Inline fetch functions in pixman-transformed.c

[profile/ivi/pixman.git] / pixman / pixman-region.c

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Copyright 1987, 1988, 1989 by
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                        All Rights Reserved

Permission to use, copy, modify, and distribute this software and its
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both that copyright notice and this permission notice appear in
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******************************************************************/

#include <stdlib.h>
#include <limits.h>
#include <string.h>
#include <stdio.h>

#define PIXREGION_NIL(reg) ((reg)->data && !(reg)->data->numRects)
/* not a region */
#define PIXREGION_NAR(reg)      ((reg)->data == pixman_brokendata)
#define PIXREGION_NUM_RECTS(reg) ((reg)->data ? (reg)->data->numRects : 1)
#define PIXREGION_SIZE(reg) ((reg)->data ? (reg)->data->size : 0)
#define PIXREGION_RECTS(reg) ((reg)->data ? (box_type_t *)((reg)->data + 1) \
                                       : &(reg)->extents)
#define PIXREGION_BOXPTR(reg) ((box_type_t *)((reg)->data + 1))
#define PIXREGION_BOX(reg,i) (&PIXREGION_BOXPTR(reg)[i])
#define PIXREGION_TOP(reg) PIXREGION_BOX(reg, (reg)->data->numRects)
#define PIXREGION_END(reg) PIXREGION_BOX(reg, (reg)->data->numRects - 1)


#undef assert
#ifdef DEBUG_PIXREGION
#define assert(expr) {if (!(expr)) \
                FatalError("Assertion failed file %s, line %d: expr\n", \
                        __FILE__, __LINE__); }
#else
#define assert(expr)
#endif

#define good(reg) assert(PREFIX(_selfcheck) (reg))

#undef MIN
#define MIN(a,b) ((a) < (b) ? (a) : (b))
#undef MAX
#define MAX(a,b) ((a) > (b) ? (a) : (b))

static const box_type_t PREFIX(_emptyBox_) = {0, 0, 0, 0};
static const region_data_type_t PREFIX(_emptyData_) = {0, 0};
static const region_data_type_t PREFIX(_brokendata_) = {0, 0};

static box_type_t *pixman_region_emptyBox = (box_type_t *)&PREFIX(_emptyBox_);
static region_data_type_t *pixman_region_emptyData = (region_data_type_t *)&PREFIX(_emptyData_);
static region_data_type_t *pixman_brokendata = (region_data_type_t *)&PREFIX(_brokendata_);

/* This function exists only to make it possible to preserve the X ABI - it should
 * go away at first opportunity.
 *
 * The problem is that the X ABI exports the three structs and has used
 * them through macros. So the X server calls this function with
 * the addresses of those structs which makes the existing code continue to
 * work.
 */
void
PREFIX(_internal_set_static_pointers) (box_type_t *empty_box,
                                       region_data_type_t *empty_data,
                                       region_data_type_t *broken_data)
{
    pixman_region_emptyBox = empty_box;
    pixman_region_emptyData = empty_data;
    pixman_brokendata = broken_data;
}

static pixman_bool_t
pixman_break (region_type_t *pReg);

/*
 * The functions in this file implement the Region abstraction used extensively
 * throughout the X11 sample server. A Region is simply a set of disjoint
 * (non-overlapping) rectangles, plus an "extent" rectangle which is the
 * smallest single rectangle that contains all the non-overlapping rectangles.
 *
 * A Region is implemented as a "y-x-banded" array of rectangles.  This array
 * imposes two degrees of order.  First, all rectangles are sorted by top side
 * y coordinate first (y1), and then by left side x coordinate (x1).
 *
 * Furthermore, the rectangles are grouped into "bands".  Each rectangle in a
 * band has the same top y coordinate (y1), and each has the same bottom y
 * coordinate (y2).  Thus all rectangles in a band differ only in their left
 * and right side (x1 and x2).  Bands are implicit in the array of rectangles:
 * there is no separate list of band start pointers.
 *
 * The y-x band representation does not minimize rectangles.  In particular,
 * if a rectangle vertically crosses a band (the rectangle has scanlines in
 * the y1 to y2 area spanned by the band), then the rectangle may be broken
 * down into two or more smaller rectangles stacked one atop the other.
 *
 *  -----------                             -----------
 *  |         |                             |         |             band 0
 *  |         |  --------                   -----------  --------
 *  |         |  |      |  in y-x banded    |         |  |      |   band 1
 *  |         |  |      |  form is          |         |  |      |
 *  -----------  |      |                   -----------  --------
 *               |      |                                |      |   band 2
 *               --------                                --------
 *
 * An added constraint on the rectangles is that they must cover as much
 * horizontal area as possible: no two rectangles within a band are allowed
 * to touch.
 *
 * Whenever possible, bands will be merged together to cover a greater vertical
 * distance (and thus reduce the number of rectangles). Two bands can be merged
 * only if the bottom of one touches the top of the other and they have
 * rectangles in the same places (of the same width, of course).
 *
 * Adam de Boor wrote most of the original region code.  Joel McCormack
 * substantially modified or rewrote most of the core arithmetic routines, and
 * added pixman_region_validate in order to support several speed improvements to
 * pixman_region_validateTree.  Bob Scheifler changed the representation to be more
 * compact when empty or a single rectangle, and did a bunch of gratuitous
 * reformatting. Carl Worth did further gratuitous reformatting while re-merging
 * the server and client region code into libpixregion.
 */

/*  true iff two Boxes overlap */
#define EXTENTCHECK(r1,r2) \
      (!( ((r1)->x2 <= (r2)->x1)  || \
          ((r1)->x1 >= (r2)->x2)  || \
          ((r1)->y2 <= (r2)->y1)  || \
          ((r1)->y1 >= (r2)->y2) ) )

/* true iff (x,y) is in Box */
#define INBOX(r,x,y) \
      ( ((r)->x2 >  x) && \
        ((r)->x1 <= x) && \
        ((r)->y2 >  y) && \
        ((r)->y1 <= y) )

/* true iff Box r1 contains Box r2 */
#define SUBSUMES(r1,r2) \
      ( ((r1)->x1 <= (r2)->x1) && \
        ((r1)->x2 >= (r2)->x2) && \
        ((r1)->y1 <= (r2)->y1) && \
        ((r1)->y2 >= (r2)->y2) )

static size_t
PIXREGION_SZOF(size_t n)
{
    size_t size = n * sizeof(box_type_t);
    if (n > UINT32_MAX / sizeof(box_type_t))
        return 0;

    if (sizeof(region_data_type_t) > UINT32_MAX - size)
        return 0;

    return size + sizeof(region_data_type_t);
}

static void *
allocData(size_t n)
{
    size_t sz = PIXREGION_SZOF(n);
    if (!sz)
        return NULL;

    return malloc(sz);
}

#define freeData(reg) if ((reg)->data && (reg)->data->size) free((reg)->data)

#define RECTALLOC_BAIL(pReg,n,bail) \
if (!(pReg)->data || (((pReg)->data->numRects + (n)) > (pReg)->data->size)) \
    if (!pixman_rect_alloc(pReg, n)) { goto bail; }

#define RECTALLOC(pReg,n) \
if (!(pReg)->data || (((pReg)->data->numRects + (n)) > (pReg)->data->size)) \
    if (!pixman_rect_alloc(pReg, n)) { return FALSE; }

#define ADDRECT(pNextRect,nx1,ny1,nx2,ny2)      \
{                                               \
    pNextRect->x1 = nx1;                        \
    pNextRect->y1 = ny1;                        \
    pNextRect->x2 = nx2;                        \
    pNextRect->y2 = ny2;                        \
    pNextRect++;                                \
}

#define NEWRECT(pReg,pNextRect,nx1,ny1,nx2,ny2)                 \
{                                                                       \
    if (!(pReg)->data || ((pReg)->data->numRects == (pReg)->data->size))\
    {                                                                   \
        if (!pixman_rect_alloc(pReg, 1))                                        \
            return FALSE;                                               \
        pNextRect = PIXREGION_TOP(pReg);                                        \
    }                                                                   \
    ADDRECT(pNextRect,nx1,ny1,nx2,ny2);                                 \
    pReg->data->numRects++;                                             \
    assert(pReg->data->numRects<=pReg->data->size);                     \
}

