ar.c

/* Copyright 1990-2011, Jsoftware Inc.  All rights reserved. */
/* License in license.txt.                                   */
/*                                                                         */
/* Adverbs: Reduce (Insert) and Outer Product                              */

#include "j.h"
#include "vasm.h"
#include "ve.h"
#include "vcomp.h"
#include "ar.h"

static DF1(jtreduce);


#define PARITY2         u=(UC*)&s; b=0; b^=*u++; b^=*u++;
#define PARITY4         u=(UC*)&s; b=0; b^=*u++; b^=*u++; b^=*u++; b^=*u++; 
#define PARITY8         u=(UC*)&s; b=0; b^=*u++; b^=*u++; b^=*u++; b^=*u++; b^=*u++; b^=*u++; b^=*u++; b^=*u++;

#if SY_64
#define PARITYW         PARITY8
#else
#define PARITYW         PARITY4
#endif  

#if SY_ALIGN
#define VDONE(T,PAR)  \
 {I q=n/sizeof(T);T s,*y=(T*)x; DO(m, s=0; DO(q, s^=*y++;); PAR; *z++=b==pc;);}

static void vdone(I m,I n,B*x,B*z,B pc){B b,*u;
 if(1==m){UI s,*xi;
  s=0; b=0;
  xi=(I*)x; DO(n/SZI, s^=*xi++;); 
  u=(B*)xi; DO(n%SZI, b^=*u++;);
  u=(B*)&s; DO(SZI,   b^=*u++;);
  *z=b==pc;
 }else if(0==n%sizeof(UI  ))VDONE(UI,  PARITYW)
 else  if(0==n%sizeof(UINT))VDONE(UINT,PARITY4)
 else  if(0==n%sizeof(US  ))VDONE(US,  PARITY2)
 else  DO(m, b=0; DO(n, b^=*x++;); *z++=b==pc;);
}
#else
static void vdone(I m,I n,B*x,B*z,B pc){B b;I q,r;UC*u;UI s,*y;
 q=n/SZI; r=n%SZI; y=(UI*)x;
 switch((r?2:0)+pc){
  case 0: DO(m, s=0; DO(q, s^=*y++;); PARITYW;                            *z++=!b;); break;
  case 1: DO(m, s=0; DO(q, s^=*y++;); PARITYW;                            *z++= b;); break;
  case 2: DO(m, s=0; DO(q, s^=*y++;); PARITYW; u=(UC*)y; DO(r, b^=*u++;); *z++=!b; x+=n; y=(UI*)x;); break;
  case 3: DO(m, s=0; DO(q, s^=*y++;); PARITYW; u=(UC*)y; DO(r, b^=*u++;); *z++= b; x+=n; y=(UI*)x;); break;
}}
#endif

#define RBFXLOOP(T,pfx)  \
 {T*xx=(T*)x,*yy,*z0,*zz=(T*)z;   \
  q=d/sizeof(T);                  \
  for(j=0;j<m;++j){               \
   yy=xx; xx-=q; z0=zz; DO(q, --xx; --yy; --zz; *zz=pfx(*xx,*yy););    \
   DO(n-2,       zz=z0; DO(q, --xx;       --zz; *zz=pfx(*xx,*zz);););  \
 }}  /* non-commutative */

#define RCFXLOOP(T,pfx)  \
 {T*xx=(T*)x,*yy,*z0,*zz=(T*)z;   \
  q=d/sizeof(T);                  \
  for(j=0;j<m;++j){               \
   yy=xx; xx+=q; z0=zz; DO(q, *zz++=pfx(*yy,*xx); ++xx; ++yy;);    \
   DO(n-2,       zz=z0; DO(q, *zz++=pfx(*zz,*xx); ++xx;      ););  \
 }}  /* commutative */

#if SY_ALIGN
#define RBFXODDSIZE(pfx,bpfx)  RBFXLOOP(C,bpfx)
#define REDUCECFX              REDUCEBFX
#else
#define RBFXODDSIZE(pfx,bpfx)  \
 {B*zz;I r,t,*xi,*yi,*zi;                                                       \
  q=d/SZI; r=d%SZI; xi=(I*)x; zz=z;                                             \
  for(j=0;j<m;++j,zz-=d){                                                       \
   yi=xi; xi=(I*)((B*)xi-d); zi=(I*)zz;                                         \
   DO(q, --xi; --yi; *--zi=pfx(*xi,*yi););                                      \
    xi=(I*)((B*)xi-r); yi=(I*)((B*)yi-r); t=pfx(*xi,*yi); MC((B*)zi-r,&t,r);    \
   DO(n-2, zi=(I*)zz; DO(q, --xi; --zi; *zi=pfx(*xi,*zi););                     \
    xi=(I*)((B*)xi-r); zi=(I*)((B*)zi-r); t=pfx(*xi,*zi); MC(    zi,  &t,r););  \
 }}  /* non-commutative */

#define RCFXODDSIZE(pfx,bpfx)  \
 {I r,t,*xi,*yi,*zi;                                                            \
  q=d/SZI; r=d%SZI;                                                             \
  for(j=0;j<m;++j,x+=d,z+=d){                                                   \
   yi=(I*)x; x+=d; xi=(I*)x; zi=(I*)z; DO(q, *zi++=pfx(*yi,*xi); ++xi; ++yi;); t=pfx(*yi,*xi); MC(zi,&t,r);    \
   DO(n-2,   x+=d; xi=(I*)x; zi=(I*)z; DO(q, *zi++=pfx(*zi,*xi); ++xi;      ); t=pfx(*zi,*xi); MC(zi,&t,r););  \
 }}  /* commutative */

