ABCDEFGHIJKLMNOPQRSTUVWXYZAAABACADAEAFAGAHAIAJAKALAMANAO
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NOTE: COPY this sheet to tweak numbers yourself. File -> Make a copy
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v2
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Constant Product: x * y = k
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Price
(token1/ token0)		Token0
(x, Eth)		Token1
(y, Dai)		Product (k)
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Add liquidity1000110001000
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Add liquidity1000110001000
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Totals220004000
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Calculate new reserves based on price change: price(x) = y/x => k/x^2
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Price
(token1/ token0)		Token0
(x, Eth)		Token1
(y, Dai)		Product (k)
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20001.4142828.4274000
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5002.8281414.2144000
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163.245553263.24555324000
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v3
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While still based on constant product, but only within limits.
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1. Example scenarios with price limits as inputs (ignoring ticks)
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NOTE: Gray cells are inputs. Try plugging in different numbers.
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InputsUseful Outputs (real liquidity)Details (virtual liquidity)Temporary variables (to manage excel formulas)
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ScenarioCurrent PriceVirtual Liquidity (L)Position Size Position Center% below% aboveLower Limit (price)Upper Limit (price)Token0 Contribution RequiredToken1 Contribution RequiredCapital Efficiency multiplierToken0 amount at lower limitToken1 amount at lower limitToken0
amount at current		Token1 amount at currentToken0 amount at upper limitToken1 amount at upper limitPrice in RangePrice above rangePrice below range
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FormulasInputInputin ticksusing geometric meanL/sqrt(low_limit)
L*sqrt(low_limit)
L/sqrt(curr_price)L*sqrt(curr_price)L/sqrt(upp_limit)L*sqrt(upp_limit)
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Add "unbounded" liquidity (equivalent to v2)1000.00400.00004.38E+1291.2649111,264.9110641.0x1.78E+300.0001.2651264.9110.0001.78E+30WAHRFALSCHFALSCH
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Add liquidity with price in range1000.0040346.410-42.26%73.21%200.0000600.00000.000000414.1104724.2x2.828565.6851.2651264.9111.633979.796FALSCHWAHRFALSCH
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Add liquidity below current price1000.0040100.000-50.00%100.00%50.0000200.00000.000000282.8427123.4x5.657282.8431.2651264.9112.828565.685FALSCHWAHRFALSCH
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Add liquidity above current price1000.0040707.107-29.29%41.42%500.00001,000.00000.000000370.4838736.3x1.789894.4271.2651264.9111.2651264.911WAHRFALSCHFALSCH
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2. Example Scenarios with price limits as inputs that are expressed as overall position size in ticks
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NOTE: Gray cells are inputs. Try plugging in different numbers.
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Fee 0.05%
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Tick Size (based on fee)0.001
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InputsUseful Outputs (real liquidity)Details (virtual liquidity)Temporary variables (to manage excel formulas)
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ScenarioCurrent PriceVirtual Liquidity (L)Position Size Position Center% below% aboveLower Limit (price)Upper Limit (price)Token0 Contribution RequiredToken1 Contribution RequiredCapital Efficiency multiplierToken0 amount at lower limitToken1 amount at lower limitToken0
amount at current		Token1 amount at currentToken0 amount at upper limitToken1 amount at upper limitPrice in RangePrice above rangePrice below range
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FormulasInputInputin ticksusing geometric meanL/sqrt(low_limit)
L*sqrt(low_limit)
L/sqrt(curr_price)L*sqrt(curr_price)L/sqrt(upp_limit)L*sqrt(upp_limit)
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Add liquidity within 1 tick band1000.004011,000.2913-0.0500%0.0500%999.79151,000.79130.0005000.1318464,002.5x1.2651264.7791.2651264.9111.2641265.411WAHRFALSCHFALSCH
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Add liquidity within 2 tick band1000.004021,000.2913-0.1498%0.1500%998.79281,001.79210.0011320.7637611,334.5x1.2661264.1471.2651264.9111.2641266.044WAHRFALSCHFALSCH
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Add liquidity within 10 tick band1000.0040101,000.2913-0.5482%0.5512%994.80751,005.80530.0036563.288269364.3x1.2681261.6231.2651264.9111.2611268.577WAHRFALSCHFALSCH
