Overlapping Pool

[samuelgrossman]

Would it be possible to see the arithmetic for the interim steps of the overlapping pool example that leads to 6055.578 price answer?

[Jeiwan]

This is somewhat tricky.
The main swap loop iterates in small steps, each step is up to 256 ticks (this happens here). A step is shorter than 256 ticks when there's an activated tick between the current tick and current_tick + 256. Also, a step is shorter when starting not from beginning of a 256-bit word. In each step, it calculates input and output amounts between the current tick and the next tick based on current liquidity (liquidity is added when a liquidity position is entered, and removed when a liquidity position is left). The amounts are calculated here.

(We're talking about the upper image)
There are 2 price ranges in that example: 4545-5500 and 5001-6250. Since the current price is ~5000, the swap starts at this price. It moves to the right until it converts all input amount (10,000 USDC) to output amount. In the range between 5000 and 5001, only liquidity of the first position is used. In the range between 5001 and 5500, liquidity of both positions is used. In the range between 5500 and 6250, only liquidity of the second position is used.
To compute the intermediate steps, you need to iteratively compute input and output amounts (with the Python calc_amount0 and calc_amount1 functions, for example) using liquidity and price range of each step. After the entire input amount is converted, the current price will be ~6055.578.

Here's real values from the swap (I extracted these by using console.log and running the test):

  Start price: 5602223755577321903022134995689
  Start tick: 85176
  Start liquidity: 1518129116516325614066
  ====================================================================================
  Current price: 5602223755577321903022134995689
  Current tick: 85176
  Current liquidity: 1518129116516325614066
  Next price: 5602783977952879635212437209189
  Amount swapped (input): 10734691719059038792
  Amount remaining: 9989265308280940961208
  ====================================================================================
  Current price: 5602783977952879635212437209189
  Current tick: 85178
  Current liquidity: 2188694397454035087752
  Next price: 5622145994867546797787171334839
  Amount swapped (input): 534879727103510395017
  Amount remaining: 9454385581177430566191
  ====================================================================================
  Current price: 5622145994867546797787171334839
  Current tick: 85247
  Current liquidity: 2188694397454035087752
  Next price: 5694568356906635577050546247497
  Amount swapped (input): 2000682749859344339854
  Amount remaining: 7453702831318086226337
  ====================================================================================
  Current price: 5694568356906635577050546247497
  Current tick: 85503
  Current liquidity: 2188694397454035087752
  Next price: 5767923636470119667816132517957
  Amount swapped (input): 2026454789676159292638
  Amount remaining: 5427248041641926933699
  ====================================================================================
  Current price: 5767923636470119667816132517957
  Current tick: 85759
  Current liquidity: 2188694397454035087752
  Next price: 5842223851049321075399999157648
  Amount swapped (input): 2052558815179543588298
  Amount remaining: 3374689226462383345401
  ====================================================================================
  Current price: 5842223851049321075399999157648
  Current tick: 86015
  Current liquidity: 2188694397454035087752
  Next price: 5875617940067453351001625213169
  Amount swapped (input): 922518624976419389367
  Amount remaining: 2452170601485963956034
  ====================================================================================
  Current price: 5875617940067453351001625213169
  Current tick: 86129
  Current liquidity: 670565280937709473686
  Next price: 5917481172940347756675672283293
  Amount swapped (input): 354318838422121276488
  Amount remaining: 2097851763063842679546
  ====================================================================================
  Current price: 5917481172940347756675672283293
  Current tick: 86271
  Current liquidity: 670565280937709473686
  Next price: 5993707931238230425450970325679
  Amount swapped (input): 645162224780711742771
  Amount remaining: 1452689538283130936775
  ====================================================================================
  Current price: 5993707931238230425450970325679
  Current tick: 86527
  Current liquidity: 670565280937709473686
  Next price: 6070916613856747075276281624828
  Amount swapped (input): 653472960976404125154
  Amount remaining: 799216577306726811621
  ====================================================================================
  Current price: 6070916613856747075276281624828
  Current tick: 86783
  Current liquidity: 670565280937709473686
  Next price: 6149119869574266119161721685201
  Amount swapped (input): 661890752938013161392
  Amount remaining: 137325824368713650229
  ====================================================================================
  Current price: 6149119869574266119161721685201
  Current tick: 87039
  Current liquidity: 670565280937709473686
  Next price: 6165345094827913637987008642386
  Amount swapped (input): 137325824368713650229
  Amount remaining: 0
  ====================================================================================
  Final price: 6165345094827913637987008642386
  Final tick: 87091
  Final liquidity: 670565280937709473686

Notice how ticks and liquidity change here. You can plug these values into the Python functions to compute amounts in each step and find the final price.

To demonstrate the idea, for the first step:

import unimath

l = 1518129116516325614066
sqrt_cur = 5602223755577321903022134995689
sqrt_target = 5602783977952879635212437209189
amount0 = unimath.calc_amount0(l, sqrt_cur, sqrt_target)
amount1 = unimath.calc_amount1(l, sqrt_cur, sqrt_target)
sqrt_next = sqrt_cur + (amount1 * 2**96) // l

sqrt_next will be equal sqrt_target until the final step, where it'll equal ~6055.578.