#define REDUCECFX(f,pfx,ipfx,spfx,bpfx,vdo)  \
 AHDRP(f,B,B){B*y=0;I d,j,q;                       \
  if(c==n){vdo; R;}                                \
  d=c/n;                                           \
  if(1==n)DO(d, *z++=*x++;)                        \
  else if(0==d%sizeof(UI  ))RCFXLOOP(UI,   pfx)    \
  else if(0==d%sizeof(UINT))RCFXLOOP(UINT,ipfx)    \
  else if(0==d%sizeof(US  ))RCFXLOOP(US,  spfx)    \
  else                      RCFXODDSIZE(pfx,bpfx)  \
 }  /* commutative */

#endif

#define REDUCEBFX(f,pfx,ipfx,spfx,bpfx,vdo)  \
 AHDRP(f,B,B){B*y=0;I d,j,q;                       \
  if(c==n){vdo; R;}                                \
  d=c/n; x+=m*c; z+=m*d;                           \
  if(1==n)DO(d, *--z=*--x;)                        \
  else if(0==d%sizeof(UI  ))RBFXLOOP(UI,   pfx)    \
  else if(0==d%sizeof(UINT))RBFXLOOP(UINT,ipfx)    \
  else if(0==d%sizeof(US  ))RBFXLOOP(US,  spfx)    \
  else                      RBFXODDSIZE(pfx,bpfx)  \
 }  /* non-commutative */

REDUCECFX(  eqinsB, EQ,  IEQ,  SEQ,  BEQ,  vdone(m,n,x,z,(B)(n%2)))
REDUCECFX(  neinsB, NE,  INE,  SNE,  BNE,  vdone(m,n,x,z,1       ))
REDUCECFX(  orinsB, OR,  IOR,  SOR,  BOR,  DO(m, *z++=1&&memchr(x,C1,n);                         x+=c;)) 
REDUCECFX( andinsB, AND, IAND, SAND, BAND, DO(m, *z++=!  memchr(x,C0,n);                         x+=c;))
REDUCEBFX(  ltinsB, LT,  ILT,  SLT,  BLT,  DO(m, *z++= *(x+n-1)&&!memchr(x,C1,n-1)?1:0;          x+=c;))
REDUCEBFX(  leinsB, LE,  ILE,  SLE,  BLE,  DO(m, *z++=!*(x+n-1)&&!memchr(x,C0,n-1)?0:1;          x+=c;))
REDUCEBFX(  gtinsB, GT,  IGT,  SGT,  BGT,  DO(m, y=memchr(x,C0,n); *z++=1&&(y?1&(y-x):1&n);      x+=c;))
REDUCEBFX(  geinsB, GE,  IGE,  SGE,  BGE,  DO(m, y=memchr(x,C1,n); *z++=!  (y?1&(y-x):1&n);      x+=c;))
REDUCEBFX( norinsB, NOR, INOR, SNOR, BNOR, DO(m, y=memchr(x,C1,n); d=y?y-x:n; *z++=(1&d)==d<n-1; x+=c;))
REDUCEBFX(nandinsB, NAND,INAND,SNAND,BNAND,DO(m, y=memchr(x,C0,n); d=y?y-x:n; *z++=(1&d)!=d<n-1; x+=c;))


#if SY_ALIGN
REDUCEPFX(plusinsB,I,B,PLUS)
#else
AHDRR(plusinsB,I,B){I d,dw,i,p,q,r,r1,s;UC*tu;UI*v;
 if(c==n&&n<SZI)DO(m, s=0; DO(n, s+=*x++;); *z++=s;)
 else if(c==n){UI t;
  p=n/SZI; q=p/255; r=p%255; r1=n%SZI; tu=(UC*)&t;
  for(i=0;i<m;++i){
   s=0; v=(UI*)x; 
   DO(q, t=0; DO(255, t+=*v++;); DO(SZI, s+=tu[i];));
         t=0; DO(r,   t+=*v++;); DO(SZI, s+=tu[i];);
   x=(B*)v; DO(r1, s+=*x++;); 
   *z++=s;
 }}else{A t;UI*tv;
  d=c/n; dw=(d+SZI-1)/SZI; p=dw*SZI; memset(z,C0,m*d*SZI);
  q=n/255; r=n%255;
  t=ga(INT,dw,1,0); if(!t)R;
  tu=(UC*)AV(t); tv=(UI*)tu; v=(UI*)x;
  for(i=0;i<m;++i,z+=d){
   DO(q, memset(tv,C0,p); DO(255, DO(dw,tv[i]+=v[i];); x+=d; v=(UI*)x;); DO(d,z[i]+=tu[i];));
         memset(tv,C0,p); DO(r,   DO(dw,tv[i]+=v[i];); x+=d; v=(UI*)x;); DO(d,z[i]+=tu[i];) ;
}}}  /* +/"r w on boolean w, originally by Roger Moore */
#endif


REDUCEOVF( plusinsI, I, I,  PLUSR, PLUSVV, PLUSRV) 
REDUCEOVF(minusinsI, I, I, MINUSR,MINUSVV,MINUSRV) 
REDUCEOVF(tymesinsI, I, I, TYMESR,TYMESVV,TYMESRV)

REDUCCPFX( plusinsO, D, I,  PLUSO)
REDUCCPFX(minusinsO, D, I, MINUSO) 
REDUCCPFX(tymesinsO, D, I, TYMESO) 

