1 /*
2 * soi.c -- SOI
3 *
4 * Simultaneous Orbit Iteration Image Generation Method. Computes
5 * rectangular regions by tracking the orbits of only a few key points.
6 *
7 * Copyright (c) 1994-1997 Michael R. Ganss. All Rights Reserved.
8 *
9 * This file is distributed under the same conditions as
10 * AlmondBread. For further information see
11 * <URL:http://www.cs.tu-berlin.de/~rms/AlmondBread>.
12 *
13 */
14 #include <time.h>
15 #include <string.h>
16 #ifdef __APPLE__
17 #include <malloc/malloc.h>
18 #elif !defined(BIG_ANSI_C)
19 #include <malloc.h>
20 #endif
21 #include "port.h"
22 #include "prototyp.h"
23
24 #define DBLS double
25 #define FABS(x) fabs(x)
26 #define FREXP(x,y) frexp(x,y)
27
28 #define TRUE 1
29 #define FALSE 0
30 #define EVERY 15
31 #define BASIN_COLOR 0
32
33 extern int rhombus_stack[10];
34 extern int rhombus_depth;
35 extern int max_rhombus_depth;
36 extern int minstackavail;
37 extern int minstack; /* need this much stack to recurse */
38 static DBLS twidth;
39 static DBLS equal;
40
41 #if 0
42 static long iteration1(register DBLS cr, register DBLS ci,
43 register DBLS re, register DBLS im,
44 long start)
45 {
46 DBLS oldreal, oldimag, newreal, newimag, magnitude;
47 long color;
48 magnitude = 0.0;
49 color = start;
50 oldreal = re;
51 oldimag = im;
52 while ((magnitude < 16.0) && (color < maxit)) {
53 newreal = oldreal * oldreal - oldimag * oldimag + cr;
54 newimag = 2 * oldreal * oldimag + ci;
55 color++;
56 oldreal = newreal;
57 oldimag = newimag;
58 magnitude = newreal * newreal + newimag * newimag;
59 }
60 if (color >= maxit) color = BASIN_COLOR;
61 return((int)color);
62 }
63 #endif
64
iteration(register DBLS cr,register DBLS ci,register DBLS re,register DBLS im,long start)65 static long iteration(register DBLS cr, register DBLS ci,
66 register DBLS re, register DBLS im,
67 long start)
68 {
69 old.x = re;
70 old.y = im;
71 tempsqrx = sqr(old.x);
72 tempsqry = sqr(old.y);
73 floatparm = &init;
74 floatparm->x = cr;
75 floatparm->y = ci;
76 while(ORBITCALC()==0 && start < maxit)
77 start++;
78 if (start >= maxit)
79 start = BASIN_COLOR;
80 return(start);
81 }
82 #if 0
83 JuliafpFractal()
84 {
85 /* floating point version of classical Mandelbrot/Julia */
86 new.x = tempsqrx - tempsqry + floatparm->x;
87 new.y = 2.0 * old.x * old.y + floatparm->y;
88 return(floatbailout());
89 }
90 #endif
91
puthline(int x1,int y1,int x2,int color)92 static void puthline(int x1,int y1,int x2,int color)
93 {
94 int x;
95 for(x=x1;x<=x2;x++)
96 (*plot)(x,y1,color);
97 }
98
putbox(int x1,int y1,int x2,int y2,int color)99 static void putbox(int x1, int y1, int x2, int y2, int color)
100 {
101 for(; y1<=y2; y1++)
102 puthline(x1,y1,x2,color);
103 }
104
105 /* maximum side length beyond which we start regular scanning instead of
106 subdividing */
107 #define SCAN 16
108
109 /* pixel interleave used in scanning */
110 #define INTERLEAVE 4
111
112 /* compute the value of the interpolation polynomial at (x,y) */
113 #define GET_REAL(x,y) \
114 interpolate(cim1,midi,cim2,\
115 interpolate(cre1,midr,cre2,zre1,zre5,zre2,x),\
116 interpolate(cre1,midr,cre2,zre6,zre9,zre7,x),\
117 interpolate(cre1,midr,cre2,zre3,zre8,zre4,x),y)
118 #define GET_IMAG(x,y) \
119 interpolate(cre1,midr,cre2,\
120 interpolate(cim1,midi,cim2,zim1,zim6,zim3,y),\
121 interpolate(cim1,midi,cim2,zim5,zim9,zim8,y),\
