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Offline operator detections: Reduce the tau from 1% to 0.5% #3742

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Merged
vedhavyas merged 1 commit into from
Jan 22, 2026
+55 −44
Merged

Offline operator detections: Reduce the tau from 1% to 0.5% #3742

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4 changes: 2 additions & 2 deletions crates/pallet-domains/src/staking_epoch.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -24,7 +24,7 @@ use parity_scale_codec::{Decode, DecodeWithMemTracking, Encode};
use scale_info::TypeInfo;
use sp_core::Get;
use sp_domains::offline_operators::{
E_BASE, LN_1_OVER_TAU_1_PERCENT, operator_expected_bundles_in_epoch,
E_BASE, LN_1_OVER_TAU_0_5_PERCENT, operator_expected_bundles_in_epoch,
};
use sp_domains::{DomainId, EpochIndex, OperatorId, OperatorRewardSource};
use sp_runtime::traits::{CheckedAdd, CheckedSub, One, Zero};
Expand Down Expand Up @@ -271,7 +271,7 @@ pub(crate) fn do_finalize_domain_epoch_staking<T: Config>(
(*operator_stake).saturated_into(),
epoch_total_stake.saturated_into(),
bundle_slot_probability,
LN_1_OVER_TAU_1_PERCENT,
LN_1_OVER_TAU_0_5_PERCENT,
E_BASE,
);

Expand Down
4 changes: 4 additions & 0 deletions crates/sp-domains/src/offline_operators.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -34,6 +34,10 @@ use sp_core::{DecodeWithMemTracking, U256};
/// Represent in FixedU128 by multiplying by 1e18 and rounding.
pub const LN_1_OVER_TAU_1_PERCENT: FixedU128 = FixedU128::from_inner(4_605_170_185_988_091_904);

// For τ = 0.5%: ln(1/τ) = ln(200) ≈ 5.298317366548036
// Represent in FixedU128 by multiplying by 1e18 and rounding.
pub const LN_1_OVER_TAU_0_5_PERCENT: FixedU128 = FixedU128::from_inner(5_298_317_366_548_036_608);

/// Threshold for number of bundles operator can produce based on their stake share.
/// Operators whose expected bundles from their threshold < E_BASE will not be checked
/// since they are not throughput relevant.
Expand Down
91 changes: 49 additions & 42 deletions crates/sp-domains/src/offline_operators/tests.rs
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Original file line number Diff line number Diff line change
@@ -1,7 +1,8 @@
use crate::bundle_producer_election::calculate_threshold;
use crate::offline_operators::{
E_BASE, LN_1_OVER_TAU_1_PERCENT, chernoff_threshold_fp, compute_e_relevance,
is_throughput_relevant_fp, operator_expected_bundles_in_epoch, p_from_threshold,
E_BASE, LN_1_OVER_TAU_0_5_PERCENT, LN_1_OVER_TAU_1_PERCENT, chernoff_threshold_fp,
compute_e_relevance, is_throughput_relevant_fp, operator_expected_bundles_in_epoch,
p_from_threshold,
};
use num_traits::{One, Zero};
use prop_test::proptest::prelude::{ProptestConfig, Strategy};
Expand All @@ -11,10 +12,6 @@ use prop_test::proptest::{prop_assert, prop_assert_eq, prop_assume, proptest};
use sp_arithmetic::traits::{SaturatedConversion, Saturating};
use sp_arithmetic::{FixedPointNumber, FixedU128};

// For τ = 0.5%: ln(1/τ) = ln(200) ≈ 5.298317366548036
// Represent in FixedU128 by multiplying by 1e18 and rounding.
const LN_1_OVER_TAU_0_5_PERCENT: FixedU128 = FixedU128::from_inner(5_298_317_366_548_036_000);

// For τ = 0.1%: ln(1/τ) = ln(1000) ≈ 6.907755278982137
// Represent in FixedU128 by multiplying by 1e18 and rounding.
const LN_1_OVER_TAU_0_1_PERCENT: FixedU128 = FixedU128::from_inner(6_907_755_278_982_137_000);
Expand All @@ -29,12 +26,22 @@ fn test_ln_1_over_tau_1_value() {
assert_eq!(LN_1_OVER_TAU_1_PERCENT, computed_ln_1_over_tau_1,);
}

