add cairo

1 files changed, 1438 insertions, 0 deletions

diff --git a/libs/cairo-1.16.0/src/cairo-polygon-reduce.c b/libs/cairo-1.16.0/src/cairo-polygon-reduce.c
new file mode 100644
index 0000000..da6c9ab
--- /dev/null
+++ b/libs/cairo-1.16.0/src/cairo-polygon-reduce.c
@@ -0,0 +1,1438 @@
+/*
+ * Copyright © 2004 Carl Worth
+ * Copyright © 2006 Red Hat, Inc.
+ * Copyright © 2008 Chris Wilson
+ *
+ * This library is free software; you can redistribute it and/or
+ * modify it either under the terms of the GNU Lesser General Public
+ * License version 2.1 as published by the Free Software Foundation
+ * (the "LGPL") or, at your option, under the terms of the Mozilla
+ * Public License Version 1.1 (the "MPL"). If you do not alter this
+ * notice, a recipient may use your version of this file under either
+ * the MPL or the LGPL.
+ *
+ * You should have received a copy of the LGPL along with this library
+ * in the file COPYING-LGPL-2.1; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA
+ * You should have received a copy of the MPL along with this library
+ * in the file COPYING-MPL-1.1
+ *
+ * The contents of this file are subject to the Mozilla Public License
+ * Version 1.1 (the "License"); you may not use this file except in
+ * compliance with the License. You may obtain a copy of the License at
+ * http://www.mozilla.org/MPL/
+ *
+ * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
+ * OF ANY KIND, either express or implied. See the LGPL or the MPL for
+ * the specific language governing rights and limitations.
+ *
+ * The Original Code is the cairo graphics library.
+ *
+ * The Initial Developer of the Original Code is Carl Worth
+ *
+ * Contributor(s):
+ *	Carl D. Worth <cworth@cworth.org>
+ *	Chris Wilson <chris@chris-wilson.co.uk>
+ */
+
+/* Provide definitions for standalone compilation */
+#include "cairoint.h"
+
+#include "cairo-error-private.h"
+#include "cairo-freelist-private.h"
+#include "cairo-combsort-inline.h"
+
+#define DEBUG_POLYGON 0
+
+typedef cairo_point_t cairo_bo_point32_t;
+
+typedef struct _cairo_bo_intersect_ordinate {
+    int32_t ordinate;
+    enum { EXACT, INEXACT } exactness;
+} cairo_bo_intersect_ordinate_t;
+
+typedef struct _cairo_bo_intersect_point {
+    cairo_bo_intersect_ordinate_t x;
+    cairo_bo_intersect_ordinate_t y;
+} cairo_bo_intersect_point_t;
+
+typedef struct _cairo_bo_edge cairo_bo_edge_t;
+
+typedef struct _cairo_bo_deferred {
+    cairo_bo_edge_t *right;
+    int32_t top;
+} cairo_bo_deferred_t;
+
+struct _cairo_bo_edge {
+    cairo_edge_t edge;
+    cairo_bo_edge_t *prev;
+    cairo_bo_edge_t *next;
+    cairo_bo_deferred_t deferred;
+};
+
+/* the parent is always given by index/2 */
+#define PQ_PARENT_INDEX(i) ((i) >> 1)
+#define PQ_FIRST_ENTRY 1
+
+/* left and right children are index * 2 and (index * 2) +1 respectively */
+#define PQ_LEFT_CHILD_INDEX(i) ((i) << 1)
+
+typedef enum {
+    CAIRO_BO_EVENT_TYPE_STOP,
+    CAIRO_BO_EVENT_TYPE_INTERSECTION,
+    CAIRO_BO_EVENT_TYPE_START
+} cairo_bo_event_type_t;
+
+typedef struct _cairo_bo_event {
+    cairo_bo_event_type_t type;
+    cairo_point_t point;
+} cairo_bo_event_t;
+
+typedef struct _cairo_bo_start_event {
+    cairo_bo_event_type_t type;
+    cairo_point_t point;
+    cairo_bo_edge_t edge;
+} cairo_bo_start_event_t;
+
+typedef struct _cairo_bo_queue_event {
+    cairo_bo_event_type_t type;
+    cairo_point_t point;
+    cairo_bo_edge_t *e1;
+    cairo_bo_edge_t *e2;
+} cairo_bo_queue_event_t;
+
+typedef struct _pqueue {
+    int size, max_size;
+
+    cairo_bo_event_t **elements;
+    cairo_bo_event_t *elements_embedded[1024];
+} pqueue_t;
+
+typedef struct _cairo_bo_event_queue {
+    cairo_freepool_t pool;
+    pqueue_t pqueue;
+    cairo_bo_event_t **start_events;
+} cairo_bo_event_queue_t;
+
+typedef struct _cairo_bo_sweep_line {
+    cairo_bo_edge_t *head;
+    int32_t current_y;
+    cairo_bo_edge_t *current_edge;
+} cairo_bo_sweep_line_t;
+
+static cairo_fixed_t
+_line_compute_intersection_x_for_y (const cairo_line_t *line,
+				    cairo_fixed_t y)
+{
+    cairo_fixed_t x, dy;
+
+    if (y == line->p1.y)
+	return line->p1.x;
+    if (y == line->p2.y)
+	return line->p2.x;
+
+    x = line->p1.x;
+    dy = line->p2.y - line->p1.y;
+    if (dy != 0) {
+	x += _cairo_fixed_mul_div_floor (y - line->p1.y,
+					 line->p2.x - line->p1.x,
+					 dy);
+    }
+
+    return x;
+}
+
+static inline int
+_cairo_bo_point32_compare (cairo_bo_point32_t const *a,
+			   cairo_bo_point32_t const *b)
+{
+    int cmp;
+
+    cmp = a->y - b->y;
+    if (cmp)
+	return cmp;
+
+    return a->x - b->x;
+}
+
+/* Compare the slope of a to the slope of b, returning 1, 0, -1 if the
+ * slope a is respectively greater than, equal to, or less than the
+ * slope of b.
+ *
+ * For each edge, consider the direction vector formed from:
+ *
+ *	top -> bottom
+ *
+ * which is:
+ *
+ *	(dx, dy) = (line.p2.x - line.p1.x, line.p2.y - line.p1.y)
+ *
+ * We then define the slope of each edge as dx/dy, (which is the
+ * inverse of the slope typically used in math instruction). We never
+ * compute a slope directly as the value approaches infinity, but we
+ * can derive a slope comparison without division as follows, (where
+ * the ? represents our compare operator).
+ *
+ * 1.	   slope(a) ? slope(b)
+ * 2.	    adx/ady ? bdx/bdy
+ * 3.	(adx * bdy) ? (bdx * ady)
+ *
+ * Note that from step 2 to step 3 there is no change needed in the
+ * sign of the result since both ady and bdy are guaranteed to be
+ * greater than or equal to 0.
