1 /*
2 * Copyright (c) 2016-2020, Yann Collet, Facebook, Inc.
3 * All rights reserved.
4 *
5 * This source code is licensed under both the BSD-style license (found in the
6 * LICENSE file in the root directory of this source tree) and the GPLv2 (found
7 * in the COPYING file in the root directory of this source tree).
8 * You may select, at your option, one of the above-listed licenses.
9 */
10
11 /*-*************************************
12 * Dependencies
13 ***************************************/
14 #include "zstd_compress_sequences.h"
15
16 /**
17 * -log2(x / 256) lookup table for x in [0, 256).
18 * If x == 0: Return 0
19 * Else: Return floor(-log2(x / 256) * 256)
20 */
21 static unsigned const kInverseProbabilityLog256[256] = {
22 0, 2048, 1792, 1642, 1536, 1453, 1386, 1329, 1280, 1236, 1197, 1162,
23 1130, 1100, 1073, 1047, 1024, 1001, 980, 960, 941, 923, 906, 889,
24 874, 859, 844, 830, 817, 804, 791, 779, 768, 756, 745, 734,
25 724, 714, 704, 694, 685, 676, 667, 658, 650, 642, 633, 626,
26 618, 610, 603, 595, 588, 581, 574, 567, 561, 554, 548, 542,
27 535, 529, 523, 517, 512, 506, 500, 495, 489, 484, 478, 473,
28 468, 463, 458, 453, 448, 443, 438, 434, 429, 424, 420, 415,
29 411, 407, 402, 398, 394, 390, 386, 382, 377, 373, 370, 366,
30 362, 358, 354, 350, 347, 343, 339, 336, 332, 329, 325, 322,
31 318, 315, 311, 308, 305, 302, 298, 295, 292, 289, 286, 282,
32 279, 276, 273, 270, 267, 264, 261, 258, 256, 253, 250, 247,
33 244, 241, 239, 236, 233, 230, 228, 225, 222, 220, 217, 215,
34 212, 209, 207, 204, 202, 199, 197, 194, 192, 190, 187, 185,
35 182, 180, 178, 175, 173, 171, 168, 166, 164, 162, 159, 157,
36 155, 153, 151, 149, 146, 144, 142, 140, 138, 136, 134, 132,
37 130, 128, 126, 123, 121, 119, 117, 115, 114, 112, 110, 108,
38 106, 104, 102, 100, 98, 96, 94, 93, 91, 89, 87, 85,
39 83, 82, 80, 78, 76, 74, 73, 71, 69, 67, 66, 64,
40 62, 61, 59, 57, 55, 54, 52, 50, 49, 47, 46, 44,
41 42, 41, 39, 37, 36, 34, 33, 31, 30, 28, 26, 25,
42 23, 22, 20, 19, 17, 16, 14, 13, 11, 10, 8, 7,
43 5, 4, 2, 1,
44 };
45
ZSTD_getFSEMaxSymbolValue(FSE_CTable const * ctable)46 static unsigned ZSTD_getFSEMaxSymbolValue(FSE_CTable const* ctable) {
47 void const* ptr = ctable;
48 U16 const* u16ptr = (U16 const*)ptr;
49 U32 const maxSymbolValue = MEM_read16(u16ptr + 1);
50 return maxSymbolValue;
51 }
52
53 /**
54 * Returns the cost in bytes of encoding the normalized count header.
55 * Returns an error if any of the helper functions return an error.
56 */
ZSTD_NCountCost(unsigned const * count,unsigned const max,size_t const nbSeq,unsigned const FSELog)57 static size_t ZSTD_NCountCost(unsigned const* count, unsigned const max,
58 size_t const nbSeq, unsigned const FSELog)
59 {
60 BYTE wksp[FSE_NCOUNTBOUND];
61 S16 norm[MaxSeq + 1];
62 const U32 tableLog = FSE_optimalTableLog(FSELog, nbSeq, max);
63 FORWARD_IF_ERROR(FSE_normalizeCount(norm, tableLog, count, nbSeq, max), "");
64 return FSE_writeNCount(wksp, sizeof(wksp), norm, max, tableLog);
65 }
66
67 /**
68 * Returns the cost in bits of encoding the distribution described by count
69 * using the entropy bound.