REDUCENAN( plusinsD, D, D, PLUS  ) 
REDUCENAN( plusinsZ, Z, Z, zplus )
REDUCEPFX( plusinsX, X, X, xplus )

REDUCEPFX(minusinsB, I, B, MINUS ) 
REDUCENAN(minusinsD, D, D, MINUS ) 
REDUCENAN(minusinsZ, Z, Z, zminus) 

REDUCEPFX(tymesinsD, D, D, TYMES ) 
REDUCEPFX(tymesinsZ, Z, Z, ztymes) 

REDUCENAN(  divinsD, D, D, DIV   )
REDUCENAN(  divinsZ, Z, Z, zdiv  )

REDUCEPFX(  maxinsI, I, I, MAX   )
REDUCEPFX(  maxinsD, D, D, MAX   )
REDUCEPFX(  maxinsX, X, X, XMAX  )
REDUCEPFX(  maxinsS, SB,SB,SBMAX )

REDUCEPFX(  mininsI, I, I, MIN   )
REDUCEPFX(  mininsD, D, D, MIN   )
REDUCEPFX(  mininsX, X, X, XMIN  )
REDUCEPFX(  mininsS, SB,SB,SBMIN )


static DF1(jtred0){DECLF;A x;I f,r,wr,*s;
 wr=AR(w); r=jt->rank?jt->rank[1]:wr; f=wr-r; s=AS(w);
 jt->rank=0;
 GA(x,AT(w),0L,r,f+s);
 R reitem(vec(INT,f,s),lamin1(df1(x,iden(fs))));
}    /* f/"r w identity case */

static DF1(jtredg){PROLOG;DECLF;A y,z;B p;C*u,*v;I i,k,n,old,r,wr,yn,yr,*ys,yt;
 RZ(w);
 ASSERT(DENSE&AT(w),EVNONCE);
 wr=AR(w); r=jt->rank?jt->rank[1]:wr; jt->rank=0;
 if(r<wr)R rank1ex(w,self,r,jtredg);
 n=IC(w); p=ARELATIVE(w);
 RZ(z=tail(w)); yt=AT(z); yn=AN(z); yr=AR(z); ys=1+AS(w);
 k=yn*bp(yt); v=CAV(w)+k*(n-1);
 old=jt->tbase+jt->ttop; 
 for(i=1;i<n;++i){
  v-=k; 
  GA(y,yt,yn,yr,ys); u=CAV(y); 
  if(p){A1*wv=(A1*)v,*yv=(A1*)u;I d=(I)w-(I)y; AFLAG(y)=AFREL; DO(yn, yv[i]=d+wv[i];);}else MC(u,v,k); 
  RZ(z=CALL2(f2,y,z,fs));
  gc(z,old);
 }
 EPILOG(z);
}    /* f/"r w for general f and 1<(-r){$w */


static C fca[]={CSTAR, CPLUS, CEQ, CMIN, CMAX, CPLUSDOT, CSTARDOT, CNE, 0};  /* commutative & associative */

static A jtredsp1a(J jt,C id,A z,A e,I n,I r,I*s){A t;B b,p=0;D d=1;
 switch(id){
  default:       ASSERT(0,EVNONCE);
  case CPLUSDOT: R n?gcd(z,e):ca(e);
  case CSTARDOT: R n?lcm(z,e):ca(e);
  case CMIN:     R n?minimum(z,e):ca(e);
  case CMAX:     R n?maximum(z,e):ca(e);
  case CPLUS:    if(n&&equ(e,zero))R z; DO(r, d*=s[i];); t=tymes(e,d>IMAX?scf(d-n):sc((I)d-n)); R n?plus (z,t):t;
  case CSTAR:    if(n&&equ(e,one ))R z; DO(r, d*=s[i];); t=expn2(e,d>IMAX?scf(d-n):sc((I)d-n)); R n?tymes(z,t):t;
  case CEQ:      p=1;  /* fall thru */
  case CNE:
   ASSERT(B01&AT(e),EVNONCE); 
   if(!n)*BAV(z)=p; 
   b=1; DO(r, if(!(s[i]%2)){b=0; break;}); 
   R !p==*BAV(e)&&b!=n%2?not(z):z;
}}   /* f/w on sparse vector w, post processing */

static A jtredsp1(J jt,A w,A self,C id,VF ado,I cv,I f,I r,I zt){A e,x,z;I m,n;P*wp;
 RZ(w);
 wp=PAV(w); e=SPA(wp,e); x=SPA(wp,x); n=AN(x); m=*AS(w);
 GA(z,zt,1,0,0);
 if(n){ado(jt,1L,n,n,AV(z),AV(x)); RE(0); if(m==n)R z;}
 R redsp1a(id,z,e,n,AR(w),AS(w));
}    /* f/"r w for sparse vector w */

