Bug Summary

File:root/firefox-clang/gfx/cairo/cairo/src/cairo-polygon-reduce.c
Warning:line 955, column 1
1st function call argument is an uninitialized value

Annotated Source Code

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clang -cc1 -cc1 -triple x86_64-pc-linux-gnu -analyze -disable-free -clear-ast-before-backend -disable-llvm-verifier -discard-value-names -main-file-name cairo-polygon-reduce.c -analyzer-checker=core -analyzer-checker=apiModeling -analyzer-checker=unix -analyzer-checker=deadcode -analyzer-checker=security.insecureAPI.UncheckedReturn -analyzer-checker=security.insecureAPI.getpw -analyzer-checker=security.insecureAPI.gets -analyzer-checker=security.insecureAPI.mktemp -analyzer-checker=security.insecureAPI.mkstemp -analyzer-checker=security.insecureAPI.vfork -analyzer-checker=nullability.NullPassedToNonnull -analyzer-checker=nullability.NullReturnedFromNonnull -analyzer-output plist -w -setup-static-analyzer -analyzer-config-compatibility-mode=true -mrelocation-model pic -pic-level 2 -fhalf-no-semantic-interposition -mframe-pointer=all -relaxed-aliasing -ffp-contract=off -fno-rounding-math -mconstructor-aliases -funwind-tables=2 -target-cpu x86-64 -tune-cpu generic -debugger-tuning=gdb -fdebug-compilation-dir=/root/firefox-clang/obj-x86_64-pc-linux-gnu/gfx/cairo/cairo/src -fcoverage-compilation-dir=/root/firefox-clang/obj-x86_64-pc-linux-gnu/gfx/cairo/cairo/src -resource-dir /usr/lib/llvm-21/lib/clang/21 -include /root/firefox-clang/config/gcc_hidden.h -include /root/firefox-clang/obj-x86_64-pc-linux-gnu/mozilla-config.h -I /root/firefox-clang/obj-x86_64-pc-linux-gnu/dist/system_wrappers -U _FORTIFY_SOURCE -D _FORTIFY_SOURCE=2 -D _GLIBCXX_ASSERTIONS -D DEBUG=1 -D HAVE_FT_LOAD_SFNT_TABLE -D PACKAGE_VERSION="moz" -D PACKAGE_BUGREPORT="http://bugzilla.mozilla.org/" -D CAIRO_HAS_PTHREAD -D _GNU_SOURCE -D MOZ_TREE_PIXMAN -D SIZEOF_VOID_P=__SIZEOF_POINTER__ -D SIZEOF_INT=__SIZEOF_INT__ -D SIZEOF_LONG=__SIZEOF_LONG__ -D SIZEOF_LONG_LONG=__SIZEOF_LONG_LONG__ -D HAVE_UINT64_T -D HAVE_CXX11_ATOMIC_PRIMITIVES -D MOZ_HAS_MOZGLUE -D MOZILLA_INTERNAL_API -D IMPL_LIBXUL -D MOZ_SUPPORT_LEAKCHECKING -D STATIC_EXPORTABLE_JS_API -I /root/firefox-clang/gfx/cairo/cairo/src -I /root/firefox-clang/obj-x86_64-pc-linux-gnu/gfx/cairo/cairo/src -I /root/firefox-clang/obj-x86_64-pc-linux-gnu/dist/include -I /root/firefox-clang/obj-x86_64-pc-linux-gnu/dist/include/nspr -I /root/firefox-clang/obj-x86_64-pc-linux-gnu/dist/include/nss -D MOZILLA_CLIENT -I /usr/include/freetype2 -I /usr/include/libpng16 -I /usr/include/freetype2 -I /usr/include/libpng16 -internal-isystem /usr/lib/llvm-21/lib/clang/21/include -internal-isystem /usr/local/include -internal-isystem /usr/lib/gcc/x86_64-linux-gnu/14/../../../../x86_64-linux-gnu/include -internal-externc-isystem /usr/include/x86_64-linux-gnu -internal-externc-isystem /include -internal-externc-isystem /usr/include -O2 -Wno-error=tautological-type-limit-compare -Wno-range-loop-analysis -Wno-error=deprecated-declarations -Wno-error=array-bounds -Wno-error=free-nonheap-object -Wno-error=atomic-alignment -Wno-error=deprecated-builtins -Wno-psabi -Wno-error=builtin-macro-redefined -Wno-unknown-warning-option -Wno-enum-compare -Wno-int-to-pointer-cast -Wno-int-conversion -Wno-incompatible-pointer-types -Wno-sign-compare -Wno-type-limits -Wno-missing-field-initializers -Wno-conversion -Wno-narrowing -Wno-switch -Wno-unused -Wno-unused-variable -Wno-error=uninitialized -Wno-absolute-value -Wno-deprecated-register -Wno-incompatible-pointer-types -Wno-macro-redefined -Wno-shift-negative-value -Wno-tautological-compare -Wno-tautological-constant-out-of-range-compare -Wno-unreachable-code -ferror-limit 19 -fstrict-flex-arrays=1 -stack-protector 2 -fstack-clash-protection -ftrivial-auto-var-init=pattern -fgnuc-version=4.2.1 -fskip-odr-check-in-gmf -vectorize-loops -vectorize-slp -analyzer-checker optin.performance.Padding -analyzer-output=html -analyzer-config stable-report-filename=true -faddrsig -D__GCC_HAVE_DWARF2_CFI_ASM=1 -o /tmp/scan-build-2025-06-30-093548-1913035-1 -x c /root/firefox-clang/gfx/cairo/cairo/src/cairo-polygon-reduce.c
1/*
2 * Copyright © 2004 Carl Worth
3 * Copyright © 2006 Red Hat, Inc.
4 * Copyright © 2008 Chris Wilson
5 *
6 * This library is free software; you can redistribute it and/or
7 * modify it either under the terms of the GNU Lesser General Public
8 * License version 2.1 as published by the Free Software Foundation
9 * (the "LGPL") or, at your option, under the terms of the Mozilla
10 * Public License Version 1.1 (the "MPL"). If you do not alter this
11 * notice, a recipient may use your version of this file under either
12 * the MPL or the LGPL.
13 *
14 * You should have received a copy of the LGPL along with this library
15 * in the file COPYING-LGPL-2.1; if not, write to the Free Software
16 * Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA
17 * You should have received a copy of the MPL along with this library
18 * in the file COPYING-MPL-1.1
19 *
20 * The contents of this file are subject to the Mozilla Public License
21 * Version 1.1 (the "License"); you may not use this file except in
22 * compliance with the License. You may obtain a copy of the License at
23 * http://www.mozilla.org/MPL/
24 *
25 * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
26 * OF ANY KIND, either express or implied. See the LGPL or the MPL for
27 * the specific language governing rights and limitations.
28 *
29 * The Original Code is the cairo graphics library.
