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Search: Move Sorting

Move Ordering

Searching the tree successively deeper is just a waste of time if we don't somehow use what we learned. Micro-Max only uses one piece of information, namely what the best move of the previous iteration was, for the purpose of searching that first.

To implement this, apart from remembering the score of the best move in m, we also keep track of what this best move was at any level, in the local variables X and Y. When a new iteration starts, we sneak in this best move before any of the other moves is considered. To this end the outer loop of the move generator, that runs through all pieces, is modified to start at the piece that could do the best move previously, rather than in the corner of the board. A local variable B keeps track of where we started the board scan, so that we know when we're done (remember the scan wraps around). This makes it easier to slip in the best move before all others, because the piece and square of origin are already that of the best move.

After generating the first target square y for this piece, we replace it by the target square of the previous best move. After searching the sub-tree for this move, we intercept the control flow, (based on the '8'-bit of Y being set) recording the score as the maximum found (since this was the first move we considered we don't have to compare with any previous best) and clearing the '8'-bit of Y to indicate that the best move is now considered. We then jump back to the beginning of the loop-over-directions of the move generator, to redo everything for the move that would have been originally generated as the first move for that piece.

Somewhat later, possibly even immediately, the best move will be generated a second time, in the course of normal move generation. To prevent it from being evaluated again (which would be quite inefficient, since it is likely to still be the best move, which will not trivially fail), we would have to test every move for being this best one (prepending an if(x!=B|y!=Z) before the code that considers the generated moves). Once transposition tables are implemented we don't have to bother with this, since re-searching this move will take the value of the original search immediately from the transposition table, an acceptable overhead.

int D(int k, int q, int l, int n)
	int m,                          /* score of best move so far    */
	    d=0,                        /* iteratively improved depth   */
	    X=0,Y=0,                    /* best move                    */
	    B,Z;                        /* move to skip, already done   */

	{	m = d>1 ? -I : EVAL();                  /* note there is no best to try if d==1 */
		B = X;                                  /* start move generation with piece here*/
		Z = 8;                                  /* nothing to skip yet: invalid square  */
		Y |= 8&Y>>4;                            /* copy 128-bit of Y to 8-bit, to ask   */
                                                        /* priority for a valid prev. best move */
		INITIALIZE_MOVE_GENERATION(B);          /* start with moves that go from B      */
			if(Y&8) y=Y;                    /* overrule generated move with best    */

			if(m>=l) goto C;
			h = d-1;                        /* new depth left                       */
			if(x-B|y-Z)                     /* skip if already done as best         */
			{	DO_MOVE;
				v = -D(24-k, -l, q>m?-q:-m, h);
				{	m=v;            /* first is always best, m was -I       */
					Z=y;            /* set this move for future skipping    */
					Y=y|S;          /* clears 8-bit now best is tried       */
					goto A;         /* try normal moves                     */
				{	m=v;
					X=x;Y=y|S;      /* remember best, set 128-bit of Y to   */
				}                       /*   indicate a best move is available  */

	    C:	;

	return m;

If the best move from the previous iteration turns out not so good after all, searching other moves of the same piece (as will be done next) often does provide a new best move quickly: In many cases the best move is to withdraw a threatened piece, and if one escape route turns out bad, another might still be good.

Castling Problems

To properly perform a castling move, the variables F and G for the Rook part have to be set, and this is only the case if the move is generated in the normal way: These variables are not remembered together with the best move. So castling can not be eligible for being sorted in front. This nuisance is solved by deriving the 'S'-bit in Y, which indicates that there is a best move that should be tried first in the next iteration, from the casting variable G. This prevents setting the 'S'-bit (i.e. the '128'-bit) when the best move is a castling. The 'S'-bit is copied to the '8'-bit of the same variable before the beginning of the next iteration, and acts as a request to sneak in the move. So castlings will not be sorted first.

However, the generation of moves will start at the King, in that case. Because the first directions in which moves are generated are the lateral ones, the castling will be found quite early, though.

