Impleent new pricing model

Author: MishkaRogachev

arbos/constraints/model.go

@@ -0,0 +1,55 @@
+// Copyright 2025, Offchain Labs, Inc.
+// For license information, see https://github.com/OffchainLabs/nitro/blob/master/LICENSE.md
+
+// The constraints package tracks the multi-dimensional gas usage to apply constraint-based pricing.
+package constraints
+
+import (
+	"math"
+	"math/big"
+
+	"github.com/offchainlabs/nitro/util/arbmath"
+)
+
+const (
+	PricingInertiaFactor = 30
+)
+
+type PricingState struct {
+	constraints ResourceConstraints
+}
+
+// UpdatePricingModel adjusts the basefee according to simplified constraint-based pricing.
+// Formula: basefee = F_min * exp( max_i ( B_i / (30 * T_i * sqrt(Δ_i)) ) )
+func (ps *PricingState) UpdatePricingModel(minBaseFee *big.Int, timePassed uint64) *big.Int {
+	var maxExponentBips arbmath.Bips
+
+	for c := range ps.constraints.All() {
+		// Decay per-constraint backlog by T_i * timePassed
+		c.RemoveFromBacklog(timePassed)
+
+		if c.Backlog == 0 || c.TargetPerSec == 0 || c.Period == 0 {
+			continue
+		}
+
+		// Compute inertia = 30 * sqrt(Δ_i)
+		inertia := PricingInertiaFactor * uint64(math.Floor(math.Sqrt(float64(c.Period))))
+
+		// Compute denominator = inertia * T_i
+		denominator := arbmath.SaturatingUMul(inertia, c.TargetPerSec)
+
+		// Normalized backlog = B_i / (inertia * T_i)
+		expBips := arbmath.NaturalToBips(arbmath.SaturatingCast[int64](c.Backlog)) / arbmath.SaturatingCast[arbmath.Bips](denominator)
+
+		// Pick the maximum exponent across all constraints
+		if expBips > maxExponentBips {
+			maxExponentBips = expBips
+		}
+	}
+
+	// Apply the maximum exponent
+	if maxExponentBips == 0 {
+		return new(big.Int).Set(minBaseFee)
+	}
+	return arbmath.BigMulByBips(minBaseFee, arbmath.ApproxExpBasisPoints(maxExponentBips, 4))
+}

