Numeric Limits

amounts

uint112

• Maximum sane amount (result of balanceOf) for external tokens

• Uniswap2 limits token amounts to this

• Spec: For an 18 decimal token, more than a million billion tokens (1e15)

small amounts

uint96

• For holding amounts that we don't expect to get quite as large, in particular reserve balances

• Can pack together with an address in a single slot

• Spec: For an 18 decimal token, more than a billion tokens (1e9)

debt amounts

uint144

• Maximum sane amount for debts

• Packs together with an amount in a single storage slot

• Spec: Should hold the maximum possible amount (uint112) but scaled by another 9 decimal places (for the internal debt precision)

  • Actual: 2e16

prices

• Minimum supported price:

  • Fraction: 1e3 / 1e18 = 1e-15

  • Tick: -345405

  • sqrtPriceX96: 2505418623681149822473

• Maximum supported price:

  • Fraction: 1e33 / 1e18 = 1e15

  • Tick: 345405

  • sqrtPriceX96: 2505410343826649584586222772852783278

The supported price range was chosen for the following reason:

• The maximum price squared fits in a uint256: 6e73 < 1e77

  • Not necessary to use FullMath library

• The maximum supported price times the maximum supported amount fits within a uint256: 5e66 < 1e77

  • Also holds with debt and its extra 9 digits of precision: 5e75 < 1e77

interestRate

int96

• "Second Percent Yield"

• Fraction scaled by 1e27

  • Example: 10% APR = 1e27 * 0.1 / (86400*365) = 1e27 * 0.000000003170979198376458650 = 3170979198376458650

• Spec: 1 billion % APR, positive or negative

interestAccumulator

uint256

• Starts at 1e27, multiplied by (1e27 + interestRate) every second

• Spec: 100% APR for 100 years

  -> 2^256
  ~= 1.1579208923e+77
  -> 10^27 * (1 + (100/100 / (86400*365)))^(86400*365*100)
  ~= 2.6881128798e+70

moduleId

uint32

• One per module, so this is way more than needed

• Divided into 3 sections

  • <500_000: Public single-proxy

  • =500_000 and <1_000_000: Public multi-proxy

  • =1_000_000: Internal

• Spec: A dozen or so modules, with room to grow in all sections

collateralFactor/borrowFactor

uint32

• Fraction between 0 and 1, scaled by 2^32 - 1

• Spec: At least 3 decimal places (overkill)