GAMM

The GAMM module (Generalized Automated Market Maker) provides the logic to create and interact with liquidity pools on the Osmosis DEX.

Contents

1. Concepts
2. Weights
3. Pool Parameters
4. Messages
5. Transactions
6. Queries and Transactions

Concepts

The x/gamm module implements an AMM using:

• Balancer style pools with varying amounts and weights of assets in pools.
• Stableswap pools have liquidity centered around a given spot price. See here for the spec of the Osmosis implementation.

Here we will explain basic GAMM concepts and give an overview of how GAMM module's code is organized to support both type of pools.

Pool

Creation of Pool

At an initial creation of the pool, a fixed amount of 100 share token is minted in the pool and sent to the creator of the pool's account. The pool share denom is in the format of gamm/pool/{poolID} and is displayed in the format of GAMM-{poolID} to the user. Pool assets are sorted in alphabetical order by default. Pool creation is possible only for at least 2 and no more than 8 denominations.

PoolCreationFee needs to be paid to create the pool. This also keeps us safe when it comes to the malicious creation of unneeded pools.

Joining Pool

When joining a pool without swapping - with JoinPool, a user can provide the maximum amount of tokens TokenInMaxs' they're willing to deposit. This argument must contain all the denominations from the pool or no tokens at all, otherwise, the tx will be aborted. If TokenInMaxs` contains no tokens, the calculations are done based on the user's balance as the only constraint.

The front end takes care of the calculation of how many share tokens the user is eligible for at the specific moment of sending the transaction.

Calculation of exactly how many tokens are needed to get the designated share is done at the moment of processing the transaction, validating that it does not exceed the maximum amount of tokens the user is willing to deposit. After the validation, GAMM share tokens of the pool are minted and sent to the user's account.

Joining the pool using a single asset is also possible with JoinSwapExternAmountIn.

Existing Join types:

• JoinPool
• JoinSwapExternAmountIn
• JoinSwapShareAmountOut

Join types code call stack and structure:

Exiting Pool

When exiting a pool, the user provides the minimum amount of tokens they are willing to receive as they are returning their shares of the pool. However, unlike joining a pool, exiting a pool requires the user to pay the exit fee, which is set as a param of the pool. The user's share tokens burnt as result. Exiting the pool using a single asset is also possible.

Exiting a pool is possible only if user will leave a positive balance for a certain denomination after exiting or positive number of LP shares. Otherwise transaction will be aborted and user will not be able to exit a pool. Therefore, it is not possible to "drain out" a pool.

When exiting a pool with a swap, both exit and swap fees are paid.

Existing Exit types:

• ExitPool
• ExitSwapExternAmountOut
• ExitSwapShareAmountIn

Exit types code call stack and structure:

Swap

During the process of swapping a specific asset, the token the user is putting into the pool is denoted as tokenIn, while the token that would be returned to the user, the asset that is being swapped for, after the swap is denoted as tokenOut throughout the module.

Given a tokenIn, the following calculations are done to calculate how many tokens are to be swapped into and removed from the pool:

tokenBalanceOut * [1 - { tokenBalanceIn / (tokenBalanceIn + (1 - swapFee) * tokenAmountIn)} ^ (tokenWeightIn / tokenWeightOut)]

The calculation is also able to be reversed, the case where user provides tokenOut. The calculation for the amount of tokens that the user should be putting in is done through the following formula:

tokenBalanceIn * [{tokenBalanceOut / (tokenBalanceOut - tokenAmountOut)} ^ (tokenWeightOut / tokenWeightIn) -1] / tokenAmountIn

Existing Swap types:

• SwapExactAmountIn
• SwapExactAmountOut

Spot Price

Meanwhile, calculation of the spot price with a swap fee is done using the following formula:

spotPrice / (1 - swapFee), where spotPrice is defined as:

(tokenBalanceIn / tokenWeightIn) / (tokenBalanceOut / tokenWeightOut)

Spot price

Multi-Hop

The multi-hop logic is handled via x/poolmanager module. Please see for details:

• https://github.com/osmosis-labs/osmosis/blob/main/x/poolmanager/README.md

Weights

Weights refer to the how we weight the reserves of assets within a pool. Its often convenient to think of weights in terms of ratios, so a 1:1 pool between "ATOM" and "BTC" is a pool where the spot price is #ATOM in pool / #BTC in pool.

