ViewVC Help
View File | Revision Log | Show Annotations | Download File | Root Listing
root/radiance/ray/src/rt/data.c
Revision: 2.37
Committed: Tue Mar 12 16:54:51 2024 UTC (2 months ago) by greg
Content type: text/plain
Branch: MAIN
Changes since 2.36: +179 -1 lines
Log Message:
perf: added datavector() call for quicker spectral interpolation

File Contents

# Content
1 #ifndef lint
2 static const char RCSid[] = "$Id: data.c,v 2.36 2023/12/13 23:26:16 greg Exp $";
3 #endif
4 /*
5 * data.c - routines dealing with interpolated data.
6 */
7
8 #include "copyright.h"
9
10 #include <time.h>
11
12 #include "platform.h"
13 #include "paths.h"
14 #include "standard.h"
15 #include "color.h"
16 #include "resolu.h"
17 #include "view.h"
18 #include "data.h"
19
20 /* picture memory usage before warning */
21 #ifndef PSIZWARN
22 #ifdef SMLMEM
23 #define PSIZWARN 3000000
24 #else
25 #define PSIZWARN 50000000
26 #endif
27 #endif
28
29 #ifndef TABSIZ
30 #define TABSIZ 997 /* table size (prime) */
31 #endif
32
33 #define hash(s) (shash(s)%TABSIZ)
34
35
36 static DATARRAY *dtab[TABSIZ]; /* data array list */
37
38 static gethfunc headaspect;
39
40
41 DATARRAY *
42 getdata( /* get data array dname */
43 char *dname
44 )
45 {
46 char *dfname;
47 FILE *fp;
48 int asize=0;
49 int i, j;
50 DATARRAY *dp;
51 /* look for array in list */
52 for (dp = dtab[hash(dname)]; dp != NULL; dp = dp->next)
53 if (!strcmp(dname, dp->name))
54 return(dp); /* found! */
55 /*
56 * If we haven't loaded the data already, we will look
57 * for it in the directories specified by the library path.
58 *
59 * The file has the following format:
60 *
61 * N
62 * beg0 end0 n0
63 * beg1 end1 n1
64 * . . .
65 * begN endN nN
66 * data, later dimensions changing faster
67 * . . .
68 *
69 * For irregularly spaced points, the following can be
70 * substituted for begi endi ni:
71 *
72 * 0 0 ni p0i p1i .. pni
73 */
74
75 if ((dfname = getpath(dname, getrlibpath(), R_OK)) == NULL) {
76 sprintf(errmsg, "cannot find data file \"%s\"", dname);
77 error(SYSTEM, errmsg);
78 }
79 if ((fp = fopen(dfname, "r")) == NULL) {
80 sprintf(errmsg, "cannot open data file \"%s\"", dfname);
81 error(SYSTEM, errmsg);
82 }
83 /* get dimensions */
84 if (fgetval(fp, 'i', &asize) <= 0)
85 goto scanerr;
86 if ((asize <= 0) | (asize > MAXDDIM)) {
87 sprintf(errmsg, "bad number of dimensions for \"%s\"", dname);
88 error(USER, errmsg);
89 }
90 if ((dp = (DATARRAY *)malloc(sizeof(DATARRAY))) == NULL)
91 goto memerr;
92 dp->name = savestr(dname);
93 dp->type = DATATY;
94 dp->nd = asize;
95 asize = 1;
96 for (i = 0; i < dp->nd; i++) {
97 if (fgetval(fp, DATATY, &dp->dim[i].org) <= 0)
98 goto scanerr;
99 if (fgetval(fp, DATATY, &dp->dim[i].siz) <= 0)
100 goto scanerr;
101 if (fgetval(fp, 'i', &dp->dim[i].ne) <= 0)
102 goto scanerr;
103 if (dp->dim[i].ne < 2)
104 goto scanerr;
105 asize *= dp->dim[i].ne;
106 if ((dp->dim[i].siz -= dp->dim[i].org) == 0) {
107 dp->dim[i].p = (DATATYPE *)
108 malloc(dp->dim[i].ne*sizeof(DATATYPE));
109 if (dp->dim[i].p == NULL)
110 goto memerr;
