Calculate intersetion of redis hll metrics

In order to enable better analysis of collected usage metrics
we should enable obtaining value of intersection of any metrics.
As a first iteration we focus on Redis HLL counter
based metrics.

lib/gitlab/usage_data_counters/aggregated_metrics/common.yml

 #- name: unique name of aggregated metric
 #  operator: aggregation operator. Valid values are:
 #             - "ANY": counts unique elements that were observed triggering any of following events
+#             - "ALL": counts unique elements that were observed triggering all of following events
 #  events: list of events names to aggregate into metric. All events in this list must have the same 'redis_slot' and 'aggregation' attributes
 #           see from lib/gitlab/usage_data_counters/known_events.yml for the list of valid events.
 ---
 - name: product_analytics_test_aggregated_metrics
   operator: ANY
   events: ['i_search_total', 'i_search_advanced', 'i_search_paid']
+- name: product_analytics_test_combined_events
+  operator: ALL
+  events: ['i_search_total', 'i_search_advanced', 'i_search_paid']

lib/gitlab/usage_data_counters/hll_redis_counter.rb

@@ -17,8 +17,10 @@ module Gitlab
 
       KNOWN_EVENTS_PATH = File.expand_path('known_events/*.yml', __dir__)
       ALLOWED_AGGREGATIONS = %i(daily weekly).freeze
+      UNION_OF_AGGREGATED_METRICS = 'ANY'
+      INTERSECTION_OF_AGGREGATED_METRICS = 'ALL'
+      ALLOWED_METRICS_AGGREGATIONS = [UNION_OF_AGGREGATED_METRICS, INTERSECTION_OF_AGGREGATED_METRICS].freeze
       AGGREGATED_METRICS_PATH = File.expand_path('aggregated_metrics/*.yml', __dir__)
-      ALLOWED_METRICS_AGGREGATIONS = %w[ANY].freeze
 
       # Track event on entity_id
       # Increment a Redis HLL counter for unique event_name and entity_id
@@ -113,9 +115,79 @@ module Gitlab
         private
 
         def calculate_count_for_aggregation(aggregation, start_date:, end_date:)
-          validate_aggregation_operator!(aggregation[:operator])
+          case aggregation[:operator]
+          when UNION_OF_AGGREGATED_METRICS
+            calculate_events_union(event_names: aggregation[:events], start_date: start_date, end_date: end_date)
+          when INTERSECTION_OF_AGGREGATED_METRICS
+            calculate_events_intersections(event_names: aggregation[:events], start_date: start_date, end_date: end_date)
+          else
+            raise UnknownAggregationOperator, "Events should be aggregated with one of operators #{ALLOWED_METRICS_AGGREGATIONS}"
+          end
+        end
+
+        # calculate intersection of 'n' sets based on inclusion exclusion principle https://en.wikipedia.org/wiki/Inclusion%E2%80%93exclusion_principle
+        # this method will be extracted to dedicated module with https://gitlab.com/gitlab-org/gitlab/-/issues/273391
+        def calculate_events_intersections(event_names:, start_date:, end_date:, subset_powers_cache: Hash.new({}))
+          # calculate power of intersection of all given metrics from inclusion exclusion principle
+          # |A + B + C| = (|A| + |B| + |C|) - (|A & B| + |A & C| + .. + |C & D|) + (|A & B & C|)  =>
+          # |A & B & C| = - (|A| + |B| + |C|) + (|A & B| + |A & C| + .. + |C & D|) + |A + B + C|
+          # |A + B + C + D| = (|A| + |B| + |C| + |D|) - (|A & B| + |A & C| + .. + |C & D|) + (|A & B & C| + |B & C & D|) - |A & B & C & D| =>
+          # |A & B & C & D| = (|A| + |B| + |C| + |D|) - (|A & B| + |A & C| + .. + |C & D|) + (|A & B & C| + |B & C & D|) - |A + B + C + D|
+
+          # calculate each components of equation except for the last one |A & B & C & D| = (|A| + |B| + |C| + |D|) - (|A & B| + |A & C| + .. + |C & D|) + (|A & B & C| + |B & C & D|) -  ...
+          subset_powers_data = subsets_intersection_powers(event_names, start_date, end_date, subset_powers_cache)
+
+          # calculate last component of the equation  |A & B & C & D| = .... - |A + B + C + D|
+          power_of_union_of_all_events = begin
+            subset_powers_cache[event_names.size][event_names.join('_+_')] ||= \
+              calculate_events_union(event_names: event_names, start_date: start_date, end_date: end_date)
+          end
 