+ *
+ * When using this slope comparison to sort edges, some care is needed
+ * when interpreting the results. Since the slope compare operates on
+ * distance vectors from top to bottom it gives a correct left to
+ * right sort for edges that have a common top point, (such as two
+ * edges with start events at the same location). On the other hand,
+ * the sense of the result will be exactly reversed for two edges that
+ * have a common stop point.
+ */
+static inline int
+_slope_compare (const cairo_bo_edge_t *a,
+		const cairo_bo_edge_t *b)
+{
+    /* XXX: We're assuming here that dx and dy will still fit in 32
+     * bits. That's not true in general as there could be overflow. We
+     * should prevent that before the tessellation algorithm
+     * begins.
+     */
+    int32_t adx = a->edge.line.p2.x - a->edge.line.p1.x;
+    int32_t bdx = b->edge.line.p2.x - b->edge.line.p1.x;
+
+    /* Since the dy's are all positive by construction we can fast
+     * path several common cases.
+     */
+
+    /* First check for vertical lines. */
+    if (adx == 0)
+	return -bdx;
+    if (bdx == 0)
+	return adx;
+
+    /* Then where the two edges point in different directions wrt x. */
+    if ((adx ^ bdx) < 0)
+	return adx;
+
+    /* Finally we actually need to do the general comparison. */
+    {
+	int32_t ady = a->edge.line.p2.y - a->edge.line.p1.y;
+	int32_t bdy = b->edge.line.p2.y - b->edge.line.p1.y;
+	cairo_int64_t adx_bdy = _cairo_int32x32_64_mul (adx, bdy);
+	cairo_int64_t bdx_ady = _cairo_int32x32_64_mul (bdx, ady);
+
+	return _cairo_int64_cmp (adx_bdy, bdx_ady);
+    }
+}
+
+/*
+ * We need to compare the x-coordinates of a pair of lines for a particular y,
+ * without loss of precision.
+ *
+ * The x-coordinate along an edge for a given y is:
+ *   X = A_x + (Y - A_y) * A_dx / A_dy
+ *
+ * So the inequality we wish to test is:
+ *   A_x + (Y - A_y) * A_dx / A_dy ∘ B_x + (Y - B_y) * B_dx / B_dy,
+ * where ∘ is our inequality operator.
+ *
+ * By construction, we know that A_dy and B_dy (and (Y - A_y), (Y - B_y)) are
+ * all positive, so we can rearrange it thus without causing a sign change:
+ *   A_dy * B_dy * (A_x - B_x) ∘ (Y - B_y) * B_dx * A_dy
+ *                                 - (Y - A_y) * A_dx * B_dy
+ *
+ * Given the assumption that all the deltas fit within 32 bits, we can compute
+ * this comparison directly using 128 bit arithmetic. For certain, but common,
+ * input we can reduce this down to a single 32 bit compare by inspecting the
+ * deltas.
+ *
+ * (And put the burden of the work on developing fast 128 bit ops, which are
+ * required throughout the tessellator.)
+ *
+ * See the similar discussion for _slope_compare().
+ */
+static int
+edges_compare_x_for_y_general (const cairo_bo_edge_t *a,
+			       const cairo_bo_edge_t *b,
+			       int32_t y)
+{
+    /* XXX: We're assuming here that dx and dy will still fit in 32
+     * bits. That's not true in general as there could be overflow. We
+     * should prevent that before the tessellation algorithm
+     * begins.
+     */
+    int32_t dx;
+    int32_t adx, ady;
+    int32_t bdx, bdy;
+    enum {
+       HAVE_NONE    = 0x0,
+       HAVE_DX      = 0x1,
+       HAVE_ADX     = 0x2,
+       HAVE_DX_ADX  = HAVE_DX | HAVE_ADX,
+       HAVE_BDX     = 0x4,
+       HAVE_DX_BDX  = HAVE_DX | HAVE_BDX,
+       HAVE_ADX_BDX = HAVE_ADX | HAVE_BDX,
+       HAVE_ALL     = HAVE_DX | HAVE_ADX | HAVE_BDX
+    } have_dx_adx_bdx = HAVE_ALL;
+
+    /* don't bother solving for abscissa if the edges' bounding boxes
+     * can be used to order them. */
+    {
+           int32_t amin, amax;
+           int32_t bmin, bmax;
+           if (a->edge.line.p1.x < a->edge.line.p2.x) {
+                   amin = a->edge.line.p1.x;
+                   amax = a->edge.line.p2.x;
+           } else {
+                   amin = a->edge.line.p2.x;
+                   amax = a->edge.line.p1.x;
+           }
+           if (b->edge.line.p1.x < b->edge.line.p2.x) {
+                   bmin = b->edge.line.p1.x;
+                   bmax = b->edge.line.p2.x;
+           } else {
+                   bmin = b->edge.line.p2.x;
+                   bmax = b->edge.line.p1.x;
+           }
+           if (amax < bmin) return -1;
+           if (amin > bmax) return +1;
+    }
+
+    ady = a->edge.line.p2.y - a->edge.line.p1.y;
+    adx = a->edge.line.p2.x - a->edge.line.p1.x;
+    if (adx == 0)
+	have_dx_adx_bdx &= ~HAVE_ADX;
+
+    bdy = b->edge.line.p2.y - b->edge.line.p1.y;
+    bdx = b->edge.line.p2.x - b->edge.line.p1.x;
+    if (bdx == 0)
+	have_dx_adx_bdx &= ~HAVE_BDX;
+
+    dx = a->edge.line.p1.x - b->edge.line.p1.x;
+    if (dx == 0)
+	have_dx_adx_bdx &= ~HAVE_DX;
+
+#define L _cairo_int64x32_128_mul (_cairo_int32x32_64_mul (ady, bdy), dx)
+#define A _cairo_int64x32_128_mul (_cairo_int32x32_64_mul (adx, bdy), y - a->edge.line.p1.y)
+#define B _cairo_int64x32_128_mul (_cairo_int32x32_64_mul (bdx, ady), y - b->edge.line.p1.y)
+    switch (have_dx_adx_bdx) {
+    default:
+    case HAVE_NONE:
+	return 0;
+    case HAVE_DX:
+	/* A_dy * B_dy * (A_x - B_x) ∘ 0 */
+	return dx; /* ady * bdy is positive definite */
+    case HAVE_ADX:
+	/* 0 ∘  - (Y - A_y) * A_dx * B_dy */
+	return adx; /* bdy * (y - a->top.y) is positive definite */
+    case HAVE_BDX:
+	/* 0 ∘ (Y - B_y) * B_dx * A_dy */
+	return -bdx; /* ady * (y - b->top.y) is positive definite */
+    case HAVE_ADX_BDX:
+	/*  0 ∘ (Y - B_y) * B_dx * A_dy - (Y - A_y) * A_dx * B_dy */
+	if ((adx ^ bdx) < 0) {
+	    return adx;
