failed attempt to save even more gas in balanced pair by interpolating from a lookup table

src/LMSRBalancedPairPrecomputed.sol

@@ -0,0 +1,261 @@
+// SPDX-License-Identifier: UNLICENSED
+pragma solidity ^0.8.30;
+
+import "forge-std/console2.sol";
+import {ABDKMath64x64} from "../lib/abdk-libraries-solidity/ABDKMath64x64.sol";
+import {LMSRStabilized} from "./LMSRStabilized.sol";
+
+/// @title LMSRBalancedPairPrecomputed
+/// @notice Balanced-pair LMSR using a precomputed lookup table for amount-out:
+///         y = b * ln(1 + α e^Δ), with Δ = (q_i - q_j)/b and α = 1 - e^{-u}, u = a/b.
+/// @dev Precomputation is done once with exp/ln; runtime swaps are interpolation-only with no transcendental ops.
+library LMSRBalancedPairPrecomputed {
+    using ABDKMath64x64 for int128;
+    using LMSRStabilized for LMSRStabilized.State;
+
+    // Q64.64 constants
+    int128 private constant ONE = 0x10000000000000000;
+
+    /// @dev Precomputation-only state; keeps table configuration and data separate from LMSR core state.
+    struct Precomp {
+        // Precompute config
+        int128 W;              // half-width for Δ band (Q64.64), table centered at 0
+        int128 uMax;           // maximum u = a/b covered (Q64.64)
+        uint256 NDelta;        // number of Δ samples (>= 2)
+        uint256 NAlpha;        // number of u/α samples (>= 2)
+        int128 deltaStep;      // step in Δ grid (Q64.64) == 2W/(NDelta-1)
+        int128 uStep;          // step in u grid (Q64.64) == uMax/(NAlpha-1)
+
+        // Grids and tables
+        int128[] deltaGrid;    // Δ_i from -W to +W, length NDelta
+        int128[] uGrid;        // u_j from 0 to uMax, length NAlpha
+        int128[] alphaLut;     // α(u_j) = 1 - exp(-u_j), length NAlpha
+        int128[][] g;          // g[j][i] = ln(1 + α_j * exp(Δ_i)), size NAlpha x NDelta
+    }
+
+    /* --------------------
+       Initialization
+       -------------------- */
+
+    /// @notice Initialize the precomputed tables (assumes plenty of gas).
+    /// @param s LMSR core state (must already represent a 2-asset pool with kappa set)
+    /// @param p Precomputed table state to be filled
+    /// @param W Half-width in Δ around parity (Q64.64), table covers Δ ∈ [-W, +W]
+    /// @param uMax Maximum u = a/b to be supported by the table (Q64.64)
+    /// @param NDelta Number of Δ samples (>= 2)
+    /// @param NAlpha Number of u/α samples (>= 2)
+    function initPrecomputed(
+        LMSRStabilized.State storage s,
+        Precomp storage p,
+        int128 W,
+        int128 uMax,
+        uint256 NDelta,
+        uint256 NAlpha
+    ) internal {
+        require(s.nAssets == 2, "Precomp: requires 2-asset pool");
+        require(s.kappa > int128(0), "Precomp: kappa>0");
+        require(W > int128(0), "Precomp: W>0");
+        require(uMax > int128(0), "Precomp: uMax>0");
+        require(NDelta >= 2, "Precomp: NDelta>=2");
+        require(NAlpha >= 2, "Precomp: NAlpha>=2");
+
+        // Store config
+        p.W = W;
+        p.uMax = uMax;
+        p.NDelta = NDelta;
+        p.NAlpha = NAlpha;
+
+        // Steps
+        p.deltaStep = _div64(_mul64(W, _fromUInt(2)), _fromUInt(NDelta - 1)); // 2W/(NDelta-1)
+        p.uStep = _div64(uMax, _fromUInt(NAlpha - 1));                        // uMax/(NAlpha-1)
+
+        // Build grids
+        p.deltaGrid = new int128[](NDelta);
+        p.uGrid = new int128[](NAlpha);
+        p.alphaLut = new int128[](NAlpha);
+        p.g = new int128[][](NAlpha);
+
+        // Δ grid from -W to +W
