| 1 | /* Copyright (c) 1994 Regents of the University of California */ | 
| 2 |  | 
| 3 | #ifndef lint | 
| 4 | static char SCCSid[] = "$SunId$ LBL"; | 
| 5 | #endif | 
| 6 |  | 
| 7 | /* | 
| 8 | *  raytrace.c - routines for tracing and shading rays. | 
| 9 | * | 
| 10 | *     8/7/85 | 
| 11 | */ | 
| 12 |  | 
| 13 | #include  "ray.h" | 
| 14 |  | 
| 15 | #include  "octree.h" | 
| 16 |  | 
| 17 | #include  "otypes.h" | 
| 18 |  | 
| 19 | #include  "otspecial.h" | 
| 20 |  | 
| 21 | #define  MAXCSET        ((MAXSET+1)*2-1)        /* maximum check set size */ | 
| 22 |  | 
| 23 | extern CUBE  thescene;                  /* our scene */ | 
| 24 | extern int  maxdepth;                   /* maximum recursion depth */ | 
| 25 | extern double  minweight;               /* minimum ray weight */ | 
| 26 | extern int  do_irrad;                   /* compute irradiance? */ | 
| 27 |  | 
| 28 | unsigned long  raynum = 0;              /* next unique ray number */ | 
| 29 | unsigned long  nrays = 0;               /* number of calls to localhit */ | 
| 30 |  | 
| 31 | static FLOAT  Lambfa[5] = {PI, PI, PI, 0.0, 0.0}; | 
| 32 | OBJREC  Lamb = { | 
| 33 | OVOID, MAT_PLASTIC, "Lambertian", | 
| 34 | {0, 5, NULL, Lambfa}, NULL, | 
| 35 | };                                      /* a Lambertian surface */ | 
| 36 |  | 
| 37 | static int  raymove(), checkset(), checkhit(); | 
| 38 |  | 
| 39 | #define  MAXLOOP        128             /* modifier loop detection */ | 
| 40 |  | 
| 41 | #define  RAYHIT         (-1)            /* return value for intercepted ray */ | 
| 42 |  | 
| 43 |  | 
| 44 | rayorigin(r, ro, rt, rw)                /* start new ray from old one */ | 
| 45 | register RAY  *r, *ro; | 
| 46 | int  rt; | 
| 47 | double  rw; | 
| 48 | { | 
| 49 | if ((r->parent = ro) == NULL) {         /* primary ray */ | 
| 50 | r->rlvl = 0; | 
| 51 | r->rweight = rw; | 
| 52 | r->crtype = r->rtype = rt; | 
| 53 | r->rsrc = -1; | 
| 54 | r->clipset = NULL; | 
| 55 | r->revf = raytrace; | 
| 56 | } else {                                /* spawned ray */ | 
| 57 | r->rlvl = ro->rlvl; | 
| 58 | if (rt & RAYREFL) { | 
| 59 | r->rlvl++; | 
| 60 | r->rsrc = -1; | 
| 61 | r->clipset = ro->clipset; | 
| 62 | } else { | 
| 63 | r->rsrc = ro->rsrc; | 
| 64 | r->clipset = ro->newcset; | 
| 65 | } | 
| 66 | r->revf = ro->revf; | 
| 67 | r->rweight = ro->rweight * rw; | 
| 68 | r->crtype = ro->crtype | (r->rtype = rt); | 
| 69 | VCOPY(r->rorg, ro->rop); | 
| 70 | } | 
| 71 | rayclear(r); | 
| 72 | return(r->rlvl <= maxdepth && r->rweight >= minweight ? 0 : -1); | 
| 73 | } | 
| 74 |  | 
| 75 |  | 
| 76 | rayclear(r)                     /* clear a ray for (re)evaluation */ | 
| 77 | register RAY  *r; | 
| 78 | { | 
| 79 | r->rno = raynum++; | 
| 80 | r->newcset = r->clipset; | 
| 81 | r->ro = NULL; | 
| 82 | r->rot = FHUGE; | 
| 83 | r->pert[0] = r->pert[1] = r->pert[2] = 0.0; | 
| 84 | setcolor(r->pcol, 1.0, 1.0, 1.0); | 
| 85 | setcolor(r->rcol, 0.0, 0.0, 0.0); | 
| 86 | r->rt = 0.0; | 
| 87 | } | 
