Bug Summary

File:root/firefox-clang/gfx/cairo/cairo/src/cairo-polygon-intersect.c
Warning:line 886, 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-intersect.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-intersect.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
46typedef struct _cairo_bo_intersect_ordinate {
47 int32_t ordinate;
48 enum { EXCESS = -1, EXACT = 0, DEFAULT = 1 } approx;
49} cairo_bo_intersect_ordinate_t;
50
51typedef struct _cairo_bo_intersect_point {
52 cairo_bo_intersect_ordinate_t x;
53 cairo_bo_intersect_ordinate_t y;
54} cairo_bo_intersect_point_t;
55
56typedef struct _cairo_bo_edge cairo_bo_edge_t;
57
58typedef struct _cairo_bo_deferred {
59 cairo_bo_edge_t *other;
60 int32_t top;
61} cairo_bo_deferred_t;
62
63struct _cairo_bo_edge {
64 int a_or_b;
65 cairo_edge_t edge;
66 cairo_bo_edge_t *prev;
67 cairo_bo_edge_t *next;
68 cairo_bo_deferred_t deferred;
69};
70
71/* the parent is always given by index/2 */
72#define PQ_PARENT_INDEX(i)((i) >> 1) ((i) >> 1)
73#define PQ_FIRST_ENTRY1 1
74
75/* left and right children are index * 2 and (index * 2) +1 respectively */
76#define PQ_LEFT_CHILD_INDEX(i)((i) << 1) ((i) << 1)
77
78typedef enum {
79 CAIRO_BO_EVENT_TYPE_STOP = -1,
80 CAIRO_BO_EVENT_TYPE_INTERSECTION,
81 CAIRO_BO_EVENT_TYPE_START
82} cairo_bo_event_type_t;
83
84typedef struct _cairo_bo_event {
85 cairo_bo_event_type_t type;
86 cairo_bo_intersect_point_t point;
87} cairo_bo_event_t;
88
89typedef struct _cairo_bo_start_event {
90 cairo_bo_event_type_t type;
91 cairo_bo_intersect_point_t point;
92 cairo_bo_edge_t edge;
93} cairo_bo_start_event_t;
94
95typedef struct _cairo_bo_queue_event {
96 cairo_bo_event_type_t type;
97 cairo_bo_intersect_point_t point;
98 cairo_bo_edge_t *e1;
99 cairo_bo_edge_t *e2;
100} cairo_bo_queue_event_t;
101
102typedef struct _pqueue {
103 int size, max_size;
104
105 cairo_bo_event_t **elements;
106 cairo_bo_event_t *elements_embedded[1024];
107} pqueue_t;
108
109typedef struct _cairo_bo_event_queue {
110 cairo_freepool_t pool;
111 pqueue_t pqueue;
112 cairo_bo_event_t **start_events;
113} cairo_bo_event_queue_t;
114
115typedef struct _cairo_bo_sweep_line {
116 cairo_bo_edge_t *head;
117 int32_t current_y;
118 cairo_bo_edge_t *current_edge;
119} cairo_bo_sweep_line_t;
120
121static cairo_fixed_t
122_line_compute_intersection_x_for_y (const cairo_line_t *line,
123 cairo_fixed_t y)
124{
125 cairo_fixed_t x, dy;
126
127 if (y == line->p1.y)
128 return line->p1.x;
129 if (y == line->p2.y)
130 return line->p2.x;
131
132 x = line->p1.x;
133 dy = line->p2.y - line->p1.y;
134 if (dy != 0) {
135 x += _cairo_fixed_mul_div_floor (y - line->p1.y,
136 line->p2.x - line->p1.x,
137 dy);
138 }
139
140 return x;
141}
142
143static inline int
144_cairo_bo_point32_compare (cairo_bo_intersect_point_t const *a,
145 cairo_bo_intersect_point_t const *b)
146{
147 int cmp;
148
149 cmp = a->y.ordinate - b->y.ordinate;
150 if (cmp)
151 return cmp;
152
153 cmp = a->y.approx - b->y.approx;
154 if (cmp)
155 return cmp;
156
157 return a->x.ordinate - b->x.ordinate;
158}
159
160/* Compare the slope of a to the slope of b, returning 1, 0, -1 if the
161 * slope a is respectively greater than, equal to, or less than the
162 * slope of b.
163 *
164 * For each edge, consider the direction vector formed from:
165 *
166 * top -> bottom
167 *
168 * which is:
169 *
170 * (dx, dy) = (line.p2.x - line.p1.x, line.p2.y - line.p1.y)
171 *
172 * We then define the slope of each edge as dx/dy, (which is the
173 * inverse of the slope typically used in math instruction). We never
174 * compute a slope directly as the value approaches infinity, but we
175 * can derive a slope comparison without division as follows, (where
176 * the ? represents our compare operator).
177 *
178 * 1. slope(a) ? slope(b)
179 * 2. adx/ady ? bdx/bdy
180 * 3. (adx * bdy) ? (bdx * ady)
181 *
182 * Note that from step 2 to step 3 there is no change needed in the
183 * sign of the result since both ady and bdy are guaranteed to be
184 * greater than or equal to 0.
185 *
186 * When using this slope comparison to sort edges, some care is needed
187 * when interpreting the results. Since the slope compare operates on
188 * distance vectors from top to bottom it gives a correct left to
189 * right sort for edges that have a common top point, (such as two
190 * edges with start events at the same location). On the other hand,
191 * the sense of the result will be exactly reversed for two edges that
192 * have a common stop point.
193 */
194static inline int
195_slope_compare (const cairo_bo_edge_t *a,
196 const cairo_bo_edge_t *b)
197{
198 /* XXX: We're assuming here that dx and dy will still fit in 32
199 * bits. That's not true in general as there could be overflow. We
200 * should prevent that before the tessellation algorithm
201 * begins.
202 */
203 int32_t adx = a->edge.line.p2.x - a->edge.line.p1.x;
204 int32_t bdx = b->edge.line.p2.x - b->edge.line.p1.x;
205
206 /* Since the dy's are all positive by construction we can fast
207 * path several common cases.
208 */
209
210 /* First check for vertical lines. */
211 if (adx == 0)
212 return -bdx;
213 if (bdx == 0)
214 return adx;
215
216 /* Then where the two edges point in different directions wrt x. */
217 if ((adx ^ bdx) < 0)
218 return adx;
219
220 /* Finally we actually need to do the general comparison. */
221 {
222 int32_t ady = a->edge.line.p2.y - a->edge.line.p1.y;
223 int32_t bdy = b->edge.line.p2.y - b->edge.line.p1.y;
224 cairo_int64_t adx_bdy = _cairo_int32x32_64_mul (adx, bdy)((int64_t) (adx) * (bdy));
225 cairo_int64_t bdx_ady = _cairo_int32x32_64_mul (bdx, ady)((int64_t) (bdx) * (ady));
226
227 return _cairo_int64_cmp (adx_bdy, bdx_ady)((adx_bdy) == (bdx_ady) ? 0 : (adx_bdy) < (bdx_ady) ? -1 :
1);
228 }
229}
230
231/*
232 * We need to compare the x-coordinates of a pair of lines for a particular y,
233 * without loss of precision.
234 *
235 * The x-coordinate along an edge for a given y is:
236 * X = A_x + (Y - A_y) * A_dx / A_dy
237 *
238 * So the inequality we wish to test is:
239 * A_x + (Y - A_y) * A_dx / A_dy ∘ B_x + (Y - B_y) * B_dx / B_dy,
240 * where ∘ is our inequality operator.
