all: replace *2, /2 by Lsh, Rsh; reuse big.Int from constants

This change aims to make more efficient usage of math/big.Int's
operations with constant values such as:

* Multiplying by 2^N: .Lsh(v, N) instead of .Mul(v, big.NewInt(2^N))
* Dividing by 2: .Rsh(v, 1) instead of .Div(v, 2)
* Comparing against 0: .Sign() == 1 instead of .Cmp(big.NewInt(0))
* Adding constant derived values: extracting them into reusable globals

consensus/ethash/consensus.go

@@ -260,7 +260,7 @@ func (ethash *Ethash) verifyHeader(chain consensus.ChainHeaderReader, header, pa
 		return err
 	}
 	// Verify that the block number is parent's +1
-	if diff := new(big.Int).Sub(header.Number, parent.Number); diff.Cmp(big.NewInt(1)) != 0 {
+	if diff := new(big.Int).Sub(header.Number, parent.Number); diff.Cmp(big1) != 0 {
 		return consensus.ErrInvalidNumber
 	}
 	if chain.Config().IsShanghai(header.Number, header.Time) {

core/types/block_test.go

@@ -206,6 +206,7 @@ var benchBuffer = bytes.NewBuffer(make([]byte, 0, 32000))
 
 func BenchmarkEncodeBlock(b *testing.B) {
 	block := makeBenchBlock()
+	b.ReportAllocs()
 	b.ResetTimer()
 
 	for i := 0; i < b.N; i++ {

core/types/bloom9_test.go

@@ -78,6 +78,8 @@ func TestBloomExtensively(t *testing.T) {
 
 func BenchmarkBloom9(b *testing.B) {
 	test := []byte("testestestest")
+	b.ReportAllocs()
+
 	for i := 0; i < b.N; i++ {
 		Bloom9(test)
 	}
@@ -86,6 +88,8 @@ func BenchmarkBloom9(b *testing.B) {
 func BenchmarkBloom9Lookup(b *testing.B) {
 	toTest := []byte("testtest")
 	bloom := new(Bloom)
+	b.ReportAllocs()
+
 	for i := 0; i < b.N; i++ {
 		bloom.Test(toTest)
 	}

core/types/transaction_signing.go

@@ -194,7 +194,7 @@ func (s cancunSigner) Sender(tx *Transaction) (common.Address, error) {
 	V, R, S := tx.RawSignatureValues()
 	// Blob txs are defined to use 0 and 1 as their recovery
 	// id, add 27 to become equivalent to unprotected Homestead signatures.
-	V = new(big.Int).Add(V, big.NewInt(27))
+	V = new(big.Int).Add(V, big27)
 	if tx.ChainId().Cmp(s.chainId) != 0 {
 		return common.Address{}, fmt.Errorf("%w: have %d want %d", ErrInvalidChainId, tx.ChainId(), s.chainId)
 	}
@@ -262,7 +262,7 @@ func (s londonSigner) Sender(tx *Transaction) (common.Address, error) {
 	V, R, S := tx.RawSignatureValues()
 	// DynamicFee txs are defined to use 0 and 1 as their recovery
 	// id, add 27 to become equivalent to unprotected Homestead signatures.
-	V = new(big.Int).Add(V, big.NewInt(27))
+	V = new(big.Int).Add(V, big27)
 	if tx.ChainId().Cmp(s.chainId) != 0 {
 		return common.Address{}, fmt.Errorf("%w: have %d want %d", ErrInvalidChainId, tx.ChainId(), s.chainId)
 	}
@@ -335,7 +335,7 @@ func (s eip2930Signer) Sender(tx *Transaction) (common.Address, error) {
 	case AccessListTxType:
 		// AL txs are defined to use 0 and 1 as their recovery
 		// id, add 27 to become equivalent to unprotected Homestead signatures.
-		V = new(big.Int).Add(V, big.NewInt(27))
+		V = new(big.Int).Add(V, big27)
 	default:
 		return common.Address{}, ErrTxTypeNotSupported
 	}
@@ -403,7 +403,7 @@ func NewEIP155Signer(chainId *big.Int) EIP155Signer {
 	}
 	return EIP155Signer{
 		chainId:    chainId,
-		chainIdMul: new(big.Int).Mul(chainId, big.NewInt(2)),
+		chainIdMul: new(big.Int).Lsh(chainId, 1), // chainId*2
 	}
 }
 