#[test]
fn test_ln_1_over_tau_0_5_value() {
// Dynamically compute ln(200) in floating point
// Convert to FixedU128 representation (scaled by 1e18)
let computed_ln_1_over_tau_0_5 = FixedU128::from_inner((f64::ln(200.0) * 1e18).round() as u128);

// Check equality of integer fixed-point representation
assert_eq!(LN_1_OVER_TAU_0_5_PERCENT, computed_ln_1_over_tau_0_5,);
}

#[test]
fn test_chernoff_basic() {
// S = 600, p = 0.05 (μ = 30). τ = 1% -> ln(100)
// S = 600, p = 0.05 (μ = 30). τ = 0.5% -> ln(200)
let s = 600u64;
let p = FixedU128::saturating_from_rational(5u128, 100u128);
let r = chernoff_threshold_fp(s, p, LN_1_OVER_TAU_1_PERCENT).unwrap();
let r = chernoff_threshold_fp(s, p, LN_1_OVER_TAU_0_5_PERCENT).unwrap();
// Chernoff is conservative; r will be noticeably below μ.
// Expect r around low/mid-teens.
assert!(r > 0 && r < 30, "r should be between 1 and 29, got {r}");
Expand Down Expand Up @@ -66,13 +73,13 @@ fn test_p_from_threshold() {
}

fn e_rel_1pct() -> u64 {
compute_e_relevance(LN_1_OVER_TAU_1_PERCENT, E_BASE)
compute_e_relevance(LN_1_OVER_TAU_0_5_PERCENT, E_BASE)
}

#[test]
fn e_relevance_is_10_for_tau_1pct() {
// 2 * ln(100) ≈ 9.21034 -> ceil = 10; max(E_BASE=3, 10) = 10
assert_eq!(e_rel_1pct(), 10);
fn e_relevance_is_11_for_tau_0_5_pct() {
// 2 * ln(200) ≈ 10.5966347331 -> ceil = 11; max(E_BASE=3, 11) = 11
assert_eq!(e_rel_1pct(), 11);
}

#[test]
Expand All @@ -84,7 +91,7 @@ fn returns_none_when_no_slots_or_zero_threshold_inputs() {
1_000, // operator_stake
1_000_000, // total_domain_stake
(1, 1), // theta
LN_1_OVER_TAU_1_PERCENT,
LN_1_OVER_TAU_0_5_PERCENT,
E_BASE,
)
.is_none()
Expand All @@ -97,7 +104,7 @@ fn returns_none_when_no_slots_or_zero_threshold_inputs() {
1_000, // operator_stake
0, // total_domain_stake
(1, 1),
LN_1_OVER_TAU_1_PERCENT,
LN_1_OVER_TAU_0_5_PERCENT,
E_BASE,
)
.is_none()
Expand All @@ -110,7 +117,7 @@ fn returns_none_when_no_slots_or_zero_threshold_inputs() {
0, // operator_stake
1_000_000_000_000_000_000, // total_domain_stake
(1, 1),
LN_1_OVER_TAU_1_PERCENT,
LN_1_OVER_TAU_0_5_PERCENT,
E_BASE,
)
.is_none()
Expand All @@ -128,7 +135,7 @@ fn small_mu_is_not_throughput_relevant() {
operator,
total,
(1, 1),
LN_1_OVER_TAU_1_PERCENT,
LN_1_OVER_TAU_0_5_PERCENT,
E_BASE,
)
.is_none()
Expand All @@ -137,19 +144,19 @@ fn small_mu_is_not_throughput_relevant() {

