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.

interface FeeTier {
    marketCapLamportsThreshold: BN;
    fees: { lpFeeBps: BN; protocolFeeBps: BN; creatorFeeBps: BN };
}

Ceiling Division

$$\text{ceilDiv}(a, b) = \frac{a + b - 1}{b}$$

function ceilDiv(a: BN, b: BN): BN {
    return a.add(b).sub(new BN(1)).div(b);
}

Virtual vs Real Reserves

Reserve Type	Includes	Used For
virtualSolReserves	Real SOL + protocol-added virtual offset	AMM formula calculation
virtualTokenReserves	Real tokens + virtual offset	AMM formula calculation
realTokenReserves	Actual tokens available	Buy output cap
realSolReserves	Actual SOL deposited	Withdrawal limit

Edge Cases

Case	Behavior
Zero amount	Returns BN(0)
Migrated curve (complete === true, zero reserves)	Returns BN(0)
Null bonding curve	Creates a fresh curve via newBondingCurve(global)
Tokens exceed real reserves	Caps at realTokenReserves
Creator fee	Only charged if bondingCurve.creator != PublicKey.default or it's a new curve

BondingCurve State

interface BondingCurve {
    virtualTokenReserves: BN;
    virtualSolReserves: BN;
    realTokenReserves: BN;
    realSolReserves: BN;
    tokenTotalSupply: BN;
    complete: boolean;        // true = graduated to AMM
    creator: PublicKey;
    isMayhemMode: boolean;
}

Patterns to Follow

• All amounts use BN (bn.js) for arbitrary-precision integer arithmetic — never use JavaScript number
• Fee amounts are in basis points (1 bps = 0.01%, 10,000 bps = 100%)
• Always deduct fees before applying the AMM formula, not after
• Use ceiling division (ceilDiv) for fee computation to ensure the protocol never loses dust
• Quote functions are pure — no network calls, no side effects, no mutable state
• Always check bondingCurve.complete before building trade instructions

Common Pitfalls

• Confusing virtual reserves (includes virtual offset) with real reserves (actual amounts)
• Not accounting for fees when quoting — raw quote functions give different results than fee-aware ones
• Trying to trade on a graduated curve (complete === true) will fail on-chain
• Fee tiers iterate in reverse order — not forward
• Market cap calculation uses mintSupply not tokenTotalSupply
• The fee stripping formula subtracts 1 from the amount first — this is intentional
• getBuySolAmountFromTokenAmountQuote adds + 1 to the result to ensure sufficient SOL