src/rt/ambient.c

/* Copyright (c) 1996 Regents of the University of California */

#ifndef lint
static char SCCSid[] = "$SunId$ LBL";
#endif

/*
 *  ambient.c - routines dealing with ambient (inter-reflected) component.
 */

#include  "ray.h"

#include  "octree.h"

#include  "otypes.h"

#include  "ambient.h"

#include  "random.h"

#ifndef  OCTSCALE
#define  OCTSCALE       1.0     /* ceil((valid rad.)/(cube size)) */
#endif

typedef struct ambtree {
        AMBVAL  *alist;         /* ambient value list */
        struct ambtree  *kid;   /* 8 child nodes */
}  AMBTREE;                     /* ambient octree */

extern CUBE  thescene;          /* contains space boundaries */

extern char  *shm_boundary;     /* memory sharing boundary */

#define  MAXASET        511     /* maximum number of elements in ambient set */
OBJECT  ambset[MAXASET+1]={0};  /* ambient include/exclude set */

double  maxarad;                /* maximum ambient radius */
double  minarad;                /* minimum ambient radius */

static AMBTREE  atrunk;         /* our ambient trunk node */

static FILE  *ambfp = NULL;     /* ambient file pointer */
static int  nunflshed = 0;      /* number of unflushed ambient values */

#ifndef SORT_THRESH
#ifdef BIGMEM
#define SORT_THRESH     ((9L<<20)/sizeof(AMBVAL))
#else
#define SORT_THRESH     ((3L<<20)/sizeof(AMBVAL))
#endif
#endif
#ifndef SORT_INTVL
#define SORT_INTVL      (SORT_THRESH*256)
#endif
#ifndef MAX_SORT_INTVL
#define MAX_SORT_INTVL  (SORT_INTVL<<4)
#endif

static COLOR  avsum = BLKCOLOR;         /* computed ambient value sum */
static unsigned int  nambvals = 0;      /* total number of indirect values */
static unsigned int  nambshare = 0;     /* number of values from file */
static unsigned long  ambclock = 0;     /* ambient access clock */
static unsigned long  lastsort = 0;     /* time of last value sort */
static long  sortintvl = SORT_INTVL;    /* time until next sort */

#define MAXACLOCK       (1L<<30)        /* clock turnover value */
        /*
         * Track access times unless we are sharing ambient values
         * through memory on a multiprocessor, when we want to avoid
         * claiming our own memory (copy on write).  Go ahead anyway
         * if more than two thirds of our values are unshared.
         */
#define tracktime       (shm_boundary == NULL || nambvals > 3*nambshare)

#define  AMBFLUSH       (BUFSIZ/AMBVALSIZ)

#define  newambval()    (AMBVAL *)bmalloc(sizeof(AMBVAL))

extern long  ftell(), lseek();
static int  initambfile(), avsave(), avinsert(), sortambvals();
static AMBVAL  *avstore();
#ifdef  F_SETLKW
static  aflock();
#endif


setambres(ar)                           /* set ambient resolution */
int  ar;
{
        ambres = ar < 0 ? 0 : ar;               /* may be done already */
                                                /* set min & max radii */
        if (ar <= 0) {
                minarad = 0;
                maxarad = thescene.cusize / 2.0;
        } else {
                minarad = thescene.cusize / ar;
                maxarad = 64 * minarad;                 /* heuristic */
                if (maxarad > thescene.cusize / 2.0)
                        maxarad = thescene.cusize / 2.0;
        }
        if (minarad <= FTINY)
                minarad = 10*FTINY;
        if (maxarad <= minarad)
                maxarad = 64 * minarad;
}


setambacc(newa)                         /* set ambient accuracy */
double  newa;
{
        double  ambdiff;

        if (newa < 0.0)
                newa = 0.0;
        ambdiff = fabs(newa - ambacc);
        if (ambdiff >= .01 && (ambacc = newa) > FTINY && nambvals > 0)
                sortambvals(1);                 /* rebuild tree */
}