70 */
ZSTD_entropyCost(unsigned const * count,unsigned const max,size_t const total)71 static size_t ZSTD_entropyCost(unsigned const* count, unsigned const max, size_t const total)
72 {
73 unsigned cost = 0;
74 unsigned s;
75 for (s = 0; s <= max; ++s) {
76 unsigned norm = (unsigned)((256 * count[s]) / total);
77 if (count[s] != 0 && norm == 0)
78 norm = 1;
79 assert(count[s] < total);
80 cost += count[s] * kInverseProbabilityLog256[norm];
81 }
82 return cost >> 8;
83 }
84
85 /**
86 * Returns the cost in bits of encoding the distribution in count using ctable.
87 * Returns an error if ctable cannot represent all the symbols in count.
88 */
ZSTD_fseBitCost(FSE_CTable const * ctable,unsigned const * count,unsigned const max)89 size_t ZSTD_fseBitCost(
90 FSE_CTable const* ctable,
91 unsigned const* count,
92 unsigned const max)
93 {
94 unsigned const kAccuracyLog = 8;
95 size_t cost = 0;
96 unsigned s;
97 FSE_CState_t cstate;
98 FSE_initCState(&cstate, ctable);
99 if (ZSTD_getFSEMaxSymbolValue(ctable) < max) {
100 DEBUGLOG(5, "Repeat FSE_CTable has maxSymbolValue %u < %u",
101 ZSTD_getFSEMaxSymbolValue(ctable), max);
102 return ERROR(GENERIC);
103 }
104 for (s = 0; s <= max; ++s) {
105 unsigned const tableLog = cstate.stateLog;
106 unsigned const badCost = (tableLog + 1) << kAccuracyLog;
107 unsigned const bitCost = FSE_bitCost(cstate.symbolTT, tableLog, s, kAccuracyLog);
108 if (count[s] == 0)
109 continue;
110 if (bitCost >= badCost) {
111 DEBUGLOG(5, "Repeat FSE_CTable has Prob[%u] == 0", s);
112 return ERROR(GENERIC);
113 }
114 cost += (size_t)count[s] * bitCost;
115 }
116 return cost >> kAccuracyLog;
117 }
118
119 /**
120 * Returns the cost in bits of encoding the distribution in count using the
121 * table described by norm. The max symbol support by norm is assumed >= max.
122 * norm must be valid for every symbol with non-zero probability in count.
123 */
ZSTD_crossEntropyCost(short const * norm,unsigned accuracyLog,unsigned const * count,unsigned const max)124 size_t ZSTD_crossEntropyCost(short const* norm, unsigned accuracyLog,
125 unsigned const* count, unsigned const max)
126 {
127 unsigned const shift = 8 - accuracyLog;
128 size_t cost = 0;
129 unsigned s;
130 assert(accuracyLog <= 8);
131 for (s = 0; s <= max; ++s) {
132 unsigned const normAcc = (norm[s] != -1) ? (unsigned)norm[s] : 1;
133 unsigned const norm256 = normAcc << shift;
134 assert(norm256 > 0);
135 assert(norm256 < 256);
136 cost += count[s] * kInverseProbabilityLog256[norm256];
137 }
138 return cost >> 8;
139 }
140
141 symbolEncodingType_e
ZSTD_selectEncodingType(FSE_repeat * repeatMode,unsigned const * count,unsigned const max,size_t const mostFrequent,size_t nbSeq,unsigned const FSELog,FSE_CTable const * prevCTable,short const * defaultNorm,U32 defaultNormLog,ZSTD_defaultPolicy_e const isDefaultAllowed,ZSTD_strategy const strategy)142 ZSTD_selectEncodingType(
143 FSE_repeat* repeatMode, unsigned const* count, unsigned const max,
144 size_t const mostFrequent, size_t nbSeq, unsigned const FSELog,
145 FSE_CTable const* prevCTable,
146 short const* defaultNorm, U32 defaultNormLog,
147 ZSTD_defaultPolicy_e const isDefaultAllowed,
148 ZSTD_strategy const strategy)
149 {
150 ZSTD_STATIC_ASSERT(ZSTD_defaultDisallowed == 0 && ZSTD_defaultAllowed != 0);
151 if (mostFrequent == nbSeq) {
152 *repeatMode = FSE_repeat_none;
153 if (isDefaultAllowed && nbSeq <= 2) {
154 /* Prefer set_basic over set_rle when there are 2 or less symbols,
155 * since RLE uses 1 byte, but set_basic uses 5-6 bits per symbol.
