gs/src/gxfill.c

/* Copyright (C) 1989, 2000 Aladdin Enterprises.  All rights reserved.

  This file is part of AFPL Ghostscript.

  AFPL Ghostscript is distributed with NO WARRANTY OF ANY KIND.  No author or
  distributor accepts any responsibility for the consequences of using it, or
  for whether it serves any particular purpose or works at all, unless he or
  she says so in writing.  Refer to the Aladdin Free Public License (the
  "License") for full details.

  Every copy of AFPL Ghostscript must include a copy of the License, normally
  in a plain ASCII text file named PUBLIC.  The License grants you the right
  to copy, modify and redistribute AFPL Ghostscript, but only under certain
  conditions described in the License.  Among other things, the License
  requires that the copyright notice and this notice be preserved on all
  copies.
*/

/*$Id: gxfill.c,v 1.8 2001/05/10 18:35:14 igorm Exp $ */
/* Lower-level path filling procedures */
#include "gx.h"
#include "gserrors.h"
#include "gsstruct.h"
#include "gxfixed.h"
#include "gxdevice.h"
#include "gzpath.h"
#include "gzcpath.h"
#include "gxdcolor.h"
#include "gxhttile.h"
#include "gxistate.h"
#include "gxpaint.h"		/* for prototypes */
#include "gsptype2.h"

/*
 * Define which fill algorithm(s) to use.  At least one of the following
 * two #defines must be included (not commented out).
 */
#define FILL_SCAN_LINES
#define FILL_TRAPEZOIDS
/*
 * Define whether to sample curves when using the scan line algorithm
 * rather than flattening them.  This produces more accurate output, at
 * some cost in time.
 */
#define FILL_CURVES

/* ---------------- Statistics ---------------- */

#ifdef DEBUG
struct stats_fill_s {
    long
	fill, fill_alloc, y_up, y_down, horiz, x_step, slow_x, iter, find_y,
	band, band_step, band_fill, afill, slant, slant_shallow, sfill,
	mq_cross, cross_slow, cross_low, order, slow_order;
} stats_fill;

#  define INCR(x) (++(stats_fill.x))
#  define INCR_EXPR(x) INCR(x)
#  define INCR_BY(x,n) (stats_fill.x += (n))
#else
#  define INCR(x) DO_NOTHING
#  define INCR_EXPR(x) discard(0)
#  define INCR_BY(x,n) DO_NOTHING
#endif

/* ---------------- Active line management ---------------- */

/* Define the structure for keeping track of active lines. */
typedef struct active_line_s active_line;
struct active_line_s {
    gs_fixed_point start;	/* x,y where line starts */
    gs_fixed_point end;		/* x,y where line ends */
    gs_fixed_point diff;	/* end - start */
#define AL_DX(alp) ((alp)->diff.x)
#define AL_DY(alp) ((alp)->diff.y)
    fixed y_fast_max;		/* can do x_at_y in fixed point */
				/* if y <= y_fast_max */
    fixed num_adjust;		/* 0 if diff.x >= 0, -diff.y + epsilon if */
				/* diff.x < 0 and division truncates */
#if ARCH_DIV_NEG_POS_TRUNCATES
    /* neg/pos truncates, we must bias the numberator. */
#  define SET_NUM_ADJUST(alp) \
    (alp)->num_adjust =\
      ((alp)->diff.x >= 0 ? 0 : -(alp)->diff.y + fixed_epsilon)
#  define ADD_NUM_ADJUST(num, alp) ((num) + (alp)->num_adjust)
#  define MAX_MINUS_NUM_ADJUST(alp) ADD_NUM_ADJUST(max_fixed, alp)
#else
    /* neg/pos takes the floor, no special action is needed. */
#  define SET_NUM_ADJUST(alp) DO_NOTHING
#  define ADD_NUM_ADJUST(num, alp) (num)
#  define MAX_MINUS_NUM_ADJUST(alp) max_fixed
#endif
#define SET_AL_POINTS(alp, startp, endp)\
  BEGIN\
    (alp)->diff.y = (endp).y - (startp).y;\
    (alp)->diff.x = (endp).x - (startp).x;\
    SET_NUM_ADJUST(alp);\
    (alp)->y_fast_max = MAX_MINUS_NUM_ADJUST(alp) /\
      (((alp)->diff.x >= 0 ? (alp)->diff.x : -(alp)->diff.x) | 1) +\
      (startp).y;\
    (alp)->start = startp, (alp)->end = endp;\
  END
    /*
     * We know that alp->start.y <= yv <= alp->end.y, because the fill loop
     * guarantees that the only lines being considered are those with this
     * property.
     */
#define AL_X_AT_Y(alp, yv)\
  ((yv) == (alp)->end.y ? (alp)->end.x :\
   ((yv) <= (alp)->y_fast_max ?\
    ADD_NUM_ADJUST(((yv) - (alp)->start.y) * AL_DX(alp), alp) / AL_DY(alp) :\
    (INCR_EXPR(slow_x),\
     fixed_mult_quo(AL_DX(alp), (yv) - (alp)->start.y, AL_DY(alp)))) +\
   (alp)->start.x)
    fixed x_current;		/* current x position */
    fixed x_next;		/* x position at end of band */
    const segment *pseg;	/* endpoint of this line */
    int direction;		/* direction of line segment */
#define DIR_UP 1
#define DIR_HORIZONTAL 0	/* (these are handled specially) */
#define DIR_DOWN (-1)
    int curve_k;		/* # of subdivisions for curves,-1 for lines */
    curve_cursor cursor;	/* cursor for curves, unused for lines */
/*
 * "Pending" lines (not reached in the Y ordering yet) use next and prev
 * to order lines by increasing starting Y.  "Active" lines (being scanned)
 * use next and prev to order lines by increasing current X, or if the
 * current Xs are equal, by increasing final X.
 */
    active_line *prev, *next;
/* Link together active_lines allocated individually */
    active_line *alloc_next;
};

/*
 * Define the ordering criterion for active lines that overlap in Y.
 * Return -1, 0, or 1 if lp1 precedes, coincides with, or follows lp2.
 *
 * The lines' x_current values are correct for some Y value that crosses
 * both of them and that is not both the start of one and the end of the
 * other.  (Neither line is horizontal.)  We want the ordering at this
 * Y value, or, of the x_current values are equal, greater Y values
 * (if any: this Y value might be the end of both lines).
 */
private int
x_order(const active_line *lp1, const active_line *lp2)
{
    bool s1;

    INCR(order);
    if (lp1->x_current < lp2->x_current)
	return -1;
    else if (lp1->x_current > lp2->x_current)
	return 1;
    /*
     * We need to compare the slopes of the lines.  Start by
     * checking one fast case, where the slopes have opposite signs.
     */
    if ((s1 = lp1->start.x < lp1->end.x) != (lp2->start.x < lp2->end.x))
	return (s1 ? 1 : -1);
    /*
     * We really do have to compare the slopes.  Fortunately, this isn't
     * needed very often.  We want the sign of the comparison
     * dx1/dy1 - dx2/dy2, or (since we know dy1 and dy2 are positive)
     * dx1 * dy2 - dx2 * dy1.  In principle, we can't simply do this using
     * doubles, since we need complete accuracy and doubles don't have
     * enough fraction bits.  However, with the usual 20+12-bit fixeds and
     * 64-bit doubles, both of the factors would have to exceed 2^15
     * device space pixels for the result to be inaccurate, so we
     * simply disregard this possibility.  ****** FIX SOMEDAY ******
     */
    INCR(slow_order);
    {
	fixed dx1 = lp1->end.x - lp1->start.x,
	    dy1 = lp1->end.y - lp1->start.y;
	fixed dx2 = lp2->end.x - lp2->start.x,
	    dy2 = lp2->end.y - lp2->start.y;
	double diff = (double)dx1 * dy2 - (double)dx2 * dy1;

	return (diff < 0 ? -1 : diff > 0 ? 1 : 0);
    }
}

/*
 * The active_line structure isn't really simple, but since its instances
 * only exist temporarily during a fill operation, we don't have to
 * worry about a garbage collection occurring.
 */
gs_private_st_simple(st_active_line, active_line, "active_line");

#ifdef DEBUG
/* Internal procedures for printing and checking active lines. */
private void
print_active_line(const char *label, const active_line * alp)
{
    dlprintf5("[f]%s 0x%lx(%d): x_current=%f x_next=%f\n",
	      label, (ulong) alp, alp->direction,
	      fixed2float(alp->x_current), fixed2float(alp->x_next));
    dlprintf5("    start=(%f,%f) pt_end=0x%lx(%f,%f)\n",
	      fixed2float(alp->start.x), fixed2float(alp->start.y),
	      (ulong) alp->pseg,
	      fixed2float(alp->end.x), fixed2float(alp->end.y));
    dlprintf2("    prev=0x%lx next=0x%lx\n",
	      (ulong) alp->prev, (ulong) alp->next);
}
private void
print_line_list(const active_line * flp)
{
    const active_line *lp;

    for (lp = flp; lp != 0; lp = lp->next) {
	fixed xc = lp->x_current, xn = lp->x_next;

	dlprintf3("[f]0x%lx(%d): x_current/next=%g",
		  (ulong) lp, lp->direction,
		  fixed2float(xc));
	if (xn != xc)
	    dprintf1("/%g", fixed2float(xn));
	dputc('\n');
    }
}
inline private void
print_al(const char *label, const active_line * alp)
{
    if (gs_debug_c('F'))
	print_active_line(label, alp);
}
private int
check_line_list(const active_line * flp)
{
    const active_line *alp;

    if (flp != 0)
	for (alp = flp->prev->next; alp != 0; alp = alp->next)
	    if (alp->next != 0 && alp->next->x_current < alp->x_current) {
		lprintf("[f]Lines out of order!\n");
		print_active_line("   1:", alp);
		print_active_line("   2:", alp->next);
		return_error(gs_error_Fatal);
	    }
    return 0;
}
#else
#define print_al(label,alp) DO_NOTHING
#endif