122 interpolate(cim1,midi,cim2,zim2,zim7,zim4,y),x)
123
124 /* compute the value of the interpolation polynomial at (x,y)
125 from saved values before interpolation failed to stay within tolerance */
126 #define GET_SAVED_REAL(x,y) \
127 interpolate(cim1,midi,cim2,\
128 interpolate(cre1,midr,cre2,sr1,sr5,sr2,x),\
129 interpolate(cre1,midr,cre2,sr6,sr9,sr7,x),\
130 interpolate(cre1,midr,cre2,sr3,sr8,sr4,x),y)
131 #define GET_SAVED_IMAG(x,y) \
132 interpolate(cre1,midr,cre2,\
133 interpolate(cim1,midi,cim2,si1,si6,si3,y),\
134 interpolate(cim1,midi,cim2,si5,si9,si8,y),\
135 interpolate(cim1,midi,cim2,si2,si7,si4,y),x)
136
137 /* compute the value of the interpolation polynomial at (x,y)
138 during scanning. Here, key values do not change, so we can precompute
139 coefficients in one direction and simply evaluate the polynomial
140 during scanning. */
141 #define GET_SCAN_REAL(x,y) \
142 interpolate(cim1,midi,cim2,\
143 EVALUATE(cre1,midr,br10,br11,br12,x),\
144 EVALUATE(cre1,midr,br20,br21,br22,x),\
145 EVALUATE(cre1,midr,br30,br31,br32,x),y)
146 #define GET_SCAN_IMAG(x,y) \
147 interpolate(cre1,midr,cre2,\
148 EVALUATE(cim1,midi,bi10,bi11,bi12,y),\
149 EVALUATE(cim1,midi,bi20,bi21,bi22,y),\
150 EVALUATE(cim1,midi,bi30,bi31,bi32,y),x)
151
152 /* compute coefficients of Newton polynomial (b0,..,b2) from
153 (x0,w0),..,(x2,w2). */
154 #define INTERPOLATE(x0,x1,x2,w0,w1,w2,b0,b1,b2) \
155 b0=w0;\
156 b1=(w1-w0)/(x1-x0);\
157 b2=((w2-w1)/(x2-x1)-b1)/(x2-x0)
158
159 /* evaluate Newton polynomial given by (x0,b0),(x1,b1) at x:=t */
160 #define EVALUATE(x0,x1,b0,b1,b2,t) \
161 ((b2*(t-x1)+b1)*(t-x0)+b0)
162
163 /* Newton Interpolation.
164 It computes the value of the interpolation polynomial given by
165 (x0,w0)..(x2,w2) at x:=t */
interpolate(DBLS x0,DBLS x1,DBLS x2,DBLS w0,DBLS w1,DBLS w2,DBLS t)166 static DBLS interpolate(DBLS x0, DBLS x1, DBLS x2,
167 DBLS w0, DBLS w1, DBLS w2,
168 DBLS t)
169 {
170 register DBLS b0=w0,b1=w1,b2=w2,b;
171
172 /*b0=(r0*b1-r1*b0)/(x1-x0);
173 b1=(r1*b2-r2*b1)/(x2-x1);
174 b0=(r0*b1-r2*b0)/(x2-x0);
175
176 return (DBLS)b0;*/
177 b=(b1-b0)/(x1-x0);
178 return (DBLS)((((b2-b1)/(x2-x1)-b)/(x2-x0))*(t-x1)+b)*(t-x0)+b0;
179 /*
180 if(t<x1)
181 return w0+((t-x0)/(x1-x0))*(w1-w0);
182 else
183 return w1+((t-x1)/(x2-x1))*(w2-w1);*/
184 }
185 #if (_MSC_VER >= 700)
186 #pragma code_seg ("soi3_text") /* place following in an overlay */
187 #endif
188
189 /* SOICompute - Perform simultaneous orbit iteration for a given rectangle
190
191 Input: cre1..cim2 : values defining the four corners of the rectangle
192 x1..y2 : corresponding pixel values
193 zre1..zim9 : intermediate iterated values of the key points (key values)
194
195 (cre1,cim1) (cre2,cim1)
196 (zre1,zim1) (zre5,zim5) (zre2,zim2)
197 +------------+------------+
198 | | |
199 | | |
200 (zre6,zim6) (zre9,zim9) (zre7,zim7)
201 | | |
202 | | |
203 +------------+------------+
204 (zre3,zim3) (zre8,zim8) (zre4,zim4)
205 (cre1,cim2) (cre2,cim2)
206
207 iter : current number of iterations
208 */
209 static DBLS zre1, zim1, zre2, zim2, zre3, zim3, zre4, zim4, zre5, zim5,
210 zre6, zim6, zre7, zim7, zre8, zim8, zre9, zim9;
211 /*
212 The purpose of this macro is to reduce the number of parameters of the
213 function rhombus(), since this is a recursive function, and stack space
214 under DOS is extremely limited.