+	} else if (a->edge.line.p1.y == b->edge.line.p1.y) { /* common origin */
+	    cairo_int64_t adx_bdy, bdx_ady;
+
+	    /* ∴ A_dx * B_dy ∘ B_dx * A_dy */
+
+	    adx_bdy = _cairo_int32x32_64_mul (adx, bdy);
+	    bdx_ady = _cairo_int32x32_64_mul (bdx, ady);
+
+	    return _cairo_int64_cmp (adx_bdy, bdx_ady);
+	} else
+	    return _cairo_int128_cmp (A, B);
+    case HAVE_DX_ADX:
+	/* A_dy * (A_x - B_x) ∘ - (Y - A_y) * A_dx */
+	if ((-adx ^ dx) < 0) {
+	    return dx;
+	} else {
+	    cairo_int64_t ady_dx, dy_adx;
+
+	    ady_dx = _cairo_int32x32_64_mul (ady, dx);
+	    dy_adx = _cairo_int32x32_64_mul (a->edge.line.p1.y - y, adx);
+
+	    return _cairo_int64_cmp (ady_dx, dy_adx);
+	}
+    case HAVE_DX_BDX:
+	/* B_dy * (A_x - B_x) ∘ (Y - B_y) * B_dx */
+	if ((bdx ^ dx) < 0) {
+	    return dx;
+	} else {
+	    cairo_int64_t bdy_dx, dy_bdx;
+
+	    bdy_dx = _cairo_int32x32_64_mul (bdy, dx);
+	    dy_bdx = _cairo_int32x32_64_mul (y - b->edge.line.p1.y, bdx);
+
+	    return _cairo_int64_cmp (bdy_dx, dy_bdx);
+	}
+    case HAVE_ALL:
+	/* XXX try comparing (a->edge.line.p2.x - b->edge.line.p2.x) et al */
+	return _cairo_int128_cmp (L, _cairo_int128_sub (B, A));
+    }
+#undef B
+#undef A
+#undef L
+}
+
+/*
+ * We need to compare the x-coordinate of a line for a particular y wrt to a
+ * given x, without loss of precision.
+ *
+ * The x-coordinate along an edge for a given y is:
+ *   X = A_x + (Y - A_y) * A_dx / A_dy
+ *
+ * So the inequality we wish to test is:
+ *   A_x + (Y - A_y) * A_dx / A_dy ∘ X
+ * where ∘ is our inequality operator.
+ *
+ * By construction, we know that A_dy (and (Y - A_y)) are
+ * all positive, so we can rearrange it thus without causing a sign change:
+ *   (Y - A_y) * A_dx ∘ (X - A_x) * A_dy
+ *
+ * Given the assumption that all the deltas fit within 32 bits, we can compute
+ * this comparison directly using 64 bit arithmetic.
+ *
+ * See the similar discussion for _slope_compare() and
+ * edges_compare_x_for_y_general().
+ */
+static int
+edge_compare_for_y_against_x (const cairo_bo_edge_t *a,
+			      int32_t y,
+			      int32_t x)
+{
+    int32_t adx, ady;
+    int32_t dx, dy;
+    cairo_int64_t L, R;
+
+    if (x < a->edge.line.p1.x && x < a->edge.line.p2.x)
+	return 1;
+    if (x > a->edge.line.p1.x && x > a->edge.line.p2.x)
+	return -1;
+
+    adx = a->edge.line.p2.x - a->edge.line.p1.x;
+    dx = x - a->edge.line.p1.x;
+
+    if (adx == 0)
+	return -dx;
+    if (dx == 0 || (adx ^ dx) < 0)
+	return adx;
+
+    dy = y - a->edge.line.p1.y;
+    ady = a->edge.line.p2.y - a->edge.line.p1.y;
+
+    L = _cairo_int32x32_64_mul (dy, adx);
+    R = _cairo_int32x32_64_mul (dx, ady);
+
+    return _cairo_int64_cmp (L, R);
+}
+
+static int
+edges_compare_x_for_y (const cairo_bo_edge_t *a,
+		       const cairo_bo_edge_t *b,
+		       int32_t y)
+{
+    /* If the sweep-line is currently on an end-point of a line,
+     * then we know its precise x value (and considering that we often need to
+     * compare events at end-points, this happens frequently enough to warrant
+     * special casing).
+     */
+    enum {
+       HAVE_NEITHER = 0x0,
+       HAVE_AX      = 0x1,
+       HAVE_BX      = 0x2,
+       HAVE_BOTH    = HAVE_AX | HAVE_BX
+    } have_ax_bx = HAVE_BOTH;
+    int32_t ax = 0, bx = 0;
+
+    if (y == a->edge.line.p1.y)
+	ax = a->edge.line.p1.x;
+    else if (y == a->edge.line.p2.y)
+	ax = a->edge.line.p2.x;
+    else
+	have_ax_bx &= ~HAVE_AX;
+
+    if (y == b->edge.line.p1.y)
+	bx = b->edge.line.p1.x;
+    else if (y == b->edge.line.p2.y)
+	bx = b->edge.line.p2.x;
+    else
+	have_ax_bx &= ~HAVE_BX;
+
+    switch (have_ax_bx) {
+    default:
+    case HAVE_NEITHER:
+	return edges_compare_x_for_y_general (a, b, y);
+    case HAVE_AX:
+	return -edge_compare_for_y_against_x (b, y, ax);
+    case HAVE_BX:
+	return edge_compare_for_y_against_x (a, y, bx);
+    case HAVE_BOTH:
+	return ax - bx;
+    }
+}
+
+static inline int
+_line_equal (const cairo_line_t *a, const cairo_line_t *b)
+{
+    return (a->p1.x == b->p1.x && a->p1.y == b->p1.y &&
+	    a->p2.x == b->p2.x && a->p2.y == b->p2.y);
+}
+
+static int
+_cairo_bo_sweep_line_compare_edges (cairo_bo_sweep_line_t	*sweep_line,
+				    const cairo_bo_edge_t	*a,
+				    const cairo_bo_edge_t	*b)
+{
+    int cmp;
+
+    /* compare the edges if not identical */
+    if (! _line_equal (&a->edge.line, &b->edge.line)) {
+	cmp = edges_compare_x_for_y (a, b, sweep_line->current_y);
+	if (cmp)
+	    return cmp;
+
+	/* The two edges intersect exactly at y, so fall back on slope
+	 * comparison. We know that this compare_edges function will be
+	 * called only when starting a new edge, (not when stopping an
+	 * edge), so we don't have to worry about conditionally inverting
+	 * the sense of _slope_compare. */
+	cmp = _slope_compare (a, b);
+	if (cmp)
+	    return cmp;
+    }
+
+    /* We've got two collinear edges now. */
+    return b->edge.bottom - a->edge.bottom;
+}
+
+static inline cairo_int64_t
+det32_64 (int32_t a, int32_t b,
+	  int32_t c, int32_t d)
+{
+    /* det = a * d - b * c */
+    return _cairo_int64_sub (_cairo_int32x32_64_mul (a, d),
+			     _cairo_int32x32_64_mul (b, c));
+}
+
+static inline cairo_int128_t
+det64x32_128 (cairo_int64_t a, int32_t       b,
+	      cairo_int64_t c, int32_t       d)
+{
+    /* det = a * d - b * c */
+    return _cairo_int128_sub (_cairo_int64x32_128_mul (a, d),
+			      _cairo_int64x32_128_mul (c, b));
+}
+
+/* Compute the intersection of two lines as defined by two edges. The
+ * result is provided as a coordinate pair of 128-bit integers.
