Enhance producer pay calculation by implementing a detailed multiplier system for active and standby producers. The new logic uses an arithmetic sequence to determine share values based on the number of active producers, improving accuracy in reward distribution.

Author: aamirpashaa

contracts/eosio.system/src/producer_pay.cpp

@@ -351,11 +351,27 @@ namespace eosiosystem {
                 break;
         }
 
-        // if we don't have standbys (21 active or less), don't attempt to calculate for standbys, just do total activecount X 2
-        // if we have standbys, do 42 shares for the top 21 plus 1 share per standby, so 42 plus the total activecount minus 21
-        uint32_t sharecount = activecount <= 21 ? (activecount * 2) : (42 + (activecount - 21));
-
-        auto shareValue = (_gstate.perblock_bucket / sharecount);
+        // the multiplier is applied to the shares, and the shares are then multiplied by the share value
+        // the share value is the total amount of the perblock bucket divided by the sum of the multipliers
+        // the sum of the multipliers is the sum of the multipliers for the active producers and the standby producers
+        // The multipliers for the active producers are 1.2, 1.18, ... , 0.82, 0.8 each multiplied by 2, and for the standby producers are 1.2, 1.18, ... , 0.82, 0.8 each multiplied by 1
+        // The multipliers forms a arithmetic sequence with a common difference of -0.02
+        // The sum of arithmetic sequence is given by n/2 * (2 * first term + (n-1) * common difference)
+        // If activecount <= 21, then the sum of the multipliers is given by (activecount)/2 * (2 * 1.2 + (activecount-1) * -0.02) * 2
+        // If activecount > 21, then the sum of the multipliers is given by 42 + ((activecount-21)/2) * (2 * 1.2 + (activecount-22) * -0.02)
+        // 42 is the sum of the multipliers for the first 21 active producers
+        // The sum_of_multipliers are as follows:
+        // activecount = 1: 2.4
+        // activecount = 2: 4.8
+        // activecount = 3: 7.2
+        // ...
+        // activecount = 21: 42
+        // activecount = 22: 43.2
+        // ...
+        // activecount = 42: 63
+        double sum_of_multipliers = activecount <= 21 ? (((activecount)/2)*(2*1.2-(activecount-1)*0.02) * 2) : (42 + ((activecount-21)/2)*(2*1.2-(activecount-22)*0.02));
+
+        auto shareValue = (_gstate.perblock_bucket / sum_of_multipliers);
         int32_t index = 0;
 
         for (const auto &prod : sortedprods) {