241 *
242 * By construction, we know that A_dy and B_dy (and (Y - A_y), (Y - B_y)) are
243 * all positive, so we can rearrange it thus without causing a sign change:
244 * A_dy * B_dy * (A_x - B_x) ∘ (Y - B_y) * B_dx * A_dy
245 * - (Y - A_y) * A_dx * B_dy
246 *
247 * Given the assumption that all the deltas fit within 32 bits, we can compute
248 * this comparison directly using 128 bit arithmetic. For certain, but common,
249 * input we can reduce this down to a single 32 bit compare by inspecting the
250 * deltas.
251 *
252 * (And put the burden of the work on developing fast 128 bit ops, which are
253 * required throughout the tessellator.)
254 *
255 * See the similar discussion for _slope_compare().
256 */
257static int
258edges_compare_x_for_y_general (const cairo_bo_edge_t *a,
259 const cairo_bo_edge_t *b,
260 int32_t y)
261{
262 /* XXX: We're assuming here that dx and dy will still fit in 32
263 * bits. That's not true in general as there could be overflow. We
264 * should prevent that before the tessellation algorithm
265 * begins.
266 */
267 int32_t dx;
268 int32_t adx, ady;
269 int32_t bdx, bdy;
270 enum {
271 HAVE_NONE = 0x0,
272 HAVE_DX = 0x1,
273 HAVE_ADX = 0x2,
274 HAVE_DX_ADX = HAVE_DX | HAVE_ADX,
275 HAVE_BDX = 0x4,
276 HAVE_DX_BDX = HAVE_DX | HAVE_BDX,
277 HAVE_ADX_BDX = HAVE_ADX | HAVE_BDX,
278 HAVE_ALL = HAVE_DX | HAVE_ADX | HAVE_BDX
279 } have_dx_adx_bdx = HAVE_ALL;
280
281 /* don't bother solving for abscissa if the edges' bounding boxes
282 * can be used to order them. */
283 {
284 int32_t amin, amax;
285 int32_t bmin, bmax;
286 if (a->edge.line.p1.x < a->edge.line.p2.x) {
287 amin = a->edge.line.p1.x;
288 amax = a->edge.line.p2.x;
289 } else {
290 amin = a->edge.line.p2.x;
291 amax = a->edge.line.p1.x;
292 }
293 if (b->edge.line.p1.x < b->edge.line.p2.x) {
294 bmin = b->edge.line.p1.x;
295 bmax = b->edge.line.p2.x;
296 } else {
297 bmin = b->edge.line.p2.x;
298 bmax = b->edge.line.p1.x;
299 }
300 if (amax < bmin) return -1;
301 if (amin > bmax) return +1;
302 }
303
304 ady = a->edge.line.p2.y - a->edge.line.p1.y;
305 adx = a->edge.line.p2.x - a->edge.line.p1.x;
306 if (adx == 0)
307 have_dx_adx_bdx &= ~HAVE_ADX;
308
309 bdy = b->edge.line.p2.y - b->edge.line.p1.y;
310 bdx = b->edge.line.p2.x - b->edge.line.p1.x;
311 if (bdx == 0)
312 have_dx_adx_bdx &= ~HAVE_BDX;
313
314 dx = a->edge.line.p1.x - b->edge.line.p1.x;
315 if (dx == 0)
316 have_dx_adx_bdx &= ~HAVE_DX;
317
318#define L _cairo_int64x32_128_mul (_cairo_int32x32_64_mul (ady, bdy), dx)_cairo_int64x64_128_mul(((int64_t) (ady) * (bdy)), ((int64_t)
(dx)))
319#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)))
320#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)))
321 switch (have_dx_adx_bdx) {
322 default:
323 case HAVE_NONE:
324 return 0;
325 case HAVE_DX:
326 /* A_dy * B_dy * (A_x - B_x) ∘ 0 */
327 return dx; /* ady * bdy is positive definite */
328 case HAVE_ADX:
329 /* 0 ∘ - (Y - A_y) * A_dx * B_dy */
330 return adx; /* bdy * (y - a->top.y) is positive definite */
331 case HAVE_BDX:
332 /* 0 ∘ (Y - B_y) * B_dx * A_dy */
333 return -bdx; /* ady * (y - b->top.y) is positive definite */
334 case HAVE_ADX_BDX:
335 /* 0 ∘ (Y - B_y) * B_dx * A_dy - (Y - A_y) * A_dx * B_dy */
336 if ((adx ^ bdx) < 0) {
337 return adx;
338 } else if (a->edge.line.p1.y == b->edge.line.p1.y) { /* common origin */
339 cairo_int64_t adx_bdy, bdx_ady;
340
341 /* ∴ A_dx * B_dy ∘ B_dx * A_dy */
342
343 adx_bdy = _cairo_int32x32_64_mul (adx, bdy)((int64_t) (adx) * (bdy));
344 bdx_ady = _cairo_int32x32_64_mul (bdx, ady)((int64_t) (bdx) * (ady));
345
346 return _cairo_int64_cmp (adx_bdy, bdx_ady)((adx_bdy) == (bdx_ady) ? 0 : (adx_bdy) < (bdx_ady) ? -1 :
1);
347 } else
348 return _cairo_int128_cmp (A, B);
349 case HAVE_DX_ADX:
350 /* A_dy * (A_x - B_x) ∘ - (Y - A_y) * A_dx */
351 if ((-adx ^ dx) < 0) {
352 return dx;
353 } else {
354 cairo_int64_t ady_dx, dy_adx;
355
356 ady_dx = _cairo_int32x32_64_mul (ady, dx)((int64_t) (ady) * (dx));
357 dy_adx = _cairo_int32x32_64_mul (a->edge.line.p1.y - y, adx)((int64_t) (a->edge.line.p1.y - y) * (adx));
358
359 return _cairo_int64_cmp (ady_dx, dy_adx)((ady_dx) == (dy_adx) ? 0 : (ady_dx) < (dy_adx) ? -1 : 1);
360 }
361 case HAVE_DX_BDX:
362 /* B_dy * (A_x - B_x) ∘ (Y - B_y) * B_dx */
363 if ((bdx ^ dx) < 0) {
364 return dx;
365 } else {
366 cairo_int64_t bdy_dx, dy_bdx;
367
368 bdy_dx = _cairo_int32x32_64_mul (bdy, dx)((int64_t) (bdy) * (dx));
369 dy_bdx = _cairo_int32x32_64_mul (y - b->edge.line.p1.y, bdx)((int64_t) (y - b->edge.line.p1.y) * (bdx));
370
371 return _cairo_int64_cmp (bdy_dx, dy_bdx)((bdy_dx) == (dy_bdx) ? 0 : (bdy_dx) < (dy_bdx) ? -1 : 1);
372 }
373 case HAVE_ALL:
374 /* XXX try comparing (a->edge.line.p2.x - b->edge.line.p2.x) et al */
375 return _cairo_int128_cmp (L, _cairo_int128_sub (B, A)_cairo_uint128_sub(B,A));
376 }
377#undef B
378#undef A
379#undef L
380}
381
382/*
383 * We need to compare the x-coordinate of a line for a particular y wrt to a
384 * given x, without loss of precision.
385 *
386 * The x-coordinate along an edge for a given y is:
387 * X = A_x + (Y - A_y) * A_dx / A_dy
388 *
389 * So the inequality we wish to test is:
390 * A_x + (Y - A_y) * A_dx / A_dy ∘ X
391 * where ∘ is our inequality operator.