setambient(afile)                       /* initialize calculation */
char  *afile;
{
        long  pos, flen;
        AMBVAL  amb;
                                                /* init ambient limits */
        setambres(ambres);
        setambacc(ambacc);
        if (afile == NULL)
                return;
        if (ambacc <= FTINY) {
                sprintf(errmsg, "zero ambient accuracy so \"%s\" not opened",
                                afile);
                error(WARNING, errmsg);
                return;
        }
                                                /* open ambient file */
        if ((ambfp = fopen(afile, "r+")) != NULL) {
                initambfile(0);
                pos = ftell(ambfp);
                while (readambval(&amb, ambfp))
                        avinsert(avstore(&amb));
                                                /* align */
                pos += (long)nambvals*AMBVALSIZ;
                flen = lseek(fileno(ambfp), 0L, 2);
                if (flen != pos) {
                        error(WARNING,
                        "ignoring last %ld values in ambient file (corrupted)",
                                        (flen - pos)/AMBVALSIZ);
                        fseek(ambfp, pos, 0);
                        ftruncate(fileno(ambfp), pos);
                }
                nambshare = nambvals;
        } else if ((ambfp = fopen(afile, "w+")) != NULL)
                initambfile(1);
        else {
                sprintf(errmsg, "cannot open ambient file \"%s\"", afile);
                error(SYSTEM, errmsg);
        }
        nunflshed++;    /* lie */
        ambsync();
}


ambnotify(obj)                  /* record new modifier */
OBJECT  obj;
{
        static int  hitlimit = 0;
        register OBJREC  *o = objptr(obj);
        register char  **amblp;

        if (hitlimit || !ismodifier(o->otype))
                return;
        for (amblp = amblist; *amblp != NULL; amblp++)
                if (!strcmp(o->oname, *amblp)) {
                        if (ambset[0] >= MAXASET) {
                                error(WARNING, "too many modifiers in ambient list");
                                hitlimit++;
                                return;         /* should this be fatal? */
                        }
                        insertelem(ambset, obj);
                        return;
                }
}


ambient(acol, r, nrm)           /* compute ambient component for ray */
COLOR  acol;
register RAY  *r;
FVECT  nrm;
{
        static int  rdepth = 0;                 /* ambient recursion */
        double  d;

        if (ambdiv <= 0)                        /* no ambient calculation */
                goto dumbamb;
                                                /* check number of bounces */
        if (rdepth >= ambounce)
                goto dumbamb;
                                                /* check ambient list */
        if (ambincl != -1 && r->ro != NULL &&
                        ambincl != inset(ambset, r->ro->omod))
                goto dumbamb;

        if (ambacc <= FTINY) {                  /* no ambient storage */
                rdepth++;
                d = doambient(acol, r, r->rweight, NULL, NULL);
                rdepth--;
                if (d <= FTINY)
                        goto dumbamb;
                return;
        }
                                                /* resort memory? */
        sortambvals(0);
                                                /* get ambient value */
        setcolor(acol, 0.0, 0.0, 0.0);
        d = sumambient(acol, r, nrm, rdepth,
                        &atrunk, thescene.cuorg, thescene.cusize);
        if (d > FTINY) {
                scalecolor(acol, 1.0/d);
                return;
        }
        rdepth++;                               /* need to cache new value */
        d = makeambient(acol, r, nrm, rdepth-1);
        rdepth--;
        if (d > FTINY)
                return;
dumbamb:                                        /* return global value */
        copycolor(acol, ambval);
        if (ambvwt <= 0 | nambvals == 0)
                return;
        scalecolor(acol, (double)ambvwt);
        addcolor(acol, avsum);                  /* average in computations */
        d = 1.0/(ambvwt+nambvals);
        scalecolor(acol, d);
}


double
sumambient(acol, r, rn, al, at, c0, s)  /* get interpolated ambient value */
COLOR  acol;
register RAY  *r;
FVECT  rn;
int  al;
AMBTREE  *at;
FVECT  c0;
double  s;
{
        double  d, e1, e2, wt, wsum;
        COLOR  ct;
        FVECT  ck0;
        int  i;
        register int  j;
        register AMBVAL  *av;

