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```
// Copyright 2019 Parity Technologies (UK) Ltd.
// This file is part of Polkadot.
// Polkadot is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// Polkadot is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
// You should have received a copy of the GNU General Public License
// along with Polkadot. If not, see <http://www.gnu.org/licenses/>.
//! Auxillary struct/enums for polkadot runtime.
use primitives::Balance;
```

```
use sr_primitives::weights::Weight;
```

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```
use sr_primitives::traits::{Convert, Saturating};
use sr_primitives::Fixed64;
use srml_support::traits::{OnUnbalanced, Currency};
use crate::{Balances, Authorship, MaximumBlockWeight, NegativeImbalance};
use crate::constants::fee::TARGET_BLOCK_FULLNESS;
/// Logic for the author to get a portion of fees.
pub struct ToAuthor;
impl OnUnbalanced<NegativeImbalance> for ToAuthor {
fn on_unbalanced(amount: NegativeImbalance) {
Balances::resolve_creating(&Authorship::author(), amount);
}
}
/// Converter for currencies to votes.
pub struct CurrencyToVoteHandler;
impl CurrencyToVoteHandler {
fn factor() -> u128 { (Balances::total_issuance() / u64::max_value() as u128).max(1) }
}
impl Convert<u128, u64> for CurrencyToVoteHandler {
fn convert(x: u128) -> u64 { (x / Self::factor()) as u64 }
}
impl Convert<u128, u128> for CurrencyToVoteHandler {
fn convert(x: u128) -> u128 { x * Self::factor() }
}
/// Handles converting a weight scalar to a fee value, based on the scale and granularity of the
/// node's balance type.
///
/// This should typically create a mapping between the following ranges:
/// - [0, system::MaximumBlockWeight]
/// - [Balance::min, Balance::max]
///
/// Yet, it can be used for any other sort of change to weight-fee. Some examples being:
/// - Setting it to `0` will essentially disable the weight fee.
/// - Setting it to `1` will cause the literal `#[weight = x]` values to be charged.
pub struct WeightToFee;
impl Convert<Weight, Balance> for WeightToFee {
fn convert(x: Weight) -> Balance {
// in Polkadot a weight of 10_000 (smallest non-zero weight) to be mapped to 10^7 units of
// fees (1/10 CENT), hence:
Balance::from(x).saturating_mul(1_000)
}
}
/// A struct that updates the weight multiplier based on the saturation level of the previous block.
/// This should typically be called once per-block.
///
/// This assumes that weight is a numeric value in the u32 range.
///
/// Given `TARGET_BLOCK_FULLNESS = 1/2`, a block saturation greater than 1/2 will cause the system
/// fees to slightly grow and the opposite for block saturations less than 1/2.
///
/// Formula:
/// diff = (target_weight - current_block_weight)
/// v = 0.00004
/// next_weight = weight * (1 + (v . diff) + (v . diff)^2 / 2)
///
/// https://research.web3.foundation/en/latest/polkadot/Token%20Economics/#relay-chain-transaction-fees
```

```
pub struct FeeMultiplierUpdateHandler;
```

```
impl Convert<(Weight, Fixed64), Fixed64> for FeeMultiplierUpdateHandler {
fn convert(previous_state: (Weight, Fixed64)) -> Fixed64 {
```

```
let (block_weight, multiplier) = previous_state;
let max_weight = MaximumBlockWeight::get();
let target_weight = (TARGET_BLOCK_FULLNESS * max_weight) as u128;
let block_weight = block_weight as u128;
// determines if the first_term is positive
let positive = block_weight >= target_weight;
let diff_abs = block_weight.max(target_weight) - block_weight.min(target_weight);
// diff is within u32, safe.
let diff = Fixed64::from_rational(diff_abs as i64, max_weight as u64);
let diff_squared = diff.saturating_mul(diff);
// 0.00004 = 4/100_000 = 40_000/10^9
let v = Fixed64::from_rational(4, 100_000);
// 0.00004^2 = 16/10^10 ~= 2/10^9. Taking the future /2 into account, then it is just 1 parts
// from a billionth.
let v_squared_2 = Fixed64::from_rational(1, 1_000_000_000);
let first_term = v.saturating_mul(diff);
// It is very unlikely that this will exist (in our poor perbill estimate) but we are giving
// it a shot.
let second_term = v_squared_2.saturating_mul(diff_squared);
if positive {
// Note: this is merely bounded by how big the multiplier and the inner value can go,
// not by any economical reasoning.
let excess = first_term.saturating_add(second_term);
```

```
multiplier.saturating_add(excess)
```

```
// Proof: first_term > second_term. Safe subtraction.
```

```
let negative = first_term - second_term;
```

```
multiplier.saturating_sub(negative)
```

```
// despite the fact that apply_to saturates weight (final fee cannot go below 0)
// it is crucially important to stop here and don't further reduce the weight fee
// multiplier. While at -1, it means that the network is so un-congested that all
// transactions have no weight fee. We stop here and only increase if the network
// became more busy.
```

```
.max(Fixed64::from_rational(-1, 1))
```