consensus/misc: reduce allocations and improve comments in CalcBaseFee (ethereum#24958)

* consensus/misc: reduce allocations in CalcBaseFee

* consensus/misc: add formulas of CalcBaseFee

Author: Jeiwan

consensus/misc/eip1559.go

@@ -58,36 +58,36 @@ func CalcBaseFee(config *params.ChainConfig, parent *types.Header) *big.Int {
 		return new(big.Int).SetUint64(params.InitialBaseFee)
 	}
 
-	var (
-		parentGasTarget          = parent.GasLimit / params.ElasticityMultiplier
-		parentGasTargetBig       = new(big.Int).SetUint64(parentGasTarget)
-		baseFeeChangeDenominator = new(big.Int).SetUint64(params.BaseFeeChangeDenominator)
-	)
+	parentGasTarget := parent.GasLimit / params.ElasticityMultiplier
 	// If the parent gasUsed is the same as the target, the baseFee remains unchanged.
 	if parent.GasUsed == parentGasTarget {
 		return new(big.Int).Set(parent.BaseFee)
 	}
+
+	var (
+		num   = new(big.Int)
+		denom = new(big.Int)
+	)
+
 	if parent.GasUsed > parentGasTarget {
 		// If the parent block used more gas than its target, the baseFee should increase.
-		gasUsedDelta := new(big.Int).SetUint64(parent.GasUsed - parentGasTarget)
-		x := new(big.Int).Mul(parent.BaseFee, gasUsedDelta)
-		y := x.Div(x, parentGasTargetBig)
-		baseFeeDelta := math.BigMax(
-			x.Div(y, baseFeeChangeDenominator),
-			common.Big1,
-		)
+		// max(1, parentBaseFee * gasUsedDelta / parentGasTarget / baseFeeChangeDenominator)
+		num.SetUint64(parent.GasUsed - parentGasTarget)
+		num.Mul(num, parent.BaseFee)
+		num.Div(num, denom.SetUint64(parentGasTarget))
+		num.Div(num, denom.SetUint64(params.BaseFeeChangeDenominator))
+		baseFeeDelta := math.BigMax(num, common.Big1)
 
-		return x.Add(parent.BaseFee, baseFeeDelta)
+		return num.Add(parent.BaseFee, baseFeeDelta)
 	} else {
 		// Otherwise if the parent block used less gas than its target, the baseFee should decrease.
-		gasUsedDelta := new(big.Int).SetUint64(parentGasTarget - parent.GasUsed)
-		x := new(big.Int).Mul(parent.BaseFee, gasUsedDelta)
-		y := x.Div(x, parentGasTargetBig)
-		baseFeeDelta := x.Div(y, baseFeeChangeDenominator)
+		// max(0, parentBaseFee * gasUsedDelta / parentGasTarget / baseFeeChangeDenominator)
+		num.SetUint64(parentGasTarget - parent.GasUsed)
+		num.Mul(num, parent.BaseFee)
+		num.Div(num, denom.SetUint64(parentGasTarget))
+		num.Div(num, denom.SetUint64(params.BaseFeeChangeDenominator))
+		baseFee := num.Sub(parent.BaseFee, num)
 
-		return math.BigMax(
-			x.Sub(parent.BaseFee, baseFeeDelta),
-			common.Big0,
-		)
+		return math.BigMax(baseFee, common.Big0)
 	}
 }