        wsum = 0.0;
                                        /* do this node */
        for (av = at->alist; av != NULL; av = av->next) {
                if (tracktime)
                        av->latick = ambclock++;
                /*
                 *  Ambient level test.
                 */
                if (av->lvl > al)       /* list sorted, so this works */
                        break;
                if (av->weight < r->rweight-FTINY)
                        continue;
                /*
                 *  Ambient radius test.
                 */
                d = av->pos[0] - r->rop[0];
                e1 = d * d;
                d = av->pos[1] - r->rop[1];
                e1 += d * d;
                d = av->pos[2] - r->rop[2];
                e1 += d * d;
                e1 /= av->rad * av->rad;
                if (e1 > ambacc*ambacc*1.21)
                        continue;
                /*
                 *  Normal direction test.
                 */
                e2 = (1.0 - DOT(av->dir, r->ron)) * r->rweight;
                if (e2 < 0.0) e2 = 0.0;
                if (e1 + e2 > ambacc*ambacc*1.21)
                        continue;
                /*
                 *  Ray behind test.
                 */
                d = 0.0;
                for (j = 0; j < 3; j++)
                        d += (r->rop[j] - av->pos[j]) *
                                        (av->dir[j] + r->ron[j]);
                if (d*0.5 < -minarad*ambacc-.001)
                        continue;
                /*
                 *  Jittering final test reduces image artifacts.
                 */
                wt = sqrt(e1) + sqrt(e2);
                if (wt > ambacc*(.9+.2*urand(9015+samplendx)))
                        continue;
                if (wt <= 1e-3)
                        wt = 1e3;
                else
                        wt = 1.0 / wt;
                wsum += wt;
                extambient(ct, av, r->rop, rn);
                scalecolor(ct, wt);
                addcolor(acol, ct);
        }
        if (at->kid == NULL)
                return(wsum);
                                        /* do children */
        s *= 0.5;
        for (i = 0; i < 8; i++) {
                for (j = 0; j < 3; j++) {
                        ck0[j] = c0[j];
                        if (1<<j & i)
                                ck0[j] += s;
                        if (r->rop[j] < ck0[j] - OCTSCALE*s)
                                break;
                        if (r->rop[j] > ck0[j] + (1.0+OCTSCALE)*s)
                                break;
                }
                if (j == 3)
                        wsum += sumambient(acol, r, rn, al, at->kid+i, ck0, s);
        }
        return(wsum);
}


double
makeambient(acol, r, rn, al)    /* make a new ambient value */
COLOR  acol;
register RAY  *r;
FVECT  rn;
int  al;
{
        AMBVAL  amb;
        FVECT   gp, gd;
                                                /* compute weight */
        amb.weight = pow(AVGREFL, (double)al);
        if (r->rweight < 0.1*amb.weight)        /* heuristic */
                amb.weight = r->rweight;
                                                /* compute ambient */
        amb.rad = doambient(acol, r, amb.weight, gp, gd);
        if (amb.rad <= FTINY)
                return(0.0);
                                                /* store it */
        VCOPY(amb.pos, r->rop);
        VCOPY(amb.dir, r->ron);
        amb.lvl = al;
        copycolor(amb.val, acol);
        VCOPY(amb.gpos, gp);
        VCOPY(amb.gdir, gd);
                                                /* insert into tree */
        avsave(&amb);                           /* and save to file */
        if (rn != r->ron)
                extambient(acol, &amb, r->rop, rn);     /* texture */
        return(amb.rad);
}


extambient(cr, ap, pv, nv)              /* extrapolate value at pv, nv */
COLOR  cr;
register AMBVAL  *ap;
FVECT  pv, nv;
{
        FVECT  v1, v2;
        register int  i;
        double  d;

        d = 1.0;                        /* zeroeth order */
                                        /* gradient due to translation */
        for (i = 0; i < 3; i++)
                d += ap->gpos[i]*(pv[i]-ap->pos[i]);
                                        /* gradient due to rotation */
        VCOPY(v1, ap->dir);
        fcross(v2, v1, nv);
        d += DOT(ap->gdir, v2);
        if (d <= 0.0) {
                setcolor(cr, 0.0, 0.0, 0.0);
                return;
        }
        copycolor(cr, ap->val);
        scalecolor(cr, d);
}


static
initambfile(creat)              /* initialize ambient file */
int  creat;
{
        extern char  *progname, *octname, VersionID[];