+        int128 startDelta = W.neg();
+        for (uint256 i = 0; i < NDelta; ) {
+            p.deltaGrid[i] = startDelta.add(_mul64(p.deltaStep, _fromUInt(i)));
+            unchecked { ++i; }
+        }
+
+        // Build u grid and alpha(u) LUT
+        for (uint256 j = 0; j < NAlpha; ) {
+            int128 uj = _mul64(p.uStep, _fromUInt(j)); // 0 .. uMax
+            p.uGrid[j] = uj;
+            // α(u) = 1 - exp(-u)
+            int128 alphaJ = ONE.sub(ABDKMath64x64.exp(uj.neg()));
+            p.alphaLut[j] = alphaJ;
+            p.g[j] = new int128[](NDelta);
+            unchecked { ++j; }
+        }
+
+        // Fill g[j][i] = ln(1 + α_j * exp(Δ_i))
+        for (uint256 j = 0; j < NAlpha; ) {
+            int128 alphaJ = p.alphaLut[j];
+            for (uint256 i = 0; i < NDelta; ) {
+                int128 eDelta = ABDKMath64x64.exp(p.deltaGrid[i]);
+                int128 inner = ONE.add(alphaJ.mul(eDelta));
+                p.g[j][i] = ABDKMath64x64.ln(inner);
+                unchecked { ++i; }
+            }
+            unchecked { ++j; }
+        }
+    }
+
+    /* --------------------
+       Swap (Interpolated)
+       -------------------- */
+
+    /// @notice Exact-input swap i -> j using the precomputed table when feasible.
+    /// @dev Falls back to exact LMSR for:
+    ///      - limitPrice > 0,
+    ///      - |Δ| > W or u not in [0, uMax],
+    ///      - non-positive amounts or degenerate b,
+    ///      - non-2-asset pools.
+    function swapAmountsForExactInput(
+        LMSRStabilized.State storage s,
+        Precomp storage p,
+        uint256 i,
+        uint256 j,
+        int128 a,
+        int128 limitPrice
+    ) internal view returns (int128 amountIn, int128 amountOut) {
+        // Validate pool shape and indices
+        if (s.nAssets != 2 || i >= 2 || j >= 2) {
+            console2.log('Precomp: fallback (nAssets)');
+            return LMSRStabilized.swapAmountsForExactInput(s.nAssets, s.kappa, s.qInternal, i, j, a, limitPrice);
+        }
+
+        // Do not handle limitPrice within the table path; use exact routine for correctness.
+        if (limitPrice > int128(0)) {
+            console2.log('Precomp: fallback (limit>0)');
+            return LMSRStabilized.swapAmountsForExactInput(s.nAssets, s.kappa, s.qInternal, i, j, a, limitPrice);
+        }
+
+        // Compute b = κ * S(q)
+        int128 sizeMetric = _computeSizeMetric(s.qInternal);
+        if (!(sizeMetric > int128(0))) {
+            console2.log('Precomp: fallback (size=0)');
+            return (int128(0), int128(0));
+        }
+        int128 b = s.kappa.mul(sizeMetric);
+        if (!(b > int128(0))) {
+            console2.log('Precomp: fallback (b<=0)');
+            return (int128(0), int128(0));
+        }
+        int128 invB = _div64(ONE, b);
+
+        // Require positive input
+        if (a <= int128(0)) {
+            console2.log('Precomp: fallback (a<0)');
+            return LMSRStabilized.swapAmountsForExactInput(s.nAssets, s.kappa, s.qInternal, i, j, a, limitPrice);
+        }
+
+        // Compute u and Δ
+        int128 u = a.mul(invB);
+        if (u < int128(0) || u > p.uMax) {
+            // outside u range - fallback
+            console2.log('Precomp: fallback (outside u)');
+            console2.log(u);
+            console2.log(p.uMax);
+            return LMSRStabilized.swapAmountsForExactInput(s.nAssets, s.kappa, s.qInternal, i, j, a, limitPrice);
+        }
+
