Accept new Phragmén solutions if they are epsilon better + Better pre-inclusion checks. (#6173)

* part1: Accept inly epsilon better solutions

* Fix pre-dispatch check

* Fix build

* review grumbles

* Epsilon -> Threshold

substrate/primitives/arithmetic/src/lib.rs

@@ -41,12 +41,89 @@ mod fixed;
 mod rational128;
 
 pub use fixed::{FixedPointNumber, Fixed64, Fixed128, FixedPointOperand};
-pub use per_things::{PerThing, Percent, PerU16, Permill, Perbill, Perquintill};
+pub use per_things::{PerThing, InnerOf, Percent, PerU16, Permill, Perbill, Perquintill};
 pub use rational128::Rational128;
 
+use sp_std::cmp::Ordering;
+
+/// Trait for comparing two numbers with an threshold.
+///
+/// Returns:
+/// - `Ordering::Greater` if `self` is greater than `other + threshold`.
+/// - `Ordering::Less` if `self` is less than `other - threshold`.
+/// - `Ordering::Equal` otherwise.
+pub trait ThresholdOrd<T> {
+	/// Compare if `self` is `threshold` greater or less than `other`.
+	fn tcmp(&self, other: &T, epsilon: T) -> Ordering;
+}
+
+impl<T> ThresholdOrd<T> for T
+where
+	T: Ord + PartialOrd + Copy + Clone + traits::Zero + traits::Saturating,
+{
+	fn tcmp(&self, other: &T, threshold: T) -> Ordering {
+		// early exit.
+		if threshold.is_zero() {
+			return self.cmp(&other)
+		}
+
+		let upper_bound = other.saturating_add(threshold);
+		let lower_bound = other.saturating_sub(threshold);
+
+		if upper_bound <= lower_bound {
+			// defensive only. Can never happen.
+			self.cmp(&other)
+		} else {
+			// upper_bound is guaranteed now to be bigger than lower.
+			match (self.cmp(&lower_bound), self.cmp(&upper_bound)) {
+				(Ordering::Greater, Ordering::Greater) => Ordering::Greater,
+				(Ordering::Less, Ordering::Less) => Ordering::Less,
+				_ => Ordering::Equal,
+			}
+		}
+
+	}
+}
+
 #[cfg(test)]
 mod tests {
 	use super::*;
+	use sp_std::cmp::Ordering;
+
+	#[test]
+	fn epsilon_ord_works() {
+		let b = 115u32;
+		let e = Perbill::from_percent(10).mul_ceil(b);
+
+		// [115 - 11,5 (103,5), 115 + 11,5 (126,5)] is all equal
+		assert_eq!(103u32.tcmp(&b, e), Ordering::Equal);
+		assert_eq!(104u32.tcmp(&b, e), Ordering::Equal);
+		assert_eq!(115u32.tcmp(&b, e), Ordering::Equal);
+		assert_eq!(120u32.tcmp(&b, e), Ordering::Equal);
+		assert_eq!(126u32.tcmp(&b, e), Ordering::Equal);
+		assert_eq!(127u32.tcmp(&b, e), Ordering::Equal);
+
+		assert_eq!(128u32.tcmp(&b, e), Ordering::Greater);
+		assert_eq!(102u32.tcmp(&b, e), Ordering::Less);
+	}
+
+	#[test]
+	fn epsilon_ord_works_with_small_epc() {
+		let b = 115u32;
+		// way less than 1 percent. threshold will be zero. Result should be same as normal ord.
+		let e = Perbill::from_parts(100) * b;
+
+		// [115 - 11,5 (103,5), 115 + 11,5 (126,5)] is all equal
+		assert_eq!(103u32.tcmp(&b, e), 103u32.cmp(&b));
+		assert_eq!(104u32.tcmp(&b, e), 104u32.cmp(&b));
+		assert_eq!(115u32.tcmp(&b, e), 115u32.cmp(&b));
+		assert_eq!(120u32.tcmp(&b, e), 120u32.cmp(&b));
+		assert_eq!(126u32.tcmp(&b, e), 126u32.cmp(&b));
+		assert_eq!(127u32.tcmp(&b, e), 127u32.cmp(&b));
+
+		assert_eq!(128u32.tcmp(&b, e), 128u32.cmp(&b));
+		assert_eq!(102u32.tcmp(&b, e), 102u32.cmp(&b));
+	}
 
 	#[test]
 	fn peru16_rational_does_not_overflow() {