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annotate mupdf-source/thirdparty/harfbuzz/docs/repacker.md @ 22:d77477b4e151

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Let _int_rc() also handle (i.e. ignore) a local version suffix
author Franz Glasner <fzglas.hg@dom66.de>
date Fri, 19 Sep 2025 12:05:57 +0200
parents b50eed0cc0ef
children
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1 # Introduction
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3 Several tables in the opentype format are formed internally by a graph of subtables. Parent node's
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4 reference their children through the use of positive offsets, which are typically 16 bits wide.
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5 Since offsets are always positive this forms a directed acyclic graph. For storage in the font file
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6 the graph must be given a topological ordering and then the subtables packed in serial according to
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7 that ordering. Since 16 bit offsets have a maximum value of 65,535 if the distance between a parent
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8 subtable and a child is more then 65,535 bytes then it's not possible for the offset to encode that
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9 edge.
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11 For many fonts with complex layout rules (such as Arabic) it's not unusual for the tables containing
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12 layout rules ([GSUB/GPOS](https://docs.microsoft.com/en-us/typography/opentype/spec/gsub)) to be
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13 larger than 65kb. As a result these types of fonts are susceptible to offset overflows when
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14 serializing to the binary font format.
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16 Offset overflows can happen for a variety of reasons and require different strategies to resolve:
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17 * Simple overflows can often be resolved with a different topological ordering.
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18 * If a subtable has many parents this can result in the link from furthest parent(s)
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19 being at risk for overflows. In these cases it's possible to duplicate the shared subtable which
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20 allows it to be placed closer to it's parent.
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21 * If subtables exist which are themselves larger than 65kb it's not possible for any offsets to point
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22 past them. In these cases the subtable can usually be split into two smaller subtables to allow
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23 for more flexibility in the ordering.
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24 * In GSUB/GPOS overflows from Lookup subtables can be resolved by changing the Lookup to an extension
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25 lookup which uses a 32 bit offset instead of 16 bit offset.
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27 In general there isn't a simple solution to produce an optimal topological ordering for a given graph.
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28 Finding an ordering which doesn't overflow is a NP hard problem. Existing solutions use heuristics
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29 which attempt a combination of the above strategies to attempt to find a non-overflowing configuration.
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31 The harfbuzz subsetting library
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32 [includes a repacking algorithm](https://github.com/harfbuzz/harfbuzz/blob/main/src/hb-repacker.hh)
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33 which is used to resolve offset overflows that are present in the subsetted tables it produces. This
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34 document provides a deep dive into how the harfbuzz repacking algorithm works.
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36 Other implementations exist, such as in
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37 [fontTools](https://github.com/fonttools/fonttools/blob/7af43123d49c188fcef4e540fa94796b3b44e858/Lib/fontTools/ttLib/tables/otBase.py#L72), however these are not covered in this document.
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39 # Foundations
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41 There's four key pieces to the harfbuzz approach:
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43 * Subtable Graph: a table's internal structure is abstracted out into a lightweight graph
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44 representation where each subtable is a node and each offset forms an edge. The nodes only need
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45 to know how many bytes the corresponding subtable occupies. This lightweight representation can
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46 be easily modified to test new ordering's and strategies as the repacking algorithm iterates.
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48 * [Topological sorting algorithm](https://en.wikipedia.org/wiki/Topological_sorting): an algorithm
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49 which given a graph gives a linear sorting of the nodes such that all offsets will be positive.
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51 * Overflow check: given a graph and a topological sorting it checks if there will be any overflows
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52 in any of the offsets. If there are overflows it returns a list of (parent, child) tuples that
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53 will overflow. Since the graph has information on the size of each subtable it's straightforward
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54 to calculate the final position of each subtable and then check if any offsets to it will
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55 overflow.