| 88 |  | 
| 89 |  | 
| 90 | raytrace(r)                     /* trace a ray and compute its value */ | 
| 91 | RAY  *r; | 
| 92 | { | 
| 93 | extern int  (*trace)(); | 
| 94 | int  gotmat; | 
| 95 |  | 
| 96 | if (localhit(r, &thescene)) | 
| 97 | gotmat = raycont(r); | 
| 98 | else if (sourcehit(r)) | 
| 99 | gotmat = rayshade(r, r->ro->omod); | 
| 100 |  | 
| 101 | if (!gotmat) | 
| 102 | objerror(r->ro, USER, "material not found"); | 
| 103 |  | 
| 104 | if (trace != NULL) | 
| 105 | (*trace)(r);            /* trace execution */ | 
| 106 | } | 
| 107 |  | 
| 108 |  | 
| 109 | raycont(r)                      /* check for clipped object and continue */ | 
| 110 | register RAY  *r; | 
| 111 | { | 
| 112 | if ((r->clipset != NULL && inset(r->clipset, r->ro->omod)) || | 
| 113 | r->ro->omod == OVOID) { | 
| 114 | raytrans(r); | 
| 115 | return(1); | 
| 116 | } | 
| 117 | return(rayshade(r, r->ro->omod)); | 
| 118 | } | 
| 119 |  | 
| 120 |  | 
| 121 | raytrans(r)                     /* transmit ray as is */ | 
| 122 | register RAY  *r; | 
| 123 | { | 
| 124 | RAY  tr; | 
| 125 |  | 
| 126 | if (rayorigin(&tr, r, TRANS, 1.0) == 0) { | 
| 127 | VCOPY(tr.rdir, r->rdir); | 
| 128 | rayvalue(&tr); | 
| 129 | copycolor(r->rcol, tr.rcol); | 
| 130 | r->rt = r->rot + tr.rt; | 
| 131 | } | 
| 132 | } | 
| 133 |  | 
| 134 |  | 
| 135 | rayshade(r, mod)                /* shade ray r with material mod */ | 
| 136 | register RAY  *r; | 
| 137 | int  mod; | 
| 138 | { | 
| 139 | static int  depth = 0; | 
| 140 | int  gotmat; | 
| 141 | register OBJREC  *m; | 
| 142 | /* check for infinite loop */ | 
| 143 | if (depth++ >= MAXLOOP) | 
| 144 | objerror(r->ro, USER, "possible modifier loop"); | 
| 145 | r->rt = r->rot;                 /* set effective ray length */ | 
| 146 | for (gotmat = 0; !gotmat && mod != OVOID; mod = m->omod) { | 
| 147 | m = objptr(mod); | 
| 148 | /****** unnecessary test since modifier() is always called | 
| 149 | if (!ismodifier(m->otype)) { | 
| 150 | sprintf(errmsg, "illegal modifier \"%s\"", m->oname); | 
| 151 | error(USER, errmsg); | 
| 152 | } | 
| 153 | ******/ | 
| 154 | /* hack for irradiance calculation */ | 
| 155 | if (do_irrad && !(r->crtype & ~(PRIMARY|TRANS))) { | 
| 156 | if (irr_ignore(m->otype)) { | 
| 157 | depth--; | 
| 158 | raytrans(r); | 
| 159 | return; | 
| 160 | } | 
| 161 | if (!islight(m->otype)) | 
| 162 | m = &Lamb; | 
| 163 | } | 
| 164 | /* materials call raytexture */ | 
| 165 | gotmat = (*ofun[m->otype].funp)(m, r); | 
| 166 | } | 
| 167 | depth--; | 
| 168 | return(gotmat); | 
| 169 | } | 
| 170 |  | 
| 171 |  | 
| 172 | raytexture(r, mod)                      /* get material modifiers */ | 
| 173 | RAY  *r; | 
| 174 | int  mod; | 
| 175 | { | 
| 176 | static int  depth = 0; | 
| 177 | register OBJREC  *m; | 
| 178 | /* check for infinite loop */ | 
| 179 | if (depth++ >= MAXLOOP) | 
| 180 | objerror(r->ro, USER, "modifier loop"); | 
| 181 | /* execute textures and patterns */ | 
| 182 | for ( ; mod != OVOID; mod = m->omod) { | 