/* Line list structure */
struct line_list_s {
    gs_memory_t *memory;
    active_line *active_area;	/* allocated active_line list */
    active_line *next_active;	/* next allocation slot */
    active_line *limit;		/* limit of local allocation */
    int close_count;		/* # of added closing lines */
    active_line *y_list;	/* Y-sorted list of pending lines */
    active_line *y_line;	/* most recently inserted line */
    active_line x_head;		/* X-sorted list of active lines */
#define x_list x_head.next
    /* Put the arrays last so the scalars will have */
    /* small displacements. */
    /* Allocate a few active_lines locally */
    /* to avoid round trips through the allocator. */
#if arch_small_memory
#  define MAX_LOCAL_ACTIVE 6	/* don't overburden the stack */
#else
#  define MAX_LOCAL_ACTIVE 20
#endif
    active_line local_active[MAX_LOCAL_ACTIVE];
};
typedef struct line_list_s line_list;
typedef line_list *ll_ptr;

/* Forward declarations */
private void init_line_list(P2(ll_ptr, gs_memory_t *));
private void unclose_path(P2(gx_path *, int));
private void free_line_list(P1(ll_ptr));
private int add_y_list(P5(gx_path *, ll_ptr, fixed, fixed,
			  const gs_fixed_rect *));
private int add_y_line(P4(const segment *, const segment *, int, ll_ptr));
private void insert_x_new(P2(active_line *, ll_ptr));
private bool end_x_line(P2(active_line *, bool));

#define FILL_LOOP_PROC(proc)\
int proc(P11(ll_ptr, gx_device *,\
  const gx_fill_params *, const gx_device_color *, gs_logical_operation_t,\
  const gs_fixed_rect *, fixed, fixed, fixed, fixed, fixed))
private FILL_LOOP_PROC(fill_loop_by_scan_lines);
private FILL_LOOP_PROC(fill_loop_by_trapezoids);

/*
 * This is the general path filling algorithm.
 * It uses the center-of-pixel rule for filling.
 * We can implement Microsoft's upper-left-corner-of-pixel rule
 * by subtracting (0.5, 0.5) from all the coordinates in the path.
 *
 * The adjust parameters are a hack for keeping regions
 * from coming out too faint: they specify an amount by which to expand
 * the sides of every filled region.
 * Setting adjust = fixed_half is supposed to produce the effect of Adobe's
 * any-part-of-pixel rule, but it doesn't quite, because of the
 * closed/open interval rule for regions.  We detect this as a special case
 * and do the slightly ugly things necessary to make it work.
 */

/*
 * Tweak the fill adjustment if necessary so that (nearly) empty
 * rectangles are guaranteed to produce some output.  This is a hack
 * to work around a bug in the Microsoft Windows PostScript driver,
 * which draws thin lines by filling zero-width rectangles, and in
 * some other drivers that try to fill epsilon-width rectangles.
 */
void
gx_adjust_if_empty(const gs_fixed_rect * pbox, gs_fixed_point * adjust)
{
    /*
     * For extremely large coordinates, the obvious subtractions could
     * overflow.  We can work around this easily by noting that since
     * we know q.{x,y} >= p.{x,y}, the subtraction overflows iff the
     * result is negative.
     */
    const fixed
          dx = pbox->q.x - pbox->p.x, dy = pbox->q.y - pbox->p.y;

    if (dx < fixed_half && dx > 0 && (dy >= int2fixed(2) || dy < 0)) {
	adjust->x = arith_rshift_1(fixed_1 + fixed_epsilon - dx);
	if_debug1('f', "[f]thin adjust_x=%g\n",
		  fixed2float(adjust->x));
    } else if (dy < fixed_half && dy > 0 && (dx >= int2fixed(2) || dx < 0)) {
	adjust->y = arith_rshift_1(fixed_1 + fixed_epsilon - dy);
	if_debug1('f', "[f]thin adjust_y=%g\n",
		  fixed2float(adjust->y));
    }
}

/*
 * The general fill  path algorithm.
 */
private int
gx_general_fill_path(gx_device * pdev, const gs_imager_state * pis,
		     gx_path * ppath, const gx_fill_params * params,
		 const gx_device_color * pdevc, const gx_clip_path * pcpath)
{
    gs_fixed_point adjust;
    gs_logical_operation_t lop = pis->log_op;
    gs_fixed_rect ibox, bbox;
    gx_device_clip cdev;
    gx_device *dev = pdev;
    gx_device *save_dev = dev;
    gx_path ffpath;
    gx_path *pfpath;
    int code;
    fixed adjust_left, adjust_right, adjust_below, adjust_above;
    int max_fill_band = dev->max_fill_band;
#define NO_BAND_MASK ((fixed)(-1) << (sizeof(fixed) * 8 - 1))
    bool fill_by_trapezoids;
    line_list lst;

    adjust = params->adjust;
    /*
     * Compute the bounding box before we flatten the path.
     * This can save a lot of time if the path has curves.
     * If the path is neither fully within nor fully outside
     * the quick-check boxes, we could recompute the bounding box
     * and make the checks again after flattening the path,
     * but right now we don't bother.
     */
    gx_path_bbox(ppath, &ibox);
    if (params->fill_zero_width)
	gx_adjust_if_empty(&ibox, &adjust);
    /* Check the bounding boxes. */
    if_debug6('f', "[f]adjust=%g,%g bbox=(%g,%g),(%g,%g)\n",
	      fixed2float(adjust.x), fixed2float(adjust.y),
	      fixed2float(ibox.p.x), fixed2float(ibox.p.y),
	      fixed2float(ibox.q.x), fixed2float(ibox.q.y));
    if (pcpath)
	gx_cpath_inner_box(pcpath, &bbox);
    else
	(*dev_proc(dev, get_clipping_box)) (dev, &bbox);
    if (!rect_within(ibox, bbox)) {
	/*
	 * Intersect the path box and the clip bounding box.
	 * If the intersection is empty, this fill is a no-op.
	 */
	if (pcpath)
	    gx_cpath_outer_box(pcpath, &bbox);
	if_debug4('f', "   outer_box=(%g,%g),(%g,%g)\n",
		  fixed2float(bbox.p.x), fixed2float(bbox.p.y),
		  fixed2float(bbox.q.x), fixed2float(bbox.q.y));
	rect_intersect(ibox, bbox);
	if (ibox.p.x - adjust.x >= ibox.q.x + adjust.x ||
	    ibox.p.y - adjust.y >= ibox.q.y + adjust.y
	    ) {			/* Intersection of boxes is empty! */
	    return 0;
	}
	/*
	 * The path is neither entirely inside the inner clip box
	 * nor entirely outside the outer clip box.
	 * If we had to flatten the path, this is where we would
	 * recompute its bbox and make the tests again,
	 * but we don't bother right now.
	 *
	 * If there is a clipping path, set up a clipping device.
	 */
	if (pcpath) {
	    dev = (gx_device *) & cdev;
	    gx_make_clip_device(&cdev, gx_cpath_list(pcpath));
	    cdev.target = save_dev;
	    cdev.max_fill_band = save_dev->max_fill_band;
	    (*dev_proc(dev, open_device)) (dev);
	}
    }
    /*
     * Compute the proper adjustment values.
     * To get the effect of the any-part-of-pixel rule,
     * we may have to tweak them slightly.
     * NOTE: We changed the adjust_right/above value from 0.5+epsilon
     * to 0.5 in release 5.01; even though this does the right thing
     * in every case we could imagine, we aren't confident that it's
     * correct.  (The old values were definitely incorrect, since they
     * caused 1-pixel-wide/high objects to color 2 pixels even if
     * they fell exactly on pixel boundaries.)
     */
    if (adjust.x == fixed_half)
	adjust_left = fixed_half - fixed_epsilon,
	    adjust_right = fixed_half /* + fixed_epsilon */ ;	/* see above */
    else
	adjust_left = adjust_right = adjust.x;
    if (adjust.y == fixed_half)
	adjust_below = fixed_half - fixed_epsilon,
	    adjust_above = fixed_half /* + fixed_epsilon */ ;	/* see above */
    else
	adjust_below = adjust_above = adjust.y;
    /* Initialize the active line list. */
    init_line_list(&lst, ppath->memory);
    /*
     * We have a choice of two different filling algorithms:
     * scan-line-based and trapezoid-based.  They compare as follows:
     *
     *      Scan    Trap
     *      ----    ----
     *       skip   +draw   0-height horizontal lines
     *       slow   +fast   rectangles
     *      +fast    slow   curves
     *      +yes     no     write pixels at most once when adjust != 0
     *
     * Normally we use the scan line algorithm for characters, where curve
     * speed is important, and for non-idempotent RasterOps, where double
     * pixel writing must be avoided, and the trapezoid algorithm otherwise.
     * However, we always use the trapezoid algorithm for rectangles.
     */
#define DOUBLE_WRITE_OK() lop_is_idempotent(lop)
#ifdef FILL_SCAN_LINES
#  ifdef FILL_TRAPEZOIDS
    fill_by_trapezoids =
	(!gx_path_has_curves(ppath) || params->flatness >= 1.0);
#  else
    fill_by_trapezoids = false;
#  endif
#else
    fill_by_trapezoids = true;
#endif
#ifdef FILL_TRAPEZOIDS
    if (fill_by_trapezoids && !DOUBLE_WRITE_OK()) {
	/* Avoid filling rectangles by scan line. */
	gs_fixed_rect rbox;

