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ShadeSwap Calculations ​

This page demonstrates how to calculate outputs of a single pair swap on ShadeSwap

BigNumber.js ​

bignumber.js is used on all computations to prevent loss of precision that normally happens with standard javascript math

Constant Product (CPMM) ​

Forward Swap ​

Standard swap calculation of output token amount for a given input.

ts
/**
* returns output of a simulated swap from token0 to token1 using the constant
* product rule for non-stable pairs.
* The swap output is rounded to the nearest integer, so inputs should be in
* raw (udenom) number form to prevent loss of precision
* */
function constantProductSwapToken0for1({
  token0LiquidityAmount,
  token1LiquidityAmount,
  token0InputAmount,
  fee,
}:{
  token0LiquidityAmount: BigNumber,
  token1LiquidityAmount: BigNumber,
  token0InputAmount: BigNumber,
  fee: BigNumber  // decimal percent
})
/**
* returns output of a simulated swap from token0 to token1 using the constant
* product rule for non-stable pairs.
* The swap output is rounded to the nearest integer, so inputs should be in
* raw (udenom) number form to prevent loss of precision
* */
function constantProductSwapToken0for1({
  token0LiquidityAmount,
  token1LiquidityAmount,
  token0InputAmount,
  fee,
}:{
  token0LiquidityAmount: BigNumber,
  token1LiquidityAmount: BigNumber,
  token0InputAmount: BigNumber,
  fee: BigNumber  // decimal percent
})
ts
/**
* returns output of a simulated swap from token1 to token0 using the constant
* product rule for non-stable pairs
* The swap output is rounded to the nearest integer, so inputs should be in
* raw (udenom) number form to prevent loss of precision
* */
function constantProductSwapToken1for0({
  token0LiquidityAmount,
  token1LiquidityAmount,
  token1InputAmount,
  fee,
}:{
  token0LiquidityAmount: BigNumber,
  token1LiquidityAmount: BigNumber,
  token1InputAmount: BigNumber,
  fee: BigNumber // decimal percent
})
/**
* returns output of a simulated swap from token1 to token0 using the constant
* product rule for non-stable pairs
* The swap output is rounded to the nearest integer, so inputs should be in
* raw (udenom) number form to prevent loss of precision
* */
function constantProductSwapToken1for0({
  token0LiquidityAmount,
  token1LiquidityAmount,
  token1InputAmount,
  fee,
}:{
  token0LiquidityAmount: BigNumber,
  token1LiquidityAmount: BigNumber,
  token1InputAmount: BigNumber,
  fee: BigNumber // decimal percent
})

Reverse Swap ​

Backwards calculation for determining a token input amount for a given output amount.

ts
/**
* returns input of a simulated swap from token0 to token1 using the constant
* product rule for non-stable pairs
* The swap output is rounded to the nearest integer, so inputs should be in
* raw (udenom) number form to prevent loss of precision
* */
function constantProductReverseSwapToken0for1({
  token0LiquidityAmount,
  token1LiquidityAmount,
  token1OutputAmount,
  fee,
}:{
  token0LiquidityAmount: BigNumber,
  token1LiquidityAmount: BigNumber,
  token1OutputAmount: BigNumber,
  fee: BigNumber // decimal percent
})
/**
* returns input of a simulated swap from token0 to token1 using the constant
* product rule for non-stable pairs
* The swap output is rounded to the nearest integer, so inputs should be in
* raw (udenom) number form to prevent loss of precision
* */
function constantProductReverseSwapToken0for1({
  token0LiquidityAmount,
  token1LiquidityAmount,
  token1OutputAmount,
  fee,
}:{
  token0LiquidityAmount: BigNumber,
  token1LiquidityAmount: BigNumber,
  token1OutputAmount: BigNumber,
  fee: BigNumber // decimal percent
})
ts
/**
* returns input of a simulated swap from token1 to token0 using the constant
* product rule for non-stable pairs
* The swap output is rounded to the nearest integer, so inputs should be in
* raw (udenom) number form to prevent loss of precision
* */
function constantProductReverseSwapToken1for0({
  token0LiquidityAmount,
  token1LiquidityAmount,
  token0OutputAmount,
  fee,
}:{
  token0LiquidityAmount: BigNumber,
  token1LiquidityAmount: BigNumber,
  token0OutputAmount: BigNumber,
  fee: BigNumber // decimal percent
})
/**
* returns input of a simulated swap from token1 to token0 using the constant
* product rule for non-stable pairs
* The swap output is rounded to the nearest integer, so inputs should be in
* raw (udenom) number form to prevent loss of precision
* */
function constantProductReverseSwapToken1for0({
  token0LiquidityAmount,
  token1LiquidityAmount,
  token0OutputAmount,
  fee,
}:{
  token0LiquidityAmount: BigNumber,
  token1LiquidityAmount: BigNumber,
  token0OutputAmount: BigNumber,
  fee: BigNumber // decimal percent
})

