(a * a * a, b * b * b, c * c * c)
}
+#[inline(always)]
+fn linear_success_probability(
+ amount_msat: u64, min_liquidity_msat: u64, max_liquidity_msat: u64,
+ min_zero_implies_no_successes: bool,
+) -> (u64, u64) {
+ let (numerator, mut denominator) =
+ (max_liquidity_msat - amount_msat,
+ (max_liquidity_msat - min_liquidity_msat).saturating_add(1));
+
+ if min_zero_implies_no_successes && min_liquidity_msat == 0 &&
+ denominator < u64::max_value() / 21
+ {
+ // If we have no knowledge of the channel, scale probability down by ~75%
+ // Note that we prefer to increase the denominator rather than decrease the numerator as
+ // the denominator is more likely to be larger and thus provide greater precision. This is
+ // mostly an overoptimization but makes a large difference in tests.
+ denominator = denominator * 21 / 16
+ }
+
+ (numerator, denominator)
+}
+
+#[inline(always)]
+fn nonlinear_success_probability(
+ amount_msat: u64, min_liquidity_msat: u64, max_liquidity_msat: u64, capacity_msat: u64,
+) -> (f64, f64) {
+ let capacity = capacity_msat as f64;
+ let min = (min_liquidity_msat as f64) / capacity;
+ let max = (max_liquidity_msat as f64) / capacity;
+ let amount = (amount_msat as f64) / capacity;
+
+ // Assume the channel has a probability density function of (x - 0.5)^2 for values from
+ // 0 to 1 (where 1 is the channel's full capacity). The success probability given some
+ // liquidity bounds is thus the integral under the curve from the amount to maximum
+ // estimated liquidity, divided by the same integral from the minimum to the maximum
+ // estimated liquidity bounds.
+ //
+ // Because the integral from x to y is simply (y - 0.5)^3 - (x - 0.5)^3, we can
+ // calculate the cumulative density function between the min/max bounds trivially. Note
+ // that we don't bother to normalize the CDF to total to 1, as it will come out in the
+ // division of num / den.
+ let (max_pow, amt_pow, min_pow) = three_f64_pow_3(max - 0.5, amount - 0.5, min - 0.5);
+ (max_pow - amt_pow, max_pow - min_pow)
+}
+
+
/// Given liquidity bounds, calculates the success probability (in the form of a numerator and
/// denominator) of an HTLC. This is a key assumption in our scoring models.
///
-/// Must not return a numerator or denominator greater than 2^31 for arguments less than 2^31.
-///
/// min_zero_implies_no_successes signals that a `min_liquidity_msat` of 0 means we've not
/// (recently) seen an HTLC successfully complete over this channel.
#[inline(always)]
debug_assert!(amount_msat < max_liquidity_msat);
debug_assert!(max_liquidity_msat <= capacity_msat);
- let (numerator, mut denominator) =
- if params.linear_success_probability {
- (max_liquidity_msat - amount_msat,
- (max_liquidity_msat - min_liquidity_msat).saturating_add(1))
- } else {
- let capacity = capacity_msat as f64;
- let min = (min_liquidity_msat as f64) / capacity;
- let max = (max_liquidity_msat as f64) / capacity;
- let amount = (amount_msat as f64) / capacity;
-
- // Assume the channel has a probability density function of (x - 0.5)^2 for values from
- // 0 to 1 (where 1 is the channel's full capacity). The success probability given some
- // liquidity bounds is thus the integral under the curve from the amount to maximum
- // estimated liquidity, divided by the same integral from the minimum to the maximum
- // estimated liquidity bounds.
- //
- // Because the integral from x to y is simply (y - 0.5)^3 - (x - 0.5)^3, we can
- // calculate the cumulative density function between the min/max bounds trivially. Note
- // that we don't bother to normalize the CDF to total to 1, as it will come out in the
- // division of num / den.
- let (max_pow, amt_pow, min_pow) = three_f64_pow_3(max - 0.5, amount - 0.5, min - 0.5);
- let num = max_pow - amt_pow;
- let den = max_pow - min_pow;
-
- // Because our numerator and denominator max out at 0.5^3 we need to multiply them by
- // quite a large factor to get something useful (ideally in the 2^30 range).
- const BILLIONISH: f64 = 1024.0 * 1024.0 * 1024.0;
- let numerator = (num * BILLIONISH) as u64 + 1;
- let denominator = (den * BILLIONISH) as u64 + 1;
- debug_assert!(numerator <= 1 << 30, "Got large numerator ({}) from float {}.", numerator, num);
- debug_assert!(denominator <= 1 << 30, "Got large denominator ({}) from float {}.", denominator, den);
- (numerator, denominator)
- };
+ if params.linear_success_probability {
+ return linear_success_probability(
+ amount_msat, min_liquidity_msat, max_liquidity_msat, min_zero_implies_no_successes
+ );
+ }
+
+ let (num, den) = nonlinear_success_probability(
+ amount_msat, min_liquidity_msat, max_liquidity_msat, capacity_msat
+ );
+
+ // Because our numerator and denominator max out at 0.5^3 we need to multiply them by
+ // quite a large factor to get something useful (ideally in the 2^30 range).
+ const BILLIONISH: f64 = 1024.0 * 1024.0 * 1024.0;
+ let numerator = (num * BILLIONISH) as u64 + 1;
+ let mut denominator = (den * BILLIONISH) as u64 + 1;
+ debug_assert!(numerator <= 1 << 30, "Got large numerator ({}) from float {}.", numerator, num);
+ debug_assert!(denominator <= 1 << 30, "Got large denominator ({}) from float {}.", denominator, den);
if min_zero_implies_no_successes && min_liquidity_msat == 0 &&
denominator < u64::max_value() / 21
(numerator, denominator)
}
+/// Given liquidity bounds, calculates the success probability (times some value) of an HTLC. This
+/// is a key assumption in our scoring models.