+ *
+ * Returns %CAIRO_BO_STATUS_INTERSECTION if there is an intersection or
+ * %CAIRO_BO_STATUS_PARALLEL if the two lines are exactly parallel.
+ */
+static cairo_bool_t
+intersect_lines (cairo_bo_edge_t		*a,
+		 cairo_bo_edge_t		*b,
+		 cairo_bo_intersect_point_t	*intersection)
+{
+    cairo_int64_t a_det, b_det;
+
+    /* XXX: We're assuming here that dx and dy will still fit in 32
+     * bits. That's not true in general as there could be overflow. We
+     * should prevent that before the tessellation algorithm begins.
+     * What we're doing to mitigate this is to perform clamping in
+     * cairo_bo_tessellate_polygon().
+     */
+    int32_t dx1 = a->edge.line.p1.x - a->edge.line.p2.x;
+    int32_t dy1 = a->edge.line.p1.y - a->edge.line.p2.y;
+
+    int32_t dx2 = b->edge.line.p1.x - b->edge.line.p2.x;
+    int32_t dy2 = b->edge.line.p1.y - b->edge.line.p2.y;
+
+    cairo_int64_t den_det;
+    cairo_int64_t R;
+    cairo_quorem64_t qr;
+
+    den_det = det32_64 (dx1, dy1, dx2, dy2);
+
+     /* Q: Can we determine that the lines do not intersect (within range)
+      * much more cheaply than computing the intersection point i.e. by
+      * avoiding the division?
+      *
+      *   X = ax + t * adx = bx + s * bdx;
+      *   Y = ay + t * ady = by + s * bdy;
+      *   ∴ t * (ady*bdx - bdy*adx) = bdx * (by - ay) + bdy * (ax - bx)
+      *   => t * L = R
+      *
+      * Therefore we can reject any intersection (under the criteria for
+      * valid intersection events) if:
+      *   L^R < 0 => t < 0, or
+      *   L<R => t > 1
+      *
+      * (where top/bottom must at least extend to the line endpoints).
+      *
+      * A similar substitution can be performed for s, yielding:
+      *   s * (ady*bdx - bdy*adx) = ady * (ax - bx) - adx * (ay - by)
+      */
+    R = det32_64 (dx2, dy2,
+		  b->edge.line.p1.x - a->edge.line.p1.x,
+		  b->edge.line.p1.y - a->edge.line.p1.y);
+    if (_cairo_int64_negative (den_det)) {
+	if (_cairo_int64_ge (den_det, R))
+	    return FALSE;
+    } else {
+	if (_cairo_int64_le (den_det, R))
+	    return FALSE;
+    }
+
+    R = det32_64 (dy1, dx1,
+		  a->edge.line.p1.y - b->edge.line.p1.y,
+		  a->edge.line.p1.x - b->edge.line.p1.x);
+    if (_cairo_int64_negative (den_det)) {
+	if (_cairo_int64_ge (den_det, R))
+	    return FALSE;
+    } else {
+	if (_cairo_int64_le (den_det, R))
+	    return FALSE;
+    }
+
+    /* We now know that the two lines should intersect within range. */
+
+    a_det = det32_64 (a->edge.line.p1.x, a->edge.line.p1.y,
+		      a->edge.line.p2.x, a->edge.line.p2.y);
+    b_det = det32_64 (b->edge.line.p1.x, b->edge.line.p1.y,
+		      b->edge.line.p2.x, b->edge.line.p2.y);
+
+    /* x = det (a_det, dx1, b_det, dx2) / den_det */
+    qr = _cairo_int_96by64_32x64_divrem (det64x32_128 (a_det, dx1,
+						       b_det, dx2),
+					 den_det);
+    if (_cairo_int64_eq (qr.rem, den_det))
+	return FALSE;
+#if 0
+    intersection->x.exactness = _cairo_int64_is_zero (qr.rem) ? EXACT : INEXACT;
+#else
+    intersection->x.exactness = EXACT;
+    if (! _cairo_int64_is_zero (qr.rem)) {
+	if (_cairo_int64_negative (den_det) ^ _cairo_int64_negative (qr.rem))
+	    qr.rem = _cairo_int64_negate (qr.rem);
+	qr.rem = _cairo_int64_mul (qr.rem, _cairo_int32_to_int64 (2));
+	if (_cairo_int64_ge (qr.rem, den_det)) {
+	    qr.quo = _cairo_int64_add (qr.quo,
+				       _cairo_int32_to_int64 (_cairo_int64_negative (qr.quo) ? -1 : 1));
+	} else
+	    intersection->x.exactness = INEXACT;
+    }
+#endif
+    intersection->x.ordinate = _cairo_int64_to_int32 (qr.quo);
+
+    /* y = det (a_det, dy1, b_det, dy2) / den_det */
+    qr = _cairo_int_96by64_32x64_divrem (det64x32_128 (a_det, dy1,
+						       b_det, dy2),
+					 den_det);
+    if (_cairo_int64_eq (qr.rem, den_det))
+	return FALSE;
+#if 0
+    intersection->y.exactness = _cairo_int64_is_zero (qr.rem) ? EXACT : INEXACT;
+#else
+    intersection->y.exactness = EXACT;
+    if (! _cairo_int64_is_zero (qr.rem)) {
+	if (_cairo_int64_negative (den_det) ^ _cairo_int64_negative (qr.rem))
+	    qr.rem = _cairo_int64_negate (qr.rem);
+	qr.rem = _cairo_int64_mul (qr.rem, _cairo_int32_to_int64 (2));
+	if (_cairo_int64_ge (qr.rem, den_det)) {
+	    qr.quo = _cairo_int64_add (qr.quo,
+				       _cairo_int32_to_int64 (_cairo_int64_negative (qr.quo) ? -1 : 1));
+	} else
+	    intersection->y.exactness = INEXACT;
+    }
+#endif
+    intersection->y.ordinate = _cairo_int64_to_int32 (qr.quo);
+
+    return TRUE;
+}
+
+static int
+_cairo_bo_intersect_ordinate_32_compare (cairo_bo_intersect_ordinate_t	a,
+					 int32_t			b)
+{
+    /* First compare the quotient */
+    if (a.ordinate > b)
+	return +1;
+    if (a.ordinate < b)
+	return -1;
+    /* With quotient identical, if remainder is 0 then compare equal */
+    /* Otherwise, the non-zero remainder makes a > b */
+    return INEXACT == a.exactness;
+}
+
+/* Does the given edge contain the given point. The point must already
+ * be known to be contained within the line determined by the edge,
+ * (most likely the point results from an intersection of this edge
+ * with another).
