add cairo

1 files changed, 2202 insertions, 0 deletions

diff --git a/libs/cairo-1.16.0/src/cairo-botor-scan-converter.c b/libs/cairo-1.16.0/src/cairo-botor-scan-converter.c
new file mode 100644
index 0000000..438f96b
--- /dev/null
+++ b/libs/cairo-1.16.0/src/cairo-botor-scan-converter.c
@@ -0,0 +1,2202 @@
+/*
+ * Copyright © 2004 Carl Worth
+ * Copyright © 2006 Red Hat, Inc.
+ * Copyright © 2007 David Turner
+ * Copyright © 2008 M Joonas Pihlaja
+ * Copyright © 2008 Chris Wilson
+ * Copyright © 2009 Intel Corporation
+ *
+ * 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>
+ *      M Joonas Pihlaja <jpihlaja@cc.helsinki.fi>
+ *	Chris Wilson <chris@chris-wilson.co.uk>
+ */
+
+/* Provide definitions for standalone compilation */
+#include "cairoint.h"
+
+#include "cairo-error-private.h"
+#include "cairo-list-inline.h"
+#include "cairo-freelist-private.h"
+#include "cairo-combsort-inline.h"
+
+#include <setjmp.h>
+
+#define STEP_X CAIRO_FIXED_ONE
+#define STEP_Y CAIRO_FIXED_ONE
+#define UNROLL3(x) x x x
+
+#define STEP_XY (2*STEP_X*STEP_Y) /* Unit area in the step. */
+#define AREA_TO_ALPHA(c)  (((c)*255 + STEP_XY/2) / STEP_XY)
+
+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;
+
+struct quorem {
+    cairo_fixed_t quo;
+    cairo_fixed_t rem;
+};
+
+struct run {
+    struct run *next;
+    int sign;
+    cairo_fixed_t y;
+};
+
+typedef struct edge {
+    cairo_list_t link;
+
+    cairo_edge_t edge;
+
+    /* Current x coordinate and advancement.
+     * Initialised to the x coordinate of the top of the
+     * edge. The quotient is in cairo_fixed_t units and the
+     * remainder is mod dy in cairo_fixed_t units.
+     */
+    cairo_fixed_t dy;
+    struct quorem x;
+    struct quorem dxdy;
+    struct quorem dxdy_full;
+
+    cairo_bool_t vertical;
+    unsigned int flags;
+
+    int current_sign;
+    struct run *runs;
+} edge_t;
+
+enum {
+    START = 0x1,
+    STOP = 0x2,
+};
+
+/* 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 {
+    EVENT_TYPE_STOP,
+    EVENT_TYPE_INTERSECTION,
+    EVENT_TYPE_START
+} event_type_t;
+
+typedef struct _event {
+    cairo_fixed_t y;
+    event_type_t type;
+} event_t;
+
+typedef struct _start_event {
+    cairo_fixed_t y;
+    event_type_t type;
+    edge_t *edge;
+} start_event_t;
+
+typedef struct _queue_event {
+    cairo_fixed_t y;
+    event_type_t type;
+    edge_t *e1;
+    edge_t *e2;
+} queue_event_t;
+
+typedef struct _pqueue {
+    int size, max_size;
+
+    event_t **elements;
+    event_t *elements_embedded[1024];
+} pqueue_t;
+
+struct cell {
+    struct cell	*prev;
+    struct cell	*next;
+    int		 x;
+    int		 uncovered_area;
+    int		 covered_height;
+};
+
+typedef struct _sweep_line {
+    cairo_list_t active;
+    cairo_list_t stopped;
+    cairo_list_t *insert_cursor;
+    cairo_bool_t is_vertical;
+
+    cairo_fixed_t current_row;
+    cairo_fixed_t current_subrow;
+
+    struct coverage {
+	struct cell head;
+	struct cell tail;
+
+	struct cell *cursor;
+	int count;
+
+	cairo_freepool_t pool;
+    } coverage;
+
+    struct event_queue {
+	pqueue_t pq;
+	event_t **start_events;
+
+	cairo_freepool_t pool;
+    } queue;
+
+    cairo_freepool_t runs;
+
+    jmp_buf unwind;
+} sweep_line_t;
+
+cairo_always_inline static struct quorem
+floored_divrem (int a, int b)
+{
+    struct quorem qr;
+    qr.quo = a/b;
+    qr.rem = a%b;
+    if ((a^b)<0 && qr.rem) {
+	qr.quo--;
+	qr.rem += b;
+    }
+    return qr;
+}
+
+static struct quorem
+floored_muldivrem(int x, int a, int b)
+{
+    struct quorem qr;
+    long long xa = (long long)x*a;
+    qr.quo = xa/b;
+    qr.rem = xa%b;
+    if ((xa>=0) != (b>=0) && qr.rem) {
+	qr.quo--;
+	qr.rem += b;
+    }
+    return qr;
+}
+
+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;
+}
+
+/*
+ * 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_edge_t *a,
+			       const cairo_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->line.p1.x < a->line.p2.x) {
+                   amin = a->line.p1.x;
+                   amax = a->line.p2.x;
+           } else {
+                   amin = a->line.p2.x;
+                   amax = a->line.p1.x;
+           }
+           if (b->line.p1.x < b->line.p2.x) {
+                   bmin = b->line.p1.x;
+                   bmax = b->line.p2.x;
+           } else {
+                   bmin = b->line.p2.x;
+                   bmax = b->line.p1.x;
+           }
+           if (amax < bmin) return -1;
+           if (amin > bmax) return +1;
+    }
+
+    ady = a->line.p2.y - a->line.p1.y;
+    adx = a->line.p2.x - a->line.p1.x;
+    if (adx == 0)
+	have_dx_adx_bdx &= ~HAVE_ADX;
+
+    bdy = b->line.p2.y - b->line.p1.y;
+    bdx = b->line.p2.x - b->line.p1.x;
+    if (bdx == 0)
+	have_dx_adx_bdx &= ~HAVE_BDX;
+
+    dx = a->line.p1.x - b->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->line.p1.y)
+#define B _cairo_int64x32_128_mul (_cairo_int32x32_64_mul (bdx, ady), y - b->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->line.p1.y == b->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->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->line.p1.y, bdx);
+
+	    return _cairo_int64_cmp (bdy_dx, dy_bdx);
+	}
+    case HAVE_ALL:
+	/* XXX try comparing (a->line.p2.x - b->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_edge_t *a,
+			      int32_t y,
+			      int32_t x)
+{
+    int32_t adx, ady;
+    int32_t dx, dy;
+    cairo_int64_t L, R;
+
