File size: 10,521 Bytes
99d3cb0 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 | """Sparse Bit Set encoding/decoding for IFT (Incremental Font Transfer).
Implements the sparse bit set format defined in the W3C IFT specification:
https://w3c.github.io/IFT/Overview.html#sparse-bit-set-decoding
"""
# Reference: https://github.com/googlefonts/fontations/blob/main/read-fonts/src/collections/int_set/sparse_bit_set.rs
import bisect
from collections import deque
from typing import Dict, Iterable, Optional, Set, Tuple
# Maximum tree height that fits within a 32-bit leaf node for each branching factor.
_BF_MAX_HEIGHT: Dict[int, int] = {2: 31, 4: 16, 8: 11, 32: 7}
class SparseBitSetDecodeError(Exception):
pass
def decode(
data: bytes, bias: int = 0, maxValue: int = 0xFFFFFFFF
) -> Tuple[Set[int], int]:
"""Decode a sparse bit set from binary data.
Args:
data: bytes-like object containing the sparse bit set encoding.
bias: integer added to each decoded value.
Returns:
A tuple (values, bytesConsumed) where values is a set of integers
and bytesConsumed is the number of bytes read from data.
"""
if not data:
raise SparseBitSetDecodeError("Empty data")
branchFactor, height = _decodeHeader(data[0])
maxHeight = _BF_MAX_HEIGHT[branchFactor]
if height > maxHeight:
raise SparseBitSetDecodeError(
f"Height {height} exceeds max {maxHeight} for branch factor {branchFactor}"
)
return _decodeImpl(data, branchFactor, height, bias, maxValue)
def _decodeImpl(
data: bytes, branchFactor: int, height: int, bias: int, maxValue: int
) -> Tuple[Set[int], int]:
if height == 0:
# 1 byte was used for the header.
return (set(), 1)
bitStream = _InputBitStream(data, branchFactor)
result: Set[int] = set()
# Queue entries are (startValue, depth), where startValue is the first
# integer that could be covered by this node.
queue: deque[Tuple[int, int]] = deque()
queue.append((0, 1))
while queue:
start, depth = queue.popleft()
bits = bitStream.next()
if bits is None:
raise SparseBitSetDecodeError("Unexpected end of data")
# all bits were were zero which is a special command to completely fill
# in all integers covered by this node.
if bits == 0:
exp = height - depth + 1
nodeSize = branchFactor**exp
fillStart = start + bias
if fillStart > maxValue:
continue
fillEnd = min(maxValue, start + nodeSize - 1 + bias)
if fillStart < 0:
fillStart = 0
if fillStart <= fillEnd:
result.update(range(fillStart, fillEnd + 1))
continue
# Non-zero node: each set bit identifies a child/value.
exp = height - depth
nextNodeSize = branchFactor**exp
while True:
bitIndex = _trailingZeros(bits, 32)
if bitIndex == 32:
break
if depth == height:
val = start + bitIndex + bias
if val > maxValue:
queue.clear()
break
if val >= 0:
result.add(val)
else:
startDelta = bitIndex * nextNodeSize
queue.append((start + startDelta, depth + 1))
bits &= ~(1 << bitIndex)
return (result, bitStream.bytesConsumed())
def encode(values: Iterable[int]) -> bytes:
"""Encode a set of integers as a sparse bit set.
Tries all branching factors and returns the shortest encoding.
Args:
values: iterable of non-negative integers.
Returns:
bytes containing the sparse bit set encoding.
"""
valuesSorted = sorted(set(values))
if not valuesSorted:
return _encodeHeader(2, 0)
maxValue = valuesSorted[-1]
valueSet = set(valuesSorted)
best: Optional[bytes] = None
for branchFactor in (2, 4, 8, 32):
height = _treeHeight(branchFactor, maxValue)
if height > _BF_MAX_HEIGHT[branchFactor]:
continue
encoded = _encodeWithBf(valueSet, branchFactor, height)
if best is None or len(encoded) < len(best):
best = encoded
if best is None:
raise ValueError(f"Cannot encode max value {maxValue}")
return best
def _encodeHeader(branchFactor: int, height: int) -> bytes:
branchFactorToId = {2: 0, 4: 1, 8: 2, 32: 3}
return bytes([(height << 2) | branchFactorToId[branchFactor]])
def _decodeHeader(headerByte: int) -> Tuple[int, int]:
id = headerByte & 0x03
idToBranchFactor = {0: 2, 1: 4, 2: 8, 3: 32}
height = (headerByte >> 2) & 0x1F
return idToBranchFactor[id], height
def _treeHeight(branchFactor: int, maxValue: int) -> int:
"""Return the minimum tree height needed to represent maxValue."""