#define DOWNSIZE(reg,numRects)                                          \
    if (((numRects) < ((reg)->data->size >> 1)) && ((reg)->data->size > 50)) \
    {                                                                   \
        region_data_type_t * NewData;                           \
        size_t data_size = PIXREGION_SZOF(numRects);                    \
        if (!data_size)                                                 \
            NewData = NULL;                                             \
        else                                                            \
            NewData = (region_data_type_t *)realloc((reg)->data, data_size); \
        if (NewData)                                                    \
        {                                                               \
            NewData->size = (numRects);                                 \
            (reg)->data = NewData;                                      \
        }                                                               \
    }

PIXMAN_EXPORT pixman_bool_t
PREFIX(_equal) (reg1, reg2)
    region_type_t * reg1;
    region_type_t * reg2;
{
    int i;
    box_type_t *rects1;
    box_type_t *rects2;

    if (reg1->extents.x1 != reg2->extents.x1) return FALSE;
    if (reg1->extents.x2 != reg2->extents.x2) return FALSE;
    if (reg1->extents.y1 != reg2->extents.y1) return FALSE;
    if (reg1->extents.y2 != reg2->extents.y2) return FALSE;
    if (PIXREGION_NUM_RECTS(reg1) != PIXREGION_NUM_RECTS(reg2)) return FALSE;

    rects1 = PIXREGION_RECTS(reg1);
    rects2 = PIXREGION_RECTS(reg2);
    for (i = 0; i != PIXREGION_NUM_RECTS(reg1); i++) {
        if (rects1[i].x1 != rects2[i].x1) return FALSE;
        if (rects1[i].x2 != rects2[i].x2) return FALSE;
        if (rects1[i].y1 != rects2[i].y1) return FALSE;
        if (rects1[i].y2 != rects2[i].y2) return FALSE;
    }
    return TRUE;
}

int
PREFIX(_print) (rgn)
    region_type_t * rgn;
{
    int num, size;
    int i;
    box_type_t * rects;

    num = PIXREGION_NUM_RECTS(rgn);
    size = PIXREGION_SIZE(rgn);
    rects = PIXREGION_RECTS(rgn);
    fprintf(stderr, "num: %d size: %d\n", num, size);
    fprintf(stderr, "extents: %d %d %d %d\n",
           rgn->extents.x1, rgn->extents.y1, rgn->extents.x2, rgn->extents.y2);
    for (i = 0; i < num; i++)
        fprintf(stderr, "%d %d %d %d \n",
                rects[i].x1, rects[i].y1, rects[i].x2, rects[i].y2);
    fprintf(stderr, "\n");
    return(num);
}


PIXMAN_EXPORT void
PREFIX(_init) (region_type_t *region)
{
    region->extents = *pixman_region_emptyBox;
    region->data = pixman_region_emptyData;
}

PIXMAN_EXPORT void
PREFIX(_init_rect) (region_type_t *region,
                    int x, int y, unsigned int width, unsigned int height)
{
    region->extents.x1 = x;
    region->extents.y1 = y;
    region->extents.x2 = x + width;
    region->extents.y2 = y + height;
    region->data = NULL;
}

PIXMAN_EXPORT void
PREFIX(_init_with_extents) (region_type_t *region, box_type_t *extents)
{
    region->extents = *extents;
    region->data = NULL;
}

PIXMAN_EXPORT void
PREFIX(_fini) (region_type_t *region)
{
    good (region);
    freeData (region);
}

PIXMAN_EXPORT int
PREFIX(_n_rects) (region_type_t *region)
{
    return PIXREGION_NUM_RECTS (region);
}

PIXMAN_EXPORT box_type_t *
PREFIX(_rectangles) (region_type_t *region,
                                  int               *n_rects)
{
    if (n_rects)
        *n_rects = PIXREGION_NUM_RECTS (region);

    return PIXREGION_RECTS (region);
}

static pixman_bool_t
pixman_break (region_type_t *region)
{
    freeData (region);
    region->extents = *pixman_region_emptyBox;
    region->data = pixman_brokendata;
    return FALSE;
}

static pixman_bool_t
pixman_rect_alloc (region_type_t * region, int n)
{
    region_data_type_t *data;

    if (!region->data)
    {
        n++;
        region->data = allocData(n);
        if (!region->data)
            return pixman_break (region);
        region->data->numRects = 1;
        *PIXREGION_BOXPTR(region) = region->extents;
    }
    else if (!region->data->size)
    {
        region->data = allocData(n);
        if (!region->data)
            return pixman_break (region);
        region->data->numRects = 0;
    }
    else
    {
        size_t data_size;
        if (n == 1)
        {
            n = region->data->numRects;
            if (n > 500) /* XXX pick numbers out of a hat */
                n = 250;
        }
        n += region->data->numRects;
        data_size = PIXREGION_SZOF(n);
        if (!data_size)
            data = NULL;
        else
            data = (region_data_type_t *)realloc(region->data, PIXREGION_SZOF(n));
        if (!data)
            return pixman_break (region);
        region->data = data;
    }
    region->data->size = n;
    return TRUE;
}

PIXMAN_EXPORT pixman_bool_t
PREFIX(_copy) (region_type_t *dst, region_type_t *src)
{
    good(dst);
    good(src);
    if (dst == src)
        return TRUE;
    dst->extents = src->extents;
    if (!src->data || !src->data->size)
    {
        freeData(dst);
        dst->data = src->data;
        return TRUE;
    }
    if (!dst->data || (dst->data->size < src->data->numRects))
    {
        freeData(dst);
        dst->data = allocData(src->data->numRects);
        if (!dst->data)
            return pixman_break (dst);
        dst->data->size = src->data->numRects;
    }
    dst->data->numRects = src->data->numRects;
    memmove((char *)PIXREGION_BOXPTR(dst),(char *)PIXREGION_BOXPTR(src),
          dst->data->numRects * sizeof(box_type_t));
    return TRUE;
}

/*======================================================================
 *          Generic Region Operator
 *====================================================================*/

/*-
 *-----------------------------------------------------------------------
 * pixman_coalesce --
 *      Attempt to merge the boxes in the current band with those in the
 *      previous one.  We are guaranteed that the current band extends to
 *      the end of the rects array.  Used only by pixman_op.
 *
 * Results:
 *      The new index for the previous band.
 *
 * Side Effects:
 *      If coalescing takes place:
 *          - rectangles in the previous band will have their y2 fields
 *            altered.
 *          - region->data->numRects will be decreased.
 *
 *-----------------------------------------------------------------------
 */
static inline int
pixman_coalesce (
    region_type_t *     region,         /* Region to coalesce                */
    int                 prevStart,      /* Index of start of previous band   */
    int                 curStart)       /* Index of start of current band    */
{
    box_type_t *        pPrevBox;       /* Current box in previous band      */
    box_type_t *        pCurBox;        /* Current box in current band       */
    int         numRects;       /* Number rectangles in both bands   */
    int y2;             /* Bottom of current band            */
    /*
     * Figure out how many rectangles are in the band.
     */
    numRects = curStart - prevStart;
    assert(numRects == region->data->numRects - curStart);

    if (!numRects) return curStart;

    /*
     * The bands may only be coalesced if the bottom of the previous
     * matches the top scanline of the current.
     */
    pPrevBox = PIXREGION_BOX(region, prevStart);
    pCurBox = PIXREGION_BOX(region, curStart);
    if (pPrevBox->y2 != pCurBox->y1) return curStart;

    /*
     * Make sure the bands have boxes in the same places. This
     * assumes that boxes have been added in such a way that they
     * cover the most area possible. I.e. two boxes in a band must
     * have some horizontal space between them.
     */
    y2 = pCurBox->y2;

    do {
        if ((pPrevBox->x1 != pCurBox->x1) || (pPrevBox->x2 != pCurBox->x2)) {
            return (curStart);
        }
        pPrevBox++;
        pCurBox++;
        numRects--;
    } while (numRects);

