''See also: [[Target]]''

=== What is difficulty? ===

Difficulty is a measure of how difficult it is to find a hash below a given [[target]]. Difficulty answers the question: "how many times more difficult is it to mine a block now, compared with how difficult it was to mine the [[Genesis block|Genesis Block]]?"

The Bitcoin network has a global block difficulty. Valid blocks must have a hash below this target.
Mining pools also have a pool-specific share difficulty setting a lower limit for shares.

=== How often does the network difficulty change? ===

See [[Target|target]].

=== What is the formula for difficulty? ===
''Difficulty_1_target is the target used in the Genesis Block and represents a difficulty of 1.''

difficulty = difficulty_1_target / current_target

(target is a 256 bit number)

difficulty_1_target can be different for various ways to measure difficulty.
Traditionally, it represents a hash where the leading 32 bits are zero and the rest are one (this is known as "pool difficulty" or "pdiff").
The Bitcoin protocol represents targets as a custom floating point type with limited precision; as a result, Bitcoin clients often approximate difficulty based on this (this is known as "bdiff").

===How is difficulty stored in blocks?===

Each block stores a packed representation (called "Bits") for its actual hexadecimal [[target]]. The target can be derived from it via a predefined formula. For example, if the packed target in the block is 0x1b0404cb, the hexadecimal target is
0x0404cb * 2**(8*(0x1b - 3)) = 0x00000000000404CB000000000000000000000000000000000000000000000000

Note that the 0x0404cb value is a signed value in this format. The largest legal value for this field is 0x7fffff. To make a larger value you must shift it down one full byte. Also 0x008000 is the smallest positive valid value.

===How is difficulty calculated? What is the difference between bdiff and pdiff?===

The highest possible target (difficulty 1) is defined as 0x1d00ffff, which gives us a hex target of
0x00ffff * 2**(8*(0x1d - 3)) = 0x00000000FFFF0000000000000000000000000000000000000000000000000000

It should be noted that pooled mining often uses non-truncated targets, which puts "pool difficulty 1" at
0x00000000FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF

So the difficulty at 0x1b0404cb is therefore:
0x00000000FFFF0000000000000000000000000000000000000000000000000000 /
0x00000000000404CB000000000000000000000000000000000000000000000000
= 16307.420938523983 (bdiff)
And:
0x00000000FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF /
0x00000000000404CB000000000000000000000000000000000000000000000000
= 16307.669773817162 (pdiff)

Here's a fast way to calculate bitcoin difficulty. It uses a modified Taylor series for the logarithm (you can see tutorials on flipcode and wikipedia) and relies on logs to transform the difficulty calculation:

<source lang="cpp">
#include <iostream>
#include <cmath>

inline float fast_log(float val)
{
int * const exp_ptr = reinterpret_cast <int *>(&val);
int x = *exp_ptr;
const int log_2 = ((x >> 23) & 255) - 128;
x &= ~(255 << 23);
x += 127 << 23;
*exp_ptr = x;

val = ((-1.0f/3) * val + 2) * val - 2.0f/3;
return ((val + log_2) * 0.69314718f);
}

float difficulty(unsigned int bits)
{
static double max_body = fast_log(0x00ffff), scaland = fast_log(256);
return exp(max_body - fast_log(bits & 0x00ffffff) + scaland * (0x1d - ((bits & 0xff000000) >> 24)));
}

int main()
{
std::cout << difficulty(0x1b0404cb) << std::endl;
return 0;
}
</source>

To see the math to go from the normal difficulty calculations (which require large big ints bigger than the space in any normal integer) to the calculation above, here's some python:

<source lang="python">
import decimal, math
l = math.log
e = math.e

print 0x00ffff * 2**(8*(0x1d - 3)) / float(0x0404cb * 2**(8*(0x1b - 3)))
print l(0x00ffff * 2**(8*(0x1d - 3)) / float(0x0404cb * 2**(8*(0x1b - 3))))
print l(0x00ffff * 2**(8*(0x1d - 3))) - l(0x0404cb * 2**(8*(0x1b - 3)))
print l(0x00ffff) + l(2**(8*(0x1d - 3))) - l(0x0404cb) - l(2**(8*(0x1b - 3)))
print l(0x00ffff) + (8*(0x1d - 3))*l(2) - l(0x0404cb) - (8*(0x1b - 3))*l(2)
print l(0x00ffff / float(0x0404cb)) + (8*(0x1d - 3))*l(2) - (8*(0x1b - 3))*l(2)
print l(0x00ffff / float(0x0404cb)) + (0x1d - 0x1b)*l(2**8)
</source>

=== What is the current difficulty? ===
[http://blockexplorer.com/q/getdifficulty Current difficulty], as output by Bitcoin's getDifficulty.

[http://bitcoin.sipa.be Graphs]

=== What is the maximum difficulty? ===

There is no minimum target. The maximum difficulty is roughly: maximum_target / 1 (since 0 would result in infinity), which is a ridiculously huge number (about 2^224).