215 */
216
217 #define RHOMBUS(CRE1,CRE2,CIM1,CIM2,X1,X2,Y1,Y2,ZRE1,ZIM1,ZRE2,ZIM2,ZRE3,ZIM3,\
218 ZRE4, ZIM4, ZRE5, ZIM5,ZRE6, ZIM6, ZRE7, ZIM7, ZRE8, ZIM8, ZRE9, ZIM9,ITER) \
219 zre1=(ZRE1);zim1=(ZIM1);\
220 zre2=(ZRE2);zim2=(ZIM2);\
221 zre3=(ZRE3);zim3=(ZIM3);\
222 zre4=(ZRE4);zim4=(ZIM4);\
223 zre5=(ZRE5);zim5=(ZIM5);\
224 zre6=(ZRE6);zim6=(ZIM6);\
225 zre7=(ZRE7);zim7=(ZIM7);\
226 zre8=(ZRE8);zim8=(ZIM8);\
227 zre9=(ZRE9);zim9=(ZIM9);\
228 status=rhombus((CRE1),(CRE2),(CIM1),(CIM2),(X1),(X2),(Y1),(Y2),(ITER))
229
rhombus(DBLS cre1,DBLS cre2,DBLS cim1,DBLS cim2,int x1,int x2,int y1,int y2,long iter)230 static int rhombus(DBLS cre1, DBLS cre2, DBLS cim1, DBLS cim2,
231 int x1, int x2, int y1, int y2, long iter)
232 {
233 /* The following variables do not need their values saved */
234 /* used in scanning */
235 static long far savecolor, color, helpcolor;
236 static int far x,y,z,savex;
237
238 #if 0
239 static DBLS far re,im,restep,imstep,interstep,helpre;
240 static DBLS far zre,zim;
241 /* interpolation coefficients */
242 static DBLS far br10,br11,br12,br20,br21,br22,br30,br31,br32;
243 static DBLS far bi10,bi11,bi12,bi20,bi21,bi22,bi30,bi31,bi32;
244 /* ratio of interpolated test point to iterated one */
245 static DBLS far l1,l2;
246 /* squares of key values */
247 static DBLS far rq1,iq1;
248 static DBLS far rq2,iq2;
249 static DBLS far rq3,iq3;
250 static DBLS far rq4,iq4;
251 static DBLS far rq5,iq5;
252 static DBLS far rq6,iq6;
253 static DBLS far rq7,iq7;
254 static DBLS far rq8,iq8;
255 static DBLS far rq9,iq9;
256
257 /* test points */
258 static DBLS far cr1,cr2;
259 static DBLS far ci1,ci2;
260 static DBLS far tzr1,tzi1,tzr2,tzi2,tzr3,tzi3,tzr4,tzi4;
261 static DBLS far trq1,tiq1,trq2,tiq2,trq3,tiq3,trq4,tiq4;
262 #else
263 #define re mem_static[ 0]
264 #define im mem_static[ 1]
265 #define restep mem_static[ 2]
266 #define imstep mem_static[ 3]
267 #define interstep mem_static[ 4]
268 #define helpre mem_static[ 5]
269 #define zre mem_static[ 6]
270 #define zim mem_static[ 7]
271 #define br10 mem_static[ 8]
272 #define br11 mem_static[ 9]
273 #define br12 mem_static[10]
274 #define br20 mem_static[11]
275 #define br21 mem_static[12]
276 #define br22 mem_static[13]
277 #define br30 mem_static[14]
278 #define br31 mem_static[15]
279 #define br32 mem_static[16]
280 #define bi10 mem_static[17]
281 #define bi11 mem_static[18]
282 #define bi12 mem_static[19]
283 #define bi20 mem_static[20]
284 #define bi21 mem_static[21]
285 #define bi22 mem_static[22]
286 #define bi30 mem_static[23]
287 #define bi31 mem_static[24]
288 #define bi32 mem_static[25]
289 #define l1 mem_static[26]
290 #define l2 mem_static[27]
291 #define rq1 mem_static[28]
292 #define iq1 mem_static[29]
293 #define rq2 mem_static[30]
294 #define iq2 mem_static[31]
295 #define rq3 mem_static[32]
296 #define iq3 mem_static[33]
297 #define rq4 mem_static[34]
298 #define iq4 mem_static[35]
299 #define rq5 mem_static[36]
300 #define iq5 mem_static[37]
301 #define rq6 mem_static[38]
302 #define iq6 mem_static[39]
303 #define rq7 mem_static[40]
304 #define iq7 mem_static[41]
305 #define rq8 mem_static[42]
306 #define iq8 mem_static[43]
307 #define rq9 mem_static[44]
308 #define iq9 mem_static[45]
309 #define cr1 mem_static[46]
310 #define cr2 mem_static[47]
311 #define ci1 mem_static[48]
312 #define ci2 mem_static[49]
313 #define tzr1 mem_static[50]
314 #define tzi1 mem_static[51]
315 #define tzr2 mem_static[52]
316 #define tzi2 mem_static[53]
