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Basic Representations: the Board

Square Numbering

Squares are designated by a 'square-number'. The '0x88' system is used, meaning that the the board actually has ranks of 16 squares, but only the first 8 squares of each rank are valid and correspond to the 8 files of the board. The two-dimensional board is mapped into a one-dimensional array, rank after rank. Due to this the 4 lowest-order bits of the square number indicate the file, and the higher-order bits the rank. This makes it easy to recognize moves that fall off the board. On the left and they move to invalid square numbers (e.g. from the h-file to the 'i-file'), that have the '8'-bit set (the i-p file have numbers 8-15). Furthermore, all moves that move off the board at the front or back move to invalid rank, and have the 128 bit set (0x80, in hexadecimal). The validity of a square-number can thus be tested by bitwise anding with 0x88 (=136). This constant (which has given the system its name) is held in the global variable M, since it is used quite a lot, thus saving a lot of characters. (If the aim would not be source size, but speed, one would of course do the opposite!)

The Board Array

The principal data structure of the program thus is the board array b[129], a one-dimensional array indexed by square-number. Because of the invalid square-numbers, only half of the array is used to store the current chess position. Blocks of 8 used and 8 unused elements alternate, the highest valid square-number is 0x77=119. A dummy square with square-number 0x80=128 (a value held in the global variable S) is included in the array. This square number is sometimes used to indicate an invalid square (e.g. in the variable that indicates on which square e.p. capture is possible when no e.p. captures are possible), to make sure there are no crashes if the program inadvertently stores something there (saving us the trouble of testing the validity of the square number before we store).

Printing the Board

Despite the non-contiguous mapping of the chess board into the b[] array, it is quite easy to step through all squares on the board, skipping the invalid ones. The expression to step from a field xto the next field, which can, for instance, be used in th increment part of a for-loop, is x = x+9 & ~8;. Due to adding 9 = 8 + 1 in stead of 1 to a square number of a square in the 'a'-'g' file, its '8'-bit gets set, which is taken care of by the & ~8, which clears it again. But doing the same in the 'h' file also gives a carry into the '8'-bit due to the addition of 1. This resets the '8'-bit, and passes the carry through to the more-significant bits, i.e. the rank number. (The & ~8 then has no effect.) If we want the board scan to 'wrap around' from h8 back to a1, we can and with ~M in stead of ~8, clearing the '128'-bit together with the '8'-bit when the rank number overflows.

In the line that prints out the board (in main()) things are done a little differently, because the fact that we 'overflow' to a new rank also has to result in the printing of a new-line. Thus it uses a normal for-loop (with i++ increment, but tests the '8'-bit to see if we run off the board inside the printf() to know what to print (a new-line character, 10, or the representation of the piece on the square, n[b[i]&15]). If this tests true, an extra i += 7 (which always evaluates non-zero, and thus considered true as well) positions us back in front of the next valid square.

Below the declaration and use of the board are highlighted. (Where the original source contained macro's for for or while loops, these are shown expanded for readability.)

/*                               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*/
  }}}while((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,K,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          */
 {for(i=0;i<121;i++)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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