implemented fractional bit cost evaluation

for FSE symbols.

While it seems to work, the gains are negligible compared to rough maxNbBits evaluation.
There are even a few losses sometimes, that still need to be explained.
Furthermode, there are still cases where btlazy2 does a better job than btopt,
which seems rather strange too.

lib/common/fse.h

@@ -577,10 +577,23 @@ MEM_STATIC void FSE_flushCState(BIT_CStream_t* bitC, const FSE_CState_t* statePt
 
 MEM_STATIC U32 FSE_getMaxNbBits(const FSE_symbolCompressionTransform* symbolTT, U32 symbolValue)
 {
-    assert(symbolValue <= FSE_MAX_SYMBOL_VALUE);
     return (symbolTT[symbolValue].deltaNbBits + ((1<<16)-1)) >> 16;
 }
 
+/* FSE_bitCost_b256() :
+ * Approximate symbol cost,
+ * provide fractional value, using fixed-point format (8 bit) */
+MEM_STATIC U32 FSE_bitCost_b256(const FSE_symbolCompressionTransform* symbolTT, U32 tableLog, U32 symbolValue)
+{
+    U32 const minNbBits = symbolTT[symbolValue].deltaNbBits >> 16;
+    U32 const threshold = (minNbBits+1) << 16;
+    assert(symbolTT[symbolValue].deltaNbBits + (1<<tableLog) <= threshold);
+    U32 const deltaFromThreshold = threshold - (symbolTT[symbolValue].deltaNbBits + (1 << tableLog));
+    U32 const normalizedDeltaFromThreshold = (deltaFromThreshold << 8) >> tableLog;   /* linear interpolation (very approximate) */
+    assert(normalizedDeltaFromThreshold <= 256);
+    return (minNbBits+1)*256 - normalizedDeltaFromThreshold;
+}
+
 
 /* ======    Decompression    ====== */
 

lib/compress/zstd_opt.c

@@ -126,11 +126,13 @@ static U32 ZSTD_litLengthPrice(U32 const litLength, const optState_t* const optP
         U32 const llCode = ZSTD_LLcode(litLength);
         FSE_CState_t cstate;
         FSE_initCState(&cstate, optPtr->symbolCosts->litlengthCTable);
-        return (LL_bits[llCode] + FSE_getMaxNbBits(cstate.symbolTT, llCode)) << 8;
+        U32 const price = LL_bits[llCode]*256 + FSE_bitCost_b256(cstate.symbolTT, cstate.stateLog, llCode);
+        DEBUGLOG(8, "ZSTD_litLengthPrice: ll=%u, bitCost=%.2f", litLength, (double)price / 256);
+        return price;
     }
     if (optPtr->priceType == zop_predef) return ZSTD_highbit32((U32)litLength+1);
 
-    /* literal Length */
+    /* dynamic statistics */
     {   U32 const llCode = ZSTD_LLcode(litLength);
         return (LL_bits[llCode] + optPtr->log2litLengthSum - ZSTD_highbit32(optPtr->litLengthFreq[llCode]+1)) << 8;
     }
@@ -156,7 +158,9 @@ static int ZSTD_litLengthContribution(U32 const litLength, const optState_t* con
         U32 const llCode = ZSTD_LLcode(litLength);
         FSE_CState_t cstate;
         FSE_initCState(&cstate, optPtr->symbolCosts->litlengthCTable);
-        return ((int)(LL_bits[llCode] + FSE_getMaxNbBits(cstate.symbolTT, llCode)) - FSE_getMaxNbBits(cstate.symbolTT, 0)) * 256;
+        return (int)(LL_bits[llCode] * 256)
+             + FSE_bitCost_b256(cstate.symbolTT, cstate.stateLog, llCode)
+             - FSE_bitCost_b256(cstate.symbolTT, cstate.stateLog, 0);
     }
     if (optPtr->priceType >= zop_predef) return ZSTD_highbit32(litLength+1);
 
@@ -205,9 +209,8 @@ ZSTD_getMatchPrice(U32 const offset, U32 const matchLength,
         FSE_CState_t mlstate, offstate;
         FSE_initCState(&mlstate, optPtr->symbolCosts->matchlengthCTable);
         FSE_initCState(&offstate, optPtr->symbolCosts->offcodeCTable);
-        return (FSE_getMaxNbBits(offstate.symbolTT, offCode) + offCode
+        return FSE_bitCost_b256(offstate.symbolTT, offstate.stateLog, offCode) + offCode*256
-             + FSE_getMaxNbBits(mlstate.symbolTT, mlCode) + ML_bits[mlCode])
+             + FSE_bitCost_b256(mlstate.symbolTT, mlstate.stateLog, mlCode) + ML_bits[mlCode]*256;
-             * 256;
     }
 
     if (optPtr->priceType == zop_predef)  /* fixed scheme, do not use statistics */

lib/decompress/huf_decompress.c

@@ -965,7 +965,7 @@ static const algo_time_t algoTime[16 /* Quantization */][3 /* single, double, qu
 U32 HUF_selectDecoder (size_t dstSize, size_t cSrcSize)
 {
     assert(dstSize > 0);
-    assert(dstSize <= 128 KB);
+    assert(dstSize <= 128*1024);
     /* decoder timing evaluation */
     {   U32 const Q = (cSrcSize >= dstSize) ? 15 : (U32)(cSrcSize * 16 / dstSize);   /* Q < 16 */
         U32 const D256 = (U32)(dstSize >> 8);