tapered evaluation

[Carbec]

Hi,

I found 2 ways to calculate this : one in https://www.chessprogramming.org/PeSTO% ... n_Function
one in https://www.chessprogramming.org/Tapered_Eval.
The first one use 24 as divider, the other one 256.
The problem is that the two methods don't give the same evaluation.
Im perplexed. Is there a "right" method ?
Thanks for input

Philippe

[syzygy]

I found 2 ways to calculate this : one in https://www.chessprogramming.org/PeSTO% ... n_Function
one in https://www.chessprogramming.org/Tapered_Eval.
The first one use 24 as divider, the other one 256.
The problem is that the two methods don't give the same evaluation.

They are the same method, just using a different granularity of "phase".

When you implement such a method in your chess engine, you will have to make various choices. The number of phases, how to calculate the phase, etc.

[Carbec]

Hi,

You are totally right, the two evaluations are identical. One less bug
Thanks for the input.

Philippe

[AngularMomentum]

Depending on how fast your engine is, you may want to use a power of 2 because regular integer division is very slow on most CPUs.

[Ras]

Depending on how fast your engine is, you may want to use a power of 2 because regular integer division is very slow on most CPUs.

Dividing by a fixed amount isn't compiled to an integer division. I don't think that you'll see measurable impact on the engine speed. See Godbolt.org as example for GCC 13 with -O2:

Code: Select all

int division(int num) {
    return num / 24;
}
division(int):
        movsx   rax, edi
        sar     edi, 31
        imul    rax, rax, 715827883
        sar     rax, 34
        sub     eax, edi
        ret

Or with 256:

Code: Select all

int division(int num) {
    return num / 256;
}
division(int):
        test    edi, edi
        lea     eax, [rdi+255]
        cmovns  eax, edi
        sar     eax, 8
        ret

[Carbec]

Hi,

Back for this problem. In fact the two evaluations are the same in general, but there are numerous occasions where they differ of 1.
This may be little, but in my program have a certain importance, in time, in nodes searched, in sometimes in PV.

Some examples , first KIWIPETE position :

Code: Select all

phase 256
info  depth 15 seldepth 29 time    486 nodes    1.743.866 nps 3.588.201 score cp -118 pv d5e6 e7e6 e2a6 e6e5 a6b7 h3g2 f3g2 b4c3 d2c3 e5f4 b7a8 b6a8 h2h3 e8g8 e4e5
info  depth 16 seldepth 30 time    965 nodes    3.380.015 nps 3.502.606 score cp  -98 pv e2a6 b4c3 d2c3 e6d5 e5g4 h3g2 f3g2 e8g8 g4f6 g7f6 c3f6 e7f6 e1g1 d5e4 g2e4
info  depth 17 seldepth 30 time  1.614 nodes    5.676.260 nps 3.516.889 score cp -136 pv e2a6 b4c3 d2c3 e6d5 e5g4 f6g4 c3g7 g4e5 g7e5 e7e5 e1g1 h3g2 f3g2 d5e4 h2h3 h8h4 a1e1
info  depth 18 seldepth 31 time  2.389 nodes    8.219.554 nps 3.440.583 score cp  -89 pv e2a6 b4c3 d2c3 e6d5 e5g4 f6g4 c3g7 h8h4 g2h3 g4e5 f3f6 h4e4 e1f1 b6c4 f1g2 e7f6 g7f6
info  depth 19 seldepth 32 time  4.972 nodes   17.212.492 nps 3.461.884 score cp -127 pv e2a6 b4c3 d2c3 e6d5 e5g4 h3g2 h1g1 f6g4 c3g7 g4h2 f3g2 h8h4 e1c1 d5e4 g2g3 h2f3 g3c7 f3g1 d1g1
info  depth 20 seldepth 34 time  7.754 nodes   25.979.618 nps 3.350.479 score cp  -75 pv e2a6 b4c3 d2c3 e6d5 e5g4 h3g2 f3g2 h8h4 c3f6 g7f6 e1c1 d5e4 c1b1 e8f8 h1e1 a8e8 f2f3 d7d5

