src/rt/data.c

/* Copyright (c) 1991 Regents of the University of California */

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

/*
 *  data.c - routines dealing with interpolated data.
 *
 *     6/4/86
 */

#include  "standard.h"

#include  "color.h"

#include  "resolu.h"

#include  "data.h"


extern char  *fgetword();

extern char  *libpath;                  /* library search path */

static DATARRAY  *dlist = NULL;         /* data array list */

static DATARRAY  *plist = NULL;         /* picture list */


DATARRAY *
getdata(dname)                          /* get data array dname */
char  *dname;
{
        char  word[64];
        char  *dfname;
        FILE  *fp;
        int  asize;
        register int  i, j;
        register DATARRAY  *dp;
                                                /* look for array in list */
        for (dp = dlist; dp != NULL; dp = dp->next)
                if (!strcmp(dname, dp->name))
                        return(dp);             /* found! */

        /*
         *      If we haven't loaded the data already, we will look
         *  for it in the directorys specified by the library path.
         *
         *      The file has the following format:
         *
         *              N
         *              beg0    end0    n0
         *              beg1    end1    n1
         *              . . .
         *              begN    endN    nN
         *              data, later dimensions changing faster
         *              . . .
         *
         *      For irregularly spaced points, the following can be
         *  substituted for begi endi ni:
         *
         *              0 0 ni p0i p1i .. pni
         */

        if ((dfname = getpath(dname, libpath, R_OK)) == NULL) {
                sprintf(errmsg, "cannot find data file \"%s\"", dname);
                error(USER, errmsg);
        }
        if ((dp = (DATARRAY *)malloc(sizeof(DATARRAY))) == NULL)
                goto memerr;

        dp->name = savestr(dname);

        if ((fp = fopen(dfname, "r")) == NULL) {
                sprintf(errmsg, "cannot open data file \"%s\"", dfname);
                error(SYSTEM, errmsg);
        }
                                                        /* get dimensions */
        if (fgetword(word, sizeof(word), fp) == NULL || !isint(word))
                goto scanerr;
        dp->nd = atoi(word);
        if (dp->nd <= 0 || dp->nd > MAXDDIM) {
                sprintf(errmsg, "bad number of dimensions for \"%s\"", dname);
                error(USER, errmsg);
        }
        asize = 1;
        for (i = 0; i < dp->nd; i++) {
                if (fgetword(word, sizeof(word), fp) == NULL || !isflt(word))
                        goto scanerr;
                dp->dim[i].org = atof(word);
                if (fgetword(word, sizeof(word), fp) == NULL || !isflt(word))
                        goto scanerr;
                dp->dim[i].siz = atof(word);
                if (fgetword(word, sizeof(word), fp) == NULL || !isint(word))
                        goto scanerr;
                dp->dim[i].ne = atoi(word);
                if (dp->dim[i].ne < 2)
                        goto scanerr;
                asize *= dp->dim[i].ne;
                if ((dp->dim[i].siz -= dp->dim[i].org) == 0) {
                        dp->dim[i].p = (double *)malloc(dp->dim[i].ne*sizeof(double));
                        if (dp->dim[i].p == NULL)
                                goto memerr;
                        for (j = 0; j < dp->dim[i].ne; j++) {
                                if (fgetword(word, sizeof(word), fp) == NULL ||
                                                !isflt(word))
                                        goto scanerr;
                                dp->dim[i].p[j] = atof(word);
                        }
                        for (j = 1; j < dp->dim[i].ne-1; j++)
                                if ((dp->dim[i].p[j-1] < dp->dim[i].p[j]) !=
                                        (dp->dim[i].p[j] < dp->dim[i].p[j+1]))
                                        goto scanerr;
                        dp->dim[i].org = dp->dim[i].p[0];
                        dp->dim[i].siz = dp->dim[i].p[dp->dim[i].ne-1]
                                                - dp->dim[i].p[0];
                } else
                        dp->dim[i].p = NULL;
        }
        if ((dp->arr = (DATATYPE *)malloc(asize*sizeof(DATATYPE))) == NULL)
                goto memerr;
        
        for (i = 0; i < asize; i++) {
                if (fgetword(word, sizeof(word), fp) == NULL || !isflt(word))
                        goto scanerr;
                dp->arr[i] = atof(word);
        }
        fclose(fp);
        dp->next = dlist;
        return(dlist = dp);

memerr:
        error(SYSTEM, "out of memory in getdata");
scanerr:
        sprintf(errmsg, "%s in data file \"%s\"",
                        feof(fp) ? "unexpected EOF" : "bad format", dfname);
        error(USER, errmsg);
}


static double  inpaspect;               /* aspect ratio of input picture */

static
headaspect(s)                           /* check string for aspect ratio */
char  *s;
{
        if (isaspect(s))
                inpaspect *= aspectval(s);
}


