pump-bonding-curve

Bonding Curve — Pricing, Quoting & AMM Mathematics

Implement and maintain the constant-product AMM bonding curve math that powers Pump token pricing — including buy/sell quoting, fee-aware calculations, market cap computation, reserve management, and edge-case handling for new, active, and migrated curves.

Context

Pump tokens are priced using a constant-product bonding curve ($x \times y = k$) where $x$ = virtual SOL reserves and $y$ = virtual token reserves. The bonding curve determines token prices during the pre-graduation phase. Once market cap reaches a threshold, the token "graduates" and migrates to a PumpAMM pool.

Key Files

• src/bondingCurve.ts — all bonding curve math functions (buy/sell quoting, market cap)
• src/fees.ts — fee computation (basis points, tiered fees, ceiling division)
• src/state.ts — BondingCurve, Global, FeeConfig, FeeTier interfaces

Constant-Product Formula

$$x \times y = k$$

Buy (tokens out for SOL in): $$\text{tokensOut} = \frac{dx \times Y}{X + dx}$$

Where $dx$ = SOL input (after fees), $X$ = virtual SOL reserves, $Y$ = virtual token reserves.

Sell (SOL out for tokens in): $$\text{solOut} = \frac{dy \times X}{Y + dy}$$

Where $dy$ = tokens sold, $X$ = virtual SOL reserves, $Y$ = virtual token reserves.

Fee Stripping

Fees are deducted from the SOL amount before applying the bonding curve formula:

inputAmount = (amount - 1) * 10000 / (totalFeeBps + 10000)

The - 1 before fee stripping is intentional to handle rounding edge cases.

Market Cap Calculation

$$\text{marketCap} = \frac{\text{virtualSolReserves} \times \text{mintSupply}}{\text{virtualTokenReserves}}$$

Where mintSupply defaults to ONE_BILLION_SUPPLY ($1 \times 10^{15}$ — 1B tokens with 6 decimals).

Fee Tiers

When a FeeConfig exists, fees are market-cap-dependent. Fee tiers are iterated in reverse order — the first tier from the end whose marketCapLamportsThreshold ≤ currentMarketCap is selected.