| 183 | m = objptr(mod); | 
| 184 | /****** unnecessary test since modifier() is always called | 
| 185 | if (!ismodifier(m->otype)) { | 
| 186 | sprintf(errmsg, "illegal modifier \"%s\"", m->oname); | 
| 187 | error(USER, errmsg); | 
| 188 | } | 
| 189 | ******/ | 
| 190 | if ((*ofun[m->otype].funp)(m, r)) | 
| 191 | objerror(r->ro, USER, "conflicting materials"); | 
| 192 | } | 
| 193 | depth--;                        /* end here */ | 
| 194 | } | 
| 195 |  | 
| 196 |  | 
| 197 | raymixture(r, fore, back, coef)         /* mix modifiers */ | 
| 198 | register RAY  *r; | 
| 199 | OBJECT  fore, back; | 
| 200 | double  coef; | 
| 201 | { | 
| 202 | RAY  fr, br; | 
| 203 | COLOR  ctmp; | 
| 204 | int  foremat, backmat; | 
| 205 | register int  i; | 
| 206 | /* clip coefficient */ | 
| 207 | if (coef > 1.0) | 
| 208 | coef = 1.0; | 
| 209 | else if (coef < 0.0) | 
| 210 | coef = 0.0; | 
| 211 | /* foreground */ | 
| 212 | copystruct(&fr, r); | 
| 213 | fr.pert[0] = fr.pert[1] = fr.pert[2] = 0.0; | 
| 214 | setcolor(fr.pcol, 1.0, 1.0, 1.0); | 
| 215 | setcolor(fr.rcol, 0.0, 0.0, 0.0); | 
| 216 | if (fore != OVOID && coef > FTINY) | 
| 217 | foremat = rayshade(&fr, fore); | 
| 218 | else | 
| 219 | foremat = 0; | 
| 220 | /* background */ | 
| 221 | copystruct(&br, r); | 
| 222 | br.pert[0] = br.pert[1] = br.pert[2] = 0.0; | 
| 223 | setcolor(br.pcol, 1.0, 1.0, 1.0); | 
| 224 | setcolor(br.rcol, 0.0, 0.0, 0.0); | 
| 225 | if (back != OVOID && coef < 1.0-FTINY) | 
| 226 | backmat = rayshade(&br, back); | 
| 227 | else | 
| 228 | backmat = foremat; | 
| 229 | /* check */ | 
| 230 | if (backmat != foremat) | 
| 231 | objerror(r->ro, USER, "mixing material with non-material"); | 
| 232 | /* sum perturbations */ | 
| 233 | for (i = 0; i < 3; i++) | 
| 234 | r->pert[i] += coef*fr.pert[i] + (1.0-coef)*br.pert[i]; | 
| 235 | /* multiply pattern colors */ | 
| 236 | scalecolor(fr.pcol, coef); | 
| 237 | scalecolor(br.pcol, 1.0-coef); | 
| 238 | copycolor(ctmp, fr.pcol); | 
| 239 | addcolor(ctmp, br.pcol); | 
| 240 | multcolor(r->pcol, ctmp); | 
| 241 | /* sum returned ray values */ | 
| 242 | scalecolor(fr.rcol, coef); | 
| 243 | scalecolor(br.rcol, 1.0-coef); | 
| 244 | addcolor(r->rcol, fr.rcol); | 
| 245 | addcolor(r->rcol, br.rcol); | 
| 246 | if (foremat) | 
| 247 | r->rt = bright(fr.rcol) > bright(br.rcol) ? fr.rt : br.rt; | 
| 248 | /* return value tells if material */ | 
| 249 | return(foremat); | 
| 250 | } | 
| 251 |  | 
| 252 |  | 
| 253 | double | 
| 254 | raynormal(norm, r)              /* compute perturbed normal for ray */ | 
| 255 | FVECT  norm; | 
| 256 | register RAY  *r; | 
| 257 | { | 
| 258 | double  newdot; | 
| 259 | register int  i; | 
| 260 |  | 
| 261 | /*      The perturbation is added to the surface normal to obtain | 
| 262 | *  the new normal.  If the new normal would affect the surface | 
| 263 | *  orientation wrt. the ray, a correction is made.  The method is | 
| 264 | *  still fraught with problems since reflected rays and similar | 
