Add smooth staking hip

HIP/hip-406.md

@@ -10,7 +10,8 @@ last-call-date-time: 2022-06-02T07:00:00Z
 release: v0.27.0
 created: 2022-03-27
 discussions-to: https://github.com/hashgraph/hedera-improvement-proposal/discussions/408
-updated: 2022-04-20, 2022-05-25, 2022-06-02, 2022-11-14, 2023-03-27
+superseded-by: 782
+updated: 2023-08-09
 ---
 
 ## Abstract

HIP/hip-782.md

@@ -0,0 +1,66 @@
+---
+hip: 782
+title: Smoothing Staking Rewards
+author: Leemon Baird <[email protected]>
+type: Standards Track
+category: Core
+needs-council-approval: Yes
+status: Accepted
+last-call-date-time: 2023-08-09T07:00:00Z"
+release: v0.40.0
+created: 2023-08-01
+discussions-to: https://github.com/hashgraph/hedera-improvement-proposal/pull/782
+replaces: 406
+updated: 2023-08-09
+---
+
+Note: This hip does not replace all of hip-406 Staking. It replaces only replaces a small part. Otherwise, hip-406 still stands.
+
+## Abstract
+
+This HIP describes a change to the staking reward system for proof of stake described in HIP-406. HIP-406 gives rewards at a constant reward rate until the unreserved balance of account `0.0.800` is empty, then suddenly drops to a near zero reward rate. This HIP defines a change so that as `0.0.800` approaches being empty, the reward rate decreases smoothly rather than with an abrupt drop.
+
+## Motivation
+
+## Rationale
+
+## User Stories
+
+## Specification
+
+In the original HIP, there is a setting `stakingRewardRate`, and rewards are given at that rate until the unreserved balance of account `0.0.800` is empty, at which point it abruptly drops to simply distributing each day whatever came in to that account the previous day, such as through transaction fees.  And there was originally a setting for the max reward emission per day. 
+
+The change is to remove both of those settings, and have `stakingRewardRate` automatically change each day, based on the balance of `0.0.800` and three settings: `maxRewardRate`, `rewardBalanceThreshold`, and `maxStakeRewarded`.  The `maxRewardRate` (in tinybars earned per hbar staked per day) is the rate to pay normally (i.e., when `0.0.800` has a large balance, and not too many hbars are staked for reward). When the balance of `0.0.800` drops below `rewardBalanceThreshold` (in tinybars), then the `stakingRewardRate` drops smoothly as the balance drops. If the hbars staked for reward exceed `maxStakeRewarded` (in tinybars), then there is a further decrease (which replaces the original absolute limit on hbars emitted per day).
+
+
+Let `unreservedBalance` (in tinybars) be the balance of account `0.0.800` minus the amount of rewards that have been earned but not yet distributed. Let `stakedForReward` (in tinybars) be the total number of hbars on Hedera that have been staked for reward (so it ignores accounts that stake but decline a reward). Then each day, just before the HIP-406 reward calculations are performed using `stakingRewardRate`, recalculate `stakingRewardRate` as follows (implemented with equivalent results, but using integer calculations, rather than the real-number calculations shown):
+
+```
+//A real number proportional to the unreserved balance, from 0 for empty, up to 1 at the threshold.
+balanceRatio = min(unreservedBalance, rewardBalanceThreshold) / rewardBalanceThreshold;
+
+stakingRewardRate = maxRewardRate 
+                      * balanceRatio * (2 – balanceRatio) 
+                      * min(1, maxStakeRewarded / stakedForReward)
+
+```
+
+## Backwards Compatibility
+
+This has no effect on HAPI or on transactions.  It just affects the amount of daily staking rewards received by accounts that stake for reward, when `0.0.800` has a low balance.
+
+## Security Implications
+
+None.
+
+## How to Teach This
+
+## Reference Implementation
+
+## Rejected Ideas
+
+## Open Issues / FAQ
+
+## Copyright/license
+
+This document is licensed under the Apache License, Version 2.0 -- see [LICENSE](../LICENSE) or (https://www.apache.org/licenses/LICENSE-2.0)