DATARRAY *
getpict(pname)                          /* get picture pname */
char  *pname;
{
        extern char  *libpath;
        char  *pfname;
        FILE  *fp;
        COLOR  *scanin;
        int  sl, ns;
        RESOLU  inpres;
        FLOAT  loc[2];
        int  y;
        register int  x, i;
        register DATARRAY  *pp;
                                                /* look for array in list */
        for (pp = plist; pp != NULL; pp = pp->next)
                if (!strcmp(pname, pp->name))
                        return(pp);             /* found! */

        if ((pfname = getpath(pname, libpath, R_OK)) == NULL) {
                sprintf(errmsg, "cannot find picture file \"%s\"", pname);
                error(USER, errmsg);
        }
        if ((pp = (DATARRAY *)calloc(3, sizeof(DATARRAY))) == NULL)
                goto memerr;

        pp[0].name = 
        pp[1].name =
        pp[2].name = savestr(pname);

        if ((fp = fopen(pfname, "r")) == NULL) {
                sprintf(errmsg, "cannot open picture file \"%s\"", pfname);
                error(SYSTEM, errmsg);
        }
                                                /* get dimensions */
        inpaspect = 1.0;
        getheader(fp, headaspect);
        if (!fgetsresolu(&inpres, fp))
                goto readerr;
        for (i = 0; i < 3; i++) {
                pp[i].nd = 2;
                pp[i].dim[0].ne = inpres.yr;
                pp[i].dim[1].ne = inpres.xr;
                pp[i].dim[0].org =
                pp[i].dim[1].org = 0.0;
                if (inpres.xr <= inpres.yr*inpaspect) {
                        pp[i].dim[0].siz = inpaspect *
                                                (double)inpres.yr/inpres.xr;
                        pp[i].dim[1].siz = 1.0;
                } else {
                        pp[i].dim[0].siz = 1.0;
                        pp[i].dim[1].siz = (double)inpres.xr/inpres.yr /
                                                inpaspect;
                }
                pp[i].dim[0].p = pp[i].dim[1].p = NULL;
                pp[i].arr = (DATATYPE *)
                                malloc(inpres.xr*inpres.yr*sizeof(DATATYPE));
                if (pp[i].arr == NULL)
                        goto memerr;
        }
                                                        /* load picture */
        sl = scanlen(&inpres);
        ns = numscans(&inpres);
        if ((scanin = (COLOR *)malloc(sl*sizeof(COLOR))) == NULL)
                goto memerr;
        for (y = 0; y < ns; y++) {
                if (freadscan(scanin, sl, fp) < 0)
                        goto readerr;
                for (x = 0; x < sl; x++) {
                        pix2loc(loc, &inpres, x, y);
                        i = (int)(loc[1]*inpres.yr)*inpres.xr +
                                        (int)(loc[0]*inpres.xr);
                        pp[0].arr[i] = colval(scanin[x],RED);
                        pp[1].arr[i] = colval(scanin[x],GRN);
                        pp[2].arr[i] = colval(scanin[x],BLU);
                }
        }
        free((char *)scanin);
        fclose(fp);
        pp[0].next =
        pp[1].next =
        pp[2].next = plist;
        return(plist = pp);

memerr:
        error(SYSTEM, "out of memory in getpict");
readerr:
        sprintf(errmsg, "bad picture file \"%s\"", pfname);
        error(USER, errmsg);
}


freedata(dname)                 /* free memory associated with dname */
char  *dname;
{
        register DATARRAY  *dp, *dpl;
        register int  i;

        for (dpl = NULL, dp = dlist; dp != NULL; dpl = dp, dp = dp->next)
                if (!strcmp(dname, dp->name)) {
                        if (dpl == NULL)
                                dlist = dp->next;
                        else
                                dpl->next = dp->next;
                        free((char *)dp->arr);
                        for (i = 0; i < dp->nd; i++)
                                if (dp->dim[i].p != NULL)
                                        free((char *)dp->dim[i].p);
                        freestr(dp->name);
                        free((char *)dp);
                        return;
                }
}