@@ -416,7 +416,11 @@ func (s EIP155Signer) Equal(s2 Signer) bool {
 	return ok && eip155.chainId.Cmp(s.chainId) == 0
 }
 
-var big8 = big.NewInt(8)
+var (
+	big8  = big.NewInt(8)
+	big27 = big.NewInt(27)
+	big35 = big.NewInt(35)
+)
 
 func (s EIP155Signer) Sender(tx *Transaction) (common.Address, error) {
 	if tx.Type() != LegacyTxType {
@@ -579,6 +583,6 @@ func deriveChainId(v *big.Int) *big.Int {
 		}
 		return new(big.Int).SetUint64((v - 35) / 2)
 	}
-	v = new(big.Int).Sub(v, big.NewInt(35))
-	return v.Div(v, big.NewInt(2))
+	v = new(big.Int).Sub(v, big35)
+	return v.Rsh(v, 1) // v/2
 }

crypto/bn256/cloudflare/lattice.go

@@ -104,12 +104,14 @@ func (l *lattice) Multi(scalar *big.Int) []uint8 {
 	return out
 }
 
+var big1 = big.NewInt(1)
+
 // round sets num to num/denom rounded to the nearest integer.
 func round(num, denom *big.Int) {
 	r := new(big.Int)
 	num.DivMod(num, denom, r)
 
 	if r.Cmp(half) == 1 {
-		num.Add(num, big.NewInt(1))
+		num.Add(num, big1)
 	}
 }

crypto/secp256k1/curve.go

@@ -224,22 +224,22 @@ func (BitCurve *BitCurve) doubleJacobian(x, y, z *big.Int) (*big.Int, *big.Int,
 	d.Mul(d, d)                 //(X1+B)²
 	d.Sub(d, a)                 //(X1+B)²-A
 	d.Sub(d, c)                 //(X1+B)²-A-C
-	d.Mul(d, big.NewInt(2))     //2*((X1+B)²-A-C)
+	d.Lsh(d, 1)                 //2*((X1+B)²-A-C)
 
 	e := new(big.Int).Mul(big.NewInt(3), a) //3*A
 	f := new(big.Int).Mul(e, e)             //E²
 
-	x3 := new(big.Int).Mul(big.NewInt(2), d) //2*D
-	x3.Sub(f, x3)                            //F-2*D
+	x3 := new(big.Int).Lsh(d, 1) //2*D
+	x3.Sub(f, x3)                //F-2*D
 	x3.Mod(x3, BitCurve.P)
 
-	y3 := new(big.Int).Sub(d, x3)                  //D-X3
-	y3.Mul(e, y3)                                  //E*(D-X3)
-	y3.Sub(y3, new(big.Int).Mul(big.NewInt(8), c)) //E*(D-X3)-8*C
+	y3 := new(big.Int).Sub(d, x3)      //D-X3
+	y3.Mul(e, y3)                      //E*(D-X3)
+	y3.Sub(y3, new(big.Int).Lsh(c, 3)) //E*(D-X3)-8*C
 	y3.Mod(y3, BitCurve.P)
 
 	z3 := new(big.Int).Mul(y, z) //Y1*Z1
-	z3.Mul(big.NewInt(2), z3)    //3*Y1*Z1
+	z3.Lsh(z3, 1)                //3*Y1*Z1
 	z3.Mod(z3, BitCurve.P)
 
 	return x3, y3, z3

signer/fourbyte/validation.go

@@ -52,7 +52,7 @@ func (db *Database) ValidateTransaction(selector *string, tx *apitypes.SendTxArg
 		// e.g. https://github.com/ethereum/go-ethereum/issues/16106.
 		if len(data) == 0 {
 			// Prevent sending ether into black hole (show stopper)
-			if tx.Value.ToInt().Cmp(big.NewInt(0)) > 0 {
+			if tx.Value.ToInt().Sign() == 1 { // Greater than 0
 				return nil, errors.New("transaction will create a contract with value but empty code")
 			}
 			// No value submitted at least, critically Warn, but don't blow up