A 2:1 pool is one where the spot price is 2*(#ATOM in pool) / #BTC in pool. This weights allows one to get the same spot price in the pool, with fewer ATOM reserves. (This comes at the cost of having higher slippage, e.g. buying 10 atoms moves the price more than a 1:1 pool with the same BTC liquidity).

Within the state machine, we represent weights as numbers, and the ratios are computed internally. So you could specify a pool between three assets, with weights 100:30:50, which is equivalent to a 10:3:5 pool.

The ratios provided in a CreatePool message, or governance proposal are capped at 2\^20. However, within the state machine they are stored with an extra 30 bits of precision, allowing for smooth changes between two weights to happen with sufficient granularity.

(Note, these docs are intended to get shuffled around as we write more of the spec for x/gamm. I just wanted to document this along with the PR, to save work for our future selves)

Network Parameters

Pools have the following parameters:

Key	Type
SwapFee	sdk.Dec
ExitFee	sdk.Dec
FutureGovernor	*FutureGovernor
Weights	*Weights
SmoothWeightChangeParams	*SmoothWeightChangeParams
PoolCreationFee	sdk.Coins

1. SwapFee - The swap fee is the cut of all swaps that goes to the Liquidity Providers (LPs) for a pool. Suppose a pool has a swap fee s. Then if a user wants to swap T tokens in the pool, sT tokens go to the LP's, and then (1 - s)T tokens are swapped according to the AMM swap function.
2. ExitFee - The exit fee is a fee that is applied to LP's that want to remove their liquidity from the pool. Suppose a pool has an exit fee e. If they currently have S LP shares, then when they remove their liquidity they get tokens worth (1 - e)S shares back. The remaining eS shares are then burned, and the tokens corresponding to these shares are kept as liquidity.
3. FutureGovernor - Osmosis plans to allow every pool to act as a DAO, with its own governance in a future upgrade. To facilitate this transition, we allow pools to specify who the governor should be as a string. There are currently 3 options for the future governor.
   • No one will govern it. This is done by leaving the future governor string as blank.
   • Allow a given address to govern it. This is done by setting the future governor as a bech32 address.
   • Lockups to a token. This is the full DAO scenario. The future governor specifies a token denomination denom, and a lockup duration duration. This says that "all tokens of denomination denom that are locked up for duration or longer, have equal say in governance of this pool".
4. Weights - This defines the weights of the pool - https://balancer.fi/whitepaper.pdf
5. SmoothWeightChangeParams - This allows pool governance to smoothly change the weights of the assets it holds in the pool. So it can slowly move from a 2:1 ratio, to a 1:1 ratio. Currently, smooth weight changes are implemented as a linear change in weight ratios over a given duration of time. So weights changed from 4:1 to 2:2 over 2 days, then at day 1 of the change, the weights would be 3:1.5, and at day 2 its 2:2, and will remain at these weight ratios.

The GAMM module also has a PoolCreationFee parameter, which currently is set to 1000000000 uosmo or 1000 OSMO.

Migration Records

Migration records are used to track a canonical link between a single balancer pool and its corresponding concentrated liquidity pool. There is a single MigrationRecords object for the entire gamm module that consists of many BalancerToConcentratedPoolLink objects. Each balancer pool can be linked to a maximum of one concentrated liquidity pool, and each concentrated liquidity pool can be linked to a maximum of one balancer pool. The entire MigrationRecords object can be either replaced through governance via ReplaceMigrationRecordsProposal or specific pool links can be added/removed/modified through governance via UpdateMigrationRecordsProposal (similar to how incentives are replaced and updated).

Messages

The x/gamm module supports the following message types:

MsgCreateBalancerPool

MsgCreateBalancerPool

MsgJoinPool

MsgJoinPool

MsgExitPool

MsgExitPool

MsgSwapExactAmountIn

MsgSwapExactAmountIn

Note, that this message was deprecated and moved to x/poolmanager. Please use the MsgSwapExactAmountIn message in x/poolmanager instead.

MsgSwapExactAmountOut

MsgSwapExactAmountOut

Note, that this message was deprecated and moved to x/poolmanager. Please use the MsgSwapExactAmountOut message in x/poolmanager instead.