Stableswap ​

Forward Swap ​

Standard swap calculation of output token amount for a given input.

ts
/**
* returns output of a simulated swap of token0 for 
* token1 using the stableswap math
* inputs token amounts must be passsed in as human readable form
* */
function stableSwapToken0for1({
  inputToken0Amount,
  poolToken0Amount,
  poolToken1Amount,
  priceRatio,
  alpha,
  gamma1,
  gamma2,
  liquidityProviderFee, 
  daoFee,
  minTradeSizeToken0For1,
  minTradeSizeToken1For0,
  priceImpactLimit,
}:{
  inputToken0Amount:BigNumber,
  poolToken0Amount: BigNumber,
  poolToken1Amount: BigNumber,
  priceRatio: BigNumber,
  alpha: BigNumber,
  gamma1: BigNumber,
  gamma2: BigNumber,
  liquidityProviderFee: BigNumber, // decimal percent
  daoFee: BigNumber, // decimal percent
  minTradeSizeToken0For1: BigNumber,
  minTradeSizeToken1For0: BigNumber,
  priceImpactLimit: BigNumber,
})
/**
* returns output of a simulated swap of token0 for 
* token1 using the stableswap math
* inputs token amounts must be passsed in as human readable form
* */
function stableSwapToken0for1({
  inputToken0Amount,
  poolToken0Amount,
  poolToken1Amount,
  priceRatio,
  alpha,
  gamma1,
  gamma2,
  liquidityProviderFee, 
  daoFee,
  minTradeSizeToken0For1,
  minTradeSizeToken1For0,
  priceImpactLimit,
}:{
  inputToken0Amount:BigNumber,
  poolToken0Amount: BigNumber,
  poolToken1Amount: BigNumber,
  priceRatio: BigNumber,
  alpha: BigNumber,
  gamma1: BigNumber,
  gamma2: BigNumber,
  liquidityProviderFee: BigNumber, // decimal percent
  daoFee: BigNumber, // decimal percent
  minTradeSizeToken0For1: BigNumber,
  minTradeSizeToken1For0: BigNumber,
  priceImpactLimit: BigNumber,
})
ts
/**
* returns output of a simulated swap of token1 for 
* token0 using the stableswap math
* inputs token amounts must be passsed in as human readable form
* */
function stableSwapToken1for0({
  inputToken1Amount,
  poolToken0Amount,
  poolToken1Amount,
  priceRatio,
  alpha,
  gamma1,
  gamma2,
  liquidityProviderFee,
  daoFee,
  minTradeSizeToken0For1,
  minTradeSizeToken1For0,
  priceImpactLimit,
}:{
  inputToken1Amount:BigNumber,
  poolToken0Amount: BigNumber,
  poolToken1Amount: BigNumber,
  priceRatio: BigNumber,
  alpha: BigNumber,
  gamma1: BigNumber,
  gamma2: BigNumber,
  liquidityProviderFee: BigNumber, // decimal percent
  daoFee: BigNumber, // decimal percent
  minTradeSizeToken0For1: BigNumber,
  minTradeSizeToken1For0: BigNumber,
  priceImpactLimit: BigNumber,
})
/**
* returns output of a simulated swap of token1 for 
* token0 using the stableswap math
* inputs token amounts must be passsed in as human readable form
* */
function stableSwapToken1for0({
  inputToken1Amount,
  poolToken0Amount,
  poolToken1Amount,
  priceRatio,
  alpha,
  gamma1,
  gamma2,
  liquidityProviderFee,
  daoFee,
  minTradeSizeToken0For1,
  minTradeSizeToken1For0,
  priceImpactLimit,
}:{
  inputToken1Amount:BigNumber,
  poolToken0Amount: BigNumber,
  poolToken1Amount: BigNumber,
  priceRatio: BigNumber,
  alpha: BigNumber,
  gamma1: BigNumber,
  gamma2: BigNumber,
  liquidityProviderFee: BigNumber, // decimal percent
  daoFee: BigNumber, // decimal percent
  minTradeSizeToken0For1: BigNumber,
  minTradeSizeToken1For0: BigNumber,
  priceImpactLimit: BigNumber,
})

Reverse Swap ​

Backwards calculation for determining a token input amount for a given output amount.