phase 24
info  depth 15 seldepth 28 time    497 nodes    1.777.346 nps 3.576.148 score cp -118 pv d5e6 e7e6 e2a6 e6e5 a6b7 h3g2 f3g2 b4c3 d2c3 e5f4 b7a8 b6a8 h2h3 e8g8 e4e5
info  depth 16 seldepth 30 time  1.217 nodes    4.210.493 nps 3.459.731 score cp -155 pv e2a6 b4c3 d2c3 e6d5 e5g4 f6g4 c3g7 h8h4 e1c1 d5e4 f3g3 h3g2 g3g2 b6a4
info  depth 17 seldepth 31 time  1.597 nodes    5.449.742 nps 3.412.487 score cp -136 pv e2a6 b4c3 d2c3 e6d5 e5g4 f6g4 c3g7 g4e5 g7e5 e7e5 g2h3 d5e4 f3a3 e5e7 a3c3 h8h4
info  depth 18 seldepth 31 time  2.190 nodes    7.332.419 nps 3.348.136 score cp -123 pv e2a6 b4c3 d2c3 e6d5 e5g4 f6g4 c3g7 g4e5 f3g3 h3g2 g3g2 e7b4 e1f1 b4b2 a1e1 b2a2 g7h8 a2a6 e1e2
info  depth 19 seldepth 34 time  3.613 nodes   11.745.577 nps 3.250.920 score cp -123 pv e2a6 b4c3 d2c3 e6d5 e5g4 f6g4 c3g7 g4e5 f3g3 h3g2 g3g2 e7b4 e1f1 b4b2 a1e1 b2a2 g7h8 a2a6 e1e2
info  depth 20 seldepth 34 time  6.172 nodes   20.161.033 nps 3.266.531 score cp -110 pv e2a6 e6d5 c3b5 e7e5 d2f4 e5b2 b5c7 e8f8 e1g1 d5e4 f3b3 b2b3 a2b3 h3g2 g1g2 a8d8 f4g5 f8g8 a6b5 h8h5

Now, FINE 70 :

Code: Select all

phase 256
info  depth 40 seldepth 46 time    240 nodes    1.369.620 nps 5.706.750 score cp   280 pv a1b1 a7b7 b1c1 b7c8 c1d2 c8d7 d2c3 d7c7 c3d3 c7b7 d3e3 b7c7 e3f2 c7d7 f2g3 d7e7 g3h4 e7f8
info  depth 41 seldepth 49 time    330 nodes    1.903.680 nps 5.768.727 score cp   446 pv a1b1 a7b8 b1c2 b8c7 c2d3 c7b7 d3e3 b7c7 e3f2 c7d7 f2g3 d7e7 g3h4 e7f8 h4g5 f8g7 g5f5 g7f7
info  depth 42 seldepth 55 time    574 nodes    3.178.934 nps 5.538.212 score cp   761 pv a1b1 a7b8 b1c2 b8c7 c2d3 c7b7 d3e3 b7c7 e3f2 c7d7 f2g3 d7e7 g3h4 e7f8 h4g5 f8g7 g5f5 g7f7
info  depth 43 seldepth 58 time 12.219 nodes   53.108.569 nps 4.346.392 score cp 2.018 pv a1b1 a7b8 b1c2 b8c7 c2d3 c7b7 d3e3 b7c7 e3f2 c7d7 f2g3 d7e7 g3h4 e7f7 h4g5 f7g7 g5f5 g7f7
info  depth 44 seldepth 57 time 13.198 nodes   57.298.440 nps 4.341.448 score cp 2.033 pv a1b1 a7b8 b1c2 b8c7 c2d3 c7b7 d3e2 b7c7 e2f2 c7d7 f2g3 d7e7 g3h4 e7f7 h4g5 f7g7 g5f5 g7f7
info  depth 45 seldepth 59 time 14.723 nodes   63.715.516 nps 4.327.617 score cp 2.070 pv a1b1 a7b8 b1c2 b8c7 c2d3 c7b7 d3e2 b7c7 e2f2 c7d7 f2g3 d7e7 g3h4 e7f7 h4h5 f7f6 h5h6 f6f7

