Approximate FSE encoding costs for selection
Estimate the cost for using FSE modes `set_basic`, `set_compressed`, and `set_repeat`, and select the one with the lowest cost. * The cost of `set_basic` is computed using the cross-entropy cost function `ZSTD_crossEntropyCost()`, using the normalized default count and the count. * The cost of `set_repeat` is computed using `FSE_bitCost()`. We check the previous table to see if it is able to represent the distribution. * The cost of `set_compressed` is computed with the entropy cost function `ZSTD_entropyCost()`, together with the cost of writing the normalized count `ZSTD_NCountCost()`.
This commit is contained in:
Nick Terrell
+7
-3
@@ -402,6 +402,7 @@ typedef struct {
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const void* stateTable;
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const void* symbolTT;
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unsigned stateLog;
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unsigned maxSymbolValue;
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} FSE_CState_t;
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static void FSE_initCState(FSE_CState_t* CStatePtr, const FSE_CTable* ct);
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@@ -538,11 +539,13 @@ MEM_STATIC void FSE_initCState(FSE_CState_t* statePtr, const FSE_CTable* ct)
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{
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const void* ptr = ct;
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const U16* u16ptr = (const U16*) ptr;
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const U32 tableLog = MEM_read16(ptr);
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const U32 tableLog = MEM_read16(u16ptr);
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const U32 maxSymbolValue = MEM_read16(u16ptr + 1);
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statePtr->value = (ptrdiff_t)1<<tableLog;
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statePtr->stateTable = u16ptr+2;
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statePtr->symbolTT = ((const U32*)ct + 1 + (tableLog ? (1<<(tableLog-1)) : 1));
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statePtr->stateLog = tableLog;
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statePtr->maxSymbolValue = maxSymbolValue;
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}
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@@ -581,12 +584,13 @@ MEM_STATIC U32 FSE_getMaxNbBits(const void* symbolTTPtr, U32 symbolValue)
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return (symbolTT[symbolValue].deltaNbBits + ((1<<16)-1)) >> 16;
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}
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/* FSE_bitCost_b256() :
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/* FSE_bitCost() :
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* Approximate symbol cost,
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* provide fractional value, using fixed-point format (accuracyLog fractional bits)
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* note: assume symbolValue is valid */
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MEM_STATIC U32 FSE_bitCost(const FSE_symbolCompressionTransform* symbolTT, U32 tableLog, U32 symbolValue, U32 accuracyLog)
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MEM_STATIC U32 FSE_bitCost(const void* symbolTTPtr, U32 tableLog, U32 symbolValue, U32 accuracyLog)
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{
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const FSE_symbolCompressionTransform* symbolTT = (const FSE_symbolCompressionTransform*) symbolTTPtr;
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U32 const minNbBits = symbolTT[symbolValue].deltaNbBits >> 16;
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U32 const threshold = (minNbBits+1) << 16;
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assert(tableLog < 16);
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+205
-34
@@ -1561,6 +1561,129 @@ void ZSTD_seqToCodes(const seqStore_t* seqStorePtr)
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mlCodeTable[seqStorePtr->longLengthPos] = MaxML;
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}
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/**
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* -log2(x / 256) lookup table for x in [0, 256).
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* If x == 0: Return 0
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* Else: Return floor(-log2(x / 256) * 256)
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*/
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static unsigned const kInverseProbabiltyLog256[256] = {
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0, 2048, 1792, 1642, 1536, 1453, 1386, 1329, 1280, 1236, 1197, 1162,
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1130, 1100, 1073, 1047, 1024, 1001, 980, 960, 941, 923, 906, 889,
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874, 859, 844, 830, 817, 804, 791, 779, 768, 756, 745, 734,
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724, 714, 704, 694, 685, 676, 667, 658, 650, 642, 633, 626,
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618, 610, 603, 595, 588, 581, 574, 567, 561, 554, 548, 542,
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535, 529, 523, 517, 512, 506, 500, 495, 489, 484, 478, 473,
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468, 463, 458, 453, 448, 443, 438, 434, 429, 424, 420, 415,
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411, 407, 402, 398, 394, 390, 386, 382, 377, 373, 370, 366,
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362, 358, 354, 350, 347, 343, 339, 336, 332, 329, 325, 322,
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318, 315, 311, 308, 305, 302, 298, 295, 292, 289, 286, 282,
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279, 276, 273, 270, 267, 264, 261, 258, 256, 253, 250, 247,
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244, 241, 239, 236, 233, 230, 228, 225, 222, 220, 217, 215,
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212, 209, 207, 204, 202, 199, 197, 194, 192, 190, 187, 185,
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182, 180, 178, 175, 173, 171, 168, 166, 164, 162, 159, 157,
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155, 153, 151, 149, 146, 144, 142, 140, 138, 136, 134, 132,
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130, 128, 126, 123, 121, 119, 117, 115, 114, 112, 110, 108,
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106, 104, 102, 100, 98, 96, 94, 93, 91, 89, 87, 85,
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83, 82, 80, 78, 76, 74, 73, 71, 69, 67, 66, 64,
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62, 61, 59, 57, 55, 54, 52, 50, 49, 47, 46, 44,
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42, 41, 39, 37, 36, 34, 33, 31, 30, 28, 26, 25,
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23, 22, 20, 19, 17, 16, 14, 13, 11, 10, 8, 7,
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5, 4, 2, 1,
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};
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/**
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* Returns the cost in bits of encoding the distribution described by count
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* using the entropy bound.