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57 * Content Aware Preprocessing: if the overflow resolver is aware of the format of the underlying
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58 tables (eg. GSUB, GPOS) then in some cases preprocessing can be done to increase the chance of
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59 successfully packing the graph. For example for GSUB and GPOS we can preprocess the graph and
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60 promote lookups to extension lookups (upgrades a 16 bit offset to 32 bits) or split large lookup
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61 subtables into two or more pieces.
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63 * Offset resolution strategies: given a particular occurrence of an overflow these strategies
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64 modify the graph to attempt to resolve the overflow.
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66 # High Level Algorithm
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68 ```
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69 def repack(graph):
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70 graph.topological_sort()
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72 if (graph.will_overflow())
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73 preprocess(graph)
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74 assign_spaces(graph)
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75 graph.topological_sort()
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77 while (overflows = graph.will_overflow()):
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78 for overflow in overflows:
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79 apply_offset_resolution_strategy (overflow, graph)
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80 graph.topological_sort()
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81 ```
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83 The actual code for this processing loop can be found in the function hb_resolve_overflows () of
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84 [hb-repacker.hh](https://github.com/harfbuzz/harfbuzz/blob/main/src/hb-repacker.hh).
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86 # Topological Sorting Algorithms
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88 The harfbuzz repacker uses two different algorithms for topological sorting:
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89 * [Kahn's Algorithm](https://en.wikipedia.org/wiki/Topological_sorting#Kahn's_algorithm)
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90 * Sorting by shortest distance
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92 Kahn's algorithm is approximately twice as fast as the shortest distance sort so that is attempted
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93 first (only on the first topological sort). If it fails to eliminate overflows then shortest distance
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94 sort will be used for all subsequent topological sorting operations.
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95
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96 ## Shortest Distance Sort
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97
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98 This algorithm orders the nodes based on total distance to each node. Nodes with a shorter distance
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99 are ordered first.
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100
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101 The "weight" of an edge is the sum of the size of the sub-table being pointed to plus 2^16 for a 16 bit
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102 offset and 2^32 for a 32 bit offset.
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103
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104 The distance of a node is the sum of all weights along the shortest path from the root to that node
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105 plus a priority modifier (used to change where nodes are placed by moving increasing or
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106 decreasing the effective distance). Ties between nodes with the same distance are broken based
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107 on the order of the offset in the sub table bytes.
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108
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109 The shortest distance to each node is determined using
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110 [Djikstra's algorithm](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm). Then the topological
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111 ordering is produce by applying a modified version of Kahn's algorithm that uses a priority queue
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112 based on the shortest distance to each node.
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113
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114 ## Optimizing the Sorting
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115
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116 The topological sorting operation is the core of the repacker and is run on each iteration so it needs
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117 to be as fast as possible. There's a few things that are done to speed up subsequent sorting
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118 operations:
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119
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120 * The number of incoming edges to each node is cached. This is required by the Kahn's algorithm
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121 portion of both sorts. Where possible when the graph is modified we manually update the cached
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122 edge counts of affected nodes.
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123
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124 * The distance to each node is cached. Where possible when the graph is modified we manually update
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125 the cached distances of any affected nodes.
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126
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127 Caching these values allows the repacker to avoid recalculating them for the full graph on each
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128 iteration.