156 * If basic encoding isn't possible, always choose RLE.
157 */
158 DEBUGLOG(5, "Selected set_basic");
159 return set_basic;
160 }
161 DEBUGLOG(5, "Selected set_rle");
162 return set_rle;
163 }
164 if (strategy < ZSTD_lazy) {
165 if (isDefaultAllowed) {
166 size_t const staticFse_nbSeq_max = 1000;
167 size_t const mult = 10 - strategy;
168 size_t const baseLog = 3;
169 size_t const dynamicFse_nbSeq_min = (((size_t)1 << defaultNormLog) * mult) >> baseLog; /* 28-36 for offset, 56-72 for lengths */
170 assert(defaultNormLog >= 5 && defaultNormLog <= 6); /* xx_DEFAULTNORMLOG */
171 assert(mult <= 9 && mult >= 7);
172 if ( (*repeatMode == FSE_repeat_valid)
173 && (nbSeq < staticFse_nbSeq_max) ) {
174 DEBUGLOG(5, "Selected set_repeat");
175 return set_repeat;
176 }
177 if ( (nbSeq < dynamicFse_nbSeq_min)
178 || (mostFrequent < (nbSeq >> (defaultNormLog-1))) ) {
179 DEBUGLOG(5, "Selected set_basic");
180 /* The format allows default tables to be repeated, but it isn't useful.
181 * When using simple heuristics to select encoding type, we don't want
182 * to confuse these tables with dictionaries. When running more careful
183 * analysis, we don't need to waste time checking both repeating tables
184 * and default tables.
185 */
186 *repeatMode = FSE_repeat_none;
187 return set_basic;
188 }
189 }
190 } else {
191 size_t const basicCost = isDefaultAllowed ? ZSTD_crossEntropyCost(defaultNorm, defaultNormLog, count, max) : ERROR(GENERIC);
192 size_t const repeatCost = *repeatMode != FSE_repeat_none ? ZSTD_fseBitCost(prevCTable, count, max) : ERROR(GENERIC);
193 size_t const NCountCost = ZSTD_NCountCost(count, max, nbSeq, FSELog);
194 size_t const compressedCost = (NCountCost << 3) + ZSTD_entropyCost(count, max, nbSeq);
195
196 if (isDefaultAllowed) {
197 assert(!ZSTD_isError(basicCost));
198 assert(!(*repeatMode == FSE_repeat_valid && ZSTD_isError(repeatCost)));
199 }
200 assert(!ZSTD_isError(NCountCost));
201 assert(compressedCost < ERROR(maxCode));
202 DEBUGLOG(5, "Estimated bit costs: basic=%u\trepeat=%u\tcompressed=%u",
203 (unsigned)basicCost, (unsigned)repeatCost, (unsigned)compressedCost);
204 if (basicCost <= repeatCost && basicCost <= compressedCost) {
205 DEBUGLOG(5, "Selected set_basic");
206 assert(isDefaultAllowed);
207 *repeatMode = FSE_repeat_none;
208 return set_basic;
209 }
210 if (repeatCost <= compressedCost) {
211 DEBUGLOG(5, "Selected set_repeat");
212 assert(!ZSTD_isError(repeatCost));
213 return set_repeat;
214 }
215 assert(compressedCost < basicCost && compressedCost < repeatCost);
216 }
217 DEBUGLOG(5, "Selected set_compressed");
218 *repeatMode = FSE_repeat_check;
219 return set_compressed;
220 }
221
222 size_t
ZSTD_buildCTable(void * dst,size_t dstCapacity,FSE_CTable * nextCTable,U32 FSELog,symbolEncodingType_e type,unsigned * count,U32 max,const BYTE * codeTable,size_t nbSeq,const S16 * defaultNorm,U32 defaultNormLog,U32 defaultMax,const FSE_CTable * prevCTable,size_t prevCTableSize,void * entropyWorkspace,size_t entropyWorkspaceSize)223 ZSTD_buildCTable(void* dst, size_t dstCapacity,
224 FSE_CTable* nextCTable, U32 FSELog, symbolEncodingType_e type,
