📜 [專欄新文章] Uniswap v3 Features Explained in Depth
✍️ 田少谷 Shao
📥 歡迎投稿: https://medium.com/taipei-ethereum-meetup #徵技術分享文 #使用心得 #教學文 #medium
Once again the game-changing DEX 🦄 👑
Image source: https://uniswap.org/blog/uniswap-v3/
Outline
0. Intro1. Uniswap & AMM recap2. Ticks 3. Concentrated liquidity4. Range orders: reversible limit orders5. Impacts of v36. Conclusion
0. Intro
The announcement of Uniswap v3 is no doubt one of the most exciting news in the DeFi place recently 🔥🔥🔥
While most have talked about the impact v3 can potentially bring on the market, seldom explain the delicate implementation techniques to realize all those amazing features, such as concentrated liquidity, limit-order-like range orders, etc.
Since I’ve covered Uniswap v1 & v2 (if you happen to know Mandarin, here are v1 & v2), there’s no reason for me to not cover v3 as well ✅
Thus, this article aims to guide readers through Uniswap v3, based on their official whitepaper and examples made on the announcement page. However, one needs not to be an engineer, as not many codes are involved, nor a math major, as the math involved is definitely taught in your high school, to fully understand the following content 😊😊😊
If you really make it through but still don’t get shxt, feedbacks are welcomed! 🙏
There should be another article focusing on the codebase, so stay tuned and let’s get started with some background noise!
1. Uniswap & AMM recap
Before diving in, we have to first recap the uniqueness of Uniswap and compare it to traditional order book exchanges.
Uniswap v1 & v2 are a kind of AMMs (automated market marker) that follow the constant product equation x * y = k, with x & y stand for the amount of two tokens X and Y in a pool and k as a constant.
Comparing to order book exchanges, AMMs, such as the previous versions of Uniswap, offer quite a distinct user experience:
AMMs have pricing functions that offer the price for the two tokens, which make their users always price takers, while users of order book exchanges can be both makers or takers.
Uniswap as well as most AMMs have infinite liquidity¹, while order book exchanges don’t. The liquidity of Uniswap v1 & v2 is provided throughout the price range [0,∞]².
Uniswap as well as most AMMs have price slippage³ and it’s due to the pricing function, while there isn’t always price slippage on order book exchanges as long as an order is fulfilled within one tick.
In an order book, each price (whether in green or red) is a tick. Image source: https://ftx.com/trade/BTC-PERP
¹ though the price gets worse over time; AMM of constant sum such as mStable does not have infinite liquidity
² the range is in fact [-∞,∞], while a price in most cases won’t be negative
³ AMM of constant sum does not have price slippage
2. Tick
The whole innovation of Uniswap v3 starts from ticks.
For those unfamiliar with what is a tick:
Source: https://www.investopedia.com/terms/t/tick.asp
By slicing the price range [0,∞] into numerous granular ticks, trading on v3 is highly similar to trading on order book exchanges, with only three differences:
The price range of each tick is predefined by the system instead of being proposed by users.
Trades that happen within a tick still follows the pricing function of the AMM, while the equation has to be updated once the price crosses the tick.
Orders can be executed with any price within the price range, instead of being fulfilled at the same one price on order book exchanges.
With the tick design, Uniswap v3 possesses most of the merits of both AMM and an order book exchange! 💯💯💯
So, how is the price range of a tick decided?
This question is actually somewhat related to the tick explanation above: the minimum tick size for stocks trading above 1$ is one cent.
The underlying meaning of a tick size traditionally being one cent is that one cent (1% of 1$) is the basis point of price changes between ticks, ex: 1.02 — 1.01 = 0.1.
Uniswap v3 employs a similar idea: compared to the previous/next price, the price change should always be 0.01% = 1 basis point.
However, notice the difference is that in the traditional basis point, the price change is defined with subtraction, while here in Uniswap it’s division.
This is how price ranges of ticks are decided⁴:
Image source: https://uniswap.org/whitepaper-v3.pdf
With the above equation, the tick/price range can be recorded in the index form [i, i+1], instead of some crazy numbers such as 1.0001¹⁰⁰ = 1.0100496621.
