # make sure to reset the ref'ed ids for when we are running this in testscour
   for rid,nodeCount in six.iteritems(findReferencedElements(doc.documentElement)):
      count = nodeCount[0]
      nodes = nodeCount[1]
      # Make sure that there's actually a defining element for the current ID name.
      # (Cyn: I've seen documents with #id references but no element with that ID!)
      if count == 1 and rid in identifiedElements:
         elem = identifiedElements[rid]
         if elem != None and elem.nodeType == 1 and elem.nodeName in ['linearGradient', 'radialGradient'] \
               and elem.namespaceURI == NS['SVG']:
            # found a gradient that is referenced by only 1 other element
            refElem = nodes[0]
            if refElem.nodeType == 1 and refElem.nodeName in ['linearGradient', 'radialGradient'] \
                  and refElem.namespaceURI == NS['SVG']:
               # elem is a gradient referenced by only one other gradient (refElem)

               # add the stops to the referencing gradient (this removes them from elem)
               if len(refElem.getElementsByTagName('stop')) == 0:
                  stopsToAdd = elem.getElementsByTagName('stop')
                  for stop in stopsToAdd:
                     refElem.appendChild(stop)

               # adopt the gradientUnits, spreadMethod,  gradientTransform attributes if
               # they are unspecified on refElem
               for attr in ['gradientUnits','spreadMethod','gradientTransform']:
                  if refElem.getAttribute(attr) == '' and not elem.getAttribute(attr) == '':
                     refElem.setAttributeNS(None, attr, elem.getAttribute(attr))

               # if both are radialGradients, adopt elem's fx,fy,cx,cy,r attributes if
               # they are unspecified on refElem
               if elem.nodeName == 'radialGradient' and refElem.nodeName == 'radialGradient':
                  for attr in ['fx','fy','cx','cy','r']:
                     if refElem.getAttribute(attr) == '' and not elem.getAttribute(attr) == '':
                        refElem.setAttributeNS(None, attr, elem.getAttribute(attr))

               # if both are linearGradients, adopt elem's x1,y1,x2,y2 attributes if
               # they are unspecified on refElem
               if elem.nodeName == 'linearGradient' and refElem.nodeName == 'linearGradient':
                  for attr in ['x1','y1','x2','y2']:
                     if refElem.getAttribute(attr) == '' and not elem.getAttribute(attr) == '':
                        refElem.setAttributeNS(None, attr, elem.getAttribute(attr))

               # now remove the xlink:href from refElem
               refElem.removeAttributeNS(NS['XLINK'], 'href')

               # now delete elem
               elem.parentNode.removeChild(elem)
               numElemsRemoved += 1
               num += 1
   return num

def removeDuplicateGradients(doc):
   global numElemsRemoved
   num = 0

   gradientsToRemove = {}
   duplicateToMaster = {}

   for gradType in ['linearGradient', 'radialGradient']:
      grads = doc.getElementsByTagName(gradType)
      for grad in grads:
         # TODO: should slice grads from 'grad' here to optimize
         for ograd in grads:
            # do not compare gradient to itself
            if grad == ograd: continue

            # compare grad to ograd (all properties, then all stops)
            # if attributes do not match, go to next gradient
            someGradAttrsDoNotMatch = False
            for attr in ['gradientUnits','spreadMethod','gradientTransform','x1','y1','x2','y2','cx','cy','fx','fy','r']:
               if grad.getAttribute(attr) != ograd.getAttribute(attr):
                  someGradAttrsDoNotMatch = True
                  break;

            if someGradAttrsDoNotMatch: continue

            # compare xlink:href values too
            if grad.getAttributeNS(NS['XLINK'], 'href') != ograd.getAttributeNS(NS['XLINK'], 'href'):
               continue

            # all gradient properties match, now time to compare stops
            stops = grad.getElementsByTagName('stop')
            ostops = ograd.getElementsByTagName('stop')

            if stops.length != ostops.length: continue

            # now compare stops
            stopsNotEqual = False
            for i in range(stops.length):
               if stopsNotEqual: break
               stop = stops.item(i)
               ostop = ostops.item(i)
               for attr in ['offset', 'stop-color', 'stop-opacity', 'style']:
                  if stop.getAttribute(attr) != ostop.getAttribute(attr):
                     stopsNotEqual = True
                     break
            if stopsNotEqual: continue

            # ograd is a duplicate of grad, we schedule it to be removed UNLESS
            # ograd is ALREADY considered a 'master' element
            if ograd not in gradientsToRemove:
               if ograd not in duplicateToMaster:
                  if grad not in gradientsToRemove:
                     gradientsToRemove[grad] = []
                  gradientsToRemove[grad].append( ograd )
                  duplicateToMaster[ograd] = grad

   # get a collection of all elements that are referenced and their referencing elements
   referencedIDs = findReferencedElements(doc.documentElement)
   for masterGrad in list(gradientsToRemove.keys()):
      master_id = masterGrad.getAttribute('id')
      for dupGrad in gradientsToRemove[masterGrad]:
         # if the duplicate gradient no longer has a parent that means it was
         # already re-mapped to another master gradient
         if not dupGrad.parentNode:
            continue

         # for each element that referenced the gradient we are going to replace dup_id with master_id
         dup_id = dupGrad.getAttribute('id')
         funcIRI = re.compile('url\([\'"]?#' + dup_id + '[\'"]?\)') # matches url(#a), url('#a') and url("#a")
         for elem in referencedIDs[dup_id][1]:
            # find out which attribute referenced the duplicate gradient
            for attr in ['fill', 'stroke']:
               v = elem.getAttribute(attr)
               (v_new, n) = funcIRI.subn('url(#'+master_id+')', v)
               if n > 0:
                  elem.setAttribute(attr, v_new)
            if elem.getAttributeNS(NS['XLINK'], 'href') == '#'+dup_id:
               elem.setAttributeNS(NS['XLINK'], 'href', '#'+master_id)
            styles = _getStyle(elem)
            for style in styles:
               v = styles[style]
               (v_new, n) = funcIRI.subn('url(#'+master_id+')', v)
               if n > 0:
                  styles[style] = v_new
            _setStyle(elem, styles)

         # now that all referencing elements have been re-mapped to the master
         # it is safe to remove this gradient from the document
         dupGrad.parentNode.removeChild(dupGrad)
         numElemsRemoved += 1
         num += 1
   return num

def _getStyle(node):
   u"""Returns the style attribute of a node as a dictionary."""
   if node.nodeType == 1 and len(node.getAttribute('style')) > 0:
      styleMap = { }
      rawStyles = node.getAttribute('style').split(';')
      for style in rawStyles:
         propval = style.split(':')
         if len(propval) == 2:
            styleMap[propval[0].strip()] = propval[1].strip()
      return styleMap
   else:
      return {}

def _setStyle(node, styleMap):
   u"""Sets the style attribute of a node to the dictionary ``styleMap``."""
   fixedStyle = ';'.join([prop + ':' + styleMap[prop] for prop in list(styleMap.keys())])
   if fixedStyle != '':
      node.setAttribute('style', fixedStyle)
   elif node.getAttribute('style'):
      node.removeAttribute('style')
   return node

def repairStyle(node, options):
   num = 0
   styleMap = _getStyle(node)
   if styleMap:

      # I've seen this enough to know that I need to correct it:
      # fill: url(#linearGradient4918) rgb(0, 0, 0);
      for prop in ['fill', 'stroke']:
         if prop in styleMap:
            chunk = styleMap[prop].split(') ')
            if len(chunk) == 2 and (chunk[0][:5] == 'url(#' or chunk[0][:6] == 'url("#' or chunk[0][:6] == "url('#") and chunk[1] == 'rgb(0, 0, 0)':
               styleMap[prop] = chunk[0] + ')'
               num += 1

      # Here is where we can weed out unnecessary styles like:
      #  opacity:1
      if 'opacity' in styleMap:
         opacity = float(styleMap['opacity'])
         # if opacity='0' then all fill and stroke properties are useless, remove them
         if opacity == 0.0:
            for uselessStyle in ['fill', 'fill-opacity', 'fill-rule', 'stroke', 'stroke-linejoin',
               'stroke-opacity', 'stroke-miterlimit', 'stroke-linecap', 'stroke-dasharray',
               'stroke-dashoffset', 'stroke-opacity']:
               if uselessStyle in styleMap and not styleInheritedByChild(node, uselessStyle):
                  del styleMap[uselessStyle]
                  num += 1

      #  if stroke:none, then remove all stroke-related properties (stroke-width, etc)
      #  TODO: should also detect if the computed value of this element is stroke="none"
      if 'stroke' in styleMap and styleMap['stroke'] == 'none':
         for strokestyle in [ 'stroke-width', 'stroke-linejoin', 'stroke-miterlimit',
               'stroke-linecap', 'stroke-dasharray', 'stroke-dashoffset', 'stroke-opacity']:
            if strokestyle in styleMap and not styleInheritedByChild(node, strokestyle):
               del styleMap[strokestyle]
               num += 1
         # we need to properly calculate computed values
         if not styleInheritedByChild(node, 'stroke'):
            if styleInheritedFromParent(node, 'stroke') in [None, 'none']:
               del styleMap['stroke']
               num += 1

      #  if fill:none, then remove all fill-related properties (fill-rule, etc)
      if 'fill' in styleMap and styleMap['fill'] == 'none':
         for fillstyle in [ 'fill-rule', 'fill-opacity' ]:
            if fillstyle in styleMap and not styleInheritedByChild(node, fillstyle):
               del styleMap[fillstyle]
               num += 1

      #  fill-opacity: 0
      if 'fill-opacity' in styleMap:
         fillOpacity = float(styleMap['fill-opacity'])
         if fillOpacity == 0.0:
            for uselessFillStyle in [ 'fill', 'fill-rule' ]:
               if uselessFillStyle in styleMap and not styleInheritedByChild(node, uselessFillStyle):
                  del styleMap[uselessFillStyle]
                  num += 1

      #  stroke-opacity: 0
      if 'stroke-opacity' in styleMap:
         strokeOpacity = float(styleMap['stroke-opacity'])
         if strokeOpacity == 0.0:
            for uselessStrokeStyle in [ 'stroke', 'stroke-width', 'stroke-linejoin', 'stroke-linecap',
                     'stroke-dasharray', 'stroke-dashoffset' ]:
               if uselessStrokeStyle in styleMap and not styleInheritedByChild(node, uselessStrokeStyle):
                  del styleMap[uselessStrokeStyle]
                  num += 1

      # stroke-width: 0
      if 'stroke-width' in styleMap:
         strokeWidth = SVGLength(styleMap['stroke-width'])
         if strokeWidth.value == 0.0:
            for uselessStrokeStyle in [ 'stroke', 'stroke-linejoin', 'stroke-linecap',
                     'stroke-dasharray', 'stroke-dashoffset', 'stroke-opacity' ]:
               if uselessStrokeStyle in styleMap and not styleInheritedByChild(node, uselessStrokeStyle):
                  del styleMap[uselessStrokeStyle]
                  num += 1

      # remove font properties for non-text elements
      # I've actually observed this in real SVG content
      if not mayContainTextNodes(node):
         for fontstyle in [ 'font-family', 'font-size', 'font-stretch', 'font-size-adjust',
                        'font-style', 'font-variant', 'font-weight',
                        'letter-spacing', 'line-height', 'kerning',
                        'text-align', 'text-anchor', 'text-decoration',
                        'text-rendering', 'unicode-bidi',
                        'word-spacing', 'writing-mode']:
            if fontstyle in styleMap:
               del styleMap[fontstyle]
               num += 1