+ *
+ * If we had exact arithmetic, then this function would simply be a
+ * matter of examining whether the y value of the point lies within
+ * the range of y values of the edge. But since intersection points
+ * are not exact due to being rounded to the nearest integer within
+ * the available precision, we must also examine the x value of the
+ * point.
+ *
+ * The definition of "contains" here is that the given intersection
+ * point will be seen by the sweep line after the start event for the
+ * given edge and before the stop event for the edge. See the comments
+ * in the implementation for more details.
+ */
+static cairo_bool_t
+_cairo_bo_edge_contains_intersect_point (cairo_bo_edge_t		*edge,
+					 cairo_bo_intersect_point_t	*point)
+{
+    int cmp_top, cmp_bottom;
+
+    /* XXX: When running the actual algorithm, we don't actually need to
+     * compare against edge->top at all here, since any intersection above
+     * top is eliminated early via a slope comparison. We're leaving these
+     * here for now only for the sake of the quadratic-time intersection
+     * finder which needs them.
+     */
+
+    cmp_top = _cairo_bo_intersect_ordinate_32_compare (point->y,
+						       edge->edge.top);
+    cmp_bottom = _cairo_bo_intersect_ordinate_32_compare (point->y,
+							  edge->edge.bottom);
+
+    if (cmp_top < 0 || cmp_bottom > 0)
+    {
+	return FALSE;
+    }
+
+    if (cmp_top > 0 && cmp_bottom < 0)
+    {
+	return TRUE;
+    }
+
+    /* At this stage, the point lies on the same y value as either
+     * edge->top or edge->bottom, so we have to examine the x value in
+     * order to properly determine containment. */
+
+    /* If the y value of the point is the same as the y value of the
+     * top of the edge, then the x value of the point must be greater
+     * to be considered as inside the edge. Similarly, if the y value
+     * of the point is the same as the y value of the bottom of the
+     * edge, then the x value of the point must be less to be
+     * considered as inside. */
+
+    if (cmp_top == 0) {
+	cairo_fixed_t top_x;
+
+	top_x = _line_compute_intersection_x_for_y (&edge->edge.line,
+						    edge->edge.top);
+	return _cairo_bo_intersect_ordinate_32_compare (point->x, top_x) > 0;
+    } else { /* cmp_bottom == 0 */
+	cairo_fixed_t bot_x;
+
+	bot_x = _line_compute_intersection_x_for_y (&edge->edge.line,
+						    edge->edge.bottom);
+	return _cairo_bo_intersect_ordinate_32_compare (point->x, bot_x) < 0;
+    }
+}
+
+/* Compute the intersection of two edges. The result is provided as a
+ * coordinate pair of 128-bit integers.
+ *
+ * Returns %CAIRO_BO_STATUS_INTERSECTION if there is an intersection
+ * that is within both edges, %CAIRO_BO_STATUS_NO_INTERSECTION if the
+ * intersection of the lines defined by the edges occurs outside of
+ * one or both edges, and %CAIRO_BO_STATUS_PARALLEL if the two edges
+ * are exactly parallel.
+ *
+ * Note that when determining if a candidate intersection is "inside"
+ * an edge, we consider both the infinitesimal shortening and the
+ * infinitesimal tilt rules described by John Hobby. Specifically, if
+ * the intersection is exactly the same as an edge point, it is
+ * effectively outside (no intersection is returned). Also, if the
+ * intersection point has the same
+ */
+static cairo_bool_t
+_cairo_bo_edge_intersect (cairo_bo_edge_t	*a,
+			  cairo_bo_edge_t	*b,
+			  cairo_bo_point32_t	*intersection)
+{
+    cairo_bo_intersect_point_t quorem;
+
+    if (! intersect_lines (a, b, &quorem))
+	return FALSE;
+
+    if (! _cairo_bo_edge_contains_intersect_point (a, &quorem))
+	return FALSE;
+
+    if (! _cairo_bo_edge_contains_intersect_point (b, &quorem))
+	return FALSE;
+
+    /* Now that we've correctly compared the intersection point and
+     * determined that it lies within the edge, then we know that we
+     * no longer need any more bits of storage for the intersection
+     * than we do for our edge coordinates. We also no longer need the
+     * remainder from the division. */
+    intersection->x = quorem.x.ordinate;
+    intersection->y = quorem.y.ordinate;
+
+    return TRUE;
+}
+
+static inline int
+cairo_bo_event_compare (const cairo_bo_event_t *a,
+			const cairo_bo_event_t *b)
+{
+    int cmp;
+
+    cmp = _cairo_bo_point32_compare (&a->point, &b->point);
+    if (cmp)
+	return cmp;
+
+    cmp = a->type - b->type;
+    if (cmp)
+	return cmp;
+
+    return a - b;
+}
+
+static inline void
+_pqueue_init (pqueue_t *pq)
+{
+    pq->max_size = ARRAY_LENGTH (pq->elements_embedded);
+    pq->size = 0;
+
+    pq->elements = pq->elements_embedded;
+}
+
+static inline void
+_pqueue_fini (pqueue_t *pq)
+{
+    if (pq->elements != pq->elements_embedded)
+	free (pq->elements);
+}
+
+static cairo_status_t
+_pqueue_grow (pqueue_t *pq)
+{
+    cairo_bo_event_t **new_elements;
+    pq->max_size *= 2;
+
+    if (pq->elements == pq->elements_embedded) {
+	new_elements = _cairo_malloc_ab (pq->max_size,
+					 sizeof (cairo_bo_event_t *));
+	if (unlikely (new_elements == NULL))
+	    return _cairo_error (CAIRO_STATUS_NO_MEMORY);
+
+	memcpy (new_elements, pq->elements_embedded,
+		sizeof (pq->elements_embedded));