317 #define tzr3 mem_static[54]
318 #define tzi3 mem_static[55]
319 #define tzr4 mem_static[56]
320 #define tzi4 mem_static[57]
321 #define trq1 mem_static[58]
322 #define tiq1 mem_static[59]
323 #define trq2 mem_static[60]
324 #define tiq2 mem_static[61]
325 #define trq3 mem_static[62]
326 #define tiq3 mem_static[63]
327 #define trq4 mem_static[64]
328 #define tiq4 mem_static[65]
329
330 #endif
331 /* number of iterations before SOI iteration cycle */
332 static long far before;
333 static int far avail;
334
335 /* the variables below need to have local copies for recursive calls */
336 int far *mem_int;
337 DBLS far *mem;
338 DBLS far *mem_static;
339 /* center of rectangle */
340 DBLS midr=(cre1+cre2)/2,midi=(cim1+cim2)/2;
341
342 #if 0
343 /* saved values of key values */
344 DBLS sr1,si1,sr2,si2,sr3,si3,sr4,si4;
345 DBLS sr5,si5,sr6,si6,sr7,si7,sr8,si8,sr9,si9;
346 /* key values for subsequent rectangles */
347 DBLS re10,re11,re12,re13,re14,re15,re16,re17,re18,re19,re20,re21;
348 DBLS im10,im11,im12,im13,im14,im15,im16,im17,im18,im19,im20,im21;
349 DBLS re91,re92,re93,re94,im91,im92,im93,im94;
350 #else
351 #define esc1 mem_int[0]
352 #define esc2 mem_int[1]
353 #define esc3 mem_int[2]
354 #define esc4 mem_int[3]
355 #define esc5 mem_int[4]
356 #define esc6 mem_int[5]
357 #define esc7 mem_int[6]
358 #define esc8 mem_int[7]
359 #define esc9 mem_int[8]
360 #define tesc1 mem_int[9]
361 #define tesc2 mem_int[10]
362 #define tesc3 mem_int[11]
363 #define tesc4 mem_int[12]
364
365 #define sr1 mem[ 0]
366 #define si1 mem[ 1]
367 #define sr2 mem[ 2]
368 #define si2 mem[ 3]
369 #define sr3 mem[ 4]
370 #define si3 mem[ 5]
371 #define sr4 mem[ 6]
372 #define si4 mem[ 7]
373 #define sr5 mem[ 8]
374 #define si5 mem[ 9]
375 #define sr6 mem[10]
376 #define si6 mem[11]
377 #define sr7 mem[12]
378 #define si7 mem[13]
379 #define sr8 mem[14]
380 #define si8 mem[15]
381 #define sr9 mem[16]
382 #define si9 mem[17]
383 #define re10 mem[18]
384 #define re11 mem[19]
385 #define re12 mem[20]
386 #define re13 mem[21]
387 #define re14 mem[22]
388 #define re15 mem[23]
389 #define re16 mem[24]
390 #define re17 mem[25]
391 #define re18 mem[26]
392 #define re19 mem[27]
393 #define re20 mem[28]
394 #define re21 mem[29]
395 #define im10 mem[30]
396 #define im11 mem[31]
397 #define im12 mem[32]
398 #define im13 mem[33]
399 #define im14 mem[34]
400 #define im15 mem[35]
401 #define im16 mem[36]
402 #define im17 mem[37]
403 #define im18 mem[38]
404 #define im19 mem[39]
405 #define im20 mem[40]
406 #define im21 mem[41]
407 #define re91 mem[42]
408 #define re92 mem[43]
409 #define re93 mem[44]
410 #define re94 mem[45]
411 #define im91 mem[46]
412 #define im92 mem[47]
413 #define im93 mem[48]
414 #define im94 mem[49]
415 #endif
416
417 int status = 0;
418 rhombus_depth++;
419
420 #if 1
421 /* what we go through under DOS to deal with memory! We re-use
422 the sizeofstring array (8k). The first 660 bytes is for
423 static variables, then we make our own "stack" with copies
424 for each recursive call of rhombus() for the rest.
425 */
426 mem_int = (int far *)sizeofstring;
427 mem_static = (DBLS far *)(mem_int + 13);
428 mem = mem_static+ 66 + 50*rhombus_depth;
429 #endif
430
431 if((avail = stackavail()) < minstackavail)
432 minstackavail = avail;
433 if(rhombus_depth > max_rhombus_depth)
434 max_rhombus_depth = rhombus_depth;
435 rhombus_stack[rhombus_depth] = avail;
436
437 if(keypressed())
438 {
439 status = 1;
440 goto rhombus_done;
441 }
