optimization: replace division/multiplication by 2^x with shifts (#15151)

see ethereum/go-ethereum#29911

Author: yperbasis

core/vm/contracts.go

@@ -342,12 +342,8 @@ type bigModExp struct {
 
 var (
 	big1      = big.NewInt(1)
-	big2      = big.NewInt(2)
 	big3      = big.NewInt(3)
-	big4      = big.NewInt(4)
 	big7      = big.NewInt(7)
-	big8      = big.NewInt(8)
-	big16     = big.NewInt(16)
 	big20     = big.NewInt(20)
 	big32     = big.NewInt(32)
 	big64     = big.NewInt(64)
@@ -374,13 +370,13 @@ func modExpMultComplexityEip198(x *big.Int) *big.Int {
 	case x.Cmp(big1024) <= 0:
 		// (x ** 2 // 4 ) + ( 96 * x - 3072)
 		x = new(big.Int).Add(
-			new(big.Int).Div(new(big.Int).Mul(x, x), big4),
+			new(big.Int).Rsh(new(big.Int).Mul(x, x), 2),
 			new(big.Int).Sub(new(big.Int).Mul(big96, x), big3072),
 		)
 	default:
 		// (x ** 2 // 16) + (480 * x - 199680)
 		x = new(big.Int).Add(
-			new(big.Int).Div(new(big.Int).Mul(x, x), big16),
+			new(big.Int).Rsh(new(big.Int).Mul(x, x), 4),
 			new(big.Int).Sub(new(big.Int).Mul(big480, x), big199680),
 		)
 	}
@@ -397,7 +393,7 @@ func modExpMultComplexityEip198(x *big.Int) *big.Int {
 // where is x is max(length_of_MODULUS, length_of_BASE)
 func modExpMultComplexityEip2565(x *big.Int) *big.Int {
 	x.Add(x, big7)
-	x.Div(x, big8)
+	x.Rsh(x, 3) // ÷8
 	return x.Mul(x, x)
 }
 
@@ -418,7 +414,7 @@ func modExpMultComplexityEip7883(x *big.Int) *big.Int {
 	if lessOrEq32 {
 		return x
 	} else {
-		return x.Mul(x, big2)
+		return x.Lsh(x, 1) // ×2
 	}
 }
 
@@ -454,9 +450,9 @@ func (c *bigModExp) RequiredGas(input []byte) uint64 {
 	if expLen.Cmp(big32) > 0 {
 		adjExpLen.Sub(expLen, big32)
 		if c.eip7883 {
-			adjExpLen.Mul(big16, adjExpLen)
+			adjExpLen.Lsh(adjExpLen, 4) // ×16
 		} else {
-			adjExpLen.Mul(big8, adjExpLen)
+			adjExpLen.Lsh(adjExpLen, 3) // ×8
 		}
 	}
 	adjExpLen.Add(adjExpLen, big.NewInt(int64(msb)))

erigon-lib/types/transaction_signing.go

@@ -56,30 +56,30 @@ func MakeSigner(config *chain.Config, blockNumber uint64, blockTime uint64) *Sig
 		signer.blob = true
 		signer.setCode = true
 		signer.chainID.Set(&chainId)
-		signer.chainIDMul.Mul(&chainId, u256.Num2)
+		signer.chainIDMul.Lsh(&chainId, 1) // ×2
 	case config.IsCancun(blockTime):
 		// All transaction types are still supported
 		signer.protected = true
 		signer.accessList = true
 		signer.dynamicFee = true
 		signer.blob = true
 		signer.chainID.Set(&chainId)
-		signer.chainIDMul.Mul(&chainId, u256.Num2)
+		signer.chainIDMul.Lsh(&chainId, 1) // ×2
 	case config.IsLondon(blockNumber):
 		signer.protected = true
 		signer.accessList = true
 		signer.dynamicFee = true
 		signer.chainID.Set(&chainId)
-		signer.chainIDMul.Mul(&chainId, u256.Num2)
+		signer.chainIDMul.Lsh(&chainId, 1) // ×2
 	case config.IsBerlin(blockNumber):
 		signer.protected = true
 		signer.accessList = true
 		signer.chainID.Set(&chainId)
-		signer.chainIDMul.Mul(&chainId, u256.Num2)
+		signer.chainIDMul.Lsh(&chainId, 1) // ×2
 	case config.IsSpuriousDragon(blockNumber):
 		signer.protected = true
 		signer.chainID.Set(&chainId)
-		signer.chainIDMul.Mul(&chainId, u256.Num2)
+		signer.chainIDMul.Lsh(&chainId, 1) // ×2
 	case config.IsHomestead(blockNumber):
 	default:
 		// Only allow malleable transactions in Frontier
@@ -110,7 +110,7 @@ func LatestSigner(config *chain.Config) *Signer {
 		panic("chainID higher than 2^256-1")
 	}
 	signer.chainID.Set(chainId)
-	signer.chainIDMul.Mul(chainId, u256.Num2)
+	signer.chainIDMul.Lsh(chainId, 1) // ×2
 	if config.ChainID != nil {
 		if config.CancunTime != nil {
 			signer.blob = true
@@ -149,7 +149,7 @@ func LatestSignerForChainID(chainID *big.Int) *Signer {
 		panic("chainID higher than 2^256-1")
 	}
 	signer.chainID.Set(chainId)
-	signer.chainIDMul.Mul(chainId, u256.Num2)
+	signer.chainIDMul.Lsh(chainId, 1) // ×2
 	signer.protected = true
 	signer.accessList = true
 	signer.dynamicFee = true
@@ -397,5 +397,5 @@ func DeriveChainId(v *uint256.Int) *uint256.Int {
 		return new(uint256.Int).SetUint64((v - 35) / 2)
 	}
 	r := new(uint256.Int).Sub(v, u256.Num35)
-	return r.Div(r, u256.Num2)
+	return r.Rsh(r, 1) // ÷2
 }

execution/consensus/ethash/consensus.go

@@ -659,10 +659,10 @@ func AccumulateRewards(config *chain.Config, header *types.Header, uncles []*typ
 		r.Add(uncleNum, u256.Num8)
 		r.Sub(r, headerNum)
 		r.Mul(r, blockReward)
-		r.Div(r, u256.Num8)
+		r.Rsh(r, 3) // ÷8
 		uncleRewards = append(uncleRewards, *r)
 
-		r.Div(blockReward, u256.Num32)
+		r.Rsh(blockReward, 5) // ÷32
 		reward.Add(reward, r)
 	}
 	return *reward, uncleRewards

txnprovider/shutter/internal/crypto/encryption.go

@@ -96,7 +96,6 @@ func fp12Exp(base *blst.Fp12, exp *big.Int) *blst.Fp12 {
 	result := &resultValue
 
 	zero := big.NewInt(0)
-	two := big.NewInt(2)
 
 	baseCopyValue := blst.Fp12One()
 	baseCopy := &baseCopyValue
@@ -108,7 +107,7 @@ func fp12Exp(base *blst.Fp12, exp *big.Int) *blst.Fp12 {
 			result.MulAssign(baseCopy)
 		}
 		baseCopy.MulAssign(baseCopy)
-		expCopy.Div(expCopy, two)
+		expCopy.Rsh(expCopy, 1) // ÷2
 	}
 
 	return result