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129
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130 The other important factor to speed is a fast priority queue which is a core datastructure to
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131 the topological sorting algorithm. Currently a basic heap based queue is used. Heap based queue's
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132 don't support fast priority decreases, but that can be worked around by just adding redundant entries
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133 to the priority queue and filtering the older ones out when poppping off entries. This is based
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134 on the recommendations in
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135 [a study of the practical performance of priority queues in Dijkstra's algorithm](https://www3.cs.stonybrook.edu/~rezaul/papers/TR-07-54.pdf)
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136
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137 ## Special Handling of 32 bit Offsets
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138
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139 If a graph contains multiple 32 bit offsets then the shortest distance sorting will be likely be
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140 suboptimal. For example consider the case where a graph contains two 32 bit offsets that each point
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141 to a subgraph which are not connected to each other. The shortest distance sort will interleave the
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142 subtables of the two subgraphs, potentially resulting in overflows. Since each of these subgraphs are
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143 independent of each other, and 32 bit offsets can point extremely long distances a better strategy is
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144 to pack the first subgraph in it's entirety and then have the second subgraph packed after with the 32
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145 bit offset pointing over the first subgraph. For example given the graph:
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146
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147
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148 ```
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149 a--- b -- d -- f
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150 \
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151 \_ c -- e -- g
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152 ```
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153
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154 Where the links from a to b and a to c are 32 bit offsets, the shortest distance sort would be:
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155
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156 ```
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157 a, b, c, d, e, f, g
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158
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159 ```
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160
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161 If nodes d and e have a combined size greater than 65kb then the offset from d to f will overflow.
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162 A better ordering is:
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163
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164 ```
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165 a, b, d, f, c, e, g
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166 ```
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167
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168 The ability for 32 bit offsets to point long distances is utilized to jump over the subgraph of
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169 b which gives the remaining 16 bit offsets a better chance of not overflowing.
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170
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171 The above is an ideal situation where the subgraphs are disconnected from each other, in practice
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172 this is often not this case. So this idea can be generalized as follows:
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173
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174 If there is a subgraph that is only reachable from one or more 32 bit offsets, then:
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175 * That subgraph can be treated as an independent unit and all nodes of the subgraph packed in isolation
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176 from the rest of the graph.
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177 * In a table that occupies less than 4gb of space (in practice all fonts), that packed independent
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178 subgraph can be placed anywhere after the parent nodes without overflowing the 32 bit offsets from
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179 the parent nodes.
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180
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181 The sorting algorithm incorporates this via a "space" modifier that can be applied to nodes in the
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182 graph. By default all nodes are treated as being in space zero. If a node is given a non-zero space, n,
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183 then the computed distance to the node will be modified by adding `n * 2^32`. This will cause that
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184 node and it's descendants to be packed between all nodes in space n-1 and space n+1. Resulting in a
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185 topological sort like:
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186
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187 ```
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188 | space 0 subtables | space 1 subtables | .... | space n subtables |
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189 ```
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190
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191 The assign_spaces() step in the high level algorithm is responsible for identifying independent
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192 subgraphs and assigning unique spaces to each one. More information on the space assignment can be
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193 found in the next section.
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194
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195 # Graph Preprocessing
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196
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197 For certain table types we can preprocess and modify the graph structure to reduce the occurences
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198 of overflows. Currently the repacker implements preprocessing only for GPOS and GSUB tables.
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199
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200 ## GSUB/GPOS Table Splitting
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201
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202 The GSUB/GPOS preprocessor scans each lookup subtable and determines if the subtable's children are
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203 so large that no overflow resolution is possible (for example a single subtable that exceeds 65kb
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204 cannot be pointed over). When such cases are detected table splitting is invoked:
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205
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206 * The subtable is first analyzed to determine the smallest number of split points that will allow
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207 for successful offset overflow resolution.
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208
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209 * Then the subtable in the graph representation is modified to actually perform the split at the
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210 previously computed split points. At a high level splits are done by inserting new subtables
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211 which contain a subset of the data of the original subtable and then shrinking the original subtable.
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212
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213 Table splitting must be aware of the underlying format of each subtable type and thus needs custom
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214 code for each subtable type. Currently subtable splitting is only supported for GPOS subtable types.
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215
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216 ## GSUB/GPOS Extension Lookup Promotion
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217
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218 In GSUB/GPOS tables lookups can be regular lookups which use 16 bit offsets to the children subtables
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219 or extension lookups which use 32 bit offsets to the children subtables. If the sub graph of all
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220 regular lookups is too large then it can be difficult to find an overflow free configuration. This
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221 can be remedied by promoting one or more regular lookups to extension lookups.