+        int128 delta = s.qInternal[i].sub(s.qInternal[j]).mul(invB);
+        int128 absDelta = delta >= int128(0) ? delta : delta.neg();
+        if (absDelta > p.W) {
+            // outside ±W band - fallback
+            console2.log('Precomp: fallback (outside W)');
+            return LMSRStabilized.swapAmountsForExactInput(s.nAssets, s.kappa, s.qInternal, i, j, a, limitPrice);
+        }
+
+        // 1D interpolation position for u (row selection)
+        (uint256 j0, int128 wu) = _interpPosition(u, p.uStep, p.NAlpha);
+        int128 oneMinusWu = ONE.sub(wu);
+
+        // Map Δ ∈ [-W, +W] to shifted in [0, 2W]
+        int128 deltaShifted = delta.add(p.W);
+        (uint256 i0, int128 wd) = _interpPosition(deltaShifted, p.deltaStep, p.NDelta);
+        int128 oneMinusWd = ONE.sub(wd);
+
+        // Interpolate along Δ within rows j0 and j0+1
+        int128 g00 = p.g[j0][i0];
+        int128 g01 = p.g[j0][i0 + 1];
+        int128 g0 = g00.mul(oneMinusWd).add(g01.mul(wd));
+
+        int128 g10 = p.g[j0 + 1][i0];
+        int128 g11 = p.g[j0 + 1][i0 + 1];
+        int128 g1 = g10.mul(oneMinusWd).add(g11.mul(wd));
+
+        // Interpolate across u between rows
+        int128 g = g0.mul(oneMinusWu).add(g1.mul(wu));
+
+        // amountOut = b * g
+        int128 out64 = b.mul(g);
+        if (out64 <= int128(0)) {
+            // Numerical guard; fallback
+            console2.log('Precomp: fallback (out<0)');
+            return LMSRStabilized.swapAmountsForExactInput(s.nAssets, s.kappa, s.qInternal, i, j, a, limitPrice);
+        }
+
+        console2.log('Precomp: success');
+        amountIn = a;
+        amountOut = out64;
+        return (amountIn, amountOut);
+    }
+
+    /* --------------------
+       Internal helpers
+       -------------------- */
+
+    /// @dev Compute size metric S(q) = sum q_i
+    function _computeSizeMetric(int128[] memory qInternal) private pure returns (int128) {
+        int128 total = int128(0);
+        for (uint256 k = 0; k < qInternal.length; ) {
+            total = total.add(qInternal[k]);
+            unchecked { ++k; }
+        }
+        return total;
+    }
+
+    /// @dev Q64.64 wrappers (avoid name conflicts and keep intent explicit)
+    function _fromUInt(uint256 x) private pure returns (int128) {
+        return ABDKMath64x64.fromUInt(x);
+    }
+    function _mul64(int128 a, int128 b) private pure returns (int128) {
+        return a.mul(b);
+    }
+    function _div64(int128 a, int128 b) private pure returns (int128) {
+        return ABDKMath64x64.div(a, b);
+    }
+
+    /// @dev Given x >= 0 and a uniform step > 0, compute index floor(x/step) clamped to [0, n-2] and fraction w in [0,1]:
+    ///      x ≈ (idx * step) * (1-w) + ((idx+1) * step) * w
+    function _interpPosition(int128 x, int128 step, uint256 n)
+        private
+        pure
+        returns (uint256 idx, int128 w)
+    {
+        // t = x/step in Q64.64
+        int128 t = _div64(x, step);
+        // floor index = uint(t) via right shift by 64 (x >= 0 ensures non-negative)
+        uint256 idxFloor = uint256(int256(t)) >> 64;
+        if (idxFloor >= n - 1) {
+            // clamp to the last segment
+            idx = n - 2;
+            w = ONE; // exact at upper bound
+            return (idx, w);
+        }
+        idx = idxFloor;
+
+        // fractional part: w = (x - idx*step) / step
+        int128 xi = _mul64(step, _fromUInt(idx));
+        int128 frac = x.sub(xi);
+        w = _div64(frac, step); // in [0,1)
+        return (idx, w);
+    }
+}