As each price is the multiplication of 1.0001 of the previous price, the price change is always 1.0001 — 1 = 0.0001 = 0.01%.
For example, when i=1, p(1) = 1.0001; when i=2, p(2) = 1.00020001.
p(2) / p(1) = 1.00020001 / 1.0001 = 1.0001
See the connection between the traditional basis point 1 cent (=1% of 1$) and Uniswap v3’s basis point 0.01%?
Image source: https://tenor.com/view/coin-master-cool-gif-19748052
But sir, are prices really granular enough? There are many shitcoins with prices less than 0.000001$. Will such prices be covered as well?
Price range: max & min
To know if an extremely small price is covered or not, we have to figure out the max & min price range of v3 by looking into the spec: there is a int24 tick state variable in UniswapV3Pool.sol.
Image source: https://uniswap.org/whitepaper-v3.pdf
The reason for a signed integer int instead of an uint is that negative power represents prices less than 1 but greater than 0.
24 bits can cover the range between 1.0001 ^ (2²³ — 1) and 1.0001 ^ -(2)²³. Even Google cannot calculate such numbers, so allow me to offer smaller values to have a rough idea of the whole price range:
1.0001 ^ (2¹⁸) = 242,214,459,604.341
1.0001 ^ -(2¹⁷) = 0.000002031888943
I think it’s safe to say that with a int24 the range can cover > 99.99% of the prices of all assets in the universe 👌
⁴ For implementation concern, however, a square root is added to both sides of the equation.
How about finding out which tick does a price belong to?
Tick index from price
The answer to this question is rather easy, as we know that p(i) = 1.0001^i, simply takes a log with base 1.0001 on both sides of the equation⁴:
Image source: https://www.codecogs.com/latex/eqneditor.php
Let’s try this out, say we wanna find out the tick index of 1000000.
Image source: https://ncalculators.com/number-conversion/log-logarithm-calculator.htm
Now, 1.0001¹³⁸¹⁶² = 999,998.678087146. Voila!
⁵ This formula is also slightly modified to fit the real implementation usage.
3. Concentrated liquidity
Now that we know how ticks and price ranges are decided, let’s talk about how orders are executed in a tick, what is concentrated liquidity and how it enables v3 to compete with stablecoin-specialized DEXs (decentralized exchange), such as Curve, by improving the capital efficiency.
Concentrated liquidity means LPs (liquidity providers) can provide liquidity to any price range/tick at their wish, which causes the liquidity to be imbalanced in ticks.
As each tick has a different liquidity depth, the corresponding pricing function x * y = k also won’t be the same!
Each tick has its own liquidity depth. Image source: https://uniswap.org/blog/uniswap-v3/
Mmm… examples are always helpful for abstract descriptions 😂
Say the original pricing function is 100(x) * 1000(y) = 100000(k), with the price of X token 1000 / 100 = 10 and we’re now in the price range [9.08, 11.08].
If the liquidity of the price range [11.08, 13.08] is the same as [9.08, 11.08], we don’t have to modify the pricing function if the price goes from 10 to 11.08, which is the boundary between two ticks.
The price of X is 1052.63 / 95 = 11.08 when the equation is 1052.63 * 95 = 100000.
However, if the liquidity of the price range [11.08, 13.08] is two times that of the current range [9.08, 11.08], balances of x and y should be doubled, which makes the equation become 2105.26 * 220 = 400000, which is (1052.63 * 2) * (110 * 2) = (100000 * 2 * 2).
We can observe the following two points from the above example:
Trades always follow the pricing function x * y = k, while once the price crosses the current price range/tick, the liquidity/equation has to be updated.
√(x * y) = √k = L is how we represent the liquidity, as I say the liquidity of x * y = 400000 is two times the liquidity of x * y = 100000, as √(400000 / 100000) = 2.
What’s more, compared to liquidity on v1 & v2 is always spread across [0,∞], liquidity on v3 can be concentrated within certain price ranges and thus results in higher capital efficiency from traders’ swapping fees!