111 for (j = 0; j < dp->dim[i].ne; j++)
112 if (fgetval(fp, DATATY, &dp->dim[i].p[j]) <= 0)
113 goto scanerr;
114 for (j = 1; j < dp->dim[i].ne-1; j++)
115 if ((dp->dim[i].p[j-1] < dp->dim[i].p[j]) !=
116 (dp->dim[i].p[j] < dp->dim[i].p[j+1]))
117 goto scanerr;
118 dp->dim[i].org = dp->dim[i].p[0];
119 dp->dim[i].siz = dp->dim[i].p[dp->dim[i].ne-1]
120 - dp->dim[i].p[0];
121 } else
122 dp->dim[i].p = NULL;
123 }
124 if ((dp->arr.d = (DATATYPE *)malloc(asize*sizeof(DATATYPE))) == NULL)
125 goto memerr;
126
127 for (i = 0; i < asize; i++)
128 if (fgetval(fp, DATATY, &dp->arr.d[i]) <= 0)
129 goto scanerr;
130 fclose(fp);
131 i = hash(dname);
132 dp->next = dtab[i];
133 return(dtab[i] = dp);
134 memerr:
135 error(SYSTEM, "out of memory in getdata");
136 scanerr:
137 sprintf(errmsg, "%s in data file \"%s\"",
138 feof(fp) ? "unexpected EOF" : "bad format", dfname);
139 error(USER, errmsg);
140 return NULL; /* pro forma return */
141 }
142
143
144 static int
145 headaspect( /* check string for aspect ratio */
146 char *s,
147 void *iap
148 )
149 {
150 char fmt[MAXFMTLEN];
151
152 if (isaspect(s))
153 *(double*)iap *= aspectval(s);
154 else if (formatval(fmt, s) && strcmp(fmt, COLRFMT))
155 *(double*)iap = 0.0;
156 return(0);
157 }
158
159 DATARRAY *
160 getpict( /* get picture pname */
161 char *pname
162 )
163 {
164 double inpaspect;
165 char *pfname;
166 FILE *fp;
167 COLR *scanin;
168 int sl, ns;
169 RESOLU inpres;
170 RREAL loc[2];
171 int y;
172 int x, i;
173 DATARRAY *pp;
174 /* look for array in list */
175 for (pp = dtab[hash(pname)]; pp != NULL; pp = pp->next)
176 if (!strcmp(pname, pp->name))
177 return(pp); /* found! */
178
179 if ((pfname = getpath(pname, getrlibpath(), R_OK)) == NULL) {
180 sprintf(errmsg, "cannot find picture file \"%s\"", pname);
181 error(SYSTEM, errmsg);
182 }
183 if ((pp = (DATARRAY *)malloc(3*sizeof(DATARRAY))) == NULL)
184 goto memerr;
185
186 pp[0].name = savestr(pname);
187
188 if ((fp = fopen(pfname, "rb")) == NULL) {
189 sprintf(errmsg, "cannot open picture file \"%s\"", pfname);
190 error(SYSTEM, errmsg);
191 }
192 /* get dimensions */
193 inpaspect = 1.0;
194 getheader(fp, headaspect, &inpaspect);
195 if (inpaspect <= FTINY || !fgetsresolu(&inpres, fp))
196 goto readerr;
197 pp[0].nd = 2;
198 pp[0].dim[0].ne = inpres.yr;
199 pp[0].dim[1].ne = inpres.xr;
200 pp[0].dim[0].org =
201 pp[0].dim[1].org = 0.0;
202 if (inpres.xr <= inpres.yr*inpaspect) {
203 pp[0].dim[0].siz = inpaspect *
204 (double)inpres.yr/inpres.xr;
205 pp[0].dim[1].siz = 1.0;
206 } else {
207 pp[0].dim[0].siz = 1.0;
208 pp[0].dim[1].siz = (double)inpres.xr/inpres.yr /
209 inpaspect;
210 }
211 pp[0].dim[0].p = pp[0].dim[1].p = NULL;
212 sl = scanlen(&inpres); /* allocate array */
213 ns = numscans(&inpres);
214 i = ns*sl*sizeof(COLR);
215 #if PSIZWARN
216 if (i > PSIZWARN) { /* memory warning */
217 sprintf(errmsg, "picture file \"%s\" using %.1f MB of memory",
218 pname, i*(1.0/(1024*1024)));
219 error(WARNING, errmsg);
220 }
221 #endif
222 if ((pp[0].arr.c = (COLR *)malloc(i)) == NULL)
223 goto memerr;
224 /* load picture */