	if (gx_path_is_rectangular(ppath, &rbox)) {
	    int x0 = fixed2int_pixround(rbox.p.x - adjust_left);
	    int y0 = fixed2int_pixround(rbox.p.y - adjust_below);
	    int x1 = fixed2int_pixround(rbox.q.x + adjust_right);
	    int y1 = fixed2int_pixround(rbox.q.y + adjust_above);

	    return gx_fill_rectangle_device_rop(x0, y0, x1 - x0, y1 - y0,
						pdevc, dev, lop);
	}
	fill_by_trapezoids = false; /* avoid double write */
    }
#endif
#undef DOUBLE_WRITE_OK
    /*
     * Pre-process curves.  When filling by trapezoids, we need to
     * flatten the path completely; when filling by scan lines, we only
     * need to monotonize it, unless FILL_CURVES is undefined.
     */
    gx_path_init_local(&ffpath, ppath->memory);
    if (!gx_path_has_curves(ppath))	/* don't need to flatten */
	pfpath = ppath;
    else
#if defined(FILL_CURVES) && defined(FILL_SCAN_LINES)
	/* Filling curves is possible. */
#  ifdef FILL_TRAPEZOIDS
	/* Not filling curves is also possible. */
    if (fill_by_trapezoids)
#  endif
#endif
#if !defined(FILL_CURVES) || defined(FILL_TRAPEZOIDS)
	/* Not filling curves is possible. */
	{
	    gx_path_init_local(&ffpath, ppath->memory);
	    code = gx_path_add_flattened_accurate(ppath, &ffpath,
						  params->flatness,
						  pis->accurate_curves);
	    if (code < 0)
		return code;
	    pfpath = &ffpath;
	}
#endif
#if defined(FILL_CURVES) && defined(FILL_SCAN_LINES)
    /* Filling curves is possible. */
#  ifdef FILL_TRAPEZOIDS
    /* Not filling curves is also possible. */
    else
#  endif
    if (gx_path_is_monotonic(ppath))
	pfpath = ppath;
    else {
	gx_path_init_local(&ffpath, ppath->memory);
	code = gx_path_add_monotonized(ppath, &ffpath);
	if (code < 0)
	    return code;
	pfpath = &ffpath;
    }
#endif
    if ((code = add_y_list(pfpath, &lst, adjust_below, adjust_above, &ibox)) < 0)
	goto nope;
    {
	FILL_LOOP_PROC((*fill_loop));

	/* Some short-sighted compilers won't allow a conditional here.... */
	if (fill_by_trapezoids)
	    fill_loop = fill_loop_by_trapezoids;
	else
	    fill_loop = fill_loop_by_scan_lines;
	code = (*fill_loop)
	    (&lst, dev, params, pdevc, lop, &ibox,
	     adjust_left, adjust_right, adjust_below, adjust_above,
	   (max_fill_band == 0 ? NO_BAND_MASK : int2fixed(-max_fill_band)));
    }
  nope:if (lst.close_count != 0)
	unclose_path(pfpath, lst.close_count);
    free_line_list(&lst);
    if (pfpath != ppath)	/* had to flatten */
	gx_path_free(pfpath, "gx_default_fill_path(flattened path)");
#ifdef DEBUG
    if (gs_debug_c('f')) {
	dlputs("[f]  # alloc    up  down horiz step slowx  iter  find  band bstep bfill\n");
	dlprintf5(" %5ld %5ld %5ld %5ld %5ld",
		  stats_fill.fill, stats_fill.fill_alloc,
		  stats_fill.y_up, stats_fill.y_down,
		  stats_fill.horiz);
	dlprintf4(" %5ld %5ld %5ld %5ld",
		  stats_fill.x_step, stats_fill.slow_x,
		  stats_fill.iter, stats_fill.find_y);
	dlprintf3(" %5ld %5ld %5ld\n",
		  stats_fill.band, stats_fill.band_step,
		  stats_fill.band_fill);
	dlputs("[f]    afill slant shall sfill mqcrs order slowo\n");
	dlprintf7("       %5ld %5ld %5ld %5ld %5ld %5ld %5ld\n",
		  stats_fill.afill, stats_fill.slant,
		  stats_fill.slant_shallow, stats_fill.sfill,
		  stats_fill.mq_cross, stats_fill.order,
		  stats_fill.slow_order);
    }
#endif
    return code;
}

/*
 * Fill a path.  This is the default implementation of the driver
 * fill_path procedure.
 */
int
gx_default_fill_path(gx_device * pdev, const gs_imager_state * pis,
		     gx_path * ppath, const gx_fill_params * params,
		 const gx_device_color * pdevc, const gx_clip_path * pcpath)
{
    if (gx_dc_is_pattern2_color(pdevc)) {
	/*  Optimization for shading fill :
	    The general path filling algorithm subdivides fill region with
	    trapezoid or rectangle subregions and then paints each subregion
	    with given color. If the color is shading, each subregion to be
	    subdivided into areas of constant color. But with radial
	    shading each area is a high order polygon, being
	    subdivided into smaller subregions, so as total number of
	    subregions grows huge. Faster processing is done here by changing
	    the order of subdivision cycles : we first subdivide the shading into
	    areas of constant color, then apply the general path filling algorithm
	    (i.e. subdivide each area into trapezoids or rectangles), using the
	    filling path as clip mask.
	*/

	gx_clip_path cpath_intersection;
	gx_path path_intersection;
	int code;

	/*  Shading fill algorithm uses "current path" parameter of the general
	    path filling algorithm as boundary of constant color area,
	    so we need to intersect the filling path with the clip path now,
	    reducing the number of pathes passed to it :
	*/
	gx_path_init_local(&path_intersection, pdev->memory);
	gx_cpath_init_local_shared(&cpath_intersection, pcpath, pdev->memory);
	if ((code = gx_cpath_intersect(&cpath_intersection, ppath, params->rule, (gs_imager_state *)pis)) >= 0)
	    code = gx_cpath_to_path(&cpath_intersection, &path_intersection);

	/* Do fill : */
	if (code >= 0)
            code = gx_dc_pattern2_fill_path_adjusted(pdevc, &path_intersection, NULL,  pdev);

	/* Destruct local data and return :*/
	gx_path_free(&path_intersection, "shading_fill_path_intersection");
	gx_cpath_free(&cpath_intersection, "shading_fill_cpath_intersection");
	return code;
    }
    return gx_general_fill_path(pdev, pis, ppath, params, pdevc, pcpath);
}

/* Initialize the line list for a path. */
private void
init_line_list(ll_ptr ll, gs_memory_t * mem)
{
    ll->memory = mem;
    ll->active_area = 0;
    ll->next_active = ll->local_active;
    ll->limit = ll->next_active + MAX_LOCAL_ACTIVE;
    ll->close_count = 0;
    ll->y_list = 0;
    ll->y_line = 0;
    INCR(fill);
}

/* Unlink any line_close segments added temporarily. */
private void
unclose_path(gx_path * ppath, int count)
{
    subpath *psub;

    for (psub = ppath->first_subpath; count != 0;
	 psub = (subpath *) psub->last->next
	)
	if (psub->last == (segment *) & psub->closer) {
	    segment *prev = psub->closer.prev, *next = psub->closer.next;

	    prev->next = next;
	    if (next)
		next->prev = prev;
	    psub->last = prev;
	    count--;
	}
}

/* Free the line list. */
private void
free_line_list(ll_ptr ll)
{
    /* Free any individually allocated active_lines. */
    gs_memory_t *mem = ll->memory;
    active_line *alp;

    while ((alp = ll->active_area) != 0) {
	active_line *next = alp->alloc_next;

	gs_free_object(mem, alp, "active line");
	ll->active_area = next;
    }
}

/*
 * Construct a Y-sorted list of segments for rasterizing a path.  We assume
 * the path is non-empty.  Only include non-horizontal lines or (monotonic)
 * curve segments where one endpoint is locally Y-minimal, and horizontal
 * lines that might color some additional pixels.
 */
private int
add_y_list(gx_path * ppath, ll_ptr ll, fixed adjust_below, fixed adjust_above,
	   const gs_fixed_rect * pbox)
{
    segment *pseg = (segment *) ppath->first_subpath;
    int close_count = 0;
    /* fixed xmin = pbox->p.x; *//* not currently used */
    fixed ymin = pbox->p.y;
    /* fixed xmax = pbox->q.x; *//* not currently used */
    fixed ymax = pbox->q.y;
    int code;

    while (pseg) {
	/* We know that pseg points to a subpath head (s_start). */
	subpath *psub = (subpath *) pseg;
	segment *plast = psub->last;
	int dir = 2;		/* hack to skip first segment */
	int first_dir, prev_dir;
	segment *prev;

	if (plast->type != s_line_close) {
	    /* Create a fake s_line_close */
	    line_close_segment *lp = &psub->closer;
	    segment *next = plast->next;

	    lp->next = next;
	    lp->prev = plast;
	    plast->next = (segment *) lp;
	    if (next)
		next->prev = (segment *) lp;
	    lp->type = s_line_close;
	    lp->pt = psub->pt;
	    lp->sub = psub;
	    psub->last = plast = (segment *) lp;
	    ll->close_count++;
	}
	while ((prev_dir = dir, prev = pseg,
		(pseg = pseg->next) != 0 && pseg->type != s_start)
	    ) {
	    /* This element is either a line or a monotonic curve segment. */
	    fixed iy = pseg->pt.y;
	    fixed py = prev->pt.y;