Let’s say if I provide liquidity in the range [1200, 2800], the capital efficiency will then be 4.24x higher than v2 with the range [0,∞] 😮😮😮 There’s a capital efficiency comparison calculator, make sure to try it out!
Image source: https://uniswap.org/blog/uniswap-v3/
It’s worth noticing that the concept of concentrated liquidity was proposed and already implemented by Kyper, prior to Uniswap, which is called Automated Price Reserve in their case.⁵
⁶ Thanks to Yenwen Feng for the information.
4. Range orders: reversible limit orders
As explained in the above section, LPs of v3 can provide liquidity to any price range/tick at their wish. Depending on the current price and the targeted price range, there are three scenarios:
current price < the targeted price range
current price > the targeted price range
current price belongs to the targeted price range
The first two scenarios are called range orders. They have unique characteristics and are essentially fee-earning reversible limit orders, which will be explained later.
The last case is the exact same liquidity providing mechanism as the previous versions: LPs provide liquidity in both tokens of the same value (= amount * price).
There’s also an identical product to the case: grid trading, a very powerful investment tool for a time of consolidation. Dunno what’s grid trading? Check out Binance’s explanation on this, as this topic won’t be covered!
In fact, LPs of Uniswap v1 & v2 are grid trading with a range of [0,∞] and the entry price as the baseline.
Range orders
To understand range orders, we’d have to first revisit how price is discovered on Uniswap with the equation x * y = k, for x & y stand for the amount of two tokens X and Y and k as a constant.
The price of X compared to Y is y / x, which means how many Y one can get for 1 unit of X, and vice versa the price of Y compared to X is x / y.
For the price of X to go up, y has to increase and x decrease.
With this pricing mechanism in mind, it’s example time!
Say an LP plans to place liquidity in the price range [15.625, 17.313], higher than the current price of X 10, when 100(x) * 1000(y) = 100000(k).
The price of X is 1250 / 80 = 15.625 when the equation is 80 * 1250 = 100000.
The price of X is 1315.789 / 76 = 17.313 when the equation is 76 * 1315.789 = 100000.
If now the price of X reaches 15.625, the only way for the price of X to go even higher is to further increase y and decrease x, which means exchanging a certain amount of X for Y.
Thus, to provide liquidity in the range [15.625, 17.313], an LP needs only to prepare 80 — 76 = 4 of X. If the price exceeds 17.313, all 4 X of the LP is swapped into 1315.789 — 1250 = 65.798 Y, and then the LP has nothing more to do with the pool, as his/her liquidity is drained.
What if the price stays in the range? It’s exactly what LPs would love to see, as they can earn swapping fees for all transactions in the range! Also, the balance of X will swing between [76, 80] and the balance of Y between [1250, 1315.789].
This might not be obvious, but the example above shows an interesting insight: if the liquidity of one token is provided, only when the token becomes more valuable will it be exchanged for the less valuable one.
…wut? 🤔
Remember that if 4 X is provided within [15.625, 17.313], only when the price of X goes up from 15.625 to 17.313 is 4 X gradually swapped into Y, the less valuable one!
What if the price of X drops back immediately after reaching 17.313? As X becomes less valuable, others are going to exchange Y for X.
The below image illustrates the scenario of DAI/USDC pair with a price range of [1.001, 1.002] well: the pool is always composed entirely of one token on both sides of the tick, while in the middle 1.001499⁶ is of both tokens.
Image source: https://uniswap.org/blog/uniswap-v3/
Similarly, to provide liquidity in a price range < current price, an LP has to prepare a certain amount of Y for others to exchange Y for X within the range.
To wrap up such an interesting feature, we know that:
Only one token is required for range orders.
Only when the current price is within the range of the range order can LP earn trading fees. This is the main reason why most people believe LPs of v3 have to monitor the price more actively to maximize their income, which also means that LPs of v3 have become arbitrageurs 🤯
I will be discussing more the impacts of v3 in 5. Impacts of v3.
⁷ 1.001499988 = √(1.0001 * 1.0002) is the geometric mean of 1.0001 and 1.0002. The implication is that the geometric mean of two prices is the average execution price within the range of the two prices.
