Ting
ContentsTime and difficulty

Time and difficulty

On this page
  1. Timestamps
  2. The retarget
  3. Exact arithmetic
  4. Where the rule comes from

Difficulty keeps blocks arriving near the target interval as hashpower comes and goes. Ting sets every block's target from one fixed schedule that starts at genesis: the further the chain falls behind the schedule, the easier mining gets, and the further it runs ahead, the harder. It depends only on timestamps recorded in the chain, never on a node's own clock. The exact rules are in section 9 of the protocol rules.

Timestamps#

A block's timestamp must be greater than the median of the timestamps of the blocks before it: the previous eleven, or, while fewer than eleven blocks exist, all of them plus the genesis timestamp. With an even number of samples, the upper of the two middle values is used. One block may carry an earlier time than its parent, but the median, and with it the earliest time the next block may carry, never moves backwards.

That is the only consensus rule about time. A node should defer a header whose timestamp is more than 7,200 seconds (two hours) ahead of its local clock, but that is admission policy, not invalidity: the same block becomes acceptable once the clock catches up. Difficulty and capacity calculations use only data in the branch.

Timestamps, like producer data, are context chosen by the miner. They are not precise, they are not unpredictable randomness and they authenticate no external identity; programs should not treat them as any of these.

The retarget#

Every block's target follows from one anchor, genesis, and one question: how far is the chain ahead of or behind its schedule? The schedule says the parent of the block at height h should have arrived interval × (h − 1) seconds after genesis.

behind = (parent timestamp − genesis timestamp) − interval × (h − 1)
target = initial target × 2^(behind / half-life)

If the chain is one half-life behind schedule, the target doubles and mining gets easier; one half-life ahead halves it. When blocks arrive exactly on time, the chain keeps its distance from the schedule and the target stays where it is.

The target against the chain's distance from schedule The horizontal axis is how far the parent block is behind schedule, in half-lives, from two ahead to two behind. The vertical axis is the target as a multiple of the initial target, on a doubling scale from a quarter to four. The target is a straight line on this scale: on schedule it is the initial target, each half-life behind doubles it, and each half-life ahead halves it. A larger target is easier to meet. ×4 ×2 ×1 ×½ ×¼ target easier ↑ harder ↓ −2 −1 0 +1 +2 ahead of schedule behind schedule half-lives behind on schedule: the initial target one half-life behind: twice the target
The target doubles for every half-life the chain falls behind schedule and halves for every half-life it runs ahead

Suppose half the hashpower leaves a chain that is on schedule, with a 12-hour half-life. Blocks start arriving about every two minutes, the chain falls behind schedule and the target rises. The chain settles about 12 hours behind schedule, where the target has doubled and the remaining miners again find a block about every 60 seconds. If the hashpower comes back, blocks arrive early, the chain catches up with its schedule and the target falls back.

There is no averaging window and no limit on how far one block can move the target. Nothing makes mining easier just because a long time has passed since the last block: being behind schedule is what matters, and a block that is early tightens the target again.

The production genesis uses a 60-second interval and a 12-hour half-life, chosen by simulating the loss and the arrival of hashpower (production profile); the experimental profile of development chains uses a two-day half-life.

Exact arithmetic#

Every node must compute the same target to the last bit, so the rule is written in integer arithmetic rather than with real powers of two. The exponent is counted in steps of 1/65536 of a half-life, a fixed cubic polynomial stands in for the fractional power of two, every division rounds down, and the result is kept between 1 and the PoW limit. The first mined block, whose parent is genesis, gets the initial target. A header's target must equal the result exactly: there is no minimum-difficulty exception triggered by the clock or by a long gap between blocks. The formula and every rounding step are in section 9.3.

Where the rule comes from#

This is the ASERT rule ("absolutely scheduled exponentially rising targets") that Bitcoin Cash has used since November 2020 as aserti3-2d. It was chosen because a window-based retarget oscillates on any chain that is not the biggest user of its hash function: hashpower arrives when difficulty is low and leaves when it rises. ASERT responds every block and cannot oscillate.

The polynomial and its fixed-point form are taken from the aserti3-2d specification, restated in the protocol rules with the genesis anchor; later changes to that document do not change Ting. Ting's targets are not interchangeable with aserti3-2d's, though. Ting rounds the exponent down where aserti3-2d truncates it toward zero, so for a block ahead of schedule Ting's target can be one 1/65536 step, about 0.001%, lower. And a Ting header carries its exact 256-bit target, where aserti3-2d stores targets in the rounded compact nBits form.