DeFiMath v4.1.0: φ(x) joins Φ(x)

The normal CDF has been in DeFiMath for as long as it has priced options. v4.1.0 adds its derivative — stdNormPDF — so both halves of the Gaussian pair are now primitives you can call directly.

What it's for

The density sits under every curvature-flavoured risk number — gamma, vega, the decay half of theta — and outside options under maximum-likelihood fits, kernel estimators, and Bayesian updates on a Gaussian prior. Until now, callers who wanted φ(x) on its own hand-rolled it from exp and a pasted 0.39894…, which is both slower than a purpose-built routine and easy to get subtly wrong at the rounding boundary.

uint256 d = Math.stdNormPDF(x);   // φ(x) — density
uint256 p = Math.stdNormCDF(x);   // Φ(x) — cumulative

At 320 gas it costs roughly half of stdNormCDF's 618 — which tends to surprise people who assume the derivative is the harder of the two. The function page explains why, with the assembly.

Upgrading

Drop-in. v4.1.0 is v4.0.0 plus one function: no renames, no signature changes, and no gas or precision movement anywhere else. Suite totals move to 755 Hardhat tests and 114 Foundry properties; the head-to-head is reproducible in defimath-compare.

Get it

npm install defimath-lib

• Release notes: github.com/MerkleBlue/defimath/releases/tag/v4.1.0
• Package: npmjs.com/package/defimath-lib

Building something that needs a Solidity math library — options, rates, risk, or just a fast exp — start with DeFiMath. Pure Solidity, MIT-licensed, zero runtime dependencies.