freepict(pname)                 /* free memory associated with pname */
char  *pname;
{
        register DATARRAY  *pp, *ppl;

        for (ppl = NULL, pp = plist; pp != NULL; ppl = pp, pp = pp->next)
                if (!strcmp(pname, pp->name)) {
                        if (ppl == NULL)
                                plist = pp->next;
                        else
                                ppl->next = pp->next;
                        free((char *)pp[0].arr);
                        free((char *)pp[1].arr);
                        free((char *)pp[2].arr);
                        freestr(pp[0].name);
                        free((char *)pp);
                        return;
                }
}


double
datavalue(dp, pt)               /* interpolate data value at a point */
register DATARRAY  *dp;
double  *pt;
{
        DATARRAY  sd;
        int  asize;
        int  lower, upper;
        register int  i;
        double  x, y, y0, y1;
                                        /* set up dimensions for recursion */
        sd.nd = dp->nd - 1;
        asize = 1;
        for (i = 0; i < sd.nd; i++) {
                sd.dim[i].org = dp->dim[i+1].org;
                sd.dim[i].siz = dp->dim[i+1].siz;
                sd.dim[i].p = dp->dim[i+1].p;
                asize *= sd.dim[i].ne = dp->dim[i+1].ne;
        }
                                        /* get independent variable */
        if (dp->dim[0].p == NULL) {             /* evenly spaced points */
                x = (pt[0] - dp->dim[0].org)/dp->dim[0].siz;
                x = x * (dp->dim[0].ne - 1);
                i = x;
                if (i < 0)
                        i = 0;
                else if (i > dp->dim[0].ne - 2)
                        i = dp->dim[0].ne - 2;
        } else {                                /* unevenly spaced points */
                if (dp->dim[0].siz > 0.0) {
                        lower = 0;
                        upper = dp->dim[0].ne;
                } else {
                        lower = dp->dim[0].ne;
                        upper = 0;
                }
                do {
                        i = (lower + upper) >> 1;
                        if (pt[0] >= dp->dim[0].p[i])
                                lower = i;
                        else
                                upper = i;
                } while (i != (lower + upper) >> 1);
                if (i > dp->dim[0].ne - 2)
                        i = dp->dim[0].ne - 2;
                x = i + (pt[0] - dp->dim[0].p[i]) /
                                (dp->dim[0].p[i+1] - dp->dim[0].p[i]);
        }
                                        /* get dependent variable */
        if (dp->nd == 1) {
                y0 = dp->arr[i];
                y1 = dp->arr[i+1];
        } else {
                sd.arr = &dp->arr[i*asize];
                y0 = datavalue(&sd, pt+1);
                sd.arr = &dp->arr[(i+1)*asize];
                y1 = datavalue(&sd, pt+1);
        }
        /*
         * Extrapolate as far as one division, then
         * taper off harmonically to zero.
         */
        if (x > i+2)
                y = (2*y1-y0)/(x-i-1);
        else if (x < i-1)
                y = (2*y0-y1)/(i-x);
        else
                y = y0*((i+1)-x) + y1*(x-i);