+    if (a->line.p1.x <= a->line.p2.x) {
+	if (x < a->line.p1.x)
+	    return 1;
+	if (x > a->line.p2.x)
+	    return -1;
+    } else {
+	if (x < a->line.p2.x)
+	    return 1;
+	if (x > a->line.p1.x)
+	    return -1;
+    }
+
+    adx = a->line.p2.x - a->line.p1.x;
+    dx = x - a->line.p1.x;
+
+    if (adx == 0)
+	return -dx;
+    if (dx == 0 || (adx ^ dx) < 0)
+	return adx;
+
+    dy = y - a->line.p1.y;
+    ady = a->line.p2.y - a->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_edge_t *a,
+		       const cairo_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;
+
+    /* XXX given we have x and dx? */
+
+    if (y == a->line.p1.y)
+	ax = a->line.p1.x;
+    else if (y == a->line.p2.y)
+	ax = a->line.p2.x;
+    else
+	have_ax_bx &= ~HAVE_AX;
+
+    if (y == b->line.p1.y)
+	bx = b->line.p1.x;
+    else if (y == b->line.p2.y)
+	bx = b->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
+slope_compare (const edge_t *a,
+	       const edge_t *b)
+{
+    cairo_int64_t L, R;
+    int cmp;
+
+    cmp = a->dxdy.quo - b->dxdy.quo;
+    if (cmp)
+	return cmp;
+
+    if (a->dxdy.rem == 0)
+	return -b->dxdy.rem;
+    if (b->dxdy.rem == 0)
+	return a->dxdy.rem;
+
+    L = _cairo_int32x32_64_mul (b->dy, a->dxdy.rem);
+    R = _cairo_int32x32_64_mul (a->dy, b->dxdy.rem);
+    return _cairo_int64_cmp (L, R);
+}
+
+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 inline int
+sweep_line_compare_edges (const edge_t	*a,
+			  const edge_t	*b,
+			  cairo_fixed_t y)
+{
+    int cmp;
+
+    if (line_equal (&a->edge.line, &b->edge.line))
+	return 0;
+
+    cmp = edges_compare_x_for_y (&a->edge, &b->edge, y);
+    if (cmp)
+	return cmp;
+
+    return slope_compare (a, b);
+}
+
+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 (const edge_t *a, const 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)) {
+	/* compute ceiling away from zero */
+	qr.quo = _cairo_int64_add (qr.quo,
+				   _cairo_int32_to_int64 (_cairo_int64_negative (qr.quo) ? -1 : 1));
+	intersection->y.exactness = INEXACT;
+    }
+#endif
+    intersection->y.ordinate = _cairo_int64_to_int32 (qr.quo);
+
+    return TRUE;
+}
+
+static int
+bo_intersect_ordinate_32_compare (int32_t a, int32_t b, int exactness)
+{
+    int cmp;
+
+    /* First compare the quotient */
+    cmp = a - b;
+    if (cmp)
+	return cmp;
+
+    /* With quotient identical, if remainder is 0 then compare equal */
+    /* Otherwise, the non-zero remainder makes a > b */
+    return -(INEXACT == 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
+bo_edge_contains_intersect_point (const 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 = bo_intersect_ordinate_32_compare (point->y.ordinate,
+						edge->edge.top,
+						point->y.exactness);
+    if (cmp_top < 0)
+	return FALSE;
+
+    cmp_bottom = bo_intersect_ordinate_32_compare (point->y.ordinate,
+						   edge->edge.bottom,
+						   point->y.exactness);
+    if (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 bo_intersect_ordinate_32_compare (top_x, point->x.ordinate, point->x.exactness) < 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 bo_intersect_ordinate_32_compare (point->x.ordinate, bot_x, point->x.exactness) < 0;
+    }
+}
+
+static cairo_bool_t
+edge_intersect (const edge_t		*a,
+		const edge_t		*b,
+		cairo_point_t	*intersection)
+{
+    cairo_bo_intersect_point_t quorem;
+
+    if (! intersect_lines (a, b, &quorem))
+	return FALSE;
+
+    if (a->edge.top != a->edge.line.p1.y || a->edge.bottom != a->edge.line.p2.y) {
+	if (! bo_edge_contains_intersect_point (a, &quorem))
+	    return FALSE;
+    }
+
+    if (b->edge.top != b->edge.line.p1.y || b->edge.bottom != b->edge.line.p2.y) {
+	if (! 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
+event_compare (const event_t *a, const event_t *b)
+{
+    return a->y - b->y;
+}
+
+static void
+pqueue_init (pqueue_t *pq)
+{
+    pq->max_size = ARRAY_LENGTH (pq->elements_embedded);
+    pq->size = 0;
+
+    pq->elements = pq->elements_embedded;
+}
+
+static void
+pqueue_fini (pqueue_t *pq)
+{
+    if (pq->elements != pq->elements_embedded)
+	free (pq->elements);
+}
+
+static cairo_bool_t
+pqueue_grow (pqueue_t *pq)
+{
+    event_t **new_elements;
+    pq->max_size *= 2;
+
+    if (pq->elements == pq->elements_embedded) {
+	new_elements = _cairo_malloc_ab (pq->max_size,
+					 sizeof (event_t *));
+	if (unlikely (new_elements == NULL))
+	    return FALSE;
+
+	memcpy (new_elements, pq->elements_embedded,
+		sizeof (pq->elements_embedded));
+    } else {
+	new_elements = _cairo_realloc_ab (pq->elements,
+					  pq->max_size,
+					  sizeof (event_t *));
+	if (unlikely (new_elements == NULL))
+	    return FALSE;
+    }
+
+    pq->elements = new_elements;
+    return TRUE;
+}
+
+static inline void
+pqueue_push (sweep_line_t *sweep_line, event_t *event)
+{
+    event_t **elements;
+    int i, parent;
+
+    if (unlikely (sweep_line->queue.pq.size + 1 == sweep_line->queue.pq.max_size)) {
+	if (unlikely (! pqueue_grow (&sweep_line->queue.pq))) {
+	    longjmp (sweep_line->unwind,
+		     _cairo_error (CAIRO_STATUS_NO_MEMORY));
+	}
+    }
+
+    elements = sweep_line->queue.pq.elements;
+    for (i = ++sweep_line->queue.pq.size;
+	 i != PQ_FIRST_ENTRY &&
+	 event_compare (event,
+			elements[parent = PQ_PARENT_INDEX (i)]) < 0;
+	 i = parent)
+    {
+	elements[i] = elements[parent];
+    }
+
+    elements[i] = event;
+}
+
+static inline void
+pqueue_pop (pqueue_t *pq)
+{
