Math

Low-level fixed-point primitives in 18-decimal format (1e18 = 1.0). All pure, gas-efficient, and validated to sub-1e-12 absolute error against reference libraries.

Contract: Math.sol

Functions

Conventions

• All values use 18-decimal fixed-point (1e18 = 1.0).
• Signedness mirrors the math: exp takes int256, returns uint256; ln takes uint256, returns int256.
• All functions are internal pure — no storage access, no external calls.

Quick example

import "defimath-lib/contracts/math/Math.sol";

uint256 x    = 2e18;                     // x = 2.0
uint256 root = DeFiMath.sqrt(x);         // root ≈ 1.41421e18
int256  lnX  = DeFiMath.ln(x);           // lnX  ≈ 0.69315e18
uint256 ePow = DeFiMath.exp(int256(x));  // ePow ≈ 7.389e18

Important notes

• Use expm1 for small x. Computing ex − 1 via exp(x) - 1e18 catastrophically cancels when |x| < 0.01. expm1 uses a Taylor series in that range and preserves full 18-digit precision.
• Use log1p for small x. Same reason — log1p(x) preserves precision near zero where ln(1 + x) would lose ~15 digits to subtraction.
• Negative exp underflows silently to 0. For x < −41.45e18, exp(x) returns 0 (not a revert) since the true value is below 1e-18 representational precision.
• CLZ requires Solidity 0.8.31 + EVM "osaka". ln, sqrt, cbrt, and sqrtTime emit the new CLZ opcode introduced in Osaka.

Limits & errors