Return to calc.c CVS log

Up to [local] / OpenXM_contrib2 / asir2018 / plot

Changed macros : QTOS->ZTOS, STOQ->STOZ etc.

/*
 * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED 
 * All rights reserved.
 * 
 * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
 * non-exclusive and royalty-free license to use, copy, modify and
 * redistribute, solely for non-commercial and non-profit purposes, the
 * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
 * conditions of this Agreement. For the avoidance of doubt, you acquire
 * only a limited right to use the SOFTWARE hereunder, and FLL or any
 * third party developer retains all rights, including but not limited to
 * copyrights, in and to the SOFTWARE.
 * 
 * (1) FLL does not grant you a license in any way for commercial
 * purposes. You may use the SOFTWARE only for non-commercial and
 * non-profit purposes only, such as academic, research and internal
 * business use.
 * (2) The SOFTWARE is protected by the Copyright Law of Japan and
 * international copyright treaties. If you make copies of the SOFTWARE,
 * with or without modification, as permitted hereunder, you shall affix
 * to all such copies of the SOFTWARE the above copyright notice.
 * (3) An explicit reference to this SOFTWARE and its copyright owner
 * shall be made on your publication or presentation in any form of the
 * results obtained by use of the SOFTWARE.
 * (4) In the event that you modify the SOFTWARE, you shall notify FLL by
 * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
 * for such modification or the source code of the modified part of the
 * SOFTWARE.
 * 
 * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
 * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
 * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
 * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
 * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY
 * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
 * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT,
 * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY
 * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL
 * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES
 * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
 * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY
 * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF
 * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART
 * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY
 * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
 * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
 *
 * $OpenXM: OpenXM_contrib2/asir2018/plot/calc.c,v 1.2 2018/09/28 08:20:29 noro Exp $
*/
#include "ca.h"
#include "parse.h"
#include "ifplot.h"
#include <math.h>
#if defined(PARI)
#include "genpari.h"
#endif

#ifndef MAXSHORT
#define MAXSHORT ((short)0x7fff)
#endif

void calc(double **tab,struct canvas *can,int nox){
  //memory_plot,IFPLOTD,INEQND,INEQNANDD,INEQNORD
  //INEQNXORD,conplotmainD
  double x,y,xstep,ystep;
  int ix,iy;
  Real r,rx,ry;
  Obj fr,g,t,s;

  if(!nox)initmarker(can,"Evaluating...");
  todouble((Obj)can->formula,(Obj *)&fr);
  xstep=(can->xmax-can->xmin)/can->width;
  ystep=(can->ymax-can->ymin)/can->height;
  MKReal(1.0,rx); MKReal(1.0,ry); // dummy real
  BDY(rx)=can->xmin;
  substr(CO,0,fr,can->vx,can->xmin?(Obj)rx:0,&t); devalr(CO,t,&g);
  BDY(ry)=can->ymin;
  substr(CO,0,g,can->vy,can->ymin?(Obj)ry:0,&t); devalr(CO,t,&s);
  can->vmax=can->vmin=ToReal(s);
  for(ix=0,x=can->xmin; ix<can->width; ix++,x+=xstep){
    BDY(rx)=x; substr(CO,0,fr,can->vx,x?(Obj)rx:0,&t);
    devalr(CO,t,&g);
    if(!nox)marker(can,DIR_X,ix);
    for(iy=0,y=can->ymin; iy<can->height; iy++,y+=ystep){
      BDY(ry)=y;
      substr(CO,0,g,can->vy,y?(Obj)ry:0,&t);
      devalr(CO,t,&s);
      tab[ix][iy]=ToReal(s);
      if(can->vmax<tab[ix][iy])can->vmax=tab[ix][iy];
      if(can->vmin>tab[ix][iy])can->vmin=tab[ix][iy];
    }
  }
}