MsgJoinSwapExternAmountIn

MsgJoinSwapExternAmountIn

MsgJoinSwapShareAmountOut

MsgJoinSwapShareAmountOut

MsgExitSwapShareAmountIn

MsgExitSwapShareAmountIn

MsgExitSwapExternAmountOut

MsgExitSwapExternAmountOut

Transactions

Create pool

Create a new liquidity pool and provide initial liquidity to it.

osmosisd tx gamm create-pool [config-file] --from --chain-id

::: details Example The JSON [config-file] must specify the following parameters:

{
 "weights": [list weighted denoms],
 "initial-deposit": [list of denoms with initial deposit amount],
 "swap-fee": [swap fee in percentage],
 "exit-fee": [exit fee in percentage],
 "future-governor": [see options in pool parameters section above]
}

Create a new 50/50 AKT-OSMO liquidity pool with a swap and exit fee of 1%.

osmosisd tx gamm create-pool --pool-file [config-file] --from WALLET_NAME --chain-id osmosis-1

The configuration json file contains the following parameters:

{
 "weights": "5ibc/1480B8FD20AD5FCAE81EA87584D269547DD4D436843C1D20F15E00EB64743EF4,5uosmo",
 "initial-deposit": "499404ibc/1480B8FD20AD5FCAE81EA87584D269547DD4D436843C1D20F15E00EB64743EF4,500000uosmo",
 "swap-fee": "0.01",
 "exit-fee": "0.01",
 "future-governor": ""
}

:::

::: warning There is now a 1000 OSMO fee for creating pools. :::

Join pool

Add liquidity to a specified pool to get an exact amount of LP shares while specifying a maximum number tokens willing to swap to receive said LP shares.

osmosisd tx gamm join-pool --pool-id --max-amounts-in --share-amount-out --from --chain-id

::: details Example

Join pool 3 with a maximum of .037753 AKT and the corresponding amount of OSMO to get an exact share amount of 1.227549469722224220 gamm/pool/3 using WALLET_NAME on the osmosis mainnet:

osmosisd tx gamm join-pool --pool-id 3 --max-amounts-in 37753ibc/1480B8FD20AD5FCAE81EA87584D269547DD4D436843C1D20F15E00EB64743EF4 --share-amount-out 1227549469722224220 --from WALLET_NAME --chain-id osmosis-1

:::

Exit pool

Remove liquidity from a specified pool with an exact amount of LP shares while specifying the minimum number of tokens willing to receive for said LP shares.

osmosisd tx gamm exit-pool --pool-id --min-amounts-out --share-amount-in --from --chain-id

::: details Example

Exit pool 3 with for exactly 1.136326462628731195 gamm/pool/3 in order to receive a minimum of .033358 AKT and the corresponding amount of OSMO using WALLET_NAME on the osmosis mainnet:

osmosisd tx gamm exit-pool --pool-id 3 --min-amounts-out 33358ibc/1480B8FD20AD5FCAE81EA87584D269547DD4D436843C1D20F15E00EB64743EF4 --share-amount-in 1136326462628731195 --from WALLET_NAME --chain-id osmosis-1

:::

Join-swap-extern-amount-in

Add liquidity to a specified pool with only one of the required assets (i.e. Join pool 1 (50/50 ATOM-OSMO) with just ATOM).

This command essentially swaps an exact amount of an asset for the required pairing and then converts the pair to a minimum of the requested LP shares in a single step (i.e. combines the swap-exact-amount-in and join-pool commands)

osmosisd tx gamm join-swap-extern-amount-in [token-in] [share-out-min-amount] --from --pool-id --chain-id

::: details Example

Join pool 3 with exactly .200000 AKT (and 0 OSMO) to get a minimum of 3.234812471272883046 gamm/pool/3 using WALLET_NAME on the osmosis mainnet:

osmosisd tx gamm join-swap-extern-amount-in 200000ibc/1480B8FD20AD5FCAE81EA87584D269547DD4D436843C1D20F15E00EB64743EF4 3234812471272883046 --pool-id 3 --from WALLET_NAME --chain-id osmosis-1

:::

Exit-swap-extern-amount-out

Remove liquidity from a specified pool with a maximum amount of LP shares and swap to an exact amount of one of the token pairs (i.e. Leave pool 1 (50/50 ATOM-OSMO) and receive 100% ATOM instead of 50% OSMO and 50% ATOM).