      # remove inkscape-specific styles
      # TODO: need to get a full list of these
      for inkscapeStyle in ['-inkscape-font-specification']:
         if inkscapeStyle in styleMap:
            del styleMap[inkscapeStyle]
            num += 1

      if 'overflow' in styleMap:
         # remove overflow from elements to which it does not apply,
         # see https://www.w3.org/TR/SVG/masking.html#OverflowProperty
         if not node.nodeName in ['svg','symbol','image','foreignObject','marker','pattern']:
            del styleMap['overflow']
            num += 1
         # if the node is not the root <svg> element the SVG's user agent style sheet
         # overrides the initial (i.e. default) value with the value 'hidden', which can consequently be removed
         # (see last bullet point in the link above)
         elif node != node.ownerDocument.documentElement:
            if styleMap['overflow'] == 'hidden':
               del styleMap['overflow']
               num += 1
         # on the root <svg> element the CSS2 default overflow="visible" is the initial value and we can remove it
         elif styleMap['overflow'] == 'visible':
            del styleMap['overflow']
            num += 1

      # now if any of the properties match known SVG attributes we prefer attributes
      # over style so emit them and remove them from the style map
      if options.style_to_xml:
         for propName in list(styleMap.keys()):
            if propName in svgAttributes:
               node.setAttribute(propName, styleMap[propName])
               del styleMap[propName]

      _setStyle(node, styleMap)

   # recurse for our child elements
   for child in node.childNodes:
      num += repairStyle(child,options)

   return num

def styleInheritedFromParent(node, style):
   """
   Returns the value of 'style' that is inherited from the parents of the passed-in node

   Warning: This method only considers presentation attributes and inline styles,
            any style sheets are ignored!
   """
   parentNode = node.parentNode;

   # return None if we reached the Document element
   if parentNode.nodeType == 9:
      return None

   # check styles first (they take precedence over presentation attributes)
   styles = _getStyle(parentNode)
   if style in styles.keys():
      value = styles[style]
      if not value == 'inherit':
         return value

   # check attributes
   value = parentNode.getAttribute(style)
   if value not in ['', 'inherit']:
      return parentNode.getAttribute(style)

   # check the next parent recursively if we did not find a value yet
   return styleInheritedFromParent(parentNode, style)

def styleInheritedByChild(node, style, nodeIsChild=False):
   """
   Returns whether 'style' is inherited by any children of the passed-in node

   If False is returned, it is guaranteed that 'style' can safely be removed
   from the passed-in node without influencing visual output of it's children

   If True is returned, the passed-in node should not have its text-based
   attributes removed.

   Warning: This method only considers presentation attributes and inline styles,
            any style sheets are ignored!
   """
   # Comment, text and CDATA nodes don't have attributes and aren't containers so they can't inherit attributes
   if node.nodeType != 1:
      return False


   if nodeIsChild:
      # if the current child node sets a new value for 'style'
      # we can stop the search in the current branch of the DOM tree

      # check attributes
      if node.getAttribute(style) not in ['', 'inherit']:
         return False
      # check styles
      styles = _getStyle(node)
      if (style in styles.keys()) and not (styles[style] == 'inherit'):
         return False
   else:
      # if the passed-in node does not have any children 'style' can obviously not be inherited
      if not node.childNodes:
         return False

   # If we have child nodes recursively check those
   if node.childNodes:
      for child in node.childNodes:
         if styleInheritedByChild(child, style, True):
            return True

   # If the current element is a container element the inherited style is meaningless
   # (since we made sure it's not inherited by any of its children)
   if node.nodeName in ['a', 'defs', 'glyph', 'g', 'marker', 'mask', 'missing-glyph', 'pattern', 'svg', 'switch', 'symbol']:
      return False

   # in all other cases we have to assume the inherited value of 'style' is meaningfull and has to be kept
   # (e.g nodes without children at the end of the DOM tree, text nodes, ...)
   return True

def mayContainTextNodes(node):
   """
   Returns True if the passed-in node is probably a text element, or at least
   one of its descendants is probably a text element.

   If False is returned, it is guaranteed that the passed-in node has no
   business having text-based attributes.

   If True is returned, the passed-in node should not have its text-based
   attributes removed.
   """
   # Cached result of a prior call?
   try:
      return node.mayContainTextNodes
   except AttributeError:
      pass

   result = True # Default value
   # Comment, text and CDATA nodes don't have attributes and aren't containers
   if node.nodeType != 1:
      result = False
   # Non-SVG elements? Unknown elements!
   elif node.namespaceURI != NS['SVG']:
      result = True
   # Blacklisted elements. Those are guaranteed not to be text elements.
   elif node.nodeName in ['rect', 'circle', 'ellipse', 'line', 'polygon',
                          'polyline', 'path', 'image', 'stop']:
      result = False
   # Group elements. If we're missing any here, the default of True is used.
   elif node.nodeName in ['g', 'clipPath', 'marker', 'mask', 'pattern',
                          'linearGradient', 'radialGradient', 'symbol']:
      result = False
      for child in node.childNodes:
         if mayContainTextNodes(child):
            result = True
   # Everything else should be considered a future SVG-version text element
   # at best, or an unknown element at worst. result will stay True.

   # Cache this result before returning it.
   node.mayContainTextNodes = result
   return result


# A list of default attributes that are safe to remove if all conditions are fulfilled
#
# Each default attribute is an object of type 'DefaultAttribute' with the following fields:
#    name       - name of the attribute to be matched
#    value      - default value of the attribute
#    units      - the unit(s) for which 'value' is valid (see 'Unit' class for possible specifications)
#    elements   - name(s) of SVG element(s) for which the attribute specification is valid
#    conditions - additional conditions that have to be fulfilled for removal of the specified default attribute
#                 implemented as lambda functions with one argument (a xml.dom.minidom node) evaluating to True or False
# When not specifying a field value, it will be ignored (i.e. always matches)
#
# Sources for this list:
#    https://www.w3.org/TR/SVG/attindex.html             (mostly implemented)
#    https://www.w3.org/TR/SVGTiny12/attributeTable.html (not yet implemented)
#    https://www.w3.org/TR/SVG2/attindex.html            (not yet implemented)
#
DefaultAttribute = namedtuple('DefaultAttribute', ['name', 'value', 'units', 'elements', 'conditions'])
DefaultAttribute.__new__.__defaults__ = (None,) * len(DefaultAttribute._fields)
default_attributes = [
   # unit systems
   DefaultAttribute('clipPathUnits', 'userSpaceOnUse', elements = 'clipPath'),
   DefaultAttribute('filterUnits', 'objectBoundingBox', elements = 'filter'),
   DefaultAttribute('gradientUnits', 'objectBoundingBox', elements = ['linearGradient', 'radialGradient']),
   DefaultAttribute('maskUnits', 'objectBoundingBox', elements = 'mask'),
   DefaultAttribute('maskContentUnits', 'userSpaceOnUse', elements = 'mask'),
   DefaultAttribute('patternUnits', 'objectBoundingBox', elements = 'pattern'),
   DefaultAttribute('patternContentUnits', 'userSpaceOnUse', elements = 'pattern'),
   DefaultAttribute('primitiveUnits', 'userSpaceOnUse', elements = 'filter'),

   DefaultAttribute('externalResourcesRequired', 'false', elements = ['a', 'altGlyph', 'animate', 'animateColor',
      'animateMotion', 'animateTransform', 'circle', 'clipPath', 'cursor', 'defs', 'ellipse', 'feImage', 'filter',
      'font', 'foreignObject', 'g', 'image', 'line', 'linearGradient', 'marker', 'mask', 'mpath', 'path', 'pattern',
      'polygon', 'polyline', 'radialGradient', 'rect', 'script', 'set', 'svg', 'switch', 'symbol', 'text', 'textPath',
      'tref', 'tspan', 'use', 'view']),

   # svg elements
   DefaultAttribute('width', 100, Unit.PCT, elements = 'svg'),
   DefaultAttribute('height', 100, Unit.PCT, elements = 'svg'),
   DefaultAttribute('baseProfile', 'none', elements = 'svg'),
   DefaultAttribute('preserveAspectRatio', 'xMidYMid meet', elements = ['feImage', 'image', 'marker', 'pattern', 'svg', 'symbol', 'view']),

   # common attributes / basic types
   DefaultAttribute('x',  0, elements = ['cursor', 'fePointLight', 'feSpotLight', 'foreignObject', 'image', 'pattern', 'rect', 'svg', 'text', 'use']),
   DefaultAttribute('y',  0, elements = ['cursor', 'fePointLight', 'feSpotLight', 'foreignObject', 'image', 'pattern', 'rect', 'svg', 'text', 'use']),
   DefaultAttribute('z',  0, elements = ['fePointLight', 'feSpotLight']),
   DefaultAttribute('x1', 0, elements = 'line'),
   DefaultAttribute('y1', 0, elements = 'line'),
   DefaultAttribute('x2', 0, elements = 'line'),
   DefaultAttribute('y2', 0, elements = 'line'),
   DefaultAttribute('cx', 0, elements = ['circle', 'ellipse']),
   DefaultAttribute('cy', 0, elements = ['circle', 'ellipse']),

   # markers
   DefaultAttribute('markerUnits', 'strokeWidth', elements = 'marker'),
   DefaultAttribute('refX', 0, elements = 'marker'),
   DefaultAttribute('refY', 0, elements = 'marker'),
   DefaultAttribute('markerHeight', 3, elements = 'marker'),
   DefaultAttribute('markerWidth', 3, elements = 'marker'),
   DefaultAttribute('orient', 0, elements = 'marker'),

   # text / textPath / tspan / tref
   DefaultAttribute('lengthAdjust', 'spacing', elements = ['text', 'textPath', 'tref', 'tspan']),
   DefaultAttribute('startOffset', 0, elements = 'textPath'),
   DefaultAttribute('method', 'align', elements = 'textPath'),
   DefaultAttribute('spacing', 'exact', elements = 'textPath'),

   # filters and masks
   DefaultAttribute('x', -10, Unit.PCT, ['filter', 'mask']),
   DefaultAttribute('x', -0.1, Unit.NONE, ['filter', 'mask'], lambda node: node.getAttribute('gradientUnits') != 'userSpaceOnUse'),
   DefaultAttribute('y', -10, Unit.PCT, ['filter', 'mask']),
   DefaultAttribute('y', -0.1, Unit.NONE, ['filter', 'mask'], lambda node: node.getAttribute('gradientUnits') != 'userSpaceOnUse'),
   DefaultAttribute('width', 120, Unit.PCT, ['filter', 'mask']),
   DefaultAttribute('width', 1.2, Unit.NONE, ['filter', 'mask'], lambda node: node.getAttribute('gradientUnits') != 'userSpaceOnUse'),
   DefaultAttribute('height', 120, Unit.PCT, ['filter', 'mask']),
   DefaultAttribute('height', 1.2, Unit.NONE, ['filter', 'mask'], lambda node: node.getAttribute('gradientUnits') != 'userSpaceOnUse'),

   # gradients
   DefaultAttribute('x1', 0, elements = 'linearGradient'),
   DefaultAttribute('y1', 0, elements = 'linearGradient'),
   DefaultAttribute('y2', 0, elements = 'linearGradient'),
   DefaultAttribute('x2', 100, Unit.PCT, 'linearGradient'),
   DefaultAttribute('x2', 1, Unit.NONE, 'linearGradient', lambda node: node.getAttribute('gradientUnits') != 'userSpaceOnUse'),
   # remove fx/fy before cx/cy to catch the case where fx = cx = 50% or fy = cy = 50% respectively
   DefaultAttribute('fx', elements = 'radialGradient', conditions = lambda node: node.getAttribute('fx') == node.getAttribute('cx')),
   DefaultAttribute('fy', elements = 'radialGradient', conditions = lambda node: node.getAttribute('fy') == node.getAttribute('cy')),
   DefaultAttribute('r',  50, Unit.PCT, 'radialGradient'),
   DefaultAttribute('r',  0.5, Unit.NONE, 'radialGradient', lambda node: node.getAttribute('gradientUnits') != 'userSpaceOnUse'),
   DefaultAttribute('cx', 50, Unit.PCT, 'radialGradient'),
   DefaultAttribute('cx', 0.5, Unit.NONE, 'radialGradient', lambda node: node.getAttribute('gradientUnits') != 'userSpaceOnUse'),
   DefaultAttribute('cy', 50, Unit.PCT, 'radialGradient'),
   DefaultAttribute('cy', 0.5, Unit.NONE, 'radialGradient', lambda node: node.getAttribute('gradientUnits') != 'userSpaceOnUse'),
   DefaultAttribute('spreadMethod', 'pad'),