DF1(jtredravel){A f,x,z;C id;I cv,n;P*wp;VF ado;
 RZ(w);
 f=VAV(self)->f;
 if(!(SPARSE&AT(w)))R reduce(AN(w)?gah(1L,w):mtv,f);
 wp=PAV(w); x=SPA(wp,x); n=AN(x);
 id=vaid(VAV(f)->f);
 while(1){
  vains(id,AT(x),&ado,&cv);
  ASSERT(ado,EVNONCE);
  GA(z,rtype(cv),1,0,0);
  if(n)ado(jt,1L,n,n,AV(z),AV(x));
  if(jt->jerr!=EWOV)R redsp1a(id,z,SPA(wp,e),n,AR(w),AS(w));;
}}  /* f/@, w */

static A jtredspd(J jt,A w,A self,C id,VF ado,I cv,I f,I r,I zt){A a,e,x,z,zx;I c,m,n,*s,t,*v,wr,*ws,xf,xr;P*wp,*zp;
 RZ(w);
 ASSERT(strchr(fca,id),EVNONCE);
 wp=PAV(w); a=SPA(wp,a); e=SPA(wp,e); x=SPA(wp,x); s=AS(x);
 xr=r; v=AV(a); DO(AN(a), if(f<v[i])--xr;); xf=AR(x)-xr;
 m=prod(xf,s); c=m?AN(x)/m:0; n=s[xf];
 GA(zx,zt,AN(x)/n,AR(x)-1,s); ICPY(xf+AS(zx),1+xf+s,xr-1); 
 ado(jt,m,c,n,AV(zx),AV(x)); RE(0);
 switch(id){
  case CPLUS: if(!equ(e,zero))RZ(e=tymes(e,sc(n))); break; 
  case CSTAR: if(!equ(e,one )&&!equ(e,zero))RZ(e=expn2(e,sc(n))); break;
  case CEQ:   ASSERT(B01&AT(x),EVNONCE); if(!*BAV(e)&&0==n%2)e=one; break;
  case CNE:   ASSERT(B01&AT(x),EVNONCE); if( *BAV(e)&&1==n%2)e=zero;
 }
 if(AT(e)!=AT(zx)){t=maxtype(AT(e),AT(zx)); if(t!=AT(zx))RZ(zx=cvt(t,zx));}
 wr=AR(w); ws=AS(w);
 GA(z,STYPE(AT(zx)),1,wr-1,ws); if(1<wr)ICPY(f+AS(z),f+1+ws,wr-1);
 zp=PAV(z);
 RZ(a=ca(a)); v=AV(a); DO(AN(a), if(f<v[i])--v[i];);
 SPB(zp,a,a);
 SPB(zp,e,cvt(AT(zx),e));
 SPB(zp,i,SPA(wp,i));
 SPB(zp,x,zx);
 R z;
}    /* f/"r w for sparse w, rank > 1, dense axis */

static B jtredspsprep(J jt,C id,I f,I zt,A a,A e,A x,A y,I*zm,I**zdv,B**zpv,I**zqv,C**zxxv,A*zsn){
     A d,p,q,sn=0,xx;B*pv;C*xxv;I*dv,j,k,m,mm,*qv=0,*u,*v,yc,yr,yr1,*yv;
 v=AS(y); yr=v[0]; yc=v[1]; yr1=yr-1;
 RZ(d=grade1(eq(a,sc(f)))); dv=AV(d); 
 DO(AN(a), if(i!=dv[i]){RZ(q=grade1p(d,y)); qv=AV(q); break;});
 GA(p,B01,yr,1,0); pv=BAV(p); memset(pv,C0,yr);
 u=yv=AV(y); m=mm=0; j=-1; if(qv)v=yv+yc*qv[0];
 for(k=0;k<yr1;++k){
  if(qv){u=v; v=yv+yc*qv[1+k];}else v=u+yc;
  DO(yc-1, if(u[dv[i]]!=v[dv[i]]){++m; pv[k]=1; mm=MAX(mm,k-j); j=k; break;});
  if(!qv)u+=yc;
 }
 if(yr){++m; pv[yr1]=1; mm=MAX(mm,yr1-j);}
 if(qv){j=mm*aii(x); GA(xx,AT(x),j,1,0); xxv=CAV(xx);}
 switch(id){
  case CPLUS: case CPLUSDOT: j=!equ(e,zero); break;
  case CSTAR: case CSTARDOT: j=!equ(e,one);  break;
  case CMIN:                 j=!equ(e,zt&B01?one :zt&INT?sc(IMAX):ainf     ); break;
  case CMAX:                 j=!equ(e,zt&B01?zero:zt&INT?sc(IMIN):scf(infm)); break;
  case CEQ:                  j=!*BAV(e);     break;
  case CNE:                  j= *BAV(e);     break;
 }
 if(j)GA(sn,INT,m,1,0);
 *zm=m; *zdv=dv; *zpv=pv; *zqv=qv; *zxxv=xxv; *zsn=sn;
 R 1;
}

static B jtredspse(J jt,C id,I wm,I xt,A e,A zx,A sn,A*ze,A*zzx){A b;B nz;I t,zt;
 RZ(b=ne(zero,sn)); nz=!all0(b); zt=AT(zx);
 switch(id){
  case CPLUS:    if(nz)RZ(zx=plus (zx,       tymes(e,sn) )); RZ(e=       tymes(e,sc(wm)) ); break; 
  case CSTAR:    if(nz)RZ(zx=tymes(zx,bcvt(1,expn2(e,sn)))); RZ(e=bcvt(1,expn2(e,sc(wm)))); break;
  case CPLUSDOT: if(nz)RZ(zx=gcd(zx,from(b,over(zero,e))));                 break;
  case CSTARDOT: if(nz)RZ(zx=lcm(zx,from(b,over(one ,e))));                 break;
  case CMIN:     if(nz)RZ(zx=minimum(zx,from(b,over(zt&B01?one: zt&INT?sc(IMAX):ainf,     e)))); break;
  case CMAX:     if(nz)RZ(zx=maximum(zx,from(b,over(zt&B01?zero:zt&INT?sc(IMIN):scf(infm),e)))); break;
  case CEQ:      ASSERT(B01&xt,EVNONCE); if(nz)RZ(zx=eq(zx,eq(zero,residue(num[2],sn)))); if(!(wm%2))e=one;  break;
  case CNE:      ASSERT(B01&xt,EVNONCE); if(nz)RZ(zx=ne(zx,eq(one, residue(num[2],sn)))); if(!(wm%2))e=zero; break;
 }
 if(AT(e)!=AT(zx)){t=maxtype(AT(e),AT(zx)); if(t!=AT(zx))RZ(zx=cvt(t,zx));}
 *ze=e; *zzx=zx;
 R 1;
}