392 *
393 * By construction, we know that A_dy (and (Y - A_y)) are
394 * all positive, so we can rearrange it thus without causing a sign change:
395 * (Y - A_y) * A_dx ∘ (X - A_x) * A_dy
396 *
397 * Given the assumption that all the deltas fit within 32 bits, we can compute
398 * this comparison directly using 64 bit arithmetic.
399 *
400 * See the similar discussion for _slope_compare() and
401 * edges_compare_x_for_y_general().
402 */
403static int
404edge_compare_for_y_against_x (const cairo_bo_edge_t *a,
405 int32_t y,
406 int32_t x)
407{
408 int32_t adx, ady;
409 int32_t dx, dy;
410 cairo_int64_t L, R;
411
412 if (x < a->edge.line.p1.x && x < a->edge.line.p2.x)
413 return 1;
414 if (x > a->edge.line.p1.x && x > a->edge.line.p2.x)
415 return -1;
416
417 adx = a->edge.line.p2.x - a->edge.line.p1.x;
418 dx = x - a->edge.line.p1.x;
419
420 if (adx == 0)
421 return -dx;
422 if (dx == 0 || (adx ^ dx) < 0)
423 return adx;
424
425 dy = y - a->edge.line.p1.y;
426 ady = a->edge.line.p2.y - a->edge.line.p1.y;
427
428 L = _cairo_int32x32_64_mul (dy, adx)((int64_t) (dy) * (adx));
429 R = _cairo_int32x32_64_mul (dx, ady)((int64_t) (dx) * (ady));
430
431 return _cairo_int64_cmp (L, R)((L) == (R) ? 0 : (L) < (R) ? -1 : 1);
432}
433
434static int
435edges_compare_x_for_y (const cairo_bo_edge_t *a,
436 const cairo_bo_edge_t *b,
437 int32_t y)
438{
439 /* If the sweep-line is currently on an end-point of a line,
440 * then we know its precise x value (and considering that we often need to
441 * compare events at end-points, this happens frequently enough to warrant
442 * special casing).
443 */
444 enum {
445 HAVE_NEITHER = 0x0,
446 HAVE_AX = 0x1,
447 HAVE_BX = 0x2,
448 HAVE_BOTH = HAVE_AX | HAVE_BX
449 } have_ax_bx = HAVE_BOTH;
450 int32_t ax = 0, bx = 0;
451
452 if (y == a->edge.line.p1.y)
453 ax = a->edge.line.p1.x;
454 else if (y == a->edge.line.p2.y)
455 ax = a->edge.line.p2.x;
456 else
457 have_ax_bx &= ~HAVE_AX;
458
459 if (y == b->edge.line.p1.y)
460 bx = b->edge.line.p1.x;
461 else if (y == b->edge.line.p2.y)
462 bx = b->edge.line.p2.x;
463 else
464 have_ax_bx &= ~HAVE_BX;
465
466 switch (have_ax_bx) {
467 default:
468 case HAVE_NEITHER:
469 return edges_compare_x_for_y_general (a, b, y);
470 case HAVE_AX:
471 return -edge_compare_for_y_against_x (b, y, ax);
472 case HAVE_BX:
473 return edge_compare_for_y_against_x (a, y, bx);
474 case HAVE_BOTH:
475 return ax - bx;
476 }
477}
478
479static inline int
480_line_equal (const cairo_line_t *a, const cairo_line_t *b)
481{
482 return a->p1.x == b->p1.x && a->p1.y == b->p1.y &&
483 a->p2.x == b->p2.x && a->p2.y == b->p2.y;
484}
485
486static int
487_cairo_bo_sweep_line_compare_edges (cairo_bo_sweep_line_t *sweep_line,
488 const cairo_bo_edge_t *a,
489 const cairo_bo_edge_t *b)
490{
491 int cmp;
492
493 /* compare the edges if not identical */
494 if (! _line_equal (&a->edge.line, &b->edge.line)) {
495 cmp = edges_compare_x_for_y (a, b, sweep_line->current_y);
496 if (cmp)
497 return cmp;
498
499 /* The two edges intersect exactly at y, so fall back on slope
500 * comparison. We know that this compare_edges function will be
501 * called only when starting a new edge, (not when stopping an
502 * edge), so we don't have to worry about conditionally inverting
503 * the sense of _slope_compare. */
504 cmp = _slope_compare (a, b);
505 if (cmp)
506 return cmp;
507 }
508
509 /* We've got two collinear edges now. */
510 return b->edge.bottom - a->edge.bottom;
511}
512
513static inline cairo_int64_t
514det32_64 (int32_t a, int32_t b,
515 int32_t c, int32_t d)
516{
517 /* det = a * d - b * c */
518 return _cairo_int64_sub (_cairo_int32x32_64_mul (a, d),((((int64_t) (a) * (d))) - (((int64_t) (b) * (c))))
519 _cairo_int32x32_64_mul (b, c))((((int64_t) (a) * (d))) - (((int64_t) (b) * (c))));
520}
521
522static inline cairo_int128_t
523det64x32_128 (cairo_int64_t a, int32_t b,
524 cairo_int64_t c, int32_t d)
525{
526 /* det = a * d - b * c */
527 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))))
528 _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))));
529}
530
531static inline cairo_bo_intersect_ordinate_t
532round_to_nearest (cairo_quorem64_t d,
533 cairo_int64_t den)
534{
535 cairo_bo_intersect_ordinate_t ordinate;
536 int32_t quo = d.quo;
537 cairo_int64_t drem_2 = _cairo_int64_mul (d.rem, _cairo_int32_to_int64 (2))((d.rem) * (((int64_t) (2))));
538
539 /* assert (! _cairo_int64_negative (den));*/
540
541 if (_cairo_int64_lt (drem_2, _cairo_int64_negate (den))((drem_2) < ((-(den))))) {
542 quo -= 1;
543 drem_2 = _cairo_int64_negate (drem_2)(-(drem_2));
544 } else if (_cairo_int64_le (den, drem_2)(!((drem_2) < (den)))) {
545 quo += 1;
546 drem_2 = _cairo_int64_negate (drem_2)(-(drem_2));
547 }
548
549 ordinate.ordinate = quo;
550 ordinate.approx = _cairo_int64_is_zero (drem_2)((drem_2) == 0) ? EXACT : _cairo_int64_negative (drem_2)((drem_2) < 0) ? EXCESS : DEFAULT;
551
552 return ordinate;
553}
554
555/* Compute the intersection of two lines as defined by two edges. The
556 * result is provided as a coordinate pair of 128-bit integers.
557 *
558 * Returns %CAIRO_BO_STATUS_INTERSECTION if there is an intersection or
559 * %CAIRO_BO_STATUS_PARALLEL if the two lines are exactly parallel.
560 */
561static cairo_bool_t
562intersect_lines (cairo_bo_edge_t *a,
563 cairo_bo_edge_t *b,
564 cairo_bo_intersect_point_t *intersection)
565{
566 cairo_int64_t a_det, b_det;
567
568 /* XXX: We're assuming here that dx and dy will still fit in 32
569 * bits. That's not true in general as there could be overflow. We
570 * should prevent that before the tessellation algorithm begins.
571 * What we're doing to mitigate this is to perform clamping in
572 * cairo_bo_tessellate_polygon().