225 unsigned* count, U32 max,
226 const BYTE* codeTable, size_t nbSeq,
227 const S16* defaultNorm, U32 defaultNormLog, U32 defaultMax,
228 const FSE_CTable* prevCTable, size_t prevCTableSize,
229 void* entropyWorkspace, size_t entropyWorkspaceSize)
230 {
231 BYTE* op = (BYTE*)dst;
232 const BYTE* const oend = op + dstCapacity;
233 DEBUGLOG(6, "ZSTD_buildCTable (dstCapacity=%u)", (unsigned)dstCapacity);
234
235 switch (type) {
236 case set_rle:
237 FORWARD_IF_ERROR(FSE_buildCTable_rle(nextCTable, (BYTE)max), "");
238 RETURN_ERROR_IF(dstCapacity==0, dstSize_tooSmall, "not enough space");
239 *op = codeTable[0];
240 return 1;
241 case set_repeat:
242 memcpy(nextCTable, prevCTable, prevCTableSize);
243 return 0;
244 case set_basic:
245 FORWARD_IF_ERROR(FSE_buildCTable_wksp(nextCTable, defaultNorm, defaultMax, defaultNormLog, entropyWorkspace, entropyWorkspaceSize), ""); /* note : could be pre-calculated */
246 return 0;
247 case set_compressed: {
248 S16 norm[MaxSeq + 1];
249 size_t nbSeq_1 = nbSeq;
250 const U32 tableLog = FSE_optimalTableLog(FSELog, nbSeq, max);
251 if (count[codeTable[nbSeq-1]] > 1) {
252 count[codeTable[nbSeq-1]]--;
253 nbSeq_1--;
254 }
255 assert(nbSeq_1 > 1);
256 FORWARD_IF_ERROR(FSE_normalizeCount(norm, tableLog, count, nbSeq_1, max), "");
257 { size_t const NCountSize = FSE_writeNCount(op, oend - op, norm, max, tableLog); /* overflow protected */
258 FORWARD_IF_ERROR(NCountSize, "FSE_writeNCount failed");
259 FORWARD_IF_ERROR(FSE_buildCTable_wksp(nextCTable, norm, max, tableLog, entropyWorkspace, entropyWorkspaceSize), "");
260 return NCountSize;
261 }
262 }
263 default: assert(0); RETURN_ERROR(GENERIC, "impossible to reach");
264 }
265 }
266
267 FORCE_INLINE_TEMPLATE size_t
ZSTD_encodeSequences_body(void * dst,size_t dstCapacity,FSE_CTable const * CTable_MatchLength,BYTE const * mlCodeTable,FSE_CTable const * CTable_OffsetBits,BYTE const * ofCodeTable,FSE_CTable const * CTable_LitLength,BYTE const * llCodeTable,seqDef const * sequences,size_t nbSeq,int longOffsets)268 ZSTD_encodeSequences_body(
269 void* dst, size_t dstCapacity,
270 FSE_CTable const* CTable_MatchLength, BYTE const* mlCodeTable,
271 FSE_CTable const* CTable_OffsetBits, BYTE const* ofCodeTable,
272 FSE_CTable const* CTable_LitLength, BYTE const* llCodeTable,
273 seqDef const* sequences, size_t nbSeq, int longOffsets)
274 {
275 BIT_CStream_t blockStream;
276 FSE_CState_t stateMatchLength;
277 FSE_CState_t stateOffsetBits;
278 FSE_CState_t stateLitLength;
279
280 RETURN_ERROR_IF(
281 ERR_isError(BIT_initCStream(&blockStream, dst, dstCapacity)),
282 dstSize_tooSmall, "not enough space remaining");
283 DEBUGLOG(6, "available space for bitstream : %i (dstCapacity=%u)",
284 (int)(blockStream.endPtr - blockStream.startPtr),
285 (unsigned)dstCapacity);
286
287 /* first symbols */
288 FSE_initCState2(&stateMatchLength, CTable_MatchLength, mlCodeTable[nbSeq-1]);
289 FSE_initCState2(&stateOffsetBits, CTable_OffsetBits, ofCodeTable[nbSeq-1]);
290 FSE_initCState2(&stateLitLength, CTable_LitLength, llCodeTable[nbSeq-1]);