Reversible limit orders
As the example in the last section demonstrates, if there is 4 X in range [15.625, 17.313], the 4 X will be completely converted into 65.798 Y when the price goes over 17.313.
We all know that a price can stay in a wide range such as [10, 11] for quite some time, while it’s unlikely so in a narrow range such as [15.625, 15.626].
Thus, if an LP provides liquidity in [15.625, 15.626], we can expect that once the price of X goes over 15.625 and immediately also 15.626, and does not drop back, all X are then forever converted into Y.
The concept of having a targeted price and the order will be executed after the price is crossed is exactly the concept of limit orders! The only difference is that if the range of a range order is not narrow enough, it’s highly possible that the conversion of tokens will be reverted once the price falls back to the range.
As price ranges follow the equation p(i) = 1.0001 ^ i, the range can be quite narrow and a range order can thus effectively serve as a limit order:
When i = 27490, 1.0001²⁷⁴⁹⁰ = 15.6248.⁸
When i = 27491, 1.0001²⁷⁴⁹¹ = 15.6264.⁸
A range of 0.0016 is not THAT narrow but can certainly satisfy most limit order use cases!
⁸ As mentioned previously in note #4, there is a square root in the equation of the price and index, thus the numbers here are for explantion only.
5. Impacts of v3
Higher capital efficiency, LPs become arbitrageurs… as v3 has made tons of radical changes, I’d like to summarize my personal takes of the impacts of v3:
Higher capital efficiency makes one of the most frequently considered indices in DeFi: TVL, total value locked, becomes less meaningful, as 1$ on Uniswap v3 might have the same effect as 100$ or even 2000$ on v2.
The ease of spot exchanging between spot exchanges used to be a huge advantage of spot markets over derivative markets. As LPs will take up the role of arbitrageurs and arbitraging is more likely to happen on v3 itself other than between DEXs, this gap is narrowed … to what extent? No idea though.
LP strategies and the aggregation of NFT of Uniswap v3 liquidity token are becoming the blue ocean for new DeFi startups: see Visor and Lixir. In fact, this might be the turning point for both DeFi and NFT: the two main reasons of blockchain going mainstream now come to the alignment of interest: solving the $$ problem 😏😏😏
In the right venue, which means a place where transaction fees are low enough, such as Optimism, we might see Algo trading firms coming in to share the market of designing LP strategies on Uniswap v3, as I believe Algo trading is way stronger than on-chain strategies or DAO voting to add liquidity that sort of thing.
After reading this article by Parsec.finance: The Dex to Rule Them All, I cannot help but wonder: maybe there is going to be centralized crypto exchanges adopting v3’s approach. The reason is that since orders of LPs in the same tick are executed pro-rata, the endless front-running speeding-competition issue in the Algo trading world, to some degree, is… solved? 🤔
Anyway, personal opinions can be biased and seriously wrong 🙈 I’m merely throwing out a sprat to catch a whale. Having a different voice? Leave your comment down below!
6. Conclusion
That was kinda tough, isn’t it? Glad you make it through here 🥂🥂🥂
There are actually many more details and also a huge section of Oracle yet to be covered. However, since this article is more about features and targeting normal DeFi users, I’ll leave those to the next one; hope there is one 😅
If you have any doubt or find any mistake, please feel free to reach out to me and I’d try to reply AFAP!
Stay tuned and in the meantime let’s wait and see how Uniswap v3 is again pioneering the innovation of DeFi 🌟
Uniswap v3 Features Explained in Depth was originally published in Taipei Ethereum Meetup on Medium, where people are continuing the conversation by highlighting and responding to this story.
👏 歡迎轉載分享鼓掌
同時也有1部Youtube影片,追蹤數超過4萬的網紅ncisofficialchannel,也在其Youtube影片中提到,Digital Single「Wonderer」 各配信サイト&サブスクリプション:https://ssm.lnk.to/Wonderer_NCIS -------------------- Everybody wants to know the secret People try and try...