src/PartyPoolBalancedPair.sol

@@ -1,15 +1,20 @@
 // SPDX-License-Identifier: UNLICENSED
 pragma solidity ^0.8.30;
 
+import {ABDKMath64x64} from "../lib/abdk-libraries-solidity/ABDKMath64x64.sol";
 import {IERC20} from "../lib/openzeppelin-contracts/contracts/token/ERC20/IERC20.sol";
+import {LMSRBalancedPairPrecomputed} from "./LMSRBalancedPairPrecomputed.sol";
 import {NativeWrapper} from "./NativeWrapper.sol";
-import {LMSRStabilizedBalancedPair} from "./LMSRStabilizedBalancedPair.sol";
 import {PartyPool} from "./PartyPool.sol";
 import {PartyPoolBase} from "./PartyPoolBase.sol";
 import {PartyPoolMintImpl} from "./PartyPoolMintImpl.sol";
 import {PartyPoolSwapImpl} from "./PartyPoolSwapImpl.sol";
 
 contract PartyPoolBalancedPair is PartyPool {
+
+    LMSRBalancedPairPrecomputed.Precomp internal _precomp;
+    bool internal _precomputed;
+
     constructor(
         address owner_,
         string memory name_,
@@ -19,17 +24,32 @@ contract PartyPoolBalancedPair is PartyPool {
         int128 kappa_,
         uint256 swapFeePpm_,
         uint256 flashFeePpm_,
-        uint256 protocolFeePpm_,             // NEW: protocol share of fees (ppm)
-        address protocolFeeAddress_,         // NEW: recipient for collected protocol tokens
+        uint256 protocolFeePpm_,
+        address protocolFeeAddress_,
         NativeWrapper wrapperToken_,
         PartyPoolSwapImpl swapMintImpl_,
         PartyPoolMintImpl mintImpl_
     )
     PartyPool(owner_, name_, symbol_, tokens_, bases_, kappa_, swapFeePpm_, flashFeePpm_, protocolFeePpm_, protocolFeeAddress_, wrapperToken_, swapMintImpl_, mintImpl_)
-    {}
+    {
+        // Initialize kappa early so precompute() can be called before initialMint()
+        _lmsr.kappa = kappa_;
+    }
+
+    function precompute(
+        int128 W,
+        int128 uMax,
+        uint256 NDelta,
+        uint256 NAlpha
+    ) external {
+        require(!_precomputed, 'Precomp: already initialized');
+        LMSRBalancedPairPrecomputed.initPrecomputed(_lmsr, _precomp, W, uMax, NDelta, NAlpha );
+        _precomputed = true;
+    }
 
     function _swapAmountsForExactInput(uint256 i, uint256 j, int128 a, int128 limitPrice) internal virtual override view
     returns (int128 amountIn, int128 amountOut) {
-        return LMSRStabilizedBalancedPair.swapAmountsForExactInput(_lmsr, i, j, a, limitPrice);
+//        return LMSRStabilizedBalancedPair.swapAmountsForExactInput(_lmsr, i, j, a, limitPrice);
+        return LMSRBalancedPairPrecomputed.swapAmountsForExactInput(_lmsr, _precomp, i, j, a, limitPrice);
     }
 }

src/PartyPoolDeployer.sol

@@ -1,10 +1,14 @@
 // SPDX-License-Identifier: UNLICENSED
 pragma solidity ^0.8.30;
 
