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v3.2.0Jun 02, 2026

DeFiMath v3.2.0: 7 new utility math primitives

Seven small utility math functions land in the Math module — mulDiv, mul, abs, min, max, clamp, avg. The kind every DeFi protocol ends up reimplementing, often without enough care. Each one is branchless where the math allows, gas-tight, and validated against BigInt references over 500+ random inputs per function. They sit alongside the existing exponential/log, root, and probability primitives in the same DeFiMath library — internal pure, inlined into your contract by the Solidity compiler, no external CALL overhead.

mulDiv and mul

mulDiv(a, b, d) computes a · b / d with full 512-bit intermediate precision — the Remco Bloemen / Uniswap V3 algorithm that splits the 512-bit product into two 256-bit words via the mulmod trick, then does 512-by-256 division using Newton-Raphson modular inverse. Reverts with named errors on d == 0 (MulDivByZeroError) or quotient overflow (MulDivOverflowError).

mul(a, b) is a specialization for the 1e18 denominator case — the most common fixed-point multiply in DeFi. All denominator-dependent constants are precomputed: the 2^18 factor in 1e18 = 2^18 · 5^18 becomes a shift, the reduced odd denominator 5^18 is a literal, and the modular inverse mod 2^256 is baked into the bytecode as 0xaccb…0669.

Realistic-input measurements (500 random pairs across 1e6..1e30):

  • mulDiv(a, b, 1e18): 155 gas
  • mul(a, b): 130 gas — ~16% cheaper, same precision

Bit-tight utilities

The remaining five round out the basics:

  • abs(int256) — 17 gas, branchless via SAR + XOR + SUB. Handles type(int256).min cleanly via two's-complement wrap.
  • min(a, b) / max(a, b) — 23 gas each, three-opcode branchless: x XOR ((x XOR y) · LT/GT).
  • clamp(x, lo, hi) — 78 gas, composed max(x, lo) then min(_, hi).
  • avg(a, b) — 21 gas, overflow-safe (a & b) + ((a ^ b) >> 1). Never wraps even at the uint256 ceiling where naive (a + b) / 2 would.

All seven are documented on the Math module page.

Get it

npm install defimath-lib