PhragMMS election. (#6685)

* Revamp npos-elections and implement phragmms

* Update primitives/npos-elections/src/phragmms.rs

* Fix build

* Some review grumbles

* Add some stuff for remote testing

* fix some of the grumbles.

* Add remote testing stuff.

* Cleanup

* fix docs

* Update primitives/arithmetic/src/rational.rs

Co-authored-by: Dan Forbes <dan@danforbes.dev>

* Small config change

* Better handling of approval_stake == 0

* Final touhces.

* Clean fuzzer a bit

* Clean fuzzer a bit

* Update primitives/npos-elections/src/balancing.rs

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

* Fix fuzzer.

* Better api for normalize

* Add noramlize_up

* A large number of small fixes.

* make it merge ready

* Fix warns

* bump

* Fix fuzzers a bit.

* Fix warns as well.

* Fix more tests.

Co-authored-by: Dan Forbes <dan@danforbes.dev>
Co-authored-by: Shawn Tabrizi <shawntabrizi@gmail.com>

substrate/primitives/npos-elections/fuzzer/src/common.rs

@@ -17,6 +17,14 @@
 
 //! Common fuzzing utils.
 
+// Each function will be used based on which fuzzer binary is being used.
+#![allow(dead_code)]
+
+use sp_npos_elections::{ElectionResult, VoteWeight, phragmms, seq_phragmen};
+use sp_std::collections::btree_map::BTreeMap;
+use sp_runtime::Perbill;
+use rand::{self, Rng, RngCore};
+
 /// 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
@@ -28,3 +36,78 @@ pub fn to_range(x: usize, a: usize, b: usize) -> usize {
 		collapsed + a
 	}
 }
+
+pub enum ElectionType {
+	Phragmen(Option<(usize, u128)>),
+	Phragmms(Option<(usize, u128)>)
+}
+
+pub type AccountId = u64;
+
+pub fn generate_random_npos_result(
+	voter_count: u64,
+	target_count: u64,
+	to_elect: usize,
+	mut rng: impl RngCore,
+	election_type: ElectionType,
+) -> (
+	ElectionResult<AccountId, Perbill>,
+	Vec<AccountId>,
+	Vec<(AccountId, VoteWeight, Vec<AccountId>)>,
+	BTreeMap<AccountId, VoteWeight>,
+) {
+	let prefix = 100_000;
+	// Note, it is important that stakes are always bigger than ed.
+	let base_stake: u64 = 1_000_000_000_000;
+	let ed: u64 = base_stake;
+
+	let mut candidates = Vec::with_capacity(target_count as usize);
+	let mut stake_of: BTreeMap<AccountId, VoteWeight> = BTreeMap::new();
+
+	(1..=target_count).for_each(|acc| {
+		candidates.push(acc);
+		let stake_var = rng.gen_range(ed, 100 * ed);
+		stake_of.insert(acc, base_stake + stake_var);
+	});
+
+	let mut voters = Vec::with_capacity(voter_count as usize);
+	(prefix ..= (prefix + voter_count)).for_each(|acc| {
+		let edge_per_this_voter = rng.gen_range(1, candidates.len());
+		// all possible targets
+		let mut all_targets = candidates.clone();
+		// we remove and pop into `targets` `edge_per_this_voter` times.
+		let targets = (0..edge_per_this_voter).map(|_| {
+			let upper = all_targets.len() - 1;
+			let idx = rng.gen_range(0, upper);
+			all_targets.remove(idx)
+		})
+		.collect::<Vec<AccountId>>();
+
+		let stake_var = rng.gen_range(ed, 100 * ed) ;
+		let stake = base_stake + stake_var;
+		stake_of.insert(acc, stake);
+		voters.push((acc, stake, targets));
+	});
+
+	(
+		match election_type {
+			ElectionType::Phragmen(conf) =>
+				seq_phragmen::<AccountId, sp_runtime::Perbill>(
+					to_elect,
+					candidates.clone(),
+					voters.clone(),
+					conf,
+				).unwrap(),
+			ElectionType::Phragmms(conf) =>
+				phragmms::<AccountId, sp_runtime::Perbill>(
+					to_elect,
+					candidates.clone(),
+					voters.clone(),
+					conf,
+				).unwrap(),
+		},
+		candidates,
+		voters,
+		stake_of,
+	)
+}