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chore: update math comments in tests
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@philbow61
philbow61 committed Nov 25, 2024
1 parent be11e7a commit c538ac8
Showing 1 changed file with 28 additions and 34 deletions.
62 changes: 28 additions & 34 deletions test/unit/goodDollar/BancorExchangeProvider.t.sol
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Original file line number Diff line number Diff line change
Expand Up @@ -587,12 +587,11 @@ contract BancorExchangeProviderTest_getAmountIn is BancorExchangeProviderTest {

function test_getAmountIn_whenTokenInIsToken_shouldReturnCorrectAmount() public {
bytes32 exchangeId = bancorExchangeProvider.createExchange(poolExchange1);
// formula: = tokenSupply * (-1 + (reserveBalance / (reserveBalance - (amountOut/(1-e))) )^reserveRatio )
// formula: amountIn = ------------------------------------------------------------------------------------------------ this is a fractional line
// formula: = (reserveBalance / (reserveBalance - (amountOut/(1-e))) )^reserveRatio
// formula: = tokenSupply * (-1 + (reserveBalance/(reserveBalance - amountOut))^reserveRatio )
// formula: amountIn = -------------------------------------------------------------------------------- ÷ (1-e)
// formula: = (reserveBalance / (reserveBalance - amountOut) )^reserveRatio

// calculation: (300000 * ( -1 + (60000 / (60000-(1/0.99)))^0.2))/(60000 / (60000-(1/0.99)))^0.2 = 1.010107812196722301
// uint256 expectedAmountIn = 1010107812196722302;
// calculation: (300000 * ( -1 + (60000 / (60000-1))^0.2))/(60000 / (60000-1))^0.2 ÷ 0.99 = 1.010107744175084961
uint256 expectedAmountIn = 1010107744175084961;
uint256 amountIn = bancorExchangeProvider.getAmountIn({
exchangeId: exchangeId,
Expand Down Expand Up @@ -621,11 +620,12 @@ contract BancorExchangeProviderTest_getAmountIn is BancorExchangeProviderTest {
function test_getAmountIn_whenTokenInIsTokenAndAmountOutIsSmall_shouldReturnCorrectAmount() public {
bytes32 exchangeId = bancorExchangeProvider.createExchange(poolExchange1);
uint256 amountOut = 1e12; // 0.000001 token
// formula: = tokenSupply * (-1 + (reserveBalance / (reserveBalance - (amountOut/(1-e))) )^reserveRatio )
// formula: amountIn = ------------------------------------------------------------------------------------------------ this is a fractional line
// formula: = (reserveBalance / (reserveBalance - (amountOut/(1-e))) )^reserveRatio
// formula: = tokenSupply * (-1 + (reserveBalance/(reserveBalance - amountOut))^reserveRatio )
// formula: amountIn = -------------------------------------------------------------------------------- ÷ (1-e)
// formula: = (reserveBalance / (reserveBalance - amountOut) )^reserveRatio

// calculation: (300000 * ( -1 + (60000 / (60000-(0.000001/0.99)))^0.2))/(60000 / (60000-(0.000001/0.99)))^0.2 ≈ 0.000001010101010107
// calculation: (300000 * ( -1 + (60000 / (60000-0.000001))^0.2))/(60000 / (60000-0.000001))^0.2 ÷ 0.99 ≈ 0.000001010101010107
// 1 wei difference due to precision loss
uint256 expectedAmountIn = 1010101010108;
uint256 amountIn = bancorExchangeProvider.getAmountIn({
exchangeId: exchangeId,
Expand Down Expand Up @@ -655,13 +655,11 @@ contract BancorExchangeProviderTest_getAmountIn is BancorExchangeProviderTest {
function test_getAmountIn_whenTokenInIsTokenAndAmountOutIsLarge_shouldReturnCorrectAmount() public {
bytes32 exchangeId = bancorExchangeProvider.createExchange(poolExchange1);
uint256 amountOut = 59000e18; // 59_000 since total reserve is 60k
// formula: = tokenSupply * (-1 + (reserveBalance / (reserveBalance - (amountOut/(1-e))) )^reserveRatio )
// formula: amountIn = ------------------------------------------------------------------------------------------------ this is a fractional line
// formula: = (reserveBalance / (reserveBalance - (amountOut/(1-e))) )^reserveRatio
// formula: = tokenSupply * (-1 + (reserveBalance/(reserveBalance - amountOut))^reserveRatio )
// formula: amountIn = -------------------------------------------------------------------------------- ÷ (1-e)
// formula: = (reserveBalance / (reserveBalance - amountOut) )^reserveRatio

// calculation: (300000 * ( -1 + (60000 / (60000-(59000/0.99)))^0.2))/(60000 / (60000-(59000/0.99)))^0.2 = 189649.078540006525698460
// TODO : update
//uint256 expectedAmountIn = 189649078540006525698460;
// calculation: (300000 * ( -1 + (60000 / (60000-59000))^0.2))/(60000 / (60000-59000))^0.2 ÷ 0.99 ≈ 169415.120269436288420151
uint256 expectedAmountIn = 169415120269436288420151;
uint256 amountIn = bancorExchangeProvider.getAmountIn({
exchangeId: exchangeId,
Expand Down Expand Up @@ -1069,8 +1067,8 @@ contract BancorExchangeProviderTest_getAmountOut is BancorExchangeProviderTest {
poolExchange1.reserveRatio = 1e8;
bytes32 exchangeId = bancorExchangeProvider.createExchange(poolExchange1);
uint256 amountIn = 1e18;
// formula: amountOut = (reserveBalance * amountIn / tokenSupply) * (1-e)
// calculation: (60_000 * 1 / 300_000) * 0.99 = 0.198
// formula: amountOut = (reserveBalance * amountIn * (1-e)) / tokenSupply
// calculation: (60_000 * 1 * 0.99) / 300_000 = 0.198
uint256 expectedAmountOut = 198000000000000000;
uint256 amountOut = bancorExchangeProvider.getAmountOut({
exchangeId: exchangeId,
Expand Down Expand Up @@ -1098,14 +1096,12 @@ contract BancorExchangeProviderTest_getAmountOut is BancorExchangeProviderTest {

