[pallet_broker] Fix adapt_price behaviour at zero

prdoc/pr_3636.prdoc

@@ -0,0 +1,15 @@
+# Schema: Polkadot SDK PRDoc Schema (prdoc) v1.0.0
+# See doc at https://raw.githubusercontent.com/paritytech/polkadot-sdk/master/prdoc/schema_user.json
+
+title: "[pallet_broker] Fix `adapt_price` behaviour at zero"
+
+doc:
+  - audience: Runtime Dev
+    description: |
+      This fixes the behaviour of `Linear` which is the default implementation of the `AdaptPrice`
+      trait in the broker pallet. Previously if cores were offered but not sold in only one sale,
+      the price would be set to zero and due to the logic being purely multiplicative, the price
+      would stay at 0 indefinitely.
+
+crates:
+  - name: pallet-broker

substrate/frame/broker/src/adapt_price.rs

@@ -19,6 +19,7 @@
 
 use crate::CoreIndex;
 use sp_arithmetic::{traits::One, FixedU64};
+use sp_runtime::Saturating;
 
 /// Type for determining how to set price.
 pub trait AdaptPrice {
@@ -49,14 +50,24 @@ impl AdaptPrice for () {
 pub struct Linear;
 impl AdaptPrice for Linear {
 	fn leadin_factor_at(when: FixedU64) -> FixedU64 {
-		FixedU64::from(2) - when
+		FixedU64::from(2).saturating_sub(when)
 	}
 	fn adapt_price(sold: CoreIndex, target: CoreIndex, limit: CoreIndex) -> FixedU64 {
 		if sold <= target {
-			FixedU64::from_rational(sold.into(), target.into())
+			// Range of [0.5, 1.0].
+			FixedU64::from_rational(1, 2).saturating_add(FixedU64::from_rational(
+				(sold).into(),
+				(target.saturating_mul(2)).into(),
+			))
 		} else {
-			FixedU64::one() +
-				FixedU64::from_rational((sold - target).into(), (limit - target).into())
+			// Range of (1.0, 2].
+
+			// Unchecked math: In this branch we know that sold < target. The limit must be >= sold
+			// by construction, and thus target must be > limit.
+			FixedU64::one().saturating_add(FixedU64::from_rational(
+				(sold - target).into(),
+				(limit - target).into(),
+			))
 		}
 	}
 }