static A jtredsps(J jt,A w,A self,C id,VF ado,I cv,I f,I r,I zt){A a,a1,e,sn,x,x1=0,y,z,zx,zy;B*pv;
     C*xv,*xxv,*zv;I*dv,i,m,n,*qv,*sv,*v,wr,xk,xt,wm,*ws,xc,yc,yr,*yu,*yv,zk;P*wp,*zp;
 RZ(w);
 ASSERT(strchr(fca,id),EVNONCE);
 wr=AR(w); ws=AS(w); wm=ws[f];
 wp=PAV(w); a=SPA(wp,a); e=SPA(wp,e); 
 y=SPA(wp,i); v=AS(y); yr=v[0]; yc=v[1]; yv=AV(y);
 x=SPA(wp,x); xt=AT(x); xc=aii(x);
 RZ(redspsprep(id,f,zt,a,e,x,y,&m,&dv,&pv,&qv,&xxv,&sn));
 xv=CAV(x); xk=xc*bp(xt);
 GA(zx,zt,m*xc,AR(x),AS(x)); *AS(zx)=m; zv=CAV(zx); zk=xc*bp(zt);
 GA(zy,INT,m*(yc-1),2,0); v=AS(zy); v[0]=m; v[1]=yc-1; yu=AV(zy);
 v=qv; if(sn)sv=AV(sn);
 for(i=0;i<m;++i){A y;B*p1;C*u;I*vv;
  p1=1+(B*)memchr(pv,C1,yr); n=p1-pv; if(sn)sv[i]=wm-n; pv=p1;
  vv=qv?yv+yc**v:yv; DO(yc-1, *yu++=vv[dv[i]];);
  if(1<n){if(qv){u=xxv; DO(n, MC(u,xv+xk*v[i],xk); u+=xk;);} ado(jt,1L,n*xc,n,zv,qv?xxv:xv); RE(0);}
  else   if(zk==xk)MC(zv,qv?xv+xk**v:xv,xk);
  else   {if(!x1)GA(x1,xt,xc,1,0); MC(AV(x1),qv?xv+xk**v:xv,xk); RZ(y=cvt(zt,x1)); MC(zv,AV(y),zk);}
  zv+=zk; if(qv)v+=n; else{xv+=n*xk; yv+=n*yc;}
 }
 if(sn)RZ(redspse(id,wm,xt,e,zx,sn,&e,&zx));
 RZ(a1=ca(a)); v=AV(a1); n=0; DO(AN(a), if(f!=v[i])v[n++]=v[i]-(f<v[i]););
 GA(z,STYPE(AT(zx)),1,wr-1,ws); if(1<r)ICPY(f+AS(z),f+1+ws,r-1);
 zp=PAV(z);
 SPB(zp,a,vec(INT,n,v)); 
 SPB(zp,e,cvt(AT(zx),e));
 SPB(zp,x,zx); 
 SPB(zp,i,zy);
 R z;
}    /* f/"r w for sparse w, rank > 1, sparse axis */

static DF1(jtreducesp){A a,g,x,y,z;B b;C id;I cv,f,n,r,rr[2],*v,wn,wr,*ws,wt,zt;P*wp;VF ado;
 RZ(w);
 wr=AR(w); r=jt->rank?jt->rank[1]:wr; f=wr-r;
 wn=AN(w); ws=AS(w); n=r?ws[f]:1;
 wt=AT(w); wt=wn?DTYPE(wt):B01;
 g=VAV(self)->f; id=vaid(g);
 if(!n)R red0(w,self);
 vains(id,wt,&ado,&cv);
 if(2==n&&!(ado&&strchr(fca,id))){
  rr[0]=0; rr[1]=r;
  jt->rank=rr; x=from(zero,w); 
  jt->rank=rr; y=from(one, w); 
  R df2(x,y,g);
 }
 if(!ado)R redg(w,self);
 if(1==n)R tail(w);
 zt=rtype(cv);
 jt->rank=0;
 if(1==wr)z=redsp1(w,self,id,ado,cv,f,r,zt);
 else{
  wp=PAV(w); a=SPA(wp,a); v=AV(a);
  b=0; DO(AN(a), if(f==v[i]){b=1; break;});
  z=b?redsps(w,self,id,ado,cv,f,r,zt):redspd(w,self,id,ado,cv,f,r,zt);
 }
 R jt->jerr==EWOV?(rr[1]=r,jt->rank=rr,reducesp(w,self)):z;
}    /* f/"r for sparse w */