| 265 | *  directions calculated from the surface normal may spawn rays behind | 
| 266 | *  the surface.  The only solution is to curb textures at high | 
| 267 | *  incidence (namely, keep DOT(rdir,pert) < Rdot). | 
| 268 | */ | 
| 269 |  | 
| 270 | for (i = 0; i < 3; i++) | 
| 271 | norm[i] = r->ron[i] + r->pert[i]; | 
| 272 |  | 
| 273 | if (normalize(norm) == 0.0) { | 
| 274 | objerror(r->ro, WARNING, "illegal normal perturbation"); | 
| 275 | VCOPY(norm, r->ron); | 
| 276 | return(r->rod); | 
| 277 | } | 
| 278 | newdot = -DOT(norm, r->rdir); | 
| 279 | if ((newdot > 0.0) != (r->rod > 0.0)) {         /* fix orientation */ | 
| 280 | for (i = 0; i < 3; i++) | 
| 281 | norm[i] += 2.0*newdot*r->rdir[i]; | 
| 282 | newdot = -newdot; | 
| 283 | } | 
| 284 | return(newdot); | 
| 285 | } | 
| 286 |  | 
| 287 |  | 
| 288 | newrayxf(r)                     /* get new tranformation matrix for ray */ | 
| 289 | RAY  *r; | 
| 290 | { | 
| 291 | static struct xfn { | 
| 292 | struct xfn  *next; | 
| 293 | FULLXF  xf; | 
| 294 | }  xfseed = { &xfseed }, *xflast = &xfseed; | 
| 295 | register struct xfn  *xp; | 
| 296 | register RAY  *rp; | 
| 297 |  | 
| 298 | /* | 
| 299 | * Search for transform in circular list that | 
| 300 | * has no associated ray in the tree. | 
| 301 | */ | 
| 302 | xp = xflast; | 
| 303 | for (rp = r->parent; rp != NULL; rp = rp->parent) | 
| 304 | if (rp->rox == &xp->xf) {               /* xp in use */ | 
| 305 | xp = xp->next;                  /* move to next */ | 
| 306 | if (xp == xflast) {             /* need new one */ | 
| 307 | xp = (struct xfn *)bmalloc(sizeof(struct xfn)); | 
| 308 | if (xp == NULL) | 
| 309 | error(SYSTEM, | 
| 310 | "out of memory in newrayxf"); | 
| 311 | /* insert in list */ | 
| 312 | xp->next = xflast->next; | 
| 313 | xflast->next = xp; | 
| 314 | break;                  /* we're done */ | 
| 315 | } | 
| 316 | rp = r;                 /* start check over */ | 
| 317 | } | 
| 318 | /* got it */ | 
| 319 | r->rox = &xp->xf; | 
| 320 | xflast = xp; | 
| 321 | } | 
| 322 |  | 
| 323 |  | 
| 324 | flipsurface(r)                  /* reverse surface orientation */ | 
| 325 | register RAY  *r; | 
| 326 | { | 
| 327 | r->rod = -r->rod; | 
| 328 | r->ron[0] = -r->ron[0]; | 
| 329 | r->ron[1] = -r->ron[1]; | 
| 330 | r->ron[2] = -r->ron[2]; | 
| 331 | r->pert[0] = -r->pert[0]; | 
| 332 | r->pert[1] = -r->pert[1]; | 
| 333 | r->pert[2] = -r->pert[2]; | 
| 334 | } | 
| 335 |  | 
| 336 |  | 
| 337 | localhit(r, scene)              /* check for hit in the octree */ | 
| 338 | register RAY  *r; | 
| 339 | register CUBE  *scene; | 
| 340 | { | 
| 341 | OBJECT  cxset[MAXCSET+1];       /* set of checked objects */ | 
| 342 | FVECT  curpos;                  /* current cube position */ | 
| 343 | int  sflags;                    /* sign flags */ | 
| 344 | double  t, dt; | 
| 345 | register int  i; | 
| 346 |  | 
| 347 | nrays++;                        /* increment trace counter */ | 
| 348 | sflags = 0; | 