function test_getAmountOut_whenTokenInIsToken_shouldReturnCorrectAmount() public {
bytes32 exchangeId = bancorExchangeProvider.createExchange(poolExchange1);
// formula: = reserveBalance * ( -1 + (tokenSupply/(tokenSupply - amountIn ))^(1/reserveRatio))
// formula: amountOut = ---------------------------------------------------------------------------------- * (1 - e)
// formula: = (tokenSupply/(tokenSupply - amountIn ))^(1/reserveRatio)
// formula: = reserveBalance * ( -1 + (tokenSupply/(tokenSupply - amountIn*(1-e)))^(1/reserveRatio))
// formula: amountOut = ----------------------------------------------------------------------------------
// formula: = (tokenSupply/(tokenSupply - amountIn*(1-e)))^(1/reserveRatio)

// calculation: ((60_000 *(-1+(300_000/(300_000-1))^5) ) / (300_000/(300_000-1))^5)*0.99 = 0.989993400021999963
// calculation: ((60_000 *(-1+(300_000/(300_000-1*0.99))^5) ) / (300_000/(300_000-1*0.99))^5) = 0.989993466021562164
// 1 wei difference due to precision loss
// TODO update comments
//uint256 expectedAmountOut = 989993400021999962;
uint256 expectedAmountOut = 989993466021562164;
uint256 amountOut = bancorExchangeProvider.getAmountOut({
exchangeId: exchangeId,
Expand Down Expand Up @@ -1134,11 +1130,11 @@ contract BancorExchangeProviderTest_getAmountOut is BancorExchangeProviderTest {
function test_getAmountOut_whenTokenInIsTokenAndAmountOutIsSmall_shouldReturnCorrectAmount() public {
bytes32 exchangeId = bancorExchangeProvider.createExchange(poolExchange1);
uint256 amountIn = 1e12; // 0.000001 token
// formula: = reserveBalance * ( -1 + (tokenSupply/(tokenSupply - amountIn ))^(1/reserveRatio))
// formula: amountOut = ---------------------------------------------------------------------------------- * (1 - e)
// formula: = (tokenSupply/(tokenSupply - amountIn ))^(1/reserveRatio)
// formula: = reserveBalance * ( -1 + (tokenSupply/(tokenSupply - amountIn * (1-e)))^(1/reserveRatio))
// formula: amountOut = ----------------------------------------------------------------------------------
// formula: = (tokenSupply/(tokenSupply - amountIn * (1-e)))^(1/reserveRatio)

// calculation: ((60_000 *(-1+(300_000/(300_000-0.000001))^5) )/(300_000/(300_000-0.000001))^5)*0.99 ≈ 0.0000009899999999934
// calculation: ((60_000 *(-1+(300_000/(300_000-0.000001*0.99))^5) )/(300_000/(300_000-0.000001*0.99))^5) = 0.0000009899999999934
uint256 expectedAmountOut = 989999999993;
uint256 amountOut = bancorExchangeProvider.getAmountOut({
exchangeId: exchangeId,
Expand Down Expand Up @@ -1167,13 +1163,12 @@ contract BancorExchangeProviderTest_getAmountOut is BancorExchangeProviderTest {
function test_getAmountOut_whenTokenInIsTokenAndAmountInIsLarge_shouldReturnCorrectAmount() public {
bytes32 exchangeId = bancorExchangeProvider.createExchange(poolExchange1);
uint256 amountIn = 299_000 * 1e18; // 299,000 tokens only 300k supply
// formula: = reserveBalance * ( -1 + (tokenSupply/(tokenSupply - amountIn ))^(1/reserveRatio))
// formula: amountOut = ---------------------------------------------------------------------------------- * (1 - e)
// formula: = (tokenSupply/(tokenSupply - amountIn ))^(1/reserveRatio)
// formula: = reserveBalance * ( -1 + (tokenSupply/(tokenSupply - amountIn * (1-e)))^(1/reserveRatio))
// formula: amountOut = ----------------------------------------------------------------------------------
// formula: = (tokenSupply/(tokenSupply - amountIn * (1-e)))^(1/reserveRatio)

// calculation: ((60_000 *(-1+(300_000/(300_000-299_000))^5) ) / (300_000/(300_000-299_000))^5)*0.99 ≈ 59399.999999975555555555
//uint256 expectedAmountOut = 59399999999975555555555;
//TODO update comments
// calculation: ((60_000 *(-1+(300_000/(300_000-299_000*0.99))^5) ) / (300_000/(300_000-299_000 *0.99))^5) = 59999999975030522464200
// 1 wei difference due to precision loss
uint256 expectedAmountOut = 59999999975030522464200;
uint256 amountOut = bancorExchangeProvider.getAmountOut({
exchangeId: exchangeId,
Expand Down Expand Up @@ -1713,7 +1708,6 @@ contract BancorExchangeProviderTest_swapOut is BancorExchangeProviderTest {
(, , uint256 tokenSupplyAfter, uint256 reserveBalanceAfter, , ) = bancorExchangeProvider.exchanges(exchangeId);

assertEq(reserveBalanceAfter, reserveBalanceBefore - amountOut);

assertEq(tokenSupplyAfter, tokenSupplyBefore - amountIn);
}

Expand Down

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