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*/
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static size_t ZSTD_entropyCost(unsigned const* count, unsigned const max, size_t const total)
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{
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unsigned cost = 0;
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unsigned s;
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for (s = 0; s <= max; ++s) {
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unsigned norm = (unsigned)((256 * count[s]) / total);
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if (count[s] != 0 && norm == 0)
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norm = 1;
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assert(count[s] < total);
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cost += count[s] * kInverseProbabiltyLog256[norm];
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}
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return cost >> 8;
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}
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/**
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* Returns the cost in bits of encoding the distribution in count using the
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* table described by norm. The max symbol support by norm is assumed >= max.
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* norm must be valid for every symbol with non-zero probability in count.
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*/
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static size_t ZSTD_crossEntropyCost(short const* norm, unsigned accuracyLog,
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unsigned const* count, unsigned const max)
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{
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unsigned const shift = 8 - accuracyLog;
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size_t cost = 0;
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unsigned s;
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assert(accuracyLog <= 8);
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for (s = 0; s <= max; ++s) {
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unsigned const normAcc = norm[s] != -1 ? norm[s] : 1;
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unsigned const norm256 = normAcc << shift;
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assert(norm256 > 0);
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assert(norm256 < 256);
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cost += count[s] * kInverseProbabiltyLog256[norm256];
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}
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return cost >> 8;
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}
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/**
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* Returns the cost in bits of encoding the distribution in count using ctable.
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* Returns an error if ctable cannot represent all the symbols in count.
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*/
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static size_t ZSTD_fseBitCost(
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FSE_CTable const* ctable,
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unsigned const* count,
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unsigned const max)
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{
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unsigned const kAccuracyLog = 8;
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size_t cost = 0;
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unsigned s;
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FSE_CState_t cstate;
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FSE_initCState(&cstate, ctable);
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if (cstate.maxSymbolValue < max) {
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DEBUGLOG(5, "Repeat FSE_CTable has maxSymbolValue %u < %u",
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cstate.maxSymbolValue, max);
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return ERROR(GENERIC);
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}
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for (s = 0; s <= max; ++s) {
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unsigned const tableLog = cstate.stateLog;
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unsigned const badCost = (tableLog + 1) << kAccuracyLog;
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unsigned const bitCost = FSE_bitCost(cstate.symbolTT, tableLog, s, kAccuracyLog);
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if (count[s] == 0)
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continue;
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if (bitCost >= badCost) {
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DEBUGLOG(5, "Repeat FSE_CTable has Prob[%u] == 0", s);
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return ERROR(GENERIC);
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}
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cost += count[s] * bitCost;
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}
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return cost >> kAccuracyLog;
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}
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/**
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* Returns the cost in bytes of encoding the normalized count header.
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* Returns an error if any of the helper functions return an error.