225 if ((scanin = (COLR *)malloc(sl*sizeof(COLR))) == NULL)
226 goto memerr;
227 for (y = 0; y < ns; y++) {
228 if (freadcolrs(scanin, sl, fp) < 0)
229 goto readerr;
230 for (x = 0; x < sl; x++) {
231 pix2loc(loc, &inpres, x, y);
232 i = (int)(loc[1]*inpres.yr)*inpres.xr +
233 (int)(loc[0]*inpres.xr);
234 copycolr(pp[0].arr.c[i], scanin[x]);
235 }
236 }
237 free(scanin);
238 fclose(fp);
239 i = hash(pname);
240 pp[0].next = dtab[i]; /* link into picture list */
241 pp[1] = pp[0];
242 pp[2] = pp[0];
243 pp[0].type = RED; /* differentiate RGB records */
244 pp[1].type = GRN;
245 pp[2].type = BLU;
246 return(dtab[i] = pp);
247 memerr:
248 error(SYSTEM, "out of memory in getpict");
249 readerr:
250 sprintf(errmsg, "bad picture file \"%s\"", pfname);
251 error(USER, errmsg);
252 return NULL; /* pro forma return */
253 }
254
255
256 /* header info type for hyperspectral image */
257 typedef struct {
258 float wlpart[4]; /* wavelength partitions */
259 int nc; /* number of components */
260 double inpaspect; /* pixel aspect ratio */
261 } SPECINFO;
262
263 static int
264 specheadline( /* get info for spectral image */
265 char *s,
266 void *cdp
267 )
268 {
269 SPECINFO *sip = (SPECINFO *)cdp;
270 char fmt[MAXFMTLEN];
271
272 if (isaspect(s))
273 sip->inpaspect *= aspectval(s);
274 else if (isncomp(s))
275 sip->nc = ncompval(s);
276 else if (iswlsplit(s))
277 wlsplitval(sip->wlpart, s);
278 else if (formatval(fmt, s) && strcmp(fmt, SPECFMT))
279 return(-1);
280 return(0);
281 }
282
283 DATARRAY *
284 getspec( /* load hyperspectral image as data */
285 char *sname
286 )
287 {
288 SPECINFO si;
289 char *pfname;
290 FILE *fp;
291 int sl, ns;
292 int y, i;
293 DATARRAY *pp;
294 /* look for array in list */
295 for (pp = dtab[hash(sname)]; pp != NULL; pp = pp->next)
296 if (!strcmp(sname, pp->name))
297 return(pp); /* found! */
298
299 if ((pfname = getpath(sname, getrlibpath(), R_OK)) == NULL) {
300 sprintf(errmsg, "cannot find hyperspectral image \"%s\"", sname);
301 error(SYSTEM, errmsg);
302 }
303 if ((fp = fopen(pfname, "rb")) == NULL) {
304 sprintf(errmsg, "cannot open hyperspectral image \"%s\"", pfname);
305 error(SYSTEM, errmsg);
306 }
307 si.wlpart[3] = 0;
308 si.nc = 0;
309 si.inpaspect = 1.0;
310 if (getheader(fp, specheadline, &si) < 0 ||
311 (si.nc <= 3) | (si.nc > MAXCSAMP) | (si.wlpart[3] < 1) ||
312 !fscnresolu(&sl, &ns, fp))
313 goto readerr;
314
315 if ((pp = (DATARRAY *)malloc(sizeof(DATARRAY))) == NULL)
316 goto memerr;
317
318 pp->name = savestr(sname);
319 pp->type = SPECTY;
320 pp->nd = 3;
321 pp->dim[0].ne = ns;
322 pp->dim[1].ne = sl;
323 pp->dim[0].org =
324 pp->dim[1].org = 0.0;
325 if (sl <= ns*si.inpaspect) {
326 pp->dim[0].siz = si.inpaspect * (double)ns/sl;
327 pp->dim[1].siz = 1.0;
328 } else {
329 pp->dim[0].siz = 1.0;
330 pp->dim[1].siz = (double)sl/ns / si.inpaspect;
331 }
332 pp->dim[2].ne = si.nc;
333 pp->dim[2].siz = si.wlpart[3] - si.wlpart[0];
334 pp->dim[2].org = si.wlpart[0] + 0.5*pp->dim[2].siz/si.nc;
335 pp->dim[2].siz *= (si.nc - 1.0)/si.nc;
336 pp->dim[0].p = pp->dim[1].p = pp->dim[2].p = NULL;
