Auto: first linear delay then exp delay

2/3 is linear and the rest (rounded down) is exp.

db/column_family.cc

@@ -904,7 +904,7 @@ int GetL0ThresholdSpeedupCompaction(int level0_file_num_compaction_trigger,
 namespace {
 const int kMemtablePenalty = 5;
 const int kNumPendingSteps = 100;
-const double kGoalMbs = 5242880.0;
+const double kGoalMbs = 3 * 1048576.0;
 }  // namespace
 
 double ColumnFamilyData::TEST_CalculateWriteDelayDivider(
@@ -1040,8 +1040,7 @@ ColumnFamilyData::CalculateWriteDelayDividerAndMaybeUpdateWriteStallCause(
   // This is calculated and set when the L0L1 compaction ends in
   // CompactionJob::Install.
   // Use this rate for the first extra slowdown files and then heavily delay the
-  // rest of the files. In any case, delay at least 2
-  // * trigger.
+  // rest of the files. In any case, delay at least 2 * trigger.
 
   // slowdown 12 ; stop 30; - start at 22
   // slowdown 12 ; stop 50; - start at 24
@@ -1054,33 +1053,51 @@ ColumnFamilyData::CalculateWriteDelayDividerAndMaybeUpdateWriteStallCause(
   auto gap = stop - slowdown;
   if ((gap > (slowdown + 2 * trigger))) {
     file_to_start_delay = slowdown + 2 * trigger;
-  } else if (slowdown + (2 * trigger) < stop) {
-    file_to_start_delay = slowdown + trigger;
   } else {
     file_to_start_delay = slowdown;
   }
-  // The goal is to reach kGoalMbs 3 steps before stop condition so that we
-  // never reach it. The formula to decide the delay percentage is: kGoalMbs =
-  // start_rate * (delay_percent ^ num_steps) where: kGoalMbs = 5 , start_rate
-  // is the l0_compaction_speed num_steps = num_L0_steps - 3.
+  // Initial delay (2/3 of the steps) is done linearly to avoid a big delay
+  // early on and the rest is exponential. For the exponential part, the goal is
+  // to reach kGoalMbs 1 step before stop condition so that we never reach it.
+  // The formula to decide the delay percentage is: kGoalMbs = start_rate *
+  // (delay_percent ^ num_delay_steps) where: start_rate is the rate at the last
+  // linear step, and num_delay_steps is num_steps_till_stop - 1.
   double l0_divider = 1;
+  const int kGoalMbStep = 1;
   const auto extra_l0_ssts =
       vstorage->l0_delay_trigger_count() - file_to_start_delay;
   if (extra_l0_ssts > 0) {
-    const auto num_L0_steps = stop - file_to_start_delay;
-    assert(num_L0_steps > 0);
-    double num_steps = num_L0_steps > 6 ? num_L0_steps - 1 : num_L0_steps;
-    auto base = (kGoalMbs / 5) / l0_base_compaction_speed();
-    // in cases where l0_base_compaction_speed() is lower than our goal Mbs
-    if (base > 1) {
-      base = 0.95;
+    const auto num_steps_till_stop = stop - file_to_start_delay;
+    assert(num_steps_till_stop > 0);
+    double num_delay_steps = num_steps_till_stop - kGoalMbStep;
+    const int linear_steps = num_delay_steps * (2.0 / 3);
+    const auto initial_linear_rate = l0_base_compaction_speed();
+    const int mb_per_linear_step =
+        (initial_linear_rate - kGoalMbs) / num_delay_steps;
+    if (extra_l0_ssts <= linear_steps) {
+      double l0_files_rate =
+          initial_linear_rate - (extra_l0_ssts * mb_per_linear_step);
+      assert(l0_files_rate > 0);
+      l0_divider = initial_linear_rate / l0_files_rate;
+    } else {
+      // calculate exponential delay from last linear step.
+      auto last_linear_step_mbs =
+          initial_linear_rate - (linear_steps * mb_per_linear_step);
+      auto base = kGoalMbs / last_linear_step_mbs;
+      // in cases where last_linear_step_mbs is lower than our goal Mbs
+      if (base > 1) {
+        base = 0.95;
+      }
+      auto num_exp_steps = num_delay_steps - linear_steps;
+      double delay_percent = std::pow(base, 1.0 / num_exp_steps);
+      assert(delay_percent > 0 && delay_percent < 1);
+      // since extra_l0_ssts == num_steps_till_stop then we're in a stop
+      // condition.
+      assert(extra_l0_ssts < num_steps_till_stop);
+      auto l0_rate = last_linear_step_mbs *
+                     std::pow(delay_percent, (extra_l0_ssts - linear_steps));
+      l0_divider = initial_linear_rate / l0_rate;
     }
-    double delay_percent = std::pow(base, 1.0 / num_steps);
-    assert(delay_percent > 0 && delay_percent < 1);
-    // since extra_l0_ssts == num_L0_steps then we're in a stop condition.
-    assert(extra_l0_ssts < num_L0_steps);
-
-    l0_divider = 1 / (std::pow(delay_percent, extra_l0_ssts));
   }
 
   if (l0_divider > biggest_divider) {