Uint128x128Math

Git Source

Author:
Trader Joe

Helper contract used for power and log calculations

State Variables

LOG_SCALE_OFFSET

uint256 constant LOG_SCALE_OFFSET = 127;

LOG_SCALE

uint256 constant LOG_SCALE = 1 << LOG_SCALE_OFFSET;

LOG_SCALE_SQUARED

uint256 constant LOG_SCALE_SQUARED = LOG_SCALE * LOG_SCALE;

Functions

log2

Calculates the binary logarithm of x.

*Based on the iterative approximation algorithm.
https://en.wikipedia.org/wiki/Binary\\_logarithm#Iterative\\_approximation\\ Requirements:

• x must be greater than zero.
  Caveats:
• The results are not perfectly accurate to the last decimal, due to the lossy precision of the iterative approximation
  Also because x is converted to an unsigned 129.127-binary fixed-point number during the operation to optimize the multiplication*

function log2(uint256 x) internal pure returns (int256 result);

Parameters

Name	Type	Description
x	uint256	The unsigned 128.128-binary fixed-point number for which to calculate the binary logarithm.

Returns

Name	Type	Description
result	int256	The binary logarithm as a signed 128.128-binary fixed-point number.

pow

Returns the value of x^y. It calculates 1 / x^abs(y) if x is bigger than 2^128.
At the end of the operations, we invert the result if needed.

function pow(uint256 x, int256 y) internal pure returns (uint256 result);

Parameters

Name	Type	Description
x	uint256	The unsigned 128.128-binary fixed-point number for which to calculate the power
y	int256	A relative number without any decimals, needs to be between ]-2^21; 2^21[

Errors

Uint128x128Math__LogUnderflow

error Uint128x128Math__LogUnderflow();

Uint128x128Math__PowUnderflow

error Uint128x128Math__PowUnderflow(uint256 x, int256 y);