30 *
31 * The Initial Developer of the Original Code is Carl Worth
32 *
33 * Contributor(s):
34 * Carl D. Worth <cworth@cworth.org>
35 * Chris Wilson <chris@chris-wilson.co.uk>
36 */
37
38/* Provide definitions for standalone compilation */
39#include "cairoint.h"
40
41#include "cairo-error-private.h"
42#include "cairo-freelist-private.h"
43#include "cairo-combsort-inline.h"
44
45#define DEBUG_POLYGON0 0
46
47typedef cairo_point_t cairo_bo_point32_t;
48
49typedef struct _cairo_bo_intersect_ordinate {
50 int32_t ordinate;
51 enum { EXACT, INEXACT } exactness;
52} cairo_bo_intersect_ordinate_t;
53
54typedef struct _cairo_bo_intersect_point {
55 cairo_bo_intersect_ordinate_t x;
56 cairo_bo_intersect_ordinate_t y;
57} cairo_bo_intersect_point_t;
58
59typedef struct _cairo_bo_edge cairo_bo_edge_t;
60
61typedef struct _cairo_bo_deferred {
62 cairo_bo_edge_t *right;
63 int32_t top;
64} cairo_bo_deferred_t;
65
66struct _cairo_bo_edge {
67 cairo_edge_t edge;
68 cairo_bo_edge_t *prev;
69 cairo_bo_edge_t *next;
70 cairo_bo_deferred_t deferred;
71};
72
73/* the parent is always given by index/2 */
74#define PQ_PARENT_INDEX(i)((i) >> 1) ((i) >> 1)
75#define PQ_FIRST_ENTRY1 1
76
77/* left and right children are index * 2 and (index * 2) +1 respectively */
78#define PQ_LEFT_CHILD_INDEX(i)((i) << 1) ((i) << 1)
79
80typedef enum {
81 CAIRO_BO_EVENT_TYPE_STOP,
82 CAIRO_BO_EVENT_TYPE_INTERSECTION,
83 CAIRO_BO_EVENT_TYPE_START
84} cairo_bo_event_type_t;
85
86typedef struct _cairo_bo_event {
87 cairo_bo_event_type_t type;
88 cairo_point_t point;
89} cairo_bo_event_t;
90
91typedef struct _cairo_bo_start_event {
92 cairo_bo_event_type_t type;
93 cairo_point_t point;
94 cairo_bo_edge_t edge;
95} cairo_bo_start_event_t;
96
97typedef struct _cairo_bo_queue_event {
98 cairo_bo_event_type_t type;
99 cairo_point_t point;
100 cairo_bo_edge_t *e1;
101 cairo_bo_edge_t *e2;
102} cairo_bo_queue_event_t;
103
104typedef struct _pqueue {
105 int size, max_size;
106
107 cairo_bo_event_t **elements;
108 cairo_bo_event_t *elements_embedded[1024];
109} pqueue_t;
110
111typedef struct _cairo_bo_event_queue {
112 cairo_freepool_t pool;
113 pqueue_t pqueue;
114 cairo_bo_event_t **start_events;
115} cairo_bo_event_queue_t;
116
117typedef struct _cairo_bo_sweep_line {
118 cairo_bo_edge_t *head;
119 int32_t current_y;
120 cairo_bo_edge_t *current_edge;
121} cairo_bo_sweep_line_t;
122
123static cairo_fixed_t
124_line_compute_intersection_x_for_y (const cairo_line_t *line,
125 cairo_fixed_t y)
126{
127 cairo_fixed_t x, dy;
128
129 if (y == line->p1.y)
130 return line->p1.x;
131 if (y == line->p2.y)
132 return line->p2.x;
133
134 x = line->p1.x;
135 dy = line->p2.y - line->p1.y;
136 if (dy != 0) {
137 x += _cairo_fixed_mul_div_floor (y - line->p1.y,
138 line->p2.x - line->p1.x,
139 dy);
140 }
141
142 return x;
143}
144
145static inline int
146_cairo_bo_point32_compare (cairo_bo_point32_t const *a,
147 cairo_bo_point32_t const *b)
148{
149 int cmp;
150
151 cmp = a->y - b->y;
152 if (cmp)
153 return cmp;
154
155 return a->x - b->x;
156}
157
158/* Compare the slope of a to the slope of b, returning 1, 0, -1 if the
159 * slope a is respectively greater than, equal to, or less than the
160 * slope of b.
161 *
162 * For each edge, consider the direction vector formed from:
163 *
164 * top -> bottom
165 *
166 * which is:
167 *
168 * (dx, dy) = (line.p2.x - line.p1.x, line.p2.y - line.p1.y)
169 *
170 * We then define the slope of each edge as dx/dy, (which is the
171 * inverse of the slope typically used in math instruction). We never
172 * compute a slope directly as the value approaches infinity, but we
173 * can derive a slope comparison without division as follows, (where
174 * the ? represents our compare operator).
175 *
176 * 1. slope(a) ? slope(b)
177 * 2. adx/ady ? bdx/bdy
178 * 3. (adx * bdy) ? (bdx * ady)
179 *
180 * Note that from step 2 to step 3 there is no change needed in the
181 * sign of the result since both ady and bdy are guaranteed to be
182 * greater than or equal to 0.
183 *
184 * When using this slope comparison to sort edges, some care is needed
185 * when interpreting the results. Since the slope compare operates on
186 * distance vectors from top to bottom it gives a correct left to
187 * right sort for edges that have a common top point, (such as two
188 * edges with start events at the same location). On the other hand,
189 * the sense of the result will be exactly reversed for two edges that
190 * have a common stop point.
191 */
192static inline int
193_slope_compare (const cairo_bo_edge_t *a,
194 const cairo_bo_edge_t *b)
195{
196 /* XXX: We're assuming here that dx and dy will still fit in 32
197 * bits. That's not true in general as there could be overflow. We
198 * should prevent that before the tessellation algorithm
199 * begins.
200 */
201 int32_t adx = a->edge.line.p2.x - a->edge.line.p1.x;
202 int32_t bdx = b->edge.line.p2.x - b->edge.line.p1.x;
203
204 /* Since the dy's are all positive by construction we can fast
205 * path several common cases.
206 */
207
208 /* First check for vertical lines. */
209 if (adx == 0)
210 return -bdx;
211 if (bdx == 0)
212 return adx;
213
214 /* Then where the two edges point in different directions wrt x. */
215 if ((adx ^ bdx) < 0)
216 return adx;
217
218 /* Finally we actually need to do the general comparison. */
219 {
220 int32_t ady = a->edge.line.p2.y - a->edge.line.p1.y;
221 int32_t bdy = b->edge.line.p2.y - b->edge.line.p1.y;
222 cairo_int64_t adx_bdy = _cairo_int32x32_64_mul (adx, bdy)((int64_t) (adx) * (bdy));
223 cairo_int64_t bdx_ady = _cairo_int32x32_64_mul (bdx, ady)((int64_t) (bdx) * (ady));
224
225 return _cairo_int64_cmp (adx_bdy, bdx_ady)((adx_bdy) == (bdx_ady) ? 0 : (adx_bdy) < (bdx_ady) ? -1 :
1);
226 }
227}
228
229/*
230 * We need to compare the x-coordinates of a pair of lines for a particular y,
231 * without loss of precision.
232 *
233 * The x-coordinate along an edge for a given y is:
234 * X = A_x + (Y - A_y) * A_dx / A_dy
235 *
236 * So the inequality we wish to test is:
237 * A_x + (Y - A_y) * A_dx / A_dy ∘ B_x + (Y - B_y) * B_dx / B_dy,
238 * where ∘ is our inequality operator.
239 *
240 * By construction, we know that A_dy and B_dy (and (Y - A_y), (Y - B_y)) are
241 * all positive, so we can rearrange it thus without causing a sign change:
242 * A_dy * B_dy * (A_x - B_x) ∘ (Y - B_y) * B_dx * A_dy
243 * - (Y - A_y) * A_dx * B_dy
244 *
245 * Given the assumption that all the deltas fit within 32 bits, we can compute
246 * this comparison directly using 128 bit arithmetic. For certain, but common,
247 * input we can reduce this down to a single 32 bit compare by inspecting the
248 * deltas.
249 *
250 * (And put the burden of the work on developing fast 128 bit ops, which are
251 * required throughout the tessellator.)
252 *
253 * See the similar discussion for _slope_compare().
254 */
255static int
256edges_compare_x_for_y_general (const cairo_bo_edge_t *a,
257 const cairo_bo_edge_t *b,
258 int32_t y)
259{
260 /* XXX: We're assuming here that dx and dy will still fit in 32
261 * bits. That's not true in general as there could be overflow. We
262 * should prevent that before the tessellation algorithm
263 * begins.