void calcq(double **tab,struct canvas *can,int nox){
  //IFPLOTQ,INEQNQ,INEQNANDQ,INEQNORQ,INEQNXORQ
  //plotoverD
  Z w,h,q1;
  Q dx,dy,xstep,ystep,c;
  P g,g1,f1,f2,x,y;
  int ix,iy;
  Obj fr,gm,t,s;
  Real r,rx,ry;

  todouble((Obj)can->formula,&fr);
  MKReal(1.0,rx); MKReal(1.0,ry); // dummy real
  BDY(rx)=can->xmin;
  substr(CO,0,fr,can->vx,can->xmin?(Obj)rx:0,&t); devalr(CO,t,&gm);
  BDY(ry)=can->ymin;
  substr(CO,0,gm,can->vy,can->ymin?(Obj)ry:0,&t); devalr(CO,t,&s);
  can->vmax=can->vmin=ToReal(s);

  subq(can->qxmax,can->qxmin,&dx); STOZ(can->width,w); divq(dx,(Q)w,&xstep);
  subq(can->qymax,can->qymin,&dy); STOZ(can->height,h); divq(dy,(Q)h,&ystep);
  MKV(can->vx,x); mulp(CO,(P)xstep,x,(P *)&t);
  addp(CO,(P)can->qxmin,(P)t,(P *)&s); substp(CO,can->formula,can->vx,(P)s,&f1);
  MKV(can->vy,y); mulp(CO,(P)ystep,y,(P *)&t);
  addp(CO,(P)can->qymin,(P)t,(P *)&s); substp(CO,f1,can->vy,(P)s,&f2);
  ptozp(f2,1,&c,&g);
  if(!nox) initmarker(can,"Evaluating...");
  for(iy=0;iy<can->height;iy++){
    marker(can,DIR_Y,iy);
    STOZ(iy,q1); substp(CO,g,can->vy,(P)q1,(P *)&t); ptozp((P)t,1,&c,&g1);
    for(ix=0;ix<can->width;ix++){
      STOZ(ix,q1);substp(CO,g1,can->vx,(P)q1,(P *)&t);
      devalr(CO,t,&s);
      tab[ix][iy]=ToReal(s);
      if(can->vmax<tab[ix][iy])can->vmax=tab[ix][iy];
      if(can->vmin>tab[ix][iy])can->vmin=tab[ix][iy];
    }
  }
}

void calcb(double **tab,struct canvas *can,int nox){
  //IFPLOTB,INEQNB,INEQNANDB,INEQNORB,INEQNXORB
  Z w,h,q1;
  Q dx,dy,xstep,ystep,c;
  P g,g1,f1,f2,x,y,t,s;
  int ix,iy,*a,*pa;
  VECT ss;
  Obj fr,gm,tm,sm;
  Real r,rx,ry;

  todouble((Obj)can->formula,&fr);
  MKReal(1.0,rx); MKReal(1.0,ry); // dummy real
  BDY(rx)=can->xmin;
  substr(CO,0,fr,can->vx,can->xmin?(Obj)rx:0,&tm); devalr(CO,tm,&gm);
  BDY(ry)=can->ymin;
  substr(CO,0,gm,can->vy,can->ymin?(Obj)ry:0,&tm); devalr(CO,tm,&sm);
  can->vmax=can->vmin=ToReal(sm);