+    event_t **elements = pq->elements;
+    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 &&
+	    event_compare (elements[child+1],
+			   elements[child]) < 0)
+	{
+	    child++;
+	}
+
+	if (event_compare (elements[child], tail) >= 0)
+	    break;
+
+	elements[i] = elements[child];
+    }
+    elements[i] = tail;
+}
+
+static inline void
+event_insert (sweep_line_t	*sweep_line,
+	      event_type_t	 type,
+	      edge_t		*e1,
+	      edge_t		*e2,
+	      cairo_fixed_t	 y)
+{
+    queue_event_t *event;
+
+    event = _cairo_freepool_alloc (&sweep_line->queue.pool);
+    if (unlikely (event == NULL)) {
+	longjmp (sweep_line->unwind,
+		 _cairo_error (CAIRO_STATUS_NO_MEMORY));
+    }
+
+    event->y = y;
+    event->type = type;
+    event->e1 = e1;
+    event->e2 = e2;
+
+    pqueue_push (sweep_line, (event_t *) event);
+}
+
+static void
+event_delete (sweep_line_t	*sweep_line,
+	      event_t		*event)
+{
+    _cairo_freepool_free (&sweep_line->queue.pool, event);
+}
+
+static inline event_t *
+event_next (sweep_line_t *sweep_line)
+{
+    event_t *event, *cmp;
+
+    event = sweep_line->queue.pq.elements[PQ_FIRST_ENTRY];
+    cmp = *sweep_line->queue.start_events;
+    if (event == NULL ||
+	(cmp != NULL && event_compare (cmp, event) < 0))
+    {
+	event = cmp;
+	sweep_line->queue.start_events++;
+    }
+    else
+    {
+	pqueue_pop (&sweep_line->queue.pq);
+    }
+
+    return event;
+}
+
+CAIRO_COMBSORT_DECLARE (start_event_sort, event_t *, event_compare)
+
+static inline void
+event_insert_stop (sweep_line_t	*sweep_line,
+		   edge_t	*edge)
+{
+    event_insert (sweep_line,
+		  EVENT_TYPE_STOP,
+		  edge, NULL,
+		  edge->edge.bottom);
+}
+
+static inline void
+event_insert_if_intersect_below_current_y (sweep_line_t	*sweep_line,
+					   edge_t	*left,
+					   edge_t	*right)
+{
+    cairo_point_t intersection;
+
+    /* start points intersect */
+    if (left->edge.line.p1.x == right->edge.line.p1.x &&
+	left->edge.line.p1.y == right->edge.line.p1.y)
+    {
+	return;
+    }
+
+    /* end points intersect, process DELETE events first */
+    if (left->edge.line.p2.x == right->edge.line.p2.x &&
+	left->edge.line.p2.y == right->edge.line.p2.y)
+    {
+	return;
+    }
+
+    if (slope_compare (left, right) <= 0)
+	return;
+
+    if (! edge_intersect (left, right, &intersection))
+	return;
+
+    event_insert (sweep_line,
+		  EVENT_TYPE_INTERSECTION,
+		  left, right,
+		  intersection.y);
+}
+
+static inline edge_t *
+link_to_edge (cairo_list_t *link)
+{
+    return (edge_t *) link;
+}
+
+static void
+sweep_line_insert (sweep_line_t	*sweep_line,
+		   edge_t	*edge)
+{
+    cairo_list_t *pos;
+    cairo_fixed_t y = sweep_line->current_subrow;
+
+    pos = sweep_line->insert_cursor;
+    if (pos == &sweep_line->active)
+	pos = sweep_line->active.next;
+    if (pos != &sweep_line->active) {
+	int cmp;
+
+	cmp = sweep_line_compare_edges (link_to_edge (pos),
+					edge,
+					y);
+	if (cmp < 0) {
+	    while (pos->next != &sweep_line->active &&
+		   sweep_line_compare_edges (link_to_edge (pos->next),
+					     edge,
+					     y) < 0)
+	    {
+		pos = pos->next;
+	    }
+	} else if (cmp > 0) {
+	    do {
+		pos = pos->prev;
+	    } while (pos != &sweep_line->active &&
+		     sweep_line_compare_edges (link_to_edge (pos),
+					       edge,
+					       y) > 0);
+	}
+    }
+    cairo_list_add (&edge->link, pos);
+    sweep_line->insert_cursor = &edge->link;
+}
+
+inline static void
+coverage_rewind (struct coverage *cells)
+{
+    cells->cursor = &cells->head;
+}
+
+static void
+coverage_init (struct coverage *cells)
+{
+    _cairo_freepool_init (&cells->pool,
+			  sizeof (struct cell));
+    cells->head.prev = NULL;
+    cells->head.next = &cells->tail;
+    cells->head.x = INT_MIN;
+    cells->tail.prev = &cells->head;
+    cells->tail.next = NULL;
+    cells->tail.x = INT_MAX;
+    cells->count = 0;
+    coverage_rewind (cells);
+}
+
+static void
+coverage_fini (struct coverage *cells)
+{
+    _cairo_freepool_fini (&cells->pool);
+}
+
+inline static void
+coverage_reset (struct coverage *cells)
+{
+    cells->head.next = &cells->tail;
+    cells->tail.prev = &cells->head;
+    cells->count = 0;
+    _cairo_freepool_reset (&cells->pool);
+    coverage_rewind (cells);
+}
+
+static struct cell *
+coverage_alloc (sweep_line_t *sweep_line,
+		struct cell *tail,
+		int x)
+{
+    struct cell *cell;
+
+    cell = _cairo_freepool_alloc (&sweep_line->coverage.pool);
+    if (unlikely (NULL == cell)) {
+	longjmp (sweep_line->unwind,
+		 _cairo_error (CAIRO_STATUS_NO_MEMORY));
+    }
+
+    tail->prev->next = cell;
+    cell->prev = tail->prev;
+    cell->next = tail;
+    tail->prev = cell;
+    cell->x = x;
+    cell->uncovered_area = 0;
+    cell->covered_height = 0;
+    sweep_line->coverage.count++;
+    return cell;
+}
+
+inline static struct cell *
+coverage_find (sweep_line_t *sweep_line, int x)
+{
+    struct cell *cell;
+
+    cell = sweep_line->coverage.cursor;
+    if (unlikely (cell->x > x)) {
+	do {
+	    if (cell->prev->x < x)
+		break;
+	    cell = cell->prev;
+	} while (TRUE);
+    } else {
+	if (cell->x == x)
+	    return cell;
+
+	do {
+	    UNROLL3({
+		    cell = cell->next;
+		    if (cell->x >= x)
+			break;
+		    });
+	} while (TRUE);
+    }
+
+    if (cell->x != x)
+	cell = coverage_alloc (sweep_line, cell, x);
+
+    return sweep_line->coverage.cursor = cell;
+}
+
+static void
