Revert "Retire null search verification"

Although does not change ELO level, it seems
verification is useful in many zugzwang positions
as reported by many sources.

So revert this simplification.

bench: 8430785
Move magic random to RKISS

When initializing the magic numbers used to
compute sliding attacks, we endless generate a
random and test it as a possible magic.

In the general case this takes a lot of iterations,
but here, insteaad of picking a casual random, we
rotate it a couple of times and generate a number that
we know has a good probability to be a magic candidate.

This is becuase the quantities by which we rotate the
number are known in advance to produce quickly a good
canidate.

The patch, inspired by DON, just moves the shuffle to RKISS
changing the boosters to take in account a left rotation
instead of a right rotation as in the original.

No functional change.
Simplify time management

Tested with simplification mode SPRT[-4, 0]

Passed both short TC
LLR: 2.95 (-2.94,2.94) [-4.00,0.00]
Total: 34102 W: 6184 L: 6144 D: 21774

And long TC
LLR: 2.96 (-2.94,2.94) [-4.00,0.00]
Total: 16518 W: 2647 L: 2545 D: 11326

And also 40/10 TC
LLR: 2.95 (-2.94,2.94) [-4.00,0.00]
Total: 22406 W: 4390 L: 4312 D: 13704

bench: 8430785
Fix a compiler warning

Latest master triggers a compiler warning due
to comparing int64_t to uint64_t.

notation.cpp: In Funktion »std::string pretty_pv(Position&, int, Value, int64_t, Move*)«:
notation.cpp:230:30: Warnung: Vergleich zwischen vorzeichenbehafteten und vorzeichenlosen Ganzzahlausdrücken [-Wsign-compare]

This patch should fix it.

No functional change.
Additional renaming from DON

Assorted renaming and triviality.

No functional change.
Fix magic boosters conversion

Fix small overflow error while converting
magic boosters from right rotate to left rotate,
in particular booster 38 was converted to 4122
instead of the corrcet value 26.

Formula used was:

s1 = original & 63, s2 = (original >> 6) & 63;
new = (64 - s1) | ((64 - s2) << 6);

Instead of:

s1 = original & 63, s2 = (original >> 6) & 63;
new = ((64 - s1) & 63) | (((64 - s2) & 63) << 6);

This has no impact in number of cycles needed, but
just in the resultig number that yields to a rotate
amount bigger than 63.

Spotted by Ehsan Rashid.

No functional change.
Return static eval when reaching MAX_PLY

Makes more sense than returning a draw score. Tested
with reduced MAX_PLY = 30 and passed both short TC
LLR: 2.95 (-2.94,2.94) [-1.50,4.50]
Total: 17434 W: 3345 L: 3194 D: 10895

And long TC
LLR: 2.97 (-2.94,2.94) [0.00,6.00]
Total: 2610 W: 488 L: 373 D: 1749

With current limit of MAX_PLY = 100 the patch should not
introduce any measurable change, nevertheless is the correct
approach.

Idea of returning eval is from  Michel Van den Bergh.

bench: 8430785
Assorted renaming in search

Inspired by DON.

No functional change.
Rename ProbCut to Multicut

The teqnique used is actually MultiCut:

https://chessprogramming.wikispaces.com/Multi-Cut

And not ProbCut:

https://chessprogramming.wikispaces.com/ProbCut

No functional change.
Reformat of eval tracing code

Also assorted rename while there.

No functional change.
Restore PorbCut name

Actually MultiCut is too different from current scheme.
Note that neither ProbCut is exactly what we do because
we try just a handful of captures instead of all moves,
nevertheless it seems more in line with what we do.

Suggested by Joona.

No functional change.
Fix material key for King

Currently king has no material key associated because
it can never happen to find a legal position without
both kings, so there is no need to keep track of it.

The consequence is that a position with only the two
kings has material key set at zero and if the material
hash table is empty any entry will match and this is
wrong.

Normally bug is hidden becuase the checking for a draw
with pos.is_draw() is done earlier than evaluate() call,
so that we never check in gameplay the material key of a
position with two kings.

Nevertheless the bug is there and can be reproduced setting
at startup a position with only two kings and typing
'eval' from prompt.

The fix is very simple: add a random key also for the king.

Also fixed the condition in material.cpp to avoid asserting
when a 'just 2 kings' postion is evaluated.

No functional change.
Increase MAX_PLY from 100 to 120

Under some very rare case 100 plies of search
could be not enough. Increasing more could lead
to crashes due to reached stack size limit on
some platforms.

Strongly requested by Uri.

bench: 8430785
Sync code style in material.cpp

Update to use common code style.

No functional change.
Update SEE to return a Value

It seems more natural because the actual returned
value is from PieceValue[] array.

No functional change.
Don't update pieceCount for ALL_PIECES

It is currently unused and only adds
overhead for nothing.

Also set proper type of chess960.

No functional change.
Avoid recalculating CheckInfo in generate_castling()

No functional change.
Distribute part of first move time to other moves

Passed both short TC:
LLR: 2.97 (-2.94,2.94) [-1.50,4.50]
Total: 18907 W: 3475 L: 3322 D: 12110

And long TC:
LLR: 2.96 (-2.94,2.94) [0.00,6.00]
Total: 19044 W: 2997 L: 2811 D: 13236

bench: 8430785
Fix an assert in Probcut

When running the following position:

8/kPp5/2P3p1/p1P1p1P1/2PpPp2/3p1p2/3P1P2/5K2 w - - 0 1

An assert is raised at depth 92:

assert(-VALUE_INFINITE <= alpha && alpha < beta && beta <= VALUE_INFINITE);

This is because it happens that beta = 29832,
so rbeta = 30032 that is > VALUE_INFINITE

Bug spotted and analyzed by Uri, fix suggested by Joerg.

Other fixes where possible but this one is pointed
exactly at the source of the bug, so it is the best
from a code documentation point of view.

bench: 8430785
Fix a warning with Intel compiler

warning #2259: non-pointer conversion from "int" to
"uint8_t={unsigned char}" may lose significant bits

No functional change