  for(iy=0;iy<can->height;iy++)for(ix=0;ix<can->width;ix++)tab[ix][iy]=1.0;
  subq(can->qxmax,can->qxmin,&dx); STOZ(can->width,w); divq(dx,(Q)w,&xstep);
  subq(can->qymax,can->qymin,&dy); STOZ(can->height,h); divq(dy,(Q)h,&ystep);
  MKV(can->vx,x); mulp(CO,(P)xstep,x,&t);
  addp(CO,(P)can->qxmin,t,&s); substp(CO,can->formula,can->vx,s,&f1);
  MKV(can->vy,y); mulp(CO,(P)ystep,y,&t);
  addp(CO,(P)can->qymin,t,&s); substp(CO,f1,can->vy,s,&f2);
  ptozp(f2,1,&c,&g);
  a=(int *)ALLOCA((MAX(can->width,can->height)+1)*sizeof(int));
  for(iy=0;iy<can->height;iy++)for(ix=0;ix<can->width;ix++)tab[ix][iy]=1.0;
  subq(can->qxmax,can->qxmin,&dx); STOZ(can->width,w); divq(dx,(Q)w,&xstep);
  subq(can->qymax,can->qymin,&dy); STOZ(can->height,h); divq(dy,(Q)h,&ystep);
  MKV(can->vx,x); mulp(CO,(P)xstep,x,&t);
  addp(CO,(P)can->qxmin,t,&s); substp(CO,can->formula,can->vx,s,&f1);
  MKV(can->vy,y); mulp(CO,(P)ystep,y,&t);
  addp(CO,(P)can->qymin,t,&s); substp(CO,f1,can->vy,s,&f2);
  ptozp(f2,1,&c,&g);
  a=(int *)ALLOCA((MAX(can->width,can->height)+1)*sizeof(int));
  for(ix=0;ix<can->width;ix++){
    STOZ(ix,q1); substp(CO,g,can->vx,(P)q1,&t); ptozp(t,1,&c,&g1);
    if(!g1)for(iy=0;iy<can->height;iy++)tab[ix][iy]=0.0;
    else if(!NUM(g1)){
      sturmseq(CO,g1,&ss);
      seproot(ss,0,can->width,a);
      for(iy=0,pa=a;iy<can->height;iy++,pa++){
        if(*pa<0||(*(pa+1)>=0&&(*pa>*(pa+1))))tab[ix][iy]=0.0;
        else {
          STOZ(iy,q1);substp(CO,g1,can->vy,(P)q1,&t);
          devalr(CO,(Obj)t,(Obj *)&s);
          tab[ix][iy]=ToReal(s);
          if(can->vmax<tab[ix][iy])can->vmax=tab[ix][iy];
          if(can->vmin>tab[ix][iy])can->vmin=tab[ix][iy];
        }
      }
    }
  }
  for(iy=0;iy<can->height;iy++){
    STOZ(iy,q1); substp(CO,g,can->vy,(P)q1,&t); ptozp(t,1,&c,&g1);
    if(!g1) for(ix=0;ix<can->width;ix++)tab[ix][iy]=0.0;
    else if(!NUM(g1)){
      sturmseq(CO,g1,&ss);
      seproot(ss,0,can->height,a);
      for(ix=0,pa=a;ix<can->width;ix++,pa++){
        if(tab[ix][iy]!=0.0){
          if(*pa<0||(*(pa+1)>=0&&(*pa>*(pa+1))))tab[ix][iy]=0.0;
          else {
            STOZ(ix,q1);substp(CO,g1,can->vx,(P)q1,&t);
            devalr(CO,(Obj)t,(Obj *)&s);
            tab[ix][iy]=ToReal(s);
            if(can->vmax<tab[ix][iy])can->vmax=tab[ix][iy];
            if(can->vmin>tab[ix][iy])can->vmin=tab[ix][iy];
          }
        }
      }
    }
  }
}

double usubstrp(P p,double r){
  DCP dc;
  int d;
  double t,pwrreal0();

  if(!p) t=0.0;
  else if(NUM(p))t=BDY((Real)p);
  else {
    dc=DC(p); t=BDY((Real)COEF(dc));
    for(d=ZTOS(DEG(dc)),dc=NEXT(dc);dc;d=ZTOS(DEG(dc)),dc=NEXT(dc)){
      t=t*pwrreal0(r,(d-ZTOS(DEG(dc))))+BDY((Real)COEF(dc));
    }
    if(d)t*=pwrreal0(r,d);
  }
  return t;
}