        return(y);
}
Revision:	2.2
Committed:	Thu Dec 19 14:54:58 1991 UTC (32 years, 4 months ago) by greg
Content type:	text/plain
Branch:	MAIN
Changes since 2.1:	+0 -1 lines
Log Message:	removed atof() declarations for NeXT
#	User	Rev	Content
1	greg	1.8	/* Copyright (c) 1991 Regents of the University of California */
2	greg	1.1
3			#ifndef lint
4			static char SCCSid[] = "$SunId$ LBL";
5			#endif
6
7			/*
8			* data.c - routines dealing with interpolated data.
9			*
10			* 6/4/86
11			*/
12
13			#include "standard.h"
14
15			#include "color.h"
16
17	greg	1.11	#include "resolu.h"
18
19	greg	1.1	#include "data.h"
20
21
22	greg	1.10	extern char *fgetword();
23
24	greg	1.1	extern char libpath; / library search path */
25
26			static DATARRAY dlist = NULL; / data array list */
27
28			static DATARRAY plist = NULL; / picture list */
29
30
31			DATARRAY *
32			getdata(dname) /* get data array dname */
33			char *dname;
34			{
35	greg	1.10	char word[64];
36	greg	1.1	char *dfname;
37			FILE *fp;
38			int asize;
39	greg	1.4	register int i, j;
40	greg	1.1	register DATARRAY *dp;
41			/* look for array in list */
42			for (dp = dlist; dp != NULL; dp = dp->next)
43			if (!strcmp(dname, dp->name))
44			return(dp); /* found! */
45
46			/*
47			* If we haven't loaded the data already, we will look
48			* for it in the directorys specified by the library path.
49			*
50			* The file has the following format:
51			*
52	greg	1.4	* N
53	greg	1.1	* beg0 end0 n0
54			* beg1 end1 n1
55			* . . .
56	greg	1.4	* begN endN nN
57	greg	1.1	* data, later dimensions changing faster
58			* . . .
59			*
60	greg	1.4	* For irregularly spaced points, the following can be
61			* substituted for begi endi ni:
62			*
63	greg	1.6	* 0 0 ni p0i p1i .. pni
64	greg	1.1	*/
65
66	greg	1.2	if ((dfname = getpath(dname, libpath, R_OK)) == NULL) {
67	greg	1.1	sprintf(errmsg, "cannot find data file \"%s\"", dname);
68			error(USER, errmsg);
69			}
70			if ((dp = (DATARRAY *)malloc(sizeof(DATARRAY))) == NULL)
71			goto memerr;
72
73			dp->name = savestr(dname);
74
75			if ((fp = fopen(dfname, "r")) == NULL) {
76			sprintf(errmsg, "cannot open data file \"%s\"", dfname);
77			error(SYSTEM, errmsg);
78			}
79			/* get dimensions */
80	greg	1.10	if (fgetword(word, sizeof(word), fp) == NULL \|\| !isint(word))
81	greg	1.1	goto scanerr;
82	greg	1.10	dp->nd = atoi(word);
83	greg	1.9	if (dp->nd <= 0 \|\| dp->nd > MAXDDIM) {
84	greg	1.1	sprintf(errmsg, "bad number of dimensions for \"%s\"", dname);
85			error(USER, errmsg);
86			}
87			asize = 1;
88			for (i = 0; i < dp->nd; i++) {
89	greg	1.10	if (fgetword(word, sizeof(word), fp) == NULL \|\| !isflt(word))
90	greg	1.6	goto scanerr;
91	greg	1.10	dp->dim[i].org = atof(word);
92			if (fgetword(word, sizeof(word), fp) == NULL \|\| !isflt(word))
93			goto scanerr;
94			dp->dim[i].siz = atof(word);
95			if (fgetword(word, sizeof(word), fp) == NULL \|\| !isint(word))
96			goto scanerr;
97			dp->dim[i].ne = atoi(word);
98	greg	1.6	if (dp->dim[i].ne < 2)
99			goto scanerr;
100			asize *= dp->dim[i].ne;
101			if ((dp->dim[i].siz -= dp->dim[i].org) == 0) {
102	greg	1.4	dp->dim[i].p = (double )malloc(dp->dim[i].nesizeof(double));
103			if (dp->dim[i].p == NULL)
104			goto memerr;
105	greg	1.10	for (j = 0; j < dp->dim[i].ne; j++) {
106			if (fgetword(word, sizeof(word), fp) == NULL \|\|
107			!isflt(word))
108	greg	1.4	goto scanerr;
109	greg	1.10	dp->dim[i].p[j] = atof(word);
110			}
111	greg	1.4	for (j = 1; j < dp->dim[i].ne-1; j++)