	    /*
	     * Segments falling entirely outside the ibox in Y
	     * are treated as though they were horizontal, *
	     * i.e., they are never put on the list.
	     */
#define COMPUTE_DIR(xo, xe, yo, ye)\
  (ye > yo ? (ye <= ymin || yo >= ymax ? 0 : DIR_UP) :\
   ye < yo ? (yo <= ymin || ye >= ymax ? 0 : DIR_DOWN) :\
   2)
#define ADD_DIR_LINES(prev2, prev, this, pdir, dir)\
  BEGIN\
    if (pdir)\
      { if ((code = add_y_line(prev2, prev, pdir, ll)) < 0) return code; }\
    if (dir)\
      { if ((code = add_y_line(prev, this, dir, ll)) < 0) return code; }\
  END
	    dir = COMPUTE_DIR(prev->pt.x, pseg->pt.x, py, iy);
	    if (dir == 2) {	/* Put horizontal lines on the list */
		/* if they would color any pixels. */
		if (fixed2int_pixround(iy - adjust_below) <
		    fixed2int_pixround(iy + adjust_above)
		    ) {
		    INCR(horiz);
		    if ((code = add_y_line(prev, pseg,
					   DIR_HORIZONTAL, ll)) < 0
			)
			return code;
		}
		dir = 0;
	    }
	    if (dir > prev_dir) {
		ADD_DIR_LINES(prev->prev, prev, pseg, prev_dir, dir);
	    } else if (prev_dir == 2)	/* first segment */
		first_dir = dir;
	    if (pseg == plast) {
		/*
		 * We skipped the first segment of the subpath, so the last
		 * segment must receive special consideration.  Note that we
		 * have `closed' all subpaths.
		 */
		if (first_dir > dir) {
		    ADD_DIR_LINES(prev, pseg, psub->next, dir, first_dir);
		}
	    }
	}
#undef COMPUTE_DIR
#undef ADD_DIR_LINES
    }
    return close_count;
}
/*
 * Internal routine to test a segment and add it to the pending list if
 * appropriate.
 */
private int
add_y_line(const segment * prev_lp, const segment * lp, int dir, ll_ptr ll)
{
    gs_fixed_point this, prev;
    active_line *alp = ll->next_active;
    fixed y_start;

    if (alp == ll->limit) {	/* Allocate separately */
	alp = gs_alloc_struct(ll->memory, active_line,
			      &st_active_line, "active line");
	if (alp == 0)
	    return_error(gs_error_VMerror);
	alp->alloc_next = ll->active_area;
	ll->active_area = alp;
	INCR(fill_alloc);
    } else
	ll->next_active++;
    this.x = lp->pt.x;
    this.y = lp->pt.y;
    prev.x = prev_lp->pt.x;
    prev.y = prev_lp->pt.y;
    switch ((alp->direction = dir)) {
	case DIR_UP:
	    y_start = prev.y;
	    SET_AL_POINTS(alp, prev, this);
	    alp->pseg = lp;
	    break;
	case DIR_DOWN:
	    y_start = this.y;
	    SET_AL_POINTS(alp, this, prev);
	    alp->pseg = prev_lp;
	    break;
	case DIR_HORIZONTAL:
	    y_start = this.y;	/* = prev.y */
	    alp->start = prev;
	    alp->end = this;
	    /* Don't need to set dx or y_fast_max */
	    alp->pseg = prev_lp;	/* may not need this either */
	    break;
	default:		/* can't happen */
	    return_error(gs_error_unregistered);
    }
    /* Insert the new line in the Y ordering */
    {
	active_line *yp = ll->y_line;
	active_line *nyp;

	if (yp == 0) {
	    alp->next = alp->prev = 0;
	    ll->y_list = alp;
	} else if (y_start >= yp->start.y) {	/* Insert the new line after y_line */
	    while (INCR_EXPR(y_up),
		   ((nyp = yp->next) != NULL &&
		    y_start > nyp->start.y)
		)
		yp = nyp;
	    alp->next = nyp;
	    alp->prev = yp;
	    yp->next = alp;
	    if (nyp)
		nyp->prev = alp;
	} else {		/* Insert the new line before y_line */
	    while (INCR_EXPR(y_down),
		   ((nyp = yp->prev) != NULL &&
		    y_start < nyp->start.y)
		)
		yp = nyp;
	    alp->prev = nyp;
	    alp->next = yp;
	    yp->prev = alp;
	    if (nyp)
		nyp->next = alp;
	    else
		ll->y_list = alp;
	}
    }
    ll->y_line = alp;
    print_al("add ", alp);
    return 0;
}

/* ---------------- Filling loop utilities ---------------- */

/* Insert a newly active line in the X ordering. */
private void
insert_x_new(active_line * alp, ll_ptr ll)
{
    active_line *next;
    active_line *prev = &ll->x_head;

    alp->x_current = alp->start.x;
    while (INCR_EXPR(x_step),
	   (next = prev->next) != 0 && x_order(next, alp) < 0
	)
	prev = next;
    alp->next = next;
    alp->prev = prev;
    if (next != 0)
	next->prev = alp;
    prev->next = alp;
}

/*
 * Handle a line segment that just ended.  Return true iff this was
 * the end of a line sequence.
 */
private bool
end_x_line(active_line *alp, bool update)
{
    const segment *pseg = alp->pseg;
    /*
     * The computation of next relies on the fact that
     * all subpaths have been closed.  When we cycle
     * around to the other end of a subpath, we must be
     * sure not to process the start/end point twice.
     */
    const segment *next =
	(alp->direction == DIR_UP ?
	 (			/* Upward line, go forward along path. */
	  pseg->type == s_line_close ?	/* end of subpath */
	  ((const line_close_segment *)pseg)->sub->next :
	  pseg->next) :
	 (			/* Downward line, go backward along path. */
	  pseg->type == s_start ?	/* start of subpath */
	  ((const subpath *)pseg)->last->prev :
	  pseg->prev)
	);
    gs_fixed_point npt;

    npt.y = next->pt.y;
    if (!update)
	return npt.y <= pseg->pt.y;
    if_debug5('F', "[F]ended 0x%lx: pseg=0x%lx y=%f next=0x%lx npt.y=%f\n",
	      (ulong) alp, (ulong) pseg, fixed2float(pseg->pt.y),
	      (ulong) next, fixed2float(npt.y));
    if (npt.y <= pseg->pt.y) {	/* End of a line sequence */
	active_line *nlp = alp->next;

	alp->prev->next = nlp;
	if (nlp)
	    nlp->prev = alp->prev;
	if_debug1('F', "[F]drop 0x%lx\n", (ulong) alp);
	return true;
    }
    alp->pseg = next;
    npt.x = next->pt.x;
    SET_AL_POINTS(alp, alp->end, npt);
    print_al("repl", alp);
    return false;
}

#define LOOP_FILL_RECTANGLE(x, y, w, h)\
  gx_fill_rectangle_device_rop(x, y, w, h, pdevc, dev, lop)
#define LOOP_FILL_RECTANGLE_DIRECT(x, y, w, h)\
  (fill_direct ?\
   (*fill_rect)(dev, x, y, w, h, cindex) :\
   gx_fill_rectangle_device_rop(x, y, w, h, pdevc, dev, lop))

/* ---------------- Trapezoid filling loop ---------------- */

/* Forward references */
private int fill_slant_adjust(P12(fixed, fixed, fixed, fixed, fixed,
				  fixed, fixed, fixed, const gs_fixed_rect *,
	     const gx_device_color *, gx_device *, gs_logical_operation_t));
private void resort_x_line(P1(active_line *));

/****** PATCH ******/
#define LOOP_FILL_TRAPEZOID_FIXED(fx0, fw0, fy0, fx1, fw1, fh)\
  loop_fill_trap(dev, fx0, fw0, fy0, fx1, fw1, fh, pbox, pdevc, lop)
private int
loop_fill_trap(gx_device * dev, fixed fx0, fixed fw0, fixed fy0,
	       fixed fx1, fixed fw1, fixed fh, const gs_fixed_rect * pbox,
	       const gx_device_color * pdevc, gs_logical_operation_t lop)
{
    fixed fy1 = fy0 + fh;
    fixed ybot = max(fy0, pbox->p.y);
    fixed ytop = min(fy1, pbox->q.y);
    gs_fixed_edge left, right;

    if (ybot >= ytop)
	return 0;
    left.start.y = right.start.y = fy0;
    left.end.y = right.end.y = fy1;
    right.start.x = (left.start.x = fx0) + fw0;
    right.end.x = (left.end.x = fx1) + fw1;
    return (*dev_proc(dev, fill_trapezoid))
	(dev, &left, &right, ybot, ytop, false, pdevc, lop);
}
/****** END PATCH ******/