337 i = ns*sl*(si.nc+1);
338 #if PSIZWARN
339 if (i > PSIZWARN) { /* memory warning */
340 sprintf(errmsg, "hyperspectral image \"%s\" using %.1f MB of memory",
341 sname, i*(1.0/(1024*1024)));
342 error(WARNING, errmsg);
343 }
344 #endif
345 if ((pp->arr.s = (uby8 *)malloc(i)) == NULL)
346 goto memerr;
347 for (y = 0; y < ns; y++) /* read each scanline */
348 if (freadscolrs(pp->arr.s + y*sl*(si.nc+1), si.nc, sl, fp) < 0)
349 goto readerr;
350 fclose(fp);
351 i = hash(sname); /* insert in hash table */
352 pp->next = dtab[i];
353 return(dtab[i] = pp);
354 memerr:
355 error(SYSTEM, "out of memory in getspec");
356 readerr:
357 sprintf(errmsg, "bad hyperspectral image \"%s\"", pfname);
358 error(USER, errmsg);
359 return NULL; /* pro forma return */
360 }
361
362
363 void
364 freedata( /* release data array reference */
365 DATARRAY *dta
366 )
367 {
368 DATARRAY head;
369 int hval, nents;
370 DATARRAY *dpl, *dp;
371 int i;
372
373 if (dta == NULL) { /* free all if NULL */
374 hval = 0; nents = TABSIZ;
375 } else {
376 hval = hash(dta->name); nents = 1;
377 if (!*dta->name) { /* not a data file? */
378 dta->next = dtab[hval];
379 dtab[hval] = dta; /* ...fake position */
380 }
381 }
382 while (nents--) {
383 head.next = dtab[hval];
384 dpl = &head;
385 while ((dp = dpl->next) != NULL)
386 if ((dta == NULL) | (dta == dp)) {
387 dpl->next = dp->next;
388 free(dp->arr.p);
389 for (i = 0; i < dp->nd; i++)
390 if (dp->dim[i].p != NULL)
391 free(dp->dim[i].p);
392 freestr(dp->name);
393 free(dp);
394 } else
395 dpl = dp;
396 dtab[hval++] = head.next;
397 }
398 }
399
400
401 /* internal call to interpolate data value or vector */
402 static double
403 data_interp(DATARRAY *dp, double *pt, double coef, DATATYPE *rvec)
404 {
405 DATARRAY sd;
406 int stride, i;
407 double x, c0, c1, y0, y1;
408 /* set up dimensions for recursion */
409 if (dp->nd > 1) {
410 sd.name = dp->name;
411 sd.type = dp->type;
412 sd.nd = dp->nd - 1;
413 memcpy(sd.dim, dp->dim+1, sd.nd*sizeof(struct dadim));
414 stride = sd.dim[i = sd.nd-1].ne + (sd.type==SPECTY);
415 while (i-- > 0)
416 stride *= sd.dim[i].ne;
417 }
418 /* get independent variable */
419 if (dp->dim[0].p == NULL) { /* evenly spaced points */
420 x = (pt[0] - dp->dim[0].org)/dp->dim[0].siz;
421 x *= (double)(dp->dim[0].ne - 1);
422 i = x;
423 if (i < 0)
424 i = 0;
425 else if (i > dp->dim[0].ne - 2)
426 i = dp->dim[0].ne - 2;
427 } else { /* unevenly spaced points */
428 int lower, upper;
429 if (dp->dim[0].siz > 0.0) {
430 lower = 0;
431 upper = dp->dim[0].ne;
432 } else {
433 lower = dp->dim[0].ne;
434 upper = 0;
435 }
436 do {
437 i = (lower + upper) >> 1;
438 if (pt[0] >= dp->dim[0].p[i])
439 lower = i;
440 else
441 upper = i;
442 } while (i != (lower + upper) >> 1);
443
444 if (i > dp->dim[0].ne - 2)
445 i = dp->dim[0].ne - 2;
446
447 x = i + (pt[0] - dp->dim[0].p[i]) /
448 (dp->dim[0].p[i+1] - dp->dim[0].p[i]);
449 }
450 /*
451 * Compute interpolation coefficients:
452 * extrapolate as far as one division, then
453 * taper off harmonically to zero.
