Merge pull request #211 from alchemyplatform/fast-exponentiation

feat: use fast exponentiation for better perf

src/utils/index.ts

@@ -1,14 +1,16 @@
 /* eslint-disable prefer-const */
 import { BigInt, BigDecimal, ethereum } from '@graphprotocol/graph-ts'
 import { Transaction } from '../types/schema'
-import { ONE_BI, ZERO_BI, ZERO_BD, ONE_BD } from '../utils/constants'
+import { ZERO_BI, ZERO_BD, ONE_BD } from '../utils/constants'
 
 export function exponentToBigDecimal(decimals: BigInt): BigDecimal {
-  let bd = BigDecimal.fromString('1')
-  for (let i = ZERO_BI; i.lt(decimals as BigInt); i = i.plus(ONE_BI)) {
-    bd = bd.times(BigDecimal.fromString('10'))
+  let resultString = '1';
+
+  for (let i = 0; i < decimals.toI32(); i++) {
+    resultString += '0';
   }
-  return bd
+
+  return BigDecimal.fromString(resultString);
 }
 
 // return 0 if denominator is 0 in division
@@ -20,22 +22,36 @@ export function safeDiv(amount0: BigDecimal, amount1: BigDecimal): BigDecimal {
   }
 }
 
-export function bigDecimalExponated(value: BigDecimal, power: BigInt): BigDecimal {
-  if (power.equals(ZERO_BI)) {
-    return ONE_BD
+/**
+ * Implements exponentiation by squaring
+ * (see https://en.wikipedia.org/wiki/Exponentiation_by_squaring )
+ * to minimize the number of BigDecimal operations and their impact on performance.
+ */
+export function fastExponentiation(value: BigDecimal, power: i32): BigDecimal {
+  if (power < 0) {
+    let result = fastExponentiation(value, -power);
+    return safeDiv(ONE_BD, result);
   }
-  let negativePower = power.lt(ZERO_BI)
-  let result = ZERO_BD.plus(value)
-  let powerAbs = power.abs()
-  for (let i = ONE_BI; i.lt(powerAbs); i = i.plus(ONE_BI)) {
-    result = result.times(value)
+
+  if (power == 0) {
+    return ONE_BD;
   }
 
-  if (negativePower) {
-    result = safeDiv(ONE_BD, result)
+  if (power == 1) {
+    return value;
   }
 
-  return result
+  let halfPower = power / 2;
+  let halfResult = fastExponentiation(value, halfPower);
+
+  // Use the fact that x ^ (2n) = (x ^ n) * (x ^ n) and we can compute (x ^ n) only once.
+  let result = halfResult.times(halfResult);
+
+  // For odd powers, x ^ (2n + 1) = (x ^ 2n) * x
+  if (power % 2 == 1) {
+    result = result.times(value);
+  }
+  return result;
 }
 
 export function tokenAmountToDecimal(tokenAmount: BigInt, exchangeDecimals: BigInt): BigDecimal {

src/utils/tick.ts

@@ -1,6 +1,6 @@
 /* eslint-disable prefer-const */
 import { BigDecimal, BigInt } from '@graphprotocol/graph-ts'
-import { bigDecimalExponated, safeDiv } from '.'
+import { fastExponentiation, safeDiv } from '.'
 import { Tick } from '../types/schema'
 import { Mint as MintEvent } from '../types/templates/Pool/Pool'
 import { ONE_BD, ZERO_BD, ZERO_BI } from './constants'
@@ -20,7 +20,7 @@ export function createTick(tickId: string, tickIdx: i32, poolId: string, event:
   tick.price1 = ONE_BD
 
   // 1.0001^tick is token1/token0.
-  let price0 = bigDecimalExponated(BigDecimal.fromString('1.0001'), BigInt.fromI32(tickIdx))
+  let price0 = fastExponentiation(BigDecimal.fromString('1.0001'), tickIdx);
   tick.price0 = price0
   tick.price1 = safeDiv(ONE_BD, price0)