+///
+/// min_zero_implies_no_successes signals that a `min_liquidity_msat` of 0 means we've not
+/// (recently) seen an HTLC successfully complete over this channel.
+#[inline(always)]
+fn success_probability_times_value(
+ amount_msat: u64, min_liquidity_msat: u64, max_liquidity_msat: u64, capacity_msat: u64,
+ params: &ProbabilisticScoringFeeParameters, min_zero_implies_no_successes: bool,
+ value: u32,
+) -> u64 {
+ debug_assert!(min_liquidity_msat <= amount_msat);
+ debug_assert!(amount_msat < max_liquidity_msat);
+ debug_assert!(max_liquidity_msat <= capacity_msat);
+
+ if params.linear_success_probability {
+ let (numerator, denominator) = linear_success_probability(
+ amount_msat, min_liquidity_msat, max_liquidity_msat, min_zero_implies_no_successes
+ );
+ return (value as u64) * numerator / denominator;
+ }
+
+ let (num, mut den) = nonlinear_success_probability(
+ amount_msat, min_liquidity_msat, max_liquidity_msat, capacity_msat
+ );
+
+ if min_zero_implies_no_successes && min_liquidity_msat == 0 {
+ // If we have no knowledge of the channel, scale probability down by ~75%
+ // Note that we prefer to increase the denominator rather than decrease the numerator as
+ // the denominator is more likely to be larger and thus provide greater precision. This is
+ // mostly an overoptimization but makes a large difference in tests.
+ den = den * 21.0 / 16.0
+ }
+
+ let res = (value as f64) * num / den;
+
+ res as u64
+}
+
impl<L: Deref<Target = u64>, HT: Deref<Target = HistoricalLiquidityTracker>, T: Deref<Target = Duration>>
DirectedChannelLiquidity< L, HT, T> {
/// Returns a liquidity penalty for routing the given HTLC `amount_msat` through the channel in
}
let max_bucket_end_pos = BUCKET_START_POS[32 - highest_max_bucket_with_points] - 1;
if payment_pos < max_bucket_end_pos {
- let (numerator, denominator) = success_probability(payment_pos as u64, 0,
- max_bucket_end_pos as u64, POSITION_TICKS as u64 - 1, params, true);
let bucket_prob_times_billion =
(min_liquidity_offset_history_buckets[0] as u64) * total_max_points
* 1024 * 1024 * 1024 / total_valid_points_tracked;
- cumulative_success_prob_times_billion += bucket_prob_times_billion *
- numerator / denominator;
+ debug_assert!(bucket_prob_times_billion < u32::max_value() as u64);
+ cumulative_success_prob_times_billion += success_probability_times_value(
+ payment_pos as u64, 0, max_bucket_end_pos as u64,
+ POSITION_TICKS as u64 - 1, params, true, bucket_prob_times_billion as u32
+ );
}
}
if payment_pos < min_bucket_start_pos {
for (max_idx, max_bucket) in max_liquidity_offset_history_buckets.iter().enumerate().take(32 - min_idx) {
let max_bucket_end_pos = BUCKET_START_POS[32 - max_idx] - 1;
- // Note that this multiply can only barely not overflow - two 16 bit ints plus
- // 30 bits is 62 bits.
- let bucket_prob_times_billion = (*min_bucket as u64) * (*max_bucket as u64)
- * 1024 * 1024 * 1024 / total_valid_points_tracked;
if payment_pos >= max_bucket_end_pos {
// Success probability 0, the payment amount may be above the max liquidity
break;
}
+ // Note that this multiply can only barely not overflow - two 16 bit ints plus
+ // 30 bits is 62 bits.
+ let bucket_prob_times_billion = ((*min_bucket as u32) * (*max_bucket as u32)) as u64
+ * 1024 * 1024 * 1024 / total_valid_points_tracked;
+ debug_assert!(bucket_prob_times_billion < u32::max_value() as u64);
cumulative_success_prob_times_billion += bucket_prob_times_billion;
}
} else {
for (max_idx, max_bucket) in max_liquidity_offset_history_buckets.iter().enumerate().take(32 - min_idx) {
let max_bucket_end_pos = BUCKET_START_POS[32 - max_idx] - 1;
- // Note that this multiply can only barely not overflow - two 16 bit ints plus
- // 30 bits is 62 bits.
- let bucket_prob_times_billion = (*min_bucket as u64) * (*max_bucket as u64)
- * 1024 * 1024 * 1024 / total_valid_points_tracked;
if payment_pos >= max_bucket_end_pos {
// Success probability 0, the payment amount may be above the max liquidity
break;
}
- let (numerator, denominator) = success_probability(payment_pos as u64,
- min_bucket_start_pos as u64, max_bucket_end_pos as u64,
- POSITION_TICKS as u64 - 1, params, true);
- cumulative_success_prob_times_billion += bucket_prob_times_billion *
- numerator / denominator;
+ // Note that this multiply can only barely not overflow - two 16 bit ints plus
+ // 30 bits is 62 bits.
+ let bucket_prob_times_billion = ((*min_bucket as u32) * (*max_bucket as u32)) as u64
+ * 1024 * 1024 * 1024 / total_valid_points_tracked;
+ debug_assert!(bucket_prob_times_billion < u32::max_value() as u64);
+ cumulative_success_prob_times_billion += success_probability_times_value(
+ payment_pos as u64, min_bucket_start_pos as u64,
+ max_bucket_end_pos as u64, POSITION_TICKS as u64 - 1, params, true,
+ bucket_prob_times_billion as u32);
}
}
}
projects / rust-lightning / commitdiff