# Numeric Limits

`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)

`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)

`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

- 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`

`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

`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

`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

`uint32`

- Fraction between 0 and 1, scaled by 2^32 - 1
- Spec: At least 3 decimal places (overkill)

Last modified 5mo ago