ts
/**
* returns input of a simulated swap of token0 for 
* token1 using the stableswap math
* inputs token amounts must be passsed in as human readable form
* */
function stableReverseSwapToken0for1({
  outputToken1Amount,
  poolToken0Amount,
  poolToken1Amount,
  priceRatio,
  alpha,
  gamma1,
  gamma2,
  liquidityProviderFee,
  daoFee,
  minTradeSizeToken0For1,
  minTradeSizeToken1For0,
  priceImpactLimit,
}:{
  outputToken1Amount:BigNumber,
  poolToken0Amount: BigNumber,
  poolToken1Amount: BigNumber,
  priceRatio: BigNumber,
  alpha: BigNumber,
  gamma1: BigNumber,
  gamma2: BigNumber,
  liquidityProviderFee: BigNumber, // decimal percent
  daoFee: BigNumber, // decimal percent
  minTradeSizeToken0For1: BigNumber,
  minTradeSizeToken1For0: BigNumber,
  priceImpactLimit: BigNumber,
})
/**
* returns input of a simulated swap of token0 for 
* token1 using the stableswap math
* inputs token amounts must be passsed in as human readable form
* */
function stableReverseSwapToken0for1({
  outputToken1Amount,
  poolToken0Amount,
  poolToken1Amount,
  priceRatio,
  alpha,
  gamma1,
  gamma2,
  liquidityProviderFee,
  daoFee,
  minTradeSizeToken0For1,
  minTradeSizeToken1For0,
  priceImpactLimit,
}:{
  outputToken1Amount:BigNumber,
  poolToken0Amount: BigNumber,
  poolToken1Amount: BigNumber,
  priceRatio: BigNumber,
  alpha: BigNumber,
  gamma1: BigNumber,
  gamma2: BigNumber,
  liquidityProviderFee: BigNumber, // decimal percent
  daoFee: BigNumber, // decimal percent
  minTradeSizeToken0For1: BigNumber,
  minTradeSizeToken1For0: BigNumber,
  priceImpactLimit: BigNumber,
})
ts
/**
* returns output of a simulated swap of token1 for 
* token0 using the stableswap math
* inputs token amounts must be passsed in as human readable form
* */
function stableReverseSwapToken1for0({
  outputToken0Amount,
  poolToken0Amount,
  poolToken1Amount,
  priceRatio,
  alpha,
  gamma1,
  gamma2,
  liquidityProviderFee,
  daoFee,
  minTradeSizeToken0For1,
  minTradeSizeToken1For0,
  priceImpactLimit,
}:{
  outputToken0Amount:BigNumber,
  poolToken0Amount: BigNumber,
  poolToken1Amount: BigNumber,
  priceRatio: BigNumber,
  alpha: BigNumber,
  gamma1: BigNumber,
  gamma2: BigNumber,
  liquidityProviderFee: BigNumber, // decimal percent
  daoFee: BigNumber, // decimal percent
  minTradeSizeToken0For1: BigNumber,
  minTradeSizeToken1For0: BigNumber,
  priceImpactLimit: BigNumber,
})
/**
* returns output of a simulated swap of token1 for 
* token0 using the stableswap math
* inputs token amounts must be passsed in as human readable form
* */
function stableReverseSwapToken1for0({
  outputToken0Amount,
  poolToken0Amount,
  poolToken1Amount,
  priceRatio,
  alpha,
  gamma1,
  gamma2,
  liquidityProviderFee,
  daoFee,
  minTradeSizeToken0For1,
  minTradeSizeToken1For0,
  priceImpactLimit,
}:{
  outputToken0Amount:BigNumber,
  poolToken0Amount: BigNumber,
  poolToken1Amount: BigNumber,
  priceRatio: BigNumber,
  alpha: BigNumber,
  gamma1: BigNumber,
  gamma2: BigNumber,
  liquidityProviderFee: BigNumber, // decimal percent
  daoFee: BigNumber, // decimal percent
  minTradeSizeToken0For1: BigNumber,
  minTradeSizeToken1For0: BigNumber,
  priceImpactLimit: BigNumber,
})

Price Impact ​

Price impact is the difference between the current market price and the price you will actually pay. This is sometimes referred to as "slippage", however slippage tends to be a misused term. Slippage is supposed to be the change in output between the time the user submits a transaction and the actual amount received due to unpredictable changes in liquidity (caused by other users' swaps).

Constant Product (CPMM) ​

ts
/**
* Inputs may either be in human readable or raw form. 
* There is no rounding performed, 
* therefore there is no risk of loss of precision
* */
function constantProductPriceImpactToken0for1({
  token0LiquidityAmount,
  token1LiquidityAmount,
  token0InputAmount,
}:{
  token0LiquidityAmount: BigNumber,
  token1LiquidityAmount: BigNumber,
  token0InputAmount: BigNumber,
})
/**
* Inputs may either be in human readable or raw form. 
* There is no rounding performed, 
* therefore there is no risk of loss of precision
* */
function constantProductPriceImpactToken0for1({
  token0LiquidityAmount,
  token1LiquidityAmount,
  token0InputAmount,
}:{
  token0LiquidityAmount: BigNumber,
  token1LiquidityAmount: BigNumber,
  token0InputAmount: BigNumber,
})
ts
/**
* Inputs may either be in human readable or raw form. 
* There is no rounding performed, therefore
* there is no risk of loss of precision
* */
function constantProductPriceImpactToken1for0({
  token0LiquidityAmount,
  token1LiquidityAmount,
  token1InputAmount,
}:{
  token0LiquidityAmount: BigNumber,
  token1LiquidityAmount: BigNumber,
  token1InputAmount: BigNumber,
})
/**
* Inputs may either be in human readable or raw form. 
* There is no rounding performed, therefore
* there is no risk of loss of precision
* */
function constantProductPriceImpactToken1for0({
  token0LiquidityAmount,
  token1LiquidityAmount,
  token1InputAmount,
}:{
  token0LiquidityAmount: BigNumber,
  token1LiquidityAmount: BigNumber,
  token1InputAmount: BigNumber,
})