454 */
455 if (x > i+2) {
456 c0 = 1./(i-1 - x);
457 c1 = -2.*c0;
458 } else if (x < i-1) {
459 c1 = 1./(i - x);
460 c0 = -2.*c1;
461 } else {
462 c0 = i+1 - x;
463 c1 = x - i;
464 }
465 c0 *= coef;
466 c1 *= coef;
467 /* check if vector interp */
468 if ((dp->nd == 2) & (rvec != NULL)) {
469 if (dp->type == DATATY) {
470 sd.arr.d = dp->arr.d + i*stride;
471 for (i = sd.dim[0].ne; i--; )
472 rvec[i] += c0*sd.arr.d[i]
473 + c1*sd.arr.d[i+stride];
474 return(0.);
475 }
476 if (dp->type == SPECTY) {
477 double f;
478 sd.arr.s = dp->arr.s + i*stride;
479 f = ldexp(1.0, (int)sd.arr.s[sd.dim[0].ne]
480 - (COLXS+8));
481 for (i = sd.dim[0].ne; i--; )
482 rvec[i] += c0*f*(sd.arr.s[i] + 0.5);
483 sd.arr.s += stride;
484 f = ldexp(1.0, (int)sd.arr.s[sd.dim[0].ne]
485 - (COLXS+8));
486 for (i = sd.dim[0].ne; i--; )
487 rvec[i] += c1*f*(sd.arr.s[i] + 0.5);
488 return(0.);
489 }
490 sd.arr.c = dp->arr.c + i*stride;
491 for (i = sd.dim[0].ne; i--; )
492 rvec[i] += c0*colrval(sd.arr.c[i],sd.type)
493 + c1*colrval(sd.arr.c[i+stride],sd.type);
494 return(0.);
495 }
496 /* get dependent variable */
497 if (dp->nd > 1) {
498 if (dp->type == DATATY) {
499 sd.arr.d = dp->arr.d + i*stride;
500 y0 = data_interp(&sd, pt+1, c0, rvec);
501 sd.arr.d += stride;
502 } else if (dp->type == SPECTY) {
503 sd.arr.s = dp->arr.s + i*stride;
504 y0 = data_interp(&sd, pt+1, c0, rvec);
505 sd.arr.s += stride;
506 } else {
507 sd.arr.c = dp->arr.c + i*stride;
508 y0 = data_interp(&sd, pt+1, c0, rvec);
509 sd.arr.c += stride;
510 }
511 y1 = data_interp(&sd, pt+1, c1, rvec);
512 } else { /* end of recursion */
513 if (dp->type == DATATY) {
514 y0 = dp->arr.d[i];
515 y1 = dp->arr.d[i+1];
516 } else if (dp->type == SPECTY) {
517 if (dp->arr.s[dp->dim[0].ne]) {
518 double f = ldexp(1.0, -(COLXS+8) +
519 (int)dp->arr.s[dp->dim[0].ne]);
520 y0 = (dp->arr.s[i] + 0.5)*f;
521 y1 = (dp->arr.s[i+1] + 0.5)*f;
522 } else
523 y0 = y1 = 0.0;
524 } else {
525 y0 = colrval(dp->arr.c[i],dp->type);
526 y1 = colrval(dp->arr.c[i+1],dp->type);
527 }
528 y0 *= c0;
529 y1 *= c1;
530 }
531 return(y0 + y1); /* coefficients already applied */
532 }
533
534
535 double
536 datavalue( /* interpolate data value at a point */
537 DATARRAY *dp,
538 double *pt
539 )
540 {
541 return(data_interp(dp, pt, 1., NULL));
542 }
543
544
545 /* Interpolate final vector corresponding to last dimension in data array */
546 DATARRAY *
547 datavector(DATARRAY *dp, double *pt)
548 {
549 DATARRAY *newdp;
550
551 if (dp->nd < 2)
552 error(INTERNAL, "datavector() called with 1-D array");
553 /* create vector array */
554 newdp = (DATARRAY *)malloc(sizeof(DATARRAY) -
555 (MAXDDIM-1)*sizeof(struct dadim) +
556 sizeof(DATATYPE)*dp->dim[dp->nd-1].ne);
557 if (newdp == NULL)
558 error(SYSTEM, "out of memory in datavector");
559 newdp->next = NULL;
560 newdp->name = dp->name;
561 newdp->type = DATATY;