#define BR2IFX(T,F)     {T*u=(T*)wv,*v=u+d,x,y;                                           \
                         GA(z,B01,wn/2,wr-1,ws); zv=BAV(z);                               \
                         if(1<d)DO(m, DO(d, x=*u++; y=*v++; *zv++=x F y; ); u+=d; v+=d;)  \
                         else   DO(m,       x=*u++; y=*u++; *zv++=x F y;               ); \
                        }
#define BR2PFX(T,F)     {T*u=(T*)wv,*v=u+d,x,y;                                           \
                         GA(z,B01,wn/2,wr-1,ws); zv=BAV(z);                               \
                         if(1<d)DO(m, DO(d, x=*u++; y=*v++; *zv++=F(x,y);); u+=d; v+=d;)  \
                         else   DO(m,       x=*u++; y=*u++; *zv++=F(x,y);              ); \
                        }
#define BTABIFX(F)      {btab[0                        ]=0 F 0;  \
                         btab[SYS&SYS_LILENDIAN?256:  1]=0 F 1;  \
                         btab[SYS&SYS_LILENDIAN?  1:256]=1 F 0;  \
                         btab[257                      ]=1 F 1;  \
                        }
#define BTABPFX(F)      {btab[0                        ]=F(0,0); \
                         btab[SYS&SYS_LILENDIAN?256:  1]=F(0,1); \
                         btab[SYS&SYS_LILENDIAN?  1:256]=F(1,0); \
                         btab[257                      ]=F(1,1); \
                        }
#define BR2CASE(t,id)   ((id)+256*(t))

static B jtreduce2(J jt,A w,C id,I f,I r,A*zz){A z=0;B b=0,btab[258],*zv;I c,d,m,wn,wr,*ws,*wv;
 wn=AN(w); wr=AR(w); ws=AS(w); wv=AV(w);
 m=prod(f,ws); c=m?wn/m:prod(r,f+ws); d=c/2;
 switch(BR2CASE(AT(w),id)){
  case BR2CASE(B01,CEQ     ): if(b=1==r)BTABIFX(==   ); break;
  case BR2CASE(B01,CNE     ): if(b=1==r)BTABIFX(!=   ); break;
  case BR2CASE(B01,CLT     ): if(b=1==r)BTABIFX(<    ); break;
  case BR2CASE(B01,CLE     ): if(b=1==r)BTABIFX(<=   ); break;
  case BR2CASE(B01,CGT     ): if(b=1==r)BTABIFX(>    ); break;
  case BR2CASE(B01,CGE     ): if(b=1==r)BTABIFX(>=   ); break;
  case BR2CASE(B01,CMAX    ):
  case BR2CASE(B01,CPLUSDOT): if(b=1==r)BTABIFX(||   ); break;
  case BR2CASE(B01,CPLUSCO ): if(b=1==r)BTABPFX(BNOR ); break;
  case BR2CASE(B01,CMIN    ):
  case BR2CASE(B01,CSTAR   ):
  case BR2CASE(B01,CSTARDOT): if(b=1==r)BTABIFX(&&   ); break;
  case BR2CASE(B01,CSTARCO ): if(b=1==r)BTABPFX(BNAND); break;
  case BR2CASE(LIT,CEQ     ): BR2IFX(C,== ); break;
  case BR2CASE(LIT,CNE     ): BR2IFX(C,!= ); break;
  case BR2CASE(INT,CEQ     ): BR2IFX(I,== ); break;
  case BR2CASE(INT,CLT     ): BR2IFX(I,<  ); break;
  case BR2CASE(INT,CLE     ): BR2IFX(I,<= ); break;
  case BR2CASE(INT,CGT     ): BR2IFX(I,>  ); break;
  case BR2CASE(INT,CGE     ): BR2IFX(I,>= ); break;
  case BR2CASE(INT,CNE     ): BR2IFX(I,!= ); break;
  case BR2CASE(FL, CEQ     ): BR2PFX(D,TEQ); break;
  case BR2CASE(FL, CLT     ): BR2PFX(D,TLT); break;
  case BR2CASE(FL, CLE     ): BR2PFX(D,TLE); break;
  case BR2CASE(FL, CGT     ): BR2PFX(D,TGT); break;
  case BR2CASE(FL, CGE     ): BR2PFX(D,TGE); break;
  case BR2CASE(FL, CNE     ): BR2PFX(D,TNE); break;
 }
 if(b){S*u=(S*)wv; GA(z,B01,wn/2,wr-1,ws); zv=BAV(z); DO(m, *zv++=btab[*u++];);}
 if(z&&1<r){I*u=f+AS(z),*v=f+1+ws; DO(r-1, *u++=*v++;);}
 *zz=z;
 R 1;
}    /* f/"r for dense w over an axis of length 2 */

static DF1(jtreduce){A z;C id;I c,cv,f,m,n,r,rr[2],t,wn,wr,*ws,wt,zt;VF ado;
 RZ(w);
 wr=AR(w); r=jt->rank?jt->rank[1]:wr; f=wr-r;
 wn=AN(w); ws=AS(w); n=r?ws[f]:1;
 if(SPARSE&AT(w))R reducesp(w,self);
 wt=AT(w); wt=wn?wt:B01;
 id=vaid(VAV(self)->f);
 switch(n){
  case 0: R red0(w,self);
  case 1: R tail(w);
  case 2: RZ(reduce2(w,id,f,r,&z)); if(z)R z;
 }
 vains(id,wt,&ado,&cv);
 if(!ado)R redg(w,self);
 zt=rtype(cv); jt->rank=0;
 GA(z,zt,wn/n,MAX(0,wr-1),ws); if(1<r)ICPY(f+AS(z),f+1+ws,r-1);
 if((t=atype(cv))&&t!=wt)RZ(w=cvt(t,w));
 m=prod(f,ws); c=m?wn/m:prod(r,f+ws);
 ado(jt,m,c,n,AV(z),AV(w));
 if(jt->jerr)R jt->jerr==EWOV?(rr[1]=r,jt->rank=rr,reduce(w,self)):0; else R cv&VRI+VRD?cvz(cv,z):z;
}    /* f/"r w main control */