264 */
265 int32_t dx;
266 int32_t adx, ady;
267 int32_t bdx, bdy;
268 enum {
269 HAVE_NONE = 0x0,
270 HAVE_DX = 0x1,
271 HAVE_ADX = 0x2,
272 HAVE_DX_ADX = HAVE_DX | HAVE_ADX,
273 HAVE_BDX = 0x4,
274 HAVE_DX_BDX = HAVE_DX | HAVE_BDX,
275 HAVE_ADX_BDX = HAVE_ADX | HAVE_BDX,
276 HAVE_ALL = HAVE_DX | HAVE_ADX | HAVE_BDX
277 } have_dx_adx_bdx = HAVE_ALL;
278
279 /* don't bother solving for abscissa if the edges' bounding boxes
280 * can be used to order them. */
281 {
282 int32_t amin, amax;
283 int32_t bmin, bmax;
284 if (a->edge.line.p1.x < a->edge.line.p2.x) {
285 amin = a->edge.line.p1.x;
286 amax = a->edge.line.p2.x;
287 } else {
288 amin = a->edge.line.p2.x;
289 amax = a->edge.line.p1.x;
290 }
291 if (b->edge.line.p1.x < b->edge.line.p2.x) {
292 bmin = b->edge.line.p1.x;
293 bmax = b->edge.line.p2.x;
294 } else {
295 bmin = b->edge.line.p2.x;
296 bmax = b->edge.line.p1.x;
297 }
298 if (amax < bmin) return -1;
299 if (amin > bmax) return +1;
300 }
301
302 ady = a->edge.line.p2.y - a->edge.line.p1.y;
303 adx = a->edge.line.p2.x - a->edge.line.p1.x;
304 if (adx == 0)
305 have_dx_adx_bdx &= ~HAVE_ADX;
306
307 bdy = b->edge.line.p2.y - b->edge.line.p1.y;
308 bdx = b->edge.line.p2.x - b->edge.line.p1.x;
309 if (bdx == 0)
310 have_dx_adx_bdx &= ~HAVE_BDX;
311
312 dx = a->edge.line.p1.x - b->edge.line.p1.x;
313 if (dx == 0)
314 have_dx_adx_bdx &= ~HAVE_DX;
315
316#define L _cairo_int64x32_128_mul (_cairo_int32x32_64_mul (ady, bdy), dx)_cairo_int64x64_128_mul(((int64_t) (ady) * (bdy)), ((int64_t)
(dx)))
317#define A _cairo_int64x32_128_mul (_cairo_int32x32_64_mul (adx, bdy), y - a->edge.line.p1.y)_cairo_int64x64_128_mul(((int64_t) (adx) * (bdy)), ((int64_t)
(y - a->edge.line.p1.y)))
318#define B _cairo_int64x32_128_mul (_cairo_int32x32_64_mul (bdx, ady), y - b->edge.line.p1.y)_cairo_int64x64_128_mul(((int64_t) (bdx) * (ady)), ((int64_t)
(y - b->edge.line.p1.y)))
319 switch (have_dx_adx_bdx) {
320 default:
321 case HAVE_NONE:
322 return 0;
323 case HAVE_DX:
324 /* A_dy * B_dy * (A_x - B_x) ∘ 0 */
325 return dx; /* ady * bdy is positive definite */
326 case HAVE_ADX:
327 /* 0 ∘ - (Y - A_y) * A_dx * B_dy */
328 return adx; /* bdy * (y - a->top.y) is positive definite */
329 case HAVE_BDX:
330 /* 0 ∘ (Y - B_y) * B_dx * A_dy */
331 return -bdx; /* ady * (y - b->top.y) is positive definite */
332 case HAVE_ADX_BDX:
333 /* 0 ∘ (Y - B_y) * B_dx * A_dy - (Y - A_y) * A_dx * B_dy */
334 if ((adx ^ bdx) < 0) {
335 return adx;
336 } else if (a->edge.line.p1.y == b->edge.line.p1.y) { /* common origin */
337 cairo_int64_t adx_bdy, bdx_ady;
338
339 /* ∴ A_dx * B_dy ∘ B_dx * A_dy */
340
341 adx_bdy = _cairo_int32x32_64_mul (adx, bdy)((int64_t) (adx) * (bdy));
342 bdx_ady = _cairo_int32x32_64_mul (bdx, ady)((int64_t) (bdx) * (ady));
343
344 return _cairo_int64_cmp (adx_bdy, bdx_ady)((adx_bdy) == (bdx_ady) ? 0 : (adx_bdy) < (bdx_ady) ? -1 :
1);
345 } else
346 return _cairo_int128_cmp (A, B);
347 case HAVE_DX_ADX:
348 /* A_dy * (A_x - B_x) ∘ - (Y - A_y) * A_dx */
349 if ((-adx ^ dx) < 0) {
350 return dx;
351 } else {
352 cairo_int64_t ady_dx, dy_adx;
353
354 ady_dx = _cairo_int32x32_64_mul (ady, dx)((int64_t) (ady) * (dx));
355 dy_adx = _cairo_int32x32_64_mul (a->edge.line.p1.y - y, adx)((int64_t) (a->edge.line.p1.y - y) * (adx));
356
357 return _cairo_int64_cmp (ady_dx, dy_adx)((ady_dx) == (dy_adx) ? 0 : (ady_dx) < (dy_adx) ? -1 : 1);
358 }
359 case HAVE_DX_BDX:
360 /* B_dy * (A_x - B_x) ∘ (Y - B_y) * B_dx */
361 if ((bdx ^ dx) < 0) {
362 return dx;
363 } else {
364 cairo_int64_t bdy_dx, dy_bdx;
365
366 bdy_dx = _cairo_int32x32_64_mul (bdy, dx)((int64_t) (bdy) * (dx));
367 dy_bdx = _cairo_int32x32_64_mul (y - b->edge.line.p1.y, bdx)((int64_t) (y - b->edge.line.p1.y) * (bdx));
368
369 return _cairo_int64_cmp (bdy_dx, dy_bdx)((bdy_dx) == (dy_bdx) ? 0 : (bdy_dx) < (dy_bdx) ? -1 : 1);
370 }
371 case HAVE_ALL:
372 /* XXX try comparing (a->edge.line.p2.x - b->edge.line.p2.x) et al */
373 return _cairo_int128_cmp (L, _cairo_int128_sub (B, A)_cairo_uint128_sub(B,A));
374 }
375#undef B
376#undef A
377#undef L
378}
379
380/*
381 * We need to compare the x-coordinate of a line for a particular y wrt to a
382 * given x, without loss of precision.
383 *
384 * The x-coordinate along an edge for a given y is:
385 * X = A_x + (Y - A_y) * A_dx / A_dy
386 *
387 * So the inequality we wish to test is:
388 * A_x + (Y - A_y) * A_dx / A_dy ∘ X
389 * where ∘ is our inequality operator.
390 *
391 * By construction, we know that A_dy (and (Y - A_y)) are
392 * all positive, so we can rearrange it thus without causing a sign change:
393 * (Y - A_y) * A_dx ∘ (X - A_x) * A_dy
394 *
395 * Given the assumption that all the deltas fit within 32 bits, we can compute
396 * this comparison directly using 64 bit arithmetic.
397 *
398 * See the similar discussion for _slope_compare() and
399 * edges_compare_x_for_y_general().
400 */
401static int
402edge_compare_for_y_against_x (const cairo_bo_edge_t *a,
403 int32_t y,
404 int32_t x)
405{
406 int32_t adx, ady;
407 int32_t dx, dy;
408 cairo_int64_t L, R;
409
410 if (x < a->edge.line.p1.x && x < a->edge.line.p2.x)
411 return 1;
412 if (x > a->edge.line.p1.x && x > a->edge.line.p2.x)
413 return -1;
414
415 adx = a->edge.line.p2.x - a->edge.line.p1.x;
416 dx = x - a->edge.line.p1.x;
417
418 if (adx == 0)
419 return -dx;
420 if (dx == 0 || (adx ^ dx) < 0)
421 return adx;
422
423 dy = y - a->edge.line.p1.y;
424 ady = a->edge.line.p2.y - a->edge.line.p1.y;
425
426 L = _cairo_int32x32_64_mul (dy, adx)((int64_t) (dy) * (adx));
427 R = _cairo_int32x32_64_mul (dx, ady)((int64_t) (dx) * (ady));
428
429 return _cairo_int64_cmp (L, R)((L) == (R) ? 0 : (L) < (R) ? -1 : 1);
430}
431
432static int
433edges_compare_x_for_y (const cairo_bo_edge_t *a,
434 const cairo_bo_edge_t *b,
435 int32_t y)
436{
437 /* If the sweep-line is currently on an end-point of a line,
438 * then we know its precise x value (and considering that we often need to
439 * compare events at end-points, this happens frequently enough to warrant
440 * special casing).
