slight error in difficulty computation

[Enzo]

I don't understand this:

$ curl --url http://***:***@127.0.0.1:8332 -H 'content-type: text/plain;'  --data-binary '{"jsonrpc": "1.0", "id":"curltest", "method": "getwork", "params": [] }'
{"result":{"midstate":"df92c2b8aac64fc5d15a0ff08a8950453ce9e8fb1ecfa39cb8aeaca78bae173a","data":"0000000174dae8b4ae722300d81693b97993f4a57dc7c8151b980d4a00003bfc00000000b79f998 e1df8db02f7d2ba1676e7060a57fa8a5764990629f53173f8b61d8c1f4dde5b591a44b9f2000000 0000000080000000000000000000000000000000000000000000000000000000000000000000000 0000000000080020000","hash1":"0000000000000000000000000000000000000000000000000000000000000000000000800000000 0000000000000000000000000000000000000000000010000","target":"0000000000000000000000000000000000000000000000f2b944000000000000"},"error":null,"id":"curltest"}

$ curl --url http://***.***@127.0.0.1:8332 -H 'content-type: text/plain;'  --data-binary '{"jsonrpc": "1.0", "id":"curltest", "method": "getdifficulty", "params": [] }'
{"result":244139.48158254,"error":null,"id":"curltest"}

$ echo "base=10;ibase=16;scale=8;00000000FFFF0000000000000000000000000000000000000000000000000000 / 00000000000044B9F20000000000000000000000000000000000000000000000" |bc
244112.48777433


Why I get 244112.48777433 instead of 244139.48158254 ?

Enzo

[1713492598]

1713492598

[realnowhereman]

Because bc is better at arbitrary precision floating point calculation than bitcoin.

Bitcoin uses an approximation:

Code:

double GetDifficulty()
{
    // Floating point number that is a multiple of the minimum difficulty,
    // minimum difficulty = 1.0.
    if (pindexBest == NULL)
        return 1.0;
    int nShift = 256 - 32 - 31; // to fit in a uint
    double dMinimum = (CBigNum().SetCompact(bnProofOfWorkLimit.GetCompact()) >> nShift).getuint();
    double dCurrently = (CBigNum().SetCompact(pindexBest->nBits) >> nShift).getuint();
    return dMinimum / dCurrently;
}

In case its not clear, it doesn't use the most significant bits, it just shifts the bignums representing the current target and the minimum target down by a fixed number of bits, and then divides those numbers to get a floating point answer.  It's not the best approximation for two reasons:

• It potentially throws away resolution by assuming knowledge of the minimum target.  Fortunately that assumption is true.
• Doubles contain more than 32 bits worth of precision, and the division is done with two 32 bit integers.

Short of implementing a full arbitrary precision floating point division (which isn't trivial), this psuedo code might be better:

Code:

unsigned int hb1, hb2;
hb1 = highest_bit( proofOfWorkLimit );
hb2 = highest_bit( currentTarget );
if( hb2 > hb1 )
  hb1 = hb2;
hb1 -= bits_of_precision_in_double;

uint64_t L = proofOfWorkLimit >> hb1;
uint64_t T = currentTarget >> hb1;

return (double)(L)/T;

To be honest though, there's no real reason to change it.  It's only used for displaying to users, never for calculations.  Other than for pride, there's no pressing need to fix it.

[Pieter Wuille]

There's already a patch to fix it, see https://github.com/bitcoin/bitcoin/pull/276

[Enzo]

Because bc is better at arbitrary precision floating point calculation than bitcoin.

So I stumbled upon a bug in bitclient (a minor bug, obviously)
I would like to  point out that there's no need of an high precision calculator: target is a big number but with few significant digits. The maximum target has only 4  significant hex digits (FFFF), I don't know how many there are in the current target but I suppose there's no need for it to have many more.