291 BIT_addBits(&blockStream, sequences[nbSeq-1].litLength, LL_bits[llCodeTable[nbSeq-1]]);
292 if (MEM_32bits()) BIT_flushBits(&blockStream);
293 BIT_addBits(&blockStream, sequences[nbSeq-1].matchLength, ML_bits[mlCodeTable[nbSeq-1]]);
294 if (MEM_32bits()) BIT_flushBits(&blockStream);
295 if (longOffsets) {
296 U32 const ofBits = ofCodeTable[nbSeq-1];
297 unsigned const extraBits = ofBits - MIN(ofBits, STREAM_ACCUMULATOR_MIN-1);
298 if (extraBits) {
299 BIT_addBits(&blockStream, sequences[nbSeq-1].offset, extraBits);
300 BIT_flushBits(&blockStream);
301 }
302 BIT_addBits(&blockStream, sequences[nbSeq-1].offset >> extraBits,
303 ofBits - extraBits);
304 } else {
305 BIT_addBits(&blockStream, sequences[nbSeq-1].offset, ofCodeTable[nbSeq-1]);
306 }
307 BIT_flushBits(&blockStream);
308
309 { size_t n;
310 for (n=nbSeq-2 ; n<nbSeq ; n--) { /* intentional underflow */
311 BYTE const llCode = llCodeTable[n];
312 BYTE const ofCode = ofCodeTable[n];
313 BYTE const mlCode = mlCodeTable[n];
314 U32 const llBits = LL_bits[llCode];
315 U32 const ofBits = ofCode;
316 U32 const mlBits = ML_bits[mlCode];
317 DEBUGLOG(6, "encoding: litlen:%2u - matchlen:%2u - offCode:%7u",
318 (unsigned)sequences[n].litLength,
319 (unsigned)sequences[n].matchLength + MINMATCH,
320 (unsigned)sequences[n].offset);
321 /* 32b*/ /* 64b*/
322 /* (7)*/ /* (7)*/
323 FSE_encodeSymbol(&blockStream, &stateOffsetBits, ofCode); /* 15 */ /* 15 */
324 FSE_encodeSymbol(&blockStream, &stateMatchLength, mlCode); /* 24 */ /* 24 */
325 if (MEM_32bits()) BIT_flushBits(&blockStream); /* (7)*/
326 FSE_encodeSymbol(&blockStream, &stateLitLength, llCode); /* 16 */ /* 33 */
327 if (MEM_32bits() || (ofBits+mlBits+llBits >= 64-7-(LLFSELog+MLFSELog+OffFSELog)))
328 BIT_flushBits(&blockStream); /* (7)*/
329 BIT_addBits(&blockStream, sequences[n].litLength, llBits);
330 if (MEM_32bits() && ((llBits+mlBits)>24)) BIT_flushBits(&blockStream);
331 BIT_addBits(&blockStream, sequences[n].matchLength, mlBits);
332 if (MEM_32bits() || (ofBits+mlBits+llBits > 56)) BIT_flushBits(&blockStream);
333 if (longOffsets) {
334 unsigned const extraBits = ofBits - MIN(ofBits, STREAM_ACCUMULATOR_MIN-1);
335 if (extraBits) {
336 BIT_addBits(&blockStream, sequences[n].offset, extraBits);
337 BIT_flushBits(&blockStream); /* (7)*/
338 }
339 BIT_addBits(&blockStream, sequences[n].offset >> extraBits,
340 ofBits - extraBits); /* 31 */
341 } else {
342 BIT_addBits(&blockStream, sequences[n].offset, ofBits); /* 31 */
343 }
344 BIT_flushBits(&blockStream); /* (7)*/
345 DEBUGLOG(7, "remaining space : %i", (int)(blockStream.endPtr - blockStream.ptr));
346 } }
347
348 DEBUGLOG(6, "ZSTD_encodeSequences: flushing ML state with %u bits", stateMatchLength.stateLog);
349 FSE_flushCState(&blockStream, &stateMatchLength);
350 DEBUGLOG(6, "ZSTD_encodeSequences: flushing Off state with %u bits", stateOffsetBits.stateLog);
351 FSE_flushCState(&blockStream, &stateOffsetBits);
352 DEBUGLOG(6, "ZSTD_encodeSequences: flushing LL state with %u bits", stateLitLength.stateLog);
353 FSE_flushCState(&blockStream, &stateLitLength);
354
355 { size_t const streamSize = BIT_closeCStream(&blockStream);
