1 files changed, 31 insertions, 0 deletions

diff --git a/src/solvers/h48/gendata_h48.h b/src/solvers/h48/gendata_h48.h
index 5da9dc3..2f55d3e 100644
--- a/src/solvers/h48/gendata_h48.h
+++ b/src/solvers/h48/gendata_h48.h
@@ -277,6 +277,37 @@ gendata_h48k2(gendata_h48_arg_t *arg)
         static const uint8_t shortdepth = 8;
         static const uint64_t capacity = 10000019;
         static const uint64_t randomizer = 10000079;
+
+        /*
+         * A good base value for the k=2 tables have few positions with value
+         * 0, because those are treated as lower bound 0 and require a second
+         * lookup in another table, and at the same time not too many positions
+         * with value 3, because some of those are under-estimates.
+         *
+         * The following values for the base have been hand-picked. I first
+         * performed some statistics on the frequency of these values, but
+         * they turned out to be unreliable. I have not figured out why yet.
+         * In the end I resorted to generating the same table with multiple
+         * base value and see what was best.
+         *
+         * A curious case is h3, which has this distribution for base 8:
+         *   [0] = 6686828
+         *   [1] = 63867852
+         *   [2] = 392789689
+         *   [3] = 477195231
+         *
+         * and this for base 9:
+         *   [0] = 70554680
+         *   [1] = 392789689
+         *   [2] = 462294676
+         *   [3] = 14900555
+         *
+         * I ended up picking base 8 to have a much lower count of elements
+         * with value 0, at the cost of a less precise estimate for the higher
+         * values. But I am not 100% confident this is the optimal choice,
+         * so I'll leave it here for future considerations.
+         */
+         
         static const uint8_t base[] = {
                 [0]  = 8,
                 [1]  = 8,