| 349 | for (i = 0; i < 3; i++) { | 
| 350 | curpos[i] = r->rorg[i]; | 
| 351 | if (r->rdir[i] > 1e-7) | 
| 352 | sflags |= 1 << i; | 
| 353 | else if (r->rdir[i] < -1e-7) | 
| 354 | sflags |= 0x10 << i; | 
| 355 | } | 
| 356 | if (sflags == 0) | 
| 357 | error(CONSISTENCY, "zero ray direction in localhit"); | 
| 358 | t = 0.0; | 
| 359 | if (!incube(scene, curpos)) { | 
| 360 | /* find distance to entry */ | 
| 361 | for (i = 0; i < 3; i++) { | 
| 362 | /* plane in our direction */ | 
| 363 | if (sflags & 1<<i) | 
| 364 | dt = scene->cuorg[i]; | 
| 365 | else if (sflags & 0x10<<i) | 
| 366 | dt = scene->cuorg[i] + scene->cusize; | 
| 367 | else | 
| 368 | continue; | 
| 369 | /* distance to the plane */ | 
| 370 | dt = (dt - r->rorg[i])/r->rdir[i]; | 
| 371 | if (dt > t) | 
| 372 | t = dt; /* farthest face is the one */ | 
| 373 | } | 
| 374 | t += FTINY;             /* fudge to get inside cube */ | 
| 375 | /* advance position */ | 
| 376 | for (i = 0; i < 3; i++) | 
| 377 | curpos[i] += r->rdir[i]*t; | 
| 378 |  | 
| 379 | if (!incube(scene, curpos))     /* non-intersecting ray */ | 
| 380 | return(0); | 
| 381 | } | 
| 382 | cxset[0] = 0; | 
| 383 | return(raymove(curpos, cxset, sflags, r, scene) == RAYHIT); | 
| 384 | } | 
| 385 |  | 
| 386 |  | 
| 387 | static int | 
| 388 | raymove(pos, cxs, dirf, r, cu)          /* check for hit as we move */ | 
| 389 | FVECT  pos;                     /* current position, modified herein */ | 
| 390 | OBJECT  *cxs;                   /* checked objects, modified by checkhit */ | 
| 391 | int  dirf;                      /* direction indicators to speed tests */ | 
| 392 | register RAY  *r; | 
| 393 | register CUBE  *cu; | 
| 394 | { | 
| 395 | int  ax; | 
| 396 | double  dt, t; | 
| 397 |  | 
| 398 | if (istree(cu->cutree)) {               /* recurse on subcubes */ | 
| 399 | CUBE  cukid; | 
| 400 | register int  br, sgn; | 
| 401 |  | 
| 402 | cukid.cusize = cu->cusize * 0.5;        /* find subcube */ | 
| 403 | VCOPY(cukid.cuorg, cu->cuorg); | 
| 404 | br = 0; | 
| 405 | if (pos[0] >= cukid.cuorg[0]+cukid.cusize) { | 
| 406 | cukid.cuorg[0] += cukid.cusize; | 
| 407 | br |= 1; | 
| 408 | } | 
| 409 | if (pos[1] >= cukid.cuorg[1]+cukid.cusize) { | 
| 410 | cukid.cuorg[1] += cukid.cusize; | 
| 411 | br |= 2; | 
| 412 | } | 
| 413 | if (pos[2] >= cukid.cuorg[2]+cukid.cusize) { | 
| 414 | cukid.cuorg[2] += cukid.cusize; | 
| 415 | br |= 4; | 
| 416 | } | 
| 417 | for ( ; ; ) { | 
| 418 | cukid.cutree = octkid(cu->cutree, br); | 
| 419 | if ((ax = raymove(pos,cxs,dirf,r,&cukid)) == RAYHIT) | 
| 420 | return(RAYHIT); | 
| 421 | sgn = 1 << ax; | 
| 422 | if (sgn & dirf)                 /* positive axis? */ | 
| 423 | if (sgn & br) | 
| 424 | return(ax);     /* overflow */ | 
| 425 | else { | 
| 426 | cukid.cuorg[ax] += cukid.cusize; | 
| 427 | br |= sgn; | 
| 428 | } | 
| 429 | else | 
| 430 | if (sgn & br) { | 
| 431 | cukid.cuorg[ax] -= cukid.cusize; | 
| 432 | br &= ~sgn; | 
| 433 | } else | 
| 434 | return(ax);     /* underflow */ | 