442 if(iter>maxit)
443 {
444 putbox(x1,y1,x2,y2,0);
445 status = 0;
446 goto rhombus_done;
447 }
448
449 if((y2-y1<=SCAN) || (avail < minstack))
450 {
451 /* finish up the image by scanning the rectangle */
452 scan:
453 INTERPOLATE(cre1,midr,cre2,zre1,zre5,zre2,br10,br11,br12);
454 INTERPOLATE(cre1,midr,cre2,zre6,zre9,zre7,br20,br21,br22);
455 INTERPOLATE(cre1,midr,cre2,zre3,zre8,zre4,br30,br31,br32);
456
457 INTERPOLATE(cim1,midi,cim2,zim1,zim6,zim3,bi10,bi11,bi12);
458 INTERPOLATE(cim1,midi,cim2,zim5,zim9,zim8,bi20,bi21,bi22);
459 INTERPOLATE(cim1,midi,cim2,zim2,zim7,zim4,bi30,bi31,bi32);
460
461 restep=(cre2-cre1)/(x2-x1);
462 imstep=(cim2-cim1)/(y2-y1);
463 interstep=INTERLEAVE*restep;
464
465 for(y=y1, im=cim1; y<y2; y++, im+=imstep)
466 {
467 if(keypressed())
468 {
469 status = 1;
470 goto rhombus_done;
471 }
472 zre=GET_SCAN_REAL(cre1,im);
473 zim=GET_SCAN_IMAG(cre1,im);
474 savecolor=iteration(cre1,im,zre,zim,iter);
475 if(savecolor < 0)
476 {
477 status = 1;
478 goto rhombus_done;
479 }
480 savex=x1;
481 for(x=x1+INTERLEAVE, re=cre1+interstep; x<x2;
482 x+=INTERLEAVE, re+=interstep)
483 {
484 zre=GET_SCAN_REAL(re,im);
485 zim=GET_SCAN_IMAG(re,im);
486
487 color=iteration(re,im,zre,zim,iter);
488 if(color < 0)
489 {
490 status = 1;
491 goto rhombus_done;
492 }
493 else if(color==savecolor)
494 continue;
495
496 for (z=x-1, helpre=re-restep; z>x-INTERLEAVE; z--,helpre-=restep)
497 {
498 zre=GET_SCAN_REAL(helpre,im);
499 zim=GET_SCAN_IMAG(helpre,im);
500 helpcolor=iteration(helpre,im,zre,zim,iter);
501 if(helpcolor < 0)
502 {
503 status = 1;
504 goto rhombus_done;
505 }
506 else if(helpcolor==savecolor)
507 break;
508 (*plot)(z,y,(int)(helpcolor&255));
509 }
510
511 if(savex<z)
512 puthline(savex, y, z, (int)(savecolor&255));
513 else
514 (*plot)(savex, y, (int)(savecolor&255));
515
516 savex = x;
517 savecolor = color;
518 }
519
520 for (z=x2-1, helpre=cre2-restep; z>savex; z--,helpre-=restep)
521 {
522 zre=GET_SCAN_REAL(helpre,im);
523 zim=GET_SCAN_IMAG(helpre,im);
524 helpcolor=iteration(helpre,im,zre,zim,iter);
525 if(helpcolor < 0)
526 {
527 status = 1;
528 goto rhombus_done;
529 }
530 else if(helpcolor==savecolor)
531 break;
532
533 (*plot)(z,y,(int)(helpcolor&255));
534 }
535
536 if(savex<z)
537 puthline(savex, y, z, (int)(savecolor&255));
538 else
539 (*plot)(savex, y, (int)(savecolor&255));
540 }
541 status = 0;
542 goto rhombus_done;
543 }
544
545 rq1=zre1*zre1; iq1=zim1*zim1;
546 rq2=zre2*zre2; iq2=zim2*zim2;
547 rq3=zre3*zre3; iq3=zim3*zim3;
548 rq4=zre4*zre4; iq4=zim4*zim4;
549 rq5=zre5*zre5; iq5=zim5*zim5;
550 rq6=zre6*zre6; iq6=zim6*zim6;
551 rq7=zre7*zre7; iq7=zim7*zim7;
552 rq8=zre8*zre8; iq8=zim8*zim8;
553 rq9=zre9*zre9; iq9=zim9*zim9;
554
555 cr1=0.75*cre1+0.25*cre2; cr2=0.25*cre1+0.75*cre2;
556 ci1=0.75*cim1+0.25*cim2; ci2=0.25*cim1+0.75*cim2;
557
558 tzr1=GET_REAL(cr1,ci1);
559 tzi1=GET_IMAG(cr1,ci1);
560
561 tzr2=GET_REAL(cr2,ci1);
562 tzi2=GET_IMAG(cr2,ci1);
563
564 tzr3=GET_REAL(cr1,ci2);
565 tzi3=GET_IMAG(cr1,ci2);
566
567 tzr4=GET_REAL(cr2,ci2);
568 tzi4=GET_IMAG(cr2,ci2);
569
570 trq1=tzr1*tzr1;
571 tiq1=tzi1*tzi1;
572
573 trq2=tzr2*tzr2;
574 tiq2=tzi2*tzi2;
575
576 trq3=tzr3*tzr3;
577 tiq3=tzi3*tzi3;
578
579 trq4=tzr4*tzr4;
580 tiq4=tzi4*tzi4;
581
582 before=iter;
583
584 for(;;)
585 {
586 sr1=zre1; si1=zim1;
587 sr2=zre2; si2=zim2;
588 sr3=zre3; si3=zim3;
589 sr4=zre4; si4=zim4;
590 sr5=zre5; si5=zim5;
591 sr6=zre6; si6=zim6;
592 sr7=zre7; si7=zim7;
593 sr8=zre8; si8=zim8;
