Lower-bound the log approximation and stop using it > ~98.5%

When we start getting a numerator and divisor particularly close to
each other, the log approximation starts to get very noisy. In
order to avoid applying scores that are basically noise (and can
range upwards of 2x the default per-hop penalty), simply consider
such cases as having a success probability of 100%.

Author: TheBlueMatt

lightning/src/routing/scoring.rs

@@ -701,6 +701,10 @@ impl<T: Time> ChannelLiquidity<T> {
 /// probabilities.
 const NEGATIVE_LOG10_UPPER_BOUND: u64 = 2;
 
+/// The rough cutoff at which our precision falls off and we should stop bothering to try to log a
+/// ratio, as X in 1/X.
+const PRECISION_LOWER_BOUND_DENOMINATOR: u64 = approx::LOWER_BITS_BOUND;
+
 /// The divisor used when computing the amount penalty.
 const AMOUNT_PENALTY_DIVISOR: u64 = 1 << 20;
 
@@ -727,9 +731,16 @@ impl<L: Deref<Target = u64>, T: Time, U: Deref<Target = T>> DirectedChannelLiqui
 		} else {
 			let numerator = (max_liquidity_msat - amount_msat).saturating_add(1);
 			let denominator = (max_liquidity_msat - min_liquidity_msat).saturating_add(1);
-			let negative_log10_times_2048 =
-				approx::negative_log10_times_2048(numerator, denominator);
-			self.combined_penalty_msat(amount_msat, negative_log10_times_2048, params)
+			if amount_msat - min_liquidity_msat < denominator / PRECISION_LOWER_BOUND_DENOMINATOR {
+				// If the failure probability is < 1.5625% (as 1 - numerator/denominator < 1/64),
+				// don't bother trying to use the log approximation as it gets too noisy to be
+				// particularly helpful, instead just round down to 0 and return the base penalty.
+				params.base_penalty_msat
+			} else {
+				let negative_log10_times_2048 =
+					approx::negative_log10_times_2048(numerator, denominator);
+				self.combined_penalty_msat(amount_msat, negative_log10_times_2048, params)
+			}
 		}
 	}
 
@@ -889,7 +900,7 @@ mod approx {
 	const BITS: u32 = 64;
 	const HIGHEST_BIT: u32 = BITS - 1;
 	const LOWER_BITS: u32 = 6;
-	const LOWER_BITS_BOUND: u64 = 1 << LOWER_BITS;
+	pub(super) const LOWER_BITS_BOUND: u64 = 1 << LOWER_BITS;
 	const LOWER_BITMASK: u64 = (1 << LOWER_BITS) - 1;
 
 	/// Look-up table for `log10(x) * 2048` where row `i` is used for each `x` having `i` as the
@@ -2007,8 +2018,8 @@ mod tests {
 		let source = source_node_id();
 		let target = target_node_id();
 
-		assert_eq!(scorer.channel_penalty_msat(42, 1_024, 1_024_000, &source, &target), 3);
-		assert_eq!(scorer.channel_penalty_msat(42, 10_240, 1_024_000, &source, &target), 6);
+		assert_eq!(scorer.channel_penalty_msat(42, 1_024, 1_024_000, &source, &target), 0);
+		assert_eq!(scorer.channel_penalty_msat(42, 10_240, 1_024_000, &source, &target), 0);
 		assert_eq!(scorer.channel_penalty_msat(42, 102_400, 1_024_000, &source, &target), 47);
 		assert_eq!(scorer.channel_penalty_msat(42, 1_024_000, 1_024_000, &source, &target), 2_000);
 
@@ -2329,11 +2340,11 @@ mod tests {
 		assert_eq!(scorer.channel_penalty_msat(42, 100_000_000, 3_950_000_000, &source, &target), 1223);
 		assert_eq!(scorer.channel_penalty_msat(42, 100_000_000, 4_950_000_000, &source, &target), 877);
 		assert_eq!(scorer.channel_penalty_msat(42, 100_000_000, 5_950_000_000, &source, &target), 845);
-		assert_eq!(scorer.channel_penalty_msat(42, 100_000_000, 6_950_000_000, &source, &target), 782);
-		assert_eq!(scorer.channel_penalty_msat(42, 100_000_000, 7_450_000_000, &source, &target), 1002);
-		assert_eq!(scorer.channel_penalty_msat(42, 100_000_000, 7_950_000_000, &source, &target), 970);
-		assert_eq!(scorer.channel_penalty_msat(42, 100_000_000, 8_950_000_000, &source, &target), 907);
-		assert_eq!(scorer.channel_penalty_msat(42, 100_000_000, 9_950_000_000, &source, &target), 877);
+		assert_eq!(scorer.channel_penalty_msat(42, 100_000_000, 6_950_000_000, &source, &target), 500);
+		assert_eq!(scorer.channel_penalty_msat(42, 100_000_000, 7_450_000_000, &source, &target), 500);
+		assert_eq!(scorer.channel_penalty_msat(42, 100_000_000, 7_950_000_000, &source, &target), 500);
+		assert_eq!(scorer.channel_penalty_msat(42, 100_000_000, 8_950_000_000, &source, &target), 500);
+		assert_eq!(scorer.channel_penalty_msat(42, 100_000_000, 9_950_000_000, &source, &target), 500);
 	}
 
 	#[test]