+coverage_render_cells (sweep_line_t *sweep_line,
+		       cairo_fixed_t left, cairo_fixed_t right,
+		       cairo_fixed_t y1, cairo_fixed_t y2,
+		       int sign)
+{
+    int fx1, fx2;
+    int ix1, ix2;
+    int dx, dy;
+
+    /* Orient the edge left-to-right. */
+    dx = right - left;
+    if (dx >= 0) {
+	ix1 = _cairo_fixed_integer_part (left);
+	fx1 = _cairo_fixed_fractional_part (left);
+
+	ix2 = _cairo_fixed_integer_part (right);
+	fx2 = _cairo_fixed_fractional_part (right);
+
+	dy = y2 - y1;
+    } else {
+	ix1 = _cairo_fixed_integer_part (right);
+	fx1 = _cairo_fixed_fractional_part (right);
+
+	ix2 = _cairo_fixed_integer_part (left);
+	fx2 = _cairo_fixed_fractional_part (left);
+
+	dx = -dx;
+	sign = -sign;
+	dy = y1 - y2;
+	y1 = y2 - dy;
+	y2 = y1 + dy;
+    }
+
+    /* Add coverage for all pixels [ix1,ix2] on this row crossed
+     * by the edge. */
+    {
+	struct quorem y = floored_divrem ((STEP_X - fx1)*dy, dx);
+	struct cell *cell;
+
+	cell = sweep_line->coverage.cursor;
+	if (cell->x != ix1) {
+	    if (unlikely (cell->x > ix1)) {
+		do {
+		    if (cell->prev->x < ix1)
+			break;
+		    cell = cell->prev;
+		} while (TRUE);
+	    } else do {
+		UNROLL3({
+			if (cell->x >= ix1)
+			    break;
+			cell = cell->next;
+			});
+	    } while (TRUE);
+
+	    if (cell->x != ix1)
+		cell = coverage_alloc (sweep_line, cell, ix1);
+	}
+
+	cell->uncovered_area += sign * y.quo * (STEP_X + fx1);
+	cell->covered_height += sign * y.quo;
+	y.quo += y1;
+
+	cell = cell->next;
+	if (cell->x != ++ix1)
+	    cell = coverage_alloc (sweep_line, cell, ix1);
+	if (ix1 < ix2) {
+	    struct quorem dydx_full = floored_divrem (STEP_X*dy, dx);
+
+	    do {
+		cairo_fixed_t y_skip = dydx_full.quo;
+		y.rem += dydx_full.rem;
+		if (y.rem >= dx) {
+		    ++y_skip;
+		    y.rem -= dx;
+		}
+
+		y.quo += y_skip;
+
+		y_skip *= sign;
+		cell->covered_height += y_skip;
+		cell->uncovered_area += y_skip*STEP_X;
+
+		cell = cell->next;
+		if (cell->x != ++ix1)
+		    cell = coverage_alloc (sweep_line, cell, ix1);
+	    } while (ix1 != ix2);
+	}
+	cell->uncovered_area += sign*(y2 - y.quo)*fx2;
+	cell->covered_height += sign*(y2 - y.quo);
+	sweep_line->coverage.cursor = cell;
+    }
+}
+
+inline static void
+full_inc_edge (edge_t *edge)
+{
+    edge->x.quo += edge->dxdy_full.quo;
+    edge->x.rem += edge->dxdy_full.rem;
+    if (edge->x.rem >= 0) {
+	++edge->x.quo;
+	edge->x.rem -= edge->dy;
+    }
+}
+
+static void
+full_add_edge (sweep_line_t *sweep_line, edge_t *edge, int sign)
+{
+    struct cell *cell;
+    cairo_fixed_t x1, x2;
+    int ix1, ix2;
+    int frac;
+
+    edge->current_sign = sign;
+
+    ix1 = _cairo_fixed_integer_part (edge->x.quo);
+
+    if (edge->vertical) {
+	frac = _cairo_fixed_fractional_part (edge->x.quo);
+	cell = coverage_find (sweep_line, ix1);
+	cell->covered_height += sign * STEP_Y;
+	cell->uncovered_area += sign * 2 * frac * STEP_Y;
+	return;
+    }
+
+    x1 = edge->x.quo;
+    full_inc_edge (edge);
+    x2 = edge->x.quo;
+
+    ix2 = _cairo_fixed_integer_part (edge->x.quo);
+
+    /* Edge is entirely within a column? */
+    if (likely (ix1 == ix2)) {
+	frac = _cairo_fixed_fractional_part (x1) +
+	       _cairo_fixed_fractional_part (x2);
+	cell = coverage_find (sweep_line, ix1);
+	cell->covered_height += sign * STEP_Y;
+	cell->uncovered_area += sign * frac * STEP_Y;
+	return;
+    }
+
+    coverage_render_cells (sweep_line, x1, x2, 0, STEP_Y, sign);
+}
+
+static void
+full_nonzero (sweep_line_t *sweep_line)
+{
+    cairo_list_t *pos;
+
+    sweep_line->is_vertical = TRUE;
+    pos = sweep_line->active.next;
+    do {
+	edge_t *left = link_to_edge (pos), *right;
+	int winding = left->edge.dir;
+
+	sweep_line->is_vertical &= left->vertical;
+
+	pos = left->link.next;
+	do {
+	    if (unlikely (pos == &sweep_line->active)) {
+		full_add_edge (sweep_line, left, +1);
+		return;
+	    }
+
+	    right = link_to_edge (pos);
+	    pos = pos->next;
+	    sweep_line->is_vertical &= right->vertical;
+
+	    winding += right->edge.dir;
+	    if (0 == winding) {
+		if (pos == &sweep_line->active ||
+		    link_to_edge (pos)->x.quo != right->x.quo)
+		{
+		    break;
+		}
+	    }
+
+	    if (! right->vertical)
+		full_inc_edge (right);
+	} while (TRUE);
+
+	full_add_edge (sweep_line, left,  +1);
+	full_add_edge (sweep_line, right, -1);
+    } while (pos != &sweep_line->active);
+}
+
+static void
+full_evenodd (sweep_line_t *sweep_line)
+{
+    cairo_list_t *pos;
+
+    sweep_line->is_vertical = TRUE;
+    pos = sweep_line->active.next;
+    do {
+	edge_t *left = link_to_edge (pos), *right;
+	int winding = 0;
+
+	sweep_line->is_vertical &= left->vertical;
+
+	pos = left->link.next;
+	do {
+	    if (pos == &sweep_line->active) {
+		full_add_edge (sweep_line, left, +1);
+		return;
+	    }
+
+	    right = link_to_edge (pos);
+	    pos = pos->next;
+	    sweep_line->is_vertical &= right->vertical;
+
+	    if (++winding & 1) {
+		if (pos == &sweep_line->active ||
+		    link_to_edge (pos)->x.quo != right->x.quo)
+		{
+		    break;
+		}
+	    }
+
+	    if (! right->vertical)
+		full_inc_edge (right);
+	} while (TRUE);
+
+	full_add_edge (sweep_line, left,  +1);
+	full_add_edge (sweep_line, right, -1);
+    } while (pos != &sweep_line->active);
+}
+
+static void
+render_rows (cairo_botor_scan_converter_t *self,
+	     sweep_line_t *sweep_line,
+	     int y, int height,
+	     cairo_span_renderer_t *renderer)
+{