594 sr9=zre9; si9=zim9;
595
596
597 #define SOI_ORBIT1(zr,rq,zi,iq,cr,ci,esc) \
598 tempsqrx = rq;\
599 tempsqry = iq;\
600 old.x = zr;\
601 old.y = zi;\
602 floatparm->x = cr;\
603 floatparm->y = ci;\
604 esc = ORBITCALC();\
605 rq = tempsqrx;\
606 iq = tempsqry;\
607 zr = new.x;\
608 zi = new.y
609
610 #define SOI_ORBIT(zr,rq,zi,iq,cr,ci,esc) \
611 zi=(zi+zi)*zr+ci;\
612 zr=rq-iq+cr;\
613 rq=zr*zr;\
614 iq=zi*zi;\
615 esc = ((rq+iq)>16.0)?1:0
616
617 /* iterate key values */
618 SOI_ORBIT(zre1,rq1,zim1,iq1,cre1,cim1,esc1);
619 /*
620 zim1=(zim1+zim1)*zre1+cim1;
621 zre1=rq1-iq1+cre1;
622 rq1=zre1*zre1;
623 iq1=zim1*zim1;
624 */
625 SOI_ORBIT(zre2,rq2,zim2,iq2,cre2,cim1,esc2);
626 /*
627 zim2=(zim2+zim2)*zre2+cim1;
628 zre2=rq2-iq2+cre2;
629 rq2=zre2*zre2;
630 iq2=zim2*zim2;
631 */
632 SOI_ORBIT(zre3,rq3,zim3,iq3,cre1,cim2,esc3);
633 /*
634 zim3=(zim3+zim3)*zre3+cim2;
635 zre3=rq3-iq3+cre1;
636 rq3=zre3*zre3;
637 iq3=zim3*zim3;
638 */
639 SOI_ORBIT(zre4,rq4,zim4,iq4,cre2,cim2,esc4);
640 /*
641 zim4=(zim4+zim4)*zre4+cim2;
642 zre4=rq4-iq4+cre2;
643 rq4=zre4*zre4;
644 iq4=zim4*zim4;
645 */
646 SOI_ORBIT(zre5,rq5,zim5,iq5,midr,cim1,esc5);
647 /*
648 zim5=(zim5+zim5)*zre5+cim1;
649 zre5=rq5-iq5+midr;
650 rq5=zre5*zre5;
651 iq5=zim5*zim5;
652 */
653 SOI_ORBIT(zre6,rq6,zim6,iq6,cre1,midi,esc6);
654 /*
655 zim6=(zim6+zim6)*zre6+midi;
656 zre6=rq6-iq6+cre1;
657 rq6=zre6*zre6;
658 iq6=zim6*zim6;
659 */
660 SOI_ORBIT(zre7,rq7,zim7,iq7,cre2,midi,esc7);
661 /*
662 zim7=(zim7+zim7)*zre7+midi;
663 zre7=rq7-iq7+cre2;
664 rq7=zre7*zre7;
665 iq7=zim7*zim7;
666 */
667 SOI_ORBIT(zre8,rq8,zim8,iq8,midr,cim2,esc8);
668 /*
669 zim8=(zim8+zim8)*zre8+cim2;
670 zre8=rq8-iq8+midr;
671 rq8=zre8*zre8;
672 iq8=zim8*zim8;
673 */
674 SOI_ORBIT(zre9,rq9,zim9,iq9,midr,midi,esc9);
675 /*
676 zim9=(zim9+zim9)*zre9+midi;
677 zre9=rq9-iq9+midr;
678 rq9=zre9*zre9;
679 iq9=zim9*zim9;
680 */
681 /* iterate test point */
682 SOI_ORBIT(tzr1,trq1,tzi1,tiq1,cr1,ci1,tesc1);
683 /*
684 tzi1=(tzi1+tzi1)*tzr1+ci1;
685 tzr1=trq1-tiq1+cr1;
686 trq1=tzr1*tzr1;
687 tiq1=tzi1*tzi1;
688 */
689
690 SOI_ORBIT(tzr2,trq2,tzi2,tiq2,cr2,ci1,tesc2);
691 /*
692 tzi2=(tzi2+tzi2)*tzr2+ci1;
693 tzr2=trq2-tiq2+cr2;
694 trq2=tzr2*tzr2;
695 tiq2=tzi2*tzi2;
696 */
697 SOI_ORBIT(tzr3,trq3,tzi3,tiq3,cr1,ci2,tesc3);
698 /*
699 tzi3=(tzi3+tzi3)*tzr3+ci2;
700 tzr3=trq3-tiq3+cr1;
701 trq3=tzr3*tzr3;
702 tiq3=tzi3*tzi3;
703 */
704 SOI_ORBIT(tzr4,trq4,tzi4,tiq4,cr2,ci2,tesc4);
705 /*
706 tzi4=(tzi4+tzi4)*tzr4+ci2;
707 tzr4=trq4-tiq4+cr2;
708 trq4=tzr4*tzr4;
709 tiq4=tzi4*tzi4;
710 */
711 iter++;
712
713 /* if one of the iterated values bails out, subdivide */
714 /*
715 if((rq1+iq1)>16.0||
716 (rq2+iq2)>16.0||
717 (rq3+iq3)>16.0||
718 (rq4+iq4)>16.0||
719 (rq5+iq5)>16.0||
720 (rq6+iq6)>16.0||
721 (rq7+iq7)>16.0||
722 (rq8+iq8)>16.0||
723 (rq9+iq9)>16.0||
724 (trq1+tiq1)>16.0||
725 (trq2+tiq2)>16.0||
726 (trq3+tiq3)>16.0||
727 (trq4+tiq4)>16.0)
728 break;
729 */
730 if(esc1||esc2||esc3||esc4||esc5||esc6||esc7||esc8||esc9||
731 tesc1||tesc2||tesc3||tesc4)
732 break;
733
734 /* if maximum number of iterations is reached, the whole rectangle
735 can be assumed part of M. This is of course best case behavior
736 of SOI, we seldomly get there */
737 if(iter>maxit)
738 {
739 putbox(x1,y1,x2,y2,0);
740 status = 0;
741 goto rhombus_done;
742 }
743
744 /* now for all test points, check whether they exceed the
745 allowed tolerance. if so, subdivide */
746 l1=GET_REAL(cr1,ci1);
747 l1=(tzr1==0.0)?
