fix: histogram clickhouse calculation

controlplane/clickhouse/migrations/20260227100333_drop_func_histogram_v2.sql

@@ -0,0 +1,20 @@
+-- migrate:up
+
+-- Drop func_histogram_v2 so it can be recreated with the corrected interpolation
+-- in the next migration. See 20260227100342_recreate_func_histogram_v2_fix_interpolation.sql.
+
+DROP FUNCTION func_histogram_v2;
+
+-- migrate:down
+
+-- Restore the original (buggy) func_histogram_v2.
+-- The b > 1 interpolation fraction here (rank / cumSum[b]) is incorrect;
+-- it was fixed in the following migration.
+
+CREATE FUNCTION func_histogram_v2 as (rank,b,buckets,bounds) ->
+    if(b = length(buckets), bounds[length(bounds)],
+       if(b > 1,
+          bounds[b-1] + (bounds[b]-bounds[b-1]) * (rank / arrayElement(arrayCumSum(buckets),b)),
+          bounds[b] * (rank / arrayElement(arrayCumSum(buckets),b))
+       )
+    );

controlplane/clickhouse/migrations/20260227100342_recreate_func_histogram_v2_fix_interpolation.sql

@@ -0,0 +1,48 @@
+-- migrate:up
+
+-- Recreates func_histogram_v2 with the corrected Prometheus bucket_quantile interpolation.
+--
+-- These three functions together implement the Prometheus bucket_quantile algorithm:
+--   1. func_rank(q, buckets)                        -> rank = q * total
+--   2. func_rank_bucket_lower_index(rank, buckets)   -> b = first bucket where cumSum >= rank
+--   3. func_histogram_v2(rank, b, buckets, bounds)   -> interpolated quantile value
+--
+-- Parameters:
+--   rank    = target count position (from func_rank)
+--   b       = 1-indexed bucket containing the rank (from func_rank_bucket_lower_index)
+--   buckets = per-bucket counts (non-cumulative), length N+1 (includes +inf bucket)
+--   bounds  = explicit histogram boundaries, length N (excludes +inf)
+--
+-- The Prometheus interpolation formula for b > 1 is:
+--   bucketStart + (bucketEnd - bucketStart) * (rank - cumSum[b-1]) / (cumSum[b] - cumSum[b-1])
+--
+-- Bug: The previous implementation used rank / cumSum[b] as the interpolation fraction,
+-- which uses the absolute rank instead of the rank relative to the bucket start.
+-- This caused quantile values to be systematically over-estimated for all buckets past
+-- the first, with increasing error for higher percentiles (p90, p95, p99).
+--
+-- Example with buckets=[10,20,30], cumSum=[10,30,60], q=0.75, rank=45, b=3:
+--   Before (wrong): fraction = 45 / 60           = 0.75
+--   After (correct): fraction = (45-30) / (60-30) = 0.50
+--
+-- Source: https://github.com/prometheus/prometheus/blob/79be1b835789d7c3fde2a907003a8799c308733f/promql/quantile.go#L74
+
+CREATE FUNCTION func_histogram_v2 as (rank,b,buckets,bounds) ->
+    if(b = length(buckets),
+       -- Case 1: rank falls in the +inf bucket, return the last finite bound
+       bounds[length(bounds)],
+       if(b > 1,
+          -- Case 2: interpolate within bucket b using the Prometheus formula:
+          --   lowerBound + (upperBound - lowerBound) * (rank - cumSum[b-1]) / (cumSum[b] - cumSum[b-1])
+          bounds[b-1] + (bounds[b]-bounds[b-1]) *
+              (minus(rank, arrayElement(arrayCumSum(buckets), minus(b, 1))) /
+               minus(arrayElement(arrayCumSum(buckets), b), arrayElement(arrayCumSum(buckets), minus(b, 1)))),
+          -- Case 3: first bucket (b=1), lower bound is 0:
+          --   upperBound * (rank / cumSum[1])
+          bounds[b] * (rank / arrayElement(arrayCumSum(buckets),b))
+       )
+    );
+
+-- migrate:down
+
+DROP FUNCTION func_histogram_v2;