+    cairo_half_open_span_t spans_stack[CAIRO_STACK_ARRAY_LENGTH (cairo_half_open_span_t)];
+    cairo_half_open_span_t *spans = spans_stack;
+    struct cell *cell;
+    int prev_x, cover;
+    int num_spans;
+    cairo_status_t status;
+
+    if (unlikely (sweep_line->coverage.count == 0)) {
+	status = renderer->render_rows (renderer, y, height, NULL, 0);
+	if (unlikely (status))
+	    longjmp (sweep_line->unwind, status);
+	return;
+    }
+
+    /* Allocate enough spans for the row. */
+
+    num_spans = 2*sweep_line->coverage.count+2;
+    if (unlikely (num_spans > ARRAY_LENGTH (spans_stack))) {
+	spans = _cairo_malloc_ab (num_spans, sizeof (cairo_half_open_span_t));
+	if (unlikely (spans == NULL)) {
+	    longjmp (sweep_line->unwind,
+		     _cairo_error (CAIRO_STATUS_NO_MEMORY));
+	}
+    }
+
+    /* Form the spans from the coverage and areas. */
+    num_spans = 0;
+    prev_x = self->xmin;
+    cover = 0;
+    cell = sweep_line->coverage.head.next;
+    do {
+	int x = cell->x;
+	int area;
+
+	if (x > prev_x) {
+	    spans[num_spans].x = prev_x;
+	    spans[num_spans].inverse = 0;
+	    spans[num_spans].coverage = AREA_TO_ALPHA (cover);
+	    ++num_spans;
+	}
+
+	cover += cell->covered_height*STEP_X*2;
+	area = cover - cell->uncovered_area;
+
+	spans[num_spans].x = x;
+	spans[num_spans].coverage = AREA_TO_ALPHA (area);
+	++num_spans;
+
+	prev_x = x + 1;
+    } while ((cell = cell->next) != &sweep_line->coverage.tail);
+
+    if (prev_x <= self->xmax) {
+	spans[num_spans].x = prev_x;
+	spans[num_spans].inverse = 0;
+	spans[num_spans].coverage = AREA_TO_ALPHA (cover);
+	++num_spans;
+    }
+
+    if (cover && prev_x < self->xmax) {
+	spans[num_spans].x = self->xmax;
+	spans[num_spans].inverse = 1;
+	spans[num_spans].coverage = 0;
+	++num_spans;
+    }
+
+    status = renderer->render_rows (renderer, y, height, spans, num_spans);
+
+    if (unlikely (spans != spans_stack))
+	free (spans);
+
+    coverage_reset (&sweep_line->coverage);
+
+    if (unlikely (status))
+	longjmp (sweep_line->unwind, status);
+}
+
+static void
+full_repeat (sweep_line_t *sweep)
+{
+    edge_t *edge;
+
+    cairo_list_foreach_entry (edge, edge_t, &sweep->active, link) {
+	if (edge->current_sign)
+	    full_add_edge (sweep, edge, edge->current_sign);
+	else if (! edge->vertical)
+	    full_inc_edge (edge);
+    }
+}
+
+static void
+full_reset (sweep_line_t *sweep)
+{
+    edge_t *edge;
+
+    cairo_list_foreach_entry (edge, edge_t, &sweep->active, link)
+	edge->current_sign = 0;
+}
+
+static void
+full_step (cairo_botor_scan_converter_t *self,
+	   sweep_line_t *sweep_line,
+	   cairo_fixed_t row,
+	   cairo_span_renderer_t *renderer)
+{
+    int top, bottom;
+
+    top = _cairo_fixed_integer_part (sweep_line->current_row);
+    bottom = _cairo_fixed_integer_part (row);
+    if (cairo_list_is_empty (&sweep_line->active)) {
+	cairo_status_t  status;
+
+	status = renderer->render_rows (renderer, top, bottom - top, NULL, 0);
+	if (unlikely (status))
+	    longjmp (sweep_line->unwind, status);
+
+	return;
+    }
+
+    if (self->fill_rule == CAIRO_FILL_RULE_WINDING)
+	full_nonzero (sweep_line);
+    else
+	full_evenodd (sweep_line);
+
+    if (sweep_line->is_vertical || bottom == top + 1) {
+	render_rows (self, sweep_line, top, bottom - top, renderer);
+	full_reset (sweep_line);
+	return;
+    }
+
+    render_rows (self, sweep_line, top++, 1, renderer);
+    do {
+	full_repeat (sweep_line);
+	render_rows (self, sweep_line, top, 1, renderer);
+    } while (++top != bottom);
+
+    full_reset (sweep_line);
+}
+
+cairo_always_inline static void
+sub_inc_edge (edge_t *edge,
+	      cairo_fixed_t height)
+{
+    if (height == 1) {
+	edge->x.quo += edge->dxdy.quo;
+	edge->x.rem += edge->dxdy.rem;
+	if (edge->x.rem >= 0) {
+	    ++edge->x.quo;
+	    edge->x.rem -= edge->dy;
+	}
+    } else {
+	edge->x.quo += height * edge->dxdy.quo;
+	edge->x.rem += height * edge->dxdy.rem;
+	if (edge->x.rem >= 0) {
+	    int carry = edge->x.rem / edge->dy + 1;
+	    edge->x.quo += carry;
+	    edge->x.rem -= carry * edge->dy;
+	}
+    }
+}
+
+static void
+sub_add_run (sweep_line_t *sweep_line, edge_t *edge, int y, int sign)
+{
+    struct run *run;
+
+    run = _cairo_freepool_alloc (&sweep_line->runs);
+    if (unlikely (run == NULL))
+	longjmp (sweep_line->unwind, _cairo_error (CAIRO_STATUS_NO_MEMORY));
+
+    run->y = y;
+    run->sign = sign;
+    run->next = edge->runs;
+    edge->runs = run;
+
+    edge->current_sign = sign;
+}
+
+inline static cairo_bool_t
+edges_coincident (edge_t *left, edge_t *right, cairo_fixed_t y)
+{
+    /* XXX is compare_x_for_y() worth executing during sub steps? */
+    return line_equal (&left->edge.line, &right->edge.line);
+    //edges_compare_x_for_y (&left->edge, &right->edge, y) >= 0;
+}
+
+static void
+sub_nonzero (sweep_line_t *sweep_line)
+{
+    cairo_fixed_t y = sweep_line->current_subrow;
+    cairo_fixed_t fy = _cairo_fixed_fractional_part (y);
+    cairo_list_t *pos;
+
+    pos = sweep_line->active.next;
+    do {
+	edge_t *left = link_to_edge (pos), *right;
+	int winding = left->edge.dir;
+
+	pos = left->link.next;
+	do {
+	    if (unlikely (pos == &sweep_line->active)) {
+		if (left->current_sign != +1)
+		    sub_add_run (sweep_line, left, fy, +1);
+		return;
+	    }
+
+	    right = link_to_edge (pos);
+	    pos = pos->next;
+
+	    winding += right->edge.dir;
+	    if (0 == winding) {
+		if (pos == &sweep_line->active ||
+		    ! edges_coincident (right, link_to_edge (pos), y))