arbos/constraints/model_test.go

@@ -0,0 +1,127 @@
+// Copyright 2025, Offchain Labs, Inc.
+// For license information, see https://github.com/OffchainLabs/nitro/blob/master/LICENSE.md
+
+package constraints
+
+import (
+	"math/big"
+	"testing"
+
+	"github.com/stretchr/testify/require"
+
+	"github.com/ethereum/go-ethereum/arbitrum/multigas"
+
+	"github.com/offchainlabs/nitro/arbos/burn"
+	"github.com/offchainlabs/nitro/arbos/l2pricing"
+	"github.com/offchainlabs/nitro/arbos/storage"
+)
+
+func TestConstraintsModelTwoResources(t *testing.T) {
+	// Params: target = 5M/sec, Δ = 10s
+	var target uint64 = 5_000_000
+	const periodSecs = PeriodSecs(10)
+	const iterations = 30
+
+	// Setup new constraint-based pricing model with 2 resources
+	constraints := NewResourceConstraints()
+	resources := EmptyResourceSet().
+		WithResources(
+			multigas.ResourceKindComputation,
+			multigas.ResourceKindStorageAccess,
+		)
+	constraints.Set(resources, periodSecs, target)
+
+	model := PricingState{constraints: *constraints}
+
+	// Base fee floor
+	baseFee := big.NewInt(100_000_000)
+
+	// Phase 1: exceed target to force fee increase
+	for i := 0; i < iterations; i++ {
+		mg := multigas.MultiGasFromPairs(
+			multigas.Pair{Kind: multigas.ResourceKindComputation, Amount: 5},
+			multigas.Pair{Kind: multigas.ResourceKindStorageAccess, Amount: 2},
+		)
+		model.constraints.Get(resources, periodSecs).AddToBacklog(mg)
+
+		newFee := model.UpdatePricingModel(baseFee, 1)
+
+		// Fee should never fall below baseFee during surge
+		require.GreaterOrEqualf(t, newFee.Cmp(baseFee), 0,
+			"fee dropped below base fee at iter %d", i)
+	}
+
+	// Phase 2: no usage, backlog drains and fee should decay back
+	for i := 0; i < iterations*2; i++ {
+		newFee := model.UpdatePricingModel(baseFee, 1)
+
+		// Fee must eventually reach the floor
+		if i == iterations*2-1 {
+			require.Equal(t, 0, newFee.Cmp(baseFee),
+				"fee should decay back to base fee")
+		}
+	}
+}
+
+func TestConstraintsModelVersusLegacy(t *testing.T) {
+	// Test parameters
+	var gasUsedPerSecond int64 = 8_000_000 // >7M target to accumulate backlog
+	var iterations int = 50
+	var periodSecs = PeriodSecs(12)
+
+	// Initialize L2PricingState with legacy pricing model
+	burner := burn.NewSystemBurner(nil, false)
+	storage := storage.NewMemoryBacked(burner)
+	require.NoError(t, l2pricing.InitializeL2PricingState(storage))
+	l2PricingState := l2pricing.OpenL2PricingState(storage)
+
+	// Match new model
+	_ = l2PricingState.SetBacklogTolerance(0) // no tolerance
+	require.NoError(t, l2PricingState.SetSpeedLimitPerSecond(l2pricing.InitialSpeedLimitPerSecondV6))
+
+	// Setup constraint-based pricing model with a single gas constraint
+	constraints := NewResourceConstraints()
+	resources := EmptyResourceSet().
+		WithResources(
+			multigas.ResourceKindComputation,
+			multigas.ResourceKindStorageAccess,
+			multigas.ResourceKindStorageGrowth,
+			multigas.ResourceKindHistoryGrowth,
+			multigas.ResourceKindWasmComputation,
+		)
+	constraints.Set(resources, periodSecs, l2pricing.InitialSpeedLimitPerSecondV6)
+	model := PricingState{
+		constraints: *constraints,
+	}
+
+	minBaseFee, _ := l2PricingState.MinBaseFeeWei()
+
+	for i := 1; i < iterations+1; i++ {
+		// L2PricingState model update
+		baseFeeLegacy, _ := l2PricingState.BaseFeeWei()
+		burner.Restrict(l2PricingState.AddToGasPool(-gasUsedPerSecond)) // negative = gas consumed
+		l2PricingState.UpdatePricingModel(baseFeeLegacy, 1, false)
+		legacyFee, _ := l2PricingState.BaseFeeWei()
+
+		// Constraint-based model update
+		// #nosec G115 -- gasUsedPerSecond is a fixed positive constant for testing
+		mg := multigas.ComputationGas(uint64(gasUsedPerSecond))
+		model.constraints.Get(resources, periodSecs).AddToBacklog(mg)
+		newFee := model.UpdatePricingModel(minBaseFee, 1)
+
+		// Expect new fee to be slightly lower (slower growth) than legacy,
+		// within about 7% after 50 iterations due to inertia differences.
+		diff := new(big.Float).Quo(
+			new(big.Float).SetInt(legacyFee),
+			new(big.Float).SetInt(newFee),
+		)
+		val, _ := diff.Float64()
+
+		require.InEpsilonf(t, 1.0, val, 0.015, // within 1.5% tolerance
+			"fees differ too much at iteration %d: legacy=%s new=%s",
+			i, legacyFee.String(), newFee.String())
+
+		// Uncomment for debug output
+		//	fmt.Printf("%-4d %-15s %-15s %-10.4f\n", i, legacyFee.String(), newFee.String(), val)
+	}
+}