void qcalc(char **tab,struct canvas *can){
  //qifplotmain(Old type)
  Z w,h,q1;
  Q dx,dy,xstep,ystep,c;
  P g,g1,f1,f2,x,y,t,s;
  int ix,iy;
  int *a,*pa;
  VECT ss;

  subq(can->qxmax,can->qxmin,&dx); STOZ(can->width,w); divq(dx,(Q)w,&xstep);
  subq(can->qymax,can->qymin,&dy); STOZ(can->height,h); divq(dy,(Q)h,&ystep);
  MKV(can->vx,x); mulp(CO,(P)xstep,x,&t); 
  addp(CO,(P)can->qxmin,t,&s); substp(CO,can->formula,can->vx,s,&f1);
  MKV(can->vy,y); mulp(CO,(P)ystep,y,&t);
  addp(CO,(P)can->qymin,t,&s); substp(CO,f1,can->vy,s,&f2);
  ptozp(f2,1,&c,&g);
  a=(int *)ALLOCA((MAX(can->width,can->height)+1)*sizeof(int));
  initmarker(can,"Horizontal scan...");
  for( ix=0; ix < can->width; ix++ ){
    marker(can,DIR_X,ix);
    STOZ(ix,q1); substp(CO,g,can->vx,(P)q1,&t); ptozp(t,1,&c,&g1);
    if( !g1 )
      for(iy=0; iy < can->height; iy++ )
        tab[ix][iy]=1;
    else if( !NUM(g1) ){
      sturmseq(CO,g1,&ss); seproot(ss,0,can->height,a);
      for(iy=0, pa=a; iy < can->height; iy++, pa++ )
        if( *pa < 0 || (*(pa+1) >= 0 && (*pa > *(pa+1))) )
          tab[ix][iy]=1;
    }
  }
  initmarker(can,"Vertical scan...");
  for( iy=0; iy < can->height; iy++ ){
    marker(can,DIR_Y,iy);
    STOZ(iy,q1); substp(CO,g,can->vy,(P)q1,&t); ptozp(t,1,&c,&g1);
    if( !g1 )
      for(ix=0; ix < can->width; ix++ )
        tab[ix][iy]=1;
    else if( !NUM(g1) ){
      sturmseq(CO,g1,&ss); seproot(ss,0,can->width,a);
      for(ix=0, pa=a; ix < can->width; ix++, pa++ )
        if( *pa < 0 || (*(pa+1) >= 0 && (*pa > *(pa+1))) )
          tab[ix][iy]=1;
    }
  }
}

void sturmseq(VL vl,P p,VECT *rp){
  P g1,g2,q,r,s,*t;
  V v;
  VECT ret;
  int i,j;
  Q b,c,l,m,h,x;
  Z d,a;

  v=VR(p);t=(P *)ALLOCA((deg(v,p)+1)*sizeof(P));
  g1=t[0]=p;diffp(vl,p,v,(P *)&a);ptozp((P)a,1,&c,&g2);t[1]=g2;
  for(i=1,h=(Q)ONE,x=(Q)ONE;;){
    if(NUM(g2)) break;
    subz(DEG(DC(g1)),DEG(DC(g2)),&d);
    l=(Q)LC(g2);
    if(sgnq(l)<0){
      chsgnq(l,&b);l=b;
    }
    addz(d,ONE,&a);pwrq(l,(Q)a,&b);mulp(vl,(P)b,g1,&s);
    divsrp(vl,s,g2,&q,&r);
    if(!r) break;
    chsgnp(r,&s);r=s;i++;
    if(NUM(r)){
      t[i]=r;break;
    }
    pwrq(h,(Q)d,&m);g1=g2;
    mulq(m,x,(Q *)&a);divsp(vl,r,(P)a,&g2);t[i]=g2;
    x=(Q)LC(g1);
    if(sgnq(x)<0){
      chsgnq(x,&b);x=b;
    }
    pwrq(x,(Q)d,(Q *)&a);mulq((Q)a,h,&b);divq(b,m,&h);
  }
  MKVECT(ret,i+1);
  for(j=0;j<=i;j++)
    ret->body[j]=(pointer)t[j];
  *rp=ret;  
}