This command essentially converts an LP share into the corresponding share of tokens and then swaps to the specified token-out in a single step (i.e. combines the swap-exact-amount-out and exit-pool commands)

osmosisd tx gamm exit-swap-extern-amount-out [token-out] [share-in-max-amount] --pool-id --from --chain-id

::: details Example

Exit pool 3 by removing a maximum of 3.408979387886193586 gamm/pool/3 and swap the OSMO portion of the LP share to receive 100% AKT in the exact amount of 0.199430 AKT:

osmosisd tx gamm exit-swap-extern-amount-out 199430ibc/1480B8FD20AD5FCAE81EA87584D269547DD4D436843C1D20F15E00EB64743EF4 3408979387886193586 --pool-id 3 --from WALLET_NAME --chain-id osmosis-1

:::

Join-swap-share-amount-out

Swap a maximum amount of a specified token for another token, similar to swapping a token on the trade screen GUI (i.e. takes the specified asset and swaps it to the other asset needed to join the specified pool) and then adds an exact amount of LP shares to the specified pool.

osmosisd tx gamm join-swap-share-amount-out [token-in-denom] [share-out-amount] [token-in-max-amount] --pool-id --from --chain-id

::: details Example

Swap a maximum of 0.312466 OSMO for the corresponding amount of AKT, then join pool 3 and receive exactly 1.4481270389710236872 gamm/pool/3:

osmosisd tx gamm join-swap-share-amount-out uosmo 14481270389710236872 312466 --pool-id 3 --from WALLET_NAME --chain-id osmosis-1

:::

Exit-swap-share-amount-in

Remove an exact amount of LP shares from a specified pool, swap the LP shares to one of the token pairs to receive a minimum of the specified token amount.

osmosisd tx gamm exit-swap-share-amount-in [token-out-denom] [share-in-amount] [token-out-min-amount] --pool-id --from --chain-id

::: details Example

Exit pool 3 by removing exactly 14.563185400026723131 gamm/pool/3 and swap the AKT portion of the LP share to receive 100% OSMO in the minimum amount of .298548 OSMO:

osmosisd tx gamm exit-swap-share-amount-in uosmo 14563185400026723131 298548 --pool-id 3 --from WALLET_NAME --chain-id osmosis-1

:::

Swap-exact-amount-in

Swap an exact amount of tokens for a minimum of another token, similar to swapping a token on the trade screen GUI.

osmosisd tx gamm swap-exact-amount-in [token-in] [token-out-min-amount] --pool-id --from --chain-id

::: details Example

Swap exactly .407239 AKT through pool 3 into a minimum of .140530 OSMO using WALLET_NAME on the osmosis mainnet:

osmosisd tx gamm swap-exact-amount-in 407239ibc/1480B8FD20AD5FCAE81EA87584D269547DD4D436843C1D20F15E00EB64743EF4 140530 --swap-route-pool-ids 3 --swap-route-denoms uosmo --from WALLET_NAME --chain-id osmosis-1

:::

Swap-exact-amount-out

Swap a maximum amount of tokens for an exact amount of another token, similar to swapping a token on the trade screen GUI.

osmosisd tx gamm swap-exact-amount-out [token-out] [token-out-max-amount] --swap-route-pool-ids --from --chain-id

::: details Example

Swap a maximum of .407239 AKT through pool 3 into exactly .140530 OSMO using WALLET_NAME on the osmosis mainnet:

osmosisd tx gamm swap-exact-amount-out 140530uosmo 407239 --swap-route-pool-ids 3 --swap-route-denoms ibc/1480B8FD20AD5FCAE81EA87584D269547DD4D436843C1D20F15E00EB64743EF4 --from WALLET_NAME --chain-id osmosis-1

:::

Queries

Queries

The Query submodule of the GAMM module provides the logic to request information from the liquidity pools. It contains the following functions:

• Estimate Swap Exact Amount In
• Estimate Swap Exact Amount Out
• Num Pools
• Pool
• Pool Assets
• Pool Params
• Pools
• Spot Price
• Total Liquidity
• Total Share

Estimate Swap Exact Amount In

Query the estimated result of the Swap Exact Amount In transaction. Note that the flags swap-route-pool and swap-route-denoms are required.

Usage

osmosisd query gamm estimate-swap-exact-amount-in <poolID> <sender> <tokenIn> [flags]

Example

Query the amount of ATOM the sender would receive for swapping 1 OSMO in pool 1.

osmosisd query gamm estimate-swap-exact-amount-in 1 osmo123nfq6m8f88m4g3sky570unsnk4zng4uqv7cm8 1000000uosmo --swap-route-pool-ids 1 --swap-route-denoms ibc/27394FB092D2ECCD56123C74F36E4C1F926001CEADA9CA97EA622B25F41E5EB2 

Estimate Swap Exact Amount Out

Query the estimated result of the Swap Exact Amount Out transaction. Note that the flags swap-route-pool and swap-route-denoms are required.