   # filter effects
   DefaultAttribute('amplitude', 1, elements = ['feFuncA', 'feFuncB', 'feFuncG', 'feFuncR']),
   DefaultAttribute('azimuth', 0, elements = 'feDistantLight'),
   DefaultAttribute('baseFrequency', 0, elements = ['feFuncA', 'feFuncB', 'feFuncG', 'feFuncR']),
   DefaultAttribute('bias', 1, elements = 'feConvolveMatrix'),
   DefaultAttribute('diffuseConstant', 1, elements = 'feDiffuseLighting'),
   DefaultAttribute('edgeMode', 'duplicate', elements = 'feConvolveMatrix'),
   DefaultAttribute('elevation', 0, elements = 'feDistantLight'),
   DefaultAttribute('exponent', 1, elements = ['feFuncA', 'feFuncB', 'feFuncG', 'feFuncR']),
   DefaultAttribute('intercept', 0, elements = ['feFuncA', 'feFuncB', 'feFuncG', 'feFuncR']),
   DefaultAttribute('k1', 0, elements = 'feComposite'),
   DefaultAttribute('k2', 0, elements = 'feComposite'),
   DefaultAttribute('k3', 0, elements = 'feComposite'),
   DefaultAttribute('k4', 0, elements = 'feComposite'),
   DefaultAttribute('mode', 'normal', elements = 'feBlend'),
   DefaultAttribute('numOctaves', 1, elements = 'feTurbulence'),
   DefaultAttribute('offset', 0, elements = ['feFuncA', 'feFuncB', 'feFuncG', 'feFuncR']),
   DefaultAttribute('operator', 'over', elements = 'feComposite'),
   DefaultAttribute('operator', 'erode', elements = 'feMorphology'),
   DefaultAttribute('order', 3, elements = 'feConvolveMatrix'),
   DefaultAttribute('pointsAtX', 0, elements = 'feSpotLight'),
   DefaultAttribute('pointsAtY', 0, elements = 'feSpotLight'),
   DefaultAttribute('pointsAtZ', 0, elements = 'feSpotLight'),
   DefaultAttribute('preserveAlpha', 'false', elements = 'feConvolveMatrix'),
   DefaultAttribute('scale', 0, elements = 'feDisplacementMap'),
   DefaultAttribute('seed', 0, elements = 'feTurbulence'),
   DefaultAttribute('specularConstant', 1, elements = 'feSpecularLighting'),
   DefaultAttribute('specularExponent', 1, elements = ['feSpecularLighting', 'feSpotLight']),
   DefaultAttribute('stdDeviation', 0, elements = 'feGaussianBlur'),
   DefaultAttribute('stitchTiles', 'noStitch', elements = 'feTurbulence'),
   DefaultAttribute('surfaceScale', 1, elements = ['feDiffuseLighting', 'feSpecularLighting']),
   DefaultAttribute('type', 'matrix', elements = 'feColorMatrix'),
   DefaultAttribute('type', 'turbulence', elements = 'feTurbulence'),
   DefaultAttribute('xChannelSelector', 'A', elements = 'feDisplacementMap'),
   DefaultAttribute('yChannelSelector', 'A', elements = 'feDisplacementMap')
]

def taint(taintedSet, taintedAttribute):
   u"""Adds an attribute to a set of attributes.

   Related attributes are also included."""
   taintedSet.add(taintedAttribute)
   if taintedAttribute == 'marker':
      taintedSet |= set(['marker-start', 'marker-mid', 'marker-end'])
   if taintedAttribute in ['marker-start', 'marker-mid', 'marker-end']:
      taintedSet.add('marker')
   return taintedSet

def removeDefaultAttributeValue(node, attribute):
   """
   Removes the DefaultAttribute 'attribute' from 'node' if specified conditions are fulfilled
   """
   if not node.hasAttribute(attribute.name):
      return 0

   if (attribute.elements is not None) and (node.nodeName not in attribute.elements):
      return 0

   # differentiate between text and numeric values
   if isinstance(attribute.value, str):
      if node.getAttribute(attribute.name) == attribute.value:
         if (attribute.conditions is None) or attribute.conditions(node):
            node.removeAttribute(attribute.name)
            return 1
   else:
      nodeValue = SVGLength(node.getAttribute(attribute.name))
      if (attribute.value is None) or ((nodeValue.value == attribute.value) and not (nodeValue.units == Unit.INVALID)):
         if (attribute.units is None) or (nodeValue.units == attribute.units) or (isinstance(attribute.units, list) and nodeValue.units in attribute.units):
            if (attribute.conditions is None) or attribute.conditions(node):
               node.removeAttribute(attribute.name)
               return 1

   return 0

def removeDefaultAttributeValues(node, options, tainted=set()):
   u"""'tainted' keeps a set of attributes defined in parent nodes.

   For such attributes, we don't delete attributes with default values."""
   num = 0
   if node.nodeType != 1: return 0

   # Conditionally remove all default attributes defined in 'default_attributes' (a list of 'DefaultAttribute's)
   for attribute in default_attributes:
      num += removeDefaultAttributeValue(node, attribute)

   # Summarily get rid of default properties
   attributes = [node.attributes.item(i).nodeName for i in range(node.attributes.length)]
   for attribute in attributes:
      if attribute not in tainted:
         if attribute in list(default_properties.keys()):
            if node.getAttribute(attribute) == default_properties[attribute]:
               node.removeAttribute(attribute)
               num += 1
            else:
               tainted = taint(tainted, attribute)
   # Properties might also occur as styles, remove them too
   styles = _getStyle(node)
   for attribute in list(styles.keys()):
      if attribute not in tainted:
         if attribute in list(default_properties.keys()):
            if styles[attribute] == default_properties[attribute]:
               del styles[attribute]
               num += 1
            else:
               tainted = taint(tainted, attribute)
   _setStyle(node, styles)

   # recurse for our child elements
   for child in node.childNodes:
      num += removeDefaultAttributeValues(child, options, tainted.copy())

   return num

rgb = re.compile(r"\s*rgb\(\s*(\d+)\s*,\s*(\d+)\s*,\s*(\d+)\s*\)\s*")
rgbp = re.compile(r"\s*rgb\(\s*(\d*\.?\d+)%\s*,\s*(\d*\.?\d+)%\s*,\s*(\d*\.?\d+)%\s*\)\s*")
def convertColor(value):
   """
      Converts the input color string and returns a #RRGGBB (or #RGB if possible) string
   """
   s = value

   if s in list(colors.keys()):
      s = colors[s]

   rgbpMatch = rgbp.match(s)
   if rgbpMatch != None:
      r = int(float(rgbpMatch.group(1)) * 255.0 / 100.0)
      g = int(float(rgbpMatch.group(2)) * 255.0 / 100.0)
      b = int(float(rgbpMatch.group(3)) * 255.0 / 100.0)
      s  = '#%02x%02x%02x' % (r, g, b)
   else:
      rgbMatch = rgb.match(s)
      if rgbMatch != None:
         r = int( rgbMatch.group(1) )
         g = int( rgbMatch.group(2) )
         b = int( rgbMatch.group(3) )
         s = '#%02x%02x%02x' % (r, g, b)

   if s[0] == '#':
      s = s.lower()
      if len(s)==7 and s[1]==s[2] and s[3]==s[4] and s[5]==s[6]:
         s = '#'+s[1]+s[3]+s[5]

   return s

def convertColors(element):
   """
      Recursively converts all color properties into #RRGGBB format if shorter
   """
   numBytes = 0

   if element.nodeType != 1: return 0

   # set up list of color attributes for each element type
   attrsToConvert = []
   if element.nodeName in ['rect', 'circle', 'ellipse', 'polygon', \
                     'line', 'polyline', 'path', 'g', 'a']:
      attrsToConvert = ['fill', 'stroke']
   elif element.nodeName in ['stop']:
      attrsToConvert = ['stop-color']
   elif element.nodeName in ['solidColor']:
      attrsToConvert = ['solid-color']

   # now convert all the color formats
   styles = _getStyle(element)
   for attr in attrsToConvert:
      oldColorValue = element.getAttribute(attr)
      if oldColorValue != '':
         newColorValue = convertColor(oldColorValue)
         oldBytes = len(oldColorValue)
         newBytes = len(newColorValue)
         if oldBytes > newBytes:
            element.setAttribute(attr, newColorValue)
            numBytes += (oldBytes - len(element.getAttribute(attr)))
      # colors might also hide in styles
      if attr in list(styles.keys()):
         oldColorValue = styles[attr]
         newColorValue = convertColor(oldColorValue)
         oldBytes = len(oldColorValue)
         newBytes = len(newColorValue)
         if oldBytes > newBytes:
            styles[attr] = newColorValue
            numBytes += (oldBytes - len(element.getAttribute(attr)))
   _setStyle(element, styles)

   # now recurse for our child elements
   for child in element.childNodes:
      numBytes += convertColors(child)

   return numBytes

# TODO: go over what this method does and see if there is a way to optimize it
# TODO: go over the performance of this method and see if I can save memory/speed by
#       reusing data structures, etc
def cleanPath(element, options):
   """
      Cleans the path string (d attribute) of the element
   """
   global numBytesSavedInPathData
   global numPathSegmentsReduced
   global numCurvesStraightened

   # this gets the parser object from svg_regex.py
   oldPathStr = element.getAttribute('d')
   path = svg_parser.parse(oldPathStr)

   # This determines whether the stroke has round linecaps.  If it does,
   # we do not want to collapse empty segments, as they are actually rendered.
   withRoundLineCaps = element.getAttribute('stroke-linecap') == 'round'

   # The first command must be a moveto, and whether it's relative (m)
   # or absolute (M), the first set of coordinates *is* absolute. So
   # the first iteration of the loop below will get x,y and startx,starty.

   # convert absolute coordinates into relative ones.
   # Reuse the data structure 'path', since we're not adding or removing subcommands.
   # Also reuse the coordinate lists since we're not adding or removing any.
   for pathIndex in range(0, len(path)):
      cmd, data = path[pathIndex] # Changes to cmd don't get through to the data structure
      i = 0
      # adjust abs to rel
      # only the A command has some values that we don't want to adjust (radii, rotation, flags)
      if cmd == 'A':
         for i in range(i, len(data), 7):
            data[i+5] -= x
            data[i+6] -= y
            x += data[i+5]
            y += data[i+6]
         path[pathIndex] = ('a', data)
      elif cmd == 'a':
         x += sum(data[5::7])
         y += sum(data[6::7])
      elif cmd == 'H':
         for i in range(i, len(data)):
            data[i] -= x
            x += data[i]
         path[pathIndex] = ('h', data)
      elif cmd == 'h':
         x += sum(data)
      elif cmd == 'V':
         for i in range(i, len(data)):
            data[i] -= y
            y += data[i]
         path[pathIndex] = ('v', data)
      elif cmd == 'v':
         y += sum(data)
      elif cmd == 'M':
         startx, starty = data[0], data[1]
         # If this is a path starter, don't convert its first
         # coordinate to relative; that would just make it (0, 0)
         if pathIndex != 0:
            data[0] -= x
            data[1] -= y

         x, y = startx, starty
         i = 2
         for i in range(i, len(data), 2):
            data[i] -= x
            data[i+1] -= y
            x += data[i]
            y += data[i+1]
         path[pathIndex] = ('m', data)
      elif cmd in ['L','T']:
         for i in range(i, len(data), 2):
            data[i] -= x
            data[i+1] -= y
            x += data[i]
            y += data[i+1]
         path[pathIndex] = (cmd.lower(), data)
      elif cmd in ['m']:
         if pathIndex == 0:
            # START OF PATH - this is an absolute moveto
            # followed by relative linetos
            startx, starty = data[0], data[1]
            x, y = startx, starty
            i = 2
         else:
            startx = x + data[0]
            starty = y + data[1]
         for i in range(i, len(data), 2):
            x += data[i]
            y += data[i+1]
      elif cmd in ['l','t']:
         x += sum(data[0::2])
         y += sum(data[1::2])
      elif cmd in ['S','Q']:
         for i in range(i, len(data), 4):
            data[i] -= x
            data[i+1] -= y
            data[i+2] -= x
            data[i+3] -= y
            x += data[i+2]
            y += data[i+3]
         path[pathIndex] = (cmd.lower(), data)
      elif cmd in ['s','q']:
         x += sum(data[2::4])
         y += sum(data[3::4])
      elif cmd == 'C':
         for i in range(i, len(data), 6):
            data[i] -= x
            data[i+1] -= y
            data[i+2] -= x
            data[i+3] -= y
            data[i+4] -= x
            data[i+5] -= y
            x += data[i+4]
            y += data[i+5]
         path[pathIndex] = ('c', data)
      elif cmd == 'c':
         x += sum(data[4::6])
         y += sum(data[5::6])
      elif cmd in ['z','Z']:
         x, y = startx, starty
         path[pathIndex] = ('z', data)