phase 24
info  depth 40 seldepth 49 time    286 nodes    1.586.482 nps 5.547.139 score cp  350 pv a1b1 a7a8 b1b2 a8b7 b2c3 b7c7 c3d3 c7b7 d3e3 b7c8 e3f2 c8d7 f2g3 d7e8 g3h4 e8f8 h4g5 f8g7 g5f5 g7f7 f5e4 f7g6 e4d3 g6f5 d3c4 f5f4 c4b5 f4e4 b5a5 e4d5 a5b6 d5c4 d4d5 c4b4 a4a5 b4b3 a5a6 b3c4
info  depth 41 seldepth 49 time    365 nodes    2.020.853 nps 5.536.583 score cp  365 pv a1b1 a7a8 b1b2 a8b7 b2c3 b7c7 c3d3 c7b7 d3e3 b7c8 e3f2 c8d7 f2g3 d7e8 g3h4 e8f8 h4g5 f8g7 g5f5 g7f7 f5e4 f7g6 e4d3 g6f5 d3c4 f5g4 c4b5 g4f4 b5a5 f4e4 a5b6 e4d5 a4a5 d5c4 d4d5 c4b4 a5a6 b4c4
info  depth 42 seldepth 54 time    673 nodes    3.295.994 nps 4.897.465 score cp  446 pv a1b1 a7a8 b1b2 a8b7 b2c3 b7c7 c3d3 c7b7 d3e3 b7c8 e3f2 c8d7 f2g3 d7e8 g3h4 e8f8 h4g5 f8g7 g5f5 g7f7 f5e4 f7g6 e4d3 g6f5 d3c4 f5f4 c4b5 f4e4 b5a5 e4d5 a5b5 d5e4 a4a5 e4d3 d4d5 d3d4 b5c6 d4e4 c6d6
info  depth 43 seldepth 57 time    938 nodes    4.591.603 nps 4.895.099 score cp  511 pv a1b1 a7a8 b1b2 a8b7 b2c3 b7c7 c3d3 c7b7 d3e3 b7c8 e3f2 c8d7 f2g3 d7e8 g3h4 e8f8 h4g5 f8g7 g5f5 g7f7 f5e4 f7g6 e4d3 g6f5 d3c4 f5f4 c4b5 f4e4 b5a5 e4d5 a5b6 d5e6 b6c6 e6f7 c6d6 f7g6 a4a5 g6h5 a5a6 h5g4
info  depth 44 seldepth 57 time  1.309 nodes    6.388.420 nps 4.880.381 score cp  672 pv a1b1 a7a8 b1b2 a8b7 b2c3 b7c7 c3d3 c7b7 d3e3 b7c8 e3f2 c8d7 f2g3 d7e8 g3h4 e8f8 h4g5 f8g7 g5f5 g7f7 f5e4 f7g6 e4d3 g6f6 d3c4 f6f5 c4b5 f5e4 b5c6 e4d4 c6d6 d4c3 d6c6 c3c2 d5d6 c2b1 c6b5 b1c1 b5a5
info  depth 45 seldepth 59 time  2.022 nodes    9.750.674 nps 4.822.291 score cp 1.092 pv a1b1 a7a8 b1b2 a8b7 b2c3 b7c7 c3d3 c7b7 d3e2 b7c8 e2f2 c8d7 f2g3 d7e8 g3h4 e8f8 h4g5 f8g7 g5f5 g7f7 f5e4 f7g6

Now, a position I call SILVER2 (from the silver suite)