Usage

osmosisd query gamm estimate-swap-exact-amount-out <poolID> <sender> <tokenOut> [flags]

Example

Query the amount of OSMO the sender would require to swap 1 ATOM out of pool 1.

osmosisd query gamm estimate-swap-exact-amount-out 1 osmo123nfq6m8f88m4g3sky570unsnk4zng4uqv7cm8 1000000ibc/27394FB092D2ECCD56123C74F36E4C1F926001CEADA9CA97EA622B25F41E5EB2 --swap-route-pool-ids 1 --swap-route-denoms uosmo

Num Pools

Query the number of active pools.

Usage

osmosisd query gamm num-pools

Pool

Query the parameter and assets of a specific pool.

Usage

osmosisd query gamm pool <poolID> [flags]

Example

Query parameters and assets from pool 1.

osmosisd query gamm pool 1

Pool Assets

Query the assets of a specific pool. This query is a reduced form of the Pool query.

Usage

osmosisd query gamm pool-assets <poolID> [flags]

Example

Query the assets from pool 1.

osmosisd query gamm pool-assets 1

Pool Params

Query the parameters of a specific pool. This query is a reduced form of the Pool query.

Usage

osmosisd query gamm pool-params <poolID> [flags]

Query the parameters from pool 1.

Example

osmosisd query gamm pool-params 1

Pools

Query parameters and assets of all active pools.

Usage

Query the price of OSMO based on the price of ATOM in pool 1.

osmosisd query gamm spot-price 1 uosmo ibc/27394FB092D2ECCD56123C74F36E4C1F926001CEADA9CA97EA622B25F41E5EB2

Total Liquidity

Query the total liquidity of all active pools.

Usage

osmosisd query gamm total-liquidity

Total Share

Query the total amount of GAMM shares of a specific pool.

Usage

osmosisd query gamm total-share <poolID> [flags]

Example

Query the total amount of GAMM shares of pool 1.

osmosisd query gamm total-share 1

Other resources

• Creating a liquidity bootstrapping pool
• Creating a pool with a pool file

Events

There are 5 types of events that exist in GAMM:

• sdk.EventTypeMessage - "message"
• types.TypeEvtPoolJoined - "pool_joined"
• types.TypeEvtPoolExited - "pool_exited"
• types.TypeEvtPoolCreated - "pool_created"
• types.TypeEvtTokenSwapped - "token_swapped"

sdk.EventTypeMessage

This event is emitted in the message server when any of the gamm messages finish execution.

types.TypeEvtPoolJoined

This event is emitted after one of JoinPool or JoinPoolNoSwap complete joining the requested pool successfully.

It consists of the following attributes:

• sdk.AttributeKeyModule - "module"
  • The value is the module's name - "gamm".
• sdk.AttributeKeySender
  • The value is the address of the sender who created the swap message.
• types.AttributeKeyPoolId
  • The value is the pool id of the pool where swap occurs.
• types.AttributeKeyTokensIn
  • The value is the string representation of the tokens being swapped in.

types.TypeEvtPoolExited

This event is emitted after ExitPool completes exiting the requested pool successfully.

It consists of the following attributes:

• sdk.AttributeKeyModule - "module"
  • The value is the module's name - "gamm".
• sdk.AttributeKeySender
  • The value is the address of the sender who created the swap message.
• types.AttributeKeyPoolId
  • The value is the pool id of the pool where swap occurs.
• types.AttributeKeyTokensOut
  • The value is the string representation of the tokens being swapped out.

types.TypeEvtPoolCreated

This event is emitted after CreatePool completes creating the requested pool successfully.

types.TypeEvtTokenSwapped

This event is emitted after one of SwapExactAmountOut or SwapExactAmountIn updates pool state successfully.

It consists of the following attributes:

• sdk.AttributeKeyModule - "module"
  • The value is the module's name - "gamm".
• sdk.AttributeKeySender
  • The value is the address of the sender who created the swap message.
• types.AttributeKeyPoolId
  • The value is the pool id of the pool where swap occurs.
• types.AttributeKeyTokensIn
  • The value is the string representation of the tokens being swapped in.
• types.AttributeKeyTokensOut
  • The value is the string representation of the tokens being swapped out.