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// This file is part of Substrate.
// Copyright (C) 2017-2022 Parity Technologies (UK) Ltd.
// SPDX-License-Identifier: Apache-2.0
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//! Voting thresholds.
use crate::Tally;
use codec::{Decode, Encode};
use scale_info::TypeInfo;
#[cfg(feature = "std")]
use serde::{Deserialize, Serialize};
use sp_runtime::traits::{IntegerSquareRoot, Zero};
use sp_std::ops::{Add, Div, Mul, Rem};
/// A means of determining if a vote is past pass threshold.
#[derive(Clone, Copy, PartialEq, Eq, Encode, Decode, sp_runtime::RuntimeDebug, TypeInfo)]
#[cfg_attr(feature = "std", derive(Serialize, Deserialize))]
pub enum VoteThreshold {
/// A supermajority of approvals is needed to pass this vote.
SuperMajorityApprove,
/// A supermajority of rejects is needed to fail this vote.
SuperMajorityAgainst,
/// A simple majority of approvals is needed to pass this vote.
SimpleMajority,
}
pub trait Approved<Balance> {
/// Given a `tally` of votes and a total size of `electorate`, this returns `true` if the
/// overall outcome is in favor of approval according to `self`'s threshold method.
fn approved(&self, tally: Tally<Balance>, electorate: Balance) -> bool;
}
/// Return `true` iff `n1 / d1 < n2 / d2`. `d1` and `d2` may not be zero.
fn compare_rationals<
T: Zero + Mul<T, Output = T> + Div<T, Output = T> + Rem<T, Output = T> + Ord + Copy,
>(
mut n1: T,
mut d1: T,
mut n2: T,
mut d2: T,
) -> bool {
// Uses a continued fractional representation for a non-overflowing compare.
// Detailed at https://janmr.com/blog/2014/05/comparing-rational-numbers-without-overflow/.
loop {
let q1 = n1 / d1;
let q2 = n2 / d2;
if q1 < q2 {
return true
}
if q2 < q1 {
return false
}
let r1 = n1 % d1;
let r2 = n2 % d2;
if r2.is_zero() {
return false
}
if r1.is_zero() {
return true
}
n1 = d2;
n2 = d1;
d1 = r2;
d2 = r1;
}
}
impl<
Balance: IntegerSquareRoot
+ Zero
+ Ord
+ Add<Balance, Output = Balance>
+ Mul<Balance, Output = Balance>
+ Div<Balance, Output = Balance>
+ Rem<Balance, Output = Balance>
+ Copy,
> Approved<Balance> for VoteThreshold
{
fn approved(&self, tally: Tally<Balance>, electorate: Balance) -> bool {
let sqrt_voters = tally.turnout.integer_sqrt();
let sqrt_electorate = electorate.integer_sqrt();
if sqrt_voters.is_zero() {
return false
}
match *self {
VoteThreshold::SuperMajorityApprove =>
compare_rationals(tally.nays, sqrt_voters, tally.ayes, sqrt_electorate),
VoteThreshold::SuperMajorityAgainst =>
compare_rationals(tally.nays, sqrt_electorate, tally.ayes, sqrt_voters),
VoteThreshold::SimpleMajority => tally.ayes > tally.nays,
}
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn should_work() {
assert!(!VoteThreshold::SuperMajorityApprove
.approved(Tally { ayes: 60, nays: 50, turnout: 110 }, 210));
assert!(VoteThreshold::SuperMajorityApprove
.approved(Tally { ayes: 100, nays: 50, turnout: 150 }, 210));
}
}