    /*
     * The bands may be merged, so set the bottom y of each box
     * in the previous band to the bottom y of the current band.
     */
    numRects = curStart - prevStart;
    region->data->numRects -= numRects;
    do {
        pPrevBox--;
        pPrevBox->y2 = y2;
        numRects--;
    } while (numRects);
    return prevStart;
}

/* Quicky macro to avoid trivial reject procedure calls to pixman_coalesce */

#define Coalesce(newReg, prevBand, curBand)                             \
    if (curBand - prevBand == newReg->data->numRects - curBand) {       \
        prevBand = pixman_coalesce(newReg, prevBand, curBand);          \
    } else {                                                            \
        prevBand = curBand;                                             \
    }

/*-
 *-----------------------------------------------------------------------
 * pixman_region_appendNonO --
 *      Handle a non-overlapping band for the union and subtract operations.
 *      Just adds the (top/bottom-clipped) rectangles into the region.
 *      Doesn't have to check for subsumption or anything.
 *
 * Results:
 *      None.
 *
 * Side Effects:
 *      region->data->numRects is incremented and the rectangles overwritten
 *      with the rectangles we're passed.
 *
 *-----------------------------------------------------------------------
 */

static inline pixman_bool_t
pixman_region_appendNonO (
    region_type_t *     region,
    box_type_t *        r,
    box_type_t *                rEnd,
    int         y1,
    int         y2)
{
    box_type_t *        pNextRect;
    int newRects;

    newRects = rEnd - r;

    assert(y1 < y2);
    assert(newRects != 0);

    /* Make sure we have enough space for all rectangles to be added */
    RECTALLOC(region, newRects);
    pNextRect = PIXREGION_TOP(region);
    region->data->numRects += newRects;
    do {
        assert(r->x1 < r->x2);
        ADDRECT(pNextRect, r->x1, y1, r->x2, y2);
        r++;
    } while (r != rEnd);

    return TRUE;
}

#define FindBand(r, rBandEnd, rEnd, ry1)                    \
{                                                           \
    ry1 = r->y1;                                            \
    rBandEnd = r+1;                                         \
    while ((rBandEnd != rEnd) && (rBandEnd->y1 == ry1)) {   \
        rBandEnd++;                                         \
    }                                                       \
}

#define AppendRegions(newReg, r, rEnd)                                  \
{                                                                       \
    int newRects;                                                       \
    if ((newRects = rEnd - r)) {                                        \
        RECTALLOC(newReg, newRects);                                    \
        memmove((char *)PIXREGION_TOP(newReg),(char *)r,                        \
              newRects * sizeof(box_type_t));                           \
        newReg->data->numRects += newRects;                             \
    }                                                                   \
}

/*-
 *-----------------------------------------------------------------------
 * pixman_op --
 *      Apply an operation to two regions. Called by pixman_region_union, pixman_region_inverse,
 *      pixman_region_subtract, pixman_region_intersect....  Both regions MUST have at least one
 *      rectangle, and cannot be the same object.
 *
 * Results:
 *      TRUE if successful.
 *
 * Side Effects:
 *      The new region is overwritten.
 *      pOverlap set to TRUE if overlapFunc ever returns TRUE.
 *
 * Notes:
 *      The idea behind this function is to view the two regions as sets.
 *      Together they cover a rectangle of area that this function divides
 *      into horizontal bands where points are covered only by one region
 *      or by both. For the first case, the nonOverlapFunc is called with
 *      each the band and the band's upper and lower extents. For the
 *      second, the overlapFunc is called to process the entire band. It
 *      is responsible for clipping the rectangles in the band, though
 *      this function provides the boundaries.
 *      At the end of each band, the new region is coalesced, if possible,
 *      to reduce the number of rectangles in the region.
 *
 *-----------------------------------------------------------------------
 */

typedef pixman_bool_t (*OverlapProcPtr)(
    region_type_t        *region,
    box_type_t *r1,
    box_type_t *r1End,
    box_type_t *r2,
    box_type_t *r2End,
    int          y1,
    int          y2,
    int          *pOverlap);

static pixman_bool_t
pixman_op(
    region_type_t *newReg,                  /* Place to store result         */
    region_type_t *       reg1,             /* First region in operation     */
    region_type_t *       reg2,             /* 2d region in operation        */
    OverlapProcPtr  overlapFunc,            /* Function to call for over-
                                             * lapping bands                 */
    int     appendNon1,             /* Append non-overlapping bands  */
                                            /* in region 1 ? */
    int     appendNon2,             /* Append non-overlapping bands  */
                                            /* in region 2 ? */
    int     *pOverlap)
{
    box_type_t * r1;                        /* Pointer into first region     */
    box_type_t * r2;                        /* Pointer into 2d region        */
    box_type_t *            r1End;                  /* End of 1st region             */
    box_type_t *            r2End;                  /* End of 2d region              */
    int     ybot;                   /* Bottom of intersection        */
    int     ytop;                   /* Top of intersection           */
    region_data_type_t *            oldData;                /* Old data for newReg           */
    int             prevBand;               /* Index of start of
                                             * previous band in newReg       */
    int             curBand;                /* Index of start of current
                                             * band in newReg                */
    box_type_t * r1BandEnd;                 /* End of current band in r1     */
    box_type_t * r2BandEnd;                 /* End of current band in r2     */
    int     top;                    /* Top of non-overlapping band   */
    int     bot;                    /* Bottom of non-overlapping band*/
    int    r1y1;                    /* Temps for r1->y1 and r2->y1   */
    int    r2y1;
    int             newSize;
    int             numRects;

    /*
     * Break any region computed from a broken region
     */
    if (PIXREGION_NAR (reg1) || PIXREGION_NAR(reg2))
        return pixman_break (newReg);

    /*
     * Initialization:
     *  set r1, r2, r1End and r2End appropriately, save the rectangles
     * of the destination region until the end in case it's one of
     * the two source regions, then mark the "new" region empty, allocating
     * another array of rectangles for it to use.
     */

    r1 = PIXREGION_RECTS(reg1);
    newSize = PIXREGION_NUM_RECTS(reg1);
    r1End = r1 + newSize;
    numRects = PIXREGION_NUM_RECTS(reg2);
    r2 = PIXREGION_RECTS(reg2);
    r2End = r2 + numRects;
    assert(r1 != r1End);
    assert(r2 != r2End);

    oldData = (region_data_type_t *)NULL;
    if (((newReg == reg1) && (newSize > 1)) ||
        ((newReg == reg2) && (numRects > 1)))
    {
        oldData = newReg->data;
        newReg->data = pixman_region_emptyData;
    }
    /* guess at new size */
    if (numRects > newSize)
        newSize = numRects;
    newSize <<= 1;
    if (!newReg->data)
        newReg->data = pixman_region_emptyData;
    else if (newReg->data->size)
        newReg->data->numRects = 0;
    if (newSize > newReg->data->size) {
        if (!pixman_rect_alloc(newReg, newSize)) {
            if (oldData)
                free (oldData);
            return FALSE;
        }
    }

    /*
     * Initialize ybot.
     * In the upcoming loop, ybot and ytop serve different functions depending
     * on whether the band being handled is an overlapping or non-overlapping
     * band.
     *  In the case of a non-overlapping band (only one of the regions
     * has points in the band), ybot is the bottom of the most recent
     * intersection and thus clips the top of the rectangles in that band.
     * ytop is the top of the next intersection between the two regions and
     * serves to clip the bottom of the rectangles in the current band.
     *  For an overlapping band (where the two regions intersect), ytop clips
     * the top of the rectangles of both regions and ybot clips the bottoms.
     */

    ybot = MIN(r1->y1, r2->y1);

