update target rewards calculations

tips/TIP-0040/tip-0040.md

@@ -564,17 +564,11 @@ The following section specifies how to convert the slot-level data into epoch-le
 
 #### Parameters needed for calculations:
 
-- `Bootstrapping Duration` = 1154 (approximately 3 years)
-- `Mana Share Coefficient` = 2 (relative to the term $\theta/(1-\theta)$ from the _IOTA 2.0 Incentives and Tokenomics
-  Whitepaper_, with $\theta = 2/3$)
-- `Final Reward = (Total Supply * Mana Share Coefficient * Generation Rate) >> (Generation Rate Exponent - Slots Per Epoch Exponent)`.
+- `Bootstrapping Duration` = 1154 epochs (approximately 3 years)
+- `Reward To Generation Ratio` = 2 (the ratio of final target rewards rate to Mana generation rate)
+- `Final Target Rewards Rate = (Total Supply * Reward To Generation Ratio * Generation Rate) >> (Generation Rate Exponent - Slots Per Epoch Exponent)`.
   - This is the constant reward per epoch after the bootstrapping phase.
-- `Decay Balancing Constant` is an integer approximation of $2^{\text{Decay Balancing Constant Coefficient}}\frac{e
-  \Delta}{T(1-\exp{(-\beta \Delta)})}$, for $Delta =$ epoch duration in years, $T=$ `Bootstrapping Duration`, and
-  $\beta=1/3$.
-  - This is the parameter to calculate the reward per epoch in the bootstrapping phase.
-- For `Decay Balancing Constant Coefficient = 8`, `Decay Balancing Constant = 696`.
-- `Initial Reward = (Final Reward * Decay Balancing Constant) >> Decay Balancing Constant Coefficient`.
+- `Initial Target Rewards Rate = Final Target Rewards Rate / ((Annual Decay Factor Percentage / 100) ^ Bootstrapping Duration In Years)`.
 - `Pool Coefficient Exponent = 11`.
 
 #### Input values
@@ -589,9 +583,9 @@ The following section specifies how to convert the slot-level data into epoch-le
 
 #### Calculations
 
-- The total target reward `Target Reward(n)` for an epoch index `n` is defined as:
-  - `Initial Reward * Decay(n)` if `n <= Bootstrapping Duration`.
-  - `Final Reward` if `n > Bootstrapping Duration`.
+- The total target rewards rate `Target Rewards Rate(n)` for an epoch index `n` is defined as:
+  - `Initial Target Rewards Rate * Decay(n)` if `n <= Bootstrapping Duration`.
+  - `Final Target Rewards Rate` if `n > Bootstrapping Duration`.
 - The Pool Reward `Pool Reward` for an epoch index `n`, and pool `i` is calculated as follows:
   - Let `Pool Coefficient` be
     `((Pool Stake(i) << Pool Coefficient Exponent)/Total Stake) + (Validator Stake(i) << Pool Coefficient Exponent) / Total Validator Stake`.
@@ -600,8 +594,8 @@ The following section specifies how to convert the slot-level data into epoch-le
       `Pool Coefficient Exponent + 1` bits.
   - Take the `Epoch Performance Factor` for the whole epoch `n` according to
     [Epoch Performance Factor](#epoch-performance-factor).
-  - Let `Scaled Pool Reward` be `Pool Coefficient * Target Reward(n) * Epoch Performance Factor`.
-    - Since `Pool Coefficient` uses at most 12 bits, `Target Reward(n)` uses at most 41 bits, and
+  - Let `Scaled Pool Reward` be `Pool Coefficient * Target Rewards Rate(n) * Epoch Performance Factor`.
+    - Since `Pool Coefficient` uses at most 12 bits, `Target Rewards Rate(n)` uses at most 41 bits, and
       `Epoch Performance Factor` uses at most 8 bits, this multiplication will not overflow using uint64 variables.
   - Finally, `Pool Reward` will be
     `((Scaled Pool Reward/Validation Blocks Per Slot) >> (Pool Coefficient Exponent + 1))`. Note that if this value is