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EVM · Formal Verification · Low-level Optimization

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Solady's cbrt, derived: The cost of broken symmetry and the 0x90b5e5 magic constant

A complete mathematical derivation of Solady's highly-optimized cbrt function. Exploring Newton's method, the asymmetry of the error map, and the origin of its magic constants.

· 21 min read
solidity math optimization solady

Solady's sqrt, derived: 80 bytes of uint256 square root from first principles

Deriving every constant in Solady's 80-byte assembly sqrt from first principles — Newton's method, quadratic convergence, and why the optimal magic constant is 1.

· 15 min read
solidity math optimization solady