441 */
442 enum {
443 HAVE_NEITHER = 0x0,
444 HAVE_AX = 0x1,
445 HAVE_BX = 0x2,
446 HAVE_BOTH = HAVE_AX | HAVE_BX
447 } have_ax_bx = HAVE_BOTH;
448 int32_t ax = 0, bx = 0;
449
450 if (y == a->edge.line.p1.y)
451 ax = a->edge.line.p1.x;
452 else if (y == a->edge.line.p2.y)
453 ax = a->edge.line.p2.x;
454 else
455 have_ax_bx &= ~HAVE_AX;
456
457 if (y == b->edge.line.p1.y)
458 bx = b->edge.line.p1.x;
459 else if (y == b->edge.line.p2.y)
460 bx = b->edge.line.p2.x;
461 else
462 have_ax_bx &= ~HAVE_BX;
463
464 switch (have_ax_bx) {
465 default:
466 case HAVE_NEITHER:
467 return edges_compare_x_for_y_general (a, b, y);
468 case HAVE_AX:
469 return -edge_compare_for_y_against_x (b, y, ax);
470 case HAVE_BX:
471 return edge_compare_for_y_against_x (a, y, bx);
472 case HAVE_BOTH:
473 return ax - bx;
474 }
475}
476
477static inline int
478_line_equal (const cairo_line_t *a, const cairo_line_t *b)
479{
480 return (a->p1.x == b->p1.x && a->p1.y == b->p1.y &&
481 a->p2.x == b->p2.x && a->p2.y == b->p2.y);
482}
483
484static int
485_cairo_bo_sweep_line_compare_edges (cairo_bo_sweep_line_t *sweep_line,
486 const cairo_bo_edge_t *a,
487 const cairo_bo_edge_t *b)
488{
489 int cmp;
490
491 /* compare the edges if not identical */
492 if (! _line_equal (&a->edge.line, &b->edge.line)) {
493 cmp = edges_compare_x_for_y (a, b, sweep_line->current_y);
494 if (cmp)
495 return cmp;
496
497 /* The two edges intersect exactly at y, so fall back on slope
498 * comparison. We know that this compare_edges function will be
499 * called only when starting a new edge, (not when stopping an
500 * edge), so we don't have to worry about conditionally inverting
501 * the sense of _slope_compare. */
502 cmp = _slope_compare (a, b);
503 if (cmp)
504 return cmp;
505 }
506
507 /* We've got two collinear edges now. */
508 return b->edge.bottom - a->edge.bottom;
509}
510
511static inline cairo_int64_t
512det32_64 (int32_t a, int32_t b,
513 int32_t c, int32_t d)
514{
515 /* det = a * d - b * c */
516 return _cairo_int64_sub (_cairo_int32x32_64_mul (a, d),((((int64_t) (a) * (d))) - (((int64_t) (b) * (c))))
517 _cairo_int32x32_64_mul (b, c))((((int64_t) (a) * (d))) - (((int64_t) (b) * (c))));
518}
519
520static inline cairo_int128_t
521det64x32_128 (cairo_int64_t a, int32_t b,
522 cairo_int64_t c, int32_t d)
523{
524 /* det = a * d - b * c */
525 return _cairo_int128_sub (_cairo_int64x32_128_mul (a, d),_cairo_uint128_sub(_cairo_int64x64_128_mul(a, ((int64_t) (d))
),_cairo_int64x64_128_mul(c, ((int64_t) (b))))
526 _cairo_int64x32_128_mul (c, b))_cairo_uint128_sub(_cairo_int64x64_128_mul(a, ((int64_t) (d))
),_cairo_int64x64_128_mul(c, ((int64_t) (b))));
527}
528
529/* Compute the intersection of two lines as defined by two edges. The
530 * result is provided as a coordinate pair of 128-bit integers.
531 *
532 * Returns %CAIRO_BO_STATUS_INTERSECTION if there is an intersection or
533 * %CAIRO_BO_STATUS_PARALLEL if the two lines are exactly parallel.
534 */
535static cairo_bool_t
536intersect_lines (cairo_bo_edge_t *a,
537 cairo_bo_edge_t *b,
538 cairo_bo_intersect_point_t *intersection)
539{
540 cairo_int64_t a_det, b_det;
541
542 /* XXX: We're assuming here that dx and dy will still fit in 32
543 * bits. That's not true in general as there could be overflow. We
544 * should prevent that before the tessellation algorithm begins.
545 * What we're doing to mitigate this is to perform clamping in
546 * cairo_bo_tessellate_polygon().
547 */
548 int32_t dx1 = a->edge.line.p1.x - a->edge.line.p2.x;
549 int32_t dy1 = a->edge.line.p1.y - a->edge.line.p2.y;
550
551 int32_t dx2 = b->edge.line.p1.x - b->edge.line.p2.x;
552 int32_t dy2 = b->edge.line.p1.y - b->edge.line.p2.y;
553
554 cairo_int64_t den_det;
555 cairo_int64_t R;
556 cairo_quorem64_t qr;
557
558 den_det = det32_64 (dx1, dy1, dx2, dy2);
559
560 /* Q: Can we determine that the lines do not intersect (within range)
561 * much more cheaply than computing the intersection point i.e. by
562 * avoiding the division?
563 *
564 * X = ax + t * adx = bx + s * bdx;
565 * Y = ay + t * ady = by + s * bdy;
566 * ∴ t * (ady*bdx - bdy*adx) = bdx * (by - ay) + bdy * (ax - bx)
567 * => t * L = R
568 *
569 * Therefore we can reject any intersection (under the criteria for
570 * valid intersection events) if:
571 * L^R < 0 => t < 0, or
572 * L<R => t > 1
573 *
574 * (where top/bottom must at least extend to the line endpoints).
575 *
576 * A similar substitution can be performed for s, yielding:
577 * s * (ady*bdx - bdy*adx) = ady * (ax - bx) - adx * (ay - by)
578 */
579 R = det32_64 (dx2, dy2,
580 b->edge.line.p1.x - a->edge.line.p1.x,
581 b->edge.line.p1.y - a->edge.line.p1.y);
582 if (_cairo_int64_negative (den_det)((den_det) < 0)) {
583 if (_cairo_int64_ge (den_det, R)(!((den_det) < (R))))
584 return FALSE0;
585 } else {
586 if (_cairo_int64_le (den_det, R)(!((R) < (den_det))))
587 return FALSE0;
588 }
589
590 R = det32_64 (dy1, dx1,
591 a->edge.line.p1.y - b->edge.line.p1.y,
592 a->edge.line.p1.x - b->edge.line.p1.x);
593 if (_cairo_int64_negative (den_det)((den_det) < 0)) {
594 if (_cairo_int64_ge (den_det, R)(!((den_det) < (R))))
595 return FALSE0;
596 } else {
597 if (_cairo_int64_le (den_det, R)(!((R) < (den_det))))
598 return FALSE0;
599 }
600
601 /* We now know that the two lines should intersect within range. */
602
603 a_det = det32_64 (a->edge.line.p1.x, a->edge.line.p1.y,
604 a->edge.line.p2.x, a->edge.line.p2.y);
605 b_det = det32_64 (b->edge.line.p1.x, b->edge.line.p1.y,
606 b->edge.line.p2.x, b->edge.line.p2.y);
607
608 /* x = det (a_det, dx1, b_det, dx2) / den_det */
609 qr = _cairo_int_96by64_32x64_divrem (det64x32_128 (a_det, dx1,
610 b_det, dx2),
611 den_det);