void seproot(VECT s,int min,int max,int *ar){
  P f,*ss;
  Q t;
  Z q;
  int i,j,k;

  ss=(P *)s->body;f=ss[0];
  for(i=min;i<=max;i++){
    STOZ(i,q);usubstqp(f,(Q)q,&t);
    if(!t)ar[i]=-1;
    else {
      ar[i]=numch(s,(Q)q,t);break;
    }
  }
  if(i>max) return;
  for(j=max;j>= min;j--){
    STOZ(j,q); usubstqp(f,(Q)q,&t);
    if(!t)ar[j]=-1;
    else {
      if(i!=j)ar[j]=numch(s,(Q)q,t);
      break;
    }
  }
  if(j<=i+1) return;
  if(ar[i]==ar[j]){
    for(k=i+1;k<j;k++)ar[k]=ar[i];
    return;
  }
  k=(i+j)/2;
  seproot(s,i,k,ar);
  seproot(s,k,j,ar);
}

int numch(VECT s,Q n,Q a0){
  int len,i,c;
  Q a;
  P *ss;

  len=s->len;ss=(P *)s->body;
  for(i=1,c=0;i<len;i++){
    usubstqp(ss[i],n,&a);
    if(a){
      if((sgnq(a)>0 && sgnq(a0)<0)||(sgnq(a)<0&&sgnq(a0)>0))c++;
      a0=a;
    }
  }
  return c;
}

void usubstqp(P p,Q r,Q *v){
  Q a,b,t;
  Z d,d1;
  DCP dc;

  if(!p)
    *v=0;
  else if(NUM(p))*v=(Q)p;
  else {
    dc=DC(p);t=(Q)COEF(dc);
    for(d=DEG(dc),dc=NEXT(dc);dc;d=DEG(dc),dc=NEXT(dc)){
      subz(d,DEG(dc),&d1);pwrq(r,(Q)d1,&a);
      mulq(t,a,&b);addq(b,(Q)COEF(dc),&t);
    }
    if(d){
      pwrq(r,(Q)d,&a);mulq(t,a,&b);t=b;
    }
    *v=t;
  }
}

Num tobf(Num,int);
void Psetprec(NODE arg,Obj *rp);

void plotcalcbf(struct canvas *can){
  Obj fr,s,t;
  Num xmin,xmax,ymin,ymax,xstep;
  Num u,v,ha,dx,dy,x;
  Num *tab;
  Real r;
  int ix;
  POINT *pa;
  double rr;
  Z prec,w,h1;
  NODE arg;