573 */
574 int32_t dx1 = a->edge.line.p1.x - a->edge.line.p2.x;
575 int32_t dy1 = a->edge.line.p1.y - a->edge.line.p2.y;
576
577 int32_t dx2 = b->edge.line.p1.x - b->edge.line.p2.x;
578 int32_t dy2 = b->edge.line.p1.y - b->edge.line.p2.y;
579
580 cairo_int64_t den_det;
581 cairo_int64_t R;
582 cairo_quorem64_t qr;
583
584 den_det = det32_64 (dx1, dy1, dx2, dy2);
585
586 /* Q: Can we determine that the lines do not intersect (within range)
587 * much more cheaply than computing the intersection point i.e. by
588 * avoiding the division?
589 *
590 * X = ax + t * adx = bx + s * bdx;
591 * Y = ay + t * ady = by + s * bdy;
592 * ∴ t * (ady*bdx - bdy*adx) = bdx * (by - ay) + bdy * (ax - bx)
593 * => t * L = R
594 *
595 * Therefore we can reject any intersection (under the criteria for
596 * valid intersection events) if:
597 * L^R < 0 => t < 0, or
598 * L<R => t > 1
599 *
600 * (where top/bottom must at least extend to the line endpoints).
601 *
602 * A similar substitution can be performed for s, yielding:
603 * s * (ady*bdx - bdy*adx) = ady * (ax - bx) - adx * (ay - by)
604 */
605 R = det32_64 (dx2, dy2,
606 b->edge.line.p1.x - a->edge.line.p1.x,
607 b->edge.line.p1.y - a->edge.line.p1.y);
608 if (_cairo_int64_le (den_det, R)(!((R) < (den_det))))
609 return FALSE0;
610
611 R = det32_64 (dy1, dx1,
612 a->edge.line.p1.y - b->edge.line.p1.y,
613 a->edge.line.p1.x - b->edge.line.p1.x);
614 if (_cairo_int64_le (den_det, R)(!((R) < (den_det))))
615 return FALSE0;
616
617 /* We now know that the two lines should intersect within range. */
618
619 a_det = det32_64 (a->edge.line.p1.x, a->edge.line.p1.y,
620 a->edge.line.p2.x, a->edge.line.p2.y);
621 b_det = det32_64 (b->edge.line.p1.x, b->edge.line.p1.y,
622 b->edge.line.p2.x, b->edge.line.p2.y);
623
624 /* x = det (a_det, dx1, b_det, dx2) / den_det */
625 qr = _cairo_int_96by64_32x64_divrem (det64x32_128 (a_det, dx1,
626 b_det, dx2),
627 den_det);
628 if (_cairo_int64_eq (qr.rem, den_det)((qr.rem) == (den_det)))
629 return FALSE0;
630
631 intersection->x = round_to_nearest (qr, den_det);
632
633 /* y = det (a_det, dy1, b_det, dy2) / den_det */
634 qr = _cairo_int_96by64_32x64_divrem (det64x32_128 (a_det, dy1,
635 b_det, dy2),
636 den_det);
637 if (_cairo_int64_eq (qr.rem, den_det)((qr.rem) == (den_det)))
638 return FALSE0;
639
640 intersection->y = round_to_nearest (qr, den_det);
641
642 return TRUE1;
643}
644
645static int
646_cairo_bo_intersect_ordinate_32_compare (cairo_bo_intersect_ordinate_t a,
647 int32_t b)
648{
649 /* First compare the quotient */
650 if (a.ordinate > b)
651 return +1;
652 if (a.ordinate < b)
653 return -1;
654
655 return a.approx; /* == EXCESS ? -1 : a.approx == EXACT ? 0 : 1;*/
656}
657
658/* Does the given edge contain the given point. The point must already
659 * be known to be contained within the line determined by the edge,
660 * (most likely the point results from an intersection of this edge
661 * with another).
662 *
663 * If we had exact arithmetic, then this function would simply be a
664 * matter of examining whether the y value of the point lies within
665 * the range of y values of the edge. But since intersection points
666 * are not exact due to being rounded to the nearest integer within
667 * the available precision, we must also examine the x value of the
668 * point.
669 *
670 * The definition of "contains" here is that the given intersection
671 * point will be seen by the sweep line after the start event for the
672 * given edge and before the stop event for the edge. See the comments
673 * in the implementation for more details.
674 */
675static cairo_bool_t
676_cairo_bo_edge_contains_intersect_point (cairo_bo_edge_t *edge,
677 cairo_bo_intersect_point_t *point)
678{
679 return _cairo_bo_intersect_ordinate_32_compare (point->y,
680 edge->edge.bottom) < 0;
681}
682
683/* Compute the intersection of two edges. The result is provided as a
684 * coordinate pair of 128-bit integers.
685 *
686 * Returns %CAIRO_BO_STATUS_INTERSECTION if there is an intersection
687 * that is within both edges, %CAIRO_BO_STATUS_NO_INTERSECTION if the
688 * intersection of the lines defined by the edges occurs outside of
689 * one or both edges, and %CAIRO_BO_STATUS_PARALLEL if the two edges
690 * are exactly parallel.
691 *
692 * Note that when determining if a candidate intersection is "inside"
693 * an edge, we consider both the infinitesimal shortening and the
694 * infinitesimal tilt rules described by John Hobby. Specifically, if
695 * the intersection is exactly the same as an edge point, it is
696 * effectively outside (no intersection is returned). Also, if the
697 * intersection point has the same
698 */
699static cairo_bool_t
700_cairo_bo_edge_intersect (cairo_bo_edge_t *a,
701 cairo_bo_edge_t *b,
702 cairo_bo_intersect_point_t *intersection)
703{
704 if (! intersect_lines (a, b, intersection))
705 return FALSE0;
706
707 if (! _cairo_bo_edge_contains_intersect_point (a, intersection))
708 return FALSE0;
709
710 if (! _cairo_bo_edge_contains_intersect_point (b, intersection))
711 return FALSE0;
712
713 return TRUE1;
714}
715
716static inline int
717cairo_bo_event_compare (const cairo_bo_event_t *a,
718 const cairo_bo_event_t *b)
719{
720 int cmp;
721
722 cmp = _cairo_bo_point32_compare (&a->point, &b->point);
723 if (cmp)
724 return cmp;
725
726 cmp = a->type - b->type;
727 if (cmp)
728 return cmp;
729
730 return a < b ? -1 : a == b ? 0 : 1;
731}
732
733static inline void
734_pqueue_init (pqueue_t *pq)
735{
736 pq->max_size = ARRAY_LENGTH (pq->elements_embedded)((int) (sizeof (pq->elements_embedded) / sizeof (pq->elements_embedded
[0])));
737 pq->size = 0;
738
739 pq->elements = pq->elements_embedded;
740}
741
742static inline void
743_pqueue_fini (pqueue_t *pq)
744{
745 if (pq->elements != pq->elements_embedded)
746 free (pq->elements);
747}
748
749static cairo_status_t
750_pqueue_grow (pqueue_t *pq)
751{
752 cairo_bo_event_t **new_elements;
753 pq->max_size *= 2;
754