112			if ((dp->dim[i].p[j-1] < dp->dim[i].p[j]) !=
113			(dp->dim[i].p[j] < dp->dim[i].p[j+1]))
114			goto scanerr;
115			dp->dim[i].org = dp->dim[i].p[0];
116			dp->dim[i].siz = dp->dim[i].p[dp->dim[i].ne-1]
117			- dp->dim[i].p[0];
118			} else
119	greg	1.6	dp->dim[i].p = NULL;
120	greg	1.1	}
121			if ((dp->arr = (DATATYPE )malloc(asizesizeof(DATATYPE))) == NULL)
122			goto memerr;
123
124	greg	1.10	for (i = 0; i < asize; i++) {
125			if (fgetword(word, sizeof(word), fp) == NULL \|\| !isflt(word))
126	greg	1.1	goto scanerr;
127	greg	1.10	dp->arr[i] = atof(word);
128			}
129	greg	1.1	fclose(fp);
130			dp->next = dlist;
131			return(dlist = dp);
132
133			memerr:
134			error(SYSTEM, "out of memory in getdata");
135			scanerr:
136			sprintf(errmsg, "%s in data file \"%s\"",
137			feof(fp) ? "unexpected EOF" : "bad format", dfname);
138			error(USER, errmsg);
139			}
140
141
142	greg	1.5	static double inpaspect; /* aspect ratio of input picture */
143
144			static
145			headaspect(s) /* check string for aspect ratio */
146			char *s;
147			{
148			if (isaspect(s))
149			inpaspect *= aspectval(s);
150			}
151
152
153	greg	1.1	DATARRAY *
154			getpict(pname) /* get picture pname */
155			char *pname;
156			{
157			extern char *libpath;
158			char *pfname;
159			FILE *fp;
160			COLOR *scanin;
161	greg	1.11	int sl, ns;
162			RESOLU inpres;
163			FLOAT loc[2];
164			int y;
165			register int x, i;
166	greg	1.1	register DATARRAY *pp;
167			/* look for array in list */
168			for (pp = plist; pp != NULL; pp = pp->next)
169			if (!strcmp(pname, pp->name))
170			return(pp); /* found! */
171
172	greg	1.2	if ((pfname = getpath(pname, libpath, R_OK)) == NULL) {
173	greg	1.1	sprintf(errmsg, "cannot find picture file \"%s\"", pname);
174			error(USER, errmsg);
175			}
176			if ((pp = (DATARRAY *)calloc(3, sizeof(DATARRAY))) == NULL)
177			goto memerr;
178
179			pp[0].name =
180			pp[1].name =
181			pp[2].name = savestr(pname);
182
183			if ((fp = fopen(pfname, "r")) == NULL) {
184			sprintf(errmsg, "cannot open picture file \"%s\"", pfname);
185			error(SYSTEM, errmsg);
186			}
187			/* get dimensions */
188	greg	1.5	inpaspect = 1.0;
189			getheader(fp, headaspect);
190	greg	1.11	if (!fgetsresolu(&inpres, fp))
191	greg	1.1	goto readerr;
192			for (i = 0; i < 3; i++) {
193			pp[i].nd = 2;
194	greg	1.11	pp[i].dim[0].ne = inpres.yr;
195			pp[i].dim[1].ne = inpres.xr;
196	greg	1.1	pp[i].dim[0].org =
197			pp[i].dim[1].org = 0.0;
198	greg	1.11	if (inpres.xr <= inpres.yr*inpaspect) {
199			pp[i].dim[0].siz = inpaspect *
200			(double)inpres.yr/inpres.xr;
201	greg	1.7	pp[i].dim[1].siz = 1.0;
202			} else {
203	greg	1.1	pp[i].dim[0].siz = 1.0;
204	greg	1.11	pp[i].dim[1].siz = (double)inpres.xr/inpres.yr /
205			inpaspect;
206	greg	1.1	}
207	greg	1.7	pp[i].dim[0].p = pp[i].dim[1].p = NULL;
208	greg	1.11	pp[i].arr = (DATATYPE *)
209			malloc(inpres.xrinpres.yrsizeof(DATATYPE));
210	greg	1.1	if (pp[i].arr == NULL)
211			goto memerr;
212			}
213			/* load picture */
214	greg	1.11	sl = scanlen(&inpres);
215			ns = numscans(&inpres);
216			if ((scanin = (COLOR )malloc(slsizeof(COLOR))) == NULL)
217	greg	1.1	goto memerr;
218	greg	1.11	for (y = 0; y < ns; y++) {
219			if (freadscan(scanin, sl, fp) < 0)
220	greg	1.1	goto readerr;
221	greg	1.11	for (x = 0; x < sl; x++) {
222			pix2loc(loc, &inpres, x, y);
223			i = (int)(loc[1]inpres.yr)inpres.xr +
224			(int)(loc[0]*inpres.xr);
225			pp[0].arr[i] = colval(scanin[x],RED);
226			pp[1].arr[i] = colval(scanin[x],GRN);