  STOZ(can->prec,prec); arg = mknode(1,prec); Psetprec(arg,&t);
  evalr(CO,(Obj)can->formula,can->prec,&fr);
  MKReal(can->xmin,r); xmin = tobf((Num)r,can->prec);
  MKReal(can->xmax,r); xmax = tobf((Num)r,can->prec);
  MKReal(can->ymin,r); ymin = tobf((Num)r,can->prec);
  MKReal(can->ymax,r); ymax = tobf((Num)r,can->prec);
  STOZ(can->width,w);
  subbf(xmax,xmin,&dx); divbf(dx,(Num)w,&xstep);
  tab=(Num *)MALLOC(can->width*sizeof(Num));
  for(ix=0,x=xmin;ix<can->width;ix++){
    substr(CO,0,fr,can->vx,(Obj)x,(Obj *)&s);
    evalr(CO,(Obj)s,can->prec,&t);
    if(t&&(OID(t)!=O_N))
      error("plotcalcbf : invalid evaluation");
    tab[ix]=(Num)t;
    addbf(x,xstep,&u); x = u;
  }
  if(!cmpbf(ymax,ymin)){
    for(ymax=ymin=tab[0],ix=1;ix<can->width;ix++){
      if(cmpbf(tab[ix],ymax)>0)ymax=tab[ix];
      if(cmpbf(tab[ix],ymin)<0)ymin=tab[ix];
    }
    can->ymax=ToReal(ymax);can->ymin=ToReal(ymin);
  }
  subbf(ymax,ymin,&dy);
  can->pa=(struct pa *)MALLOC(sizeof(struct pa));
  can->pa[0].length=can->width;
  can->pa[0].pos=pa=(POINT *)MALLOC(can->width*sizeof(POINT));
  STOZ(can->height-1,h1);
  for(ix=0;ix<can->width;ix++){
    XC(pa[ix])=ix; 
    subbf(ymax,tab[ix],&u); divbf(u,dy,&v); mulbf(v,(Num)h1,&u);
    rr = ToReal(u);
    if(rr>MAXSHORT)YC(pa[ix])=MAXSHORT;
    else if(rr<-MAXSHORT)YC(pa[ix])=-MAXSHORT;
    else YC(pa[ix])=(long)rr;
  }
}

void plotcalc(struct canvas *can){
  //plot,memory_plot,plotover,plot_resize
  double x,xmin,xstep,ymax,ymin,dy,*tab,usubstrp();
  int ix,w,h;
  Real r,rx;
  Obj fr,t,s;
  POINT *pa;

  if ( can->prec ) {
    plotcalcbf(can);
    return;
  }
  todouble((Obj)can->formula,&fr);
  w=can->width;h=can->height;
  xmin=can->xmin;xstep=(can->xmax-can->xmin)/w;
  tab=(double *)ALLOCA(w*sizeof(double));
  MKReal(1,rx); // dummy real number
  for(ix=0,x=xmin;ix<w;ix++,x+=xstep){
    // full substitution
    BDY(rx)=x;
    substr(CO,0,fr,can->vx,x?(Obj)rx:0,&s);
    devalr(CO,(Obj)s,&t);
    if(t&&(OID(t)!=O_N||NID((Num)t)!=N_R))
      error("plotcalc : invalid evaluation");
    tab[ix]=ToReal((Num)t);  
  }
  if(can->ymax==can->ymin){
    for(ymax=ymin=tab[0],ix=1;ix<w;ix++){
      if(tab[ix]>ymax)ymax=tab[ix];
      if(tab[ix]<ymin)ymin=tab[ix];
    }
    can->ymax=ymax;can->ymin=ymin;
  } else {
    ymax=can->ymax;ymin=can->ymin;
  }
  dy=ymax-ymin;
  can->pa=(struct pa *)MALLOC(sizeof(struct pa));
  can->pa[0].length=w;
  can->pa[0].pos=pa=(POINT *)MALLOC(w*sizeof(POINT));
  for(ix=0;ix<w;ix++){
    double t;
    XC(pa[ix])=ix; 
    t=(h-1)*(ymax-tab[ix])/dy;
    if(t>MAXSHORT)YC(pa[ix])=MAXSHORT;
    else if(t<-MAXSHORT)YC(pa[ix])=-MAXSHORT;
    else YC(pa[ix])=(long)t;
  }
}

void polarcalc(struct canvas *can){
  double xmax,xmin,ymax,ymin,dx,dy,pmin,pstep,tr,p,*tabx,*taby;
  double usubstrp();
  int i,nstep,w,h;
  POINT *pa;
  Real r;
  Obj fr,t,s;

  todouble((Obj)can->formula,&fr);
  w=can->width; h=can->height; nstep=can->nzstep;
  pmin=can->zmin; pstep=(can->zmax-can->zmin)/nstep;
  tabx=(double *)ALLOCA(nstep*sizeof(double));
  taby=(double *)ALLOCA(nstep*sizeof(double));
  MKReal(1,r); // dummy real number