356 RETURN_ERROR_IF(streamSize==0, dstSize_tooSmall, "not enough space");
357 return streamSize;
358 }
359 }
360
361 static size_t
ZSTD_encodeSequences_default(void * dst,size_t dstCapacity,FSE_CTable const * CTable_MatchLength,BYTE const * mlCodeTable,FSE_CTable const * CTable_OffsetBits,BYTE const * ofCodeTable,FSE_CTable const * CTable_LitLength,BYTE const * llCodeTable,seqDef const * sequences,size_t nbSeq,int longOffsets)362 ZSTD_encodeSequences_default(
363 void* dst, size_t dstCapacity,
364 FSE_CTable const* CTable_MatchLength, BYTE const* mlCodeTable,
365 FSE_CTable const* CTable_OffsetBits, BYTE const* ofCodeTable,
366 FSE_CTable const* CTable_LitLength, BYTE const* llCodeTable,
367 seqDef const* sequences, size_t nbSeq, int longOffsets)
368 {
369 return ZSTD_encodeSequences_body(dst, dstCapacity,
370 CTable_MatchLength, mlCodeTable,
371 CTable_OffsetBits, ofCodeTable,
372 CTable_LitLength, llCodeTable,
373 sequences, nbSeq, longOffsets);
374 }
375
376
377 #if DYNAMIC_BMI2
378
379 static TARGET_ATTRIBUTE("bmi2") size_t
ZSTD_encodeSequences_bmi2(void * dst,size_t dstCapacity,FSE_CTable const * CTable_MatchLength,BYTE const * mlCodeTable,FSE_CTable const * CTable_OffsetBits,BYTE const * ofCodeTable,FSE_CTable const * CTable_LitLength,BYTE const * llCodeTable,seqDef const * sequences,size_t nbSeq,int longOffsets)380 ZSTD_encodeSequences_bmi2(
381 void* dst, size_t dstCapacity,
382 FSE_CTable const* CTable_MatchLength, BYTE const* mlCodeTable,
383 FSE_CTable const* CTable_OffsetBits, BYTE const* ofCodeTable,
384 FSE_CTable const* CTable_LitLength, BYTE const* llCodeTable,
385 seqDef const* sequences, size_t nbSeq, int longOffsets)
386 {
387 return ZSTD_encodeSequences_body(dst, dstCapacity,
388 CTable_MatchLength, mlCodeTable,
389 CTable_OffsetBits, ofCodeTable,
390 CTable_LitLength, llCodeTable,
391 sequences, nbSeq, longOffsets);
392 }
393
394 #endif
395
ZSTD_encodeSequences(void * dst,size_t dstCapacity,FSE_CTable const * CTable_MatchLength,BYTE const * mlCodeTable,FSE_CTable const * CTable_OffsetBits,BYTE const * ofCodeTable,FSE_CTable const * CTable_LitLength,BYTE const * llCodeTable,seqDef const * sequences,size_t nbSeq,int longOffsets,int bmi2)396 size_t ZSTD_encodeSequences(
397 void* dst, size_t dstCapacity,
398 FSE_CTable const* CTable_MatchLength, BYTE const* mlCodeTable,
399 FSE_CTable const* CTable_OffsetBits, BYTE const* ofCodeTable,
400 FSE_CTable const* CTable_LitLength, BYTE const* llCodeTable,
401 seqDef const* sequences, size_t nbSeq, int longOffsets, int bmi2)
402 {
403 DEBUGLOG(5, "ZSTD_encodeSequences: dstCapacity = %u", (unsigned)dstCapacity);
404 #if DYNAMIC_BMI2
405 if (bmi2) {
406 return ZSTD_encodeSequences_bmi2(dst, dstCapacity,
407 CTable_MatchLength, mlCodeTable,
408 CTable_OffsetBits, ofCodeTable,
409 CTable_LitLength, llCodeTable,
410 sequences, nbSeq, longOffsets);
411 }
412 #endif
413 (void)bmi2;
414 return ZSTD_encodeSequences_default(dst, dstCapacity,
415 CTable_MatchLength, mlCodeTable,
416 CTable_OffsetBits, ofCodeTable,
417 CTable_LitLength, llCodeTable,
418 sequences, nbSeq, longOffsets);
419 }
420