+    } else {
+	new_elements = _cairo_realloc_ab (pq->elements,
+					  pq->max_size,
+					  sizeof (cairo_bo_event_t *));
+	if (unlikely (new_elements == NULL))
+	    return _cairo_error (CAIRO_STATUS_NO_MEMORY);
+    }
+
+    pq->elements = new_elements;
+    return CAIRO_STATUS_SUCCESS;
+}
+
+static inline cairo_status_t
+_pqueue_push (pqueue_t *pq, cairo_bo_event_t *event)
+{
+    cairo_bo_event_t **elements;
+    int i, parent;
+
+    if (unlikely (pq->size + 1 == pq->max_size)) {
+	cairo_status_t status;
+
+	status = _pqueue_grow (pq);
+	if (unlikely (status))
+	    return status;
+    }
+
+    elements = pq->elements;
+
+    for (i = ++pq->size;
+	 i != PQ_FIRST_ENTRY &&
+	 cairo_bo_event_compare (event,
+				 elements[parent = PQ_PARENT_INDEX (i)]) < 0;
+	 i = parent)
+    {
+	elements[i] = elements[parent];
+    }
+
+    elements[i] = event;
+
+    return CAIRO_STATUS_SUCCESS;
+}
+
+static inline void
+_pqueue_pop (pqueue_t *pq)
+{
+    cairo_bo_event_t **elements = pq->elements;
+    cairo_bo_event_t *tail;
+    int child, i;
+
+    tail = elements[pq->size--];
+    if (pq->size == 0) {
+	elements[PQ_FIRST_ENTRY] = NULL;
+	return;
+    }
+
+    for (i = PQ_FIRST_ENTRY;
+	 (child = PQ_LEFT_CHILD_INDEX (i)) <= pq->size;
+	 i = child)
+    {
+	if (child != pq->size &&
+	    cairo_bo_event_compare (elements[child+1],
+				    elements[child]) < 0)
+	{
+	    child++;
+	}
+
+	if (cairo_bo_event_compare (elements[child], tail) >= 0)
+	    break;
+
+	elements[i] = elements[child];
+    }
+    elements[i] = tail;
+}
+
+static inline cairo_status_t
+_cairo_bo_event_queue_insert (cairo_bo_event_queue_t	*queue,
+			      cairo_bo_event_type_t	 type,
+			      cairo_bo_edge_t		*e1,
+			      cairo_bo_edge_t		*e2,
+			      const cairo_point_t	 *point)
+{
+    cairo_bo_queue_event_t *event;
+
+    event = _cairo_freepool_alloc (&queue->pool);
+    if (unlikely (event == NULL))
+	return _cairo_error (CAIRO_STATUS_NO_MEMORY);
+
+    event->type = type;
+    event->e1 = e1;
+    event->e2 = e2;
+    event->point = *point;
+
+    return _pqueue_push (&queue->pqueue, (cairo_bo_event_t *) event);
+}
+
+static void
+_cairo_bo_event_queue_delete (cairo_bo_event_queue_t *queue,
+			      cairo_bo_event_t	     *event)
+{
+    _cairo_freepool_free (&queue->pool, event);
+}
+
+static cairo_bo_event_t *
+_cairo_bo_event_dequeue (cairo_bo_event_queue_t *event_queue)
+{
+    cairo_bo_event_t *event, *cmp;
+
+    event = event_queue->pqueue.elements[PQ_FIRST_ENTRY];
+    cmp = *event_queue->start_events;
+    if (event == NULL ||
+	(cmp != NULL && cairo_bo_event_compare (cmp, event) < 0))
+    {
+	event = cmp;
+	event_queue->start_events++;
+    }
+    else
+    {
+	_pqueue_pop (&event_queue->pqueue);
+    }
+
+    return event;
+}
+
+CAIRO_COMBSORT_DECLARE (_cairo_bo_event_queue_sort,
+			cairo_bo_event_t *,
+			cairo_bo_event_compare)
+
+static void
+_cairo_bo_event_queue_init (cairo_bo_event_queue_t	 *event_queue,
+			    cairo_bo_event_t		**start_events,
+			    int				  num_events)
+{
+    _cairo_bo_event_queue_sort (start_events, num_events);
+    start_events[num_events] = NULL;
+
+    event_queue->start_events = start_events;
+
+    _cairo_freepool_init (&event_queue->pool,
+			  sizeof (cairo_bo_queue_event_t));
+    _pqueue_init (&event_queue->pqueue);
+    event_queue->pqueue.elements[PQ_FIRST_ENTRY] = NULL;
+}
+
+static cairo_status_t
+_cairo_bo_event_queue_insert_stop (cairo_bo_event_queue_t	*event_queue,
+				   cairo_bo_edge_t		*edge)
+{
+    cairo_bo_point32_t point;
+
+    point.y = edge->edge.bottom;
+    point.x = _line_compute_intersection_x_for_y (&edge->edge.line,
+						  point.y);
+    return _cairo_bo_event_queue_insert (event_queue,
+					 CAIRO_BO_EVENT_TYPE_STOP,
+					 edge, NULL,
+					 &point);
+}
+
+static void
+_cairo_bo_event_queue_fini (cairo_bo_event_queue_t *event_queue)
+{
+    _pqueue_fini (&event_queue->pqueue);
+    _cairo_freepool_fini (&event_queue->pool);
+}
+
+static inline cairo_status_t
+_cairo_bo_event_queue_insert_if_intersect_below_current_y (cairo_bo_event_queue_t	*event_queue,
+							   cairo_bo_edge_t	*left,
+							   cairo_bo_edge_t *right)
+{
+    cairo_bo_point32_t intersection;
+
+    if (_line_equal (&left->edge.line, &right->edge.line))
+	return CAIRO_STATUS_SUCCESS;
+
+    /* The names "left" and "right" here are correct descriptions of
+     * the order of the two edges within the active edge list. So if a
+     * slope comparison also puts left less than right, then we know
+     * that the intersection of these two segments has already
+     * occurred before the current sweep line position. */
+    if (_slope_compare (left, right) <= 0)
+	return CAIRO_STATUS_SUCCESS;
+
+    if (! _cairo_bo_edge_intersect (left, right, &intersection))
+	return CAIRO_STATUS_SUCCESS;
+
+    return _cairo_bo_event_queue_insert (event_queue,
+					 CAIRO_BO_EVENT_TYPE_INTERSECTION,
+					 left, right,
+					 &intersection);
+}
+
+static void
+_cairo_bo_sweep_line_init (cairo_bo_sweep_line_t *sweep_line)
+{
+    sweep_line->head = NULL;
+    sweep_line->current_y = INT32_MIN;
+    sweep_line->current_edge = NULL;
+}
+
+static cairo_status_t
