Rename Palette to FRAME (#4182)

* palette -> frame

* PALETTE, Palette -> FRAME

* Move folder pallete -> frame

* Update docs/Structure.adoc

Co-Authored-By: Benjamin Kampmann <ben.kampmann@googlemail.com>

* Update docs/README.adoc

Co-Authored-By: Benjamin Kampmann <ben.kampmann@googlemail.com>

* Update README.adoc

substrate/frame/democracy/src/vote_threshold.rs

@@ -0,0 +1,102 @@
+// Copyright 2017-2019 Parity Technologies (UK) Ltd.
+// This file is part of Substrate.
+
+// Substrate is free software: you can redistribute it and/or modify
+// it under the terms of the GNU General Public License as published by
+// the Free Software Foundation, either version 3 of the License, or
+// (at your option) any later version.
+
+// Substrate is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+
+// You should have received a copy of the GNU General Public License
+// along with Substrate.  If not, see <http://www.gnu.org/licenses/>.
+
+//! Voting thresholds.
+
+#[cfg(feature = "std")]
+use serde::{Serialize, Deserialize};
+use codec::{Encode, Decode};
+use sr_primitives::traits::{Zero, IntegerSquareRoot};
+use rstd::ops::{Add, Mul, Div, Rem};
+
+/// A means of determining if a vote is past pass threshold.
+#[derive(Clone, Copy, PartialEq, Eq, Encode, Decode, sr_primitives::RuntimeDebug)]
+#[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 `approve` votes for and `against` votes against from a total electorate size of
+	/// `electorate` (`electorate - (approve + against)` are abstainers), then returns true if the
+	/// overall outcome is in favor of approval.
+	fn approved(&self, approve: Balance, against: Balance, voters: 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 {
+	/// Given `approve` votes for and `against` votes against from a total electorate size of
+	/// `electorate` of whom `voters` voted (`electorate - voters` are abstainers) then returns true if the
+	/// overall outcome is in favor of approval.
+	///
+	/// We assume each *voter* may cast more than one *vote*, hence `voters` is not necessarily equal to
+	/// `approve + against`.
+	fn approved(&self, approve: Balance, against: Balance, voters: Balance, electorate: Balance) -> bool {
+		let sqrt_voters = voters.integer_sqrt();
+		let sqrt_electorate = electorate.integer_sqrt();
+		if sqrt_voters.is_zero() { return false; }
+		match *self {
+			VoteThreshold::SuperMajorityApprove =>
+				compare_rationals(against, sqrt_voters, approve, sqrt_electorate),
+			VoteThreshold::SuperMajorityAgainst =>
+				compare_rationals(against, sqrt_electorate, approve, sqrt_voters),
+			VoteThreshold::SimpleMajority => approve > against,
+		}
+	}
+}
+
+#[cfg(test)]
+mod tests {
+	use super::*;
+
+	#[test]
+	fn should_work() {
+		assert_eq!(VoteThreshold::SuperMajorityApprove.approved(60, 50, 110, 210), false);
+		assert_eq!(VoteThreshold::SuperMajorityApprove.approved(100, 50, 150, 210), true);
+	}
+}