    /*
     * prevBand serves to mark the start of the previous band so rectangles
     * can be coalesced into larger rectangles. qv. pixman_coalesce, above.
     * In the beginning, there is no previous band, so prevBand == curBand
     * (curBand is set later on, of course, but the first band will always
     * start at index 0). prevBand and curBand must be indices because of
     * the possible expansion, and resultant moving, of the new region's
     * array of rectangles.
     */
    prevBand = 0;

    do {
        /*
         * This algorithm proceeds one source-band (as opposed to a
         * destination band, which is determined by where the two regions
         * intersect) at a time. r1BandEnd and r2BandEnd serve to mark the
         * rectangle after the last one in the current band for their
         * respective regions.
         */
        assert(r1 != r1End);
        assert(r2 != r2End);

        FindBand(r1, r1BandEnd, r1End, r1y1);
        FindBand(r2, r2BandEnd, r2End, r2y1);

        /*
         * First handle the band that doesn't intersect, if any.
         *
         * Note that attention is restricted to one band in the
         * non-intersecting region at once, so if a region has n
         * bands between the current position and the next place it overlaps
         * the other, this entire loop will be passed through n times.
         */
        if (r1y1 < r2y1) {
            if (appendNon1) {
                top = MAX(r1y1, ybot);
                bot = MIN(r1->y2, r2y1);
                if (top != bot) {
                    curBand = newReg->data->numRects;
                    pixman_region_appendNonO(newReg, r1, r1BandEnd, top, bot);
                    Coalesce(newReg, prevBand, curBand);
                }
            }
            ytop = r2y1;
        } else if (r2y1 < r1y1) {
            if (appendNon2) {
                top = MAX(r2y1, ybot);
                bot = MIN(r2->y2, r1y1);
                if (top != bot) {
                    curBand = newReg->data->numRects;
                    pixman_region_appendNonO(newReg, r2, r2BandEnd, top, bot);
                    Coalesce(newReg, prevBand, curBand);
                }
            }
            ytop = r1y1;
        } else {
            ytop = r1y1;
        }

        /*
         * Now see if we've hit an intersecting band. The two bands only
         * intersect if ybot > ytop
         */
        ybot = MIN(r1->y2, r2->y2);
        if (ybot > ytop) {
            curBand = newReg->data->numRects;
            (* overlapFunc)(newReg, r1, r1BandEnd, r2, r2BandEnd, ytop, ybot,
                            pOverlap);
            Coalesce(newReg, prevBand, curBand);
        }

        /*
         * If we've finished with a band (y2 == ybot) we skip forward
         * in the region to the next band.
         */
        if (r1->y2 == ybot) r1 = r1BandEnd;
        if (r2->y2 == ybot) r2 = r2BandEnd;

    } while (r1 != r1End && r2 != r2End);

    /*
     * Deal with whichever region (if any) still has rectangles left.
     *
     * We only need to worry about banding and coalescing for the very first
     * band left.  After that, we can just group all remaining boxes,
     * regardless of how many bands, into one final append to the list.
     */

    if ((r1 != r1End) && appendNon1) {
        /* Do first nonOverlap1Func call, which may be able to coalesce */
        FindBand(r1, r1BandEnd, r1End, r1y1);
        curBand = newReg->data->numRects;
        pixman_region_appendNonO(newReg, r1, r1BandEnd, MAX(r1y1, ybot), r1->y2);
        Coalesce(newReg, prevBand, curBand);
        /* Just append the rest of the boxes  */
        AppendRegions(newReg, r1BandEnd, r1End);

    } else if ((r2 != r2End) && appendNon2) {
        /* Do first nonOverlap2Func call, which may be able to coalesce */
        FindBand(r2, r2BandEnd, r2End, r2y1);
        curBand = newReg->data->numRects;
        pixman_region_appendNonO(newReg, r2, r2BandEnd, MAX(r2y1, ybot), r2->y2);
        Coalesce(newReg, prevBand, curBand);
        /* Append rest of boxes */
        AppendRegions(newReg, r2BandEnd, r2End);
    }

    if (oldData)
        free(oldData);

    if (!(numRects = newReg->data->numRects))
    {
        freeData(newReg);
        newReg->data = pixman_region_emptyData;
    }
    else if (numRects == 1)
    {
        newReg->extents = *PIXREGION_BOXPTR(newReg);
        freeData(newReg);
        newReg->data = (region_data_type_t *)NULL;
    }
    else
    {
        DOWNSIZE(newReg, numRects);
    }

    return TRUE;
}

/*-
 *-----------------------------------------------------------------------
 * pixman_set_extents --
 *      Reset the extents of a region to what they should be. Called by
 *      pixman_region_subtract and pixman_region_intersect as they can't figure it out along the
 *      way or do so easily, as pixman_region_union can.
 *
 * Results:
 *      None.
 *
 * Side Effects:
 *      The region's 'extents' structure is overwritten.
 *
 *-----------------------------------------------------------------------
 */
static void
pixman_set_extents (region_type_t *region)
{
    box_type_t *box, *boxEnd;

    if (!region->data)
        return;
    if (!region->data->size)
    {
        region->extents.x2 = region->extents.x1;
        region->extents.y2 = region->extents.y1;
        return;
    }

    box = PIXREGION_BOXPTR(region);
    boxEnd = PIXREGION_END(region);

    /*
     * Since box is the first rectangle in the region, it must have the
     * smallest y1 and since boxEnd is the last rectangle in the region,
     * it must have the largest y2, because of banding. Initialize x1 and
     * x2 from  box and boxEnd, resp., as good things to initialize them
     * to...
     */
    region->extents.x1 = box->x1;
    region->extents.y1 = box->y1;
    region->extents.x2 = boxEnd->x2;
    region->extents.y2 = boxEnd->y2;

    assert(region->extents.y1 < region->extents.y2);
    while (box <= boxEnd) {
        if (box->x1 < region->extents.x1)
            region->extents.x1 = box->x1;
        if (box->x2 > region->extents.x2)
            region->extents.x2 = box->x2;
        box++;
    };

    assert(region->extents.x1 < region->extents.x2);
}

/*======================================================================
 *          Region Intersection
 *====================================================================*/
/*-
 *-----------------------------------------------------------------------
 * pixman_region_intersectO --
 *      Handle an overlapping band for pixman_region_intersect.
 *
 * Results:
 *      TRUE if successful.
 *
 * Side Effects:
 *      Rectangles may be added to the region.
 *
 *-----------------------------------------------------------------------
 */
/*ARGSUSED*/
static pixman_bool_t
pixman_region_intersectO (region_type_t *region,
                          box_type_t    *r1,
                          box_type_t    *r1End,
                          box_type_t    *r2,
                          box_type_t    *r2End,
                          int                y1,
                          int                y2,
                          int               *pOverlap)
{
    int         x1;
    int         x2;
    box_type_t *        pNextRect;

    pNextRect = PIXREGION_TOP(region);

    assert(y1 < y2);
    assert(r1 != r1End && r2 != r2End);

    do {
        x1 = MAX(r1->x1, r2->x1);
        x2 = MIN(r1->x2, r2->x2);

        /*
         * If there's any overlap between the two rectangles, add that
         * overlap to the new region.
         */
        if (x1 < x2)
            NEWRECT(region, pNextRect, x1, y1, x2, y2);