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*/
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static size_t ZSTD_NCountCost(unsigned const* count, unsigned const max,
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size_t const nbSeq, unsigned const FSELog)
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{
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BYTE wksp[FSE_NCOUNTBOUND];
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S16 norm[MaxSeq + 1];
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const U32 tableLog = FSE_optimalTableLog(FSELog, nbSeq, max);
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CHECK_F(FSE_normalizeCount(norm, tableLog, count, nbSeq, max));
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return FSE_writeNCount(wksp, sizeof(wksp), norm, max, tableLog);
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}
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typedef enum {
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ZSTD_defaultDisallowed = 0,
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ZSTD_defaultAllowed = 1
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@@ -1568,37 +1691,73 @@ typedef enum {
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MEM_STATIC
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symbolEncodingType_e ZSTD_selectEncodingType(
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FSE_repeat* repeatMode, size_t const mostFrequent, size_t nbSeq,
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U32 defaultNormLog, ZSTD_defaultPolicy_e const isDefaultAllowed)
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FSE_repeat* repeatMode, unsigned const* count, unsigned const max,
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size_t const mostFrequent, size_t nbSeq, unsigned const FSELog,
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FSE_CTable const* prevCTable,
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short const* defaultNorm, U32 defaultNormLog,
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ZSTD_defaultPolicy_e const isDefaultAllowed,
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ZSTD_strategy const strategy)
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{
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#define MIN_SEQ_FOR_DYNAMIC_FSE 64
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#define MAX_SEQ_FOR_STATIC_FSE 1000
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ZSTD_STATIC_ASSERT(ZSTD_defaultDisallowed == 0 && ZSTD_defaultAllowed != 0);
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if ((mostFrequent == nbSeq) && (!isDefaultAllowed || nbSeq > 2)) {
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if (mostFrequent == nbSeq) {
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*repeatMode = FSE_repeat_none;
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if (isDefaultAllowed && nbSeq <= 2) {
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/* Prefer set_basic over set_rle when there are 2 or less symbols,
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* since RLE uses 1 byte, but set_basic uses 5-6 bits per symbol.
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* If basic encoding isn't possible, always choose RLE.
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*/
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DEBUGLOG(5, "Selected set_basic");
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return set_basic;
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}
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DEBUGLOG(5, "Selected set_rle");
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/* Prefer set_basic over set_rle when there are 2 or less symbols,
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* since RLE uses 1 byte, but set_basic uses 5-6 bits per symbol.
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* If basic encoding isn't possible, always choose RLE.
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*/
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*repeatMode = FSE_repeat_check;
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return set_rle;
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}
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if ( isDefaultAllowed
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&& (*repeatMode == FSE_repeat_valid) && (nbSeq < MAX_SEQ_FOR_STATIC_FSE)) {
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DEBUGLOG(5, "Selected set_repeat");
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return set_repeat;
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}
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if ( isDefaultAllowed
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&& ((nbSeq < MIN_SEQ_FOR_DYNAMIC_FSE) || (mostFrequent < (nbSeq >> (defaultNormLog-1)))) ) {
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DEBUGLOG(5, "Selected set_basic");
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/* The format allows default tables to be repeated, but it isn't useful.
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* When using simple heuristics to select encoding type, we don't want
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* to confuse these tables with dictionaries. When running more careful
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* analysis, we don't need to waste time checking both repeating tables
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* and default tables.
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*/
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*repeatMode = FSE_repeat_none;
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return set_basic;
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if (strategy < ZSTD_lazy) {
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if (isDefaultAllowed) {
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if ((*repeatMode == FSE_repeat_valid) && (nbSeq < MAX_SEQ_FOR_STATIC_FSE)) {
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DEBUGLOG(5, "Selected set_repeat");
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return set_repeat;
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}
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if ((nbSeq < MIN_SEQ_FOR_DYNAMIC_FSE) || (mostFrequent < (nbSeq >> (defaultNormLog-1)))) {
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DEBUGLOG(5, "Selected set_basic");
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/* The format allows default tables to be repeated, but it isn't useful.
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* When using simple heuristics to select encoding type, we don't want
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* to confuse these tables with dictionaries. When running more careful
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* analysis, we don't need to waste time checking both repeating tables
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* and default tables.