   # remove empty segments
   # Reuse the data structure 'path' and the coordinate lists, even if we're
   # deleting items, because these deletions are relatively cheap.
   if not withRoundLineCaps:
      for pathIndex in range(0, len(path)):
         cmd, data = path[pathIndex]
         i = 0
         if cmd in ['m','l','t']:
            if cmd == 'm':
               # remove m0,0 segments
               if pathIndex > 0 and data[0] == data[i+1] == 0:
                  # 'm0,0 x,y' can be replaces with 'lx,y',
                  # except the first m which is a required absolute moveto
                  path[pathIndex] = ('l', data[2:])
                  numPathSegmentsReduced += 1
               else: # else skip move coordinate
                  i = 2
            while i < len(data):
               if data[i] == data[i+1] == 0:
                  del data[i:i+2]
                  numPathSegmentsReduced += 1
               else:
                  i += 2
         elif cmd == 'c':
            while i < len(data):
               if data[i] == data[i+1] == data[i+2] == data[i+3] == data[i+4] == data[i+5] == 0:
                  del data[i:i+6]
                  numPathSegmentsReduced += 1
               else:
                  i += 6
         elif cmd == 'a':
            while i < len(data):
               if data[i+5] == data[i+6] == 0:
                  del data[i:i+7]
                  numPathSegmentsReduced += 1
               else:
                  i += 7
         elif cmd == 'q':
            while i < len(data):
               if data[i] == data[i+1] == data[i+2] == data[i+3] == 0:
                  del data[i:i+4]
                  numPathSegmentsReduced += 1
               else:
                  i += 4
         elif cmd in ['h','v']:
            oldLen = len(data)
            path[pathIndex] = (cmd, [coord for coord in data if coord != 0])
            numPathSegmentsReduced += len(path[pathIndex][1]) - oldLen

   # fixup: Delete subcommands having no coordinates.
   path = [elem for elem in path if len(elem[1]) > 0 or elem[0] == 'z']

   # convert straight curves into lines
   newPath = [path[0]]
   for (cmd,data) in path[1:]:
      i = 0
      newData = data
      if cmd == 'c':
         newData = []
         while i < len(data):
            # since all commands are now relative, we can think of previous point as (0,0)
            # and new point (dx,dy) is (data[i+4],data[i+5])
            # eqn of line will be y = (dy/dx)*x or if dx=0 then eqn of line is x=0
            (p1x,p1y) = (data[i],data[i+1])
            (p2x,p2y) = (data[i+2],data[i+3])
            dx = data[i+4]
            dy = data[i+5]

            foundStraightCurve = False

            if dx == 0:
               if p1x == 0 and p2x == 0:
                  foundStraightCurve = True
            else:
               m = dy/dx
               if p1y == m*p1x and p2y == m*p2x:
                  foundStraightCurve = True

            if foundStraightCurve:
               # flush any existing curve coords first
               if newData:
                  newPath.append( (cmd,newData) )
                  newData = []
               # now create a straight line segment
               newPath.append( ('l', [dx,dy]) )
               numCurvesStraightened += 1
            else:
               newData.extend(data[i:i+6])

            i += 6
      if newData or cmd == 'z' or cmd == 'Z':
         newPath.append( (cmd,newData) )
   path = newPath

   # collapse all consecutive commands of the same type into one command
   prevCmd = ''
   prevData = []
   newPath = []
   for (cmd,data) in path:
      # flush the previous command if it is not the same type as the current command
      if prevCmd != '':
         if cmd != prevCmd or cmd == 'm':
            newPath.append( (prevCmd, prevData) )
            prevCmd = ''
            prevData = []

      # if the previous and current commands are the same type,
      # or the previous command is moveto and the current is lineto, collapse,
      # but only if they are not move commands (since move can contain implicit lineto commands)
      if (cmd == prevCmd or (cmd == 'l' and prevCmd == 'm')) and cmd != 'm':
         prevData.extend(data)

      # save last command and data
      else:
         prevCmd = cmd
         prevData = data
   # flush last command and data
   if prevCmd != '':
      newPath.append( (prevCmd, prevData) )
   path = newPath

   # convert to shorthand path segments where possible
   newPath = []
   for (cmd,data) in path:
      # convert line segments into h,v where possible
      if cmd == 'l':
         i = 0
         lineTuples = []
         while i < len(data):
            if data[i] == 0:
               # vertical
               if lineTuples:
                  # flush the existing line command
                  newPath.append( ('l', lineTuples) )
                  lineTuples = []
               # append the v and then the remaining line coords
               newPath.append( ('v', [data[i+1]]) )
               numPathSegmentsReduced += 1
            elif data[i+1] == 0:
               if lineTuples:
                  # flush the line command, then append the h and then the remaining line coords
                  newPath.append( ('l', lineTuples) )
                  lineTuples = []
               newPath.append( ('h', [data[i]]) )
               numPathSegmentsReduced += 1
            else:
               lineTuples.extend(data[i:i+2])
            i += 2
         if lineTuples:
            newPath.append( ('l', lineTuples) )
      # also handle implied relative linetos
      elif cmd == 'm':
         i = 2
         lineTuples = [data[0], data[1]]
         while i < len(data):
            if data[i] == 0:
               # vertical
               if lineTuples:
                  # flush the existing m/l command
                  newPath.append( (cmd, lineTuples) )
                  lineTuples = []
                  cmd = 'l' # dealing with linetos now
               # append the v and then the remaining line coords
               newPath.append( ('v', [data[i+1]]) )
               numPathSegmentsReduced += 1
            elif data[i+1] == 0:
               if lineTuples:
                  # flush the m/l command, then append the h and then the remaining line coords
                  newPath.append( (cmd, lineTuples) )
                  lineTuples = []
                  cmd = 'l' # dealing with linetos now
               newPath.append( ('h', [data[i]]) )
               numPathSegmentsReduced += 1
            else:
               lineTuples.extend(data[i:i+2])
            i += 2
         if lineTuples:
            newPath.append( (cmd, lineTuples) )
      # convert Bézier curve segments into s where possible
      elif cmd == 'c':
         # set up the assumed bezier control point as the current point, i.e. (0,0) since we're using relative coords
         bez_ctl_pt = (0, 0)
         # however if the previous command was 's' the assumed control point is a reflection of the previous control point at the current point
         if len(newPath):
            (prevCmd, prevData) = newPath[-1]
            if prevCmd == 's':
               bez_ctl_pt = (prevData[-2]-prevData[-4], prevData[-1]-prevData[-3])
         i = 0
         curveTuples = []
         while i < len(data):
            # rotate by 180deg means negate both coordinates
            # if the previous control point is equal then we can substitute a
            # shorthand bezier command
            if bez_ctl_pt[0] == data[i] and bez_ctl_pt[1] == data[i+1]:
               if curveTuples:
                  newPath.append( ('c', curveTuples) )
                  curveTuples = []
               # append the s command
               newPath.append( ('s', [data[i+2], data[i+3], data[i+4], data[i+5]]) )
               numPathSegmentsReduced += 1
            else:
               j = 0
               while j <= 5:
                  curveTuples.append(data[i+j])
                  j += 1

            # set up control point for next curve segment
            bez_ctl_pt = (data[i+4]-data[i+2], data[i+5]-data[i+3])
            i += 6

         if curveTuples:
            newPath.append( ('c', curveTuples) )
      # convert quadratic curve segments into t where possible
      elif cmd == 'q':
         quad_ctl_pt = (0,0)
         i = 0
         curveTuples = []
         while i < len(data):
            if quad_ctl_pt[0] == data[i] and quad_ctl_pt[1] == data[i+1]:
               if curveTuples:
                  newPath.append( ('q', curveTuples) )
                  curveTuples = []
               # append the t command
               newPath.append( ('t', [data[i+2], data[i+3]]) )
               numPathSegmentsReduced += 1
            else:
               j = 0;
               while j <= 3:
                  curveTuples.append(data[i+j])
                  j += 1

            quad_ctl_pt = (data[i+2]-data[i], data[i+3]-data[i+1])
            i += 4

         if curveTuples:
            newPath.append( ('q', curveTuples) )
      else:
         newPath.append( (cmd, data) )
   path = newPath

   # for each h or v, collapse unnecessary coordinates that run in the same direction
   # i.e. "h-100-100" becomes "h-200" but "h300-100" does not change
   # Reuse the data structure 'path', since we're not adding or removing subcommands.
   # Also reuse the coordinate lists, even if we're deleting items, because these
   # deletions are relatively cheap.
   for pathIndex in range(1, len(path)):
      cmd, data = path[pathIndex]
      if cmd in ['h','v'] and len(data) > 1:
         coordIndex = 1
         while coordIndex < len(data):
            if isSameSign(data[coordIndex - 1], data[coordIndex]):
               data[coordIndex - 1] += data[coordIndex]
               del data[coordIndex]
               numPathSegmentsReduced += 1
            else:
               coordIndex += 1

   # it is possible that we have consecutive h, v, c, t commands now
   # so again collapse all consecutive commands of the same type into one command
   prevCmd = ''
   prevData = []
   newPath = [path[0]]
   for (cmd,data) in path[1:]:
      # flush the previous command if it is not the same type as the current command
      if prevCmd != '':
         if cmd != prevCmd or cmd == 'm':
            newPath.append( (prevCmd, prevData) )
            prevCmd = ''
            prevData = []

      # if the previous and current commands are the same type, collapse
      if cmd == prevCmd and cmd != 'm':
            prevData.extend(data)

      # save last command and data
      else:
         prevCmd = cmd
         prevData = data
   # flush last command and data
   if prevCmd != '':
      newPath.append( (prevCmd, prevData) )
   path = newPath

   newPathStr = serializePath(path, options)

   # if for whatever reason we actually made the path longer don't use it
   # TODO: maybe we could compare path lengths after each optimization step and use the shortest
   if len(newPathStr) <= len(oldPathStr):
      numBytesSavedInPathData += ( len(oldPathStr) - len(newPathStr) )
      element.setAttribute('d', newPathStr)



def parseListOfPoints(s):
   """
      Parse string into a list of points.

