關於 square pricing ，我們在網路上蒐集到這些相關的討論、資訊與評價

The Deco X68 covers 5,500 square feet with speeds up to 3,600 Mbps.

📜 [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

接下來！
5/08(Sat) Bei City Rock Festival 春響音樂節
Bei City Rock Festival 春響音樂節 2021



photo by Leon's Photography × 周愚民

Seven hours of indie rock bands and four food vendors set in the heart of Maji Square! You ready to rock this town!?!
準備好迎接這個春天最大的LIVE音樂盛會！ 七個全台最紅最屌的獨立搖滾樂團連唱七小時，從放克、金屬、迪斯可、流行到搖滾唱好唱滿，陪你嗨整夜！ 唱累了還有多款特色調酒及四家異國美食攤販，讓你吃飽喝足後繼續跳！ 這麼炸的組合僅此一夜在Maji集食行樂轟炸你的小宇宙，錯過就再也沒有！還在等什麼？我們5/8見！
★ 樂團 ★
晚上 7-8 - Gold Seal
晚上 8-9 - Pangolin
晚上 9-10 - The Getaway Pricks
晚上 10-11 - P!SCO
晚上 11-12 - 88Balaz
晚上 12-1 - Mary Bites Kerry

ϟϟϟ P!SCO ϟϟϟ
2010年成立於台北，P!SCO被樂迷封為「最能挑戰肌耐力極限的跳舞搖滾樂團」，2016年入圍金音獎最佳現場演出獎，由主唱、吉他、bass、鼓和鍵盤組成的五人編制，強調視覺與聽覺兼具的表演方式，其獨特亮眼的舞台魅力絕對要看現場才能體會！
融合搖滾、電子、古典等元素的多元曲風難以被定義，non-stop表演形態讓演出絕不冷場。此外，P!SCO也非常重視與台下的互動，從簡單的手勢、吶喊口號到大合唱，讓所有來看表演的樂迷們都成為參與者，創造出台灣前所未見的演出風格，吸引受眾目光。
每場演出，P!SCO都會在舞台上掛一面彩虹旗，表達對LGBT與弱勢族群的支持。2019年釋出新歌〈光圈〉，描述從小因性別傾向被欺負而不斷質疑自己的痛苦，此曲在網路平台的播放成績十分亮眼，也使P!SCO的彩虹形象變得更加鮮明。
由於總是能將場子搞熱，P!SCO時常受邀參與大大小小的音樂祭。成軍九年以來，不僅走遍台灣各大live house與大型音樂活動，亦曾參與過日本富士電視台、愛知電視台錄影，並前往日本、韓國、馬來西亞、新加坡、港澳中國等數個國家、超過20個城市進行演出。
ϟϟϟ. 88Balaz ϟϟϟ
88balaz是一隻來自台北的標準4件式搖滾樂團，現場常常加上打擊樂手和手風琴手音樂以藍調搖滾為基調，大量的龐克能量和噪音吉他。歌詞描述人在每個成長時期荒謬卻日常中實在上演發生的掙扎。看似率性諷刺，藏著細膩的意念。用粗糙直接的方式撞進你心裡，持續不間斷在台灣，日本，中國，美國，東南亞巡演。曾經多次獲得台灣各種音樂獎項，包括最佳專輯，最佳樂團，及最佳現場演出。要讓搖滾樂充滿你生活的每個地方、每個大。小。洞。讓你每個毛細孔都不再鬱悶大噴發！在最絕望的時候，像是最粗的沙紙一般，抹平藏在心裡的那些坑坑洞洞！
ϟϟϟ Mary Bites Kerry ϟϟϟ
2009年成立的瑪莉咬凱利，是台灣少數融合管樂的 大編制搖滾男子團體。曲風是台灣難得的 ska 加上 punk 還有 ska-punk 融合而成，雖然已經從新鮮有趣變成靠經 典曲目生存的老牌樂團，但活力依然不減，他們在舞台上 蹦蹦跳跳，大唱大叫，歡樂的氣氛總是能感染台下的老老 少少。團員人數最多曾經來到十一人，雖然這樣的優勢一直沒有反應在臉書粉絲頁上，但至少現場不會呈現台上比台下還多人的情況。想要笑一下、跳一下、發洩一下、放鬆一下，或者只是想看一下帥哥，那來看瑪莉咬凱利絕對是個好選擇!
ϟϟϟ Pangolin ϟϟϟ
2013在台北成立的英美四人樂團。樂團第三代成員擅長受龐克影響的搖滾曲風和斯卡風的迪斯可情歌。Pangolin習慣讓樂團的存在慫恿觀眾活動筋骨，每首歌越跳越嗨。
ϟϟϟ The Getaway Pricks ϟϟϟ
要來像颱風、地震般搖滾你的身心。他們唯一的要求就是要你百分之百進入派對模式來玩。還有你的靈魂。他們可能也會給你要那個。
———————————————
GENERAL ADMISSION PRICING 票
超級早鳥 400NT
早鳥 500NT
門票 600NT
➤包含一杯330ml 的啤酒或調酒
➤室內場地。別擔心天氣
———————————————
🥙美食🥙
- SKB Burger
- Sausage Shack
- Chinita's Cubanos
- Wei's Bakery
———————————————
———————————————
———————————————
ENGLISH VERSION
Get ready for the biggest live music party of the spring! Seven hours of indie rock bands and four food vendors set in the heart of Maji Square! You ready to rock this town!?!
THIS IS GONNA BE EPIC!!!
———————————————
ϟϟϟϟ Pangolin ϟϟϟ