        /*
         * Advance the pointer(s) with the leftmost right side, since the next
         * rectangle on that list may still overlap the other region's
         * current rectangle.
         */
        if (r1->x2 == x2) {
            r1++;
        }
        if (r2->x2 == x2) {
            r2++;
        }
    } while ((r1 != r1End) && (r2 != r2End));

    return TRUE;
}

PIXMAN_EXPORT pixman_bool_t
PREFIX(_intersect) (region_type_t *     newReg,
                         region_type_t *        reg1,
                         region_type_t *        reg2)
{
    good(reg1);
    good(reg2);
    good(newReg);
   /* check for trivial reject */
    if (PIXREGION_NIL(reg1)  || PIXREGION_NIL(reg2) ||
        !EXTENTCHECK(&reg1->extents, &reg2->extents))
    {
        /* Covers about 20% of all cases */
        freeData(newReg);
        newReg->extents.x2 = newReg->extents.x1;
        newReg->extents.y2 = newReg->extents.y1;
        if (PIXREGION_NAR(reg1) || PIXREGION_NAR(reg2))
        {
            newReg->data = pixman_brokendata;
            return FALSE;
        }
        else
            newReg->data = pixman_region_emptyData;
    }
    else if (!reg1->data && !reg2->data)
    {
        /* Covers about 80% of cases that aren't trivially rejected */
        newReg->extents.x1 = MAX(reg1->extents.x1, reg2->extents.x1);
        newReg->extents.y1 = MAX(reg1->extents.y1, reg2->extents.y1);
        newReg->extents.x2 = MIN(reg1->extents.x2, reg2->extents.x2);
        newReg->extents.y2 = MIN(reg1->extents.y2, reg2->extents.y2);
        freeData(newReg);
        newReg->data = (region_data_type_t *)NULL;
    }
    else if (!reg2->data && SUBSUMES(&reg2->extents, &reg1->extents))
    {
        return PREFIX(_copy) (newReg, reg1);
    }
    else if (!reg1->data && SUBSUMES(&reg1->extents, &reg2->extents))
    {
        return PREFIX(_copy) (newReg, reg2);
    }
    else if (reg1 == reg2)
    {
        return PREFIX(_copy) (newReg, reg1);
    }
    else
    {
        /* General purpose intersection */
        int overlap; /* result ignored */
        if (!pixman_op(newReg, reg1, reg2, pixman_region_intersectO, FALSE, FALSE,
                        &overlap))
            return FALSE;
        pixman_set_extents(newReg);
    }

    good(newReg);
    return(TRUE);
}

#define MERGERECT(r)                                            \
{                                                               \
    if (r->x1 <= x2) {                                          \
        /* Merge with current rectangle */                      \
        if (r->x1 < x2) *pOverlap = TRUE;                               \
        if (x2 < r->x2) x2 = r->x2;                             \
    } else {                                                    \
        /* Add current rectangle, start new one */              \
        NEWRECT(region, pNextRect, x1, y1, x2, y2);             \
        x1 = r->x1;                                             \
        x2 = r->x2;                                             \
    }                                                           \
    r++;                                                        \
}

/*======================================================================
 *          Region Union
 *====================================================================*/

/*-
 *-----------------------------------------------------------------------
 * pixman_region_unionO --
 *      Handle an overlapping band for the union operation. Picks the
 *      left-most rectangle each time and merges it into the region.
 *
 * Results:
 *      TRUE if successful.
 *
 * Side Effects:
 *      region is overwritten.
 *      pOverlap is set to TRUE if any boxes overlap.
 *
 *-----------------------------------------------------------------------
 */
static pixman_bool_t
pixman_region_unionO (
    region_type_t        *region,
    box_type_t *r1,
    box_type_t *r1End,
    box_type_t *r2,
    box_type_t *r2End,
    int   y1,
    int   y2,
    int           *pOverlap)
{
    box_type_t *     pNextRect;
    int        x1;     /* left and right side of current union */
    int        x2;

    assert (y1 < y2);
    assert(r1 != r1End && r2 != r2End);

    pNextRect = PIXREGION_TOP(region);

    /* Start off current rectangle */
    if (r1->x1 < r2->x1)
    {
        x1 = r1->x1;
        x2 = r1->x2;
        r1++;
    }
    else
    {
        x1 = r2->x1;
        x2 = r2->x2;
        r2++;
    }
    while (r1 != r1End && r2 != r2End)
    {
        if (r1->x1 < r2->x1) MERGERECT(r1) else MERGERECT(r2);
    }

    /* Finish off whoever (if any) is left */
    if (r1 != r1End)
    {
        do
        {
            MERGERECT(r1);
        } while (r1 != r1End);
    }
    else if (r2 != r2End)
    {
        do
        {
            MERGERECT(r2);
        } while (r2 != r2End);
    }

    /* Add current rectangle */
    NEWRECT(region, pNextRect, x1, y1, x2, y2);

    return TRUE;
}

/* Convenience function for performing union of region with a
 * single rectangle
 */
PIXMAN_EXPORT pixman_bool_t
PREFIX(_union_rect) (region_type_t *dest,
                          region_type_t *source,
                          int x, int y,
                          unsigned int width, unsigned int height)
{
    region_type_t region;

    if (!width || !height)
        return PREFIX(_copy) (dest, source);
    region.data = NULL;
    region.extents.x1 = x;
    region.extents.y1 = y;
    region.extents.x2 = x + width;
    region.extents.y2 = y + height;

    return PREFIX(_union) (dest, source, &region);
}

PIXMAN_EXPORT pixman_bool_t
PREFIX(_union) (region_type_t *newReg,
                     region_type_t *reg1,
                     region_type_t *reg2)
{
    int overlap; /* result ignored */

    /* Return TRUE if some overlap
     * between reg1, reg2
     */
    good(reg1);
    good(reg2);
    good(newReg);
    /*  checks all the simple cases */

    /*
     * Region 1 and 2 are the same
     */
    if (reg1 == reg2)
    {
        return PREFIX(_copy) (newReg, reg1);
    }

    /*
     * Region 1 is empty
     */
    if (PIXREGION_NIL(reg1))
    {
        if (PIXREGION_NAR(reg1))
            return pixman_break (newReg);
        if (newReg != reg2)
            return PREFIX(_copy) (newReg, reg2);
        return TRUE;
    }

    /*
     * Region 2 is empty
     */
    if (PIXREGION_NIL(reg2))
    {
        if (PIXREGION_NAR(reg2))
            return pixman_break (newReg);
        if (newReg != reg1)
            return PREFIX(_copy) (newReg, reg1);
        return TRUE;
    }

    /*
     * Region 1 completely subsumes region 2
     */
    if (!reg1->data && SUBSUMES(&reg1->extents, &reg2->extents))
    {
        if (newReg != reg1)
            return PREFIX(_copy) (newReg, reg1);
        return TRUE;
    }

    /*
     * Region 2 completely subsumes region 1
     */
    if (!reg2->data && SUBSUMES(&reg2->extents, &reg1->extents))
    {
        if (newReg != reg2)
            return PREFIX(_copy) (newReg, reg2);
        return TRUE;
    }

    if (!pixman_op(newReg, reg1, reg2, pixman_region_unionO, TRUE, TRUE, &overlap))
        return FALSE;

    newReg->extents.x1 = MIN(reg1->extents.x1, reg2->extents.x1);
    newReg->extents.y1 = MIN(reg1->extents.y1, reg2->extents.y1);
    newReg->extents.x2 = MAX(reg1->extents.x2, reg2->extents.x2);
    newReg->extents.y2 = MAX(reg1->extents.y2, reg2->extents.y2);
    good(newReg);
    return TRUE;
}

/*======================================================================
 *          Batch Rectangle Union
 *====================================================================*/

#define ExchangeRects(a, b) \
{                           \
    box_type_t     t;       \
    t = rects[a];           \
    rects[a] = rects[b];    \
    rects[b] = t;           \
}

static void
QuickSortRects(
    box_type_t     rects[],
    int        numRects)
{
    int y1;
    int x1;
    int        i, j;
    box_type_t *r;

    /* Always called with numRects > 1 */

    do
    {
        if (numRects == 2)
        {
            if (rects[0].y1 > rects[1].y1 ||
                    (rects[0].y1 == rects[1].y1 && rects[0].x1 > rects[1].x1))
                ExchangeRects(0, 1);
            return;
        }

        /* Choose partition element, stick in location 0 */
        ExchangeRects(0, numRects >> 1);
        y1 = rects[0].y1;
        x1 = rects[0].x1;

        /* Partition array */
        i = 0;
        j = numRects;
        do
        {
            r = &(rects[i]);
            do
            {
                r++;
                i++;
            } while (i != numRects &&
                     (r->y1 < y1 || (r->y1 == y1 && r->x1 < x1)));
            r = &(rects[j]);
            do
            {
                r--;
                j--;
            } while (y1 < r->y1 || (y1 == r->y1 && x1 < r->x1));
            if (i < j)
                ExchangeRects(i, j);
        } while (i < j);

