Avoid roundoff trouble in choose_lts_step_size

src/Time/ChooseLtsStepSize.cpp

@@ -18,10 +18,11 @@ TimeDelta choose_lts_step_size(const Time& time, const double desired_step) {
   const TimeDelta full_slab =
       desired_step > 0.0 ? time.slab().duration() : -time.slab().duration();
   const double desired_step_count = full_slab.value() / desired_step;
-  const size_t desired_step_power =
-      desired_step_count <= 1
-          ? 0
-          : static_cast<size_t>(std::ceil(std::log2(desired_step_count)));
+  // log2 is a slowly increasing function, so log2(2^n + eps) may give
+  // n because of floating-point truncation.  The inner ceil call
+  // avoids this problem.
+  const auto desired_step_power =
+      static_cast<size_t>(std::ceil(std::log2(std::ceil(desired_step_count))));
 
   // Ensure we will hit the slab boundary if we continue taking
   // constant-sized steps.

tests/Unit/Time/Actions/Test_ChangeStepSize.cpp

@@ -3,6 +3,7 @@
 
 #include "Framework/TestingFramework.hpp"
 
+#include <limits>
 #include <memory>
 #include <pup.h>
 #include <string>
@@ -207,6 +208,20 @@ SPECTRE_TEST_CASE("Unit.Time.Actions.ChangeStepSize", "[Unit][Time][Actions]") {
           reject_step ? -slab.duration() / 8 : -slab.duration() / 4,
           reject_step ? std::optional{std::make_unique<StepRejector>(0.5)}
                       : std::nullopt);
+
+    // Check for roundoff issues
+    check(true, std::make_unique<TimeSteppers::AdamsBashforth>(1), {},
+          slab.start() + slab.duration() / 4,
+          slab_length / 16. / (1.0 + std::numeric_limits<double>::epsilon()),
+          slab.duration() / 32,
+          reject_step ? std::optional{std::make_unique<StepRejector>(0.5)}
+                      : std::nullopt);
+    check(false, std::make_unique<TimeSteppers::AdamsBashforth>(1), {},
+          slab.end() - slab.duration() / 4,
+          slab_length / 16. / (1.0 + std::numeric_limits<double>::epsilon()),
+          -slab.duration() / 32,
+          reject_step ? std::optional{std::make_unique<StepRejector>(0.5)}
+                      : std::nullopt);
   }
 
   {