Below the code that controls move ordering (by determining the best move, and make it jump the queue in the next iteration) is highlighted:

/*                               micro-Max,                                */
/* A chess program smaller than 2KB (of non-blank source), by H.G. Muller  */
/* version 3.2 (2000 characters) features:                                 */
/* - recursive negamax search                                              */
/* - quiescence search with recaptures                                     */
/* - recapture extensions                                                  */
/* - (internal) iterative deepening                                        */
/* - best-move-first 'sorting'                                             */
/* - a hash table storing score and best move                              */
/* - full FIDE rules (expt minor ptomotion) and move-legality checking     */

#define F(I,S,N) for(I=S;I<N;I++)
#define W(A) while(A)
#define K(A,B) *(int*)(T+A+(B&8)+S*(B&7))
#define J(A) K(y+A,b[y])-K(x+A,u)-K(H+A,t)

#define U 16777224
struct _ {int K,V;char X,Y,D;} A[U];           /* hash table, 16M+8 entries*/

int V=112,M=136,S=128,I=8e3,C=799,Q,N,i;       /* V=0x70=rank mask, M=0x88 */

char O,K,L,
w[]={0,1,1,3,-1,3,5,9},                        /* relative piece values    */
o[]={-16,-15,-17,0,1,16,0,1,16,15,17,0,14,18,31,33,0, /* step-vector lists */
     7,-1,11,6,8,3,6,                          /* 1st dir. in o[] per piece*/
     6,3,5,7,4,5,3,6},                         /* initial piece setup      */
b[129],                                        /* board: half of 16x8+dummy*/
T[1035],                                       /* hash translation table   */