      Returns a list containing an even number of coordinate strings
   """
   i = 0

   # (wsp)? comma-or-wsp-separated coordinate pairs (wsp)?
   # coordinate-pair = coordinate comma-or-wsp coordinate
   # coordinate = sign? integer
   # comma-wsp: (wsp+ comma? wsp*) | (comma wsp*)
   ws_nums = re.split(r"\s*[\s,]\s*", s.strip())
   nums = []

   # also, if 100-100 is found, split it into two also
   #  <polygon points="100,-100,100-100,100-100-100,-100-100" />
   for i in range(len(ws_nums)):
      negcoords = ws_nums[i].split("-")

      # this string didn't have any negative coordinates
      if len(negcoords) == 1:
         nums.append(negcoords[0])
      # we got negative coords
      else:
         for j in range(len(negcoords)):
            # first number could be positive
            if j == 0:
               if negcoords[0] != '':
                  nums.append(negcoords[0])
            # otherwise all other strings will be negative
            else:
               # unless we accidentally split a number that was in scientific notation
               # and had a negative exponent (500.00e-1)
               prev = "";
               if len(nums):
                  prev = nums[len(nums)-1]
               if prev and prev[len(prev)-1] in ['e', 'E']:
                  nums[len(nums)-1] = prev + '-' + negcoords[j]
               else:
                  nums.append( '-'+negcoords[j] )

   # if we have an odd number of points, return empty
   if len(nums) % 2 != 0: return []

   # now resolve into Decimal values
   i = 0
   while i < len(nums):
      try:
         nums[i] = getcontext().create_decimal(nums[i])
         nums[i + 1] = getcontext().create_decimal(nums[i + 1])
      except InvalidOperation: # one of the lengths had a unit or is an invalid number
         return []

      i += 2

   return nums



def cleanPolygon(elem, options):
   """
      Remove unnecessary closing point of polygon points attribute
   """
   global numPointsRemovedFromPolygon

   pts = parseListOfPoints(elem.getAttribute('points'))
   N = len(pts)/2
   if N >= 2:
      (startx,starty) = pts[:2]
      (endx,endy) = pts[-2:]
      if startx == endx and starty == endy:
         del pts[-2:]
         numPointsRemovedFromPolygon += 1
   elem.setAttribute('points', scourCoordinates(pts, options, True))



def cleanPolyline(elem, options):
   """
      Scour the polyline points attribute
   """
   pts = parseListOfPoints(elem.getAttribute('points'))
   elem.setAttribute('points', scourCoordinates(pts, options, True))



def serializePath(pathObj, options):
   """
      Reserializes the path data with some cleanups.
   """
   # elliptical arc commands must have comma/wsp separating the coordinates
   # this fixes an issue outlined in Fix https://bugs.launchpad.net/scour/+bug/412754
   return ''.join([cmd + scourCoordinates(data, options, (cmd == 'a'))  for cmd, data  in pathObj])



def serializeTransform(transformObj):
   """
      Reserializes the transform data with some cleanups.
   """
   return ' '.join(
      [command + '(' + ' '.join(
         [scourUnitlessLength(number) for number in numbers]
      ) + ')'
      for command, numbers in transformObj]
   )



def scourCoordinates(data, options, forceCommaWsp = False):
   """
      Serializes coordinate data with some cleanups:
         - removes all trailing zeros after the decimal
         - integerize coordinates if possible
         - removes extraneous whitespace
         - adds spaces between values in a subcommand if required (or if forceCommaWsp is True)
   """
   if data != None:
      newData = []
      c = 0
      previousCoord = ''
      for coord in data:
         scouredCoord = scourUnitlessLength(coord, needsRendererWorkaround=options.renderer_workaround)
         # only need the comma if the current number starts with a digit
         # (numbers can start with - without needing a comma before)
         # or if forceCommaWsp is True
         # or if this number starts with a dot and the previous number
         #   had *no* dot or exponent (so we can go like -5.5.5 for -5.5,0.5
         #   and 4e4.5 for 40000,0.5)
         if c > 0 and (forceCommaWsp
            or scouredCoord[0].isdigit()
            or (scouredCoord[0] == '.' and not ('.' in previousCoord or 'e' in previousCoord))
            ):
            newData.append( ' ' )

         # add the scoured coordinate to the path string
         newData.append( scouredCoord )
         previousCoord = scouredCoord
         c += 1

      # What we need to do to work around GNOME bugs 548494, 563933 and
      # 620565, which are being fixed and unfixed in Ubuntu, is
      # to make sure that a dot doesn't immediately follow a command
      # (so 'h50' and 'h0.5' are allowed, but not 'h.5').
      # Then, we need to add a space character after any coordinates
      # having an 'e' (scientific notation), so as to have the exponent
      # separate from the next number.
      if options.renderer_workaround:
         if len(newData) > 0:
            for i in range(1, len(newData)):
               if newData[i][0] == '-' and 'e' in newData[i - 1]:
                  newData[i - 1] += ' '
            return ''.join(newData)
      else:
         return ''.join(newData)

   return ''



def scourLength(length):
   """
   Scours a length. Accepts units.
   """
   length = SVGLength(length)

   return scourUnitlessLength(length.value) + Unit.str(length.units)



def scourUnitlessLength(length, needsRendererWorkaround=False): # length is of a numeric type
   """
   Scours the numeric part of a length only. Does not accept units.

   This is faster than scourLength on elements guaranteed not to
   contain units.
   """
   if not isinstance(length, Decimal):
      length = getcontext().create_decimal(str(length))

   # reduce numeric precision
   # plus() corresponds to the unary prefix plus operator and applies context precision and rounding
   length = scouringContext.plus(length)

   # remove trailing zeroes as we do not care for significance
   intLength = length.to_integral_value()
   if length == intLength:
      length = Decimal(intLength)
   else:
      length = length.normalize()

   # gather the non-scientific notation version of the coordinate.
   # this may actually be in scientific notation if the value is
   # sufficiently large or small, so this is a misnomer.
   nonsci = six.text_type(length).lower().replace("e+", "e")
   if not needsRendererWorkaround:
      if len(nonsci) > 2 and nonsci[:2] == '0.':
         nonsci = nonsci[1:] # remove the 0, leave the dot
      elif len(nonsci) > 3 and nonsci[:3] == '-0.':
         nonsci = '-' + nonsci[2:] # remove the 0, leave the minus and dot

   # Gather the scientific notation version of the coordinate which
   # can only be shorter if the length of the number is at least 4 characters (e.g. 1000 = 1e3).
   if len(nonsci) > 3:
      # We have to implement this ourselves since both 'normalize()' and 'to_sci_string()'
      # don't handle negative exponents in a reasonable way (e.g. 0.000001 remains unchanged)
      exponent = length.adjusted() # how far do we have to shift the dot?
      length = length.scaleb(-exponent).normalize() # shift the dot and remove potential trailing zeroes

      sci = six.text_type(length) + 'e' + six.text_type(exponent)

      if len(sci) < len(nonsci):
         return sci
      else:
         return nonsci
   else:
      return nonsci



def reducePrecision(element):
   """
   Because opacities, letter spacings, stroke widths and all that don't need
   to be preserved in SVG files with 9 digits of precision.

   Takes all of these attributes, in the given element node and its children,
   and reduces their precision to the current Decimal context's precision.
   Also checks for the attributes actually being lengths, not 'inherit', 'none'
   or anything that isn't an SVGLength.

   Returns the number of bytes saved after performing these reductions.
   """
   num = 0

   styles = _getStyle(element)
   for lengthAttr in ['opacity', 'flood-opacity', 'fill-opacity',
                  'stroke-opacity', 'stop-opacity', 'stroke-miterlimit',
                  'stroke-dashoffset', 'letter-spacing', 'word-spacing',
                  'kerning', 'font-size-adjust', 'font-size',
                  'stroke-width']:
      val = element.getAttribute(lengthAttr)
      if val != '':
         valLen = SVGLength(val)
         if valLen.units != Unit.INVALID: # not an absolute/relative size or inherit, can be % though
            newVal = scourLength(val)
            if len(newVal) < len(val):
               num += len(val) - len(newVal)
               element.setAttribute(lengthAttr, newVal)
      # repeat for attributes hidden in styles
      if lengthAttr in list(styles.keys()):
         val = styles[lengthAttr]
         valLen = SVGLength(val)
         if valLen.units != Unit.INVALID:
            newVal = scourLength(val)
            if len(newVal) < len(val):
               num += len(val) - len(newVal)
               styles[lengthAttr] = newVal
   _setStyle(element, styles)

   for child in element.childNodes:
      if child.nodeType == 1:
         num += reducePrecision(child)

   return num



def optimizeAngle(angle):
   """
   Because any rotation can be expressed within 360 degrees
   of any given number, and since negative angles sometimes
   are one character longer than corresponding positive angle,
   we shorten the number to one in the range to [-90, 270[.
   """
   # First, we put the new angle in the range ]-360, 360[.
   # The modulo operator yields results with the sign of the
   # divisor, so for negative dividends, we preserve the sign
   # of the angle.
   if angle < 0:     angle %= -360
   else:             angle %=  360
   # 720 degrees is unneccessary, as 360 covers all angles.
   # As "-x" is shorter than "35x" and "-xxx" one character
   # longer than positive angles <= 260, we constrain angle
   # range to [-90, 270[ (or, equally valid: ]-100, 260]).
   if  angle >= 270: angle -=  360
   elif angle < -90: angle +=  360
   return angle



def optimizeTransform(transform):
   """
   Optimises a series of transformations parsed from a single
   transform="" attribute.

   The transformation list is modified in-place.
   """
   # FIXME: reordering these would optimize even more cases:
   #   first: Fold consecutive runs of the same transformation
   #   extra:  Attempt to cast between types to create sameness:
   #     "matrix(0 1 -1 0 0 0) rotate(180) scale(-1)" all
   #     are rotations (90, 180, 180) -- thus "rotate(90)"
   #  second: Simplify transforms where numbers are optional.
   #   third: Attempt to simplify any single remaining matrix()
   #
   # if there's only one transformation and it's a matrix,
   # try to make it a shorter non-matrix transformation
   # NOTE: as matrix(a b c d e f) in SVG means the matrix:
   # |¯  a  c  e  ¯|   make constants   |¯  A1  A2  A3  ¯|
   # |   b  d  f   |  translating them  |   B1  B2  B3   |
   # |_  0  0  1  _|  to more readable  |_  0    0   1  _|
   if len(transform) == 1 and transform[0][0] == 'matrix':
      matrix = A1, B1, A2, B2, A3, B3 = transform[0][1]
      # |¯  1  0  0  ¯|
      # |   0  1  0   |  Identity matrix (no transformation)
      # |_  0  0  1  _|
      if matrix == [1, 0, 0, 1, 0, 0]:
         del transform[0]
      # |¯  1  0  X  ¯|
      # |   0  1  Y   |  Translation by (X, Y).
      # |_  0  0  1  _|
      elif (A1 ==  1 and A2 ==  0
       and  B1 ==  0 and B2 ==  1):
         transform[0] = ('translate', [A3, B3])
      # |¯  X  0  0  ¯|
      # |   0  Y  0   |  Scaling by (X, Y).
      # |_  0  0  1  _|
      elif (             A2 ==  0 and A3 ==  0
       and  B1 ==  0 and              B3 ==  0):
         transform[0] = ('scale', [A1, B2])
      # |¯  cos(A) -sin(A)    0    ¯|  Rotation by angle A,
      # |   sin(A)  cos(A)    0     |  clockwise, about the origin.
      # |_    0       0       1    _|  A is in degrees, [-180...180].
      elif (A1 == B2 and -1 <= A1 <= 1 and A3 == 0
       and -B1 == A2 and -1 <= B1 <= 1 and B3 == 0
       # as cos² A + sin² A == 1 and as decimal trig is approximate:
       # FIXME: the "epsilon" term here should really be some function
       #        of the precision of the (sin|cos)_A terms, not 1e-15:
       and  abs((B1 ** 2) + (A1 ** 2) - 1) < Decimal("1e-15")):
         sin_A, cos_A = B1, A1
         # while asin(A) and acos(A) both only have an 180° range
         # the sign of sin(A) and cos(A) varies across quadrants,
         # letting us hone in on the angle the matrix represents:
         # -- => < -90 | -+ => -90..0 | ++ => 0..90 | +- => >= 90
         #
         # http://en.wikipedia.org/wiki/File:Sine_cosine_plot.svg
         # shows asin has the correct angle the middle quadrants:
         A = Decimal(str(math.degrees(math.asin(float(sin_A)))))
         if cos_A < 0: # otherwise needs adjusting from the edges
            if sin_A < 0:
               A = -180 - A
            else:
               A =  180 - A
         transform[0] = ('rotate', [A])