/* Main filling loop.  Takes lines off of y_list and adds them to */
/* x_list as needed.  band_mask limits the size of each band, */
/* by requiring that ((y1 - 1) & band_mask) == (y0 & band_mask). */
private int
fill_loop_by_trapezoids(ll_ptr ll, gx_device * dev,
	       const gx_fill_params * params, const gx_device_color * pdevc,
		     gs_logical_operation_t lop, const gs_fixed_rect * pbox,
			fixed adjust_left, fixed adjust_right,
		    fixed adjust_below, fixed adjust_above, fixed band_mask)
{
    int rule = params->rule;
    const fixed y_limit = pbox->q.y;
    active_line *yll = ll->y_list;
    fixed y;
    int code;
    bool fill_direct = color_writes_pure(pdevc, lop);
    gx_color_index cindex;

    dev_proc_fill_rectangle((*fill_rect));
/*
 * Define a faster test for
 *      fixed2int_pixround(y - below) != fixed2int_pixround(y + above)
 * where we know
 *      0 <= below <= _fixed_pixround_v,
 *      0 <= above <= min(fixed_half, fixed_1 - below).
 * Subtracting out the integer parts, this is equivalent to
 *      fixed2int_pixround(fixed_fraction(y) - below) !=
 *        fixed2int_pixround(fixed_fraction(y) + above)
 * or to
 *      fixed2int(fixed_fraction(y) + _fixed_pixround_v - below) !=
 *        fixed2int(fixed_fraction(y) + _fixed_pixround_v + above)
 * Letting A = _fixed_pixround_v - below and B = _fixed_pixround_v + above,
 * we can rewrite this as
 *      fixed2int(fixed_fraction(y) + A) != fixed2int(fixed_fraction(y) + B)
 * Because of the range constraints given above, this is true precisely when
 *      fixed_fraction(y) + A < fixed_1 && fixed_fraction(y) + B >= fixed_1
 * or equivalently
 *      fixed_fraction(y + B) < B - A.
 * i.e.
 *      fixed_fraction(y + _fixed_pixround_v + above) < below + above
 */
    fixed y_span_delta = _fixed_pixround_v + adjust_above;
    fixed y_span_limit = adjust_below + adjust_above;

#define ADJUSTED_Y_SPANS_PIXEL(y)\
  (fixed_fraction((y) + y_span_delta) < y_span_limit)

    if (yll == 0)
	return 0;		/* empty list */
    if (fill_direct)
	cindex = pdevc->colors.pure,
	    fill_rect = dev_proc(dev, fill_rectangle);
    y = yll->start.y;		/* first Y value */
    ll->x_list = 0;
    ll->x_head.x_current = min_fixed;	/* stop backward scan */
    while (1) {
	fixed y1;
	active_line *endp, *alp, *stopx;
	fixed x;
	int draw;

	INCR(iter);
	/* Move newly active lines from y to x list. */
	while (yll != 0 && yll->start.y == y) {
	    active_line *ynext = yll->next;	/* insert smashes next/prev links */

	    if (yll->direction == DIR_HORIZONTAL) {
		/*
		 * This is a hack to make sure that isolated horizontal
		 * lines get stroked.
		 */
		int yi = fixed2int_pixround(y - adjust_below);
		int xi, wi;

		if (yll->start.x <= yll->end.x)
		    xi = fixed2int_pixround(yll->start.x -
					    adjust_left),
			wi = fixed2int_pixround(yll->end.x +
						adjust_right) - xi;
		else
		    xi = fixed2int_pixround(yll->end.x -
					    adjust_left),
			wi = fixed2int_pixround(yll->start.x +
						adjust_right) - xi;
		code = LOOP_FILL_RECTANGLE_DIRECT(xi, yi, wi, 1);
		if (code < 0)
		    return code;
	    } else
		insert_x_new(yll, ll);
	    yll = ynext;
	}
	/* Check whether we've reached the maximum y. */
	if (y >= y_limit)
	    break;
	if (ll->x_list == 0) {	/* No active lines, skip to next start */
	    if (yll == 0)
		break;		/* no lines left */
	    y = yll->start.y;
	    continue;
	}
	/* Find the next evaluation point. */
	/* Start by finding the smallest y value */
	/* at which any currently active line ends */
	/* (or the next to-be-active line begins). */
	y1 = (yll != 0 ? yll->start.y : y_limit);
	/* Make sure we don't exceed the maximum band height. */
	{
	    fixed y_band = y | ~band_mask;

	    if (y1 > y_band)
		y1 = y_band + 1;
	}
	for (alp = ll->x_list; alp != 0; alp = alp->next)
	    if (alp->end.y < y1)
		y1 = alp->end.y;
#ifdef DEBUG
	if (gs_debug_c('F')) {
	    dlprintf2("[F]before loop: y=%f y1=%f:\n",
		      fixed2float(y), fixed2float(y1));
	    print_line_list(ll->x_list);
	}
#endif
	/* Now look for line intersections before y1. */
	x = min_fixed;
#define HAVE_PIXELS()\
  (fixed_pixround(y - adjust_below) < fixed_pixround(y1 + adjust_above))
	draw = (HAVE_PIXELS()? 1 : -1);
	/*
	 * Loop invariants:
	 *      alp = endp->next;
	 *      for all lines lp from stopx up to alp,
	 *        lp->x_next = AL_X_AT_Y(lp, y1).
	 */
	for (alp = stopx = ll->x_list;
	     INCR_EXPR(find_y), alp != 0;
	     endp = alp, alp = alp->next
	    ) {
	    fixed nx = AL_X_AT_Y(alp, y1);
	    fixed dx_old, dx_den;

	    /* Check for intersecting lines. */
	    if (nx >= x)
		x = nx;
	    else if
		    (draw >= 0 &&	/* don't bother if no pixels */
		     (dx_old = alp->x_current - endp->x_current) >= 0 &&
		     (dx_den = dx_old + endp->x_next - nx) > dx_old
		) {		/* Make a good guess at the intersection */
		/* Y value using only local information. */
		fixed dy = y1 - y, y_new;

		if_debug3('F', "[F]cross: dy=%g, dx_old=%g, dx_new=%g\n",
			  fixed2float(dy), fixed2float(dx_old),
			  fixed2float(dx_den - dx_old));
		/* Do the computation in single precision */
		/* if the values are small enough. */
		y_new =
		    ((dy | dx_old) < 1L << (size_of(fixed) * 4 - 1) ?
		     dy * dx_old / dx_den :
		     (INCR_EXPR(mq_cross), fixed_mult_quo(dy, dx_old, dx_den)))
		    + y;
		/* The crossing value doesn't have to be */
		/* very accurate, but it does have to be */
		/* greater than y and less than y1. */
		if_debug3('F', "[F]cross y=%g, y_new=%g, y1=%g\n",
			  fixed2float(y), fixed2float(y_new),
			  fixed2float(y1));
		stopx = alp;
		if (y_new <= y) {
		    /*
		     * This isn't possible.  Recompute the intersection
		     * accurately.
		     */
		    fixed ys, xs0, xs1, ye, xe0, xe1, dy, dx0, dx1;

		    INCR(cross_slow);
		    if (endp->start.y < alp->start.y)
			ys = alp->start.y,
			    xs0 = AL_X_AT_Y(endp, ys), xs1 = alp->start.x;
		    else
			ys = endp->start.y,
			    xs0 = endp->start.x, xs1 = AL_X_AT_Y(alp, ys);
		    if (endp->end.y > alp->end.y)
			ye = alp->end.y,
			    xe0 = AL_X_AT_Y(endp, ye), xe1 = alp->end.x;
		    else
			ye = endp->end.y,
			    xe0 = endp->end.x, xe1 = AL_X_AT_Y(alp, ye);
		    dy = ye - ys;
		    dx0 = xe0 - xs0;
		    dx1 = xe1 - xs1;
		    /* We need xs0 + cross * dx0 == xs1 + cross * dx1. */
		    if (dx0 == dx1) {
			/* The two lines are coincident.  Do nothing. */
			y_new = y1;
		    } else {
			double cross = (double)(xs0 - xs1) / (dx1 - dx0);

			y_new = (fixed)(ys + cross * dy);
			if (y_new <= y) {
			    /*
			     * This can only happen through some kind of
			     * numeric disaster, but we have to check.
			     */
			    INCR(cross_low);
			    y_new = y + fixed_epsilon;
			}
		    }
		}
		if (y_new < y1) {
		    y1 = y_new;
		    nx = AL_X_AT_Y(alp, y1);
		    draw = 0;
		}
		if (nx > x)
		    x = nx;
	    }
	    alp->x_next = nx;
	}
	/* Recompute next_x for lines before the intersection. */
	for (alp = ll->x_list; alp != stopx; alp = alp->next)
	    alp->x_next = AL_X_AT_Y(alp, y1);
#ifdef DEBUG
	if (gs_debug_c('F')) {
	    dlprintf1("[F]after loop: y1=%f\n", fixed2float(y1));
	    print_line_list(ll->x_list);
	}
#endif
	/* Fill a multi-trapezoid band for the active lines. */
	/* Don't bother if no pixel centers lie within the band. */
	if (draw > 0 || (draw == 0 && HAVE_PIXELS())) {
	    fixed height = y1 - y;
	    fixed xlbot, xltop;	/* as of last "outside" line */
	    int inside = 0;
	    active_line *nlp;

