Define integer sqrt for reward quotient (#2)

runtime/src/utils.rs

@@ -14,19 +14,8 @@
 // You should have received a copy of the GNU General Public License
 // along with Substrate.  If not, see <http://www.gnu.org/licenses/>.
 
-use primitives::H256;
-use runtime_primitives::traits::{DigestItem as DigestItemT};
 use rstd::prelude::*;
 
-#[derive(Clone, PartialEq, Eq)]
-#[cfg_attr(feature = "std", derive(Debug, Serialize, Deserialize))]
-pub enum Never { }
-
-impl DigestItemT for Never {
-	type Hash = H256;
-	type AuthorityId = Never;
-}
-
 pub fn split(list: Vec<usize>, n: usize) -> Vec<Vec<usize>> {
 	let mut ret = Vec::new();
 	for i in 0..n {
@@ -36,3 +25,13 @@ pub fn split(list: Vec<usize>, n: usize) -> Vec<Vec<usize>> {
 	}
 	ret
 }
+
+pub fn sqrt(n: u128) -> u128 {
+	let mut x = n;
+	let mut y = (x + 1) / 2;
+	while y < x {
+		x = y;
+		y = (x + n / x) / 2;
+	}
+	x
+}

runtime/src/validation.rs

@@ -22,6 +22,7 @@ use rstd::collections::btree_map::BTreeMap;
 use state::{ActiveState, CrystallizedState, BlockVoteInfo, CrosslinkRecord};
 use attestation::AttestationRecord;
 use consts::{CYCLE_LENGTH, WEI_PER_ETH, BASE_REWARD_QUOTIENT, SQRT_E_DROP_TIME, SLOT_DURATION, MIN_DYNASTY_LENGTH, SHARD_COUNT};
+use utils::sqrt;
 use ::ShardId;
 
 pub fn validate_block_pre_processing_conditions() { }
@@ -169,7 +170,7 @@ pub fn calculate_ffg_rewards<BlockHashesBySlot: StorageMap<u64, H256, Query=Opti
 	let total_deposits = crystallized_state.total_deposits();
 	let total_deposits_in_eth = total_deposits / WEI_PER_ETH;
 
-	let reward_quotient = BASE_REWARD_QUOTIENT * total_deposits_in_eth / 2;
+	let reward_quotient = BASE_REWARD_QUOTIENT * sqrt(total_deposits_in_eth);
 	let quadratic_penalty_quotient = (SQRT_E_DROP_TIME / SLOT_DURATION).pow(2);
 
 	let last_state_recalc = crystallized_state.last_state_recalc;