   # Simplify transformations where numbers are optional.
   for type, args in transform:
      if type == 'translate':
         # Only the X coordinate is required for translations.
         # If the Y coordinate is unspecified, it's 0.
         if len(args) == 2 and args[1] == 0:
            del args[1]
      elif type == 'rotate':
         args[0] = optimizeAngle(args[0]) # angle
         # Only the angle is required for rotations.
         # If the coordinates are unspecified, it's the origin (0, 0).
         if len(args) == 3 and args[1] == args[2] == 0:
            del args[1:]
      elif type == 'scale':
         # Only the X scaling factor is required.
         # If the Y factor is unspecified, it's the same as X.
         if len(args) == 2 and args[0] == args[1]:
            del args[1]

   # Attempt to coalesce runs of the same transformation.
   # Translations followed immediately by other translations,
   # rotations followed immediately by other rotations,
   # scaling followed immediately by other scaling,
   # are safe to add.
   # Identity skewX/skewY are safe to remove, but how do they accrete?
   # |¯    1     0    0    ¯|
   # |   tan(A)  1    0     |  skews X coordinates by angle A
   # |_    0     0    1    _|
   #
   # |¯    1  tan(A)  0    ¯|
   # |     0     1    0     |  skews Y coordinates by angle A
   # |_    0     0    1    _|
   #
   # FIXME: A matrix followed immediately by another matrix
   #   would be safe to multiply together, too.
   i = 1
   while i < len(transform):
      currType, currArgs = transform[i]
      prevType, prevArgs = transform[i - 1]
      if currType == prevType == 'translate':
         prevArgs[0] += currArgs[0] # x
         # for y, only add if the second translation has an explicit y
         if len(currArgs) == 2:
            if len(prevArgs) == 2:
               prevArgs[1] += currArgs[1] # y
            elif len(prevArgs) == 1:
               prevArgs.append(currArgs[1]) # y
         del transform[i]
         if prevArgs[0] == prevArgs[1] == 0:
            # Identity translation!
            i -= 1
            del transform[i]
      elif (currType == prevType == 'rotate'
            and len(prevArgs) == len(currArgs) == 1):
         # Only coalesce if both rotations are from the origin.
         prevArgs[0] = optimizeAngle(prevArgs[0] + currArgs[0])
         del transform[i]
      elif currType == prevType == 'scale':
         prevArgs[0] *= currArgs[0] # x
         # handle an implicit y
         if len(prevArgs) == 2 and len(currArgs) == 2:
            # y1 * y2
            prevArgs[1] *= currArgs[1]
         elif len(prevArgs) == 1 and len(currArgs) == 2:
            # create y2 = uniformscalefactor1 * y2
            prevArgs.append(prevArgs[0] * currArgs[1])
         elif len(prevArgs) == 2 and len(currArgs) == 1:
            # y1 * uniformscalefactor2
            prevArgs[1] *= currArgs[0]
         del transform[i]
         if prevArgs[0] == prevArgs[1] == 1:
            # Identity scale!
            i -= 1
            del transform[i]
      else:
         i += 1

   # Some fixups are needed for single-element transformation lists, since
   # the loop above was to coalesce elements with their predecessors in the
   # list, and thus it required 2 elements.
   i = 0
   while i < len(transform):
      currType, currArgs = transform[i]
      if ((currType == 'skewX' or currType == 'skewY')
        and len(currArgs) == 1 and currArgs[0] == 0):
         # Identity skew!
         del transform[i]
      elif ((currType == 'rotate')
        and len(currArgs) == 1 and currArgs[0] == 0):
         # Identity rotation!
         del transform[i]
      else:
         i += 1



def optimizeTransforms(element, options):
   """
   Attempts to optimise transform specifications on the given node and its children.

   Returns the number of bytes saved after performing these reductions.
   """
   num = 0

   for transformAttr in ['transform', 'patternTransform', 'gradientTransform']:
      val = element.getAttribute(transformAttr)
      if val != '':
         transform = svg_transform_parser.parse(val)

         optimizeTransform(transform)

         newVal = serializeTransform(transform)

         if len(newVal) < len(val):
            if len(newVal):
               element.setAttribute(transformAttr, newVal)
            else:
               element.removeAttribute(transformAttr)
            num += len(val) - len(newVal)

   for child in element.childNodes:
      if child.nodeType == 1:
         num += optimizeTransforms(child, options)

   return num



def removeComments(element):
   """
      Removes comments from the element and its children.
   """
   global numCommentBytes

   if isinstance(element, xml.dom.minidom.Comment):
      numCommentBytes += len(element.data)
      element.parentNode.removeChild(element)
   else:
      for subelement in element.childNodes[:]:
         removeComments(subelement)



def embedRasters(element, options):
   import base64
   import urllib
   """
      Converts raster references to inline images.
      NOTE: there are size limits to base64-encoding handling in browsers
   """
   global numRastersEmbedded

   href = element.getAttributeNS(NS['XLINK'],'href')

   # if xlink:href is set, then grab the id
   if href != '' and len(href) > 1:
      # find if href value has filename ext
      ext = os.path.splitext(os.path.basename(href))[1].lower()[1:]

      # look for 'png', 'jpg', and 'gif' extensions
      if ext == 'png' or ext == 'jpg' or ext == 'gif':

         # file:// URLs denote files on the local system too
         if href[:7] == 'file://':
            href = href[7:]
         # does the file exist?
         if os.path.isfile(href):
            # if this is not an absolute path, set path relative
            # to script file based on input arg
            infilename = '.'
            if options.infilename: infilename = options.infilename
            href = os.path.join(os.path.dirname(infilename), href)

         rasterdata = ''
         # test if file exists locally
         if os.path.isfile(href):
            # open raster file as raw binary
            raster = open( href, "rb")
            rasterdata = raster.read()
         elif href[:7] == 'http://':
            webFile = urllib.urlopen( href )
            rasterdata = webFile.read()
            webFile.close()

         # ... should we remove all images which don't resolve?
         if rasterdata != '':
            # base64-encode raster
            b64eRaster = base64.b64encode( rasterdata )

            # set href attribute to base64-encoded equivalent
            if b64eRaster != '':
               # PNG and GIF both have MIME Type 'image/[ext]', but
               # JPEG has MIME Type 'image/jpeg'
               if ext == 'jpg':
                  ext = 'jpeg'

               element.setAttributeNS(NS['XLINK'], 'href', 'data:image/' + ext + ';base64,' + b64eRaster)
               numRastersEmbedded += 1
               del b64eRaster



def properlySizeDoc(docElement, options):
   # get doc width and height
   w = SVGLength(docElement.getAttribute('width'))
   h = SVGLength(docElement.getAttribute('height'))

   # if width/height are not unitless or px then it is not ok to rewrite them into a viewBox.
   # well, it may be OK for Web browsers and vector editors, but not for librsvg.
   if options.renderer_workaround:
      if ((w.units != Unit.NONE and w.units != Unit.PX) or
         (h.units != Unit.NONE and h.units != Unit.PX)):
          return

   # else we have a statically sized image and we should try to remedy that

   # parse viewBox attribute
   vbSep = re.split("\\s*\\,?\\s*", docElement.getAttribute('viewBox'), 3)
   # if we have a valid viewBox we need to check it
   vbWidth,vbHeight = 0,0
   if len(vbSep) == 4:
      try:
         # if x or y are specified and non-zero then it is not ok to overwrite it
         vbX = float(vbSep[0])
         vbY = float(vbSep[1])
         if vbX != 0 or vbY != 0:
            return

         # if width or height are not equal to doc width/height then it is not ok to overwrite it
         vbWidth = float(vbSep[2])
         vbHeight = float(vbSep[3])
         if vbWidth != w.value or vbHeight != h.value:
            return
      # if the viewBox did not parse properly it is invalid and ok to overwrite it
      except ValueError:
         pass

   # at this point it's safe to set the viewBox and remove width/height
   docElement.setAttribute('viewBox', '0 0 %s %s' % (w.value, h.value))
   docElement.removeAttribute('width')
   docElement.removeAttribute('height')



def remapNamespacePrefix(node, oldprefix, newprefix):
   if node == None or node.nodeType != 1: return

   if node.prefix == oldprefix:
      localName = node.localName
      namespace = node.namespaceURI
      doc = node.ownerDocument
      parent = node.parentNode

      # create a replacement node
      newNode = None
      if newprefix != '':
         newNode = doc.createElementNS(namespace, newprefix+":"+localName)
      else:
         newNode = doc.createElement(localName);

      # add all the attributes
      attrList = node.attributes
      for i in range(attrList.length):
         attr = attrList.item(i)
         newNode.setAttributeNS( attr.namespaceURI, attr.localName, attr.nodeValue)

      # clone and add all the child nodes
      for child in node.childNodes:
         newNode.appendChild(child.cloneNode(True))

      # replace old node with new node
      parent.replaceChild( newNode, node )
      # set the node to the new node in the remapped namespace prefix
      node = newNode

   # now do all child nodes
   for child in node.childNodes:
      remapNamespacePrefix(child, oldprefix, newprefix)



def makeWellFormed(str):
   # Don't escape quotation marks for now as they are fine in text nodes
   # as well as in attributes if used reciprocally
   #    xml_ents = { '<':'&lt;', '>':'&gt;', '&':'&amp;', "'":'&apos;', '"':'&quot;'}
   xml_ents = { '<':'&lt;', '>':'&gt;', '&':'&amp;'}

#  starr = []
#  for c in str:
#     if c in xml_ents:
#        starr.append(xml_ents[c])
#     else:
#        starr.append(c)

   # this list comprehension is short-form for the above for-loop:
   return ''.join([xml_ents[c] if c in xml_ents else c for c in str])



# hand-rolled serialization function that has the following benefits:
# - pretty printing
# - somewhat judicious use of whitespace
# - ensure id attributes are first
def serializeXML(element, options, ind = 0, preserveWhitespace = False):
   outParts = []

   indent = ind
   I=''
   newline = ''
   if options.newlines:
      if options.indent_type == 'tab': I='\t'
      elif options.indent_type == 'space': I=' '
      I *= options.indent_depth
      newline = '\n'

   outParts.extend([(I * ind), '<', element.nodeName])

   # always serialize the id or xml:id attributes first
   if element.getAttribute('id') != '':
      id = element.getAttribute('id')
      quot = '"'
      if id.find('"') != -1:
         quot = "'"
      outParts.extend([' id=', quot, id, quot])
   if element.getAttribute('xml:id') != '':
      id = element.getAttribute('xml:id')
      quot = '"'
      if id.find('"') != -1:
         quot = "'"
      outParts.extend([' xml:id=', quot, id, quot])

   # now serialize the other attributes
   known_attr = [
      # TODO: Maybe update with full list from https://www.w3.org/TR/SVG/attindex.html
      # (but should be kept inuitively ordered)
      'id', 'class',
      'transform',
      'x', 'y', 'z', 'width', 'height', 'x1', 'x2', 'y1', 'y2',
      'dx', 'dy', 'rotate', 'startOffset', 'method', 'spacing',
      'cx', 'cy', 'r', 'rx', 'ry', 'fx', 'fy',
      'd', 'points',
   ] + sorted(svgAttributes) + [
      'style',
   ]
   attrList = element.attributes
   attrName2Index = dict([(attrList.item(i).nodeName, i) for i in range(attrList.length)])
   # use custom order for known attributes and alphabetical order for the rest
   attrIndices = []
   for name in known_attr:
      if name in attrName2Index:
         attrIndices.append(attrName2Index[name])
         del attrName2Index[name]
   attrIndices += [attrName2Index[name] for name in sorted(attrName2Index.keys())]
   for index in attrIndices:
      attr = attrList.item(index)
      if attr.nodeName == 'id' or attr.nodeName == 'xml:id': continue
      # if the attribute value contains a double-quote, use single-quotes
      quot = '"'
      if attr.nodeValue.find('"') != -1:
         quot = "'"

      attrValue = makeWellFormed( attr.nodeValue )
      if attr.nodeName == 'style':
          # sort declarations
          attrValue = ';'.join([p for p in sorted(attrValue.split(';'))])

      outParts.append(' ')
      # preserve xmlns: if it is a namespace prefix declaration
      if attr.prefix != None:
         outParts.extend([attr.prefix, ':'])
      elif attr.namespaceURI != None:
         if attr.namespaceURI == 'http://www.w3.org/2000/xmlns/' and attr.nodeName.find('xmlns') == -1:
            outParts.append('xmlns:')
         elif attr.namespaceURI == 'http://www.w3.org/1999/xlink':
            outParts.append('xlink:')
      outParts.extend([attr.localName, '=', quot, attrValue, quot])

      if attr.nodeName == 'xml:space':
         if attrValue == 'preserve':
            preserveWhitespace = True
         elif attrValue == 'default':
            preserveWhitespace = False