The actual maximum difficulty is when current_target=0, but we would not be able to calculate the difficulty if that happened. (fortunately it never will, so we're ok.)

=== Can the network difficulty go down? ===
Yes it can. See discussion in [[target]].

=== What is the minimum difficulty? ===
The minimum difficulty, when the target is at the maximum allowed value, is 1.

=== What network hash rate results in a given difficulty? ===
The difficulty is adjusted every 2016 blocks based on the [[Block_timestamp|time]] it took to find the previous 2016 blocks. At the desired rate of one block each 10 minutes, 2016 blocks would take exactly two weeks to find. If the previous 2016 blocks took more than two weeks to find, the difficulty is reduced. If they took less than two weeks, the difficulty is increased. The change in difficulty is in proportion to the amount of time over or under two weeks the previous 2016 blocks took to find.

To find a block, the hash must be less than the target. The hash is effectively a random number between 0 and 2**256-1. The offset for difficulty 1 is
0xffff * 2**208
and for difficulty D is
(0xffff * 2**208)/D

The expected number of hashes we need to calculate to find a block with difficulty D is therefore
D * 2**256 / (0xffff * 2**208)
or just
D * 2**48 / 0xffff

The difficulty is set such that the previous 2016 blocks would have been found at the rate of one every 10 minutes, so we were calculating (D * 2**48 / 0xffff) hashes in 600 seconds. That means the hash rate of the network was
D * 2**48 / 0xffff / 600
over the previous 2016 blocks. Can be further simplified to
D * 2**32 / 600
without much loss of accuracy.

At difficulty 1, that is around 7 Mhashes per second.

At the time of writing, the difficulty is 22012.4941572, which means that over the previous set of 2016 blocks found the average network hash rate was
22012.4941572 * 2**32 / 600 = around 157 Ghashes per second.

=== How soon might I expect to generate a block? ===
(The [https://www.bitcointalk.org/index.php?topic=1682.0 eternal question].)

The average time to find a block can be approximated by calculating:
time = difficulty * 2**32 / hashrate
where difficulty is the current difficulty, hashrate is the number of hashes your miner calculates per second, and time is the average in seconds between the blocks you find.

For example, using Python we calculate the average time to generate a block using a 1Ghash/s mining rig when the difficulty is 20000:
$ python -c "print 20000 * 2**32 / 10**9 / 60 / 60.0"
23.85
and find that it takes just under 24 hours on average.

* Any one grinding of the hash stands the same chance of "winning" as any other. The numbers game is how many attempts your hardware can make per second.
* You need to know the difficulty (above) and your khash/sec rate (reported by the client).
** [[Mining Hardware Comparison]] has some stats that may help you predict what you could get.
* Visit a calculator or perform the maths yourself,
** http://www.alloscomp.com/bitcoin/calculator.php
** http://www.vnbitcoin.org/bitcoincalculator.php
** https://bitknock.com/calculator
**https://99bitcoins.com/bitcoin-mining-calculator
* Remember it's just probability! There are no guarantees you will win every N days.

==Related Links==

* [https://docs.google.com/spreadsheet/ccc?key=0AiFMBvXvL2dtdEZkR2J4eU5rS3B4ei1iUmJxSWNlQ0E Bitcoin Difficulty History]
* [https://www.bitcoinmining.com/what-is-bitcoin-mining-difficulty/ What is Bitcoin Mining Difficulty?]
* See also: [[Target]]

[[Category:Technical]]
[[Category:Vocabulary]]

[[pl:Trudność]]

Target

2020-01-09T16:42:16Z

Angus Adams:

''See also: [[Difficulty]]''

The '''target''' is a 256-bit number (extremely large) that all Bitcoin clients share. The SHA-256 [https://wiki.bitcoinsv.io/index.php/Mining#Hashing hash] of a [[Block hashing algorithm|block's header]] must be less than or equal to the current target for the block to be accepted by the network. The lower the target, the more [[difficulty|difficult]] it is to generate a block.

It's important to realize that block generation is not a long, set problem (like doing a million hashes), but more like a lottery. Each hash basically gives you a random number between 0 and the maximum value of a 256-bit number (2^256-1). If your hash is below the target, then you win. If not, you increment the nonce (completely changing the hash) and try again.

The bitcoin network tries to produce one block every ten minutes on average. As mining hash power changes over time, it achieves this through changing the target value.

Historically (prior to forking from BTC in August 2017), bitcoin changed its target every 2016 blocks (exactly two weeks if a block time of 10 minutes was kept perfectly). This change in the target is known as a 'difficulty adjustment'. Under the original difficulty adjustment paradigm, when adjusting the target, every bitcoin client compared the actual time it took to generate 2016 blocks with the two week goal, and modified the target by the percentage difference. A single retarget never changes the target by more than a factor of 4 either way to prevent large changes in difficulty.