#ifdef  F_SETLKW
        aflock(creat ? F_WRLCK : F_RDLCK);
#endif
#ifdef MSDOS
        setmode(fileno(ambfp), O_BINARY);
#endif
        setbuf(ambfp, bmalloc(BUFSIZ+8));
        if (creat) {                    /* new file */
                newheader("RADIANCE", ambfp);
                fprintf(ambfp, "%s -av %g %g %g -ab %d -aa %g ",
                                progname, colval(ambval,RED),
                                colval(ambval,GRN), colval(ambval,BLU),
                                ambounce, ambacc);
                fprintf(ambfp, "-ad %d -as %d -ar %d %s\n",
                                ambdiv, ambssamp, ambres,
                                octname==NULL ? "" : octname);
                fprintf(ambfp, "SOFTWARE= %s\n", VersionID);
                fputformat(AMBFMT, ambfp);
                putc('\n', ambfp);
                putambmagic(ambfp);
        } else if (checkheader(ambfp, AMBFMT, NULL) < 0 || !hasambmagic(ambfp))
                error(USER, "bad ambient file");
}


static
avsave(av)                              /* insert and save an ambient value */
AMBVAL  *av;
{
        avinsert(avstore(av));
        if (ambfp == NULL)
                return;
        if (writambval(av, ambfp) < 0)
                goto writerr;
        if (++nunflshed >= AMBFLUSH)
                if (ambsync() == EOF)
                        goto writerr;
        return;
writerr:
        error(SYSTEM, "error writing ambient file");
}


static AMBVAL *
avstore(aval)                           /* allocate memory and store aval */
register AMBVAL  *aval;
{
        register AMBVAL  *av;

        if ((av = newambval()) == NULL)
                error(SYSTEM, "out of memory in avstore");
        copystruct(av, aval);
        av->latick = ambclock;
        av->next = NULL;
        addcolor(avsum, av->val);       /* add to sum for averaging */
        nambvals++;
        return(av);
}


#define ATALLOCSZ       512             /* #/8 trees to allocate at once */

static AMBTREE  *atfreelist = NULL;     /* free ambient tree structures */


static
AMBTREE *
newambtree()                            /* allocate 8 ambient tree structs */
{
        register AMBTREE  *atp, *upperlim;

        if (atfreelist == NULL) {       /* get more nodes */
                atfreelist = (AMBTREE *)bmalloc(ATALLOCSZ*8*sizeof(AMBTREE));
                if (atfreelist == NULL)
                        return(NULL);
                                        /* link new free list */
                upperlim = atfreelist + 8*(ATALLOCSZ-1);
                for (atp = atfreelist; atp < upperlim; atp += 8)
                        atp->kid = atp + 8;
                atp->kid = NULL;
        }
        atp = atfreelist;
        atfreelist = atp->kid;
        bzero((char *)atp, 8*sizeof(AMBTREE));
        return(atp);
}


static
freeambtree(atp)                        /* free 8 ambient tree structs */
AMBTREE  *atp;
{
        atp->kid = atfreelist;
        atfreelist = atp;
}


static
avinsert(av)                            /* insert ambient value in our tree */
register AMBVAL  *av;
{
        register AMBTREE  *at;
        register AMBVAL  *ap;
        AMBVAL  avh;
        FVECT  ck0;
        double  s;
        int  branch;
        register int  i;

        if (av->rad <= FTINY)
                error(CONSISTENCY, "zero ambient radius in avinsert");
        at = &atrunk;
        VCOPY(ck0, thescene.cuorg);
        s = thescene.cusize;
        while (s*(OCTSCALE/2) > av->rad*ambacc) {
                if (at->kid == NULL)
                        if ((at->kid = newambtree()) == NULL)
                                error(SYSTEM, "out of memory in avinsert");
                s *= 0.5;
                branch = 0;
                for (i = 0; i < 3; i++)
                        if (av->pos[i] > ck0[i] + s) {
                                ck0[i] += s;
                                branch |= 1 << i;
                        }
                at = at->kid + branch;
        }
        avh.next = at->alist;           /* order by increasing level */
        for (ap = &avh; ap->next != NULL; ap = ap->next)
                if (ap->next->lvl >= av->lvl)
                        break;
        av->next = ap->next;
        ap->next = av;
        at->alist = avh.next;
}


static
unloadatree(at, f)                      /* unload an ambient value tree */
register AMBTREE  *at;
int     (*f)();
{
        register AMBVAL  *av;
        register int  i;
                                        /* transfer values at this node */
        for (av = at->alist; av != NULL; av = at->alist) {
                at->alist = av->next;
                (*f)(av);
        }
        if (at->kid == NULL)
                return;
        for (i = 0; i < 8; i++)         /* transfer and free children */
                unloadatree(at->kid+i, f);
        freeambtree(at->kid);
        at->kid = NULL;
}