static A jtredcatsp(J jt,A w,A z,I r){A a,q,x,y;B*b;I c,d,e,f,j,k,m,n,n1,p,*u,*v,wr,*ws,xr;P*wp,*zp;
 ws=AS(w); wr=AR(w); f=wr-r; p=ws[1+f];
 wp=PAV(w); x=SPA(wp,x); y=SPA(wp,i); a=SPA(wp,a); v=AV(a); 
 m=*AS(y); n=AN(a); n1=n-1; xr=AR(x);
 RZ(b=bfi(wr,a,1));
 c=b[f]; d=b[1+f]; if(c&&d)b[f]=0; e=f+!c;
 j=0; DO(n, if(e==v[i]){j=i; break;}); 
 k=1; DO(f, if(!b[i])++k;);
 zp=PAV(z); SPB(zp,e,ca(SPA(wp,e)));
 GA(q,INT,n-(c&&d),1,0); v=AV(q); DO(wr, if(b[i])*v++=i-(i>f);); SPB(zp,a,q);
 if(c&&d){          /* sparse sparse */
  SPB(zp,x,ca(x));
  SPB(zp,i,q=repeatr(ne(a,sc(f)),y));
  v=j+AV(q); u=j+AV(y);
  DO(m, *v=p*u[0]+u[1]; v+=n1; u+=n;);
 }else if(!c&&!d){  /* dense dense */
  u=AS(x); GA(q,AT(x),AN(x),xr-1,u); v=k+AS(q); *v=u[k]*u[1+k]; ICPY(1+v,2+k+u,xr-k-2);
  MC(AV(q),AV(x),AN(x)*bp(AT(x)));
  SPB(zp,x,q); SPB(zp,i,ca(y));
 }else{             /* other */
  GA(q,INT,xr,1,0); v=AV(q); 
  if(1!=k){*v++=0; *v++=k; e=0; DO(xr-1, ++e; if(e!=k)*v++=e;); RZ(x=cant2(q,x));}
  v=AV(q); u=AS(x); *v=u[0]*u[1]; ICPY(1+v,2+u,xr-1); RZ(x=reshape(vec(INT,xr-1,v),x));
  e=ws[f+c]; RZ(y=repeat(sc(e),y)); v=j+AV(y);
  if(c)DO(m, k=p**v; DO(e, *v=k+  i; v+=n;);)
  else DO(m, k=  *v; DO(e, *v=k+p*i; v+=n;);); 
  RZ(q=grade1(y)); RZ(y=from(q,y)); RZ(x=from(q,x));
  SPB(zp,x,x); SPB(zp,i,y);
 }
 R z;
}    /* ,/"r w for sparse w, 2<r */

static DF1(jtredcat){A z;B b;I f,r,*s,*v,wr;
 RZ(w);
 wr=AR(w); r=jt->rank?jt->rank[1]:wr; f=wr-r; s=AS(w); jt->rank=0;
 b=1==r&&1==s[f];
 if(2>r&&!b)R ca(w);
 GA(z,AT(w),AN(w),wr-1,s); 
 if(!b){v=f+AS(z); RE(*v=mult(s[f],s[1+f])); ICPY(1+v,2+f+s,r-2);}
 if(SPARSE&AT(w))R redcatsp(w,z,r);
 MC(AV(z),AV(w),AN(w)*bp(AT(w)));
 if(ARELATIVE(w)){AFLAG(z)=AFREL; z=relocate((I)w-(I)z,z);}
 R z;
}    /* ,/"r w */

static DF1(jtredsemi){I f,n,r,*s,wr;
 RZ(w);
 wr=AR(w); r=jt->rank?jt->rank[1]:wr; f=wr-r; s=AS(w); n=r?s[f]:1;
 if(2>n){ASSERT(n,EVDOMAIN); R tail(w);}
 if(BOX&AT(w))R irs2(rank1ex(curtail(w),0L,r-1,jtbox),tail(w),0L,r,r-1,jtover);
 else R irs1(w,0L,r-1,jtbox);
}    /* ;/"r w */

static DF1(jtredstitch){A c,y;I f,n,r,*s,*v,wr;
 RZ(w);
 wr=AR(w); r=jt->rank?jt->rank[1]:wr; f=wr-r; jt->rank=0;
 s=AS(w); n=r?s[f]:1;
 ASSERT(n,EVDOMAIN);
 if(1==n)R irs1(w,0L,r,jthead);
 if(1==r)R 2==n?ca(w):irs2(irs2(num[-2],w,0L,0L,1L,jtdrop),irs2(num[-2],w,0L,0L,1L,jttake),0L,1L,0L,jtover);
 if(2==r)R irs1(w,0L,2L,jtcant1);
 RZ(c=IX(wr)); v=AV(c); v[f]=f+1; v[f+1]=f; RZ(y=cant2(c,w));
 if(SPARSE&AT(w)){A x;
  GA(x,INT,f+r-1,1,0); v=AV(x); ICPY(v,AS(y),f+1);
  RE(v[f+1]=mult(s[f],s[f+2])); ICPY(v+f+2,s+3+f,r-3);
  R reshape(x,y);
 }else{
  v=AS(y); 
  RE(v[f+1]=mult(s[f],s[f+2])); ICPY(v+f+2,s+3+f,r-3);
  --AR(y); 
  R y;
}}   /* ,./"r w */