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*/
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*repeatMode = FSE_repeat_none;
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return set_basic;
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}
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}
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} else {
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size_t const basicCost = isDefaultAllowed ? ZSTD_crossEntropyCost(defaultNorm, defaultNormLog, count, max) : ERROR(GENERIC);
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size_t const repeatCost = *repeatMode != FSE_repeat_none ? ZSTD_fseBitCost(prevCTable, count, max) : ERROR(GENERIC);
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size_t const NCountCost = ZSTD_NCountCost(count, max, nbSeq, FSELog);
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size_t const compressedCost = (NCountCost << 3) + ZSTD_entropyCost(count, max, nbSeq);
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if (isDefaultAllowed) {
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assert(!ZSTD_isError(basicCost));
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assert(!(*repeatMode == FSE_repeat_valid && ZSTD_isError(repeatCost)));
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}
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assert(!ZSTD_isError(NCountCost));
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assert(compressedCost < ERROR(maxCode));
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DEBUGLOG(5, "Estimated bit costs: basic=%u\trepeat=%u\tcompressed=%u",
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(U32)basicCost, (U32)repeatCost, (U32)compressedCost);
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if (basicCost <= repeatCost && basicCost <= compressedCost) {
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DEBUGLOG(5, "Selected set_basic");
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assert(isDefaultAllowed);
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*repeatMode = FSE_repeat_none;
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return set_basic;
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}
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if (repeatCost <= compressedCost) {
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DEBUGLOG(5, "Selected set_repeat");
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assert(!ZSTD_isError(repeatCost));
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return set_repeat;
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}
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assert(compressedCost < basicCost && compressedCost < repeatCost);
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}
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DEBUGLOG(5, "Selected set_compressed");
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*repeatMode = FSE_repeat_check;
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@@ -1803,6 +1962,7 @@ MEM_STATIC size_t ZSTD_compressSequences_internal(seqStore_t* seqStorePtr,
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const int bmi2)
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{
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const int longOffsets = cctxParams->cParams.windowLog > STREAM_ACCUMULATOR_MIN;
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ZSTD_strategy const strategy = cctxParams->cParams.strategy;
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U32 count[MaxSeq+1];
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FSE_CTable* CTable_LitLength = nextEntropy->litlengthCTable;
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FSE_CTable* CTable_OffsetBits = nextEntropy->offcodeCTable;
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@@ -1844,13 +2004,20 @@ MEM_STATIC size_t ZSTD_compressSequences_internal(seqStore_t* seqStorePtr,
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else
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op[0]=0xFF, MEM_writeLE16(op+1, (U16)(nbSeq - LONGNBSEQ)), op+=3;
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if (nbSeq==0) {
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memcpy(nextEntropy->litlengthCTable, prevEntropy->litlengthCTable, sizeof(prevEntropy->litlengthCTable));
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nextEntropy->litlength_repeatMode = prevEntropy->litlength_repeatMode;
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memcpy(nextEntropy->offcodeCTable, prevEntropy->offcodeCTable, sizeof(prevEntropy->offcodeCTable));
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nextEntropy->offcode_repeatMode = prevEntropy->offcode_repeatMode;
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memcpy(nextEntropy->matchlengthCTable, prevEntropy->matchlengthCTable, sizeof(prevEntropy->matchlengthCTable));
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nextEntropy->matchlength_repeatMode = prevEntropy->matchlength_repeatMode;
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return op - ostart;
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/* Check that all the Huffman data is first */
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ZSTD_STATIC_ASSERT(offsetof(ZSTD_entropyCTables_t, hufCTable) == 0);
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ZSTD_STATIC_ASSERT(
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offsetof(ZSTD_entropyCTables_t, hufCTable_repeatMode) ==
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sizeof(prevEntropy->hufCTable));
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ZSTD_STATIC_ASSERT(
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offsetof(ZSTD_entropyCTables_t, offcodeCTable) ==
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sizeof(prevEntropy->hufCTable) + sizeof(prevEntropy->hufCTable_repeatMode));
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/* Copy starting at the first FSE element */
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memcpy(
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nextEntropy->offcodeCTable,
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prevEntropy->offcodeCTable,
