Update polkadot inflation to take into account auctions (#5872)

* Update polkadot inflation to take into account auctions

* a possible solution -- but needs a rather untrivial data seeding

* some additional comments

* Use LOWEST_PUBLIC_ID as a guide to filter out system/common good para ids

* Fixes

* move tests

* fix

Co-authored-by: Keith Yeung <kungfukeith11@gmail.com>
Co-authored-by: Shawn Tabrizi <shawntabrizi@gmail.com>

polkadot/runtime/common/src/impls.rs

@@ -18,6 +18,8 @@
 
 use crate::NegativeImbalance;
 use frame_support::traits::{Currency, Imbalance, OnUnbalanced};
+use primitives::v2::Balance;
+use sp_runtime::Perquintill;
 
 /// Logic for the author to get a portion of fees.
 pub struct ToAuthor<R>(sp_std::marker::PhantomData<R>);
@@ -57,6 +59,45 @@ where
 	}
 }
 
+pub fn era_payout(
+	total_staked: Balance,
+	non_gilt_issuance: Balance,
+	max_annual_inflation: Perquintill,
+	period_fraction: Perquintill,
+	auctioned_slots: u64,
+) -> (Balance, Balance) {
+	use pallet_staking_reward_fn::compute_inflation;
+	use sp_runtime::traits::Saturating;
+
+	let min_annual_inflation = Perquintill::from_rational(25u64, 1000u64);
+	let delta_annual_inflation = max_annual_inflation.saturating_sub(min_annual_inflation);
+
+	// 30% reserved for up to 60 slots.
+	let auction_proportion = Perquintill::from_rational(auctioned_slots.min(60), 200u64);
+
+	// Therefore the ideal amount at stake (as a percentage of total issuance) is 75% less the
+	// amount that we expect to be taken up with auctions.
+	let ideal_stake = Perquintill::from_percent(75).saturating_sub(auction_proportion);
+
+	let stake = Perquintill::from_rational(total_staked, non_gilt_issuance);
+	let falloff = Perquintill::from_percent(5);
+	let adjustment = compute_inflation(stake, ideal_stake, falloff);
+	let staking_inflation =
+		min_annual_inflation.saturating_add(delta_annual_inflation * adjustment);
+
+	let max_payout = period_fraction * max_annual_inflation * non_gilt_issuance;
+	let staking_payout = (period_fraction * staking_inflation) * non_gilt_issuance;
+	let rest = max_payout.saturating_sub(staking_payout);
+
+	let other_issuance = non_gilt_issuance.saturating_sub(total_staked);
+	if total_staked > other_issuance {
+		let _cap_rest = Perquintill::from_rational(other_issuance, total_staked) * staking_payout;
+		// We don't do anything with this, but if we wanted to, we could introduce a cap on the
+		// treasury amount with: `rest = rest.min(cap_rest);`
+	}
+	(staking_payout, rest)
+}
+
 #[cfg(test)]
 mod tests {
 	use super::*;
@@ -209,4 +250,44 @@ mod tests {
 			assert_eq!(Balances::free_balance(Treasury::account_id()), 8);
 		});
 	}
+
+	#[test]
+	fn compute_inflation_should_give_sensible_results() {
+		assert_eq!(
+			pallet_staking_reward_fn::compute_inflation(
+				Perquintill::from_percent(75),
+				Perquintill::from_percent(75),
+				Perquintill::from_percent(5),
+			),
+			Perquintill::one()
+		);
+		assert_eq!(
+			pallet_staking_reward_fn::compute_inflation(
+				Perquintill::from_percent(50),
+				Perquintill::from_percent(75),
+				Perquintill::from_percent(5),
+			),
+			Perquintill::from_rational(2u64, 3u64)
+		);
+		assert_eq!(
+			pallet_staking_reward_fn::compute_inflation(
+				Perquintill::from_percent(80),
+				Perquintill::from_percent(75),
+				Perquintill::from_percent(5),
+			),
+			Perquintill::from_rational(1u64, 2u64)
+		);
+	}
+
+	#[test]
+	fn era_payout_should_give_sensible_results() {
+		assert_eq!(
+			era_payout(75, 100, Perquintill::from_percent(10), Perquintill::one(), 0,),
+			(10, 0)
+		);
+		assert_eq!(
+			era_payout(80, 100, Perquintill::from_percent(10), Perquintill::one(), 0,),
+			(6, 4)
+		);
+	}
 }