612 if (_cairo_int64_eq (qr.rem, den_det)((qr.rem) == (den_det)))
613 return FALSE0;
614#if 0
615 intersection->x.exactness = _cairo_int64_is_zero (qr.rem)((qr.rem) == 0) ? EXACT : INEXACT;
616#else
617 intersection->x.exactness = EXACT;
618 if (! _cairo_int64_is_zero (qr.rem)((qr.rem) == 0)) {
619 if (_cairo_int64_negative (den_det)((den_det) < 0) ^ _cairo_int64_negative (qr.rem)((qr.rem) < 0))
620 qr.rem = _cairo_int64_negate (qr.rem)(-(qr.rem));
621 qr.rem = _cairo_int64_mul (qr.rem, _cairo_int32_to_int64 (2))((qr.rem) * (((int64_t) (2))));
622 if (_cairo_int64_ge (qr.rem, den_det)(!((qr.rem) < (den_det)))) {
623 qr.quo = _cairo_int64_add (qr.quo,((qr.quo) + (((int64_t) (((qr.quo) < 0) ? -1 : 1))))
624 _cairo_int32_to_int64 (_cairo_int64_negative (qr.quo) ? -1 : 1))((qr.quo) + (((int64_t) (((qr.quo) < 0) ? -1 : 1))));
625 } else
626 intersection->x.exactness = INEXACT;
627 }
628#endif
629 intersection->x.ordinate = _cairo_int64_to_int32 (qr.quo)((int32_t) (qr.quo));
630
631 /* y = det (a_det, dy1, b_det, dy2) / den_det */
632 qr = _cairo_int_96by64_32x64_divrem (det64x32_128 (a_det, dy1,
633 b_det, dy2),
634 den_det);
635 if (_cairo_int64_eq (qr.rem, den_det)((qr.rem) == (den_det)))
636 return FALSE0;
637#if 0
638 intersection->y.exactness = _cairo_int64_is_zero (qr.rem)((qr.rem) == 0) ? EXACT : INEXACT;
639#else
640 intersection->y.exactness = EXACT;
641 if (! _cairo_int64_is_zero (qr.rem)((qr.rem) == 0)) {
642 if (_cairo_int64_negative (den_det)((den_det) < 0) ^ _cairo_int64_negative (qr.rem)((qr.rem) < 0))
643 qr.rem = _cairo_int64_negate (qr.rem)(-(qr.rem));
644 qr.rem = _cairo_int64_mul (qr.rem, _cairo_int32_to_int64 (2))((qr.rem) * (((int64_t) (2))));
645 if (_cairo_int64_ge (qr.rem, den_det)(!((qr.rem) < (den_det)))) {
646 qr.quo = _cairo_int64_add (qr.quo,((qr.quo) + (((int64_t) (((qr.quo) < 0) ? -1 : 1))))
647 _cairo_int32_to_int64 (_cairo_int64_negative (qr.quo) ? -1 : 1))((qr.quo) + (((int64_t) (((qr.quo) < 0) ? -1 : 1))));
648 } else
649 intersection->y.exactness = INEXACT;
650 }
651#endif
652 intersection->y.ordinate = _cairo_int64_to_int32 (qr.quo)((int32_t) (qr.quo));
653
654 return TRUE1;
655}
656
657static int
658_cairo_bo_intersect_ordinate_32_compare (cairo_bo_intersect_ordinate_t a,
659 int32_t b)
660{
661 /* First compare the quotient */
662 if (a.ordinate > b)
663 return +1;
664 if (a.ordinate < b)
665 return -1;
666 /* With quotient identical, if remainder is 0 then compare equal */
667 /* Otherwise, the non-zero remainder makes a > b */
668 return INEXACT == a.exactness;
669}
670
671/* Does the given edge contain the given point. The point must already
672 * be known to be contained within the line determined by the edge,
673 * (most likely the point results from an intersection of this edge
674 * with another).
675 *
676 * If we had exact arithmetic, then this function would simply be a
677 * matter of examining whether the y value of the point lies within
678 * the range of y values of the edge. But since intersection points
679 * are not exact due to being rounded to the nearest integer within
680 * the available precision, we must also examine the x value of the
681 * point.
682 *
683 * The definition of "contains" here is that the given intersection
684 * point will be seen by the sweep line after the start event for the
685 * given edge and before the stop event for the edge. See the comments
686 * in the implementation for more details.
687 */
688static cairo_bool_t
689_cairo_bo_edge_contains_intersect_point (cairo_bo_edge_t *edge,
690 cairo_bo_intersect_point_t *point)
691{
692 int cmp_top, cmp_bottom;
693
694 /* XXX: When running the actual algorithm, we don't actually need to
695 * compare against edge->top at all here, since any intersection above
696 * top is eliminated early via a slope comparison. We're leaving these
697 * here for now only for the sake of the quadratic-time intersection
698 * finder which needs them.
699 */
700
701 cmp_top = _cairo_bo_intersect_ordinate_32_compare (point->y,
702 edge->edge.top);
703 cmp_bottom = _cairo_bo_intersect_ordinate_32_compare (point->y,
704 edge->edge.bottom);
705
706 if (cmp_top < 0 || cmp_bottom > 0)
707 {
708 return FALSE0;
709 }
710
711 if (cmp_top > 0 && cmp_bottom < 0)
712 {
713 return TRUE1;
714 }
715
716 /* At this stage, the point lies on the same y value as either
717 * edge->top or edge->bottom, so we have to examine the x value in
718 * order to properly determine containment. */
719
720 /* If the y value of the point is the same as the y value of the
721 * top of the edge, then the x value of the point must be greater
722 * to be considered as inside the edge. Similarly, if the y value
723 * of the point is the same as the y value of the bottom of the
724 * edge, then the x value of the point must be less to be
725 * considered as inside. */
726
727 if (cmp_top == 0) {
728 cairo_fixed_t top_x;
729
730 top_x = _line_compute_intersection_x_for_y (&edge->edge.line,
731 edge->edge.top);
732 return _cairo_bo_intersect_ordinate_32_compare (point->x, top_x) > 0;
733 } else { /* cmp_bottom == 0 */
734 cairo_fixed_t bot_x;
735
736 bot_x = _line_compute_intersection_x_for_y (&edge->edge.line,
737 edge->edge.bottom);
738 return _cairo_bo_intersect_ordinate_32_compare (point->x, bot_x) < 0;
739 }
740}
741
742/* Compute the intersection of two edges. The result is provided as a
743 * coordinate pair of 128-bit integers.
744 *
745 * Returns %CAIRO_BO_STATUS_INTERSECTION if there is an intersection
746 * that is within both edges, %CAIRO_BO_STATUS_NO_INTERSECTION if the
747 * intersection of the lines defined by the edges occurs outside of
748 * one or both edges, and %CAIRO_BO_STATUS_PARALLEL if the two edges
749 * are exactly parallel.