[samuelgrossman]

Thank you! Perfect

…

On Sat, Oct 8, 2022 at 5:55 AM Ivan Kuznetsov ***@***.***> wrote: This is somewhat tricky. The main swap loop iterates in small steps, each step is up to 256 ticks (this happens here <https://github.com/Jeiwan/uniswapv3-code/blob/main/src/UniswapV3Pool.sol#L423>). A step is shorter than 256 ticks when there's an activated tick between the current tick and current_tick + 256. Also, a step is shorter when starting not from beginning of a 256-bit word. In each step, it calculates input and output amounts between the current tick and the next tick based on current liquidity (liquidity is added when a liquidity position is entered, and removed when a liquidity position is left). The amounts are calculated here <https://github.com/Jeiwan/uniswapv3-code/blob/main/src/UniswapV3Pool.sol#L436> . [image: Partially overlapping liquidity positions] <https://camo.githubusercontent.com/01d861ab5f00e06b401aba92697503dca5a0a231074cf29910ed4d7ed893b592/68747470733a2f2f756e69737761707633626f6f6b2e636f6d2f696d616765732f6d696c6573746f6e655f332f737761705f7061727469616c6c795f6f7665726c617070696e675f70726963655f72616e6765732e706e67> (We're talking about the upper image) There are 2 price ranges in that example: 4545-5500 and 5001-6250. Since the current price is ~5000, the swap starts at this price. It moves to the right until it converts all input amount (10,000 USDC) to output amount. In the range between 5000 and 5001, only liquidity of the first position is used. In the range between 5001 and 5500, liquidity of both positions is used. In the range between 5500 and 6250, only liquidity of the second position is used. To compute the intermediate steps, you need to iteratively compute input and output amounts (with the Python calc_amount0 and calc_amount1 functions, for example) using liquidity and price range of each step. After the entire input amount is converted, the current price will be ~6055.578. Here's real values from the swap (I extracted these by using console.log and running the test): ==================================================================================== Current price: 5602223755577321903022134995689 Current tick: 85176 Current liquidity: 1518129116516325614066 Next price: 5602783977952879635212437209189 Amount swapped (input): 10734691719059038792 Amount remaining: 9989265308280940961208 ==================================================================================== Current price: 5602783977952879635212437209189 Current tick: 85178 Current liquidity: 2188694397454035087752 Next price: 5622145994867546797787171334839 Amount swapped (input): 534879727103510395017 Amount remaining: 9454385581177430566191 ==================================================================================== Current price: 5622145994867546797787171334839 Current tick: 85247 Current liquidity: 2188694397454035087752 Next price: 5694568356906635577050546247497 Amount swapped (input): 2000682749859344339854 Amount remaining: 7453702831318086226337 ==================================================================================== Current price: 5694568356906635577050546247497 Current tick: 85503 Current liquidity: 2188694397454035087752 Next price: 5767923636470119667816132517957 Amount swapped (input): 2026454789676159292638 Amount remaining: 5427248041641926933699 ==================================================================================== Current price: 5767923636470119667816132517957 Current tick: 85759 Current liquidity: 2188694397454035087752 Next price: 5842223851049321075399999157648 Amount swapped (input): 2052558815179543588298 Amount remaining: 3374689226462383345401 ==================================================================================== Current price: 5842223851049321075399999157648 Current tick: 86015 Current liquidity: 2188694397454035087752 Next price: 5875617940067453351001625213169 Amount swapped (input): 922518624976419389367 Amount remaining: 2452170601485963956034 ==================================================================================== Current price: 5875617940067453351001625213169 Current tick: 86129 Current liquidity: 670565280937709473686 Next price: 5917481172940347756675672283293 Amount swapped (input): 354318838422121276488 Amount remaining: 2097851763063842679546 ==================================================================================== Current price: 5917481172940347756675672283293 Current tick: 86271 Current liquidity: 670565280937709473686 Next price: 5993707931238230425450970325679 Amount swapped (input): 645162224780711742771 Amount remaining: 1452689538283130936775 ==================================================================================== Current price: 5993707931238230425450970325679 Current tick: 86527 Current liquidity: 670565280937709473686 Next price: 6070916613856747075276281624828 Amount swapped (input): 653472960976404125154 Amount remaining: 799216577306726811621 ==================================================================================== Current price: 6070916613856747075276281624828 Current tick: 86783 Current liquidity: 670565280937709473686 Next price: 6149119869574266119161721685201 Amount swapped (input): 661890752938013161392 Amount remaining: 137325824368713650229 ==================================================================================== Current price: 6149119869574266119161721685201 Current tick: 87039 Current liquidity: 670565280937709473686 Next price: 6165345094827913637987008642386 Amount swapped (input): 137325824368713650229 Amount remaining: 0 Final price: 6165345094827913637987008642386 Final tick: 87091 Final liquidity: 670565280937709473686 Notice how ticks and liquidity change here. You can plug these values into the Python functions to compute amounts in each step and find the final price. — Reply to this email directly, view it on GitHub <#11 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AD6A5OIF54M2CEF2N3OBAQDWCFAJPANCNFSM6AAAAAAQ6TUXRE> . You are receiving this because you authored the thread.Message ID: ***@***.***>