#[test]
fn relevant_operator_produces_some_expectations() {
// S = 600, share ~ 2% => μ ≈ 12 >= 10 -> Some(...)
// S = 600, share ~ 2% => μ ≈ 12 >= 11 -> Some(...)
let total = 1_000_000_000_000_000_000u128;
let operator = total / 50; // 2%
let operator = total / 30; // 3.33%
let exp = operator_expected_bundles_in_epoch(
600,
operator,
total,
(1, 1),
LN_1_OVER_TAU_1_PERCENT,
LN_1_OVER_TAU_0_5_PERCENT,
E_BASE,
)
.expect("should be relevant");
// expected_bundles should be >= E_relevance (10) for τ=1%
// expected_bundles should be >= E_relevance (11) for τ=0.5%
assert!(exp.expected_bundles >= e_rel_1pct());
// Chernoff threshold is a lower bound; must be <= expected_bundles
assert!(exp.min_required_bundles <= exp.expected_bundles);
Expand All @@ -167,7 +174,7 @@ fn near_full_stake_behaves_sensibly() {
operator,
total,
(1, 1),
LN_1_OVER_TAU_1_PERCENT,
LN_1_OVER_TAU_0_5_PERCENT,
E_BASE,
)
.expect("should be relevant");
Expand All @@ -187,9 +194,9 @@ fn monotonic_in_stake_when_relevant() {
let tests = [
(total / 200, false), // 0.5% -> not relevant (μ≈3)
(total / 100, false), // 1% -> not relevant (μ≈6)
(total / 59, true), // ~1.695% -> μ_floor >= 10 -> relevant
(total / 50, true), // 2% -> μ≈12
(total / 20, true), // 5% -> μ≈30
(total / 59, false), // ~1.695% -> μ_floor >= 10 -> not relevant
(total / 50, true), // 2% -> μ≈12 relevant
(total / 20, true), // 5% -> μ≈30 relevant
];

let mut last_exp_bundles = 0u64;
Expand All @@ -200,7 +207,7 @@ fn monotonic_in_stake_when_relevant() {
stake,
total,
(1, 1),
LN_1_OVER_TAU_1_PERCENT,
LN_1_OVER_TAU_0_5_PERCENT,
E_BASE,
);

Expand Down Expand Up @@ -255,16 +262,16 @@ fn chernoff_monotone_in_tau() {
fn chernoff_edges_p_zero_or_one() {
let s = 123u64;
let r_zero =
chernoff_threshold_fp(s, FixedU128::from_inner(0), LN_1_OVER_TAU_1_PERCENT).unwrap();
chernoff_threshold_fp(s, FixedU128::from_inner(0), LN_1_OVER_TAU_0_5_PERCENT).unwrap();
assert_eq!(r_zero, 0);
let r_one = chernoff_threshold_fp(s, FixedU128::one(), LN_1_OVER_TAU_1_PERCENT).unwrap();
let r_one = chernoff_threshold_fp(s, FixedU128::one(), LN_1_OVER_TAU_0_5_PERCENT).unwrap();
assert_eq!(r_one, s);
}

#[test]
fn throughput_relevance_boundary() {
// Construct p so that floor(S * p) == E_relevance, should be relevant.
let e_rel = compute_e_relevance(LN_1_OVER_TAU_1_PERCENT, E_BASE); // 10
let e_rel = compute_e_relevance(LN_1_OVER_TAU_0_5_PERCENT, E_BASE); // 11
let s = 600u64;
let p = FixedU128::saturating_from_rational(e_rel as u128, s as u128);
// at boundary is not relevant
Expand All @@ -288,12 +295,12 @@ fn operator_expected_bundles_theta_one() {
operator,
total,
(1, 1),
LN_1_OVER_TAU_1_PERCENT,
LN_1_OVER_TAU_0_5_PERCENT,
E_BASE,
)
.expect("relevant operator should produce expectations");
// Expected bundles >= relevance floor
assert!(out.expected_bundles >= compute_e_relevance(LN_1_OVER_TAU_1_PERCENT, E_BASE));
assert!(out.expected_bundles >= compute_e_relevance(LN_1_OVER_TAU_0_5_PERCENT, E_BASE));
// r <= expected
assert!(out.min_required_bundles <= out.expected_bundles);
// monotone sanity: increasing S increases expected bundles
Expand All @@ -302,7 +309,7 @@ fn operator_expected_bundles_theta_one() {
operator,
total,
(1, 1),
LN_1_OVER_TAU_1_PERCENT,
LN_1_OVER_TAU_0_5_PERCENT,
E_BASE,
)
.expect("still relevant at larger S");
Expand All @@ -315,13 +322,13 @@ fn operator_expected_bundles_theta_half_not_relevant() {
let s = 600u64;
let total = 1_000_000_000_000_000_000u128;
let operator = total / 50; // 2% stake; μ would be ~12 at theta=1
// theta = 1/2 -> μ ≈ 6 -> below 10 => None
// theta = 1/2 -> μ ≈ 6 -> below 11 => None
let out = operator_expected_bundles_in_epoch(
s,
operator,
total,
(1, 2),
LN_1_OVER_TAU_1_PERCENT,
LN_1_OVER_TAU_0_5_PERCENT,
E_BASE,
);
assert!(out.is_none());
Expand All @@ -338,11 +345,11 @@ fn operator_expected_bundles_handles_huge_total_and_small_op() {
operator,
total,
(1, 1),
LN_1_OVER_TAU_1_PERCENT,
LN_1_OVER_TAU_0_5_PERCENT,
E_BASE,
)
.expect("should be relevant");
assert!(out.expected_bundles >= compute_e_relevance(LN_1_OVER_TAU_1_PERCENT, E_BASE));
assert!(out.expected_bundles >= compute_e_relevance(LN_1_OVER_TAU_0_5_PERCENT, E_BASE));
assert!(out.min_required_bundles <= out.expected_bundles);
}

