feat: make inflation follow a polynomial distribution

proto/nibiru/inflation/v1/genesis.proto

@@ -23,14 +23,20 @@ message Params {
   // inflation_enabled is the parameter that enables inflation and halts
   // increasing the skipped_epochs
   bool inflation_enabled = 1;
-  // exponential_calculation takes in the variables to calculate exponential
+  // polynomial_factors takes in the variables to calculate polynomial
   // inflation
-  ExponentialCalculation exponential_calculation = 2
-      [ (gogoproto.nullable) = false ];
+  repeated string polynomial_factors = 2[
+    (gogoproto.customtype) = "github.com/cosmos/cosmos-sdk/types.Dec",
+    (gogoproto.nullable) = false
+  ];
   // inflation_distribution of the minted denom
   InflationDistribution inflation_distribution = 3
       [ (gogoproto.nullable) = false ];
   // epochs_per_period is the number of epochs that must pass before a new
   // period is created
   uint64 epochs_per_period = 4;
+
+  // max_period is the maximum number of periods that have inflation being 
+  // paid off. After this period, inflation will be disabled.
+  uint64 max_period = 5;
 }

proto/nibiru/inflation/v1/inflation.proto

@@ -28,25 +28,3 @@ message InflationDistribution {
     (gogoproto.nullable) = false
   ];
 }
-
-// ExponentialCalculation holds factors to calculate exponential inflation on
-// each period. Calculation reference:
-// periodProvision = exponentialDecay
-// f(x)            = a * (1 - r) ^ x + c
-message ExponentialCalculation {
-  // a defines the initial value
-  string a = 1 [
-    (gogoproto.customtype) = "github.com/cosmos/cosmos-sdk/types.Dec",
-    (gogoproto.nullable) = false
-  ];
-  // r defines the reduction factor
-  string r = 2 [
-    (gogoproto.customtype) = "github.com/cosmos/cosmos-sdk/types.Dec",
-    (gogoproto.nullable) = false
-  ];
-  // c defines the parameter for long term inflation
-  string c = 3 [
-    (gogoproto.customtype) = "github.com/cosmos/cosmos-sdk/types.Dec",
-    (gogoproto.nullable) = false
-  ];
-}

x/inflation/keeper/inflation.go

@@ -28,7 +28,7 @@ func (k Keeper) MintAndAllocateInflation(
 	}
 
 	// Allocate minted coins according to allocation proportions (staking, strategic, community pool)
-	return k.AllocateExponentialInflation(ctx, coins, params)
+	return k.AllocatePolynomialInflation(ctx, coins, params)
 }
 
 // MintCoins implements an alias call to the underlying supply keeper's
@@ -38,12 +38,12 @@ func (k Keeper) MintCoins(ctx sdk.Context, coin sdk.Coin) error {
 	return k.bankKeeper.MintCoins(ctx, types.ModuleName, coins)
 }
 
-// AllocateExponentialInflation allocates coins from the inflation to external
+// AllocatePolynomialInflation allocates coins from the inflation to external
 // modules according to allocation proportions:
 //   - staking rewards -> sdk `auth` module fee collector
 //   - strategic reserves -> root account of x/sudo module
 //   - community pool -> `sdk `distr` module community pool
-func (k Keeper) AllocateExponentialInflation(
+func (k Keeper) AllocatePolynomialInflation(
 	ctx sdk.Context,
 	mintedCoin sdk.Coin,
 	params types.Params,

x/inflation/keeper/inflation_test.go

@@ -129,10 +129,10 @@ func TestGetCirculatingSupplyAndInflationRate(t *testing.T) {
 			sdk.TokensFromConsensusPower(400_000_000, sdk.DefaultPowerReduction),
 			func(nibiruApp *app.NibiruApp, ctx sdk.Context) {
 				nibiruApp.InflationKeeper.SetParams(ctx, types.Params{
-					EpochsPerPeriod:        0,
-					InflationEnabled:       true,
-					ExponentialCalculation: types.DefaultExponentialCalculation,
-					InflationDistribution:  types.DefaultInflationDistribution,
+					EpochsPerPeriod:       0,
+					InflationEnabled:      true,
+					PolynomialFactors:     types.DefaultPolynomialFactors,
+					InflationDistribution: types.DefaultInflationDistribution,
 				})
 			},
 			sdk.ZeroDec(),
@@ -177,7 +177,7 @@ func TestGetters(t *testing.T) {
 	nibiruApp, ctx := testapp.NewNibiruTestAppAndContext()
 	k := nibiruApp.InflationKeeper
 	require.NotPanics(t, func() {
-		_ = k.ExponentialCalculation(ctx)
+		_ = k.PolynomialFactors(ctx)
 		_ = k.InflationDistribution(ctx)
 		_ = k.InflationEnabled(ctx)
 		_ = k.EpochsPerPeriod(ctx)

x/inflation/keeper/params.go

@@ -18,8 +18,8 @@ func (k Keeper) SetParams(ctx sdk.Context, params types.Params) {
 }
 
 // VotePeriod returns the number of blocks during which voting takes place.
-func (k Keeper) ExponentialCalculation(ctx sdk.Context) (res types.ExponentialCalculation) {
-	k.paramSpace.Get(ctx, types.KeyExponentialCalculation, &res)
+func (k Keeper) PolynomialFactors(ctx sdk.Context) (res []sdk.Dec) {
+	k.paramSpace.Get(ctx, types.KeyPolynomialFactors, &res)
 	return
 }