562 newdp->nd = 1; /* vector data goes here */
563 newdp->dim[0] = dp->dim[dp->nd-1];
564 newdp->arr.d = (DATATYPE *)(newdp->dim + 1);
565 memset(newdp->arr.d, 0, sizeof(DATATYPE)*newdp->dim[0].ne);
566
567 (void)data_interp(dp, pt, 1., newdp->arr.d);
568
569 return(newdp); /* will be free'd using free() */
570 }
571
572
573 #if 0
574 double
575 datavalue( /* interpolate data value at a point */
576 DATARRAY *dp,
577 double *pt
578 )
579 {
580 DATARRAY sd;
581 int asize;
582 int lower, upper;
583 int i;
584 double x, y0, y1;
585 /* set up dimensions for recursion */
586 if (dp->nd > 1) {
587 sd.name = dp->name;
588 sd.type = dp->type;
589 sd.nd = dp->nd - 1;
590 asize = 1;
591 for (i = 0; i < sd.nd; i++) {
592 sd.dim[i].org = dp->dim[i+1].org;
593 sd.dim[i].siz = dp->dim[i+1].siz;
594 sd.dim[i].p = dp->dim[i+1].p;
595 asize *= (sd.dim[i].ne = dp->dim[i+1].ne) +
596 ((sd.type==SPECTY) & (i==sd.nd-1));
597 }
598 }
599 /* get independent variable */
600 if (dp->dim[0].p == NULL) { /* evenly spaced points */
601 x = (pt[0] - dp->dim[0].org)/dp->dim[0].siz;
602 x *= (double)(dp->dim[0].ne - 1);
603 i = x;
604 if (i < 0)
605 i = 0;
606 else if (i > dp->dim[0].ne - 2)
607 i = dp->dim[0].ne - 2;
608 } else { /* unevenly spaced points */
609 if (dp->dim[0].siz > 0.0) {
610 lower = 0;
611 upper = dp->dim[0].ne;
612 } else {
613 lower = dp->dim[0].ne;
614 upper = 0;
615 }
616 do {
617 i = (lower + upper) >> 1;
618 if (pt[0] >= dp->dim[0].p[i])
619 lower = i;
620 else
621 upper = i;
622 } while (i != (lower + upper) >> 1);
623
624 if (i > dp->dim[0].ne - 2)
625 i = dp->dim[0].ne - 2;
626
627 x = i + (pt[0] - dp->dim[0].p[i]) /
628 (dp->dim[0].p[i+1] - dp->dim[0].p[i]);
629 }
630 /* get dependent variable */
631 if (dp->nd > 1) {
632 if (dp->type == DATATY) {
633 sd.arr.d = dp->arr.d + i*asize;
634 y0 = datavalue(&sd, pt+1);
635 sd.arr.d += asize;
636 y1 = datavalue(&sd, pt+1);
637 } else if (dp->type == SPECTY) {
638 sd.arr.s = dp->arr.s + i*asize;
639 y0 = datavalue(&sd, pt+1);
640 sd.arr.s += asize;
641 y1 = datavalue(&sd, pt+1);
642 } else {
643 sd.arr.c = dp->arr.c + i*asize;
644 y0 = datavalue(&sd, pt+1);
645 sd.arr.c += asize;
646 y1 = datavalue(&sd, pt+1);
647 }
648 } else {
649 if (dp->type == DATATY) {
650 y0 = dp->arr.d[i];
651 y1 = dp->arr.d[i+1];
652 } else if (dp->type == SPECTY) {
653 if (dp->arr.s[dp->dim[0].ne]) {
654 double f = ldexp(1.0, -(COLXS+8) +
655 (int)dp->arr.s[dp->dim[0].ne]);
656 y0 = (dp->arr.s[i] + 0.5)*f;
657 y1 = (dp->arr.s[i+1] + 0.5)*f;
658 } else
659 y0 = y1 = 0.0;
660 } else {
661 y0 = colrval(dp->arr.c[i],dp->type);
662 y1 = colrval(dp->arr.c[i+1],dp->type);
663 }
664 }
665 /*
666 * Extrapolate as far as one division, then
667 * taper off harmonically to zero.
668 */
669 if (x > i+2)
670 return( (2*y1-y0)/(x-(i-1)) );
671
672 if (x < i-1)
673 return( (2*y0-y1)/(i-x) );
674
675 return( y0*((i+1)-x) + y1*(x-i) );
676 }
677 #endif