Code: Select all

phase 256
info  depth 15 seldepth 28 time    513 nodes    1.537.017 nps 2.996.134 score cp   52 pv f1c4 c6e5 c4e2 d7d5 e1g1 e8g8 b1d2 c7c6 a1c1 c5b6 f2f4 f6h6 g1h1 c6c5 d4b5
info  depth 16 seldepth 29 time    825 nodes    2.487.445 nps 3.015.084 score cp   52 pv f1c4 c6e5 c4e2 d7d5 e1g1 e8g8 b1d2 c7c6 a1c1 c5b6 f2f4 f6h6 g1h1 c6c5 d4b5
info  depth 17 seldepth 31 time  1.625 nodes    4.933.289 nps 3.035.870 score cp   50 pv f1c4 c6e5 c4e2 d7d5 e1g1 e8g8 b1d2 a7a6 b2b4 c5a7 f2f4 f6h6 g1h1 c8d7 a1b1 c7c6
info  depth 18 seldepth 32 time  4.143 nodes   12.672.343 nps 3.058.735 score cp   25 pv f1b5 a7a6 b5c6 d7c6 d1h5 c5d4 c3d4 f6g6 h5g6 h7g6 e1g1 c8e6 b1d2 h8h5 f2f3 e8c8 b2b3 f7f6
info  depth 19 seldepth 36 time  9.918 nodes   29.514.036 nps 2.975.805 score cp   39 pv b1d2 c6d4 e4e5 d4c2 d1c2 f6e5 d2c4 e5e6 e1c1 c5e3 c4e3 e6a2 f1c4 a2a1 c1d2 a1a5 b2b4 a5h5 d2c1 e8g8 c1b1
info  depth 20 seldepth 33 time 11.919 nodes   35.500.467 nps 2.978.476 score cp   24 pv b1d2 c6d4 e4e5 d4c2 d1c2 f6e5 d2c4 e5e6 e1c1 d7d6 e3c5 d6c5 c4e3 e8g8 f1c4 e6g6 c2g6 e7g6 d1d5 b7b6

phase 24
info  depth 15 seldepth 26 time    438 nodes    1.305.749 nps 2.981.162 score cp   53 pv f1c4 c6e5 c4e2 e8g8 b2b4 c5b6 e1g1 c7c5 d4c2 c5b4 c3b4 a7a5 b4a5 b6e3 f2e3
info  depth 16 seldepth 28 time    725 nodes    2.179.723 nps 3.006.514 score cp   41 pv f1c4 c6e5 c4e2 e8g8 b2b4 c5b6 e1g1 d7d5 b1d2 c7c5 b4c5 b6c5 f2f4 f6h6 a1b1 a7a6
info  depth 17 seldepth 29 time  1.168 nodes    3.541.427 nps 3.032.043 score cp   41 pv f1c4 c6e5 c4e2 e8g8 b2b4 c5b6 e1g1 d7d5 b1d2 c7c6 f2f4 f6h6 h2h3 c8h3 g2h3 h6h3 f4e5
info  depth 18 seldepth 34 time  2.509 nodes    7.589.445 nps 3.024.888 score cp   31 pv f1c4 c6e5 c4e2 f6g6 e1g1 d7d6 g1h1 g6e4 b1d2 e4g6 d4b5 e8g8 b5c7 a8b8 d2c4 c5e3 f2e3
info  depth 19 seldepth 33 time  4.307 nodes   12.851.959 nps 2.983.970 score cp   28 pv f1c4 c6e5 d1b3 c7c6 e1g1 e8g8 b1d2 e5c4 b3c4 c5b6 a1e1 d7d5 e4d5 e7d5 d2e4 f6g6 c4d3 c8g4 e3g5
info  depth 20 seldepth 36 time 10.598 nodes   31.760.799 nps 2.996.867 score cp   29 pv f1c4 c6e5 c4e2 f6g6 e1g1 d7d6 g1h1 g6e4 b1d2 e4g6 d4b5 c5e3 b5c7 e8d8 c7a8 e3f4 g2g3 f4d2 d1d2 c8d7

Is this normal ? or something caused by my program ?
As I see, the "phase 24" is better in my case.

Thanks
Philippe

[Carbec]

I forgot to give the positions :

KIWIPETE = "r3k2r/p1ppqpb1/bn2pnp1/3PN3/1p2P3/2N2Q1p/PPPBBPPP/R3K2R w KQkq - 0 1";
FINE_70 = "8/k7/3p4/p2P1p2/P2P1P2/8/8/K7 w - -";
SILVER2 = "r1b1k2r/ppppnppp/2n2q2/2b5/3NP3/2P1B3/PP3PPP/RN1QKB1R w KQkq - 0 1";