Stableswap ​

ts
/**
* returns price impact of a simulated swap of token0 
* for token1 inputs token amounts must be passsed in 
* as human readable form (do not use udenom)
* */
function stableSwapPriceImpactToken0For1({
  inputToken0Amount,
  poolToken0Amount,
  poolToken1Amount,
  priceRatio,
  alpha,
  gamma1,
  gamma2,
  liquidityProviderFee,
  daoFee,
  minTradeSizeToken0For1,
  minTradeSizeToken1For0,
  priceImpactLimit,
}:{
  inputToken0Amount:BigNumber,
  poolToken0Amount: BigNumber,
  poolToken1Amount: BigNumber,
  priceRatio: BigNumber,
  alpha: BigNumber,
  gamma1: BigNumber,
  gamma2: BigNumber,
  liquidityProviderFee: BigNumber,
  daoFee: BigNumber,
  minTradeSizeToken0For1: BigNumber,
  minTradeSizeToken1For0: BigNumber,
  priceImpactLimit: BigNumber,
})
/**
* returns price impact of a simulated swap of token0 
* for token1 inputs token amounts must be passsed in 
* as human readable form (do not use udenom)
* */
function stableSwapPriceImpactToken0For1({
  inputToken0Amount,
  poolToken0Amount,
  poolToken1Amount,
  priceRatio,
  alpha,
  gamma1,
  gamma2,
  liquidityProviderFee,
  daoFee,
  minTradeSizeToken0For1,
  minTradeSizeToken1For0,
  priceImpactLimit,
}:{
  inputToken0Amount:BigNumber,
  poolToken0Amount: BigNumber,
  poolToken1Amount: BigNumber,
  priceRatio: BigNumber,
  alpha: BigNumber,
  gamma1: BigNumber,
  gamma2: BigNumber,
  liquidityProviderFee: BigNumber,
  daoFee: BigNumber,
  minTradeSizeToken0For1: BigNumber,
  minTradeSizeToken1For0: BigNumber,
  priceImpactLimit: BigNumber,
})
ts
/**
* returns price impact of a simulated swap of token1 
* for token0 inputs token amounts must be passsed in 
* as human readable form (do not use udenom).
* */
function stableSwapPriceImpactToken1For0({
  inputToken1Amount,
  poolToken0Amount,
  poolToken1Amount,
  priceRatio,
  alpha,
  gamma1,
  gamma2,
  liquidityProviderFee,
  daoFee,
  minTradeSizeToken0For1,
  minTradeSizeToken1For0,
  priceImpactLimit,
}:{
  inputToken1Amount:BigNumber,
  poolToken0Amount: BigNumber,
  poolToken1Amount: BigNumber,
  priceRatio: BigNumber,
  alpha: BigNumber,
  gamma1: BigNumber,
  gamma2: BigNumber,
  liquidityProviderFee: BigNumber,
  daoFee: BigNumber,
  minTradeSizeToken0For1: BigNumber,
  minTradeSizeToken1For0: BigNumber,
  priceImpactLimit: BigNumber,
})
/**
* returns price impact of a simulated swap of token1 
* for token0 inputs token amounts must be passsed in 
* as human readable form (do not use udenom).
* */
function stableSwapPriceImpactToken1For0({
  inputToken1Amount,
  poolToken0Amount,
  poolToken1Amount,
  priceRatio,
  alpha,
  gamma1,
  gamma2,
  liquidityProviderFee,
  daoFee,
  minTradeSizeToken0For1,
  minTradeSizeToken1For0,
  priceImpactLimit,
}:{
  inputToken1Amount:BigNumber,
  poolToken0Amount: BigNumber,
  poolToken1Amount: BigNumber,
  priceRatio: BigNumber,
  alpha: BigNumber,
  gamma1: BigNumber,
  gamma2: BigNumber,
  liquidityProviderFee: BigNumber,
  daoFee: BigNumber,
  minTradeSizeToken0For1: BigNumber,
  minTradeSizeToken1For0: BigNumber,
  priceImpactLimit: BigNumber,
})