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Add liquidity within 20 tick band1000.0040201,000.2913-1.0440%1.0550%989.84841,010.84440.0068036.436814191.1x1.2711258.4741.2651264.9111.2581271.751WAHRFALSCHFALSCH
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Add liquidity within 101 tick band1000.00401011,000.2913-4.9222%5.1770%951.05491,052.07670.03170331.34394740.1x1.2971233.5671.2651264.9111.2331297.429WAHRFALSCHFALSCH
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Add liquidity within 1001 tick band1000.004010011,000.2913-39.3621%64.9133%606.55571,649.61380.280064279.7769664.5x1.624985.1341.2651264.9110.9851624.618WAHRFALSCHFALSCH
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Add liquidity within 10001 tick band1000.0040100011,000.2913-99.3249%14711.6839%6.7534148,159.98781.1609921,160.9618951.1x15.392103.9491.2651264.9110.10415396.622WAHRFALSCHFALSCH
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Add liquidity within 100001 tick band1000.00401000011,000.2913-100.0000%505930666641210000000000.00%0.00005.06E+241.2649111,264.9110641.0x89958508133.0230.0001.2651264.9110.00089984714445123.600WAHRFALSCHFALSCH
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Totals
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3. Example Scenarios with desired capital efficiency as inputs
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Fee 0.05%
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Tick Size (based on fee)0.001
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InputsUseful Outputs (real liquidity)Details (virtual liquidity)Temporary variables (to manage excel formulas)
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ScenarioCurrent PriceVirtual Liquidity (L)Position Size Position Center% below% aboveLower Limit (price)Upper Limit (price)Token0 Contribution RequiredToken1 Contribution RequiredCapital Efficiency multiplierToken0 amount at lower limitToken1 amount at lower limitToken0
amount at current		Token1 amount at currentToken0 amount at upper limitToken1 amount at upper limitPrice in RangePrice above rangePrice below range
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FormulasInputInputapproximately
in ticks		InputL/sqrt(low_limit)
L*sqrt(low_limit)
L/sqrt(curr_price)L*sqrt(curr_price)L/sqrt(upp_limit)L*sqrt(upp_limit)
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Add liquidity for 4002.5x cap efficiency1000.004011,000.2913-0.0500%0.0500%999.79151,000.79130.0005000.1318464,002.5x1.2651264.7791.2651264.9111.2641265.411WAHRFALSCHFALSCH
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Add liquidity for 2000x cap efficiency1000.004031,000.2913-0.1000%0.1001%999.29131,001.29240.0008170.4483172,000.0x1.2651264.4631.2651264.9111.2641265.728WAHRFALSCHFALSCH
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Add liquidity for 1000x cap efficiency1000.004051,000.2913-0.1999%0.2003%998.29171,002.29490.0014491.0808651,000.0x1.2661263.8301.2651264.9111.2631266.362WAHRFALSCHFALSCH
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Add liquidity for 500x cap efficiency1000.004091,000.2913-0.3996%0.4012%996.29421,004.30450.0027142.345960500.0x1.2671262.5651.2651264.9111.2621267.631WAHRFALSCHFALSCH
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Add liquidity for 250x cap efficiency1000.0040171,000.2913-0.7984%0.8048%992.30501,008.34190.0052434.876150250.0x1.2701260.0351.2651264.9111.2601270.176WAHRFALSCHFALSCH
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Add liquidity for 100x cap efficiency1000.0040411,000.2913-1.9900%2.0304%980.38551,020.60130.01283112.466722100.0x1.2781252.4441.2651264.9111.2521277.874WAHRFALSCHFALSCH
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Add liquidity for 50x cap efficiency1000.0040811,000.2913-3.9600%4.1233%960.67981,041.53610.02547925.11767550.0x1.2911239.7931.2651264.9111.2391290.914WAHRFALSCHFALSCH
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Add liquidity for 10x cap efficiency1000.00404231,000.2913-19.0000%23.46%810.23601,234.92760.126657126.32529910.0x1.4051138.5861.2651264.9111.1381405.661WAHRFALSCHFALSCH
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Add liquidity for 5x cap efficiency1000.00408951,000.2913-36.0000%56.25%640.18641,562.95520.253130252.8348285.0x1.5811012.0761.2651264.9111.0121581.369WAHRFALSCHFALSCH
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Add liquidity for 2x cap efficiency1000.004027751,000.2913-75.0000%300.00%250.07284,001.16530.632548632.3634172.0x2.529632.5481.2651264.9110.6322530.191WAHRFALSCHFALSCH
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Add liquidity for 1.5x cap efficiency1000.004043971,000.2913-88.8889%800.00%111.14359,002.62180.843335843.2126321.5x3.794421.6981.2651264.9110.4223795.286WAHRFALSCHFALSCH
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Add liquidity for 1.1x cap efficiency1000.004095971,000.2913-99.1736%12000.00%8.2669121,035.24921.1499361,149.9024011.1x13.912115.0091.2651264.9110.11513916.048WAHRFALSCHFALSCH
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Add liquidity for 1x cap efficiency1000.0040#DIV/0!1,000.2913-100.0000%#DIV/0!0.0000#DIV/0!#DIV/0!#DIV/0!1.0x#DIV/0!0.0001.2651264.911#DIV/0!#DIV/0!#DIV/0!#DIV/0!FALSCH
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Totals
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