Post forking from BTC in August 2017, bitcoin changed the original difficulty adjustment algorithm to what was named the Emergency Difficulty Adjustment (EDA) algorithm. The EDA had the capacity to update the target value every time a new block was found (as opposed to every 2016 blocks), while still targeting a ten minute block time average. The EDA was changed to the Difficulty Adjustment Algorithm (DAA) on 17 November 2017 to address instabilities associated with the EDA. The DAA uses a moving average of the last 144 blocks to determine changes to the target and like the EDA, the target can change every block.

The reason the EDA (and later, it's improvement, the DAA) needed to be implemented was because of the fork from BTC (creating BCH) in August 2017. Because it was expected that BCH would garner significantly less hash power than BTC, measures were put in place so that block production on BCH would not slow to a crawl due to inheriting BTC's target difficulty and a small number of miners.

It is proposed that bitcoin will move back to the original difficulty adjustment algorithm (still used by BTC) in the future.

=== What is the maximum target? ===
The maximum target used by SHA256 mining devices is:
0x00000000FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
Because Bitcoin stores the target as a floating-point type, this is truncated:
0x00000000FFFF0000000000000000000000000000000000000000000000000000

This is the target used in the [[Genesis block|Genesis Block]] and represents a [[difficulty]] of 1.

Since a lower target makes Bitcoin generation more difficult, the maximum target is the ''lowest'' possible [[difficulty]].

==Related Links==
See also [[Difficulty]]

[[Category:Technical]]
[[Category:Vocabulary]]

Target

2020-01-09T16:41:27Z

Angus Adams: /* What is the maximum target? */

''See also: [[Difficulty]]''

The '''target''' is a 256-bit number (extremely large) that all Bitcoin clients share. The SHA-256 [https://wiki.bitcoinsv.io/index.php/Mining#Hashing hash] of a [[Block hashing algorithm|block's header]] must be less than or equal to the current target for the block to be accepted by the network. The lower the target, the more [[difficulty|difficult]] it is to generate a block.

It's important to realize that block generation is not a long, set problem (like doing a million hashes), but more like a lottery. Each hash basically gives you a random number between 0 and the maximum value of a 256-bit number (2^256-1). If your hash is below the target, then you win. If not, you increment the nonce (completely changing the hash) and try again.

The bitcoin network tries to produce one block every ten minutes on average. As mining hash power changes over time, it achieves this through changing the target value.

Historically (prior to forking from BTC in August 2017), bitcoin changed its target every 2016 blocks (exactly two weeks if a block time of 10 minutes was kept perfectly). This change in the target is known as a 'difficulty adjustment'. Under the original difficulty adjustment paradigm, when adjusting the target, every bitcoin client compared the actual time it took to generate 2016 blocks with the two week goal, and modified the target by the percentage difference. A single retarget never changes the target by more than a factor of 4 either way to prevent large changes in difficulty.

Post forking from BTC in August 2017, bitcoin changed the original difficulty adjustment algorithm to what was named the Emergency Difficulty Adjustment (EDA) algorithm. The EDA had the capacity to update the target value every time a new block was found (as opposed to every 2016 blocks), while still targeting a ten minute block time average. The EDA was changed to the Difficulty Adjustment Algorithm (DAA) on 17 November 2017 to address instabilities associated with the EDA. The DAA uses a moving average of the last 144 blocks to determine changes to the target and like the EDA, the target can change every block.

The reason the EDA (and later, it's improvement, the DAA) needed to be implemented was because of the fork from BTC (creating BCH) in August 2017. Because it was expected that BCH would garner significantly less hash power than BTC, measures were put in place so that block production on BCH would not slow to a crawl due to inheriting BTC's target difficulty and a small number of miners.

It is proposed that bitcoin will move back to the original difficulty adjustment algorithm (still used by BTC) in the future.

=== What is the target now? ===
* [http://blockexplorer.com/q/getdifficulty Current difficulty], as output by Bitcoin's getDifficulty

=== When does the target change next? ===

* [http://blockexplorer.com/q/nextretarget Next retarget]

=== What has the target been in the past? ===

* [http://blockexplorer.com/q/nethash Difficulty history, (at column 5)]
* [http://www.bitcointalk.org/index.php?topic=2345.msg31405#msg31405 Re: difficulty over time data?]
* [http://bitcoin.sipa.be/ Bitcoin network graphs]

=== What is the maximum target? ===
The maximum target used by SHA256 mining devices is:
0x00000000FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
Because Bitcoin stores the target as a floating-point type, this is truncated:
0x00000000FFFF0000000000000000000000000000000000000000000000000000

This is the target used in the [[Genesis block|Genesis Block]] and represents a [[difficulty]] of 1.

Since a lower target makes Bitcoin generation more difficult, the maximum target is the ''lowest'' possible [[difficulty]].

==Related Links==
See also [[Difficulty]]

[[Category:Technical]]
[[Category:Vocabulary]]