+		{
+		    break;
+		}
+	    }
+
+	    if (right->current_sign)
+		sub_add_run (sweep_line, right, fy, 0);
+	} while (TRUE);
+
+	if (left->current_sign != +1)
+	    sub_add_run (sweep_line, left, fy, +1);
+	if (right->current_sign != -1)
+	    sub_add_run (sweep_line, right, fy, -1);
+    } while (pos != &sweep_line->active);
+}
+
+static void
+sub_evenodd (sweep_line_t *sweep_line)
+{
+    cairo_fixed_t y = sweep_line->current_subrow;
+    cairo_fixed_t fy = _cairo_fixed_fractional_part (y);
+    cairo_list_t *pos;
+
+    pos = sweep_line->active.next;
+    do {
+	edge_t *left = link_to_edge (pos), *right;
+	int winding = 0;
+
+	pos = left->link.next;
+	do {
+	    if (unlikely (pos == &sweep_line->active)) {
+		if (left->current_sign != +1)
+		    sub_add_run (sweep_line, left, fy, +1);
+		return;
+	    }
+
+	    right = link_to_edge (pos);
+	    pos = pos->next;
+
+	    if (++winding & 1) {
+		if (pos == &sweep_line->active ||
+		    ! edges_coincident (right, link_to_edge (pos), y))
+		{
+		    break;
+		}
+	    }
+
+	    if (right->current_sign)
+		sub_add_run (sweep_line, right, fy, 0);
+	} while (TRUE);
+
+	if (left->current_sign != +1)
+	    sub_add_run (sweep_line, left, fy, +1);
+	if (right->current_sign != -1)
+	    sub_add_run (sweep_line, right, fy, -1);
+    } while (pos != &sweep_line->active);
+}
+
+cairo_always_inline static void
+sub_step (cairo_botor_scan_converter_t *self,
+	  sweep_line_t *sweep_line)
+{
+    if (cairo_list_is_empty (&sweep_line->active))
+	return;
+
+    if (self->fill_rule == CAIRO_FILL_RULE_WINDING)
+	sub_nonzero (sweep_line);
+    else
+	sub_evenodd (sweep_line);
+}
+
+static void
+coverage_render_runs (sweep_line_t *sweep, edge_t *edge,
+		      cairo_fixed_t y1, cairo_fixed_t y2)
+{
+    struct run tail;
+    struct run *run = &tail;
+
+    tail.next = NULL;
+    tail.y = y2;
+
+    /* Order the runs top->bottom */
+    while (edge->runs) {
+	struct run *r;
+
+	r = edge->runs;
+	edge->runs = r->next;
+	r->next = run;
+	run = r;
+    }
+
+    if (run->y > y1)
+	sub_inc_edge (edge, run->y - y1);
+
+    do {
+	cairo_fixed_t x1, x2;
+
+	y1 = run->y;
+	y2 = run->next->y;
+
+	x1 = edge->x.quo;
+	if (y2 - y1 == STEP_Y)
+	    full_inc_edge (edge);
+	else
+	    sub_inc_edge (edge, y2 - y1);
+	x2 = edge->x.quo;
+
+	if (run->sign) {
+	    int ix1, ix2;
+
+	    ix1 = _cairo_fixed_integer_part (x1);
+	    ix2 = _cairo_fixed_integer_part (x2);
+
+	    /* Edge is entirely within a column? */
+	    if (likely (ix1 == ix2)) {
+		struct cell *cell;
+		int frac;
+
+		frac = _cairo_fixed_fractional_part (x1) +
+		       _cairo_fixed_fractional_part (x2);
+		cell = coverage_find (sweep, ix1);
+		cell->covered_height += run->sign * (y2 - y1);
+		cell->uncovered_area += run->sign * (y2 - y1) * frac;
+	    } else {
+		coverage_render_cells (sweep, x1, x2, y1, y2, run->sign);
+	    }
+	}
+
+	run = run->next;
+    } while (run->next != NULL);
+}
+
+static void
+coverage_render_vertical_runs (sweep_line_t *sweep, edge_t *edge, cairo_fixed_t y2)
+{
+    struct cell *cell;
+    struct run *run;
+    int height = 0;
+
+    for (run = edge->runs; run != NULL; run = run->next) {
+	if (run->sign)
+	    height += run->sign * (y2 - run->y);
+	y2 = run->y;
+    }
+
+    cell = coverage_find (sweep, _cairo_fixed_integer_part (edge->x.quo));
+    cell->covered_height += height;
+    cell->uncovered_area += 2 * _cairo_fixed_fractional_part (edge->x.quo) * height;
+}
+
+cairo_always_inline static void
+sub_emit (cairo_botor_scan_converter_t *self,
+	  sweep_line_t *sweep,
+	  cairo_span_renderer_t *renderer)
+{
+    edge_t *edge;
+
+    sub_step (self, sweep);
+
+    /* convert the runs into coverages */
+
+    cairo_list_foreach_entry (edge, edge_t, &sweep->active, link) {
+	if (edge->runs == NULL) {
+	    if (! edge->vertical) {
+		if (edge->flags & START) {
+		    sub_inc_edge (edge,
+				  STEP_Y - _cairo_fixed_fractional_part (edge->edge.top));
+		    edge->flags &= ~START;
+		} else
+		    full_inc_edge (edge);
+	    }
+	} else {
+	    if (edge->vertical) {
+		coverage_render_vertical_runs (sweep, edge, STEP_Y);
+	    } else {
+		int y1 = 0;
+		if (edge->flags & START) {
+		    y1 = _cairo_fixed_fractional_part (edge->edge.top);
+		    edge->flags &= ~START;
+		}
+		coverage_render_runs (sweep, edge, y1, STEP_Y);
+	    }
+	}
+	edge->current_sign = 0;
+	edge->runs = NULL;
+    }
+
+    cairo_list_foreach_entry (edge, edge_t, &sweep->stopped, link) {
+	int y2 = _cairo_fixed_fractional_part (edge->edge.bottom);
+	if (edge->vertical) {
+	    coverage_render_vertical_runs (sweep, edge, y2);
+	} else {
+	    int y1 = 0;
+	    if (edge->flags & START)
+		y1 = _cairo_fixed_fractional_part (edge->edge.top);
+	    coverage_render_runs (sweep, edge, y1, y2);
+	}
+    }
+    cairo_list_init (&sweep->stopped);
+
+    _cairo_freepool_reset (&sweep->runs);
+
+    render_rows (self, sweep,
+		 _cairo_fixed_integer_part (sweep->current_row), 1,
+		 renderer);
+}
+
+static void
+sweep_line_init (sweep_line_t	 *sweep_line,
+		 event_t	**start_events,
+		 int		  num_events)
+{
+    cairo_list_init (&sweep_line->active);
+    cairo_list_init (&sweep_line->stopped);
+    sweep_line->insert_cursor = &sweep_line->active;
+
+    sweep_line->current_row = INT32_MIN;
+    sweep_line->current_subrow = INT32_MIN;
+
+    coverage_init (&sweep_line->coverage);
+    _cairo_freepool_init (&sweep_line->runs, sizeof (struct run));