755 if (pq->elements == pq->elements_embedded) {
756 new_elements = _cairo_malloc_ab (pq->max_size,
757 sizeof (cairo_bo_event_t *));
758 if (unlikely (new_elements == NULL)(__builtin_expect (!!(new_elements == ((void*)0)), 0)))
759 return _cairo_error (CAIRO_STATUS_NO_MEMORY);
760
761 memcpy (new_elements, pq->elements_embedded,
762 sizeof (pq->elements_embedded));
763 } else {
764 new_elements = _cairo_realloc_ab (pq->elements,
765 pq->max_size,
766 sizeof (cairo_bo_event_t *));
767 if (unlikely (new_elements == NULL)(__builtin_expect (!!(new_elements == ((void*)0)), 0)))
768 return _cairo_error (CAIRO_STATUS_NO_MEMORY);
769 }
770
771 pq->elements = new_elements;
772 return CAIRO_STATUS_SUCCESS;
773}
774
775static inline cairo_status_t
776_pqueue_push (pqueue_t *pq, cairo_bo_event_t *event)
777{
778 cairo_bo_event_t **elements;
779 int i, parent;
780
781 if (unlikely (pq->size + 1 == pq->max_size)(__builtin_expect (!!(pq->size + 1 == pq->max_size), 0)
)) {
782 cairo_status_t status;
783
784 status = _pqueue_grow (pq);
785 if (unlikely (status)(__builtin_expect (!!(status), 0)))
786 return status;
787 }
788
789 elements = pq->elements;
790
791 for (i = ++pq->size;
792 i != PQ_FIRST_ENTRY1 &&
793 cairo_bo_event_compare (event,
794 elements[parent = PQ_PARENT_INDEX (i)((i) >> 1)]) < 0;
795 i = parent)
796 {
797 elements[i] = elements[parent];
798 }
799
800 elements[i] = event;
801
802 return CAIRO_STATUS_SUCCESS;
803}
804
805static inline void
806_pqueue_pop (pqueue_t *pq)
807{
808 cairo_bo_event_t **elements = pq->elements;
809 cairo_bo_event_t *tail;
810 int child, i;
811
812 tail = elements[pq->size--];
813 if (pq->size == 0) {
814 elements[PQ_FIRST_ENTRY1] = NULL((void*)0);
815 return;
816 }
817
818 for (i = PQ_FIRST_ENTRY1;
819 (child = PQ_LEFT_CHILD_INDEX (i)((i) << 1)) <= pq->size;
820 i = child)
821 {
822 if (child != pq->size &&
823 cairo_bo_event_compare (elements[child+1],
824 elements[child]) < 0)
825 {
826 child++;
827 }
828
829 if (cairo_bo_event_compare (elements[child], tail) >= 0)
830 break;
831
832 elements[i] = elements[child];
833 }
834 elements[i] = tail;
835}
836
837static inline cairo_status_t
838_cairo_bo_event_queue_insert (cairo_bo_event_queue_t *queue,
839 cairo_bo_event_type_t type,
840 cairo_bo_edge_t *e1,
841 cairo_bo_edge_t *e2,
842 const cairo_bo_intersect_point_t *point)
843{
844 cairo_bo_queue_event_t *event;
845
846 event = _cairo_freepool_alloc (&queue->pool);
847 if (unlikely (event == NULL)(__builtin_expect (!!(event == ((void*)0)), 0)))
848 return _cairo_error (CAIRO_STATUS_NO_MEMORY);
849
850 event->type = type;
851 event->e1 = e1;
852 event->e2 = e2;
853 event->point = *point;
854
855 return _pqueue_push (&queue->pqueue, (cairo_bo_event_t *) event);
856}
857
858static void
859_cairo_bo_event_queue_delete (cairo_bo_event_queue_t *queue,
860 cairo_bo_event_t *event)
861{
862 _cairo_freepool_free (&queue->pool, event);
863}
864
865static cairo_bo_event_t *
866_cairo_bo_event_dequeue (cairo_bo_event_queue_t *event_queue)
867{
868 cairo_bo_event_t *event, *cmp;
869
870 event = event_queue->pqueue.elements[PQ_FIRST_ENTRY1];
871 cmp = *event_queue->start_events;
872 if (event == NULL((void*)0) ||
873 (cmp != NULL((void*)0) && cairo_bo_event_compare (cmp, event) < 0))
874 {
875 event = cmp;
876 event_queue->start_events++;
877 }
878 else
879 {
880 _pqueue_pop (&event_queue->pqueue);
881 }
882
883 return event;
884}
885
886CAIRO_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); }
25
←
The value 0 is assigned to 'i'
→
26
←
Loop condition is true. Entering loop body
→
27
←
1st function call argument is an uninitialized value
887 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); }
888 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); }
889
890static void
891_cairo_bo_event_queue_init (cairo_bo_event_queue_t *event_queue,
892 cairo_bo_event_t **start_events,
893 int num_events)
894{
895 _cairo_bo_event_queue_sort (start_events, num_events);
24
←
Calling '_cairo_bo_event_queue_sort'
→
896 start_events[num_events] = NULL((void*)0);
897
898 event_queue->start_events = start_events;
899
900 _cairo_freepool_init (&event_queue->pool,
901 sizeof (cairo_bo_queue_event_t));
902 _pqueue_init (&event_queue->pqueue);
903 event_queue->pqueue.elements[PQ_FIRST_ENTRY1] = NULL((void*)0);
904}
905
906static cairo_status_t
907event_queue_insert_stop (cairo_bo_event_queue_t *event_queue,
908 cairo_bo_edge_t *edge)
909{
910 cairo_bo_intersect_point_t point;
911
912 point.y.ordinate = edge->edge.bottom;
913 point.y.approx = EXACT;
914 point.x.ordinate = _line_compute_intersection_x_for_y (&edge->edge.line,
915 point.y.ordinate);
916 point.x.approx = EXACT;
917
918 return _cairo_bo_event_queue_insert (event_queue,
919 CAIRO_BO_EVENT_TYPE_STOP,
920 edge, NULL((void*)0),
921 &point);
922}
923
924static void
925_cairo_bo_event_queue_fini (cairo_bo_event_queue_t *event_queue)
926{
927 _pqueue_fini (&event_queue->pqueue);
928 _cairo_freepool_fini (&event_queue->pool);
929}
930
931static inline cairo_status_t
932event_queue_insert_if_intersect_below_current_y (cairo_bo_event_queue_t *event_queue,
933 cairo_bo_edge_t *left,
934 cairo_bo_edge_t *right)
935{
936 cairo_bo_intersect_point_t intersection;
937
938 if (_line_equal (&left->edge.line, &right->edge.line))
939 return CAIRO_STATUS_SUCCESS;
940
941 /* The names "left" and "right" here are correct descriptions of
942 * the order of the two edges within the active edge list. So if a
943 * slope comparison also puts left less than right, then we know
944 * that the intersection of these two segments has already
945 * occurred before the current sweep line position. */
946 if (_slope_compare (left, right) <= 0)
947 return CAIRO_STATUS_SUCCESS;
948
949 if (! _cairo_bo_edge_intersect (left, right, &intersection))
950 return CAIRO_STATUS_SUCCESS;
951
952 return _cairo_bo_event_queue_insert (event_queue,
953 CAIRO_BO_EVENT_TYPE_INTERSECTION,
954 left, right,
955 &intersection);
956}
957
958static void