	    INCR(band);
	    for (x = min_fixed, alp = ll->x_list; alp != 0; alp = nlp) {
		fixed xbot = alp->x_current;
		fixed xtop = alp->x_current = alp->x_next;
		fixed wtop;
		int xi, xli;
		int code;

		print_al("step", alp);
		INCR(band_step);
		nlp = alp->next;
		/* Handle ended or out-of-order lines.  After this, */
		/* the only member of alp we use is alp->direction. */
		if (alp->end.y != y1 || !end_x_line(alp, true)) {
		    if (xtop <= x)
			resort_x_line(alp);
		    else
			x = xtop;
		}
		/* rule = -1 for winding number rule, i.e. */
		/* we are inside if the winding number is non-zero; */
		/* rule = 1 for even-odd rule, i.e. */
		/* we are inside if the winding number is odd. */
#define INSIDE_PATH_P() ((inside & rule) != 0)
		if (!INSIDE_PATH_P()) {		/* i.e., outside */
		    inside += alp->direction;
		    if (INSIDE_PATH_P())	/* about to go in */
			xlbot = xbot, xltop = xtop;
		    continue;
		}
		/* We're inside a region being filled. */
		inside += alp->direction;
		if (INSIDE_PATH_P())	/* not about to go out */
		    continue;
#undef INSIDE_PATH_P
		/* We just went from inside to outside, so fill the region. */
		wtop = xtop - xltop;
		INCR(band_fill);
		/*
		 * If lines are temporarily out of order, we might have
		 * xtop < xltop.  Patch this up now if necessary.  Note that
		 * we can't test wtop < 0, because the subtraction might
		 * overflow.
		 */
		if (xtop < xltop) {
		    if_debug2('f', "[f]patch %g,%g\n",
			      fixed2float(xltop), fixed2float(xtop));
		    xtop = xltop += arith_rshift(wtop, 1);
		    wtop = 0;
		}
		if ((adjust_left | adjust_right) != 0) {
		    xlbot -= adjust_left;
		    xbot += adjust_right;
		    xltop -= adjust_left;
		    xtop += adjust_right;
		    wtop = xtop - xltop;
		}
		if ((xli = fixed2int_var_pixround(xltop)) ==
		    fixed2int_var_pixround(xlbot) &&
		    (xi = fixed2int_var_pixround(xtop)) ==
		    fixed2int_var_pixround(xbot)
		    ) {		/* Rectangle. */
		    int yi = fixed2int_pixround(y - adjust_below);
		    int wi = fixed2int_pixround(y1 + adjust_above) - yi;

		    code = LOOP_FILL_RECTANGLE_DIRECT(xli, yi,
						      xi - xli, wi);
		} else if ((adjust_below | adjust_above) != 0) {
		    /*
		     * We want to get the effect of filling an area whose
		     * outline is formed by dragging a square of side adj2
		     * along the border of the trapezoid.  This is *not*
		     * equivalent to simply expanding the corners by
		     * adjust: There are 3 cases needing different
		     * algorithms, plus rectangles as a fast special case.
		     */
		    fixed wbot = xbot - xlbot;

		    if (xltop <= xlbot) {
			if (xtop >= xbot) {	/* Top wider than bottom. */
			    code = LOOP_FILL_TRAPEZOID_FIXED(
					      xlbot, wbot, y - adjust_below,
						       xltop, wtop, height);
			    if (ADJUSTED_Y_SPANS_PIXEL(y1)) {
				if (code < 0)
				    return code;
				INCR(afill);
				code = LOOP_FILL_RECTANGLE_DIRECT(
				 xli, fixed2int_pixround(y1 - adjust_below),
				     fixed2int_var_pixround(xtop) - xli, 1);
			    }
			} else {	/* Slanted trapezoid. */
			    code = fill_slant_adjust(xlbot, xbot, y,
					  xltop, xtop, height, adjust_below,
						     adjust_above, pbox,
						     pdevc, dev, lop);
			}
		    } else {
			if (xtop <= xbot) {	/* Bottom wider than top. */
			    if (ADJUSTED_Y_SPANS_PIXEL(y)) {
				INCR(afill);
				xli = fixed2int_var_pixround(xlbot);
				code = LOOP_FILL_RECTANGLE_DIRECT(
				  xli, fixed2int_pixround(y - adjust_below),
				     fixed2int_var_pixround(xbot) - xli, 1);
				if (code < 0)
				    return code;
			    }
			    code = LOOP_FILL_TRAPEZOID_FIXED(
					      xlbot, wbot, y + adjust_above,
						       xltop, wtop, height);
			} else {	/* Slanted trapezoid. */
			    code = fill_slant_adjust(xlbot, xbot, y,
					  xltop, xtop, height, adjust_below,
						     adjust_above, pbox,
						     pdevc, dev, lop);
			}
		    }
		} else		/* No Y adjustment. */
		    code = LOOP_FILL_TRAPEZOID_FIXED(xlbot, xbot - xlbot,
						     y, xltop, wtop, height);
		if (code < 0)
		    return code;
	    }
	} else {
	    /* Just scan for ended or out-of-order lines. */
	    active_line *nlp;

	    for (x = min_fixed, alp = ll->x_list; alp != 0;
		 alp = nlp
		) {
		fixed nx = alp->x_current = alp->x_next;

		nlp = alp->next;
		if_debug4('F',
			  "[F]check 0x%lx,x=%g 0x%lx,x=%g\n",
			  (ulong) alp->prev, fixed2float(x),
			  (ulong) alp, fixed2float(nx));
		if (alp->end.y == y1) {
		    if (end_x_line(alp, true))
			continue;
		}
		if (nx <= x)
		    resort_x_line(alp);
		else
		    x = nx;
	    }
	}
#ifdef DEBUG
	if (gs_debug_c('f')) {
	    int code = check_line_list(ll->x_list);

	    if (code < 0)
		return code;
	}
#endif
	y = y1;
    }
    return 0;
}

/*
 * Handle the case of a slanted trapezoid with adjustment.
 * To do this exactly right requires filling a central trapezoid
 * (or rectangle) plus two horizontal almost-rectangles.
 */
private int
fill_slant_adjust(fixed xlbot, fixed xbot, fixed y,
		  fixed xltop, fixed xtop, fixed height, fixed adjust_below,
		  fixed adjust_above, const gs_fixed_rect * pbox,
		  const gx_device_color * pdevc, gx_device * dev,
		  gs_logical_operation_t lop)
{
    fixed y1 = y + height;

    dev_proc_fill_trapezoid((*fill_trap)) =
	dev_proc(dev, fill_trapezoid);
    const fixed yb = y - adjust_below;
    const fixed ya = y + adjust_above;
    const fixed y1b = y1 - adjust_below;
    const fixed y1a = y1 + adjust_above;
    const gs_fixed_edge *plbot;
    const gs_fixed_edge *prbot;
    const gs_fixed_edge *pltop;
    const gs_fixed_edge *prtop;
    gs_fixed_edge vert_left, slant_left, vert_right, slant_right;
    int code;

    INCR(slant);

    /* Set up all the edges, even though we may not need them all. */

    if (xlbot < xltop) {	/* && xbot < xtop */
	vert_left.start.x = vert_left.end.x = xlbot;
	vert_left.start.y = yb, vert_left.end.y = ya;
	vert_right.start.x = vert_right.end.x = xtop;
	vert_right.start.y = y1b, vert_right.end.y = y1a;
	slant_left.start.y = ya, slant_left.end.y = y1a;
	slant_right.start.y = yb, slant_right.end.y = y1b;
	plbot = &vert_left, prbot = &slant_right,
	    pltop = &slant_left, prtop = &vert_right;
    } else {
	vert_left.start.x = vert_left.end.x = xltop;
	vert_left.start.y = y1b, vert_left.end.y = y1a;
	vert_right.start.x = vert_right.end.x = xbot;
	vert_right.start.y = yb, vert_right.end.y = ya;
	slant_left.start.y = yb, slant_left.end.y = y1b;
	slant_right.start.y = ya, slant_right.end.y = y1a;
	plbot = &slant_left, prbot = &vert_right,
	    pltop = &vert_left, prtop = &slant_right;
    }
    slant_left.start.x = xlbot, slant_left.end.x = xltop;
    slant_right.start.x = xbot, slant_right.end.x = xtop;

    if (ya >= y1b) {
	/*
	 * The upper and lower adjustment bands overlap.
	 * Since the entire entity is less than 2 pixels high
	 * in this case, we could handle it very efficiently
	 * with no more than 2 rectangle fills, but for right now
	 * we don't attempt to do this.
	 */
	int iyb = fixed2int_var_pixround(yb);
	int iya = fixed2int_var_pixround(ya);
	int iy1b = fixed2int_var_pixround(y1b);
	int iy1a = fixed2int_var_pixround(y1a);