-          count_unique_events(event_names: aggregation[:events], start_date: start_date, end_date: end_date) do |events|
+          # in order to determine if part of equation (|A & B & C|, |A & B & C & D|), that represents the intersection that we need to calculate,
+          # is positive or negative in particular equation we need to determine if number of subsets is even or odd. Please take a look at two examples below
+          # |A + B + C| = (|A| + |B| + |C|) - (|A & B| + |A & C| + .. + |C & D|) + |A & B & C|  =>
+          # |A & B & C| = - (|A| + |B| + |C|) + (|A & B| + |A & C| + .. + |C & D|) + |A + B + C|
+          # |A + B + C + D| = (|A| + |B| + |C| + |D|) - (|A & B| + |A & C| + .. + |C & D|) + (|A & B & C| + |B & C & D|) - |A & B & C & D| =>
+          # |A & B & C & D| = (|A| + |B| + |C| + |D|) - (|A & B| + |A & C| + .. + |C & D|) + (|A & B & C| + |B & C & D|) - |A + B + C + D|
+          subset_powers_size_even = subset_powers_data.size.even?
+
+          # sum all components of equation except for the last one |A & B & C & D| = (|A| + |B| + |C| + |D|) - (|A & B| + |A & C| + .. + |C & D|) + (|A & B & C| + |B & C & D|) -  ... =>
+          sum_of_all_subset_powers = sum_subset_powers(subset_powers_data, subset_powers_size_even)
+
+          # add last component of the equation |A & B & C & D| = sum_of_all_subset_powers - |A + B + C + D|
+          sum_of_all_subset_powers + (subset_powers_size_even ? power_of_union_of_all_events : -power_of_union_of_all_events)
+        end
+
+        def sum_subset_powers(subset_powers_data, subset_powers_size_even)
+          sum_without_sign =  subset_powers_data.to_enum.with_index.sum do |value, index|
+            (index + 1).odd? ? value : -value
+          end
+
+          (subset_powers_size_even ? -1 : 1) * sum_without_sign
+        end
+
+        def subsets_intersection_powers(event_names, start_date, end_date, subset_powers_cache)
+          subset_sizes = (1..(event_names.size - 1))
+
+          subset_sizes.map do |subset_size|
+            if subset_size > 1
+              # calculate sum of powers of intersection between each subset (with given size) of metrics:  #|A + B + C + D| = ... - (|A & B| + |A & C| + .. + |C & D|)
+              event_names.combination(subset_size).sum do |events_subset|
+                subset_powers_cache[subset_size][events_subset.join('_&_')] ||= \
+                  calculate_events_intersections(event_names: events_subset, start_date: start_date, end_date: end_date, subset_powers_cache: subset_powers_cache)
+              end
+            else
+              # calculate sum of powers of each set (metric) alone  #|A + B + C + D| = (|A| + |B| + |C| + |D|) - ...
+              event_names.sum do |event|
+                subset_powers_cache[subset_size][event] ||= \
+                  unique_events(event_names: event, start_date: start_date, end_date: end_date)
+              end
+            end
+          end
+        end
+
+        def calculate_events_union(event_names:, start_date:, end_date:)
+          count_unique_events(event_names: event_names, start_date: start_date, end_date: end_date) do |events|
             raise SlotMismatch, events unless events_in_same_slot?(events)
             raise AggregationMismatch, events unless events_same_aggregation?(events)
           end
@@ -226,12 +298,6 @@ module Gitlab
           end.flatten
         end
 
-        def validate_aggregation_operator!(operator)
-          return true if ALLOWED_METRICS_AGGREGATIONS.include?(operator)
-
-          raise UnknownAggregationOperator.new("Events should be aggregated with one of operators #{ALLOWED_METRICS_AGGREGATIONS}")
-        end
-
         def weekly_redis_keys(events:, start_date:, end_date:)
           weeks = end_date.to_date.cweek - start_date.to_date.cweek
           weeks = 1 if weeks == 0

spec/lib/gitlab/usage_data_counters/hll_redis_counter_spec.rb

@@ -277,29 +277,23 @@ RSpec.describe Gitlab::UsageDataCounters::HLLRedisCounter, :clean_gitlab_redis_s
     end
   end
 