959_cairo_bo_sweep_line_init (cairo_bo_sweep_line_t *sweep_line)
960{
961 sweep_line->head = NULL((void*)0);
962 sweep_line->current_y = INT32_MIN(-2147483647-1);
963 sweep_line->current_edge = NULL((void*)0);
964}
965
966static cairo_status_t
967sweep_line_insert (cairo_bo_sweep_line_t *sweep_line,
968 cairo_bo_edge_t *edge)
969{
970 if (sweep_line->current_edge != NULL((void*)0)) {
971 cairo_bo_edge_t *prev, *next;
972 int cmp;
973
974 cmp = _cairo_bo_sweep_line_compare_edges (sweep_line,
975 sweep_line->current_edge,
976 edge);
977 if (cmp < 0) {
978 prev = sweep_line->current_edge;
979 next = prev->next;
980 while (next != NULL((void*)0) &&
981 _cairo_bo_sweep_line_compare_edges (sweep_line,
982 next, edge) < 0)
983 {
984 prev = next, next = prev->next;
985 }
986
987 prev->next = edge;
988 edge->prev = prev;
989 edge->next = next;
990 if (next != NULL((void*)0))
991 next->prev = edge;
992 } else if (cmp > 0) {
993 next = sweep_line->current_edge;
994 prev = next->prev;
995 while (prev != NULL((void*)0) &&
996 _cairo_bo_sweep_line_compare_edges (sweep_line,
997 prev, edge) > 0)
998 {
999 next = prev, prev = next->prev;
1000 }
1001
1002 next->prev = edge;
1003 edge->next = next;
1004 edge->prev = prev;
1005 if (prev != NULL((void*)0))
1006 prev->next = edge;
1007 else
1008 sweep_line->head = edge;
1009 } else {
1010 prev = sweep_line->current_edge;
1011 edge->prev = prev;
1012 edge->next = prev->next;
1013 if (prev->next != NULL((void*)0))
1014 prev->next->prev = edge;
1015 prev->next = edge;
1016 }
1017 } else {
1018 sweep_line->head = edge;
1019 }
1020
1021 sweep_line->current_edge = edge;
1022
1023 return CAIRO_STATUS_SUCCESS;
1024}
1025
1026static void
1027_cairo_bo_sweep_line_delete (cairo_bo_sweep_line_t *sweep_line,
1028 cairo_bo_edge_t *edge)
1029{
1030 if (edge->prev != NULL((void*)0))
1031 edge->prev->next = edge->next;
1032 else
1033 sweep_line->head = edge->next;
1034
1035 if (edge->next != NULL((void*)0))
1036 edge->next->prev = edge->prev;
1037
1038 if (sweep_line->current_edge == edge)
1039 sweep_line->current_edge = edge->prev ? edge->prev : edge->next;
1040}
1041
1042static void
1043_cairo_bo_sweep_line_swap (cairo_bo_sweep_line_t *sweep_line,
1044 cairo_bo_edge_t *left,
1045 cairo_bo_edge_t *right)
1046{
1047 if (left->prev != NULL((void*)0))
1048 left->prev->next = right;
1049 else
1050 sweep_line->head = right;
1051
1052 if (right->next != NULL((void*)0))
1053 right->next->prev = left;
1054
1055 left->next = right->next;
1056 right->next = left;
1057
1058 right->prev = left->prev;
1059 left->prev = right;
1060}
1061
1062static inline cairo_bool_t
1063edges_colinear (const cairo_bo_edge_t *a, const cairo_bo_edge_t *b)
1064{
1065 if (_line_equal (&a->edge.line, &b->edge.line))
1066 return TRUE1;
1067
1068 if (_slope_compare (a, b))
1069 return FALSE0;
1070
1071 /* The choice of y is not truly arbitrary since we must guarantee that it
1072 * is greater than the start of either line.
1073 */
1074 if (a->edge.line.p1.y == b->edge.line.p1.y) {
1075 return a->edge.line.p1.x == b->edge.line.p1.x;
1076 } else if (a->edge.line.p1.y < b->edge.line.p1.y) {
1077 return edge_compare_for_y_against_x (b,
1078 a->edge.line.p1.y,
1079 a->edge.line.p1.x) == 0;
1080 } else {
1081 return edge_compare_for_y_against_x (a,
1082 b->edge.line.p1.y,
1083 b->edge.line.p1.x) == 0;
1084 }
1085}
1086
1087static void
1088edges_end (cairo_bo_edge_t *left,
1089 int32_t bot,
1090 cairo_polygon_t *polygon)
1091{
1092 cairo_bo_deferred_t *l = &left->deferred;
1093 cairo_bo_edge_t *right = l->other;
1094
1095 assert(right->deferred.other == NULL)((void) sizeof ((right->deferred.other == ((void*)0)) ? 1 :
0), __extension__ ({ if (right->deferred.other == ((void*
)0)) ; else __assert_fail ("right->deferred.other == NULL"
, "/root/firefox-clang/gfx/cairo/cairo/src/cairo-polygon-intersect.c"
, 1095, __extension__ __PRETTY_FUNCTION__); }));
1096 if (likely (l->top < bot)(__builtin_expect (!!(l->top < bot), 1))) {
1097 _cairo_polygon_add_line (polygon, &left->edge.line, l->top, bot, 1);
1098 _cairo_polygon_add_line (polygon, &right->edge.line, l->top, bot, -1);
1099 }
1100
1101 l->other = NULL((void*)0);
1102}
1103
1104static inline void
1105edges_start_or_continue (cairo_bo_edge_t *left,
1106 cairo_bo_edge_t *right,
1107 int top,
1108 cairo_polygon_t *polygon)
1109{
1110 assert (right != NULL)((void) sizeof ((right != ((void*)0)) ? 1 : 0), __extension__
({ if (right != ((void*)0)) ; else __assert_fail ("right != NULL"
, "/root/firefox-clang/gfx/cairo/cairo/src/cairo-polygon-intersect.c"
, 1110, __extension__ __PRETTY_FUNCTION__); }));
1111 assert (right->deferred.other == NULL)((void) sizeof ((right->deferred.other == ((void*)0)) ? 1 :
0), __extension__ ({ if (right->deferred.other == ((void*
)0)) ; else __assert_fail ("right->deferred.other == NULL"
, "/root/firefox-clang/gfx/cairo/cairo/src/cairo-polygon-intersect.c"
, 1111, __extension__ __PRETTY_FUNCTION__); }));
1112
1113 if (left->deferred.other == right)
1114 return;
1115
1116 if (left->deferred.other != NULL((void*)0)) {
1117 if (edges_colinear (left->deferred.other, right)) {
1118 cairo_bo_edge_t *old = left->deferred.other;
1119
1120 /* continuation on right, extend right to cover both */
1121 assert (old->deferred.other == NULL)((void) sizeof ((old->deferred.other == ((void*)0)) ? 1 : 0
), __extension__ ({ if (old->deferred.other == ((void*)0))
; else __assert_fail ("old->deferred.other == NULL", "/root/firefox-clang/gfx/cairo/cairo/src/cairo-polygon-intersect.c"
, 1121, __extension__ __PRETTY_FUNCTION__); }));
1122 assert (old->edge.line.p2.y > old->edge.line.p1.y)((void) sizeof ((old->edge.line.p2.y > old->edge.line
.p1.y) ? 1 : 0), __extension__ ({ if (old->edge.line.p2.y >
old->edge.line.p1.y) ; else __assert_fail ("old->edge.line.p2.y > old->edge.line.p1.y"
, "/root/firefox-clang/gfx/cairo/cairo/src/cairo-polygon-intersect.c"
, 1122, __extension__ __PRETTY_FUNCTION__); }));
1123
