Rework perft implementation

Unify various perft functions and move all the code
to search.cpp.

Avoid perft implementation to be splitted between
benchmark.cpp (where it has no reason to be) and
search.cpp

No functional and no speed change (tested).
Move to_char() and to_string() to notation
Where they better belong.

Also, this removes '#include <string>' from types.h, which reduces the amount of code to compile (every
translation unit includes types.h).

No functional change.
Retire move_to_san()

Now "Write Search Log" will pring moves in UCI format, consistent with all the rest. This functionality is
not aimed at end-users anyway. It's hardly useful at all, in fact. Also, pretty-printing SAN moves is
something that better belongs in the GUI than in the engine.

No functional change.
Fix perft 1

Compute correct number of moves for this corner case.

A smal bug crept in after recent perft rework.

No functional change.