        /* Move partition element back to middle */
        ExchangeRects(0, j);

        /* Recurse */
        if (numRects-j-1 > 1)
            QuickSortRects(&rects[j+1], numRects-j-1);
        numRects = j;
    } while (numRects > 1);
}

/*-
 *-----------------------------------------------------------------------
 * pixman_region_validate --
 *
 *      Take a ``region'' which is a non-y-x-banded random collection of
 *      rectangles, and compute a nice region which is the union of all the
 *      rectangles.
 *
 * Results:
 *      TRUE if successful.
 *
 * Side Effects:
 *      The passed-in ``region'' may be modified.
 *      pOverlap set to TRUE if any retangles overlapped,
 *      else FALSE;
 *
 * Strategy:
 *      Step 1. Sort the rectangles into ascending order with primary key y1
 *              and secondary key x1.
 *
 *      Step 2. Split the rectangles into the minimum number of proper y-x
 *              banded regions.  This may require horizontally merging
 *              rectangles, and vertically coalescing bands.  With any luck,
 *              this step in an identity transformation (ala the Box widget),
 *              or a coalescing into 1 box (ala Menus).
 *
 *      Step 3. Merge the separate regions down to a single region by calling
 *              pixman_region_union.  Maximize the work each pixman_region_union call does by using
 *              a binary merge.
 *
 *-----------------------------------------------------------------------
 */

static pixman_bool_t
validate (region_type_t * badreg,
          int *pOverlap)
{
    /* Descriptor for regions under construction  in Step 2. */
    typedef struct {
        region_type_t   reg;
        int         prevBand;
        int         curBand;
    } RegionInfo;

             int        numRects;   /* Original numRects for badreg         */
             RegionInfo *ri;        /* Array of current regions             */
             int        numRI;      /* Number of entries used in ri         */
             int        sizeRI;     /* Number of entries available in ri    */
             int        i;          /* Index into rects                     */
    int j;          /* Index into ri                        */
    RegionInfo *rit;       /* &ri[j]                                */
    region_type_t *  reg;        /* ri[j].reg                       */
    box_type_t *        box;        /* Current box in rects                 */
    box_type_t *        riBox;      /* Last box in ri[j].reg                */
    region_type_t *  hreg;       /* ri[j_half].reg                          */
    pixman_bool_t ret = TRUE;

    *pOverlap = FALSE;
    if (!badreg->data)
    {
        good(badreg);
        return TRUE;
    }
    numRects = badreg->data->numRects;
    if (!numRects)
    {
        if (PIXREGION_NAR(badreg))
            return FALSE;
        good(badreg);
        return TRUE;
    }
    if (badreg->extents.x1 < badreg->extents.x2)
    {
        if ((numRects) == 1)
        {
            freeData(badreg);
            badreg->data = (region_data_type_t *) NULL;
        }
        else
        {
            DOWNSIZE(badreg, numRects);
        }
        good(badreg);
        return TRUE;
    }

    /* Step 1: Sort the rects array into ascending (y1, x1) order */
    QuickSortRects(PIXREGION_BOXPTR(badreg), numRects);

    /* Step 2: Scatter the sorted array into the minimum number of regions */

    /* Set up the first region to be the first rectangle in badreg */
    /* Note that step 2 code will never overflow the ri[0].reg rects array */
    ri = (RegionInfo *) pixman_malloc_ab (4, sizeof(RegionInfo));
    if (!ri)
        return pixman_break (badreg);
    sizeRI = 4;
    numRI = 1;
    ri[0].prevBand = 0;
    ri[0].curBand = 0;
    ri[0].reg = *badreg;
    box = PIXREGION_BOXPTR(&ri[0].reg);
    ri[0].reg.extents = *box;
    ri[0].reg.data->numRects = 1;
    badreg->extents = *pixman_region_emptyBox;
    badreg->data = pixman_region_emptyData;

    /* Now scatter rectangles into the minimum set of valid regions.  If the
       next rectangle to be added to a region would force an existing rectangle
       in the region to be split up in order to maintain y-x banding, just
       forget it.  Try the next region.  If it doesn't fit cleanly into any
       region, make a new one. */

    for (i = numRects; --i > 0;)
    {
        box++;
        /* Look for a region to append box to */
        for (j = numRI, rit = ri; --j >= 0; rit++)
        {
            reg = &rit->reg;
            riBox = PIXREGION_END(reg);

            if (box->y1 == riBox->y1 && box->y2 == riBox->y2)
            {
                /* box is in same band as riBox.  Merge or append it */
                if (box->x1 <= riBox->x2)
                {
                    /* Merge it with riBox */
                    if (box->x1 < riBox->x2) *pOverlap = TRUE;
                    if (box->x2 > riBox->x2) riBox->x2 = box->x2;
                }
                else
                {
                    RECTALLOC_BAIL(reg, 1, bail);
                    *PIXREGION_TOP(reg) = *box;
                    reg->data->numRects++;
                }
                goto NextRect;   /* So sue me */
            }
            else if (box->y1 >= riBox->y2)
            {
                /* Put box into new band */
                if (reg->extents.x2 < riBox->x2) reg->extents.x2 = riBox->x2;
                if (reg->extents.x1 > box->x1)   reg->extents.x1 = box->x1;
                Coalesce(reg, rit->prevBand, rit->curBand);
                rit->curBand = reg->data->numRects;
                RECTALLOC_BAIL(reg, 1, bail);
                *PIXREGION_TOP(reg) = *box;
                reg->data->numRects++;
                goto NextRect;
            }
            /* Well, this region was inappropriate.  Try the next one. */
        } /* for j */

        /* Uh-oh.  No regions were appropriate.  Create a new one. */
        if (sizeRI == numRI)
        {
            size_t data_size;
            
            /* Oops, allocate space for new region information */
            sizeRI <<= 1;

            data_size = sizeRI * sizeof(RegionInfo);
            if (data_size / sizeRI != sizeof(RegionInfo))
                goto bail;
            rit = (RegionInfo *) realloc(ri, data_size);
            if (!rit)
                goto bail;
            ri = rit;
            rit = &ri[numRI];
        }
        numRI++;
        rit->prevBand = 0;
        rit->curBand = 0;
        rit->reg.extents = *box;
        rit->reg.data = (region_data_type_t *)NULL;
        if (!pixman_rect_alloc(&rit->reg, (i+numRI) / numRI)) /* MUST force allocation */
            goto bail;
NextRect: ;
    } /* for i */

    /* Make a final pass over each region in order to Coalesce and set
       extents.x2 and extents.y2 */

    for (j = numRI, rit = ri; --j >= 0; rit++)
    {
        reg = &rit->reg;
        riBox = PIXREGION_END(reg);
        reg->extents.y2 = riBox->y2;
        if (reg->extents.x2 < riBox->x2) reg->extents.x2 = riBox->x2;
        Coalesce(reg, rit->prevBand, rit->curBand);
        if (reg->data->numRects == 1) /* keep unions happy below */
        {
            freeData(reg);
            reg->data = (region_data_type_t *)NULL;
        }
    }

    /* Step 3: Union all regions into a single region */
    while (numRI > 1)
    {
        int half = numRI/2;
        for (j = numRI & 1; j < (half + (numRI & 1)); j++)
        {
            reg = &ri[j].reg;
            hreg = &ri[j+half].reg;
            if (!pixman_op(reg, reg, hreg, pixman_region_unionO, TRUE, TRUE, pOverlap))
                ret = FALSE;
            if (hreg->extents.x1 < reg->extents.x1)
                reg->extents.x1 = hreg->extents.x1;
            if (hreg->extents.y1 < reg->extents.y1)
                reg->extents.y1 = hreg->extents.y1;
            if (hreg->extents.x2 > reg->extents.x2)
                reg->extents.x2 = hreg->extents.x2;
            if (hreg->extents.y2 > reg->extents.y2)
                reg->extents.y2 = hreg->extents.y2;
            freeData(hreg);
        }
        numRI -= half;
        if (!ret)
            goto bail;
    }
    *badreg = ri[0].reg;
    free(ri);
    good(badreg);
    return ret;
bail:
    for (i = 0; i < numRI; i++)
        freeData(&ri[i].reg);
    free (ri);

    return pixman_break (badreg);
}

/*======================================================================
 *                Region Subtraction
 *====================================================================*/