  for(i=0,p=pmin;i<nstep;i++,p+= pstep){
    // full substitution
    BDY(r)=p;
    substr(CO,0,fr,can->vx,p?(Obj)r:0,&s);
    devalr(CO,(Obj)s,&t);
    if(t&&(OID(t)!=O_N||NID((Num)t)!=N_R))
      error("polarcalc : invalid evaluation");
    tr=ToReal((Num)t);  
    tabx[i]=tr*cos(p);
    taby[i]=tr*sin(p);
  }
  xmax=xmin=tabx[0];
  ymax=ymin=taby[0];
  for(i=1;i<nstep;i++){
    if(tabx[i]>xmax)xmax=tabx[i];
    if(tabx[i]<xmin)xmin=tabx[i];
    if(taby[i]>ymax)ymax=taby[i];
    if(taby[i]<ymin)ymin=taby[i];
  }
  can->xmax=xmax;can->xmin=xmin;
  can->ymax=ymax;can->ymin=ymin;
  dx=xmax-xmin;
  dy=ymax-ymin;
  can->pa=(struct pa *)MALLOC(sizeof(struct pa));
  can->pa[0].length=nstep;
  can->pa[0].pos=pa=(POINT *)MALLOC(w*sizeof(POINT));
  for(i=0;i<nstep;i++){
    XC(pa[i])=(w-1)*(tabx[i]-xmin)/dx; 
    YC(pa[i])=(h-1)*(ymax-taby[i])/dy; 
  }
}

void polarcalcNG(struct canvas *can){
  //polarplotNG
  double xmax,xmin,ymax,ymin,dx,dy,pmin,pstep,tr,p, *tabx,*taby;
  double usubstrp();
  int i,ix,iy,nstep,w,h;
  POINT *pa;
  Real r;
  Obj fr,t,s;

  todouble((Obj)can->formula,&fr);
  w=can->width; h=can->height; nstep=can->nzstep;
  pmin=can->zmin; pstep=(can->zmax-can->zmin)/nstep;
  tabx=(double *)ALLOCA(nstep*sizeof(double));
  taby=(double *)ALLOCA(nstep*sizeof(double));
  MKReal(1,r); // dummy real number

  for(i=0,p=pmin;i<nstep;i++,p+= pstep){
    // full substitution
    BDY(r)=p;
    substr(CO,0,fr,can->vx,p?(Obj)r:0,&s);
    devalr(CO,(Obj)s,&t);
    if(t&&(OID(t)!=O_N||NID((Num)t)!=N_R))
      error("polarcalc : invalid evaluation");
    tr=ToReal((Num)t);  
    tabx[i]=tr*cos(p);
    taby[i]=tr*sin(p);
    if(i==0){
      xmax=xmin=tabx[0];
      ymax=ymin=taby[0];
    } else {
      if(tabx[i]>xmax)xmax=tabx[i];
      if(tabx[i]<xmin)xmin=tabx[i];
      if(taby[i]>ymax)ymax=taby[i];
      if(taby[i]<ymin)ymin=taby[i];
    }
  }
  can->xmax=xmax;can->xmin=xmin;
  can->ymax=ymax;can->ymin=ymin;
  dx=xmax-xmin;
  dy=ymax-ymin;
  can->pa=(struct pa *)MALLOC(sizeof(struct pa));
  can->pa[0].length=nstep;
  can->pa[0].pos=pa=(POINT *)MALLOC(w*sizeof(POINT));
  for(i=0;i<nstep;i++){
    XC(pa[i])=(w-1)*(tabx[i]-xmin)/dx; 
    YC(pa[i])=(h-1)*(ymax-taby[i])/dy; 
  }
}

