Pricing + Decimal scaling

Solidity cannot handle decimals -> are scaled up to integers

The number of decimals in ERC20 determines the factor used to represent the decimal number as uint.

• For instance 18 means that the value is stored in an uint as decimalValue * 10**18.

• 100.103 => is stored as uint 100103000000000000000 (100.103 *10**18)

• 0.000340 => stored as uint 340000000000000 (0.00034*10**18)

Let us refer to this as the 'solidity decimal scale up effect'

Converting 1 DAI to WETH (18 dp -> 18 dp)

assume DAI/ETH: 394725760000000

1e18 x 394725760000000 = 394725760000000...(18 more '0's)

1e18 x 0.00039472576e18 = 0.00039472576 *e18 *e18

• *e18 is the factor to represent the number of decimal places.

• when multiplying two integers (both have solidity decimal scale up effect), and the scale up effect is applied twice

• which is why we divide by decimals after multiplication.

  • 1e18 x 0.00039472576e18 = 0.00039472576 *e18

this is a result of using the scale up approach, due to the inability of Solidity to handle decimals.

Converting between different decimal representations

• TokenA is set up with 18 decimals

• TokenB is set up with 6 decimals

If you want to convert between different representations you have to multiply or divide depending on the difference in decimals count:

**To convert valueA to valueB: (18 dp -> 6 dp)
    valueB = valueA / 10**(A.decimals - B.decimals)
    valueB = valueA / (10**(18-6))

Normalize the from_token by stripping it of its decimal places. (because of the solidity decimal scale up effect)

Then we scale up by the TokenB (to token) decimals

Vice versa

**To convert valueB to valueA: (6 dp -> 18 dp)
    valueA = valueB * 10**(B.decimals - A.decimals)
    valueA = valueB * (10**(18-6))

    valueA = (valueB / 10**6) * 10**18

naturally division will lead to precision loss.

Weaving pricing into scaling

getMaxDebt() | how much DAI for WETH?

USING WETH COLLATERAL TO BORROW DAI

getMaxDebt() | how much USDC for WETH?

For two tokens with different decimals precision, the decimal precision of their price would match the token with the larger decimal precision Example: TokenA -> 6 dp TokenB -> 18 dp TokenA /TokenB price is returned as 18 dp; else we would incorrectly truncate the precision of tokenB,

This is why the chainlink pricefeed for USDC/ETH is in 18dp.

Old illustration