Grammar fix in MovePicker::next_move

Thanks to Lyudmil Antonov and Michel Van den Bergh
for spotting this and suggesting the fix.

No functional change.
Fix null reduction formula

Depth is already dependent on the actual value
of ONE_PLY, in particular can be expressed like:

Depth = n * ONE_PLY

And because formula is used to calculate R that is
also dependent on the value of ONE_PLY and can be
expressed like:

R = x * ONE_PLY

We don't want to divide depth by a 'ply' value but
directly by an integer number.

Spotted by sf-x

No functional change.
Reduce VALUE_KNOWN_WIN to 10000

With some positions like

8/8/8/2p2K2/1pp5/br1p1b2/2p2r2/qqkqq3 w - -

The eval score is higher than VALUE_INFINITE because
is the sum of VALUE_KNOWN_WIN plus a big material
advantage. This leads to an assert. Here are the
steps to reproduce:

Compile SF with debug=yes then do

./stockfish
position fen 8/8/8/2p2K2/1pp5/br1p1b2/2p2r2/qqkqq3 w - -
go depth 1

This patch fixes the issue in this case, but do exsist
other positions for which the patch is not enough and
we will need to limit the eval score to be sure not
overflow the limit.

Note that is not possible to increase the value of
VALUE_INFINITE because should remain within int16_t
type to be stored in a TT entry.

bench: 7356053
Tweak bishop PSQT tables

Tuned after 49K iterations of SPSA.

Passed both short TC:
LLR: 2.97 (-2.94,2.94) [-1.50,4.50]
Total: 14231 W: 2684 L: 2542 D: 9005

And long TC:
LLR: 2.94 (-2.94,2.94) [0.00,4.00]
Total: 87556 W: 13757 L: 13342 D: 60457

bench: 6875743
H-file penalty and center bonus

After almost 50K at long TC it seems
slightly positive:

ELO: 1.73 +-1.8 (95%) LOS: 97.3%
Total: 47122 W: 7507 L: 7273 D: 32342

bench: 8430785
Better document razoring

Use ralpha instead of rbeta

* rbeta is confusing people. It took THREE attempts to code razoring
at PV nodes correctly in a recent test, because of the rbeta trick.
Unnecessary tricks should be avoided.

* The more correct and self-documenting way of doing this, is to say
that we use a zero window around alpha-margin, not beta-margin.
The fact that, because we only do it at PV nodes, alpha happens to be
beta-1 and that the current stuff with rbeta works, may be correct,
but is confusing.

Remove the misleading and partially erroneous comment about returning
v + margin:

* comments should explain what the code does, not what it could have done.

* this comment is partially wrong in saying that v+margin is "logical",
  and that it is "surprising" that is doesn't work.

From a theoretical perspective, at least 3 ways of doing this are equally
defendable:

1/ fail hard: return alpha: The most conservative. We bet that the search
will fail low, but we don't know by how much and don't want to take risks.

2/ aggressive fail soft: return v (what the current code does). This
corresponds to normal fail soft, with the added assumption that we don't
care about the reduction effect (see below point 3/)

3/ conservative fail soft: return v + margin. If the reduced search (qsearch)
gives us a score <= v, we bet that the non reduced search will give us a
score <= v + margin.

* Saying that 2/ is "logical" implies that 1/ and 3/ are not, which is
arguably wrong. Besides, experimental results tell us that 2/ beats 3/,
and that's not something we can argue against: experimental results are
the only trusted metric.

* Also, with the benefit of hindsight, I don't think the fact that 2/ is
better than 3/ is surprising at all. The point is that it is YOUR turn to
move, and you are assuming that by NOT playing (and letting the opponent
capture your hanging pieces in QS) you cannot generally GAIN razor_margin(depth).

No functional change.
Better document null search window

Hopefully this patch makes the code more:

* Self-documenting: Null search is always a zero window search,
  because it is testing for a fail high. It should never be done
  on a full window! The current code only works because we don't
  do it at PV nodes, and therefore (alpha, beta) = (beta-1, beta):
  that's the kind of "clever" trick we should avoid.

* Idiot-proof: If we want to enable null search at PV nodes, all we
  need to do now is comment out the !PvNode condition. It's that simple!

In theory, null search should not be done at PV nodes, because PV nodes
should never fail high. But in practice, they DO fail high, because of
aspiration windows, and search inconsistencies, for example. So it makes
sense to keep that flexibility in the code.

No functional change.
Retire null search verification

Tested with SPRT in simplification mode [-4.00,0.00],
this ensures that the patch is (very probably) not
a regression.

Passed both short TC
LLR: 2.95 (-2.94,2.94) [-4.00,0.00]
Total: 27543 W: 4278 L: 4209 D: 19056

And long TC
LLR: 2.95 (-2.94,2.94) [-4.00,0.00]
Total: 39483 W: 7325 L: 7305 D: 24853

bench: 8347121
Don't fear races when are harmless

Actually race conditions do exist in an engine, just
think for a moment to TT concurrent access. Racy code
is not a problem per se, if the consequences are well
known and correctly handled.

In case of TT access we ensure that the TT move is validated
before to be tried, here we just retry the same move in less
that 1 case out of a million: this is totally harmless considering
that very probably the second time the move is tried we get
immediately a TT hit and search quickly returns.

So we simplify the code for no harm.

No fuctional change (in single thread case)
Inline common path of pos.gives_check

Test for common case which, when running default
stockfish bench, avoids 96% of 19 million calls to
pos.gives_check().

Yields to a 2-4% speed up according to platform.

Passed fishtest at STC
LLR: 2.97 (-2.94,2.94) [-1.50,4.50]
Total: 12441 W: 2333 L: 2196 D: 7912
http://tests.stockfishchess.org/tests/view/52f02d790ebc5901df50f887

Passed fishtest at LTC
LLR: 2.97 (-2.94,2.94) [0.00,6.00]
Total: 42175 W: 6702 L: 6409 D: 29064
http://tests.stockfishchess.org/tests/view/52f0dbe00ebc5901df50f8a0

No functional change.
Rewrite previous patch removing the macro

No functional change.
Assorted tweaks from DON

Mainly renames and some little code style improvment,
inspired by looking at DON sources:

https://github.com/erashid/DON

No functional change.
Faster handling of king captures in Position::see

Another SEE speed up that passed the SPRT short TC test!

LLR: 2.96 (-2.94,2.94) [-1.50,4.50]
Total: 81337 W: 15060 L: 14745 D: 51532

No functional change.
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