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() {

substrate/primitives/arithmetic/src/per_things.rs

@@ -25,6 +25,9 @@ use crate::traits::{
 };
 use sp_debug_derive::RuntimeDebug;
 
+/// Get the inner type of a `PerThing`.
+pub type InnerOf<P> = <P as PerThing>::Inner;
+
 /// Something that implements a fixed point ration with an arbitrary granularity `X`, as _parts per
 /// `X`_.
 pub trait PerThing:
@@ -312,8 +315,7 @@ macro_rules! implement_per_thing {
 		///
 		#[doc = $title]
 		#[cfg_attr(feature = "std", derive(Serialize, Deserialize))]
-		#[derive(Encode, Copy, Clone, Default, PartialEq, Eq, PartialOrd, Ord,
-				 RuntimeDebug, CompactAs)]
+		#[derive(Encode, Copy, Clone, PartialEq, Eq, PartialOrd, Ord, RuntimeDebug, CompactAs)]
 		pub struct $name($type);
 
 		impl PerThing for $name {
@@ -566,6 +568,12 @@ macro_rules! implement_per_thing {
 			}
 		}
 
+		impl Default for $name {
+			fn default() -> Self {
+				<Self as PerThing>::zero()
+			}
+		}
+
 		/// Non-overflow multiplication.
 		///
 		/// This is tailored to be used with a balance type.

substrate/primitives/phragmen/fuzzer/src/common.rs

@@ -19,8 +19,8 @@
 
 /// converts x into the range [a, b] in a pseudo-fair way.
 pub fn to_range(x: usize, a: usize, b: usize) -> usize {
-	// does not work correctly if b < 2*a
-	assert!(b > 2 * a);
+	// does not work correctly if b < 2 * a
+	assert!(b >= 2 * a);
 	let collapsed = x % b;
 	if collapsed >= a {
 		collapsed

substrate/primitives/phragmen/fuzzer/src/equalize.rs

@@ -131,7 +131,7 @@ fn main() {
 				return;
 			}
 
-			let enhance = is_score_better(initial_score, final_score);
+			let enhance = is_score_better(final_score, initial_score, Perbill::zero());
 
 			println!(
 				"iter = {} // {:?} -> {:?} [{}]",
@@ -140,6 +140,7 @@ fn main() {
 				final_score,
 				enhance,
 			);
+
 			// if more than one iteration has been done, or they must be equal.
 			assert!(enhance || initial_score == final_score || i == 0)
 		});

substrate/primitives/phragmen/src/lib.rs

@@ -36,7 +36,7 @@
 
 use sp_std::{prelude::*, collections::btree_map::BTreeMap, fmt::Debug, cmp::Ordering, convert::TryFrom};
 use sp_arithmetic::{
-	PerThing, Rational128,
+	PerThing, Rational128, ThresholdOrd,
 	helpers_128bit::multiply_by_rational,
 	traits::{Zero, Saturating, Bounded, SaturatedConversion},
 };
@@ -614,23 +614,36 @@ pub fn evaluate_support<AccountId>(
 	[min_support, sum, sum_squared]
 }
 
-/// Compares two sets of phragmen scores based on desirability and returns true if `that` is
-/// better than `this`.
+/// Compares two sets of phragmen scores based on desirability and returns true if `this` is
+/// better than `that`.
 ///
-/// Evaluation is done in a lexicographic manner.
+/// Evaluation is done in a lexicographic manner, and if each element of `this` is `that * epsilon`
+/// greater or less than `that`.
 ///
 /// Note that the third component should be minimized.
-pub fn is_score_better(this: PhragmenScore, that: PhragmenScore) -> bool {
-	match that
+pub fn is_score_better<P: PerThing>(this: PhragmenScore, that: PhragmenScore, epsilon: P) -> bool
+	where ExtendedBalance: From<sp_arithmetic::InnerOf<P>>
+{
+	match this
 		.iter()
 		.enumerate()
-		.map(|(i, e)| e.cmp(&this[i]))
-		.collect::<Vec<Ordering>>()
+		.map(|(i, e)| (
+			e.ge(&that[i]),
+			e.tcmp(&that[i], epsilon.mul_ceil(that[i])),
+		))
+		.collect::<Vec<(bool, Ordering)>>()
 		.as_slice()
 	{
-		[Ordering::Greater, _, _] => true,
-		[Ordering::Equal, Ordering::Greater, _] => true,
-		[Ordering::Equal, Ordering::Equal, Ordering::Less] => true,
+		// epsilon better in the score[0], accept.
+		[(_, Ordering::Greater), _, _] => true,
+
+		// less than epsilon better in score[0], but more than epsilon better in the second.
+		[(true, Ordering::Equal), (_, Ordering::Greater), _] => true,
+
+		// less than epsilon better in score[0, 1], but more than epsilon better in the third
+		[(true, Ordering::Equal), (true, Ordering::Equal), (_, Ordering::Less)] => true,
+
+		// anything else is not a good score.
 		_ => false,
 	}
 }

substrate/primitives/phragmen/src/reduce.rs

@@ -640,8 +640,8 @@ fn reduce_all<A: IdentifierT>(assignments: &mut Vec<StakedAssignment<A>>) -> u32
 	num_changed
 }
 