+
+    start_event_sort (start_events, num_events);
+    start_events[num_events] = NULL;
+
+    sweep_line->queue.start_events = start_events;
+
+    _cairo_freepool_init (&sweep_line->queue.pool,
+			  sizeof (queue_event_t));
+    pqueue_init (&sweep_line->queue.pq);
+    sweep_line->queue.pq.elements[PQ_FIRST_ENTRY] = NULL;
+}
+
+static void
+sweep_line_delete (sweep_line_t	*sweep_line,
+		   edge_t	*edge)
+{
+    if (sweep_line->insert_cursor == &edge->link)
+	sweep_line->insert_cursor = edge->link.prev;
+
+    cairo_list_del (&edge->link);
+    if (edge->runs)
+	cairo_list_add_tail (&edge->link, &sweep_line->stopped);
+    edge->flags |= STOP;
+}
+
+static void
+sweep_line_swap (sweep_line_t	*sweep_line,
+		 edge_t	*left,
+		 edge_t	*right)
+{
+    right->link.prev = left->link.prev;
+    left->link.next = right->link.next;
+    right->link.next = &left->link;
+    left->link.prev = &right->link;
+    left->link.next->prev = &left->link;
+    right->link.prev->next = &right->link;
+}
+
+static void
+sweep_line_fini (sweep_line_t *sweep_line)
+{
+    pqueue_fini (&sweep_line->queue.pq);
+    _cairo_freepool_fini (&sweep_line->queue.pool);
+    coverage_fini (&sweep_line->coverage);
+    _cairo_freepool_fini (&sweep_line->runs);
+}
+
+static cairo_status_t
+botor_generate (cairo_botor_scan_converter_t	 *self,
+		event_t				**start_events,
+		cairo_span_renderer_t		 *renderer)
+{
+    cairo_status_t status;
+    sweep_line_t sweep_line;
+    cairo_fixed_t ybot;
+    event_t *event;
+    cairo_list_t *left, *right;
+    edge_t *e1, *e2;
+    int bottom;
+
+    sweep_line_init (&sweep_line, start_events, self->num_edges);
+    if ((status = setjmp (sweep_line.unwind)))
+	goto unwind;
+
+    ybot = self->extents.p2.y;
+    sweep_line.current_subrow = self->extents.p1.y;
+    sweep_line.current_row = _cairo_fixed_floor (self->extents.p1.y);
+    event = *sweep_line.queue.start_events++;
+    do {
+	/* Can we process a full step in one go? */
+	if (event->y >= sweep_line.current_row + STEP_Y) {
+	    bottom = _cairo_fixed_floor (event->y);
+	    full_step (self, &sweep_line, bottom, renderer);
+	    sweep_line.current_row = bottom;
+	    sweep_line.current_subrow = bottom;
+	}
+
+	do {
+	    if (event->y > sweep_line.current_subrow) {
+		sub_step (self, &sweep_line);
+		sweep_line.current_subrow = event->y;
+	    }
+
+	    do {
+		/* Update the active list using Bentley-Ottmann */
+		switch (event->type) {
+		case EVENT_TYPE_START:
+		    e1 = ((start_event_t *) event)->edge;
+
+		    sweep_line_insert (&sweep_line, e1);
+		    event_insert_stop (&sweep_line, e1);
+
+		    left = e1->link.prev;
+		    right = e1->link.next;
+
+		    if (left != &sweep_line.active) {
+			event_insert_if_intersect_below_current_y (&sweep_line,
+								   link_to_edge (left), e1);
+		    }
+
+		    if (right != &sweep_line.active) {
+			event_insert_if_intersect_below_current_y (&sweep_line,
+								   e1, link_to_edge (right));
+		    }
+
+		    break;
+
+		case EVENT_TYPE_STOP:
+		    e1 = ((queue_event_t *) event)->e1;
+		    event_delete (&sweep_line, event);
+
+		    left = e1->link.prev;
+		    right = e1->link.next;
+
+		    sweep_line_delete (&sweep_line, e1);
+
+		    if (left != &sweep_line.active &&
+			right != &sweep_line.active)
+		    {
+			 event_insert_if_intersect_below_current_y (&sweep_line,
+								    link_to_edge (left),
+								    link_to_edge (right));
+		    }
+
+		    break;
+
+		case EVENT_TYPE_INTERSECTION:
+		    e1 = ((queue_event_t *) event)->e1;
+		    e2 = ((queue_event_t *) event)->e2;
+
+		    event_delete (&sweep_line, event);
+		    if (e1->flags & STOP)
+			break;
+		    if (e2->flags & STOP)
+			break;
+
+		    /* skip this intersection if its edges are not adjacent */
+		    if (&e2->link != e1->link.next)
+			break;
+
+		    left = e1->link.prev;
+		    right = e2->link.next;
+
+		    sweep_line_swap (&sweep_line, e1, e2);
+
+		    /* after the swap e2 is left of e1 */
+		    if (left != &sweep_line.active) {
+			event_insert_if_intersect_below_current_y (&sweep_line,
+								   link_to_edge (left), e2);
+		    }
+
+		    if (right != &sweep_line.active) {
+			event_insert_if_intersect_below_current_y (&sweep_line,
+								   e1, link_to_edge (right));
+		    }
+
+		    break;
+		}
+
+		event = event_next (&sweep_line);
+		if (event == NULL)
+		    goto end;
+	    } while (event->y == sweep_line.current_subrow);
+	} while (event->y < sweep_line.current_row + STEP_Y);
+
+	bottom = sweep_line.current_row + STEP_Y;
+	sub_emit (self, &sweep_line, renderer);
+	sweep_line.current_subrow = bottom;
+	sweep_line.current_row = sweep_line.current_subrow;
+    } while (TRUE);
+
+  end:
+    /* flush any partial spans */
+    if (sweep_line.current_subrow != sweep_line.current_row) {
+	sub_emit (self, &sweep_line, renderer);
+	sweep_line.current_row += STEP_Y;
+	sweep_line.current_subrow = sweep_line.current_row;
+    }
+    /* clear the rest */
+    if (sweep_line.current_subrow < ybot) {
+	bottom = _cairo_fixed_integer_part (sweep_line.current_row);
+	status = renderer->render_rows (renderer,
+					bottom, _cairo_fixed_integer_ceil (ybot) - bottom,
+					NULL, 0);
+    }
+
+ unwind:
+    sweep_line_fini (&sweep_line);
+
+    return status;
+}
+
+static cairo_status_t
+_cairo_botor_scan_converter_generate (void			*converter,
+				      cairo_span_renderer_t	*renderer)
+{