static AMBVAL   **avlist1, **avlist2;   /* ambient value lists for sorting */
static int      i_avlist;               /* index for lists */


static
av2list(av)
AMBVAL  *av;
{
#ifdef DEBUG
        if (i_avlist >= nambvals)
                error(CONSISTENCY, "too many ambient values in av2list1");
#endif
        avlist1[i_avlist] = avlist2[i_avlist] = av;
        i_avlist++;
}


static int
alatcmp(avp1, avp2)                     /* compare ambient values for MRA */
AMBVAL  **avp1, **avp2;
{
        register long  lc = (**avp2).latick - (**avp1).latick;
        return(lc<0 ? -1 : lc>0 ? 1 : 0);
}


static int
aposcmp(avp1, avp2)                     /* compare ambient value positions */
AMBVAL  **avp1, **avp2;
{
        return(*avp1 - *avp2);
}


#if  1
static int
avlmemi(avaddr)                         /* find list position from address */
AMBVAL  *avaddr;
{
        register AMBVAL  **avlpp;

        avlpp = (AMBVAL **)bsearch((char *)&avaddr, (char *)avlist2,
                        nambvals, sizeof(AMBVAL *), aposcmp);
        if (avlpp == NULL)
                error(CONSISTENCY, "address not found in avlmemi");
        return(avlpp - avlist2);
}
#else
#define avlmemi(avaddr) ((AMBVAL **)bsearch((char *)&avaddr,(char *)avlist2, \
                                nambvals,sizeof(AMBVAL *),aposcmp) - avlist2)
#endif


static
sortambvals(always)                     /* resort ambient values */
int     always;
{
        AMBTREE  oldatrunk;
        AMBVAL  tav, *tap, *pnext;
        register int    i, j;
                                        /* see if it's time yet */
        if (!always && (ambclock < lastsort+sortintvl ||
                        nambvals < SORT_THRESH))
                return;
        /*
         * The idea here is to minimize memory thrashing
         * in VM systems by improving reference locality.
         * We do this by periodically sorting our stored ambient
         * values in memory in order of most recently to least
         * recently accessed.  This ordering was chosen so that new
         * ambient values (which tend to be less important) go into
         * higher memory with the infrequently accessed values.
         *      Since we expect our values to need sorting less
         * frequently as the process continues, we double our
         * waiting interval after each call.
         *      This routine is also called by setambacc() with
         * the "always" parameter set to 1 so that the ambient
         * tree will be rebuilt with the new accuracy parameter.
         */
        if (tracktime) {                /* allocate pointer arrays to sort */
                avlist1 = (AMBVAL **)malloc(nambvals*sizeof(AMBVAL *));
                avlist2 = (AMBVAL **)malloc(nambvals*sizeof(AMBVAL *));
        } else
                avlist1 = avlist2 = NULL;
        if (avlist2 == NULL) {          /* no time tracking -- rebuild tree? */
                if (avlist1 != NULL)
                        free((char *)avlist1);
                if (always) {           /* rebuild without sorting */
                        copystruct(&oldatrunk, &atrunk);
                        atrunk.alist = NULL;
                        atrunk.kid = NULL;
                        unloadatree(&oldatrunk, avinsert);
                }
        } else {                        /* sort memory by last access time */
                /*
                 * Sorting memory is tricky because it isn't contiguous.
                 * We have to sort an array of pointers by MRA and also
                 * by memory position.  We then copy values in "loops"
                 * to minimize memory hits.  Nevertheless, we will visit
                 * everyone at least twice, and this is an expensive process
                 * when we're thrashing, which is when we need to do it.
                 */
#ifdef DEBUG
                sprintf(errmsg, "sorting %u ambient values at ambclock=%lu...",
                                nambvals, ambclock);
                eputs(errmsg);
#endif
                i_avlist = 0;
                unloadatree(&atrunk, av2list);  /* empty current tree */
#ifdef DEBUG
                if (i_avlist < nambvals)
                        error(CONSISTENCY, "missing ambient values in sortambvals");
#endif
                qsort((char *)avlist1, nambvals, sizeof(AMBVAL *), alatcmp);
                qsort((char *)avlist2, nambvals, sizeof(AMBVAL *), aposcmp);
                for (i = 0; i < nambvals; i++) {
                        if (avlist1[i] == NULL)
                                continue;
                        tap = avlist2[i];
                        copystruct(&tav, tap);
                        for (j = i; (pnext = avlist1[j]) != tap;
                                        j = avlmemi(pnext)) {
                                copystruct(avlist2[j], pnext);
                                avinsert(avlist2[j]);
                                avlist1[j] = NULL;
                        }
                        copystruct(avlist2[j], &tav);
                        avinsert(avlist2[j]);
                        avlist1[j] = NULL;
                }
                free((char *)avlist1);
                free((char *)avlist2);
                                                /* compute new sort interval */
                sortintvl = ambclock - lastsort;
                if (sortintvl >= MAX_SORT_INTVL/2)
                        sortintvl = MAX_SORT_INTVL;
                else
                        sortintvl <<= 1;        /* wait twice as long next */
#ifdef DEBUG
                eputs("done\n");
#endif
        }
        if (ambclock >= MAXACLOCK)
                ambclock = MAXACLOCK/2;
        lastsort = ambclock;
}