748 (l1==0.0)?1.0:1000.0:
749 l1/tzr1;
750 if(FABS(1.0-l1)>twidth)
751 break;
752
753 l2=GET_IMAG(cr1,ci1);
754 l2=(tzi1==0.0)?
755 (l2==0.0)?1.0:1000.0:
756 l2/tzi1;
757 if(FABS(1.0-l2)>twidth)
758 break;
759
760 l1=GET_REAL(cr2,ci1);
761 l1=(tzr2==0.0)?
762 (l1==0.0)?1.0:1000.0:
763 l1/tzr2;
764 if(FABS(1.0-l1)>twidth)
765 break;
766
767 l2=GET_IMAG(cr2,ci1);
768 l2=(tzi2==0.0)?
769 (l2==0.0)?1.0:1000.0:
770 l2/tzi2;
771 if(FABS(1.0-l2)>twidth)
772 break;
773
774 l1=GET_REAL(cr1,ci2);
775 l1=(tzr3==0.0)?
776 (l1==0.0)?1.0:1000.0:
777 l1/tzr3;
778 if(FABS(1.0-l1)>twidth)
779 break;
780
781 l2=GET_IMAG(cr1,ci2);
782 l2=(tzi3==0.0)?
783 (l2==0.0)?1.0:1000.0:
784 l2/tzi3;
785 if(FABS(1.0-l2)>twidth)
786 break;
787
788 l1=GET_REAL(cr2,ci2);
789 l1=(tzr4==0.0)?
790 (l1==0.0)?1.0:1000.0:
791 l1/tzr4;
792 if(FABS(1.0-l1)>twidth)
793 break;
794
795 l2=GET_IMAG(cr2,ci2);
796 l2=(tzi4==0.0)?
797 (l2==0.0)?1.0:1000.0:
798 l2/tzi4;
799 if(FABS(1.0-l2)>twidth)
800 break;
801 }
802
803 iter--;
804
805 /* this is a little heuristic I tried to improve performance. */
806 if(iter-before<10)
807 {
808 zre1=sr1; zim1=si1;
809 zre2=sr2; zim2=si2;
810 zre3=sr3; zim3=si3;
811 zre4=sr4; zim4=si4;
812 zre5=sr5; zim5=si5;
813 zre6=sr6; zim6=si6;
814 zre7=sr7; zim7=si7;
815 zre8=sr8; zim8=si8;
816 zre9=sr9; zim9=si9;
817 goto scan;
818 }
819
820 /* compute key values for subsequent rectangles */
821
822 re10=interpolate(cre1,midr,cre2,sr1,sr5,sr2,cr1);
823 im10=interpolate(cre1,midr,cre2,si1,si5,si2,cr1);
824
825 re11=interpolate(cre1,midr,cre2,sr1,sr5,sr2,cr2);
826 im11=interpolate(cre1,midr,cre2,si1,si5,si2,cr2);
827
828 re20=interpolate(cre1,midr,cre2,sr3,sr8,sr4,cr1);
829 im20=interpolate(cre1,midr,cre2,si3,si8,si4,cr1);
830
831 re21=interpolate(cre1,midr,cre2,sr3,sr8,sr4,cr2);
832 im21=interpolate(cre1,midr,cre2,si3,si8,si4,cr2);
833
834 re15=interpolate(cre1,midr,cre2,sr6,sr9,sr7,cr1);
835 im15=interpolate(cre1,midr,cre2,si6,si9,si7,cr1);
836
837 re16=interpolate(cre1,midr,cre2,sr6,sr9,sr7,cr2);
838 im16=interpolate(cre1,midr,cre2,si6,si9,si7,cr2);
839
840 re12=interpolate(cim1,midi,cim2,sr1,sr6,sr3,ci1);
841 im12=interpolate(cim1,midi,cim2,si1,si6,si3,ci1);
842
843 re14=interpolate(cim1,midi,cim2,sr2,sr7,sr4,ci1);
844 im14=interpolate(cim1,midi,cim2,si2,si7,si4,ci1);
845
846 re17=interpolate(cim1,midi,cim2,sr1,sr6,sr3,ci2);
847 im17=interpolate(cim1,midi,cim2,si1,si6,si3,ci2);
848
849 re19=interpolate(cim1,midi,cim2,sr2,sr7,sr4,ci2);
