Revert "Further increase safe checks bonus"

This reverts commit 4bc2374450e30101392 for
two reasons.

First regression testing shows almost equal
score:

Before the patch:
ELO: 49.75 +-2.5 (95%) LOS: 100.0%
Total: 27205 W: 7113 L: 3244 D: 16848

After the patch:
ELO: 48.87 +-2.9 (95%) LOS: 100.0%
Total: 20860 W: 5478 L: 2563 D: 12819

Second, and more sensible to me, this patch
increases safe check bonuses to 4 times their
original value (!) and considering:

- Values were already well tuned

- Values are highly critical

- King safety is highly critical, very TC
  dependent and very difficult to test

- Our testing coverage is partial (self-testing,
  blitz times)

I think is better to be safe than sorry and so
I revert the patch.

bench: 8440524
Fix build on Intel compiler

Due to a strange issue (bug?) the ternary
operator does not return a BitCountType for
icc, so revert to the expression.

The same patch was already applied in
9749f1f14c956133c2f42f96592b

Thanks to NssY Wanyonyi for pointing out
this.

No functional change.
Fix pos.count<ALL_PIECES>()

It was never updated !

Currently it only affects evaluate_passed_pawns()
and in particularly the rule to increase the bonus
if we have more non-pawn pieces. We could simply use
popcount() instead and avoid the little slowdown
in put_piece() and remove_piece(), but this would
leave a very subtle and tricky hole where people
are forced to remember that pos.count<ALL_PIECES>()
does not work. This is not obvious and so dangerous.

Thanks to Ronald de Man for spotting this.

bench: 7931424
Further improve chain pawn evaluation

Passed both short TC:
LLR: 2.96 (-2.94,2.94) [-1.50,4.50]
Total: 28299 W: 5854 L: 5667 D: 16778

And long TC:
LLR: 2.96 (-2.94,2.94) [0.00,6.00]
Total: 9738 W: 1797 L: 1644 D: 6297

bench: 9294116
Restore behaviour after count<ALL_PIECES> fix

Because pos.count<ALL_PIECES>(Us) was always zero,
rewrite the formula as if this would still be
the case.

bench: 8510004
Re-add "Further increase safe checks bonus"

After 40K games at 60 secs, result is still
not clear, but not a regression against SF 4

After
ELO: 50.11 +-2.1 (95%) LOS: 100.0%
Total: 40000 W: 10547 L: 4817 D: 24636

Before
ELO: 49.51 +-2.1 (95%) LOS: 100.0%
Total: 40000 W: 10483 L: 4821 D: 24696

So re-apply the patch to avoid to
special-case this one.

bench: 7403882
Tweak again chain pawn bonus

This is the first chain bonus version
from Ralph that also passed both

Short TC:
LLR: 2.96 (-2.94,2.94) [-1.50,4.50]
Total: 23460 W: 4727 L: 4556 D: 14177

And long TC:
LLR: 2.95 (-2.94,2.94) [0.00,6.00]
Total: 31858 W: 5497 L: 5240 D: 21121

And performed better against current
committed version, always at 60secs:

LLR: -2.94 (-2.94,2.94) [-3.00,3.00]
Total: 26301 W: 4477 L: 4580 D: 17244

This test was done by Leonid.

bench: 8455956
Simplify futility margins formula

New formula mathces the old formula until d = 45

Test code:

int main() {

  for(int d=1; d<=45; d++)
  {
     int a = int(log(double(d * d) / 2) / log(2.0) + 1.001);
     int b = int(2.9 * log(double(d)));

     if (a != b) std::cout << d << std::endl;
  }

  return 0;
}

bench: 8455956
Simplify futility move count formula

Simpler formula but introduces some slight changes if d >= 10

Original code grows like  0.225 * d^1.8
New code grows like       0.222 * d^1.8

Full list of values:

d old new diff
--------------
0 2 2 0
1 2 2 0
2 3 3 0
3 4 4 0
4 5 5 0
5 6 6 0
6 7 7 0
7 9 9 0
8 11 11 0
9 13 13 0
10 15 16 1
11 18 19 1
12 21 21 0
13 24 24 0
14 27 28 1
15 31 31 0
16 35 35 0
17 39 38 -1
18 42 42 0
19 47 46 -1
20 51 51 0
21 55 55 0
22 60 60 0
23 65 65 0
24 70 70 0
25 75 75 0
26 81 80 -1
27 87 86 -1
28 92 91 -1
29 98 97 -1
30 104 103 -1
31 111 109 -2

Test code:

int main() {

  for(int d=0; d<32; d++)
  {
     int a = int(3 + 0.3 * pow(double(d), 1.8)) * 3/4 + (2 < d && d < 5);
     int b = int(2.4 + 0.222 * pow(d + 0.0, 1.8));

     std::cout << d << " " << a << " " << b << " " << b-a << std::endl;
  }

  return 0;
}

bench: 8350690
Use flip_sq idea in endgame.cpp

The normalising transformation is computed all at
once by the helper function get_flip_sq and then
applied immediately to the relevant squares as soon
as they are loaded from the position class.

bench: 8350690
Further smplify pawn endgames

Dumb down a bit the code and trade some possible
speed (but this is far from hot path anyhow) for
some added readability for the layman.

No functional change.
Penalty for Knight when enemy pawns are few

This seems more a material imbalance topic,
anyhow test is good and so patch is applied
as is.

Passed both short TC:
LLR: 2.96 (-2.94,2.94) [-1.50,4.50]
Total: 17391 W: 3548 L: 3393 D: 10450

And long TC:
LLR: 3.00 (-2.94,2.94) [0.00,6.00]
Total: 34660 W: 5972 L: 5700 D: 22988

bench: 8291883
Prefer file_bb() to FileBB[]

No functional change.
Retire mirror()

Inline the only caller site.

No functional change.