A four-piece Anglo–American musical outfit originally formed in Taipei in 2013. Now on their third iteration of band members and armed with punk-infused rock chops and ska-inspired disco thrash ballads, Pangolin habitually stare into the abyss of their own existential existence, taunting their audiences to get little looser and dance a little harder with each song.
ϟϟϟ The Getaway Pricks ϟϟϟ
The Getaway Pricks are here to rock you like a typhoon, and shake you like an earthquake.The only thing they ask for in return is that you show up in Full Party Mode®️.
ϟϟϟ Mary Bites Kerry ϟϟϟ
Founded in 2009 Mary Bites Kerry is one of the rare Taiwanese bands to mix a brass section to a punchy rock structure. It's one of the even more rare Ska band of Taiwan that also plays Punk, which makes it the only Ska Punk band of the island.
Started with a fresh sound and the sweet taste of youth (back at that time), Mary Bites Kerry has become a veteran band in the Taiwan scene, but don't be fooled: Mary has teeth and still bites with energy. When it's about getting a crowd crazy with music, MBK sets the tone and -and the bar- high. Once with up to 11 musicians on stage, the now 8 pieces formation has always met warm enthusiasm all around Taiwan and abroad.
ϟϟϟ. 88Balaz ϟϟϟ
88BALAZ is a standard 4-piece rock band from Taipei. The live performance often accompany by percussion and accordion. The music is based on blues rock and bring in strong punk energy and noise guitar. The lyrics describe the struggles and ridiculous in growth period. The lyrics seem to be satirical, but they contain delicate ideas, hit into your heart in a rough and straightforward way.
ϟϟϟ P!SCO ϟϟϟ
P!SCO is and has been one of the hottest Indie band on the scene for the last 10 years! Get ready for the non stop, jaw dropping action that is P!SCO!
ϟϟϟ Gold Seal ϟϟϟ
Gold Seal combines heavy grooves and hot improvisations with embellishments of classic roots. Gold Seal is affected by progressive and heavy rock sensitivity, creating all the original music with depth and variability to make you move.
—————————————————
➤ RULES & REGULATIONS
➤Family Friendly ( children under 12 Free)
➤No Animals allowed
➤Drink Responsibly. If you are deemed too intoxicated you may be asked to leave
➤No outside food or drinks permitted
➤About refunds pleas see accupass rules.

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