+    cairo_botor_scan_converter_t *self = converter;
+    start_event_t stack_events[CAIRO_STACK_ARRAY_LENGTH (start_event_t)];
+    start_event_t *events;
+    event_t *stack_event_ptrs[ARRAY_LENGTH (stack_events) + 1];
+    event_t **event_ptrs;
+    struct _cairo_botor_scan_converter_chunk *chunk;
+    cairo_status_t status;
+    int num_events;
+    int i, j;
+
+    num_events = self->num_edges;
+    if (unlikely (0 == num_events)) {
+	return renderer->render_rows (renderer,
+				      _cairo_fixed_integer_floor (self->extents.p1.y),
+				      _cairo_fixed_integer_ceil (self->extents.p2.y) -
+				      _cairo_fixed_integer_floor (self->extents.p1.y),
+				      NULL, 0);
+    }
+
+    events = stack_events;
+    event_ptrs = stack_event_ptrs;
+    if (unlikely (num_events >= ARRAY_LENGTH (stack_events))) {
+	events = _cairo_malloc_ab_plus_c (num_events,
+					  sizeof (start_event_t) + sizeof (event_t *),
+					  sizeof (event_t *));
+	if (unlikely (events == NULL))
+	    return _cairo_error (CAIRO_STATUS_NO_MEMORY);
+
+	event_ptrs = (event_t **) (events + num_events);
+    }
+
+    j = 0;
+    for (chunk = &self->chunks; chunk != NULL; chunk = chunk->next) {
+	edge_t *edge;
+
+	edge = chunk->base;
+	for (i = 0; i < chunk->count; i++) {
+	    event_ptrs[j] = (event_t *) &events[j];
+
+	    events[j].y = edge->edge.top;
+	    events[j].type = EVENT_TYPE_START;
+	    events[j].edge = edge;
+
+	    edge++, j++;
+	}
+    }
+
+    status = botor_generate (self, event_ptrs, renderer);
+
+    if (events != stack_events)
+	free (events);
+
+    return status;
+}
+
+static edge_t *
+botor_allocate_edge (cairo_botor_scan_converter_t *self)
+{
+    struct _cairo_botor_scan_converter_chunk *chunk;
+
+    chunk = self->tail;
+    if (chunk->count == chunk->size) {
+	int size;
+
+	size = chunk->size * 2;
+	chunk->next = _cairo_malloc_ab_plus_c (size,
+					       sizeof (edge_t),
+					       sizeof (struct _cairo_botor_scan_converter_chunk));
+	if (unlikely (chunk->next == NULL))
+	    return NULL;
+
+	chunk = chunk->next;
+	chunk->next = NULL;
+	chunk->count = 0;
+	chunk->size = size;
+	chunk->base = chunk + 1;
+	self->tail = chunk;
+    }
+
+    return (edge_t *) chunk->base + chunk->count++;
+}
+
+static cairo_status_t
+botor_add_edge (cairo_botor_scan_converter_t *self,
+		const cairo_edge_t *edge)
+{
+    edge_t *e;
+    cairo_fixed_t dx, dy;
+
+    e = botor_allocate_edge (self);
+    if (unlikely (e == NULL))
+	return _cairo_error (CAIRO_STATUS_NO_MEMORY);
+
+    cairo_list_init (&e->link);
+    e->edge = *edge;
+
+    dx = edge->line.p2.x - edge->line.p1.x;
+    dy = edge->line.p2.y - edge->line.p1.y;
+    e->dy = dy;
+
+    if (dx == 0) {
+	e->vertical = TRUE;
+	e->x.quo = edge->line.p1.x;
+	e->x.rem = 0;
+	e->dxdy.quo = 0;
+	e->dxdy.rem = 0;
+	e->dxdy_full.quo = 0;
+	e->dxdy_full.rem = 0;
+    } else {
+	e->vertical = FALSE;
+	e->dxdy = floored_divrem (dx, dy);
+	if (edge->top == edge->line.p1.y) {
+	    e->x.quo = edge->line.p1.x;
+	    e->x.rem = 0;
+	} else {
+	    e->x = floored_muldivrem (edge->top - edge->line.p1.y,
+				      dx, dy);
+	    e->x.quo += edge->line.p1.x;
+	}
+
+	if (_cairo_fixed_integer_part (edge->bottom) - _cairo_fixed_integer_part (edge->top) > 1) {
+	    e->dxdy_full = floored_muldivrem (STEP_Y, dx, dy);
+	} else {
+	    e->dxdy_full.quo = 0;
+	    e->dxdy_full.rem = 0;
+	}
+    }
+
+    e->x.rem = -e->dy;
+    e->current_sign = 0;
+    e->runs = NULL;
+    e->flags = START;
+
+    self->num_edges++;
+
+    return CAIRO_STATUS_SUCCESS;
+}
+
+#if 0
+static cairo_status_t
+_cairo_botor_scan_converter_add_edge (void		*converter,
+				      const cairo_point_t *p1,
+				      const cairo_point_t *p2,
+				      int top, int bottom,
+				      int dir)
+{
+    cairo_botor_scan_converter_t *self = converter;
+    cairo_edge_t edge;
+
+    edge.line.p1 = *p1;
+    edge.line.p2 = *p2;
+    edge.top = top;
+    edge.bottom = bottom;
+    edge.dir = dir;
+
+    return botor_add_edge (self, &edge);
+}
+#endif
+
+cairo_status_t
+_cairo_botor_scan_converter_add_polygon (cairo_botor_scan_converter_t *converter,
+					 const cairo_polygon_t *polygon)
+{
+    cairo_botor_scan_converter_t *self = converter;
+    cairo_status_t status;
+    int i;
+
+    for (i = 0; i < polygon->num_edges; i++) {
+	status = botor_add_edge (self, &polygon->edges[i]);
+	if (unlikely (status))
+	    return status;
+    }
+
+    return CAIRO_STATUS_SUCCESS;
+}
+
+static void
+_cairo_botor_scan_converter_destroy (void *converter)
+{
+    cairo_botor_scan_converter_t *self = converter;
+    struct _cairo_botor_scan_converter_chunk *chunk, *next;
+
+    for (chunk = self->chunks.next; chunk != NULL; chunk = next) {
+	next = chunk->next;
+	free (chunk);
+    }
+}
+
+void
+_cairo_botor_scan_converter_init (cairo_botor_scan_converter_t *self,
+				  const cairo_box_t *extents,
+				  cairo_fill_rule_t fill_rule)
+{
+    self->base.destroy     = _cairo_botor_scan_converter_destroy;
+    self->base.generate    = _cairo_botor_scan_converter_generate;
+
+    self->extents   = *extents;
+    self->fill_rule = fill_rule;
+
+    self->xmin = _cairo_fixed_integer_floor (extents->p1.x);
+    self->xmax = _cairo_fixed_integer_ceil (extents->p2.x);
+
+    self->chunks.base = self->buf;
+    self->chunks.next = NULL;
+    self->chunks.count = 0;
+    self->chunks.size = sizeof (self->buf) / sizeof (edge_t);
+    self->tail = &self->chunks;
+
+    self->num_edges = 0;
+}