Trying to understand nbits value from stratum protocol

I'm looking at the stratum protocol and I'm having a problem with the nbits value of the mining.notify method. I have trouble calculating it, I assume it's the currency difficulty.

I pull a notify from a dogecoin pool and it returned 1b3cc366 and at the time the difficulty was 1078.52975077.

I'm assuming here that 1b3cc366 should give me 1078.52975077 when converted. But I can't seem to do the conversion right.

I've looked here, here and also tried the .NET function BitConverter.Int64BitsToDouble.

Can someone help me understand what the nbits value signify?

Solution

You are right, nbits is current network difficulty.

Difficulty encoding is throughly described here.

Hexadecimal representation like 0x1b3cc366 consists of two parts:

0x1b -- number of bytes in a target
0x3cc366 -- target prefix

This means that valid hash should be less than 0x3cc366000000000000000000000000000000000000000000000000 (it is exactly 0x1b = 27 bytes long).

Floating point representation of difficulty shows how much current target is harder than the one used in the genesis block.

Satoshi decided to use 0x1d00ffff as a difficulty for the genesis block, so the target was 0x00ffff0000000000000000000000000000000000000000000000000000.

And 1078.52975077 is how much current target is greater than the initial one:

$ echo 'ibase=16;FFFF0000000000000000000000000000000000000000000000000000 / 3CC366000000000000000000000000000000000000000000000000' | bc -l
1078.52975077482646448605