   # if no children, self-close
   children = element.childNodes
   if children.length > 0:
      outParts.append('>')

      onNewLine = False
      for child in element.childNodes:
         # element node
         if child.nodeType == 1:
            if preserveWhitespace:
               outParts.append(serializeXML(child, options, 0, preserveWhitespace))
            else:
               outParts.extend([newline, serializeXML(child, options, indent + 1, preserveWhitespace)])
               onNewLine = True
         # text node
         elif child.nodeType == 3:
            # trim it only in the case of not being a child of an element
            # where whitespace might be important
            if preserveWhitespace:
               outParts.append(makeWellFormed(child.nodeValue))
            else:
               outParts.append(makeWellFormed(child.nodeValue.strip()))
         # CDATA node
         elif child.nodeType == 4:
            outParts.extend(['<![CDATA[', child.nodeValue, ']]>'])
         # Comment node
         elif child.nodeType == 8:
            outParts.extend(['<!--', child.nodeValue, '-->'])
         # TODO: entities, processing instructions, what else?
         else: # ignore the rest
            pass

      if onNewLine: outParts.append(I * ind)
      outParts.extend(['</', element.nodeName, '>'])
      if indent > 0: outParts.append(newline)
   else:
      outParts.append('/>')
      if indent > 0: outParts.append(newline)

   return "".join(outParts)



# this is the main method
# input is a string representation of the input XML
# returns a string representation of the output XML
def scourString(in_string, options=None):
   # sanitize options (take missing attributes from defaults, discard unknown attributes)
   options = sanitizeOptions(options)

   # create decimal context with reduced precision for scouring numbers
   # calculations should be done in the default context (precision defaults to 28 significant digits) to minimize errors
   global scouringContext
   scouringContext = Context(prec = options.digits)

   global numAttrsRemoved
   global numStylePropsFixed
   global numElemsRemoved
   global numBytesSavedInColors
   global numCommentsRemoved
   global numBytesSavedInIDs
   global numBytesSavedInLengths
   global numBytesSavedInTransforms
   doc = xml.dom.minidom.parseString(in_string)

   # determine number of flowRoot elements in input document
   # flowRoot elements don't render at all on current browsers (04/2016)
   cnt_flowText_el = len(doc.getElementsByTagName('flowRoot'))
   if cnt_flowText_el:
      errmsg = "SVG input document uses {} flow text elements, which won't render on browsers!".format(cnt_flowText_el)
      if options.error_on_flowtext:
         raise Exception(errmsg)
      else:
         print("WARNING: {}".format(errmsg), file = options.ensure_value("stdout", sys.stdout))

   # remove descriptive elements
   removeDescriptiveElements(doc, options)

   # for whatever reason this does not always remove all inkscape/sodipodi attributes/elements
   # on the first pass, so we do it multiple times
   # does it have to do with removal of children affecting the childlist?
   if options.keep_editor_data == False:
      while removeNamespacedElements( doc.documentElement, unwanted_ns ) > 0:
         pass
      while removeNamespacedAttributes( doc.documentElement, unwanted_ns ) > 0:
         pass

      # remove the xmlns: declarations now
      xmlnsDeclsToRemove = []
      attrList = doc.documentElement.attributes
      for index in range(attrList.length):
         if attrList.item(index).nodeValue in unwanted_ns:
            xmlnsDeclsToRemove.append(attrList.item(index).nodeName)

      for attr in xmlnsDeclsToRemove:
         doc.documentElement.removeAttribute(attr)
         numAttrsRemoved += 1

   # ensure namespace for SVG is declared
   # TODO: what if the default namespace is something else (i.e. some valid namespace)?
   if doc.documentElement.getAttribute('xmlns') != 'http://www.w3.org/2000/svg':
      doc.documentElement.setAttribute('xmlns', 'http://www.w3.org/2000/svg')
      # TODO: throw error or warning?

   # check for redundant and unused SVG namespace declarations
   def xmlnsUnused(prefix, namespace):
      if doc.getElementsByTagNameNS(namespace, "*"):
         return False
      else:
         for element in doc.getElementsByTagName("*"):
            for attribute in element.attributes.values():
               if attribute.name.startswith(prefix):
                  return False
      return True

   attrList = doc.documentElement.attributes
   xmlnsDeclsToRemove = []
   redundantPrefixes = []
   for i in range(attrList.length):
      attr = attrList.item(i)
      name = attr.nodeName
      val = attr.nodeValue
      if name[0:6] == 'xmlns:':
         if val == 'http://www.w3.org/2000/svg':
            redundantPrefixes.append(name[6:])
            xmlnsDeclsToRemove.append(name)
         elif xmlnsUnused(name[6:], val):
            xmlnsDeclsToRemove.append(name)

   for attrName in xmlnsDeclsToRemove:
      doc.documentElement.removeAttribute(attrName)
      numAttrsRemoved += 1

   for prefix in redundantPrefixes:
      remapNamespacePrefix(doc.documentElement, prefix, '')

   if options.strip_comments:
      numCommentsRemoved = removeComments(doc)

   if options.strip_xml_space_attribute and doc.documentElement.hasAttribute('xml:space'):
      doc.documentElement.removeAttribute('xml:space')
      numAttrsRemoved += 1

   # repair style (remove unnecessary style properties and change them into XML attributes)
   numStylePropsFixed = repairStyle(doc.documentElement, options)

   # convert colors to #RRGGBB format
   if options.simple_colors:
      numBytesSavedInColors = convertColors(doc.documentElement)

   # remove unreferenced gradients/patterns outside of defs
   # and most unreferenced elements inside of defs
   while removeUnreferencedElements(doc, options.keep_defs) > 0:
      pass

   # remove empty defs, metadata, g
   # NOTE: these elements will be removed if they just have whitespace-only text nodes
   for tag in ['defs', 'title', 'desc', 'metadata', 'g']:
      for elem in doc.documentElement.getElementsByTagName(tag):
         removeElem = not elem.hasChildNodes()
         if removeElem == False:
            for child in elem.childNodes:
               if child.nodeType in [1, 4, 8]:
                  break
               elif child.nodeType == 3 and not child.nodeValue.isspace():
                  break
            else:
               removeElem = True
         if removeElem:
            elem.parentNode.removeChild(elem)
            numElemsRemoved += 1

   if options.strip_ids:
      bContinueLooping = True
      while bContinueLooping:
         identifiedElements = unprotected_ids(doc, options)
         referencedIDs = findReferencedElements(doc.documentElement)
         bContinueLooping = (removeUnreferencedIDs(referencedIDs, identifiedElements) > 0)

   while removeDuplicateGradientStops(doc) > 0:
      pass

   # remove gradients that are only referenced by one other gradient
   while collapseSinglyReferencedGradients(doc) > 0:
      pass

   # remove duplicate gradients
   while removeDuplicateGradients(doc) > 0:
      pass

   # create <g> elements if there are runs of elements with the same attributes.
   # this MUST be before moveCommonAttributesToParentGroup.
   if options.group_create:
      createGroupsForCommonAttributes(doc.documentElement)

   # move common attributes to parent group
   # NOTE: the if the <svg> element's immediate children
   # all have the same value for an attribute, it must not
   # get moved to the <svg> element. The <svg> element
   # doesn't accept fill=, stroke= etc.!
   referencedIds = findReferencedElements(doc.documentElement)
   for child in doc.documentElement.childNodes:
      numAttrsRemoved += moveCommonAttributesToParentGroup(child, referencedIds)

   # remove unused attributes from parent
   numAttrsRemoved += removeUnusedAttributesOnParent(doc.documentElement)

   # Collapse groups LAST, because we've created groups. If done before
   # moveAttributesToParentGroup, empty <g>'s may remain.
   if options.group_collapse:
      while removeNestedGroups(doc.documentElement) > 0:
         pass

   # remove unnecessary closing point of polygons and scour points
   for polygon in doc.documentElement.getElementsByTagName('polygon'):
      cleanPolygon(polygon, options)

   # scour points of polyline
   for polyline in doc.documentElement.getElementsByTagName('polyline'):
      cleanPolyline(polyline, options)

   # clean path data
   for elem in doc.documentElement.getElementsByTagName('path'):
      if elem.getAttribute('d') == '':
         elem.parentNode.removeChild(elem)
      else:
         cleanPath(elem, options)

   # shorten ID names as much as possible
   if options.shorten_ids:
      numBytesSavedInIDs += shortenIDs(doc, options.shorten_ids_prefix, unprotected_ids(doc, options))

   # scour lengths (including coordinates)
   for type in ['svg', 'image', 'rect', 'circle', 'ellipse', 'line', 'linearGradient', 'radialGradient', 'stop', 'filter']:
      for elem in doc.getElementsByTagName(type):
         for attr in ['x', 'y', 'width', 'height', 'cx', 'cy', 'r', 'rx', 'ry',
                  'x1', 'y1', 'x2', 'y2', 'fx', 'fy', 'offset']:
            if elem.getAttribute(attr) != '':
               elem.setAttribute(attr, scourLength(elem.getAttribute(attr)))

   # more length scouring in this function
   numBytesSavedInLengths = reducePrecision(doc.documentElement)

   # remove default values of attributes
   numAttrsRemoved += removeDefaultAttributeValues(doc.documentElement, options)

   # reduce the length of transformation attributes
   numBytesSavedInTransforms = optimizeTransforms(doc.documentElement, options)

   # convert rasters references to base64-encoded strings
   if options.embed_rasters:
      for elem in doc.documentElement.getElementsByTagName('image'):
         embedRasters(elem, options)

   # properly size the SVG document (ideally width/height should be 100% with a viewBox)
   if options.enable_viewboxing:
      properlySizeDoc(doc.documentElement, options)

   # output the document as a pretty string with a single space for indent
   # NOTE: removed pretty printing because of this problem:
   # http://ronrothman.com/public/leftbraned/xml-dom-minidom-toprettyxml-and-silly-whitespace/
   # rolled our own serialize function here to save on space, put id first, customize indentation, etc
#  out_string = doc.documentElement.toprettyxml(' ')
   out_string = serializeXML(doc.documentElement, options) + '\n'

   # now strip out empty lines
   lines = []
   # Get rid of empty lines
   for line in out_string.splitlines(True):
      if line.strip():
         lines.append(line)

   # return the string with its XML prolog and surrounding comments
   if options.strip_xml_prolog == False:
      total_output = '<?xml version="1.0" encoding="UTF-8"'
      if doc.standalone:
         total_output += ' standalone="yes"'
      total_output += '?>\n'
   else:
      total_output = ""

   for child in doc.childNodes:
      if child.nodeType == 1:
         total_output += "".join(lines)
      else: # doctypes, entities, comments
         total_output += child.toxml() + '\n'

   return total_output



# used mostly by unit tests
# input is a filename
# returns the minidom doc representation of the SVG
def scourXmlFile(filename, options=None):
   with open(filename, "rb") as f:
      in_string = f.read()
   out_string = scourString(in_string, options)

   doc = xml.dom.minidom.parseString(out_string.encode('utf-8'))