-  context 'aggregated metrics' do
+  context 'aggregated_metrics_data' do
     let(:known_events) do
       [
         { name: 'event1_slot', redis_slot: "slot", category: 'category1', aggregation: "weekly" },
         { name: 'event2_slot', redis_slot: "slot", category: 'category2', aggregation: "weekly" },
-        { name: 'event3', category: 'category2', aggregation: "weekly" }
-      ].map(&:with_indifferent_access)
-    end
-
-    let(:aggregated_metrics) do
-      [
-        { name: 'gmau_1', events: %w[event1_slot event2_slot], operator: "ANY" },
-        { name: 'gmau_2', events: %w[event3], operator: "ANY" }
+        { name: 'event3_slot', redis_slot: "slot", category: 'category3', aggregation: "weekly" },
+        { name: 'event5_slot', redis_slot: "slot", category: 'category4', aggregation: "weekly" },
+        { name: 'event4', category: 'category2', aggregation: "weekly" }
       ].map(&:with_indifferent_access)
     end
 
     before do
       allow(described_class).to receive(:known_events).and_return(known_events)
-      allow(described_class).to receive(:aggregated_metrics).and_return(aggregated_metrics)
     end
 
     shared_examples 'aggregated_metrics_data' do
-      context 'no combination is tracked' do
+      context 'no aggregated metrics is defined' do
         it 'returns empty hash' do
           allow(described_class).to receive(:aggregated_metrics).and_return([])
 
@@ -307,33 +301,76 @@ RSpec.describe Gitlab::UsageDataCounters::HLLRedisCounter, :clean_gitlab_redis_s
         end
       end
 
-      context 'there are some combinations defined' do
+      context 'there are aggregated metrics defined' do
+        before do
+          allow(described_class).to receive(:aggregated_metrics).and_return(aggregated_metrics)
+        end
+
+        context 'with ALL operator' do
+          let(:aggregated_metrics) do
+            [
+              { name: 'gmau_1', events: %w[event1_slot event2_slot], operator: "ALL" },
+              { name: 'gmau_2', events: %w[event1_slot event2_slot event3_slot], operator: "ALL" },
+              { name: 'gmau_3', events: %w[event1_slot event2_slot event3_slot event5_slot], operator: "ALL" },
+              { name: 'gmau_4', events: %w[event4], operator: "ALL" }
+            ].map(&:with_indifferent_access)
+          end
+
+          it 'returns the number of unique events for all known events' do
+            results = {
+              'gmau_1' => 3,
+              'gmau_2' => 2,
+              'gmau_3' => 1,
+              'gmau_4' => 3
+            }
+
+            expect(aggregated_metrics_data).to eq(results)
+          end
+        end
+
+        context 'with ANY operator' do
+          let(:aggregated_metrics) do
+            [
+              { name: 'gmau_1', events: %w[event3_slot event5_slot], operator: "ANY" },
+              { name: 'gmau_2', events: %w[event1_slot event2_slot event3_slot event5_slot], operator: "ANY" },
+              { name: 'gmau_3', events: %w[event4], operator: "ANY" }
+            ].map(&:with_indifferent_access)
+          end
+
           it 'returns the number of unique events for all known events' do
             results = {
               'gmau_1' => 2,
-            'gmau_2' => 3
+              'gmau_2' => 3,
+              'gmau_3' => 3
             }
 
             expect(aggregated_metrics_data).to eq(results)
           end
         end
       end
+    end
 
     describe '.aggregated_metrics_weekly_data' do
       subject(:aggregated_metrics_data) { described_class.aggregated_metrics_weekly_data }
 
       before do
         described_class.track_event(entity1, 'event1_slot', 2.days.ago)
+        described_class.track_event(entity2, 'event1_slot', 2.days.ago)
+        described_class.track_event(entity3, 'event1_slot', 2.days.ago)
         described_class.track_event(entity1, 'event2_slot', 2.days.ago)
+        described_class.track_event(entity2, 'event2_slot', 3.days.ago)
         described_class.track_event(entity3, 'event2_slot', 3.days.ago)
+        described_class.track_event(entity1, 'event3_slot', 3.days.ago)
+        described_class.track_event(entity2, 'event3_slot', 3.days.ago)
+        described_class.track_event(entity2, 'event5_slot', 3.days.ago)
 