「abstract meaning」的推薦目錄:
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abstract meaning 在 讀書e誌 Facebook 的精選貼文
"Blockchain Chicken Farm" (區塊鏈養雞場)
中國農村的科技逆襲!(希望有出版社來翻譯)
”一行行代碼為永恆奠基,就像一粒粒沙平息咆哮的大海” 阿里巴巴雲計算博物館的標語
記得去年在大陸曾經有一個機會參加企業家們的聚集,其中有一名養殖業的企業大老知道我是科技業的人時,非常認真地問我 “請問現在AI辨識技術可以做到豬臉辨識嗎?” 。大概有那麼一秒的時間我以為他在開玩笑,但後來他描述中國需要產出食物的規模是如此浩大,願意去做這些苦力工作的人又很少,對於一個每年要養隻上百萬頭豬的養殖場,各種的人工智慧和自動化技術,不是一個要拿去融資A輪B輪的口號,而是企業能夠經營下去的必要條件。
同事推薦的一本好書,讓我非常的驚艷。同樣是講到中國與美國在科技發展的差異,對於人工智慧使用的不同哲學,相較於李開復之前那本人工智慧書的“科技精英”角度,這本書在技術與人性中更加有刃有餘,並且更加詩意,更加有靈魂!不但讓人很容易明白最新科技在矽谷和中國鄉下的不同反應方式,更是交織在歷史人文的故事中,在他這個第二代華裔美國人的口中,更加鮮明並且發人深省。
當區塊鏈養雞,人工智慧養豬,各式基因改造農場,碰上農村包圍城市,淘寶村,返鄉創業,戶口制度等等,衝擊下的許多小人物故事,既新鮮,卻也無奈。作者寫這本書同時也提醒了美國讀者們,關於矽谷菁英的驕傲,都市人的優越感,以及西方世界的偏見。
這本上週才出版的書,也非常即時的討論這現在的中美貿易戰,討論著日益嚴重的貧富不均問題,也說明了為什麼佩佩豬在社群媒體是上被禁止的。
但我覺得最棒的一點是,在這些最新科技奇特的用途之下,作者深刻的反省。他說在古老中國的文化裡面,農夫的工作並非在產值最大化,而是如何照顧土地,使其生生不息。在西方世界眼中的落後中國農村,甚至是嚴厲限制農民工的制度,科技在這些農村中的體現其實是超乎一般人所理解的。所有人跟他分享自己故事時,總是帶著一絲的驕傲,卻也感受到是另一種向著都市階級的一種逆襲。
"Humility in Innovation" (謙卑的創新)是我看見作者貫穿全書的主軸。她說到現在科技業急急忙忙地想著如何規模化,都是數量的規模化。但是否應該要思考時間的規模化?也就是讓整個模式可以隨著時間,有永續的可能,這包含了對環境的友善,提供人們平等的機會,也提供真正的自由。讓工作和生活,不是去追逐一個永遠摸不到的未來,而是重新回到找尋此時此刻的意義。
"Transforming work into abstract, quantifiable, optimized labor erases “any of the human and social purposes or the creative satisfactions that Work has always had in other societies.” It is easy to automate work using AI once you’ve made work devoid of meaning."
“把工作變成抽象量化並且優化的勞動,抹煞了工作在其他的社會中一直帶來的人性和社會價值目的或者是創意所帶來的成就感。當你把工作的意義感奪去時,用人工智慧把它自動化就變得很簡單了”
全文與紐約時報介紹在部落格中
https://dushuyizhi.net/blockchain-chicken-farm-區塊鏈養雞場/
#BlockChainChickenFarm #區塊鏈養雞場
#XiaoWeiWang
abstract meaning 在 寶靈魔法學院 Facebook 的最佳貼文
في عام 1545 ادخل الرياضي الايطالي جيرولامو كاردانو الارقام المعقدة رياضيا. استُخدِمت هذه الصيغ المعقدة لوصف الطبيعة الكمية منذ 1925. مشكلة هذه الارقام انها خيالية اي لا معنى فيزيائي لها ورغم ذلك فهي مقبولة في فيزياء الكم. اول محاولة لتفسيرها فيزيائيا نشرتُها عام 2012 و طورتُها خلال عامي 2016-2019. ليُصبع التعقيد هذا نتيجة مشكلة فيزيائية وليس مجرد صيغة رياضية مجردة. وادخلتُ مصطلح التعقيد كظاهرة فيزيائية.