   # since minidom does not seem to parse DTDs properly
   # manually declare all attributes with name "id" to be of type ID
   # (otherwise things like doc.getElementById() won't work)
   all_nodes = doc.getElementsByTagName("*")
   for node in all_nodes:
      try:
         node.setIdAttribute('id')
      except:
         pass

   return doc



# GZ: Seems most other commandline tools don't do this, is it really wanted?
class HeaderedFormatter(optparse.IndentedHelpFormatter):
   """
      Show application name, version number, and copyright statement
      above usage information.
   """
   def format_usage(self, usage):
      return "%s %s\n%s\n%s" % (APP, VER, COPYRIGHT,
         optparse.IndentedHelpFormatter.format_usage(self, usage))



# GZ: would prefer this to be in a function or class scope, but tests etc need
#     access to the defaults anyway
_options_parser = optparse.OptionParser(
   usage="%prog [INPUT.SVG [OUTPUT.SVG]] [OPTIONS]",
   description=("If the input/output files are not specified, stdin/stdout are used. "
                "If the input/output files are specified with a svgz extension, "
                "then compressed SVG is assumed."),
   formatter=HeaderedFormatter(max_help_position=33),
   version=VER)

_options_parser.add_option("-q", "--quiet",
   action="store_true", dest="quiet", default=False,
   help="suppress non-error output")
_options_parser.add_option("-v", "--verbose",
   action="store_true", dest="verbose", default=False,
   help="verbose output (optimization statistics, etc.)")
_options_parser.add_option("-i",
   action="store", dest="infilename", metavar="INPUT.SVG",
   help="alternative way to specify input filename")
_options_parser.add_option("-o",
   action="store", dest="outfilename", metavar="OUTPUT.SVG",
   help="alternative way to specify output filename")

_option_group_optimization = optparse.OptionGroup(_options_parser, "Optimization")
_option_group_optimization.add_option("-p", "--set-precision",
   action="store", type=int, dest="digits", default=5, metavar="NUM",
   help="set number of significant digits (default: %default)")
_option_group_optimization.add_option("--disable-simplify-colors",
   action="store_false", dest="simple_colors", default=True,
   help="won't convert all colors to #RRGGBB format")
_option_group_optimization.add_option("--disable-style-to-xml",
   action="store_false", dest="style_to_xml", default=True,
   help="won't convert styles into XML attributes")
_option_group_optimization.add_option("--disable-group-collapsing",
   action="store_false", dest="group_collapse", default=True,
   help="won't collapse <g> elements")
_option_group_optimization.add_option("--create-groups",
   action="store_true", dest="group_create", default=False,
   help="create <g> elements for runs of elements with identical attributes")
_option_group_optimization.add_option("--keep-editor-data",
   action="store_true", dest="keep_editor_data", default=False,
   help="won't remove Inkscape, Sodipodi, Adobe Illustrator or Sketch elements and attributes")
_option_group_optimization.add_option("--keep-unreferenced-defs",
   action="store_true", dest="keep_defs", default=False,
   help="won't remove elements within the defs container that are unreferenced")
_option_group_optimization.add_option("--renderer-workaround",
   action="store_true", dest="renderer_workaround", default=True,
   help="work around various renderer bugs (currently only librsvg) (default)")
_option_group_optimization.add_option("--no-renderer-workaround",
   action="store_false", dest="renderer_workaround", default=True,
   help="do not work around various renderer bugs (currently only librsvg)")
_options_parser.add_option_group(_option_group_optimization)

_option_group_document = optparse.OptionGroup(_options_parser, "SVG document")
_option_group_document.add_option("--strip-xml-prolog",
   action="store_true", dest="strip_xml_prolog", default=False,
   help="won't output the XML prolog (<?xml ?>)")
_option_group_document.add_option("--remove-titles",
   action="store_true", dest="remove_titles", default=False,
   help="remove <title> elements")
_option_group_document.add_option("--remove-descriptions",
   action="store_true", dest="remove_descriptions", default=False,
   help="remove <desc> elements")
_option_group_document.add_option("--remove-metadata",
   action="store_true", dest="remove_metadata", default=False,
   help="remove <metadata> elements (which may contain license/author information etc.)")
_option_group_document.add_option("--remove-descriptive-elements",
   action="store_true", dest="remove_descriptive_elements", default=False,
   help="remove <title>, <desc> and <metadata> elements")
_option_group_document.add_option("--enable-comment-stripping",
   action="store_true", dest="strip_comments", default=False,
   help="remove all comments (<!-- -->)")
_option_group_document.add_option("--disable-embed-rasters",
   action="store_false", dest="embed_rasters", default=True,
   help="won't embed rasters as base64-encoded data")
_option_group_document.add_option("--enable-viewboxing",
   action="store_true", dest="enable_viewboxing", default=False,
   help="changes document width/height to 100%/100% and creates viewbox coordinates")
_options_parser.add_option_group(_option_group_document)

_option_group_formatting = optparse.OptionGroup(_options_parser, "Output formatting")
_option_group_formatting.add_option("--indent",
   action="store", type="string", dest="indent_type", default="space", metavar="TYPE",
   help="indentation of the output: none, space, tab (default: %default)")
_option_group_formatting.add_option("--nindent",
   action="store", type=int, dest="indent_depth", default=1, metavar="NUM",
   help="depth of the indentation, i.e. number of spaces/tabs: (default: %default)")
_option_group_formatting.add_option("--no-line-breaks",
   action="store_false", dest="newlines", default=True,
   help="do not create line breaks in output"
        "(also disables indentation; might be overriden by xml:space=\"preserve\")")
_option_group_formatting.add_option("--strip-xml-space",
   action="store_true", dest="strip_xml_space_attribute", default=False,
   help="strip the xml:space=\"preserve\" attribute from the root SVG element")
_options_parser.add_option_group(_option_group_formatting)

_option_group_ids = optparse.OptionGroup(_options_parser, "ID attributes")
_option_group_ids.add_option("--enable-id-stripping",
   action="store_true", dest="strip_ids", default=False,
   help="remove all unreferenced IDs")
_option_group_ids.add_option("--shorten-ids",
   action="store_true", dest="shorten_ids", default=False,
   help="shorten all IDs to the least number of letters possible")
_option_group_ids.add_option("--shorten-ids-prefix",
   action="store", type="string", dest="shorten_ids_prefix", default="", metavar="PREFIX",
   help="add custom prefix to shortened IDs")
_option_group_ids.add_option("--protect-ids-noninkscape",
   action="store_true", dest="protect_ids_noninkscape", default=False,
   help="don't remove IDs not ending with a digit")
_option_group_ids.add_option("--protect-ids-list",
   action="store", type="string", dest="protect_ids_list", metavar="LIST",
   help="don't remove IDs given in this comma-separated list")
_option_group_ids.add_option("--protect-ids-prefix",
   action="store", type="string", dest="protect_ids_prefix", metavar="PREFIX",
   help="don't remove IDs starting with the given prefix")
_options_parser.add_option_group(_option_group_ids)

_option_group_compatibility = optparse.OptionGroup(_options_parser, "SVG compatibility checks")
_option_group_compatibility.add_option("--error-on-flowtext",
   action="store_true", dest="error_on_flowtext", default=False,
   help="In case the input SVG uses flow text, bail out with error. Otherwise only warn. (default: False)")
_options_parser.add_option_group(_option_group_compatibility)



def parse_args(args=None, ignore_additional_args=False):
   options, rargs = _options_parser.parse_args(args)

   if rargs:
      if not options.infilename:
         options.infilename = rargs.pop(0)
      if not options.outfilename and rargs:
         options.outfilename = rargs.pop(0)
      if not ignore_additional_args and rargs:
         _options_parser.error("Additional arguments not handled: %r, see --help" % rargs)
   if options.digits < 0:
      _options_parser.error("Can't have negative significant digits, see --help")
   if not options.indent_type in ["tab", "space", "none"]:
      _options_parser.error("Invalid value for --indent, see --help")
   if options.indent_depth < 0:
      _options_parser.error("Value for --nindent should be positive (or zero), see --help")
   if options.infilename and options.outfilename and options.infilename == options.outfilename:
      _options_parser.error("Input filename is the same as output filename")

   return options



def generateDefaultOptions():
   ## FIXME: clean up this mess/hack and refactor arg parsing to argparse
   class Struct:
       def __init__(self, **entries):
           self.__dict__.update(entries)

   d = parse_args(args = [], ignore_additional_args = True).__dict__.copy()

   return Struct(**d)



# sanitizes options by updating attributes in a set of defaults options while discarding unknown attributes
def sanitizeOptions(options):
   optionsDict = dict((key, getattr(options, key)) for key in dir(options) if not key.startswith('__'))

   sanitizedOptions = _options_parser.get_default_values()
   sanitizedOptions._update_careful(optionsDict)

   return sanitizedOptions



def maybe_gziped_file(filename, mode="r"):
   if os.path.splitext(filename)[1].lower() in (".svgz", ".gz"):
      import gzip
      return gzip.GzipFile(filename, mode)
   return open(filename, mode)



def getInOut(options):
   if options.infilename:
      infile = maybe_gziped_file(options.infilename, "rb")
      # GZ: could catch a raised IOError here and report
   else:
      # GZ: could sniff for gzip compression here
      #
      # open the binary buffer of stdin and let XML parser handle decoding
      try:
         infile = sys.stdin.buffer
      except AttributeError:
         infile = sys.stdin
      # the user probably does not want to manually enter SVG code into the terminal...
      if sys.stdin.isatty():
         _options_parser.error("No input file specified, see --help for detailed usage information")

   if options.outfilename:
      outfile = maybe_gziped_file(options.outfilename, "wb")
   else:
      # open the binary buffer of stdout as the output is already encoded
      try:
         outfile = sys.stdout.buffer
      except AttributeError:
         outfile = sys.stdout
      # redirect informational output to stderr when SVG is output to stdout
      options.stdout = sys.stderr

   return [infile, outfile]



def getReport():
   return ' Number of elements removed: ' + str(numElemsRemoved) + os.linesep + \
      ' Number of attributes removed: ' + str(numAttrsRemoved) + os.linesep + \
      ' Number of unreferenced id attributes removed: ' + str(numIDsRemoved) + os.linesep + \
      ' Number of style properties fixed: ' + str(numStylePropsFixed) + os.linesep + \
      ' Number of raster images embedded inline: ' + str(numRastersEmbedded) + os.linesep + \
      ' Number of path segments reduced/removed: ' + str(numPathSegmentsReduced) + os.linesep + \
      ' Number of bytes saved in path data: ' + str(numBytesSavedInPathData) + os.linesep + \
      ' Number of bytes saved in colors: ' + str(numBytesSavedInColors) + os.linesep + \
      ' Number of points removed from polygons: ' + str(numPointsRemovedFromPolygon) + os.linesep + \
      ' Number of bytes saved in comments: ' + str(numCommentBytes) + os.linesep + \
      ' Number of bytes saved in id attributes: ' + str(numBytesSavedInIDs) + os.linesep + \
      ' Number of bytes saved in lengths: ' + str(numBytesSavedInLengths) + os.linesep + \
      ' Number of bytes saved in transformations: ' + str(numBytesSavedInTransforms)



def start(options, input, output):

   start = walltime()

   # do the work
   in_string = input.read()
   out_string = scourString(in_string, options).encode("UTF-8")
   output.write(out_string)

   # Close input and output files
   input.close()
   output.close()

   end = walltime()

   # run-time in ms
   duration = int(round((end - start) * 1000.))

   oldsize = len(in_string)
   newsize = len(out_string)
   sizediff = (newsize / oldsize) * 100.

   if not options.quiet:
      print('Scour processed file "{}" in {} ms: {}/{} bytes new/orig -> {:.1f}%'.format(
         input.name,
         duration,
         newsize,
         oldsize,
         sizediff), file = options.ensure_value("stdout", sys.stdout))
      if options.verbose:
         print(getReport(), file = options.ensure_value("stdout", sys.stdout))


def run():
   options = parse_args()
   (input, output) = getInOut(options)
   start(options, input, output)


if __name__ == '__main__':
   run()