/*
void ineqncalc(double **tab,struct canvas *can,int nox){
  double x,y,xmin,ymin,xstep,ystep;
  int ix,iy,w,h;
  Real r,rx,ry;
  Obj fr,g,t,s;
  V vx,vy;

  if(!nox) initmarker(can,"Evaluating...");
  todouble((Obj)can->formula,&fr);
  vx=can->vx;vy=can->vy;
  w=can->width;h=can->height; 
  xmin=can->xmin;xstep=(can->xmax-can->xmin)/w;
  ymin=can->ymin;ystep=(can->ymin-can->ymin)/h;
  MKReal(1.0,rx); MKReal(1.0,ry); // dummy real

  for(ix=0,x=xmin;ix<=w;ix++,x+=xstep){
    BDY(rx)=x; substr(CO,0,fr,vx,x?(Obj)rx:0,&t);
    devalr(CO,t,&g);
    if(!nox) marker(can,DIR_X,ix);
    for(iy=0,y=ymin;iy<=h;iy++,y+=ystep){
      BDY(ry)=y;
      substr(CO,0,g,vy,y?(Obj)ry:0,&t);
      devalr(CO,t,&s);
      tab[ix][iy]=ToReal(s);
    }
  }
}
*/

#if defined(INTERVAL)
void itvcalc(double **mask, struct canvas *can, int nox){
  //ITVIFPLOT
  double x,y,xstep,ystep,dx,dy,wx,wy;
  int idv,ix,iy,idx,idy;
  Itv ity,itx,ddx,ddy;
  Real r,rx,ry,rx1,ry1,rdx,rdy,rdx1,rdy1;
  V vx,vy;
  Obj fr,g,t,s;

  idv=can->division;
  todouble((Obj)can->formula,&fr);
  vx=can->vx; vy=can->vy;
  xstep=(can->xmax-can->xmin)/can->width;
  ystep=(can->ymax-can->ymin)/can->height;
  if(idv!=0){
    wx=xstep/can->division;
    wy=ystep/can->division;
  }
  MKReal(can->ymin,ry1);
  for(iy=0,y=can->ymin; iy<can->height; iy++,y+=ystep){
    ry=ry1;
    MKReal(y+ystep,ry1);
    istoitv((Num)(ry1),(Num)ry,&ity);
    substr(CO,0,(Obj)fr,vy,(Obj)ity,&t);
    MKReal(can->xmin,rx1);
    for(ix=0,x=can->xmin; ix<can->width; ix++,x+=xstep){
      rx=rx1;
      MKReal(x+xstep,rx1);
      istoitv((Num)(rx1),(Num)rx,&itx);
      substr(CO,0,(Obj)fr,vx,(Obj)itx,&t);
      MKReal(can->ymin,ry1);
      for(iy=0,y=can->ymin; iy<can->height; iy++,y+=ystep){
        ry=ry1;
        MKReal(y+ystep,ry1);
        istoitv((Num)ry,(Num)ry1,&ity);
        substr(CO,0,(Obj)t,vy,(Obj)ity,&g);
        if(compnum(0,0,(Num)g))mask[ix][iy]=-1;
        else {
          mask[ix][iy]=0;
/*
          if(idv==0) mask[ix][iy]=0;
          else {
            MKReal(y,rdy1);
            for(idy=0,dy=y;idy<idv;dy+=wy,idy++){
              rdy=rdy1;
              MKReal(dy+wy,rdy1);
              istoitv((Num)rdy,(Num)rdy1,&ddy);
              substr(CO,0,(Obj)fr,vy,(Obj)ddy,&t);
              MKReal(x,rdx1);
              for(idx=0,dx=x;idx<idx;dx+=wx,idx++){
                rdx=rdx1;
                MKReal(dx+wx,rdx1);
                istoitv((Num)rdx,(Num)rdx1,&ddx);
                substr(CO,0,(Obj)t,vx,(Obj)ddx,&g);
                if(!compnum(0,0,(Num)g)){
                  mask[ix][iy]=0;
                  break;
                }
              }
              if(mask[ix][iy]==0)break;
            }
          }
*/
        }
      }
    }
  }
}
#endif