/*-
 *-----------------------------------------------------------------------
 * pixman_region_subtractO --
 *      Overlapping band subtraction. x1 is the left-most point not yet
 *      checked.
 *
 * Results:
 *      TRUE if successful.
 *
 * Side Effects:
 *      region may have rectangles added to it.
 *
 *-----------------------------------------------------------------------
 */
/*ARGSUSED*/
static pixman_bool_t
pixman_region_subtractO (
    region_type_t *     region,
    box_type_t *        r1,
    box_type_t *                r1End,
    box_type_t *        r2,
    box_type_t *                r2End,
    int         y1,
    int         y2,
    int         *pOverlap)
{
    box_type_t *        pNextRect;
    int         x1;

    x1 = r1->x1;

    assert(y1<y2);
    assert(r1 != r1End && r2 != r2End);

    pNextRect = PIXREGION_TOP(region);

    do
    {
        if (r2->x2 <= x1)
        {
            /*
             * Subtrahend entirely to left of minuend: go to next subtrahend.
             */
            r2++;
        }
        else if (r2->x1 <= x1)
        {
            /*
             * Subtrahend preceeds minuend: nuke left edge of minuend.
             */
            x1 = r2->x2;
            if (x1 >= r1->x2)
            {
                /*
                 * Minuend completely covered: advance to next minuend and
                 * reset left fence to edge of new minuend.
                 */
                r1++;
                if (r1 != r1End)
                    x1 = r1->x1;
            }
            else
            {
                /*
                 * Subtrahend now used up since it doesn't extend beyond
                 * minuend
                 */
                r2++;
            }
        }
        else if (r2->x1 < r1->x2)
        {
            /*
             * Left part of subtrahend covers part of minuend: add uncovered
             * part of minuend to region and skip to next subtrahend.
             */
            assert(x1<r2->x1);
            NEWRECT(region, pNextRect, x1, y1, r2->x1, y2);

            x1 = r2->x2;
            if (x1 >= r1->x2)
            {
                /*
                 * Minuend used up: advance to new...
                 */
                r1++;
                if (r1 != r1End)
                    x1 = r1->x1;
            }
            else
            {
                /*
                 * Subtrahend used up
                 */
                r2++;
            }
        }
        else
        {
            /*
             * Minuend used up: add any remaining piece before advancing.
             */
            if (r1->x2 > x1)
                NEWRECT(region, pNextRect, x1, y1, r1->x2, y2);
            r1++;
            if (r1 != r1End)
                x1 = r1->x1;
        }
    } while ((r1 != r1End) && (r2 != r2End));

    /*
     * Add remaining minuend rectangles to region.
     */
    while (r1 != r1End)
    {
        assert(x1<r1->x2);
        NEWRECT(region, pNextRect, x1, y1, r1->x2, y2);
        r1++;
        if (r1 != r1End)
            x1 = r1->x1;
    }
    return TRUE;
}

/*-
 *-----------------------------------------------------------------------
 * pixman_region_subtract --
 *      Subtract regS from regM and leave the result in regD.
 *      S stands for subtrahend, M for minuend and D for difference.
 *
 * Results:
 *      TRUE if successful.
 *
 * Side Effects:
 *      regD is overwritten.
 *
 *-----------------------------------------------------------------------
 */
PIXMAN_EXPORT pixman_bool_t
PREFIX(_subtract) (region_type_t *      regD,
                       region_type_t *  regM,
                       region_type_t *  regS)
{
    int overlap; /* result ignored */

    good(regM);
    good(regS);
    good(regD);
   /* check for trivial rejects */
    if (PIXREGION_NIL(regM) || PIXREGION_NIL(regS) ||
        !EXTENTCHECK(&regM->extents, &regS->extents))
    {
        if (PIXREGION_NAR (regS))
            return pixman_break (regD);
        return PREFIX(_copy) (regD, regM);
    }
    else if (regM == regS)
    {
        freeData(regD);
        regD->extents.x2 = regD->extents.x1;
        regD->extents.y2 = regD->extents.y1;
        regD->data = pixman_region_emptyData;
        return TRUE;
    }

    /* Add those rectangles in region 1 that aren't in region 2,
       do yucky substraction for overlaps, and
       just throw away rectangles in region 2 that aren't in region 1 */
    if (!pixman_op(regD, regM, regS, pixman_region_subtractO, TRUE, FALSE, &overlap))
        return FALSE;

    /*
     * Can't alter RegD's extents before we call pixman_op because
     * it might be one of the source regions and pixman_op depends
     * on the extents of those regions being unaltered. Besides, this
     * way there's no checking against rectangles that will be nuked
     * due to coalescing, so we have to examine fewer rectangles.
     */
    pixman_set_extents(regD);
    good(regD);
    return TRUE;
}

/*======================================================================
 *          Region Inversion
 *====================================================================*/

/*-
 *-----------------------------------------------------------------------
 * pixman_region_inverse --
 *      Take a region and a box and return a region that is everything
 *      in the box but not in the region. The careful reader will note
 *      that this is the same as subtracting the region from the box...
 *
 * Results:
 *      TRUE.
 *
 * Side Effects:
 *      newReg is overwritten.
 *
 *-----------------------------------------------------------------------
 */
pixman_bool_t
PIXMAN_EXPORT PREFIX(_inverse) (region_type_t *           newReg,       /* Destination region */
                      region_type_t *     reg1,         /* Region to invert */
                      box_type_t *        invRect)      /* Bounding box for inversion */
{
    region_type_t         invReg;       /* Quick and dirty region made from the
                                 * bounding box */
    int   overlap;      /* result ignored */

    good(reg1);
    good(newReg);
   /* check for trivial rejects */
    if (PIXREGION_NIL(reg1) || !EXTENTCHECK(invRect, &reg1->extents))
    {
        if (PIXREGION_NAR(reg1))
            return pixman_break (newReg);
        newReg->extents = *invRect;
        freeData(newReg);
        newReg->data = (region_data_type_t *)NULL;
        return TRUE;
    }

    /* Add those rectangles in region 1 that aren't in region 2,
       do yucky substraction for overlaps, and
       just throw away rectangles in region 2 that aren't in region 1 */
    invReg.extents = *invRect;
    invReg.data = (region_data_type_t *)NULL;
    if (!pixman_op(newReg, &invReg, reg1, pixman_region_subtractO, TRUE, FALSE, &overlap))
        return FALSE;

    /*
     * Can't alter newReg's extents before we call pixman_op because
     * it might be one of the source regions and pixman_op depends
     * on the extents of those regions being unaltered. Besides, this
     * way there's no checking against rectangles that will be nuked
     * due to coalescing, so we have to examine fewer rectangles.
     */
    pixman_set_extents(newReg);
    good(newReg);
    return TRUE;
}

/*
 *   RectIn(region, rect)
 *   This routine takes a pointer to a region and a pointer to a box
 *   and determines if the box is outside/inside/partly inside the region.
 *
 *   The idea is to travel through the list of rectangles trying to cover the
 *   passed box with them. Anytime a piece of the rectangle isn't covered
 *   by a band of rectangles, partOut is set TRUE. Any time a rectangle in
 *   the region covers part of the box, partIn is set TRUE. The process ends
 *   when either the box has been completely covered (we reached a band that
 *   doesn't overlap the box, partIn is TRUE and partOut is false), the
 *   box has been partially covered (partIn == partOut == TRUE -- because of
 *   the banding, the first time this is true we know the box is only
 *   partially in the region) or is outside the region (we reached a band
 *   that doesn't overlap the box at all and partIn is false)
 */

pixman_region_overlap_t
PIXMAN_EXPORT PREFIX(_contains_rectangle) (region_type_t *  region,
                                 box_type_t *     prect)
{
    int x;
    int y;
    box_type_t *     pbox;
    box_type_t *     pboxEnd;
    int                 partIn, partOut;
    int                 numRects;

    good(region);
    numRects = PIXREGION_NUM_RECTS(region);
    /* useful optimization */
    if (!numRects || !EXTENTCHECK(&region->extents, prect))
        return(PIXMAN_REGION_OUT);

    if (numRects == 1)
    {
        /* We know that it must be PIXMAN_REGION_IN or PIXMAN_REGION_PART */
        if (SUBSUMES(&region->extents, prect))
            return(PIXMAN_REGION_IN);
        else
            return(PIXMAN_REGION_PART);
    }

    partOut = FALSE;
    partIn = FALSE;