Expand Down Expand Up @@ -414,7 +421,7 @@ proptest! {
let stake = operator_stake_strategy(total).new_tree(&mut TestRunner::default()).unwrap().current();

let out = operator_expected_bundles_in_epoch(
s, stake, total, theta, LN_1_OVER_TAU_1_PERCENT, E_BASE
s, stake, total, theta, LN_1_OVER_TAU_0_5_PERCENT, E_BASE
);

let mu_floor = mu_floor_from_threshold(s, stake, total, theta);
Expand Down Expand Up @@ -460,10 +467,10 @@ proptest! {
prop_assume!(stake_hi >= stake_lo);

let out_lo = operator_expected_bundles_in_epoch(
s, stake_lo, total, theta, LN_1_OVER_TAU_1_PERCENT, E_BASE
s, stake_lo, total, theta, LN_1_OVER_TAU_0_5_PERCENT, E_BASE
);
let out_hi = operator_expected_bundles_in_epoch(
s, stake_hi, total, theta, LN_1_OVER_TAU_1_PERCENT, E_BASE
s, stake_hi, total, theta, LN_1_OVER_TAU_0_5_PERCENT, E_BASE
);

if let Some(exp_lo) = out_lo {
Expand Down Expand Up @@ -495,10 +502,10 @@ proptest! {
let (s_min, s_max) = if s1 <= s2 { (s1, s2) } else { (s2, s1) };

let out_min = operator_expected_bundles_in_epoch(
s_min, stake, total, theta, LN_1_OVER_TAU_1_PERCENT, E_BASE
s_min, stake, total, theta, LN_1_OVER_TAU_0_5_PERCENT, E_BASE
);
let out_max = operator_expected_bundles_in_epoch(
s_max, stake, total, theta, LN_1_OVER_TAU_1_PERCENT, E_BASE
s_max, stake, total, theta, LN_1_OVER_TAU_0_5_PERCENT, E_BASE
);

if let Some(exp_min) = out_min {
Expand Down Expand Up @@ -533,10 +540,10 @@ proptest! {
let theta_hi = (num_hi, den);

let out_lo = operator_expected_bundles_in_epoch(
s, stake, total, theta_lo, LN_1_OVER_TAU_1_PERCENT, E_BASE
s, stake, total, theta_lo, LN_1_OVER_TAU_0_5_PERCENT, E_BASE
);
let out_hi = operator_expected_bundles_in_epoch(
s, stake, total, theta_hi, LN_1_OVER_TAU_1_PERCENT, E_BASE
s, stake, total, theta_hi, LN_1_OVER_TAU_0_5_PERCENT, E_BASE
);

if let Some(exp_lo) = out_lo {
Expand Down
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