Implement Balancer math on Uv3

common/calculate-swap3.ts

@@ -162,7 +162,7 @@ export function addPosition(
     maxTick,
     deltaL
   )
-  console.log(`Deducting required N: ${requiredN} and required Y: ${requiredY}`)
+  // console.log(`Deducting required N: ${requiredN} and required Y: ${requiredY}`)
 
   // Add liquidity as we pass through the smaller tick
   const minTickState = pool.tickStates[minTick] || {
@@ -187,6 +187,41 @@ export function addPosition(
   return pool
 }
 
+export function addBalancer(pool: Swap3Pool, p: number, deltaL: number) {
+  // TODO: math is borked, shouldn't be returning infinity
+  function tickL(tick: number) {
+    const q = 1 - p
+    return deltaL * 2 * p ** q * q ** p * 1.0001 ** ((p - 0.5) * tick)
+  }
+
+  // See how much liquidity is provided at +/- 5pp around p
+  // const minTick = fromProb(p - 0.1)
+  // const maxTick = fromProb(p + 0.05)
+  const minTick = fromProb(0.000001)
+  const maxTick = fromProb(0.999999)
+  let totalN = 0
+  let totalY = 0
+  const stride = 300
+  for (let t = minTick; t <= maxTick; t += stride) {
+    // console.log('liquidity at tick ', t, toProb(t), tickL(t))
+    const { requiredN, requiredY } = calculateLPCost(
+      fromProb(p),
+      t,
+      t + stride,
+      tickL(t)
+    )
+    totalN += requiredN
+    totalY += requiredY
+    // Add liquidity
+    addPosition(pool, t, t + stride, tickL(t))
+  }
+
+  console.log('rough number of ticks', (maxTick - minTick) / stride)
+  console.log(`Total N: ${totalN} and total Y: ${totalY}`)
+  grossLiquidity(pool)
+  return pool
+}
+
 // This also mutates the pool directly
 export function grossLiquidity(pool: Swap3Pool) {
   let liquidityGross = 0

web/pages/swap.tsx

@@ -1,4 +1,5 @@
 import {
+  addBalancer,
   addPosition,
   buyYes,
   calculateLPCost,
@@ -203,8 +204,9 @@ export default function Swap() {
     tick: fromProb(0.3),
     tickStates: [],
   }
-  INIT_POOL = addPosition(INIT_POOL, -(2 ** 23), 2 ** 20, 100)
-  INIT_POOL = addPosition(INIT_POOL, fromProb(0.32), fromProb(0.35), 100)
+  INIT_POOL = addPosition(INIT_POOL, -(2 ** 23), 2 ** 20, 1)
+  // INIT_POOL = addPosition(INIT_POOL, fromProb(0.32), fromProb(0.35), 100)
+  INIT_POOL = addBalancer(INIT_POOL, 0.3, 100)
   INIT_POOL = grossLiquidity(INIT_POOL)
 
   const [pool, setPool] = useState(INIT_POOL)
@@ -215,7 +217,7 @@ export default function Swap() {
   return (
     <Col className="mx-auto max-w-2xl gap-10 p-4">
       {/* <BalanceTable /> */}
-      <PoolTable pool={pool} />
+      {/* <PoolTable pool={pool} /> */}
       <Graph
         pool={pool}
         previewMarker={