1124 if (old->edge.line.p1.y < right->edge.line.p1.y)
1125 right->edge.line.p1 = old->edge.line.p1;
1126 if (old->edge.line.p2.y > right->edge.line.p2.y)
1127 right->edge.line.p2 = old->edge.line.p2;
1128 left->deferred.other = right;
1129 return;
1130 }
1131
1132 edges_end (left, top, polygon);
1133 }
1134
1135 if (! edges_colinear (left, right)) {
1136 left->deferred.top = top;
1137 left->deferred.other = right;
1138 }
1139}
1140
1141#define is_zero(w)((w)[0] == 0 || (w)[1] == 0) ((w)[0] == 0 || (w)[1] == 0)
1142
1143static inline void
1144active_edges (cairo_bo_edge_t *left,
1145 int32_t top,
1146 cairo_polygon_t *polygon)
1147{
1148 cairo_bo_edge_t *right;
1149 int winding[2] = {0, 0};
1150
1151 /* Yes, this is naive. Consider this a placeholder. */
1152
1153 while (left != NULL((void*)0)) {
1154 assert (is_zero (winding))((void) sizeof ((((winding)[0] == 0 || (winding)[1] == 0)) ? 1
: 0), __extension__ ({ if (((winding)[0] == 0 || (winding)[1
] == 0)) ; else __assert_fail ("is_zero (winding)", "/root/firefox-clang/gfx/cairo/cairo/src/cairo-polygon-intersect.c"
, 1154, __extension__ __PRETTY_FUNCTION__); }));
1155
1156 do {
1157 winding[left->a_or_b] += left->edge.dir;
1158 if (! is_zero (winding)((winding)[0] == 0 || (winding)[1] == 0))
1159 break;
1160
1161 if unlikely ((left->deferred.other))(__builtin_expect (!!((left->deferred.other)), 0))
1162 edges_end (left, top, polygon);
1163
1164 left = left->next;
1165 if (! left)
1166 return;
1167 } while (1);
1168
1169 right = left->next;
1170 while (right) {
1171 if unlikely ((right->deferred.other))(__builtin_expect (!!((right->deferred.other)), 0))
1172 edges_end (right, top, polygon);
1173
1174 winding[right->a_or_b] += right->edge.dir;
1175 if (is_zero (winding)((winding)[0] == 0 || (winding)[1] == 0)) {
1176 if (right->next == NULL((void*)0) ||
1177 ! edges_colinear (right, right->next))
1178 break;
1179 }
1180
1181 right = right->next;
1182 };
1183 if (! right)
1184 return;
1185
1186 edges_start_or_continue (left, right, top, polygon);
1187
1188 left = right->next;
1189 }
1190}
1191
1192static cairo_status_t
1193intersection_sweep (cairo_bo_event_t **start_events,
1194 int num_events,
1195 cairo_polygon_t *polygon)
1196{
1197 cairo_status_t status = CAIRO_STATUS_SUCCESS; /* silence compiler */
1198 cairo_bo_event_queue_t event_queue;
1199 cairo_bo_sweep_line_t sweep_line;
1200 cairo_bo_event_t *event;
1201 cairo_bo_edge_t *left, *right;
1202 cairo_bo_edge_t *e1, *e2;
1203
1204 _cairo_bo_event_queue_init (&event_queue, start_events, num_events);
23
←
Calling '_cairo_bo_event_queue_init'
→
1205 _cairo_bo_sweep_line_init (&sweep_line);
1206
1207 while ((event = _cairo_bo_event_dequeue (&event_queue))) {
1208 if (event->point.y.ordinate != sweep_line.current_y) {
1209 active_edges (sweep_line.head,
1210 sweep_line.current_y,
1211 polygon);
1212 sweep_line.current_y = event->point.y.ordinate;
1213 }
1214
1215 switch (event->type) {
1216 case CAIRO_BO_EVENT_TYPE_START:
1217 e1 = &((cairo_bo_start_event_t *) event)->edge;
1218
1219 status = sweep_line_insert (&sweep_line, e1);
1220 if (unlikely (status)(__builtin_expect (!!(status), 0)))
1221 goto unwind;
1222
1223 status = event_queue_insert_stop (&event_queue, e1);
1224 if (unlikely (status)(__builtin_expect (!!(status), 0)))
1225 goto unwind;
1226
1227 left = e1->prev;
1228 right = e1->next;
1229
1230 if (left != NULL((void*)0)) {
1231 status = event_queue_insert_if_intersect_below_current_y (&event_queue, left, e1);
1232 if (unlikely (status)(__builtin_expect (!!(status), 0)))
1233 goto unwind;
1234 }
1235
1236 if (right != NULL((void*)0)) {
1237 status = event_queue_insert_if_intersect_below_current_y (&event_queue, e1, right);
1238 if (unlikely (status)(__builtin_expect (!!(status), 0)))
1239 goto unwind;
1240 }
1241
1242 break;
1243
1244 case CAIRO_BO_EVENT_TYPE_STOP:
1245 e1 = ((cairo_bo_queue_event_t *) event)->e1;
1246 _cairo_bo_event_queue_delete (&event_queue, event);
1247
1248 if (e1->deferred.other)
1249 edges_end (e1, sweep_line.current_y, polygon);
1250
1251 left = e1->prev;
1252 right = e1->next;
1253
1254 _cairo_bo_sweep_line_delete (&sweep_line, e1);
1255
1256 if (left != NULL((void*)0) && right != NULL((void*)0)) {
1257 status = event_queue_insert_if_intersect_below_current_y (&event_queue, left, right);
1258 if (unlikely (status)(__builtin_expect (!!(status), 0)))
1259 goto unwind;
1260 }
1261
1262 break;
1263
1264 case CAIRO_BO_EVENT_TYPE_INTERSECTION:
1265 e1 = ((cairo_bo_queue_event_t *) event)->e1;
1266 e2 = ((cairo_bo_queue_event_t *) event)->e2;
1267 _cairo_bo_event_queue_delete (&event_queue, event);
1268
1269 /* skip this intersection if its edges are not adjacent */
1270 if (e2 != e1->next)
1271 break;
1272
1273 if (e1->deferred.other)
1274 edges_end (e1, sweep_line.current_y, polygon);
1275 if (e2->deferred.other)
1276 edges_end (e2, sweep_line.current_y, polygon);
1277
1278 left = e1->prev;
1279 right = e2->next;
1280
1281 _cairo_bo_sweep_line_swap (&sweep_line, e1, e2);
1282
1283 /* after the swap e2 is left of e1 */
1284
1285 if (left != NULL((void*)0)) {
1286 status = event_queue_insert_if_intersect_below_current_y (&event_queue, left, e2);
1287 if (unlikely (status)(__builtin_expect (!!(status), 0)))
1288 goto unwind;
1289 }
1290
1291 if (right != NULL((void*)0)) {
1292 status = event_queue_insert_if_intersect_below_current_y (&event_queue, e1, right);
1293 if (unlikely (status)(__builtin_expect (!!(status), 0)))
1294 goto unwind;
1295 }
1296
1297 break;
1298 }
1299 }
1300
1301 unwind:
1302 _cairo_bo_event_queue_fini (&event_queue);
1303
1304 return status;
1305}
1306
1307cairo_status_t
1308_cairo_polygon_intersect (cairo_polygon_t *a, int winding_a,
1309 cairo_polygon_t *b, int winding_b)
1310{
1311 cairo_status_t status;
1312 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))];
1313 cairo_bo_start_event_t *events;
1314 cairo_bo_event_t *stack_event_ptrs[ARRAY_LENGTH (stack_events)((int) (sizeof (stack_events) / sizeof (stack_events[0]))) + 1];