In 1545, the Italian mathematician Gerolamo Cardano has introduced the complex numbers. These complex forms has been utilised to describe quantum nature since 1925. The problem of these numbers is its imaginary nature and has no physical meaning. In spite of this problem the complex numbers are accepted. I did the first attempt to explain it physically and was published in 2012. It has been developed during the years 2016-2019. For me the complexity is due to a physical problem and not just an abstract mathematical form. I introduced the term complexification as a result of physical phenomenon.
abstract meaning 在 ncisofficialchannel Youtube 的最佳貼文
Digital Single「Wonderer」
各配信サイト&サブスクリプション:https://ssm.lnk.to/Wonderer_NCIS
--------------------
Everybody wants to know the secret
People try and try to make it meaningful
Time after time, another story
You’ve heard it all, it could be boring
A boy and girl, a special journey
The scent of spring, her hair was flowing
(And yet again)
The summer sun delivers damage
Unending need, a test of patience
A falling out, it can’t be salvaged
And with the snow, it ends in silence
Maybe it all was meant to be
After all, what’s happened can’t be undone
Pain is the pleasure to start anew
Only those who take the leap of faith will know
You’ll know
Tomorrow comes without a stop your time will come to be in front
Although right now the sorrow seems like it’ll never disappear
Tomorrow comes without a stop your time will come to be in front
Although right now the sorrow seems like it’ll never disappear
Tomorrow comes wow oh oh
The sorrow’s gone wow oh oh
Tomorrow comes wow oh oh
The sorrow’s gone wow oh oh
Everybody wants to know the secret
People try and try to make a meaning
You wonder, slowly ponder
searching through the binary
Keep scrolling on
Keep scrolling on
You try and try to understand it all
Tomorrow comes without a stop your time will come to be in front
Although right now the sorrow seems like it’ll never disappear
Tomorrow comes without a stop your time will come to be in front
Although right now the sorrow seems like it’ll never disappear
Tomorrow comes wow oh oh
The sorrow’s gone wow oh oh
Tomorrow comes wow oh oh
The sorrow’s gone wow oh oh
--------------------
【和訳】
誰しも秘密を知りたがる
人は意味を求めてる
何度も繰り返すあのストーリー
聞いたことあるから退屈かもしれない
少年と少女 特別な旅
春の香り 髪が風になびいていた
また繰り返す
夏の太陽が痛みをくれる
激しく求め合い試し合って
仲違いしては、雪の中静かに終わる
全てなるべくしてなったのかもしれない
やり直しはきかないんだ
痛みは新たな旅の喜び
一回飛び出せばわかるさ
君にも
明日は止めどなく押し寄せて
君の出番が来る
今は悲しみが永遠に
続くような気がするけれど
明日は止めどなく押し寄せて
そして、君の出番が来る
今は悲しみが永遠に
続くような気がするけれど
明日は来る
悲しみは消えて
明日は来る
悲しみは消えて
誰しも秘密を知りたがる
人は意味を求めてる
想いめぐらせ、考えて
バイナリーの中
スクロールし続ける
スクロールし続ける
君は全てを理解しようとしてる
明日は止めどなく押し寄せて
君の出番が来る
今は悲しみが永遠に
続くような気がするけれど
明日は止めどなく押し寄せて
そして、君の出番が来る
今は悲しみが永遠に
続くような気がするけれど
明日は来る
悲しみは消えて
明日は来る
悲しみは消えて
--------------------
▼Staff Credit
Director:Shin Ishihara
Cinematographer:Satoshi Imamura(Things.)
Motion Graphics:SHOTARO
Light:Takumi Toratani
Production Manager:Kei Kawaguchi
--------------------
Official Web Site:https://www.ncis.jp/
Twitter:https://twitter.com/NCIS_BANDS
Instagram:https://www.instagram.com/nothingscarvedinstone/
LINE:https://line.me/ti/p/@ncis_official
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