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222
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223 During preprocessing the graph is scanned to determine the size of the subgraph of regular lookups.
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224 If the graph is found to be too big then the analysis finds a set of lookups to promote to reduce
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225 the subgraph size. Lastly the graph is modified to convert those lookups to extension lookups.
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226
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227 # Offset Resolution Strategies
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228
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229 ## Space Assignment
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230
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231 The goal of space assignment is to find connected subgraphs that are only reachable via 32 bit offsets
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232 and then assign each such subgraph to a unique non-zero space. The algorithm is roughly:
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233
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234 1. Collect the set, `S`, of nodes that are children of 32 bit offsets.
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235
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236 2. Do a directed traversal from each node in `S` and collect all encountered nodes into set `T`.
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237 Mark all nodes in the graph that are not in `T` as being in space 0.
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238
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239 3. Set `next_space = 1`.
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240
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241 4. While set `S` is not empty:
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242
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243 a. Pick a node `n` in set `S` then perform an undirected graph traversal and find the set `Q` of
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244 nodes that are reachable from `n`.
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245
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246 b. During traversal if a node, `m`, has a edge to a node in space 0 then `m` must be duplicated
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247 to disconnect it from space 0.
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248
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249 d. Remove all nodes in `Q` from `S` and assign all nodes in `Q` to `next_space`.
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250
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251
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252 c. Increment `next_space` by one.
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253
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254
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255 ## Manual Iterative Resolutions
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256
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257 For each overflow in each iteration the algorithm will attempt to apply offset overflow resolution
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258 strategies to eliminate the overflow. The type of strategy applied is dependent on the characteristics
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259 of the overflowing link:
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260
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261 * If the overflowing offset is inside a space other than space 0 and the subgraph space has more
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262 than one 32 bit offset pointing into the subgraph then subdivide the space by moving subgraph
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263 from one of the 32 bit offsets into a new space via the duplication of shared nodes.
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264
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265 * If the overflowing offset is pointing to a subtable with more than one incoming edge: duplicate
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266 the node so that the overflowing offset is pointing at it's own copy of that node.
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267
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268 * Otherwise, attempt to move the child subtable closer to it's parent. This is accomplished by
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269 raising the priority of all children of the parent. Next time the topological sort is run the
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270 children will be ordered closer to the parent.
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271
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272 # Test Cases
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273
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274 The harfbuzz repacker has tests defined using generic graphs: https://github.com/harfbuzz/harfbuzz/blob/main/src/test-repacker.cc
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275
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276 # Future Improvements
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277
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278 Currently for GPOS tables the repacker implementation is sufficient to handle both subsetting and the
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279 general case of font compilation repacking. However for GSUB the repacker is only sufficient for
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280 subsetting related overflows. To enable general case repacking of GSUB, support for splitting of
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281 GSUB subtables will need to be added. Other table types such as COLRv1 shouldn't require table
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282 splitting due to the wide use of 24 bit offsets throughout the table.
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283
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284 Beyond subtable splitting there are a couple of "nice to have" improvements, but these are not required
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285 to support the general case:
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286
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287 * Extension demotion: currently extension promotion is supported but in some cases if the non-extension
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288 subgraph is underfilled then packed size can be reduced by demoting extension lookups back to regular
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289 lookups.
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290
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291 * Currently only children nodes are moved to resolve offsets. However, in many cases moving a parent
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292 node closer to it's children will have less impact on the size of other offsets. Thus the algorithm
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Franz Glasner <fzglas.hg@dom66.de>
parents:
diff changeset
293 should use a heuristic (based on parent and child subtable sizes) to decide if the children's
b50eed0cc0ef ADD: MuPDF v1.26.7: the MuPDF source as downloaded by a default build of PyMuPDF 1.26.4.
Franz Glasner <fzglas.hg@dom66.de>
parents:
diff changeset
294 priority should be increased or the parent's priority decreased.