Optimize calendar:gregorian_days_to_date/1

This patch improves the performance of calendar:gregorian_days_to_date/1
by changing the algorithm for finding the year to log-logarithmic.
The old implementation has linear complexity, which makes function
too slow for large values.
For example:
There is an API that allows you to create events for future dates.
There are users of this API who, for some reasons, choose dates
very far in the future. In such conditions, function works very slow.
New implementation based on interpolation search, takes 1 or 2
iterations at most cases and free from such a flaw.
A unit test was also developed to illustrate the speed of a function
at large values.

1 files changed, 28 insertions, 11 deletions

diff --git a/lib/stdlib/src/calendar.erl b/lib/stdlib/src/calendar.erl
index bb5d450cd6..3a083d9fda 100644
--- a/lib/stdlib/src/calendar.erl
+++ b/lib/stdlib/src/calendar.erl
@@ -529,24 +529,41 @@ valid_date({Y, M, D}) ->
 
 %% day_to_year(DayOfEpoch) = {Year, DayOfYear}
 %%
-%% The idea here is to first guess a year, and then adjust. Although
-%% the implementation is recursive, at most 1 or 2 recursive steps
+%% The idea here is to first set the upper and lower bounds for a year,
+%% and then adjust a range by interpolation search. Although complexity
+%% of the algorithm is log(log(n)), at most 1 or 2 recursive steps
 %% are taken.
-%% If DayOfEpoch is very large, we need far more than 1 or 2 iterations,
-%% since we just subtract a yearful of days at a time until we're there.
 %%
 -spec day_to_year(non_neg_integer()) -> {year(), day_of_year()}.
 day_to_year(DayOfEpoch) when DayOfEpoch >= 0 ->
-    Y0 = DayOfEpoch div ?DAYS_PER_YEAR,
-    {Y1, D1} = dty(Y0, DayOfEpoch, dy(Y0)),
+    YMax = DayOfEpoch div ?DAYS_PER_YEAR,
+    YMin = DayOfEpoch div ?DAYS_PER_LEAP_YEAR,
+    {Y1, D1} = dty(YMin, YMax, DayOfEpoch, dy(YMin), dy(YMax)),
     {Y1, DayOfEpoch - D1}.
 
--spec dty(year(), non_neg_integer(), non_neg_integer()) ->
+-spec dty(year(), year(), non_neg_integer(), non_neg_integer(),
+    non_neg_integer()) ->
 		{year(), non_neg_integer()}.
-dty(Y, D1, D2) when D1 < D2 -> 
-    dty(Y-1, D1, dy(Y-1));
-dty(Y, _D1, D2) ->
-    {Y, D2}.
+dty(Min, Max, _D1, DMin, _DMax) when Min == Max ->
+    {Min, DMin};
+dty(Min, Max, D1, DMin, DMax) ->
+    Diff = Max - Min,
+    Mid = Min + (Diff * (D1 - DMin)) div (DMax - DMin),
+    MidLength =
+        case is_leap_year(Mid) of
+            true -> ?DAYS_PER_LEAP_YEAR;
+            false -> ?DAYS_PER_YEAR
+        end,
+    case dy(Mid) of
+        D2 when D1 < D2 ->
+            NewMax = Mid - 1,
+            dty(Min, NewMax, D1, DMin, dy(NewMax));
+        D2 when D1 - D2 >= MidLength ->
+            NewMin = Mid + 1,
+            dty(NewMin, Max, D1, dy(NewMin), DMax);
+        D2 ->
+            {Mid, D2}
+    end.
 
 %%
 %% The Gregorian days of the iso week 01 day 1 for a given year.