What's the purpose of those constants in the zstd normalization algorithm?

Question

I was looking at the normalization algorithm used in the fse implementation in the zstd repository and I don't understand some parts as:

static U32 const rtbTable[] = {     0, 473195, 504333, 520860, 550000, 700000, 750000, 830000 };

I tried to run that code with various inputs and I get a good result since the normalization output sum has also to be equal to 2^tableLog. It seems to be a table of thresholds to make proba -= 1 or proba +=1 for all proba < 8. Furthermore, the vStep variable is also mysterious for me =-)

Here is the full function:

size_t FSE_normalizeCount (short* normalizedCounter, unsigned tableLog,
                           const unsigned* count, size_t total,
                           unsigned maxSymbolValue, unsigned useLowProbCount)
{
    /* Sanity checks */
    if (tableLog==0) tableLog = FSE_DEFAULT_TABLELOG;
    if (tableLog < FSE_MIN_TABLELOG) return ERROR(GENERIC);   /* Unsupported size */
    if (tableLog > FSE_MAX_TABLELOG) return ERROR(tableLog_tooLarge);   /* Unsupported size */
    if (tableLog < FSE_minTableLog(total, maxSymbolValue)) return ERROR(GENERIC);   /* Too small tableLog, compression potentially impossible */


    {   static U32 const rtbTable[] = {     0, 473195, 504333, 520860, 550000, 700000, 750000, 830000 };
        short const lowProbCount = useLowProbCount ? -1 : 1;
        U64 const scale = 62 - tableLog;
        U64 const step = ZSTD_div64((U64)1<<62, (U32)total);   /* <== here, one division ! */
        U64 const vStep = 1ULL<<(scale-20);
        int stillToDistribute = 1<<tableLog;
        unsigned s;
        unsigned largest=0;
        short largestP=0;
        U32 lowThreshold = (U32)(total >> tableLog);


        for (s=0; s<=maxSymbolValue; s++) {
            if (count[s] == total) return 0;   /* rle special case */
            if (count[s] == 0) { normalizedCounter[s]=0; continue; }
            if (count[s] <= lowThreshold) {
                normalizedCounter[s] = lowProbCount;
                stillToDistribute--;
            } else {
                short proba = (short)((count[s]*step) >> scale);
                if (proba<8) {
                    U64 restToBeat = vStep * rtbTable[proba];
                    proba += (count[s]*step) - ((U64)proba<<scale) > restToBeat;
                }
                if (proba > largestP) { largestP=proba; largest=s; }
                normalizedCounter[s] = proba;
                stillToDistribute -= proba;
        }   }
        if (-stillToDistribute >= (normalizedCounter[largest] >> 1)) {
            /* corner case, need another normalization method */
            size_t const errorCode = FSE_normalizeM2(normalizedCounter, tableLog, count, total, maxSymbolValue, lowProbCount);
            if (FSE_isError(errorCode)) return errorCode;
        }
        else normalizedCounter[largest] += (short)stillToDistribute;
    }

}

If you want the link of the file: you can look here

Someone knows what's the purpose of those variables? Are they related to a known normalization algorithm?