227			pp[2].arr[i] = colval(scanin[x],BLU);
228			}
229	greg	1.1	}
230			free((char *)scanin);
231			fclose(fp);
232			pp[0].next =
233			pp[1].next =
234			pp[2].next = plist;
235			return(plist = pp);
236
237			memerr:
238			error(SYSTEM, "out of memory in getpict");
239			readerr:
240			sprintf(errmsg, "bad picture file \"%s\"", pfname);
241			error(USER, errmsg);
242			}
243
244
245			freedata(dname) /* free memory associated with dname */
246			char *dname;
247			{
248			register DATARRAY dp, dpl;
249	greg	1.4	register int i;
250	greg	1.1
251			for (dpl = NULL, dp = dlist; dp != NULL; dpl = dp, dp = dp->next)
252			if (!strcmp(dname, dp->name)) {
253			if (dpl == NULL)
254			dlist = dp->next;
255			else
256			dpl->next = dp->next;
257			free((char *)dp->arr);
258	greg	1.4	for (i = 0; i < dp->nd; i++)
259			if (dp->dim[i].p != NULL)
260			free((char *)dp->dim[i].p);
261	greg	1.1	freestr(dp->name);
262			free((char *)dp);
263			return;
264			}
265			}
266
267
268			freepict(pname) /* free memory associated with pname */
269			char *pname;
270			{
271			register DATARRAY pp, ppl;
272
273			for (ppl = NULL, pp = plist; pp != NULL; ppl = pp, pp = pp->next)
274			if (!strcmp(pname, pp->name)) {
275			if (ppl == NULL)
276			plist = pp->next;
277			else
278			ppl->next = pp->next;
279			free((char *)pp[0].arr);
280			free((char *)pp[1].arr);
281			free((char *)pp[2].arr);
282			freestr(pp[0].name);
283			free((char *)pp);
284			return;
285			}
286			}
287
288
289			double
290			datavalue(dp, pt) /* interpolate data value at a point */
291			register DATARRAY *dp;
292			double *pt;
293			{
294			DATARRAY sd;
295			int asize;
296	greg	1.6	int lower, upper;
297	greg	1.1	register int i;
298			double x, y, y0, y1;
299	greg	1.4	/* set up dimensions for recursion */
300	greg	1.1	sd.nd = dp->nd - 1;
301			asize = 1;
302			for (i = 0; i < sd.nd; i++) {
303			sd.dim[i].org = dp->dim[i+1].org;
304			sd.dim[i].siz = dp->dim[i+1].siz;
305	greg	1.4	sd.dim[i].p = dp->dim[i+1].p;
306	greg	1.1	asize *= sd.dim[i].ne = dp->dim[i+1].ne;
307			}
308	greg	1.4	/* get independent variable */
309			if (dp->dim[0].p == NULL) { /* evenly spaced points */
310			x = (pt[0] - dp->dim[0].org)/dp->dim[0].siz;
311			x = x * (dp->dim[0].ne - 1);
312			i = x;
313			if (i < 0)
314			i = 0;
315			else if (i > dp->dim[0].ne - 2)
316			i = dp->dim[0].ne - 2;
317			} else { /* unevenly spaced points */
318	greg	1.6	if (dp->dim[0].siz > 0.0) {
319			lower = 0;
320			upper = dp->dim[0].ne;
321			} else {
322			lower = dp->dim[0].ne;
323			upper = 0;
324			}
325			do {
326			i = (lower + upper) >> 1;
327			if (pt[0] >= dp->dim[0].p[i])
328			lower = i;
329	greg	1.8	else
330	greg	1.6	upper = i;
331			} while (i != (lower + upper) >> 1);
332	greg	1.8	if (i > dp->dim[0].ne - 2)
333	greg	1.4	i = dp->dim[0].ne - 2;
334			x = i + (pt[0] - dp->dim[0].p[i]) /
335			(dp->dim[0].p[i+1] - dp->dim[0].p[i]);
336			}
337			/* get dependent variable */
338	greg	1.1	if (dp->nd == 1) {
339			y0 = dp->arr[i];
340			y1 = dp->arr[i+1];
341			} else {
342			sd.arr = &dp->arr[i*asize];
343			y0 = datavalue(&sd, pt+1);
344			sd.arr = &dp->arr[(i+1)*asize];
345			y1 = datavalue(&sd, pt+1);
346			}
347			/*
348			* Extrapolate as far as one division, then
349			* taper off harmonically to zero.
350			*/
351			if (x > i+2)
352			y = (2*y1-y0)/(x-i-1);
353			else if (x < i-1)
354			y = (2*y0-y1)/(i-x);
355			else
356			y = y0((i+1)-x) + y1(x-i);
357
358			return(y);
359			}