750 *
751 * Note that when determining if a candidate intersection is "inside"
752 * an edge, we consider both the infinitesimal shortening and the
753 * infinitesimal tilt rules described by John Hobby. Specifically, if
754 * the intersection is exactly the same as an edge point, it is
755 * effectively outside (no intersection is returned). Also, if the
756 * intersection point has the same
757 */
758static cairo_bool_t
759_cairo_bo_edge_intersect (cairo_bo_edge_t *a,
760 cairo_bo_edge_t *b,
761 cairo_bo_point32_t *intersection)
762{
763 cairo_bo_intersect_point_t quorem;
764
765 if (! intersect_lines (a, b, &quorem))
766 return FALSE0;
767
768 if (! _cairo_bo_edge_contains_intersect_point (a, &quorem))
769 return FALSE0;
770
771 if (! _cairo_bo_edge_contains_intersect_point (b, &quorem))
772 return FALSE0;
773
774 /* Now that we've correctly compared the intersection point and
775 * determined that it lies within the edge, then we know that we
776 * no longer need any more bits of storage for the intersection
777 * than we do for our edge coordinates. We also no longer need the
778 * remainder from the division. */
779 intersection->x = quorem.x.ordinate;
780 intersection->y = quorem.y.ordinate;
781
782 return TRUE1;
783}
784
785static inline int
786cairo_bo_event_compare (const cairo_bo_event_t *a,
787 const cairo_bo_event_t *b)
788{
789 int cmp;
790
791 cmp = _cairo_bo_point32_compare (&a->point, &b->point);
792 if (cmp)
793 return cmp;
794
795 cmp = a->type - b->type;
796 if (cmp)
797 return cmp;
798
799 return a - b;
800}
801
802static inline void
803_pqueue_init (pqueue_t *pq)
804{
805 pq->max_size = ARRAY_LENGTH (pq->elements_embedded)((int) (sizeof (pq->elements_embedded) / sizeof (pq->elements_embedded
[0])));
806 pq->size = 0;
807
808 pq->elements = pq->elements_embedded;
809}
810
811static inline void
812_pqueue_fini (pqueue_t *pq)
813{
814 if (pq->elements != pq->elements_embedded)
815 free (pq->elements);
816}
817
818static cairo_status_t
819_pqueue_grow (pqueue_t *pq)
820{
821 cairo_bo_event_t **new_elements;
822 pq->max_size *= 2;
823
824 if (pq->elements == pq->elements_embedded) {
825 new_elements = _cairo_malloc_ab (pq->max_size,
826 sizeof (cairo_bo_event_t *));
827 if (unlikely (new_elements == NULL)(__builtin_expect (!!(new_elements == ((void*)0)), 0)))
828 return _cairo_error (CAIRO_STATUS_NO_MEMORY);
829
830 memcpy (new_elements, pq->elements_embedded,
831 sizeof (pq->elements_embedded));
832 } else {
833 new_elements = _cairo_realloc_ab (pq->elements,
834 pq->max_size,
835 sizeof (cairo_bo_event_t *));
836 if (unlikely (new_elements == NULL)(__builtin_expect (!!(new_elements == ((void*)0)), 0)))
837 return _cairo_error (CAIRO_STATUS_NO_MEMORY);
838 }
839
840 pq->elements = new_elements;
841 return CAIRO_STATUS_SUCCESS;
842}
843
844static inline cairo_status_t
845_pqueue_push (pqueue_t *pq, cairo_bo_event_t *event)
846{
847 cairo_bo_event_t **elements;
848 int i, parent;
849
850 if (unlikely (pq->size + 1 == pq->max_size)(__builtin_expect (!!(pq->size + 1 == pq->max_size), 0)
)) {
851 cairo_status_t status;
852
853 status = _pqueue_grow (pq);
854 if (unlikely (status)(__builtin_expect (!!(status), 0)))
855 return status;
856 }
857
858 elements = pq->elements;
859
860 for (i = ++pq->size;
861 i != PQ_FIRST_ENTRY1 &&
862 cairo_bo_event_compare (event,
863 elements[parent = PQ_PARENT_INDEX (i)((i) >> 1)]) < 0;
864 i = parent)
865 {
866 elements[i] = elements[parent];
867 }
868
869 elements[i] = event;
870
871 return CAIRO_STATUS_SUCCESS;
872}
873
874static inline void
875_pqueue_pop (pqueue_t *pq)
876{
877 cairo_bo_event_t **elements = pq->elements;
878 cairo_bo_event_t *tail;
879 int child, i;
880
881 tail = elements[pq->size--];
882 if (pq->size == 0) {
883 elements[PQ_FIRST_ENTRY1] = NULL((void*)0);
884 return;
885 }
886
887 for (i = PQ_FIRST_ENTRY1;
888 (child = PQ_LEFT_CHILD_INDEX (i)((i) << 1)) <= pq->size;
889 i = child)
890 {
891 if (child != pq->size &&
892 cairo_bo_event_compare (elements[child+1],
893 elements[child]) < 0)
894 {
895 child++;
896 }
897
898 if (cairo_bo_event_compare (elements[child], tail) >= 0)
899 break;
900
901 elements[i] = elements[child];
902 }
903 elements[i] = tail;
904}
905
906static inline cairo_status_t
907_cairo_bo_event_queue_insert (cairo_bo_event_queue_t *queue,
908 cairo_bo_event_type_t type,
909 cairo_bo_edge_t *e1,
910 cairo_bo_edge_t *e2,
911 const cairo_point_t *point)
912{
913 cairo_bo_queue_event_t *event;
914
915 event = _cairo_freepool_alloc (&queue->pool);
916 if (unlikely (event == NULL)(__builtin_expect (!!(event == ((void*)0)), 0)))
917 return _cairo_error (CAIRO_STATUS_NO_MEMORY);
918
919 event->type = type;
920 event->e1 = e1;
921 event->e2 = e2;
922 event->point = *point;
923
924 return _pqueue_push (&queue->pqueue, (cairo_bo_event_t *) event);
925}
926
927static void
928_cairo_bo_event_queue_delete (cairo_bo_event_queue_t *queue,
929 cairo_bo_event_t *event)
930{
931 _cairo_freepool_free (&queue->pool, event);
932}
933
934static cairo_bo_event_t *
935_cairo_bo_event_dequeue (cairo_bo_event_queue_t *event_queue)
936{
937 cairo_bo_event_t *event, *cmp;
938
939 event = event_queue->pqueue.elements[PQ_FIRST_ENTRY1];
940 cmp = *event_queue->start_events;
941 if (event == NULL((void*)0) ||
942 (cmp != NULL((void*)0) && cairo_bo_event_compare (cmp, event) < 0))
943 {
944 event = cmp;
945 event_queue->start_events++;
946 }
947 else
948 {
949 _pqueue_pop (&event_queue->pqueue);
950 }
951
952 return event;
953}
954
955CAIRO_COMBSORT_DECLARE (_cairo_bo_event_queue_sort,static void _cairo_bo_event_queue_sort (cairo_bo_event_t * *base
, unsigned int nmemb) { unsigned int gap = nmemb; unsigned int
i, j; int swapped; do { gap = _cairo_combsort_newgap (gap); swapped
= gap > 1; for (i = 0; i < nmemb-gap ; i++) { j = i + gap
; if (cairo_bo_event_compare (base[i], base[j]) > 0 ) { cairo_bo_event_t
* tmp; tmp = base[i]; base[i] = base[j]; base[j] = tmp; swapped
= 1; } } } while (swapped); }
11
←
The value 0 is assigned to 'i'
→
12
←
Loop condition is true. Entering loop body
→
13
←
1st function call argument is an uninitialized value
956 cairo_bo_event_t *,static void _cairo_bo_event_queue_sort (cairo_bo_event_t * *base
, unsigned int nmemb) { unsigned int gap = nmemb; unsigned int
i, j; int swapped; do { gap = _cairo_combsort_newgap (gap); swapped
= gap > 1; for (i = 0; i < nmemb-gap ; i++) { j = i + gap
; if (cairo_bo_event_compare (base[i], base[j]) > 0 ) { cairo_bo_event_t
* tmp; tmp = base[i]; base[i] = base[j]; base[j] = tmp; swapped
= 1; } } } while (swapped); }
957 cairo_bo_event_compare)static void _cairo_bo_event_queue_sort (cairo_bo_event_t * *base
, unsigned int nmemb) { unsigned int gap = nmemb; unsigned int
i, j; int swapped; do { gap = _cairo_combsort_newgap (gap); swapped
= gap > 1; for (i = 0; i < nmemb-gap ; i++) { j = i + gap
; if (cairo_bo_event_compare (base[i], base[j]) > 0 ) { cairo_bo_event_t
* tmp; tmp = base[i]; base[i] = base[j]; base[j] = tmp; swapped
= 1; } } } while (swapped); }
958
959static void
960_cairo_bo_event_queue_init (cairo_bo_event_queue_t *event_queue,
961 cairo_bo_event_t **start_events,