-/// Reduce the given [`Vec<StakedAssignment<IdentifierT>>`]. This removes redundant edges from without changing the
-/// overall backing of any of the elected candidates.
+/// Reduce the given [`Vec<StakedAssignment<IdentifierT>>`]. This removes redundant edges from
+/// without changing the overall backing of any of the elected candidates.
 ///
 /// Returns the number of edges removed.
 ///

substrate/primitives/phragmen/src/tests.rs

@@ -616,28 +616,153 @@ fn assignment_convert_works() {
 }
 
 #[test]
-fn score_comparison_is_lexicographical() {
+fn score_comparison_is_lexicographical_no_epsilon() {
+	let epsilon = Perbill::zero();
 	// only better in the fist parameter, worse in the other two ✅
 	assert_eq!(
-		is_score_better([10, 20, 30], [12, 10, 35]),
+		is_score_better([12, 10, 35], [10, 20, 30], epsilon),
 		true,
 	);
 
 	// worse in the first, better in the other two ❌
 	assert_eq!(
-		is_score_better([10, 20, 30], [9, 30, 10]),
+		is_score_better([9, 30, 10], [10, 20, 30], epsilon),
 		false,
 	);
 
 	// equal in the first, the second one dictates.
 	assert_eq!(
-		is_score_better([10, 20, 30], [10, 25, 40]),
+		is_score_better([10, 25, 40], [10, 20, 30], epsilon),
 		true,
 	);
 
 	// equal in the first two, the last one dictates.
 	assert_eq!(
-		is_score_better([10, 20, 30], [10, 20, 40]),
+		is_score_better([10, 20, 40], [10, 20, 30], epsilon),
+		false,
+	);
+}
+
+#[test]
+fn score_comparison_with_epsilon() {
+	let epsilon = Perbill::from_percent(1);
+
+	{
+		// no more than 1 percent (10) better in the first param.
+		assert_eq!(
+			is_score_better([1009, 5000, 100000], [1000, 5000, 100000], epsilon),
+			false,
+		);
+
+		// now equal, still not better.
+		assert_eq!(
+			is_score_better([1010, 5000, 100000], [1000, 5000, 100000], epsilon),
+			false,
+		);
+
+		// now it is.
+		assert_eq!(
+			is_score_better([1011, 5000, 100000], [1000, 5000, 100000], epsilon),
+			true,
+		);
+	}
+
+	{
+		// First score score is epsilon better, but first score is no longer `ge`. Then this is
+		// still not a good solution.
+		assert_eq!(
+			is_score_better([999, 6000, 100000], [1000, 5000, 100000], epsilon),
+			false,
+		);
+	}
+
+	{
+		// first score is equal or better, but not epsilon. Then second one is the determinant.
+		assert_eq!(
+			is_score_better([1005, 5000, 100000], [1000, 5000, 100000], epsilon),
+			false,
+		);
+
+		assert_eq!(
+			is_score_better([1005, 5050, 100000], [1000, 5000, 100000], epsilon),
+			false,
+		);
+
+		assert_eq!(
+			is_score_better([1005, 5051, 100000], [1000, 5000, 100000], epsilon),
+			true,
+		);
+	}
+
+	{
+		// first score and second are equal or less than epsilon more, third is determinant.
+		assert_eq!(
+			is_score_better([1005, 5025, 100000], [1000, 5000, 100000], epsilon),
+			false,
+		);
+
+		assert_eq!(
+			is_score_better([1005, 5025, 99_000], [1000, 5000, 100000], epsilon),
+			false,
+		);
+
+		assert_eq!(
+			is_score_better([1005, 5025, 98_999], [1000, 5000, 100000], epsilon),
+			true,
+		);
+	}
+}
+
+#[test]
+fn score_comparison_large_value() {
+	// some random value taken from eras in kusama.
+	let initial = [12488167277027543u128, 5559266368032409496, 118749283262079244270992278287436446];
+	// this claim is 0.04090% better in the third component. It should be accepted as better if
+	// epsilon is smaller than 5/10_0000
+	let claim = [12488167277027543u128, 5559266368032409496, 118700736389524721358337889258988054];
+
+	assert_eq!(
+		is_score_better(
+			claim.clone(),
+			initial.clone(),
+			Perbill::from_rational_approximation(1u32, 10_000),
+		),
+		true,
+	);
+
+	assert_eq!(
+		is_score_better(
+			claim.clone(),
+			initial.clone(),
+			Perbill::from_rational_approximation(2u32, 10_000),
+		),
+		true,
+	);
+
+	assert_eq!(
+		is_score_better(
+			claim.clone(),
+			initial.clone(),
+			Perbill::from_rational_approximation(3u32, 10_000),
+		),
+		true,
+	);
+
+	assert_eq!(
+		is_score_better(
+			claim.clone(),
+			initial.clone(),
+			Perbill::from_rational_approximation(4u32, 10_000),
+		),
+		true,
+	);
+
+	assert_eq!(
+		is_score_better(
+			claim.clone(),
+			initial.clone(),
+			Perbill::from_rational_approximation(5u32, 10_000),
+		),
 		false,
 	);
 }