ContinuousIndexingMath

Git Source

Author: M^0 Labs

State Variables

SECONDS_PER_YEAR

The number of seconds in a year.

uint32 internal constant SECONDS_PER_YEAR = 31_536_000;

BPS_SCALED_ONE

100% in basis points.

uint16 internal constant BPS_SCALED_ONE = 1e4;

EXP_SCALED_ONE

The scaling of rates in for exponent math.

uint56 internal constant EXP_SCALED_ONE = 1e12;

Functions

divideDown

Helper function to calculate (x * EXP_SCALED_ONE) / index, rounded down.

Inspired by USM (https://github.com/usmfum/USM/blob/master/contracts/WadMath.sol)

function divideDown(uint240 x, uint128 index) internal pure returns (uint112 z);

divideUp

Helper function to calculate (x * EXP_SCALED_ONE) / index, rounded up.

Inspired by USM (https://github.com/usmfum/USM/blob/master/contracts/WadMath.sol)

function divideUp(uint240 x, uint128 index) internal pure returns (uint112 z);

multiplyDown

Helper function to calculate (x * index) / EXP_SCALED_ONE, rounded down.

Inspired by USM (https://github.com/usmfum/USM/blob/master/contracts/WadMath.sol)

function multiplyDown(uint112 x, uint128 index) internal pure returns (uint240 z);

multiplyUp

Helper function to calculate (x * index) / EXP_SCALED_ONE, rounded up.

Inspired by USM (https://github.com/usmfum/USM/blob/master/contracts/WadMath.sol)

function multiplyUp(uint112 x, uint128 index) internal pure returns (uint240 z);

multiplyIndicesDown

Helper function to calculate (index * deltaIndex) / EXP_SCALED_ONE, rounded down.

Inspired by USM (https://github.com/usmfum/USM/blob/master/contracts/WadMath.sol)

function multiplyIndicesDown(uint128 index, uint48 deltaIndex) internal pure returns (uint144 z);

multiplyIndicesUp

Helper function to calculate (index * deltaIndex) / EXP_SCALED_ONE, rounded up.

Inspired by USM (https://github.com/usmfum/USM/blob/master/contracts/WadMath.sol)

function multiplyIndicesUp(uint128 index, uint48 deltaIndex) internal pure returns (uint144 z);

getContinuousIndex

Helper function to calculate e^rt (continuous compounding formula).

uint64 yearlyRate can accommodate 1000% interest per year.

uint32 time can accommodate 100 years.

type(uint64).max * type(uint32).max / SECONDS_PER_YEAR fits in a uint72.

function getContinuousIndex(uint64 yearlyRate, uint32 time) internal pure returns (uint48 index);

exponent

Helper function to calculate y = e^x using R(4,4) Padé approximation: e(x) = (1 + x/2 + 3(x^2)/28 + x^3/84 + x^4/1680) / (1 - x/2 + 3(x^2)/28 - x^3/84 + x^4/1680) See: https://en.wikipedia.org/wiki/Pad%C3%A9_table See: https://www.wolframalpha.com/input?i=PadeApproximant%5Bexp%5Bx%5D%2C%7Bx%2C0%2C%7B4%2C+4%7D%7D%5D Despite itself being a whole number, x represents a real number scaled by EXP_SCALED_ONE, thus allowing for y = e^x where x is a real number.

Output y for a uint72 input x will fit in uint48

function exponent(uint72 x) internal pure returns (uint48 y);

convertToBasisPoints

Helper function to convert 12-decimal representation to basis points.

function convertToBasisPoints(uint64 input) internal pure returns (uint40);

Parameters

Name	Type	Description
input	uint64	The input in 12-decimal representation.

Returns

Name	Type	Description
<none>	uint40	The output in basis points.

convertFromBasisPoints

Helper function to convert basis points to 12-decimal representation.

function convertFromBasisPoints(uint32 input) internal pure returns (uint64);

Parameters

Name	Type	Description
input	uint32	The input in basis points.

Returns

Name	Type	Description
<none>	uint64	The output in 12-decimal representation.

Errors

DivisionByZero

Emitted when a division by zero occurs.

error DivisionByZero();