-import "./PartyPoolMintImpl.sol";
-import "./PartyPoolSwapImpl.sol";
+import {ABDKMath64x64} from "../lib/abdk-libraries-solidity/ABDKMath64x64.sol";
+import {IERC20} from "../lib/openzeppelin-contracts/contracts/token/ERC20/IERC20.sol";
+import {IPartyPool} from "./IPartyPool.sol";
+import {NativeWrapper} from "./NativeWrapper.sol";
 import {PartyPool} from "./PartyPool.sol";
 import {PartyPoolBalancedPair} from "./PartyPoolBalancedPair.sol";
+import {PartyPoolMintImpl} from "./PartyPoolMintImpl.sol";
+import {PartyPoolSwapImpl} from "./PartyPoolSwapImpl.sol";
 
 // This pattern is needed because the PartyPlanner constructs two different types of pools (regular and balanced-pair)
 // but doesn't have room to store the initialization code of both contracts. Therefore, we delegate pool construction.
@@ -77,7 +81,7 @@ contract PartyPoolBalancedPairDeployer is IPartyPoolDeployer {
         PartyPoolSwapImpl swapImpl_,
         PartyPoolMintImpl mintImpl_
     ) external returns (IPartyPool) {
-        return new PartyPoolBalancedPair(
+        PartyPoolBalancedPair pool = new PartyPoolBalancedPair(
             owner_,
             name_,
             symbol_,
@@ -92,5 +96,14 @@ contract PartyPoolBalancedPairDeployer is IPartyPoolDeployer {
             swapImpl_,
             mintImpl_
         );
+
+        pool.precompute(
+            ABDKMath64x64.divu(25,10_000), // ±25 bps
+            ABDKMath64x64.divu(10, 100), // taking up to 10% of the pool
+            20, // num Δ samples
+            20  // num α samples
+        );
+
+        return pool;
     }
 }

test/Deploy.sol

@@ -1,6 +1,7 @@
 // SPDX-License-Identifier: UNLICENSED
 pragma solidity ^0.8.30;
 
+import {ABDKMath64x64} from "../lib/abdk-libraries-solidity/ABDKMath64x64.sol";
 import {IERC20} from "../lib/openzeppelin-contracts/contracts/token/ERC20/IERC20.sol";
 import {NativeWrapper} from "../src/NativeWrapper.sol";
 import {PartyPlanner} from "../src/PartyPlanner.sol";
@@ -66,23 +67,31 @@ library Deploy {
         NativeWrapper wrapper,
         bool _stable
     ) internal returns (PartyPool) {
-        return _stable && tokens_.length == 2 ?
-        new PartyPoolBalancedPair(
-            owner_,
-            name_,
-            symbol_,
-            tokens_,
-            bases_,
-            _kappa,
-            _swapFeePpm,
-            _flashFeePpm,
-            PROTOCOL_FEE_PPM,
-            PROTOCOL_FEE_RECEIVER,
-            wrapper,
-            new PartyPoolSwapImpl(wrapper),
-            new PartyPoolMintImpl(wrapper)
-        ) :
-        new PartyPool(
+        if(_stable && tokens_.length == 2) {
+            PartyPoolBalancedPair pool = new PartyPoolBalancedPair(
+                owner_,
+                name_,
+                symbol_,
+                tokens_,
+                bases_,
+                _kappa,
+                _swapFeePpm,
+                _flashFeePpm,
+                PROTOCOL_FEE_PPM,
+                PROTOCOL_FEE_RECEIVER,
+                wrapper,
+                new PartyPoolSwapImpl(wrapper),
+                new PartyPoolMintImpl(wrapper)
+            );
+            pool.precompute(
+                ABDKMath64x64.divu(25,10_000), // ±25 bps
+                ABDKMath64x64.divu(10, 100), // taking up to 10% of the pool
+                20, // num Δ samples
+                20  // num α samples
+            );
+            return pool;
+        }
+        return new PartyPool(
             owner_,
             name_,
             symbol_,