#ifdef  F_SETLKW

static
aflock(typ)                     /* lock/unlock ambient file */
int  typ;
{
        static struct flock  fls;       /* static so initialized to zeroes */

        fls.l_type = typ;
        if (fcntl(fileno(ambfp), F_SETLKW, &fls) < 0)
                error(SYSTEM, "cannot (un)lock ambient file");
}


int
ambsync()                       /* synchronize ambient file */
{
        static FILE  *ambinp = NULL;
        static long  lastpos = -1;
        long  flen;
        AMBVAL  avs;
        register int  n;

        if (nunflshed == 0)
                return(0);
        if (lastpos < 0)        /* initializing (locked in initambfile) */
                goto syncend;
                                /* gain exclusive access */
        aflock(F_WRLCK);
                                /* see if file has grown */
        if ((flen = lseek(fileno(ambfp), 0L, 2)) < 0)
                goto seekerr;
        if (n = flen - lastpos) {               /* file has grown */
                if (ambinp == NULL) {           /* use duplicate filedes */
                        ambinp = fdopen(dup(fileno(ambfp)), "r");
                        if (ambinp == NULL)
                                error(SYSTEM, "fdopen failed in ambsync");
                }
                if (fseek(ambinp, lastpos, 0) < 0)
                        goto seekerr;
                while (n >= AMBVALSIZ) {        /* load contributed values */
                        if (!readambval(&avs, ambinp)) {
                                sprintf(errmsg,
                                "ambient file corrupted near character %ld",
                                                flen - n);
                                error(WARNING, errmsg);
                                break;
                        }
                        avinsert(avstore(&avs));
                        n -= AMBVALSIZ;
                }
                /*** seek always as safety measure
                if (n) ***/                     /* alignment */
                        if (lseek(fileno(ambfp), flen-n, 0) < 0)
                                goto seekerr;
        }
#ifdef  DEBUG
        if (ambfp->_ptr - ambfp->_base != nunflshed*AMBVALSIZ) {
                sprintf(errmsg, "ambient file buffer at %d rather than %d",
                                ambfp->_ptr - ambfp->_base,
                                nunflshed*AMBVALSIZ);
                error(CONSISTENCY, errmsg);
        }
#endif
syncend:
        n = fflush(ambfp);                      /* calls write() at last */
        if ((lastpos = lseek(fileno(ambfp), 0L, 1)) < 0)
                goto seekerr;
        aflock(F_UNLCK);                        /* release file */
        nunflshed = 0;
        return(n);
seekerr:
        error(SYSTEM, "seek failed in ambsync");
}

#else

int
ambsync()                       /* flush ambient file */
{
        if (nunflshed == 0)
                return(0);
        nunflshed = 0;
        return(fflush(ambfp));
}

#endif
Revision:	2.38
Committed:	Tue Jul 9 13:32:35 1996 UTC (27 years, 9 months ago) by greg
Content type:	text/plain
Branch:	MAIN
Changes since 2.37:	+4 -3 lines
Log Message:	fixed potential problem with alatcmp() function on 16-bit machines made error-reporting version of avlmemi() the default