962 int num_events)
963{
964 _cairo_bo_event_queue_sort (start_events, num_events);
10
←
Calling '_cairo_bo_event_queue_sort'
→
965 start_events[num_events] = NULL((void*)0);
966
967 event_queue->start_events = start_events;
968
969 _cairo_freepool_init (&event_queue->pool,
970 sizeof (cairo_bo_queue_event_t));
971 _pqueue_init (&event_queue->pqueue);
972 event_queue->pqueue.elements[PQ_FIRST_ENTRY1] = NULL((void*)0);
973}
974
975static cairo_status_t
976_cairo_bo_event_queue_insert_stop (cairo_bo_event_queue_t *event_queue,
977 cairo_bo_edge_t *edge)
978{
979 cairo_bo_point32_t point;
980
981 point.y = edge->edge.bottom;
982 point.x = _line_compute_intersection_x_for_y (&edge->edge.line,
983 point.y);
984 return _cairo_bo_event_queue_insert (event_queue,
985 CAIRO_BO_EVENT_TYPE_STOP,
986 edge, NULL((void*)0),
987 &point);
988}
989
990static void
991_cairo_bo_event_queue_fini (cairo_bo_event_queue_t *event_queue)
992{
993 _pqueue_fini (&event_queue->pqueue);
994 _cairo_freepool_fini (&event_queue->pool);
995}
996
997static inline cairo_status_t
998_cairo_bo_event_queue_insert_if_intersect_below_current_y (cairo_bo_event_queue_t *event_queue,
999 cairo_bo_edge_t *left,
1000 cairo_bo_edge_t *right)
1001{
1002 cairo_bo_point32_t intersection;
1003
1004 if (_line_equal (&left->edge.line, &right->edge.line))
1005 return CAIRO_STATUS_SUCCESS;
1006
1007 /* The names "left" and "right" here are correct descriptions of
1008 * the order of the two edges within the active edge list. So if a
1009 * slope comparison also puts left less than right, then we know
1010 * that the intersection of these two segments has already
1011 * occurred before the current sweep line position. */
1012 if (_slope_compare (left, right) <= 0)
1013 return CAIRO_STATUS_SUCCESS;
1014
1015 if (! _cairo_bo_edge_intersect (left, right, &intersection))
1016 return CAIRO_STATUS_SUCCESS;
1017
1018 return _cairo_bo_event_queue_insert (event_queue,
1019 CAIRO_BO_EVENT_TYPE_INTERSECTION,
1020 left, right,
1021 &intersection);
1022}
1023
1024static void
1025_cairo_bo_sweep_line_init (cairo_bo_sweep_line_t *sweep_line)
1026{
1027 sweep_line->head = NULL((void*)0);
1028 sweep_line->current_y = INT32_MIN(-2147483647-1);
1029 sweep_line->current_edge = NULL((void*)0);
1030}
1031
1032static cairo_status_t
1033_cairo_bo_sweep_line_insert (cairo_bo_sweep_line_t *sweep_line,
1034 cairo_bo_edge_t *edge)
1035{
1036 if (sweep_line->current_edge != NULL((void*)0)) {
1037 cairo_bo_edge_t *prev, *next;
1038 int cmp;
1039
1040 cmp = _cairo_bo_sweep_line_compare_edges (sweep_line,
1041 sweep_line->current_edge,
1042 edge);
1043 if (cmp < 0) {
1044 prev = sweep_line->current_edge;
1045 next = prev->next;
1046 while (next != NULL((void*)0) &&
1047 _cairo_bo_sweep_line_compare_edges (sweep_line,
1048 next, edge) < 0)
1049 {
1050 prev = next, next = prev->next;
1051 }
1052
1053 prev->next = edge;
1054 edge->prev = prev;
1055 edge->next = next;
1056 if (next != NULL((void*)0))
1057 next->prev = edge;
1058 } else if (cmp > 0) {
1059 next = sweep_line->current_edge;
1060 prev = next->prev;
1061 while (prev != NULL((void*)0) &&
1062 _cairo_bo_sweep_line_compare_edges (sweep_line,
1063 prev, edge) > 0)
1064 {
1065 next = prev, prev = next->prev;
1066 }
1067
1068 next->prev = edge;
1069 edge->next = next;
1070 edge->prev = prev;
1071 if (prev != NULL((void*)0))
1072 prev->next = edge;
1073 else
1074 sweep_line->head = edge;
1075 } else {
1076 prev = sweep_line->current_edge;
1077 edge->prev = prev;
1078 edge->next = prev->next;
1079 if (prev->next != NULL((void*)0))
1080 prev->next->prev = edge;
1081 prev->next = edge;
1082 }
1083 } else {
1084 sweep_line->head = edge;
1085 }
1086
1087 sweep_line->current_edge = edge;
1088
1089 return CAIRO_STATUS_SUCCESS;
1090}
1091
1092static void
1093_cairo_bo_sweep_line_delete (cairo_bo_sweep_line_t *sweep_line,
1094 cairo_bo_edge_t *edge)
1095{
1096 if (edge->prev != NULL((void*)0))
1097 edge->prev->next = edge->next;
1098 else
1099 sweep_line->head = edge->next;
1100
1101 if (edge->next != NULL((void*)0))
1102 edge->next->prev = edge->prev;
1103
1104 if (sweep_line->current_edge == edge)
1105 sweep_line->current_edge = edge->prev ? edge->prev : edge->next;
1106}
1107
1108static void
1109_cairo_bo_sweep_line_swap (cairo_bo_sweep_line_t *sweep_line,
1110 cairo_bo_edge_t *left,
1111 cairo_bo_edge_t *right)
1112{
1113 if (left->prev != NULL((void*)0))
1114 left->prev->next = right;
1115 else
1116 sweep_line->head = right;
1117
1118 if (right->next != NULL((void*)0))
1119 right->next->prev = left;
1120
1121 left->next = right->next;
1122 right->next = left;
1123
1124 right->prev = left->prev;
1125 left->prev = right;
1126}
1127
1128static inline cairo_bool_t
1129edges_colinear (const cairo_bo_edge_t *a, const cairo_bo_edge_t *b)
1130{
1131 if (_line_equal (&a->edge.line, &b->edge.line))
1132 return TRUE1;
1133
1134 if (_slope_compare (a, b))
1135 return FALSE0;
1136
1137 /* The choice of y is not truly arbitrary since we must guarantee that it
1138 * is greater than the start of either line.
1139 */
1140 if (a->edge.line.p1.y == b->edge.line.p1.y) {
1141 return a->edge.line.p1.x == b->edge.line.p1.x;
1142 } else if (a->edge.line.p2.y == b->edge.line.p2.y) {
1143 return a->edge.line.p2.x == b->edge.line.p2.x;
1144 } else if (a->edge.line.p1.y < b->edge.line.p1.y) {
1145 return edge_compare_for_y_against_x (b,
1146 a->edge.line.p1.y,
1147 a->edge.line.p1.x) == 0;
1148 } else {
1149 return edge_compare_for_y_against_x (a,
1150 b->edge.line.p1.y,
1151 b->edge.line.p1.x) == 0;
1152 }
1153}
1154
1155static void
1156_cairo_bo_edge_end (cairo_bo_edge_t *left,
1157 int32_t bot,
1158 cairo_polygon_t *polygon)
1159{
1160 cairo_bo_deferred_t *d = &left->deferred;
1161
1162 if (likely (d->top < bot)(__builtin_expect (!!(d->top < bot), 1))) {
1163 _cairo_polygon_add_line (polygon,
1164 &left->edge.line,
1165 d->top, bot,
1166 1);
1167 _cairo_polygon_add_line (polygon,
1168 &d->right->edge.line,
1169 d->top, bot,
1170 -1);
1171 }
1172
1173 d->right = NULL((void*)0);
1174}
1175
1176
1177static inline void
1178_cairo_bo_edge_start_or_continue (cairo_bo_edge_t *left,
1179 cairo_bo_edge_t *right,
1180 int top,
1181 cairo_polygon_t *polygon)
1182{
1183 if (left->deferred.right == right)
1184 return;
1185
1186 if (left->deferred.right != NULL((void*)0)) {
1187 if (right != NULL((void*)0) && edges_colinear (left->deferred.right, right))
1188 {
1189 /* continuation on right, so just swap edges */
1190 left->deferred.right = right;
1191 return;
1192 }
1193
1194 _cairo_bo_edge_end (left, top, polygon);
1195 }
1196
1197 if (right != NULL((void*)0) && ! edges_colinear (left, right)) {
1198 left->deferred.top = top;
1199 left->deferred.right = right;
1200 }
1201}
1202
1203static inline void
1204_active_edges_to_polygon (cairo_bo_edge_t *left,
1205 int32_t top,
1206 cairo_fill_rule_t fill_rule,
1207 cairo_polygon_t *polygon)
1208{
1209 cairo_bo_edge_t *right;
1210 unsigned int mask;
1211
1212 if (fill_rule == CAIRO_FILL_RULE_WINDING)
1213 mask = ~0;
1214 else
1215 mask = 1;
1216
1217 while (left != NULL((void*)0)) {
1218 int in_out = left->edge.dir;
1219