850 im19=interpolate(cim1,midi,cim2,si2,si7,si4,ci2);
851
852 re13=interpolate(cim1,midi,cim2,sr5,sr9,sr8,ci1);
853 im13=interpolate(cim1,midi,cim2,si5,si9,si8,ci1);
854
855 re18=interpolate(cim1,midi,cim2,sr5,sr9,sr8,ci2);
856 im18=interpolate(cim1,midi,cim2,si5,si9,si8,ci2);
857
858 re91=GET_SAVED_REAL(cr1,ci1);
859 re92=GET_SAVED_REAL(cr2,ci1);
860 re93=GET_SAVED_REAL(cr1,ci2);
861 re94=GET_SAVED_REAL(cr2,ci2);
862
863 im91=GET_SAVED_IMAG(cr1,ci1);
864 im92=GET_SAVED_IMAG(cr2,ci1);
865 im93=GET_SAVED_IMAG(cr1,ci2);
866 im94=GET_SAVED_IMAG(cr2,ci2);
867
868 RHOMBUS(cre1,midr,cim1,midi,x1,((x1+x2)>>1),y1,((y1+y2)>>1),
869 sr1,si1,
870 sr5,si5,
871 sr6,si6,
872 sr9,si9,
873 re10,im10,
874 re12,im12,
875 re13,im13,
876 re15,im15,
877 re91,im91,
878 iter);
879 RHOMBUS(midr,cre2,cim1,midi,(x1+x2)>>1,x2,y1,(y1+y2)>>1,
880 sr5,si5,
881 sr2,si2,
882 sr9,si9,
883 sr7,si7,
884 re11,im11,
885 re13,im13,
886 re14,im14,
887 re16,im16,
888 re92,im92,
889 iter);
890 RHOMBUS(cre1,midr,midi,cim2,x1,(x1+x2)>>1,(y1+y2)>>1,y2,
891 sr6,si6,
892 sr9,si9,
893 sr3,si3,
894 sr8,si8,
895 re15,im15,
896 re17,im17,
897 re18,im18,
898 re20,im20,
899 re93,im93,
900 iter);
901 RHOMBUS(midr,cre2,midi,cim2,(x1+x2)>>1,x2,(y1+y2)>>1,y2,
902 sr9,si9,
903 sr7,si7,
904 sr8,si8,
905 sr4,si4,
906 re16,im16,
907 re18,im18,
908 re19,im19,
909 re21,im21,
910 re94,im94,
911 iter);
912 rhombus_done:
913 rhombus_depth--;
914 return(status);
915 }
916
917 #if (_MSC_VER >= 700)
918 #pragma code_seg ()
919 #endif
920
soi(void)921 void soi(void)
922 {
923 int status;
924 DBLS tolerance=0.1;
925 DBLS stepx, stepy;
926 DBLS xxminl, xxmaxl, yyminl, yymaxl;
927 minstackavail = 30000;
928 rhombus_depth = -1;
929 max_rhombus_depth = 0;
930 if(bf_math)
931 {
932 xxminl = (DBLS)bftofloat(bfxmin);
933 yyminl = (DBLS)bftofloat(bfymin);
934 xxmaxl = (DBLS)bftofloat(bfxmax);
935 yymaxl = (DBLS)bftofloat(bfymax);
936 }
937 else
938 {
939 xxminl = xxmin;
940 yyminl = yymin;
941 xxmaxl = xxmax;
942 yymaxl = yymax;
943 }
944 twidth=tolerance/(xdots-1);
945 stepx = (xxmaxl - xxminl) / xdots;
946 stepy = (yyminl - yymaxl) / ydots;
947 equal = (stepx < stepy ? stepx : stepy);
948
949 RHOMBUS(xxminl,xxmaxl,yymaxl,yyminl,
950 0,xdots,0,ydots,
951 xxminl,yymaxl,
952 xxmaxl,yymaxl,
953 xxminl,yyminl,
954 xxmaxl,yyminl,
955 (xxmaxl+xxminl)/2,yymaxl,
956 xxminl,(yymaxl+yyminl)/2,
957 xxmaxl,(yymaxl+yyminl)/2,
958 (xxmaxl+xxminl)/2,yyminl,
959 (xxminl+xxmaxl)/2,(yymaxl+yyminl)/2,
960 1);
961 }
962