height = 1
capacity = branchFactor
while capacity <= maxValue:
capacity *= branchFactor
height += 1
return height
def _encodeWithBf(valueSet: Set[int], branchFactor: int, height: int) -> bytes:
if height == 0:
return _encodeHeader(branchFactor, 0)
# Build layers bottom-up: layer 0 = leaves (individual values),
# each higher layer groups bf children into one parent bitmask.
layers: list[Dict[int, int]] = [{}] # list of dicts: nodeIndex -> bitmask
for v in valueSet:
nodeIndex = v // branchFactor
bitPos = v % branchFactor
if nodeIndex not in layers[0]:
layers[0][nodeIndex] = 0
layers[0][nodeIndex] |= 1 << bitPos
for _ in range(1, height):
prevLayer = layers[-1]
newLayer: Dict[int, int] = {}
for nodeIndex, bitmask in prevLayer.items():
parentIndex = nodeIndex // branchFactor
bitPos = nodeIndex % branchFactor
if parentIndex not in newLayer:
newLayer[parentIndex] = 0
newLayer[parentIndex] |= 1 << bitPos
layers.append(newLayer)
# For zero-node optimization: track count of values in sorted list.
valuesSorted = sorted(valueSet)
def rangeCount(lo: int, hi: int) -> int:
return bisect.bisect_right(valuesSorted, hi) - bisect.bisect_left(
valuesSorted, lo
)
# Emit nodes BFS order (root to leaves).
# Queue entries: (nodeIndex, depthFromRoot, rangeStart, rangeEnd)
stream = _OutputBitStream(branchFactor)
subtreeSize = branchFactor**height
queue: deque[Tuple[int, int, int, int]] = deque([(0, 0, 0, subtreeSize - 1)])
while queue:
nodeIndex, depth, rangeStart, rangeEnd = queue.popleft()
layerIdx = height - 1 - depth # layers[0]=leaves, layers[height-1]=root
bitmask = (
layers[layerIdx].get(nodeIndex, 0) if 0 <= layerIdx < len(layers) else 0
)
# Zero-node optimization: if entire range is filled on an INTERNAL node,
# write 0 and skip children. At leaf level we always write the explicit
# bitmask so the encoding matches the reference.
if (
depth < height - 1
and rangeCount(rangeStart, rangeEnd) == rangeEnd - rangeStart + 1
):
stream.write(0)
continue
stream.write(bitmask)
if bitmask != 0 and depth < height - 1:
childSize = (rangeEnd - rangeStart + 1) // branchFactor
bits = bitmask
while bits:
bitIndex = _trailingZeros(bits, 32)
childIndex = nodeIndex * branchFactor + bitIndex
childStart = rangeStart + bitIndex * childSize
childEnd = childStart + childSize - 1
queue.append((childIndex, depth + 1, childStart, childEnd))
bits &= ~(1 << bitIndex)
return _encodeHeader(branchFactor, height) + stream.toBytes()
def _trailingZeros(val: int, maxBits: int) -> int:
if val == 0:
return maxBits
count = 0
while (val & 1) == 0:
val >>= 1
count += 1
return count
class _InputBitStream:
"""Reads bit nodes from a byte array, starting after the header byte."""
def __init__(self, data: bytes, branchFactor: int):
self.data = data
self.branchFactor = branchFactor
self.byteIndex = 1 # skip the header byte
self.subIndex = 0 # bit offset within current byte (for bf=2,4)
def next(self) -> Optional[int]:
if self.branchFactor in (2, 4):
if self.byteIndex >= len(self.data):
return None
mask = (1 << self.branchFactor) - 1
val = (self.data[self.byteIndex] >> self.subIndex) & mask
self.subIndex += self.branchFactor
if self.subIndex >= 8:
self.subIndex = 0
self.byteIndex += 1
return val
elif self.branchFactor == 8:
if self.byteIndex >= len(self.data):
return None
val = self.data[self.byteIndex]
self.byteIndex += 1
return val
elif self.branchFactor == 32:
if self.byteIndex + 3 >= len(self.data):
return None
b = self.data
i = self.byteIndex
val = b[i] | (b[i + 1] << 8) | (b[i + 2] << 16) | (b[i + 3] << 24)
self.byteIndex += 4
return val
return None
def bytesConsumed(self) -> int:
return self.byteIndex + (1 if self.subIndex > 0 else 0)
class _OutputBitStream:
"""Writes bit nodes into a byte array."""
def __init__(self, branchFactor: int):
self.branchFactor = branchFactor
self.data = bytearray()
self.subIndex = 0 # bit offset within current byte (for bf=2,4)
def write(self, value: int) -> None:
if self.branchFactor in (2, 4):
mask = (1 << self.branchFactor) - 1
value &= mask
if self.subIndex == 0:
self.data.append(0)
self.data[-1] |= value << self.subIndex
self.subIndex += self.branchFactor
if self.subIndex >= 8:
self.subIndex = 0
elif self.branchFactor == 8:
self.data.append(value & 0xFF)
elif self.branchFactor == 32:
self.data.append(value & 0xFF)
self.data.append((value >> 8) & 0xFF)
self.data.append((value >> 16) & 0xFF)
self.data.append((value >> 24) & 0xFF)
def toBytes(self) -> bytes:
return bytes(self.data)
|