+_cairo_bo_sweep_line_insert (cairo_bo_sweep_line_t	*sweep_line,
+			     cairo_bo_edge_t		*edge)
+{
+    if (sweep_line->current_edge != NULL) {
+	cairo_bo_edge_t *prev, *next;
+	int cmp;
+
+	cmp = _cairo_bo_sweep_line_compare_edges (sweep_line,
+						  sweep_line->current_edge,
+						  edge);
+	if (cmp < 0) {
+	    prev = sweep_line->current_edge;
+	    next = prev->next;
+	    while (next != NULL &&
+		   _cairo_bo_sweep_line_compare_edges (sweep_line,
+						       next, edge) < 0)
+	    {
+		prev = next, next = prev->next;
+	    }
+
+	    prev->next = edge;
+	    edge->prev = prev;
+	    edge->next = next;
+	    if (next != NULL)
+		next->prev = edge;
+	} else if (cmp > 0) {
+	    next = sweep_line->current_edge;
+	    prev = next->prev;
+	    while (prev != NULL &&
+		   _cairo_bo_sweep_line_compare_edges (sweep_line,
+						       prev, edge) > 0)
+	    {
+		next = prev, prev = next->prev;
+	    }
+
+	    next->prev = edge;
+	    edge->next = next;
+	    edge->prev = prev;
+	    if (prev != NULL)
+		prev->next = edge;
+	    else
+		sweep_line->head = edge;
+	} else {
+	    prev = sweep_line->current_edge;
+	    edge->prev = prev;
+	    edge->next = prev->next;
+	    if (prev->next != NULL)
+		prev->next->prev = edge;
+	    prev->next = edge;
+	}
+    } else {
+	sweep_line->head = edge;
+    }
+
+    sweep_line->current_edge = edge;
+
+    return CAIRO_STATUS_SUCCESS;
+}
+
+static void
+_cairo_bo_sweep_line_delete (cairo_bo_sweep_line_t	*sweep_line,
+			     cairo_bo_edge_t	*edge)
+{
+    if (edge->prev != NULL)
+	edge->prev->next = edge->next;
+    else
+	sweep_line->head = edge->next;
+
+    if (edge->next != NULL)
+	edge->next->prev = edge->prev;
+
+    if (sweep_line->current_edge == edge)
+	sweep_line->current_edge = edge->prev ? edge->prev : edge->next;
+}
+
+static void
+_cairo_bo_sweep_line_swap (cairo_bo_sweep_line_t	*sweep_line,
+			   cairo_bo_edge_t		*left,
+			   cairo_bo_edge_t		*right)
+{
+    if (left->prev != NULL)
+	left->prev->next = right;
+    else
+	sweep_line->head = right;
+
+    if (right->next != NULL)
+	right->next->prev = left;
+
+    left->next = right->next;
+    right->next = left;
+
+    right->prev = left->prev;
+    left->prev = right;
+}
+
+static inline cairo_bool_t
+edges_colinear (const cairo_bo_edge_t *a, const cairo_bo_edge_t *b)
+{
+    if (_line_equal (&a->edge.line, &b->edge.line))
+	return TRUE;
+
+    if (_slope_compare (a, b))
+	return FALSE;
+
+    /* The choice of y is not truly arbitrary since we must guarantee that it
+     * is greater than the start of either line.
+     */
+    if (a->edge.line.p1.y == b->edge.line.p1.y) {
+	return a->edge.line.p1.x == b->edge.line.p1.x;
+    } else if (a->edge.line.p2.y == b->edge.line.p2.y) {
+	return a->edge.line.p2.x == b->edge.line.p2.x;
+    } else if (a->edge.line.p1.y < b->edge.line.p1.y) {
+	return edge_compare_for_y_against_x (b,
+					     a->edge.line.p1.y,
+					     a->edge.line.p1.x) == 0;
+    } else {
+	return edge_compare_for_y_against_x (a,
+					     b->edge.line.p1.y,
+					     b->edge.line.p1.x) == 0;
+    }
+}
+
+static void
+_cairo_bo_edge_end (cairo_bo_edge_t	*left,
+		    int32_t		 bot,
+		    cairo_polygon_t	*polygon)
+{
+    cairo_bo_deferred_t *d = &left->deferred;
+
+    if (likely (d->top < bot)) {
+	_cairo_polygon_add_line (polygon,
+				 &left->edge.line,
+				 d->top, bot,
+				 1);
+	_cairo_polygon_add_line (polygon,
+				 &d->right->edge.line,
+				 d->top, bot,
+				 -1);
+    }
+
+    d->right = NULL;
+}
+
+
+static inline void
+_cairo_bo_edge_start_or_continue (cairo_bo_edge_t	*left,
+				  cairo_bo_edge_t	*right,
+				  int			 top,
+				  cairo_polygon_t	*polygon)
+{
+    if (left->deferred.right == right)
+	return;
+
+    if (left->deferred.right != NULL) {
+	if (right != NULL && edges_colinear (left->deferred.right, right))
+	{
+	    /* continuation on right, so just swap edges */
+	    left->deferred.right = right;
+	    return;
+	}
+
+	_cairo_bo_edge_end (left, top, polygon);
+    }
+
+    if (right != NULL && ! edges_colinear (left, right)) {
+	left->deferred.top = top;
+	left->deferred.right = right;
+    }
+}
+
+static inline void
+_active_edges_to_polygon (cairo_bo_edge_t		*left,
+			  int32_t			 top,
+			  cairo_fill_rule_t		 fill_rule,
+			  cairo_polygon_t	        *polygon)
+{
+    cairo_bo_edge_t *right;
+    unsigned int mask;
+
+    if (fill_rule == CAIRO_FILL_RULE_WINDING)
+	mask = ~0;
+    else
+	mask = 1;
+
+    while (left != NULL) {
+	int in_out = left->edge.dir;
+
+	right = left->next;
+	if (left->deferred.right == NULL) {
+	    while (right != NULL && right->deferred.right == NULL)
+		right = right->next;
+
+	    if (right != NULL && edges_colinear (left, right)) {
+		/* continuation on left */
+		left->deferred = right->deferred;
+		right->deferred.right = NULL;
+	    }
+	}
+
+	right = left->next;
+	while (right != NULL) {
+	    if (right->deferred.right != NULL)
+		_cairo_bo_edge_end (right, top, polygon);
+
+	    in_out += right->edge.dir;
+	    if ((in_out & mask) == 0) {
+		/* skip co-linear edges */
+		if (right->next == NULL || !edges_colinear (right, right->next))
+		    break;
+	    }
+
+	    right = right->next;
+	}
+
+	_cairo_bo_edge_start_or_continue (left, right, top, polygon);
