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script/research/lotterysim/pid/pid.md: further simplyfied total tokens calculation

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aggstam
2023-07-06 17:50:29 +03:00
parent 8415d6e522
commit 86c9f36aff
1 changed files with 6 additions and 27 deletions
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script/research/lotterysim/pid/pid.md
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@@ -13,8 +13,11 @@ To generate the slot sigmas, we have to perform the following:
1. Calculate the inverse probability `f` of becoming a block producer (winning the lottery)
having all the tokens, represented as Float10.
2. Calculate network total tokens, deriving from genesis stake, genesis mint,
and all block rewarded tokens, represented as Float10.
2. Retrieve network total tokens, up until the provided slot, represented as Float10.
Since each slot contains the total tokens up until that point, we simply grab the
previous slot total tokens. Additionally, each slot will contain its reward.
That enables to be flexible on reward scheme, since both constant and variable
rewards can be used.
3. Calculate the sigmas using previous 2 numbers, represented as pallas::Base.
Each step will be further described in the sub-sections following.
@@ -25,7 +28,7 @@ Pseudocode:
/// corresponding to provided slot consensus state.
fn sigmas() -> (pallas::Base, pallas::Base) {
let f: Float10 = calculate_f();
let total_tokens: Float10 = total_tokens();
let total_tokens: Float10 = previous_slot.total_tokens;
calculate_sigmas(f, total_tokens)
}
```
@@ -70,30 +73,6 @@ fn calculate_f() -> Float10 {
}
```
## Calculate total tokens
In this step we calculate network total tokens.
Pseudocode:
```
/// Network total tokens, assuming constant reward.
/// Only used for fine-tuning. Since a genesis staker
/// is needed to progress the blockchain, we know that
/// total tokens > 0, as genesis_tokens > 0.
fn total_tokens() -> u64 {
// Retrieve existing blocks count, excluding genesis,
// up until current slot
let blocks = blockchain.len_until(slot) - 1;
// Calculate rewarded slots, including previous slot
// longest fork proposals
let rewarded_slots = blocks + previous_slot.longest_fork_length;
// Calculate rewarded tokens
let rewarded_tokens = rewarded_slots * REWARD
rewarded_tokens + genesis_tokens
}
```
## Calculate sigmas
Finally we can produce the slot sigmas, based on previous calculations.