Math Contract

The FXSwap Math contract implements the two-coin StableSwap-style invariant used by deployed FXSwap pools. It is not the TwocryptoMath.vy contract used by ordinary Twocrypto-NG pools.

Contract Source & Deployment

The deployed FXSwap pool returns its Math address from MATH(). The verified source is closest to StableswapMath.vy at commit 387fbe5, compiled with Vyper 0.4.3.

Read MATH() from the target pool. The reviewed contract reports version() == "v0.1.0".

The pool normalizes its two balances to common precision before calling these methods. Unless reproducing the invariant for research or simulation, integrations should use pool and Views methods rather than call Math directly.

AMM Math Functions

get_y

Math.get_y(_amp: uint256, _gamma: uint256, xp: uint256[2], D: uint256, i: uint256) -> uint256[2]: pure

Solves the StableSwap invariant for normalized balance xp[i] while holding D and the other balance constant.

Input	Meaning
_amp	Amplification value in the pool's contract precision
_gamma	Unused compatibility argument
xp	Two normalized balances in common precision
D	Current invariant
i	Balance index to solve; must be 0 or 1

The first return element is the solved balance. The second is always 0 and exists for Twocrypto interface compatibility. The function iterates up to 255 times and reverts with Did not converge if it does not reach one-unit precision.

newton_D

Math.newton_D(_amp: uint256, gamma: uint256, _xp: uint256[2], K0_prev: uint256 = 0) -> uint256: pure

Calculates invariant D for two normalized balances and the supplied amplification.

gamma and K0_prev are unused compatibility arguments. The function returns 0 when both balances sum to zero. For non-zero supply it iterates up to 255 times and reverts with Did not converge if convergence fails.

get_p

Math.get_p(_xp: uint256[2], _D: uint256, _A_gamma: uint256[2]) -> uint256: pure

Returns the normalized derivative dx₀/dx₁ with 1e18 precision. _A_gamma[0] supplies amplification; the compatibility gamma value is not used by this StableSwap-style calculation.

The pool multiplies the result by price_scale and divides by 1e18 to store last_prices.

wad_exp

Math.wad_exp(x: int256) -> uint256: pure

Returns eˣ where x and the result use 1e18 fixed-point precision. The pool uses it to calculate the EMA decay factor for price_oracle.

version

Math.version() -> String[8]: view

Returns "v0.1.0" for the reviewed deployed Math contract.

Compatibility boundary

FXSwap retains the Twocrypto-compatible Math call shape so the pool can use shared periphery interfaces. That compatibility does not make the algorithms interchangeable:

• gamma does not shape the deployed FXSwap invariant;
• get_y returns [y, 0] rather than a Cryptoswap solver result;
• newton_D ignores gamma and K0_prev; and
• the invariant concentrates around a variable price_scale using StableSwap-style math.

Allowlist the pool version together with its MATH() and VIEW() addresses. Do not substitute an ordinary Twocrypto-NG Math contract because the ABI appears compatible.