week1_ticks_and_Q64_96.md

Ticks and Q64.96 Numbers

Ticks Insight #1 Ticks break up the continuous finite price curve into a curve with evenly spaced discrete points.

Each discrete point represents a specific price at which trades can occur.

Ticks Insight #2 The gap between two adjacent ticks - called tick spacing - is the smallest relative price movement possible for a given pair of assets in a pool.

Ticks <> Prices

The relative price of an asset at a given tick is represented by this neat little equation:

$p(i) = 1.0001^{i}$

Ticks represent price based on the price of Token 0 relative to Token 1.

The sorting of token based on lexicographically sorting their contract addresses.

If A is 0x000.., while B is 0x123.. then A is Token 0 and B is the Token 1.

💡 Uniswap v4 has support for pools with native tokens

1.0001 was chosen because for each tick, the relative price moves by 0.01%, this movement is called a basis point or bps.

Basis Point	Percentage
1	0.01%
10	0.10%
50	0.50%
100	1.00%
275	2.75%
400	4.00%
1000	10.00%
ticks stored in int24 the MIN_TICK and MAX_TICK are in range [-887_272, 887_272]

Liquidity Math

$L_x = x * (sqrt{P} * sqrt{p_b})\over(sqrt{p_b}-sqrt{P})$

$y = L_x(sqrt{P} - sqrt{p_a})$

Q64.96 Number

Q64.96 is a way represented rational numbers that uses 64 bits for integer part and 96 bits for fractional part

$Q = D * (2^k)\ where\ k\ =\ 96$ D is decimal notation of the number

For example: 1.000234 * 2^96 = 79246701904292675448540839620.378624

how this works, take a look at getSqrtRatioAtTick and getTickAtSqrtRatio LINK