1315 cairo_bo_event_t **event_ptrs;
1316 int num_events;
1317 int i, j;
1318
1319 /* XXX lazy */
1320 if (winding_a != CAIRO_FILL_RULE_WINDING) {
7
←
Assuming 'winding_a' is equal to CAIRO_FILL_RULE_WINDING
→
8
←
Taking false branch
→
1321 status = _cairo_polygon_reduce (a, winding_a);
1322 if (unlikely (status)(__builtin_expect (!!(status), 0)))
1323 return status;
1324 }
1325
1326 if (winding_b
8.1
'winding_b' is equal to CAIRO_FILL_RULE_WINDING
 != CAIRO_FILL_RULE_WINDING) {
9
←
Taking false branch
→
1327 status = _cairo_polygon_reduce (b, winding_b);
1328 if (unlikely (status)(__builtin_expect (!!(status), 0)))
1329 return status;
1330 }
1331
1332 if (unlikely (0 == a->num_edges)(__builtin_expect (!!(0 == a->num_edges), 0)))
10
←
Assuming 0 is not equal to field 'num_edges'
→
11
←
Taking false branch
→
1333 return CAIRO_STATUS_SUCCESS;
1334
1335 if (unlikely (0 == b->num_edges)(__builtin_expect (!!(0 == b->num_edges), 0))) {
12
←
Assuming 0 is not equal to field 'num_edges'
→
13
←
Taking false branch
→
1336 a->num_edges = 0;
1337 return CAIRO_STATUS_SUCCESS;
1338 }
1339
1340 events = stack_events;
1341 event_ptrs = stack_event_ptrs;
1342 num_events = a->num_edges + b->num_edges;
1343 if (num_events > ARRAY_LENGTH (stack_events)((int) (sizeof (stack_events) / sizeof (stack_events[0])))) {
14
←
Assuming the condition is false
→
15
←
Taking false branch
→
1344 events = _cairo_malloc_ab_plus_c (num_events,
1345 sizeof (cairo_bo_start_event_t) +
1346 sizeof (cairo_bo_event_t *),
1347 sizeof (cairo_bo_event_t *));
1348 if (unlikely (events == NULL)(__builtin_expect (!!(events == ((void*)0)), 0)))
1349 return _cairo_error (CAIRO_STATUS_NO_MEMORY);
1350
1351 event_ptrs = (cairo_bo_event_t **) (events + num_events);
1352 }
1353
1354 j = 0;
1355 for (i = 0; i < a->num_edges; i++) {
16
←
Assuming 'i' is >= field 'num_edges'
→
17
←
Loop condition is false. Execution continues on line 1374
→
1356 event_ptrs[j] = (cairo_bo_event_t *) &events[j];
1357
1358 events[j].type = CAIRO_BO_EVENT_TYPE_START;
1359 events[j].point.y.ordinate = a->edges[i].top;
1360 events[j].point.y.approx = EXACT;
1361 events[j].point.x.ordinate =
1362 _line_compute_intersection_x_for_y (&a->edges[i].line,
1363 events[j].point.y.ordinate);
1364 events[j].point.x.approx = EXACT;
1365
1366 events[j].edge.a_or_b = 0;
1367 events[j].edge.edge = a->edges[i];
1368 events[j].edge.deferred.other = NULL((void*)0);
1369 events[j].edge.prev = NULL((void*)0);
1370 events[j].edge.next = NULL((void*)0);
1371 j++;
1372 }
1373
1374 for (i = 0; i < b->num_edges; i++) {
18
←
Assuming 'i' is >= field 'num_edges'
→
19
←
Loop condition is false. Execution continues on line 1392
→
1375 event_ptrs[j] = (cairo_bo_event_t *) &events[j];
1376
1377 events[j].type = CAIRO_BO_EVENT_TYPE_START;
1378 events[j].point.y.ordinate = b->edges[i].top;
1379 events[j].point.y.approx = EXACT;
1380 events[j].point.x.ordinate =
1381 _line_compute_intersection_x_for_y (&b->edges[i].line,
1382 events[j].point.y.ordinate);
1383 events[j].point.x.approx = EXACT;
1384
1385 events[j].edge.a_or_b = 1;
1386 events[j].edge.edge = b->edges[i];
1387 events[j].edge.deferred.other = NULL((void*)0);
1388 events[j].edge.prev = NULL((void*)0);
1389 events[j].edge.next = NULL((void*)0);
1390 j++;
1391 }
1392 assert (j == num_events)((void) sizeof ((j == num_events) ? 1 : 0), __extension__ ({ if
(j == num_events) ; else __assert_fail ("j == num_events", "/root/firefox-clang/gfx/cairo/cairo/src/cairo-polygon-intersect.c"
, 1392, __extension__ __PRETTY_FUNCTION__); }));
20
←
Assuming 'j' is equal to 'num_events'
→
21
←
Taking true branch
→
1393
1394#if 0
1395 {
1396 FILE *file = fopen ("clip_a.txt", "w");
1397 _cairo_debug_print_polygon (file, a);
1398 fclose (file);
1399 }
1400 {
1401 FILE *file = fopen ("clip_b.txt", "w");
1402 _cairo_debug_print_polygon (file, b);
1403 fclose (file);
1404 }
1405#endif
1406
1407 a->num_edges = 0;
1408 status = intersection_sweep (event_ptrs, num_events, a);
22
←
Calling 'intersection_sweep'
→
1409 if (events != stack_events)
1410 free (events);
1411
1412#if 0
1413 {
1414 FILE *file = fopen ("clip_result.txt", "w");
1415 _cairo_debug_print_polygon (file, a);
1416 fclose (file);
1417 }
1418#endif
1419
1420 return status;
1421}
1422
1423cairo_status_t
1424_cairo_polygon_intersect_with_boxes (cairo_polygon_t *polygon,
1425 cairo_fill_rule_t *winding,
1426 cairo_box_t *boxes,
1427 int num_boxes)
1428{
1429 cairo_polygon_t b;
1430 cairo_status_t status;
1431 int n;
1432
1433 if (num_boxes == 0) {
1
Assuming 'num_boxes' is not equal to 0
→
2
←
Taking false branch
→
1434 polygon->num_edges = 0;
1435 return CAIRO_STATUS_SUCCESS;
1436 }
1437
1438 for (n = 0; n < num_boxes; n++) {
3
←
Assuming 'n' is >= 'num_boxes'
→
4
←
Loop condition is false. Execution continues on line 1448
→
1439 if (polygon->extents.p1.x >= boxes[n].p1.x &&
1440 polygon->extents.p2.x <= boxes[n].p2.x &&
1441 polygon->extents.p1.y >= boxes[n].p1.y &&
1442 polygon->extents.p2.y <= boxes[n].p2.y)
1443 {
1444 return CAIRO_STATUS_SUCCESS;
1445 }
1446 }
1447
1448 _cairo_polygon_init (&b, NULL((void*)0), 0);
1449 for (n = 0; n
4.1
'n' is >= 'num_boxes'
 < num_boxes; n++) {
5
←
Loop condition is false. Execution continues on line 1468
→
1450 if (boxes[n].p2.x > polygon->extents.p1.x &&
1451 boxes[n].p1.x < polygon->extents.p2.x &&
1452 boxes[n].p2.y > polygon->extents.p1.y &&
1453 boxes[n].p1.y < polygon->extents.p2.y)
1454 {
1455 cairo_point_t p1, p2;
1456
1457 p1.y = boxes[n].p1.y;
1458 p2.y = boxes[n].p2.y;
1459
1460 p2.x = p1.x = boxes[n].p1.x;
1461 _cairo_polygon_add_external_edge (&b, &p1, &p2);
1462
1463 p2.x = p1.x = boxes[n].p2.x;
1464 _cairo_polygon_add_external_edge (&b, &p2, &p1);
1465 }
1466 }
1467
1468 status = _cairo_polygon_intersect (polygon, *winding,
6
←
Calling '_cairo_polygon_intersect'
→
1469 &b, CAIRO_FILL_RULE_WINDING);
1470 _cairo_polygon_fini (&b);
1471
1472 *winding = CAIRO_FILL_RULE_WINDING;
1473 return status;
1474}