Use a formula for chain membership bonus

Passed both short TC:
LLR: 2.96 (-2.94,2.94) [-1.50,4.50]
Total: 5087 W: 1072 L: 951 D: 3064

And long TC:
LLR: 2.95 (-2.94,2.94) [0.00,6.00]
Total: 28620 W: 5042 L: 4798 D: 18780

bench: 7995098
Set timer to a fixed interval

And remove a complex (and broken) formula.

Indeed previous code was broken in case of TC with big
time increments where available_time() was too similar
to total time yielding to many time losses, so for instance:

go wtime 2600 winc 2600
info nodes 4432770 time 2601 <-- time forfeit!

maximum search time = 2530 ms
available_time = 2300 ms

For a reference and further details see:

https://groups.google.com/forum/?fromgroups=#!topic/fishcooking/dCPAvQDcm2E

Speed tested with bench disabling timer alltogheter vs timer set at
max resolution, showed we have no speed regressions both in single
core and when using all physical cores.

No functional change.
Test Easy Move if no BestMoveChanges

In case we find a very good move after a
troubled start, we don't return immediately
anymore.

Tested directly at long TC where it passed:
LLR: 2.95 (-2.94,2.94) [0.00,6.00]
Total: 13910 W: 2397 L: 2228 D: 9285

bench: 7995098
Zero redundant material imbalance terms

First coefficient in the SameColor array does an
equivalent job when folded into the LinearCoefficients
array.

All of the diagonal terms in the OppositeColor array
are redundant due to cancellation.

No functional change.
Zero more redundant coefficients

Coefficients for Bishop<->BishopPair and Bishop<->Bishop
are also pretty much redundant. By altering the values
in LinearCoefficients[] these coefficients can be zeroed
without changing the imbalance calculations in any position
with less than 3 bishops for one side.

bench: 7995098
Two more parameters eliminated

RedundantRook and RedundantQueen replaced by simple
variable RedundantMajor. Also the SameColor coefficient
for Queen<->Queen has been set by definition to 0.

The remaining 5 parameters:

LinearCoefficients[ROOK]
LinearCoefficients[QUEEN]
QuadraticCoefficientsSameColor[ROOK][ROOK]
QuadraticCoefficientsSameColor[QUEEN][ROOK]
RedundantMajor

are sufficient to equate the material imbalances for the
5 common material configurations of R, RR, Q, QR and QRR
to any desired values simultaneously.

With the chosen parameters there should be no functional
change unless one side has more than 2 rooks or more
than 1 queen. For example bench from the start position
using the commands:

./stockfish
go depth 16

produces identical output except for one extra node
in the last iteration.

bench: 8198094
Retire eval margin and gains

1/ eval margin and gains removed:
 - gains removed by Value(128): search() and qsearch() now behave consistently!

2/ futility_margin()
 - testing showed that there is no added value in this weird (log(depth), movecount)
   formula, and a much simpler linear formula is just as good. In fact, it is most
   likely better, as it is not yet optimally tuned.
 - the new simplified formula also means we get rid of FutilityMargins[], its
   initialization code, and more importantly ss->futilityMoveCount, and the hacky
   code that updates it throughout the search().
 - the current formula gives negative futility margins, and there is a hidden interaction
   between the move coutn pruning formula and the futility margin one: what happens is
   that MCP is supposed to be triggered before we use the non-sensical negative futility
   margins.

3/ unify pre & post futility pruning
 - pre futility pruning (what SF calls value based pruning) used depth < 7 plies,
   while post futility pruning (what SF calls static null move pruning) used depth < 4 plies.
 - also the condition depth < 7 in pre futility pruning was not obvious, and it seemd
   to be depth < 16 (futility_margin() returns an infinite value when depth >= 7).

Tested with fixed number of games both at short TC:
ELO: 0.82 +-2.1 (95%) LOS: 77.3%
Total: 40000 W: 7939 L: 7845 D: 24216

And long TC
ELO: 0.59 +-2.0 (95%) LOS: 71.9%
Total: 40000 W: 6876 L: 6808 D: 26316

bench: 10206576
Restrict mobility of pinned pieces

Passed both short TC:
LLR: 3.00 (-2.94,2.94) [-1.50,4.50]
Total: 54342 W: 10950 L: 10692 D: 32700

And long TC:
LLR: 2.95 (-2.94,2.94) [0.00,6.00]
Total: 61976 W: 10654 L: 10251 D: 41071

This patch introduces a slowdown of 3.5 % !!!!!

bench: 7911558
Revert "Retire eval margin and gains"

This reverts commit ecd07e51d0f03ccd3e41e5634518b299989254dd.

Patch was incorrect and partial. It will be reapplied in
the correct form.

bench: 9189063
Futility pruning simplification

1/ eval margin and gains removed:
16bit are now free on TT entries, due to the removal of eval margin. may be useful
in the future :) gains removed: use instead by Value(128). search() and qsearch()
are now consistent in this regard.

2/ futility_margin()
linear formula instead of complex (log(depth), movecount) formula.

3/ unify pre & post futility pruning
pre futility pruning used depth < 7 plies, while post futility pruning used
depth < 4 plies. Now it's always depth < 7.