| 435 | } | 
| 436 | /*NOTREACHED*/ | 
| 437 | } | 
| 438 | if (isfull(cu->cutree) && checkhit(r, cu, cxs)) | 
| 439 | return(RAYHIT); | 
| 440 | /* advance to next cube */ | 
| 441 | if (dirf&0x11) { | 
| 442 | dt = dirf&1 ? cu->cuorg[0] + cu->cusize : cu->cuorg[0]; | 
| 443 | t = (dt - pos[0])/r->rdir[0]; | 
| 444 | ax = 0; | 
| 445 | } else | 
| 446 | t = FHUGE; | 
| 447 | if (dirf&0x22) { | 
| 448 | dt = dirf&2 ? cu->cuorg[1] + cu->cusize : cu->cuorg[1]; | 
| 449 | dt = (dt - pos[1])/r->rdir[1]; | 
| 450 | if (dt < t) { | 
| 451 | t = dt; | 
| 452 | ax = 1; | 
| 453 | } | 
| 454 | } | 
| 455 | if (dirf&0x44) { | 
| 456 | dt = dirf&4 ? cu->cuorg[2] + cu->cusize : cu->cuorg[2]; | 
| 457 | dt = (dt - pos[2])/r->rdir[2]; | 
| 458 | if (dt < t) { | 
| 459 | t = dt; | 
| 460 | ax = 2; | 
| 461 | } | 
| 462 | } | 
| 463 | pos[0] += r->rdir[0]*t; | 
| 464 | pos[1] += r->rdir[1]*t; | 
| 465 | pos[2] += r->rdir[2]*t; | 
| 466 | return(ax); | 
| 467 | } | 
| 468 |  | 
| 469 |  | 
| 470 | static | 
| 471 | checkhit(r, cu, cxs)            /* check for hit in full cube */ | 
| 472 | register RAY  *r; | 
| 473 | CUBE  *cu; | 
| 474 | OBJECT  *cxs; | 
| 475 | { | 
| 476 | OBJECT  oset[MAXSET+1]; | 
| 477 | register OBJREC  *o; | 
| 478 | register int  i; | 
| 479 |  | 
| 480 | objset(oset, cu->cutree); | 
| 481 | checkset(oset, cxs);                    /* eliminate double-checking */ | 
| 482 | for (i = oset[0]; i > 0; i--) { | 
| 483 | o = objptr(oset[i]); | 
| 484 | (*ofun[o->otype].funp)(o, r); | 
| 485 | } | 
| 486 | if (r->ro == NULL) | 
| 487 | return(0);                      /* no scores yet */ | 
| 488 |  | 
| 489 | return(incube(cu, r->rop));             /* hit OK if in current cube */ | 
| 490 | } | 
| 491 |  | 
| 492 |  | 
| 493 | static | 
| 494 | checkset(os, cs)                /* modify checked set and set to check */ | 
| 495 | register OBJECT  *os;                   /* os' = os - cs */ | 
| 496 | register OBJECT  *cs;                   /* cs' = cs + os */ | 
| 497 | { | 
| 498 | OBJECT  cset[MAXCSET+MAXSET+1]; | 
| 499 | register int  i, j; | 
| 500 | int  k; | 
| 501 | /* copy os in place, cset <- cs */ | 
| 502 | cset[0] = 0; | 
| 503 | k = 0; | 
| 504 | for (i = j = 1; i <= os[0]; i++) { | 
| 505 | while (j <= cs[0] && cs[j] < os[i]) | 
| 506 | cset[++cset[0]] = cs[j++]; | 
| 507 | if (j > cs[0] || os[i] != cs[j]) {      /* object to check */ | 
| 508 | os[++k] = os[i]; | 
| 509 | cset[++cset[0]] = os[i]; | 
| 510 | } | 
| 511 | } | 
| 512 | if (!(os[0] = k))               /* new "to check" set size */ | 
| 513 | return;                 /* special case */ | 
| 514 | while (j <= cs[0])              /* get the rest of cs */ | 
| 515 | cset[++cset[0]] = cs[j++]; | 
| 516 | if (cset[0] > MAXCSET)          /* truncate "checked" set if nec. */ | 
| 517 | cset[0] = MAXCSET; | 
| 518 | /* setcopy(cs, cset); */        /* copy cset back to cs */ | 
| 519 | os = cset; | 
| 520 | for (i = os[0]; i-- >= 0; ) | 
| 521 | *cs++ = *os++; | 
| 522 | } |