         # events out of time scope
         described_class.track_event(entity3, 'event2_slot', 8.days.ago)
 
         # events in different slots
-        described_class.track_event(entity1, 'event3', 2.days.ago)
-        described_class.track_event(entity2, 'event3', 2.days.ago)
-        described_class.track_event(entity4, 'event3', 2.days.ago)
+        described_class.track_event(entity1, 'event4', 2.days.ago)
+        described_class.track_event(entity2, 'event4', 2.days.ago)
+        described_class.track_event(entity4, 'event4', 2.days.ago)
       end
 
       it_behaves_like 'aggregated_metrics_data'
@@ -342,21 +379,58 @@ RSpec.describe Gitlab::UsageDataCounters::HLLRedisCounter, :clean_gitlab_redis_s
     describe '.aggregated_metrics_monthly_data' do
       subject(:aggregated_metrics_data) { described_class.aggregated_metrics_monthly_data }
 
+      it_behaves_like 'aggregated_metrics_data' do
         before do
           described_class.track_event(entity1, 'event1_slot', 2.days.ago)
-        described_class.track_event(entity1, 'event2_slot', 10.days.ago)
-        described_class.track_event(entity3, 'event2_slot', 4.weeks.ago.advance(days: 1))
+          described_class.track_event(entity2, 'event1_slot', 2.days.ago)
+          described_class.track_event(entity3, 'event1_slot', 2.days.ago)
+          described_class.track_event(entity1, 'event2_slot', 2.days.ago)
+          described_class.track_event(entity2, 'event2_slot', 3.days.ago)
+          described_class.track_event(entity3, 'event2_slot', 3.days.ago)
+          described_class.track_event(entity1, 'event3_slot', 3.days.ago)
+          described_class.track_event(entity2, 'event3_slot', 10.days.ago)
+          described_class.track_event(entity2, 'event5_slot', 4.weeks.ago.advance(days: 1))
 
           # events out of time scope
-        described_class.track_event(entity3, 'event2_slot', 4.weeks.ago.advance(days: -1))
+          described_class.track_event(entity1, 'event5_slot', 4.weeks.ago.advance(days: -1))
 
           # events in different slots
-        described_class.track_event(entity1, 'event3', 2.days.ago)
-        described_class.track_event(entity2, 'event3', 2.days.ago)
-        described_class.track_event(entity4, 'event3', 2.days.ago)
+          described_class.track_event(entity1, 'event4', 2.days.ago)
+          described_class.track_event(entity2, 'event4', 2.days.ago)
+          described_class.track_event(entity4, 'event4', 2.days.ago)
+        end
       end
 
-      it_behaves_like 'aggregated_metrics_data'
+      context 'Redis calls' do
+        let(:aggregated_metrics) do
+          [
+            { name: 'gmau_3', events: %w[event1_slot event2_slot event3_slot event5_slot], operator: "ALL" }
+          ].map(&:with_indifferent_access)
+        end
+
+        let(:known_events) do
+          [
+            { name: 'event1_slot', redis_slot: "slot", category: 'category1', aggregation: "weekly" },
+            { name: 'event2_slot', redis_slot: "slot", category: 'category2', aggregation: "weekly" },
+            { name: 'event3_slot', redis_slot: "slot", category: 'category3', aggregation: "weekly" },
+            { name: 'event5_slot', redis_slot: "slot", category: 'category4', aggregation: "weekly" }
+          ].map(&:with_indifferent_access)
+        end
+
+        it 'caches intermediate operations' do
+          allow(described_class).to receive(:known_events).and_return(known_events)
+          allow(described_class).to receive(:aggregated_metrics).and_return(aggregated_metrics)
+
+          4.downto(1) do |subset_size|
+            known_events.combination(subset_size).each do |events|
+              keys = described_class.send(:weekly_redis_keys, events: events, start_date: 4.weeks.ago.to_date, end_date: Date.current)
+              expect(Gitlab::Redis::HLL).to receive(:count).with(keys: keys).once.and_return(0)
+            end
+          end
+
+          subject
+        end
+      end
     end
   end
 end