	INCR(slant_shallow);
	if (iy1b > iyb) {
	    code = (*fill_trap) (dev, plbot, prbot,
				 yb, y1b, false, pdevc, lop);
	    if (code < 0)
		return code;
	}
	if (iya > iy1b) {
	    int ix = fixed2int_var_pixround(vert_left.start.x);
	    int iw = fixed2int_var_pixround(vert_right.start.x) - ix;

	    code = LOOP_FILL_RECTANGLE(ix, iy1b, iw, iya - iy1b);
	    if (code < 0)
		return code;
	}
	if (iy1a > iya)
	    code = (*fill_trap) (dev, pltop, prtop,
				 ya, y1a, false, pdevc, lop);
	else
	    code = 0;
    } else {
	/*
	 * Clip the trapezoid if possible.  This can save a lot
	 * of work when filling paths that cross band boundaries.
	 */
	fixed yac;

	if (pbox->p.y < ya) {
	    code = (*fill_trap) (dev, plbot, prbot,
				 yb, ya, false, pdevc, lop);
	    if (code < 0)
		return code;
	    yac = ya;
	} else
	    yac = pbox->p.y;
	if (pbox->q.y > y1b) {
	    code = (*fill_trap) (dev, &slant_left, &slant_right,
				 yac, y1b, false, pdevc, lop);
	    if (code < 0)
		return code;
	    code = (*fill_trap) (dev, pltop, prtop,
				 y1b, y1a, false, pdevc, lop);
	} else
	    code = (*fill_trap) (dev, &slant_left, &slant_right,
				 yac, pbox->q.y, false, pdevc, lop);
    }
    return code;
}

/* Re-sort the x list by moving alp backward to its proper spot. */
private void
resort_x_line(active_line * alp)
{
    active_line *prev = alp->prev;
    active_line *next = alp->next;

    prev->next = next;
    if (next)
	next->prev = prev;
    while (x_order(prev, alp) > 0) {
	if_debug2('F', "[F]swap 0x%lx,0x%lx\n",
		  (ulong) alp, (ulong) prev);
	next = prev, prev = prev->prev;
    }
    alp->next = next;
    alp->prev = prev;
    /* next might be null, if alp was in the correct spot already. */
    if (next)
	next->prev = alp;
    prev->next = alp;
}

/* ---------------- Range list management ---------------- */

/*
 * We originally thought we would store fixed values in coordinate ranges,
 * but it turned out we want to store integers.
 */
typedef int coord_value_t;
#define MIN_COORD_VALUE min_int
#define MAX_COORD_VALUE max_int
/*
 * The invariant for coord_range_ts in a coord_range_list_t:
 *	if prev == 0:
 *		next != 0
 *		rmin == rmax == MIN_COORD_VALUE
 *	else if next == 0:
 *		prev != 0
 *		rmin == rmax == MAX_COORD_VALUE
 *	else
 *		rmin < rmax
 *	if prev != 0:
 *		prev->next == this
 *		prev->rmax < rmin
 *	if next != 0:
 *		next->prev = this
 *		next->rmin > rmax
 * A coord_range_list_t has a boundary element at each end to avoid having
 * to test for null pointers in the insertion loop.  The boundary elements
 * are the only empty ranges.
 */
typedef struct coord_range_s coord_range_t;
struct coord_range_s {
    coord_value_t rmin, rmax;
    coord_range_t *prev, *next;
    coord_range_t *alloc_next;
};
/* We declare coord_range_ts as simple because they only exist transiently. */
gs_private_st_simple(st_coord_range, coord_range_t, "coord_range_t");

typedef struct coord_range_list_s {
    gs_memory_t *memory;
    struct rl_ {
	coord_range_t *first, *next, *limit;
    } local;
    coord_range_t *allocated;
    coord_range_t *freed;
    coord_range_t *current;
    coord_range_t first, last;
} coord_range_list_t;

private coord_range_t *
range_alloc(coord_range_list_t *pcrl)
{
    coord_range_t *pcr;

    if (pcrl->freed) {
	pcr = pcrl->freed;
	pcrl->freed = pcr->next;
    } else if (pcrl->local.next < pcrl->local.limit)
	pcr = pcrl->local.next++;
    else {
	pcr = gs_alloc_struct(pcrl->memory, coord_range_t, &st_coord_range,
			      "range_alloc");
	if (pcr == 0)
	    return 0;
	pcr->alloc_next = pcrl->allocated;
	pcrl->allocated = pcr;
    }
    return pcr;
}

private void
range_delete(coord_range_list_t *pcrl, coord_range_t *pcr)
{
    if_debug3('Q', "[Qr]delete 0x%lx: [%d,%d)\n", (ulong)pcr, pcr->rmin,
	      pcr->rmax);
    pcr->prev->next = pcr->next;
    pcr->next->prev = pcr->prev;
    pcr->next = pcrl->freed;
    pcrl->freed = pcr;
}

private void
range_list_clear(coord_range_list_t *pcrl)
{
    if_debug0('Q', "[Qr]clearing\n");
    pcrl->first.next = &pcrl->last;
    pcrl->last.prev = &pcrl->first;
    pcrl->current = &pcrl->last;
}

/* ------ "Public" procedures ------ */

/* Initialize a range list.  We require num_local >= 2. */
private void range_list_clear(P1(coord_range_list_t *));
private void
range_list_init(coord_range_list_t *pcrl, coord_range_t *pcr_local,
		int num_local, gs_memory_t *mem)
{
    pcrl->memory = mem;
    pcrl->local.first = pcrl->local.next = pcr_local;
    pcrl->local.limit = pcr_local + num_local;
    pcrl->allocated = pcrl->freed = 0;
    pcrl->first.rmin = pcrl->first.rmax = MIN_COORD_VALUE;
    pcrl->first.prev = 0;
    pcrl->last.rmin = pcrl->last.rmax = MAX_COORD_VALUE;
    pcrl->last.next = 0;
    range_list_clear(pcrl);
}

/* Reset an initialized range list to the empty state. */
private void
range_list_reset(coord_range_list_t *pcrl)
{
    if (pcrl->first.next != &pcrl->last) {
	pcrl->last.prev->next = pcrl->freed;
	pcrl->freed = pcrl->first.next;
	range_list_clear(pcrl);
    }
}

/*
 * Move the cursor to the beginning of a range list, in the belief that
 * the next added ranges will roughly parallel the existing ones.
 * (Only affects performance, not function.)
 */
inline private void
range_list_rescan(coord_range_list_t *pcrl)
{
    pcrl->current = pcrl->first.next;
}

/* Free a range list. */
private void
range_list_free(coord_range_list_t *pcrl)
{
    coord_range_t *pcr;

    while ((pcr = pcrl->allocated) != 0) {
	coord_range_t *next = pcr->alloc_next;

	gs_free_object(pcrl->memory, pcr, "range_list_free");
	pcrl->allocated = next;
    }
}

/* Add a range. */
private int
range_list_add(coord_range_list_t *pcrl, coord_value_t rmin, coord_value_t rmax)
{
    coord_range_t *pcr = pcrl->current;

    if (rmin >= rmax)
	return 0;
    /*
     * Usually, ranges are added in increasing order within each scan line,
     * and overlapping ranges don't differ much.  Optimize accordingly.
     */
 top:
    if (rmax < pcr->rmin) {
	if (rmin > pcr->prev->rmax)
	    goto ins;
	pcr = pcr->prev;
	goto top;
    }
    if (rmin > pcr->rmax) {
	pcr = pcr->next;
	if (rmax < pcr->rmin)
	    goto ins;
	goto top;
    }
    /*
     * Now we know that (rmin,rmax) overlaps (pcr->rmin,pcr->rmax).
     * Don't delete or merge into the special min and max ranges.
     */
    while (rmin <= pcr->prev->rmax) {
	/* Merge the range below pcr into this one. */
	if (!pcr->prev->prev)
	    break;		/* don't merge into the min range */
	pcr->rmin = pcr->prev->rmin;
	range_delete(pcrl, pcr->prev);
    }
    while (rmax >= pcr->next->rmin) {
	/* Merge the range above pcr into this one. */
	if (!pcr->next->next)
	    break;		/* don't merge into the max range */
	pcr->rmax = pcr->next->rmax;
	range_delete(pcrl, pcr->next);
    }
    /*
     * Now we know that the union of (rmin,rmax) and (pcr->rmin,pcr->rmax)
     * doesn't overlap or abut either adjacent range, except that it may
     * abut if the adjacent range is the special min or max range.
     */
    if (rmin < pcr->rmin) {
	if_debug3('Q', "[Qr]update 0x%lx => [%d,%d)\n", (ulong)pcr, rmin,
		  pcr->rmax);
	pcr->rmin = rmin;
    }
    if (rmax > pcr->rmax) {
	if_debug3('Q', "[Qr]update 0x%lx => [%d,%d)\n", (ulong)pcr, pcr->rmin,
		  rmax);
	pcr->rmax = rmax;
    }
    pcrl->current = pcr->next;
    return 0;
 ins:
    /* Insert a new range below pcr. */
    {
	coord_range_t *prev = range_alloc(pcrl);

	if (prev == 0)
	    return_error(gs_error_VMerror);
	if_debug3('Q', "[Qr]insert 0x%lx: [%d,%d)\n", (ulong)prev, rmin, rmax);
	prev->rmin = rmin, prev->rmax = rmax;
	(prev->prev = pcr->prev)->next = prev;
	prev->next = pcr;
	pcr->prev = prev;
    }
    pcrl->current = pcr;
    return 0;
}

/* ---------------- Scan line filling loop ---------------- */

/* Forward references */
private int merge_ranges(P6(coord_range_list_t *pcrl, ll_ptr ll,
			    fixed y_min, fixed y_top,
			    fixed adjust_left, fixed adjust_right));
private void set_scan_line_points(P2(active_line *, fixed));