1220 right = left->next;
1221 if (left->deferred.right == NULL((void*)0)) {
1222 while (right != NULL((void*)0) && right->deferred.right == NULL((void*)0))
1223 right = right->next;
1224
1225 if (right != NULL((void*)0) && edges_colinear (left, right)) {
1226 /* continuation on left */
1227 left->deferred = right->deferred;
1228 right->deferred.right = NULL((void*)0);
1229 }
1230 }
1231
1232 right = left->next;
1233 while (right != NULL((void*)0)) {
1234 if (right->deferred.right != NULL((void*)0))
1235 _cairo_bo_edge_end (right, top, polygon);
1236
1237 in_out += right->edge.dir;
1238 if ((in_out & mask) == 0) {
1239 /* skip co-linear edges */
1240 if (right->next == NULL((void*)0) || !edges_colinear (right, right->next))
1241 break;
1242 }
1243
1244 right = right->next;
1245 }
1246
1247 _cairo_bo_edge_start_or_continue (left, right, top, polygon);
1248
1249 left = right;
1250 if (left != NULL((void*)0))
1251 left = left->next;
1252 }
1253}
1254
1255
1256static cairo_status_t
1257_cairo_bentley_ottmann_tessellate_bo_edges (cairo_bo_event_t **start_events,
1258 int num_events,
1259 cairo_fill_rule_t fill_rule,
1260 cairo_polygon_t *polygon)
1261{
1262 cairo_status_t status = CAIRO_STATUS_SUCCESS; /* silence compiler */
1263 cairo_bo_event_queue_t event_queue;
1264 cairo_bo_sweep_line_t sweep_line;
1265 cairo_bo_event_t *event;
1266 cairo_bo_edge_t *left, *right;
1267 cairo_bo_edge_t *e1, *e2;
1268
1269 _cairo_bo_event_queue_init (&event_queue, start_events, num_events);
9
←
Calling '_cairo_bo_event_queue_init'
→
1270 _cairo_bo_sweep_line_init (&sweep_line);
1271
1272 while ((event = _cairo_bo_event_dequeue (&event_queue))) {
1273 if (event->point.y != sweep_line.current_y) {
1274 _active_edges_to_polygon (sweep_line.head,
1275 sweep_line.current_y,
1276 fill_rule, polygon);
1277
1278 sweep_line.current_y = event->point.y;
1279 }
1280
1281 switch (event->type) {
1282 case CAIRO_BO_EVENT_TYPE_START:
1283 e1 = &((cairo_bo_start_event_t *) event)->edge;
1284
1285 status = _cairo_bo_sweep_line_insert (&sweep_line, e1);
1286 if (unlikely (status)(__builtin_expect (!!(status), 0)))
1287 goto unwind;
1288
1289 status = _cairo_bo_event_queue_insert_stop (&event_queue, e1);
1290 if (unlikely (status)(__builtin_expect (!!(status), 0)))
1291 goto unwind;
1292
1293 left = e1->prev;
1294 right = e1->next;
1295
1296 if (left != NULL((void*)0)) {
1297 status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, left, e1);
1298 if (unlikely (status)(__builtin_expect (!!(status), 0)))
1299 goto unwind;
1300 }
1301
1302 if (right != NULL((void*)0)) {
1303 status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, e1, right);
1304 if (unlikely (status)(__builtin_expect (!!(status), 0)))
1305 goto unwind;
1306 }
1307
1308 break;
1309
1310 case CAIRO_BO_EVENT_TYPE_STOP:
1311 e1 = ((cairo_bo_queue_event_t *) event)->e1;
1312 _cairo_bo_event_queue_delete (&event_queue, event);
1313
1314 left = e1->prev;
1315 right = e1->next;
1316
1317 _cairo_bo_sweep_line_delete (&sweep_line, e1);
1318
1319 if (e1->deferred.right != NULL((void*)0))
1320 _cairo_bo_edge_end (e1, e1->edge.bottom, polygon);
1321
1322 if (left != NULL((void*)0) && right != NULL((void*)0)) {
1323 status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, left, right);
1324 if (unlikely (status)(__builtin_expect (!!(status), 0)))
1325 goto unwind;
1326 }
1327
1328 break;
1329
1330 case CAIRO_BO_EVENT_TYPE_INTERSECTION:
1331 e1 = ((cairo_bo_queue_event_t *) event)->e1;
1332 e2 = ((cairo_bo_queue_event_t *) event)->e2;
1333 _cairo_bo_event_queue_delete (&event_queue, event);
1334
1335 /* skip this intersection if its edges are not adjacent */
1336 if (e2 != e1->next)
1337 break;
1338
1339 left = e1->prev;
1340 right = e2->next;
1341
1342 _cairo_bo_sweep_line_swap (&sweep_line, e1, e2);
1343
1344 /* after the swap e2 is left of e1 */
1345
1346 if (left != NULL((void*)0)) {
1347 status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, left, e2);
1348 if (unlikely (status)(__builtin_expect (!!(status), 0)))
1349 goto unwind;
1350 }
1351
1352 if (right != NULL((void*)0)) {
1353 status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, e1, right);
1354 if (unlikely (status)(__builtin_expect (!!(status), 0)))
1355 goto unwind;
1356 }
1357
1358 break;
1359 }
1360 }
1361
1362 unwind:
1363 _cairo_bo_event_queue_fini (&event_queue);
1364
1365 return status;
1366}
1367
1368cairo_status_t
1369_cairo_polygon_reduce (cairo_polygon_t *polygon,
1370 cairo_fill_rule_t fill_rule)
1371{
1372 cairo_status_t status;
1373 cairo_bo_start_event_t stack_events[CAIRO_STACK_ARRAY_LENGTH (cairo_bo_start_event_t)((512 * sizeof (int)) / sizeof(cairo_bo_start_event_t))];
1374 cairo_bo_start_event_t *events;
1375 cairo_bo_event_t *stack_event_ptrs[ARRAY_LENGTH (stack_events)((int) (sizeof (stack_events) / sizeof (stack_events[0]))) + 1];
1376 cairo_bo_event_t **event_ptrs;
1377 int num_limits;
1378 int num_events;
1379 int i;
1380
1381 num_events = polygon->num_edges;
1382 if (unlikely (0 == num_events)(__builtin_expect (!!(0 == num_events), 0)))
1
Assuming 'num_events' is not equal to 0
→
2
←
Taking false branch
→
1383 return CAIRO_STATUS_SUCCESS;
1384
1385 if (DEBUG_POLYGON0) {
3
←
Taking false branch
→
1386 FILE *file = fopen ("reduce_in.txt", "w");
1387 _cairo_debug_print_polygon (file, polygon);
1388 fclose (file);
1389 }
1390
1391 events = stack_events;
1392 event_ptrs = stack_event_ptrs;
1393 if (num_events > ARRAY_LENGTH (stack_events)((int) (sizeof (stack_events) / sizeof (stack_events[0])))) {
4
←
Assuming the condition is false
→
5
←
Taking false branch
→
1394 events = _cairo_malloc_ab_plus_c (num_events,
1395 sizeof (cairo_bo_start_event_t) +
1396 sizeof (cairo_bo_event_t *),
1397 sizeof (cairo_bo_event_t *));
1398 if (unlikely (events == NULL)(__builtin_expect (!!(events == ((void*)0)), 0)))
1399 return _cairo_error (CAIRO_STATUS_NO_MEMORY);
1400
1401 event_ptrs = (cairo_bo_event_t **) (events + num_events);
1402 }
1403
1404 for (i = 0; i < num_events; i++) {
6
←
Assuming 'i' is >= 'num_events'
→
7
←
Loop condition is false. Execution continues on line 1419
→
1405 event_ptrs[i] = (cairo_bo_event_t *) &events[i];
1406
1407 events[i].type = CAIRO_BO_EVENT_TYPE_START;
1408 events[i].point.y = polygon->edges[i].top;
1409 events[i].point.x =
1410 _line_compute_intersection_x_for_y (&polygon->edges[i].line,
1411 events[i].point.y);
1412
1413 events[i].edge.edge = polygon->edges[i];
1414 events[i].edge.deferred.right = NULL((void*)0);
1415 events[i].edge.prev = NULL((void*)0);
1416 events[i].edge.next = NULL((void*)0);
1417 }
1418
1419 num_limits = polygon->num_limits; polygon->num_limits = 0;
1420 polygon->num_edges = 0;
1421
1422 status = _cairo_bentley_ottmann_tessellate_bo_edges (event_ptrs,
8
←
Calling '_cairo_bentley_ottmann_tessellate_bo_edges'
→
1423 num_events,
1424 fill_rule,
1425 polygon);
1426 polygon->num_limits = num_limits;
1427
1428 if (events != stack_events)
1429 free (events);
1430
1431 if (DEBUG_POLYGON0) {
1432 FILE *file = fopen ("reduce_out.txt", "w");
1433 _cairo_debug_print_polygon (file, polygon);
1434 fclose (file);
1435 }
1436
1437 return status;
1438}