+
+	left = right;
+	if (left != NULL)
+	    left = left->next;
+    }
+}
+
+
+static cairo_status_t
+_cairo_bentley_ottmann_tessellate_bo_edges (cairo_bo_event_t   **start_events,
+					    int			 num_events,
+					    cairo_fill_rule_t	 fill_rule,
+					    cairo_polygon_t	*polygon)
+{
+    cairo_status_t status = CAIRO_STATUS_SUCCESS; /* silence compiler */
+    cairo_bo_event_queue_t event_queue;
+    cairo_bo_sweep_line_t sweep_line;
+    cairo_bo_event_t *event;
+    cairo_bo_edge_t *left, *right;
+    cairo_bo_edge_t *e1, *e2;
+
+    _cairo_bo_event_queue_init (&event_queue, start_events, num_events);
+    _cairo_bo_sweep_line_init (&sweep_line);
+
+    while ((event = _cairo_bo_event_dequeue (&event_queue))) {
+	if (event->point.y != sweep_line.current_y) {
+	    _active_edges_to_polygon (sweep_line.head,
+				      sweep_line.current_y,
+				      fill_rule, polygon);
+
+	    sweep_line.current_y = event->point.y;
+	}
+
+	switch (event->type) {
+	case CAIRO_BO_EVENT_TYPE_START:
+	    e1 = &((cairo_bo_start_event_t *) event)->edge;
+
+	    status = _cairo_bo_sweep_line_insert (&sweep_line, e1);
+	    if (unlikely (status))
+		goto unwind;
+
+	    status = _cairo_bo_event_queue_insert_stop (&event_queue, e1);
+	    if (unlikely (status))
+		goto unwind;
+
+	    left = e1->prev;
+	    right = e1->next;
+
+	    if (left != NULL) {
+		status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, left, e1);
+		if (unlikely (status))
+		    goto unwind;
+	    }
+
+	    if (right != NULL) {
+		status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, e1, right);
+		if (unlikely (status))
+		    goto unwind;
+	    }
+
+	    break;
+
+	case CAIRO_BO_EVENT_TYPE_STOP:
+	    e1 = ((cairo_bo_queue_event_t *) event)->e1;
+	    _cairo_bo_event_queue_delete (&event_queue, event);
+
+	    left = e1->prev;
+	    right = e1->next;
+
+	    _cairo_bo_sweep_line_delete (&sweep_line, e1);
+
+	    if (e1->deferred.right != NULL)
+		_cairo_bo_edge_end (e1, e1->edge.bottom, polygon);
+
+	    if (left != NULL && right != NULL) {
+		status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, left, right);
+		if (unlikely (status))
+		    goto unwind;
+	    }
+
+	    break;
+
+	case CAIRO_BO_EVENT_TYPE_INTERSECTION:
+	    e1 = ((cairo_bo_queue_event_t *) event)->e1;
+	    e2 = ((cairo_bo_queue_event_t *) event)->e2;
+	    _cairo_bo_event_queue_delete (&event_queue, event);
+
+	    /* skip this intersection if its edges are not adjacent */
+	    if (e2 != e1->next)
+		break;
+
+	    left = e1->prev;
+	    right = e2->next;
+
+	    _cairo_bo_sweep_line_swap (&sweep_line, e1, e2);
+
+	    /* after the swap e2 is left of e1 */
+
+	    if (left != NULL) {
+		status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, left, e2);
+		if (unlikely (status))
+		    goto unwind;
+	    }
+
+	    if (right != NULL) {
+		status = _cairo_bo_event_queue_insert_if_intersect_below_current_y (&event_queue, e1, right);
+		if (unlikely (status))
+		    goto unwind;
+	    }
+
+	    break;
+	}
+    }
+
+ unwind:
+    _cairo_bo_event_queue_fini (&event_queue);
+
+    return status;
+}
+
+cairo_status_t
+_cairo_polygon_reduce (cairo_polygon_t *polygon,
+		       cairo_fill_rule_t fill_rule)
+{
+    cairo_status_t status;
+    cairo_bo_start_event_t stack_events[CAIRO_STACK_ARRAY_LENGTH (cairo_bo_start_event_t)];
+    cairo_bo_start_event_t *events;
+    cairo_bo_event_t *stack_event_ptrs[ARRAY_LENGTH (stack_events) + 1];
+    cairo_bo_event_t **event_ptrs;
+    int num_limits;
+    int num_events;
+    int i;
+
+    num_events = polygon->num_edges;
+    if (unlikely (0 == num_events))
+	return CAIRO_STATUS_SUCCESS;
+
+    if (DEBUG_POLYGON) {
+	FILE *file = fopen ("reduce_in.txt", "w");
+	_cairo_debug_print_polygon (file, polygon);
+	fclose (file);
+    }
+
+    events = stack_events;
+    event_ptrs = stack_event_ptrs;
+    if (num_events > ARRAY_LENGTH (stack_events)) {
+	events = _cairo_malloc_ab_plus_c (num_events,
+					  sizeof (cairo_bo_start_event_t) +
+					  sizeof (cairo_bo_event_t *),
+					  sizeof (cairo_bo_event_t *));
+	if (unlikely (events == NULL))
+	    return _cairo_error (CAIRO_STATUS_NO_MEMORY);
+
+	event_ptrs = (cairo_bo_event_t **) (events + num_events);
+    }
+
+    for (i = 0; i < num_events; i++) {
+	event_ptrs[i] = (cairo_bo_event_t *) &events[i];
+
+	events[i].type = CAIRO_BO_EVENT_TYPE_START;
+	events[i].point.y = polygon->edges[i].top;
+	events[i].point.x =
+	    _line_compute_intersection_x_for_y (&polygon->edges[i].line,
+						events[i].point.y);
+
+	events[i].edge.edge = polygon->edges[i];
+	events[i].edge.deferred.right = NULL;
+	events[i].edge.prev = NULL;
+	events[i].edge.next = NULL;
+    }
+
+    num_limits = polygon->num_limits; polygon->num_limits = 0;
+    polygon->num_edges = 0;
+
+    status = _cairo_bentley_ottmann_tessellate_bo_edges (event_ptrs,
+							 num_events,
+							 fill_rule,
+							 polygon);
+    polygon->num_limits = num_limits;
+
+    if (events != stack_events)
+	free (events);
+
+    if (DEBUG_POLYGON) {
+	FILE *file = fopen ("reduce_out.txt", "w");
+	_cairo_debug_print_polygon (file, polygon);
+	fclose (file);
+    }
+
+    return status;
+}