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.