/* Main filling loop. */
private int
fill_loop_by_scan_lines(ll_ptr ll, gx_device * dev,
			const gx_fill_params * params,
			const gx_device_color * pdevc,
			gs_logical_operation_t lop, const gs_fixed_rect * pbox,
			fixed adjust_left, fixed adjust_right,
			fixed adjust_below, fixed adjust_above,
			fixed band_mask)
{
    int rule = params->rule;
    fixed fixed_flat = float2fixed(params->flatness);
    bool fill_direct = color_writes_pure(pdevc, lop);
    gx_color_index cindex;
    dev_proc_fill_rectangle((*fill_rect));
    active_line *yll = ll->y_list;
    fixed y_limit = pbox->q.y;
    /*
     * The meaning of adjust_below (B) and adjust_above (A) is that the
     * pixels that would normally be painted at coordinate Y get "smeared"
     * to coordinates Y-B through Y+A-epsilon, inclusive.  This is
     * equivalent to saying that the pixels actually painted at coordinate Y
     * are those contributed by scan lines Y-A+epsilon through Y+B,
     * inclusive.  (A = B = 0 is a special case, equivalent to B = 0, A =
     * epsilon.)
     */
    fixed y_frac_min =
	(adjust_above == fixed_0 ? fixed_half :
	 fixed_half + fixed_epsilon - adjust_above);
    fixed y_frac_max =
	fixed_half + adjust_below;
    int y0 = fixed2int(min_fixed);
    fixed y_bot = min_fixed;	/* normally int2fixed(y0) + y_frac_min */
    fixed y_top = min_fixed;	/* normally int2fixed(y0) + y_frac_max */
    coord_range_list_t rlist;
    coord_range_t rlocal[MAX_LOCAL_ACTIVE];
    int code = 0;

    if (yll == 0)		/* empty list */
	return 0;
    range_list_init(&rlist, rlocal, countof(rlocal), ll->memory);
    if (fill_direct)
	cindex = pdevc->colors.pure,
	    fill_rect = dev_proc(dev, fill_rectangle);
    ll->x_list = 0;
    ll->x_head.x_current = min_fixed;	/* stop backward scan */
    while (code >= 0) {
	active_line *alp, *nlp;
	fixed y, x;
	bool new_band;

	INCR(iter);

	/*
	 * Find the next sampling point, either the bottom of a sampling
	 * band or a line start.
	 */

	if (ll->x_list == 0)
	    y = (yll == 0 ? y_limit : yll->start.y);
	else {
	    y = y_bot + fixed_1;
	    if (yll != 0)
		y = min(y, yll->start.y);
	    for (alp = ll->x_list; alp != 0; alp = alp->next)
		if (!end_x_line(alp, false))
		    y = min(y, alp->end.y);
	}

	/* Move newly active lines from y to x list. */

	while (yll != 0 && yll->start.y == y) {
	    active_line *ynext = yll->next;	/* insert smashes next/prev links */

	    if (yll->direction == DIR_HORIZONTAL) {
		/* Ignore for now. */
	    } else {
		insert_x_new(yll, ll);
		set_scan_line_points(yll, fixed_flat);
	    }
	    yll = ynext;
	}

	/* Update active lines to y. */

	x = min_fixed;
	for (alp = ll->x_list; alp != 0; alp = nlp) {
	    fixed nx;

	    nlp = alp->next;
	  e:if (alp->end.y <= y) {
		if (end_x_line(alp, true))
		    continue;
		set_scan_line_points(alp, fixed_flat);
		goto e;
	    }
	    nx = alp->x_current =
		(alp->start.y >= y ? alp->start.x :
		 alp->curve_k < 0 ?
		 AL_X_AT_Y(alp, y) :
		 gx_curve_x_at_y(&alp->cursor, y));
	    if (nx < x) {
		/* Move this line backward in the list. */
		active_line *ilp = alp;

		while (nx < (ilp = ilp->prev)->x_current)
		    DO_NOTHING;
		/* Now ilp->x_current <= nx < ilp->next->x_cur. */
		alp->prev->next = alp->next;
		if (alp->next)
		    alp->next->prev = alp->prev;
		if (ilp->next)
		    ilp->next->prev = alp;
		alp->next = ilp->next;
		ilp->next = alp;
		alp->prev = ilp;
		continue;
	    }
	    x = nx;
	}

	if (y > y_top || y >= y_limit) {
	    /* We're beyond the end of the previous sampling band. */
	    const coord_range_t *pcr;

	    /* Fill the ranges for y0. */

	    for (pcr = rlist.first.next; pcr != &rlist.last;
		 pcr = pcr->next
		 ) {
		int x0 = pcr->rmin, x1 = pcr->rmax;

		if_debug4('Q', "[Qr]draw 0x%lx: [%d,%d),%d\n", (ulong)pcr,
			  x0, x1, y0);
		code = LOOP_FILL_RECTANGLE_DIRECT(x0, y0, x1 - x0, 1);
		if_debug3('F', "[F]drawing [%d:%d),%d\n", x0, x1, y0);
		if (code < 0)
		    goto done;
	    }
	    range_list_reset(&rlist);

	    /* Check whether we've reached the maximum y. */

	    if (y >= y_limit)
		break;

	    /* Reset the sampling band. */

	    y0 = fixed2int(y);
	    if (fixed_fraction(y) < y_frac_min)
		--y0;
	    y_bot = int2fixed(y0) + y_frac_min;
	    y_top = int2fixed(y0) + y_frac_max;
	    new_band = true;
	} else
	    new_band = false;

	if (y <= y_top) {
	    /*
	     * We're within the same Y pixel.  Merge regions for segments
	     * starting here (at y), up to y_top or the end of the segment.
	     * If this is the first sampling within the band, run the
	     * fill/eofill algorithm.
	     */
	    fixed y_min;

	    if (new_band) {
		/*
		 * rule = -1 for winding number rule, i.e.
		 * we are inside if the winding number is non-zero;
		 * rule = 1 for even-odd rule, i.e.
		 * we are inside if the winding number is odd.
		 */
		int inside = 0;

#define INSIDE_PATH_P() ((inside & rule) != 0)
		INCR(band);
		for (alp = ll->x_list; alp != 0; alp = alp->next) {
		    int x0 = fixed2int_pixround(alp->x_current - adjust_left);

		    for (;;) {
			/* We're inside a filled region. */
			print_al("step", alp);
			INCR(band_step);
			inside += alp->direction;
			if (!INSIDE_PATH_P())
			    break;
			/*
			 * Since we're dealing with closed paths, the test
			 * for alp == 0 shouldn't be needed, but we may have
			 * omitted lines that are to the right of the
			 * clipping region.
			 */
			if ((alp = alp->next) == 0)
			    goto out;
		    }
#undef INSIDE_PATH_P
		    /* We just went from inside to outside, so fill the region. */
		    code = range_list_add(&rlist, x0,
					  fixed2int_rounded(alp->x_current +
							    adjust_right));
		    if (code < 0)
			goto done;
		}
	    out:
		y_min = min_fixed;
	    } else
		y_min = y;
	    code = merge_ranges(&rlist, ll, y_min, y_top, adjust_left,
				adjust_right);
	} /* else y < y_bot + 1, do nothing */
    }
 done:
    range_list_free(&rlist);
    return code;
}

/*
 * Merge regions for active segments starting at a given Y, or all active
 * segments, up to the end of the sampling band or the end of the segment,
 * into the range list.
 */
private int
merge_ranges(coord_range_list_t *pcrl, ll_ptr ll, fixed y_min, fixed y_top,
	     fixed adjust_left, fixed adjust_right)
{
    active_line *alp, *nlp;
    int code = 0;

    range_list_rescan(pcrl);
    for (alp = ll->x_list; alp != 0 && code >= 0; alp = nlp) {
	fixed x0 = alp->x_current, x1, xt;

	nlp = alp->next;
	if (alp->start.y < y_min)
	    continue;
	if (alp->end.y < y_top)
	    x1 = alp->end.x;
	else if (alp->curve_k < 0)
	    x1 = AL_X_AT_Y(alp, y_top);
	else
	    x1 = gx_curve_x_at_y(&alp->cursor, y_top);
	if (x0 > x1)
	    xt = x0, x0 = x1, x1 = xt;
	code = range_list_add(pcrl,
			      fixed2int_pixround(x0 - adjust_left),
			      fixed2int_rounded(x1 + adjust_right));
    }
    return code;
}

/*
 * Set curve_k and, if necessary, the curve rendering parameters for
 * the current segment of an active line.
 */
private void
set_scan_line_points(active_line * alp, fixed fixed_flat)
{
    const segment *pseg = alp->pseg;
    const gs_fixed_point *pp0;

    if (alp->direction < 0) {
	pseg =
	    (pseg->type == s_line_close ?
	     ((const line_close_segment *)pseg)->sub->next :
	     pseg->next);
	if (pseg->type != s_curve) {
	    alp->curve_k = -1;
	    return;
	}
	pp0 = &alp->end;
    } else {
	if (pseg->type != s_curve) {
	    alp->curve_k = -1;
	    return;
	}
	pp0 = &alp->start;
    }
    {
	const curve_segment *const pcseg = (const curve_segment *)pseg;

	alp->curve_k =
	    gx_curve_log2_samples(pp0->x, pp0->y, pcseg, fixed_flat);
	gx_curve_cursor_init(&alp->cursor, pp0->x, pp0->y, pcseg,
			     alp->curve_k);
    }
}