n[]=".?+nkbrq?*?NKBRQ";                        /* piece symbols on printout*/

D(k,q,l,e,J,Z,E,z,n)    /* recursive minimax search, k=moving side, n=depth*/
int k,q,l,e,J,Z,E,z,n;  /* (q,l)=window, e=current eval. score, E=e.p. sqr.*/
{                       /* e=score, z=prev.dest; J,Z=hashkeys; return score*/
 int j,r,m,v,d,h,i=9,F,G;
 char t,p,u,x,y,X,Y,H,B;
 struct _*a=A;
                                               /* lookup pos. in hash table*/
 j=(k*E^J)&U-9;                                /* try 8 consec. locations  */
 W((h=A[++j].K)&&h-Z&&--i);                    /* first empty or match     */
 a+=i?j:0;                                     /* dummy A[0] if miss & full*/
 if(a->K)                                      /* hit: pos. is in hash tab */
 {d=a->D;v=a->V;X=a->X;                        /* examine stored data      */
  if(d>=n)                                     /* if depth sufficient:     */
  {if(v>=l|X&S&&v<=q|X&8)return v;             /* use if window compatible */
   d=n-1;                                      /* or use as iter. start    */
  }X&=~M;Y=a->Y;                               /*      with best-move hint */
  Y=d?Y:0;                                     /* don't try best at d=0    */
 }else d=X=Y=0;                                /* start iter., no best yet */
 N++;                                          /* node count (for timing)  */
 W(d++<n|z==8&N<1e7&d<98)                      /* iterative deepening loop */
 {x=B=X;                                       /* start scan at prev. best */
  Y|=8&Y>>4;                                   /* request try noncastl. 1st*/
  m=d>1?-I:e;                                  /* unconsidered:static eval */
  do{u=b[x];                                   /* scan board looking for   */
   if(u&k)                                     /*  own piece (inefficient!)*/
   {r=p=u&7;                                   /* p = piece type (set r>0) */
    j=o[p+16];                                 /* first step vector f.piece*/
    W(r=p>2&r<0?-r:-o[++j])                    /* loop over directions o[] */
    {A:                                        /* resume normal after best */
     y=x;F=G=S;                                /* (x,y)=move, (F,G)=castl.R*/
     do{H=y+=r;                                /* y traverses ray          */
      if(Y&8)H=y=Y&~M;                         /* sneak in prev. best move */
      if(y&M)break;                            /* board edge hit           */
      if(p<3&y==E)H=y^16;                      /* shift capt.sqr. H if e.p.*/
      t=b[H];if(t&k|p<3&!(r&7)!=!t)break;      /* capt. own, bad pawn mode */
      i=99*w[t&7];                             /* value of capt. piece t   */
      if(i<0||E-S&&b[E]&&y-E<2&E-y<2)m=I;      /* K capt. or bad castling  */
      if(m>=l)goto C;                          /* abort on fail high       */
      if(h=d-(y!=z))                           /* remaining depth(-recapt.)*/
      {v=p<6?b[x+8]-b[y+8]:0;                  /* center positional pts.   */
       b[G]=b[H]=b[x]=0;b[y]=u&31;             /* do move, strip virgin-bit*/
       if(!(G&M)){b[F]=k+6;v+=30;}             /* castling: put R & score  */
       if(p<3)                                 /* pawns:                   */
       {v-=9*(((x-2)&M||b[x-2]!=u)+            /* structure, undefended    */
              ((x+2)&M||b[x+2]!=u)-1);         /*        squares plus bias */
        if(y+r+1&S){b[y]|=7;i+=C;}             /* promote p to Q, add score*/
       v=-D(24-k,-l-(l>e),m>q?-m:-q,-e-v-i,    /* recursive eval. of reply */
            J+J(0),Z+J(8)+G-S,F,y,h);          /* J,Z: hash keys           */
       v-=v>e;                                 /* delayed-gain penalty     */
       if(z==9)                                /* called as move-legality  */
       {if(v!=-I&x==K&y==L)                    /*   checker: if move found */
        {Q=-e-i;O=F;return l;}                 /*   & not in check, signal */
        v=m;                                   /* (prevent fail-lows on    */
       }                                       /*   K-capt. replies)       */
       b[G]=k+38;b[F]=b[y]=0;b[x]=u;b[H]=t;    /* undo move,G can be dummy */
       if(Y&8){m=v;Y&=~8;goto A;}              /* best=1st done,redo normal*/
       if(v>m){m=v;X=x;Y=y|S&G;}               /* update max, mark with S  */
      }                                        /*          if non castling */
      t+=p<5;                                  /* fake capt. for nonsliding*/
      if(p<3&6*k+(y&V)==S                      /* pawn on 3rd/6th, or      */
          ||(u&~24)==36&j==7&&                 /* virgin K moving sideways,*/
          G&M&&b[G=(x|7)-(r>>1&7)]&32          /* 1st, virgin R in corner G*/
          &&!(b[G^1]|b[G^2])                   /* 2 empty sqrs. next to R  */
      ){F=y;t--;}                              /* unfake capt., enable e.p.*/
     }W(!t);                                   /* if not capt. continue ray*/
  }}}W((x=x+9&~M)-B);                          /* next sqr. of board, wrap */
C:if(m>I/4|m<-I/4)d=99;                        /* mate is indep. of depth  */
  m=m+I?m:-D(24-k,-I,I,0,J,Z,S,z,1)/2;         /* best loses K: (stale)mate*/
  if(!a->K|(a->X&M)!=M|a->D<=d)                /* if new/better type/depth:*/
  {a->K=Z;a->V=m;a->D=d;A->K=0;                /* store in hash,dummy stays*/
   a->X=X|8*(m>q)|S*(m<l);a->Y=Y;              /* empty, type (limit/exact)*/
  }                                            /*    encoded in X S,8 bits */
/*if(z==8)printf("%2d ply, %9d searched, %6d by (%2x,%2x)\n",d-1,N,m,X,Y&0x77);*/
 return m;                                     

 int j,k=8,*p,c[9];

 {b[i]=(b[i+V]=o[i+24]+40)+8;b[i+16]=18;b[i+96]=9;   /* initial board setup*/
  F(j,0,8)b[16*j+i+8]=(i-4)*(i-4)+(j-3.5)*(j-3.5);   /* center-pts table   */
 }                                                   /*(in unused half b[])*/

 W(1)                                                /* play loop          */
 {F(i,0,121)printf(" %c",i&8&&(i+=7)?10:n[b[i]&15]); /* print board        */
  p=c;W((*p++=getchar())>10);                        /* read input line    */
  if(*c-10){K=c[0]-16*c[1]+C;L=c[2]-16*c[3]+C;}else  /* parse entered move */
   D(k,-I,I,Q,1,1,O,8,0);                            /* or think up one    */
  F(i,0,U)A[i].K=0;                                  /* clear hash table   */
  if(D(k,-I,I,Q,1,1,O,9,2)==I)k^=24;                 /* check legality & do*/
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