static DF1(jtredstiteach){A*wv,y;I n,p,r,t,wd;
 RZ(w);
 n=AN(w);
 if(!(2<n&&1==AR(w)&&BOX&AT(w)))R reduce(w,self);
 wv=AAV(w); wd=(I)w*ARELATIVE(w); y=WVR(0); p=IC(y); t=AT(y);
 DO(n, y=WVR(i); r=AR(y); if(!(r&&r<=2&&p==IC(y)&&t==AT(y)))R reduce(w,self););
 R box(razeh(w));
}    /* ,.&.>/ w */

static DF1(jtredcateach){A*u,*v,*wv,x,*xv,z,*zv;I f,m,mn,n,r,wd,wr,*ws,zm,zn;
 RZ(w);
 wr=AR(w); ws=AS(w); r=jt->rank?jt->rank[1]:wr; f=wr-r; jt->rank=0;
 n=r?ws[f]:1;
 if(!r||1>=n)R reshape(repeat(ne(sc(f),IX(wr)),shape(w)),n?w:ace);
 if(!(BOX&AT(w)))R df1(cant2(sc(f),w),qq(ds(CBOX),one));
 zn=AN(w)/n; zm=prod(f,ws); m=zm?AN(w)/(zm*n):prod(r-1,ws+f+1); mn=m*n;
 GA(z,BOX,zn,wr-1,ws); ICPY(AS(z)+f,ws+f+1,r-1);
 GA(x,BOX,n,1,0); xv=AAV(x);
 zv=AAV(z); wv=AAV(w); wd=(I)w*ARELATIVE(w);
 DO(zm, u=wv; DO(m, v=u++; DO(n, xv[i]=AADR(wd,*v); v+=m;); RZ(*zv++=raze(x));); wv+=mn;);
 R z;
}    /* ,&.>/"r w */

static DF2(jtoprod){R df2(a,w,VAV(self)->h);}


F1(jtslash){A h;AF f1=jtreduce;C c;V*v;
 RZ(w);
 if(NOUN&AT(w))R evger(w,sc(GINSERT));
 v=VAV(w); 
 switch(v->id){
  case CCOMMA:  f1=jtredcat;    break;
  case CCOMDOT: f1=jtredstitch; break;
  case CSEMICO: f1=jtredsemi;   break;
  case CUNDER:  if(COPE==ID(v->g)){c=ID(v->f); if(c==CCOMMA)f1=jtredcateach; else if(c==CCOMDOT)f1=jtredstiteach;}
 }
 RZ(h=qq(w,v2(lr(w),RMAX)));
 R fdef(CSLASH,VERB, f1,jtoprod, w,0L,h, 0L, RMAX,RMAX,RMAX);
}

A jtaslash (J jt,C c,    A w){RZ(   w); R df1(  w,   slash(ds(c))     );}
A jtaslash1(J jt,C c,    A w){RZ(   w); R df1(  w,qq(slash(ds(c)),one));}
A jtatab   (J jt,C c,A a,A w){RZ(a&&w); R df2(a,w,   slash(ds(c))     );}


static AHDRR(jtmeanD,D,D){I d,i;D*y;D v,*zz;
 d=c/n;
 NAN0;
 if(1==d)DO(m, v=   *x++; DO(n-1, v+=*x++;); *z++=v/n;)
 else for(i=0;i<m;++i){
  y=x; x+=d; zz=z; DO(d, *z++ =*x+++   *y++;);
  DO(n-3,    z=zz; DO(d, *z+++=*x++;        ));
             z=zz; DO(d, *z   =(*z+*x++)/n; ++z;);
 }
 NAN1V;
}    /* based on REDUCEPFX; 2<n */

static AHDRR(jtmeanI,D,I){I d,i;I*y;D v,*zz;
 d=c/n;
 if(1==d)DO(m, v=(D)*x++; DO(n-1, v+=*x++;); *z++=v/n;)
 else for(i=0;i<m;++i){
  y=x; x+=d; zz=z; DO(d, *z++ =*x+++(D)*y++;);
  DO(n-3,    z=zz; DO(d, *z+++=*x++;        ));
             z=zz; DO(d, *z   =(*z+*x++)/n; ++z;);
}}   /* based on REDUCEPFX; 2<n */

DF1(jtmean){A z;I c,f,m,n,r,wn,wr,*ws,wt;
 RZ(w);
 wr=AR(w); r=jt->rank?jt->rank[1]:wr; f=wr-r; jt->rank=0;
 wt=AT(w); wn=AN(w); ws=AS(w); n=r?ws[f]:1;
 if(!(wn&&2<n&&wt&INT+FL))R divide(df1(w,qq(slash(ds(CPLUS)),sc(r))),sc(n));
 GA(z,FL,wn/n,MAX(0,wr-1),ws); if(1<r)ICPY(f+AS(z),f+1+ws,r-1);
 m=prod(f,ws); c=m?wn/m:prod(r,f+ws);
 if(wt&INT)meanI(m,c,n,DAV(z), AV(w)); 
 else      meanD(m,c,n,DAV(z),DAV(w));
 RE(0); R z;
}    /* (+/%#)"r w */