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sizeof(*prevEntropy) - offsetof(ZSTD_entropyCTables_t, offcodeCTable));
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return op - ostart;
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}
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/* seqHead : flags for FSE encoding type */
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@@ -1863,7 +2030,9 @@ MEM_STATIC size_t ZSTD_compressSequences_internal(seqStore_t* seqStorePtr,
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size_t const mostFrequent = FSE_countFast_wksp(count, &max, llCodeTable, nbSeq, workspace);
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DEBUGLOG(5, "Building LL table");
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nextEntropy->litlength_repeatMode = prevEntropy->litlength_repeatMode;
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LLtype = ZSTD_selectEncodingType(&nextEntropy->litlength_repeatMode, mostFrequent, nbSeq, LL_defaultNormLog, ZSTD_defaultAllowed);
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LLtype = ZSTD_selectEncodingType(&nextEntropy->litlength_repeatMode, count, max, mostFrequent, nbSeq, LLFSELog, prevEntropy->litlengthCTable, LL_defaultNorm, LL_defaultNormLog, ZSTD_defaultAllowed, strategy);
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assert(set_basic < set_compressed && set_rle < set_compressed);
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assert(!(LLtype < set_compressed && nextEntropy->litlength_repeatMode != FSE_repeat_none)); /* We don't copy tables */
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{ size_t const countSize = ZSTD_buildCTable(op, oend - op, CTable_LitLength, LLFSELog, (symbolEncodingType_e)LLtype,
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count, max, llCodeTable, nbSeq, LL_defaultNorm, LL_defaultNormLog, MaxLL,
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prevEntropy->litlengthCTable, sizeof(prevEntropy->litlengthCTable),
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@@ -1878,7 +2047,8 @@ MEM_STATIC size_t ZSTD_compressSequences_internal(seqStore_t* seqStorePtr,
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ZSTD_defaultPolicy_e const defaultPolicy = (max <= DefaultMaxOff) ? ZSTD_defaultAllowed : ZSTD_defaultDisallowed;
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DEBUGLOG(5, "Building OF table");
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nextEntropy->offcode_repeatMode = prevEntropy->offcode_repeatMode;
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Offtype = ZSTD_selectEncodingType(&nextEntropy->offcode_repeatMode, mostFrequent, nbSeq, OF_defaultNormLog, defaultPolicy);
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Offtype = ZSTD_selectEncodingType(&nextEntropy->offcode_repeatMode, count, max, mostFrequent, nbSeq, OffFSELog, prevEntropy->offcodeCTable, OF_defaultNorm, OF_defaultNormLog, defaultPolicy, strategy);
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assert(!(Offtype < set_compressed && nextEntropy->offcode_repeatMode != FSE_repeat_none)); /* We don't copy tables */
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{ size_t const countSize = ZSTD_buildCTable(op, oend - op, CTable_OffsetBits, OffFSELog, (symbolEncodingType_e)Offtype,
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count, max, ofCodeTable, nbSeq, OF_defaultNorm, OF_defaultNormLog, DefaultMaxOff,
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prevEntropy->offcodeCTable, sizeof(prevEntropy->offcodeCTable),
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@@ -1891,7 +2061,8 @@ MEM_STATIC size_t ZSTD_compressSequences_internal(seqStore_t* seqStorePtr,
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size_t const mostFrequent = FSE_countFast_wksp(count, &max, mlCodeTable, nbSeq, workspace);
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DEBUGLOG(5, "Building ML table");
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nextEntropy->matchlength_repeatMode = prevEntropy->matchlength_repeatMode;
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MLtype = ZSTD_selectEncodingType(&nextEntropy->matchlength_repeatMode, mostFrequent, nbSeq, ML_defaultNormLog, ZSTD_defaultAllowed);
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MLtype = ZSTD_selectEncodingType(&nextEntropy->matchlength_repeatMode, count, max, mostFrequent, nbSeq, MLFSELog, prevEntropy->matchlengthCTable, ML_defaultNorm, ML_defaultNormLog, ZSTD_defaultAllowed, strategy);
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assert(!(MLtype < set_compressed && nextEntropy->matchlength_repeatMode != FSE_repeat_none)); /* We don't copy tables */
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{ size_t const countSize = ZSTD_buildCTable(op, oend - op, CTable_MatchLength, MLFSELog, (symbolEncodingType_e)MLtype,
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count, max, mlCodeTable, nbSeq, ML_defaultNorm, ML_defaultNormLog, MaxML,
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prevEntropy->matchlengthCTable, sizeof(prevEntropy->matchlengthCTable),
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@@ -53,11 +53,15 @@ typedef struct ZSTD_prefixDict_s {
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} ZSTD_prefixDict;
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typedef struct {
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/* Huffman data
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* Must be before the FSE data.
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*/
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U32 hufCTable[HUF_CTABLE_SIZE_U32(255)];
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HUF_repeat hufCTable_repeatMode;
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/* FSE data */
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FSE_CTable offcodeCTable[FSE_CTABLE_SIZE_U32(OffFSELog, MaxOff)];
|
||||
FSE_CTable matchlengthCTable[FSE_CTABLE_SIZE_U32(MLFSELog, MaxML)];
|
||||
FSE_CTable litlengthCTable[FSE_CTABLE_SIZE_U32(LLFSELog, MaxLL)];
|
||||
HUF_repeat hufCTable_repeatMode;
|
||||
FSE_repeat offcode_repeatMode;
|
||||
FSE_repeat matchlength_repeatMode;
|
||||
FSE_repeat litlength_repeatMode;
|
||||
|
||||
Reference in New Issue
Block a user