Tested with fixed number of games both at short TC:
ELO: 0.82 +-2.1 (95%) LOS: 77.3%
Total: 40000 W: 7939 L: 7845 D: 24216

And long TC
ELO: 0.59 +-2.0 (95%) LOS: 71.9%
Total: 40000 W: 6876 L: 6808 D: 26316

bench 7243575
Fix compile in debug mode

No functional change.
Fix printing of incorrect PV in some cases

As, Gary (that analyzed the bug) says:

SF does not print a PV when the original best move fails low,
we hit our time allowance, and stop the search.  The output from
the SF search is below.  It was failing low on Ne1 at depth 34.
Then, we get bestmove Qd3, but no PV change.

info depth 34 seldepth 45 score cp 38 upperbound nodes 483484489 nps 15464575 time 31264 multipv 1 pv f3e1 h5h4 e1d3 h4g3 f2g3 a6f6 f1f6 e7f6 d1a4 f6e7 a1f1 d8f8 a4b3 b7b6 b3c2 f7f6 c2a4 h3g5 b2b3 g5f7 a4c6 f7d6 h1g2 f6f5 e4f5 d6f5
info depth 34 seldepth 45 score cp 38 upperbound nodes 483484489 nps 15464575 time 31264 multipv 1 pv f3e1 h5h4 e1d3 h4g3 f2g3 a6f6 f1f6 e7f6 d1a4 f6e7 a1f1 d8f8 a4b3 b7b6 b3c2 f7f6 c2a4 h3g5 b2b3 g5f7 a4c6 f7d6 h1g2 f6f5 e4f5 d6f5
info depth 34 seldepth 47 score cp 30 upperbound nodes 2112334132 nps 17255517 time 122415 multipv 1 pv f3e1 h5h4 d1a4 a6f6 e1d3 d8f8 a4c2 h4g3 f2g3 f6f1 a1f1 h7g8 b2b3 f7f6 a3a4 b7b6
info depth 34 seldepth 47 score cp 30 upperbound nodes 2112334132 nps 17255517 time 122415 multipv 1 pv f3e1 h5h4 d1a4 a6f6 e1d3 d8f8 a4c2 h4g3 f2g3 f6f1 a1f1 h7g8 b2b3 f7f6 a3a4 b7b6
info nodes 18235667001 time 969824
bestmove e2d3 ponder c8d7

Looking at the code, if we hit Signals.stop, we return from id_loop
before printing any PV.  It is possible for us to have resorted the
RootMove list though, which will change the move that is actually
played.

No functional change.
Remove RedundantMajor

But compensate by reducing rook and queen
value by 53 = (160 / 3)

Material imbalances are affected as follows:

       Red. Major   Rook  Queen  Total
QRR      +160      -2*53    -53     +1
QR       +160        -53    -53    +54
RR       +160      -2*53      0    +54
R           0        -53      0    -53
Q           0          0    -53    -53

so that the imbalance changes by at most 54 + 53 = 107 units.
This corresponds to appromximately 3.5cp in the final evaluation.

Verified with fixed number 40000 games at both short
and long TC it does not regress.

Short TC 15+0.05
ELO: 1.93 +-2.1 (95%) LOS: 96.6%
Total: 40000 W: 7520 L: 7298 D: 25182

Long TC 60+0.05
ELO: -0.33 +-1.9 (95%) LOS: 36.5%
Total: 39663 W: 6067 L: 6105 D: 27491

bench: 6703846
Evaluate mobility of pinned pieces exactly

Previously some squares could be "incorrectly" awarded
to a pinned piece.

e.g. in 3k4/1q6/3b4/3Q4/8/5K2/B7/8 b - - 0 1 the black
bishop get 4 squares too many and the white queen gets 6.

Passed both short TC.
LLR: 2.97 (-2.94,2.94) [-1.50,4.50]
Total: 4871 W: 934 L: 817 D: 3120

And long TC:
LLR: 2.96 (-2.94,2.94) [0.00,6.00]
Total: 38968 W: 6113 L: 5837 D: 27018

bench: 9282549
Simplify squares_aligned()

Use newly introduced LineBB[]

No functional change.
Rename squares_aligned()

Rename to the shorter but still
clear aligned()

No functional change.
Remove opposed flag for doubled pawns

Actually, it is not used, as both arrays have the
same values. Some local tests in either direction
showed no improvement.

Also some minor corrections in the comments.

No functional change.
Reintroduce gains

This seems a die hard idea :-)

Passed both short TC
LLR: 2.97 (-2.94,2.94) [-1.50,4.50]
Total: 17485 W: 3307 L: 3156 D: 11022

And long TC
LLR: 2.97 (-2.94,2.94) [0.00,6.00]
Total: 38181 W: 6002 L: 5729 D: 26450

bench: 8659830
Faster castling in Chess960 case

Only rook attackers has to be considered, all other attackers are
already handled in the lines above.

No functional change.
Simplify generate<EVASIONS>

Use the newly introduced LineBB[] to simplify this
super hot-path function.

Verified with perft we don't have any speed regression, although
the number of squares removed is less than before in case of
contact check.

Insipred by DiscoCheck implementation.

Perft numbers are the same, but we have an harmless functional
change due to reorder of moves, because now some illegal moves
are no more detected at generation time, but in the search.

bench: 8331357