    /* (x,y) starts at upper left of rect, moving to the right and down */
    x = prect->x1;
    y = prect->y1;

    /* can stop when both partOut and partIn are TRUE, or we reach prect->y2 */
    for (pbox = PIXREGION_BOXPTR(region), pboxEnd = pbox + numRects;
         pbox != pboxEnd;
         pbox++)
    {

        if (pbox->y2 <= y)
           continue;    /* getting up to speed or skipping remainder of band */

        if (pbox->y1 > y)
        {
           partOut = TRUE;      /* missed part of rectangle above */
           if (partIn || (pbox->y1 >= prect->y2))
              break;
           y = pbox->y1;        /* x guaranteed to be == prect->x1 */
        }

        if (pbox->x2 <= x)
           continue;            /* not far enough over yet */

        if (pbox->x1 > x)
        {
           partOut = TRUE;      /* missed part of rectangle to left */
           if (partIn)
              break;
        }

        if (pbox->x1 < prect->x2)
        {
            partIn = TRUE;      /* definitely overlap */
            if (partOut)
               break;
        }

        if (pbox->x2 >= prect->x2)
        {
           y = pbox->y2;        /* finished with this band */
           if (y >= prect->y2)
              break;
           x = prect->x1;       /* reset x out to left again */
        }
        else
        {
            /*
             * Because boxes in a band are maximal width, if the first box
             * to overlap the rectangle doesn't completely cover it in that
             * band, the rectangle must be partially out, since some of it
             * will be uncovered in that band. partIn will have been set true
             * by now...
             */
            partOut = TRUE;
            break;
        }
    }

    if (partIn)
    {
        if (y < prect->y2)
            return PIXMAN_REGION_PART;
        else
            return PIXMAN_REGION_IN;
    }
    else
    {
        return PIXMAN_REGION_OUT;
    }
}

/* PREFIX(_translate) (region, x, y)
   translates in place
*/

PIXMAN_EXPORT void
PREFIX(_translate) (region_type_t * region, int x, int y)
{
    int x1, x2, y1, y2;
    int nbox;
    box_type_t * pbox;

    good(region);
    region->extents.x1 = x1 = region->extents.x1 + x;
    region->extents.y1 = y1 = region->extents.y1 + y;
    region->extents.x2 = x2 = region->extents.x2 + x;
    region->extents.y2 = y2 = region->extents.y2 + y;
    if (((x1 - SHRT_MIN)|(y1 - SHRT_MIN)|(SHRT_MAX - x2)|(SHRT_MAX - y2)) >= 0)
    {
        if (region->data && (nbox = region->data->numRects))
        {
            for (pbox = PIXREGION_BOXPTR(region); nbox--; pbox++)
            {
                pbox->x1 += x;
                pbox->y1 += y;
                pbox->x2 += x;
                pbox->y2 += y;
            }
        }
        return;
    }
    if (((x2 - SHRT_MIN)|(y2 - SHRT_MIN)|(SHRT_MAX - x1)|(SHRT_MAX - y1)) <= 0)
    {
        region->extents.x2 = region->extents.x1;
        region->extents.y2 = region->extents.y1;
        freeData(region);
        region->data = pixman_region_emptyData;
        return;
    }
    if (x1 < SHRT_MIN)
        region->extents.x1 = SHRT_MIN;
    else if (x2 > SHRT_MAX)
        region->extents.x2 = SHRT_MAX;
    if (y1 < SHRT_MIN)
        region->extents.y1 = SHRT_MIN;
    else if (y2 > SHRT_MAX)
        region->extents.y2 = SHRT_MAX;
    if (region->data && (nbox = region->data->numRects))
    {
        box_type_t * pboxout;

        for (pboxout = pbox = PIXREGION_BOXPTR(region); nbox--; pbox++)
        {
            pboxout->x1 = x1 = pbox->x1 + x;
            pboxout->y1 = y1 = pbox->y1 + y;
            pboxout->x2 = x2 = pbox->x2 + x;
            pboxout->y2 = y2 = pbox->y2 + y;
            if (((x2 - SHRT_MIN)|(y2 - SHRT_MIN)|
                 (SHRT_MAX - x1)|(SHRT_MAX - y1)) <= 0)
            {
                region->data->numRects--;
                continue;
            }
            if (x1 < SHRT_MIN)
                pboxout->x1 = SHRT_MIN;
            else if (x2 > SHRT_MAX)
                pboxout->x2 = SHRT_MAX;
            if (y1 < SHRT_MIN)
                pboxout->y1 = SHRT_MIN;
            else if (y2 > SHRT_MAX)
                pboxout->y2 = SHRT_MAX;
            pboxout++;
        }
        if (pboxout != pbox)
        {
            if (region->data->numRects == 1)
            {
                region->extents = *PIXREGION_BOXPTR(region);
                freeData(region);
                region->data = (region_data_type_t *)NULL;
            }
            else
                pixman_set_extents(region);
        }
    }
}

PIXMAN_EXPORT void
PREFIX(_reset) (region_type_t *region, box_type_t *box)
{
    good(region);
    assert(box->x1<=box->x2);
    assert(box->y1<=box->y2);
    region->extents = *box;
    freeData(region);
    region->data = (region_data_type_t *)NULL;
}

/* box is "return" value */
PIXMAN_EXPORT int
PREFIX(_contains_point) (region_type_t * region,
                             int x, int y,
                             box_type_t * box)
{
    box_type_t *pbox, *pboxEnd;
    int numRects;

    good(region);
    numRects = PIXREGION_NUM_RECTS(region);
    if (!numRects || !INBOX(&region->extents, x, y))
        return(FALSE);
    if (numRects == 1)
    {
        if (box)
            *box = region->extents;

        return(TRUE);
    }
    for (pbox = PIXREGION_BOXPTR(region), pboxEnd = pbox + numRects;
         pbox != pboxEnd;
         pbox++)
    {
        if (y >= pbox->y2)
           continue;            /* not there yet */
        if ((y < pbox->y1) || (x < pbox->x1))
           break;               /* missed it */
        if (x >= pbox->x2)
           continue;            /* not there yet */

        if (box)
            *box = *pbox;

        return(TRUE);
    }
    return(FALSE);
}

PIXMAN_EXPORT int
PREFIX(_not_empty) (region_type_t * region)
{
    good(region);
    return(!PIXREGION_NIL(region));
}

PIXMAN_EXPORT box_type_t *
PREFIX(_extents) (region_type_t * region)
{
    good(region);
    return(&region->extents);
}

/*
    Clip a list of scanlines to a region.  The caller has allocated the
    space.  FSorted is non-zero if the scanline origins are in ascending
    order.
    returns the number of new, clipped scanlines.
*/

PIXMAN_EXPORT pixman_bool_t
PREFIX(_selfcheck) (reg)
    region_type_t * reg;
{
    int i, numRects;

    if ((reg->extents.x1 > reg->extents.x2) ||
        (reg->extents.y1 > reg->extents.y2))
        return FALSE;
    numRects = PIXREGION_NUM_RECTS(reg);
    if (!numRects)
        return ((reg->extents.x1 == reg->extents.x2) &&
                (reg->extents.y1 == reg->extents.y2) &&
                (reg->data->size || (reg->data == pixman_region_emptyData)));
    else if (numRects == 1)
        return (!reg->data);
    else
    {
        box_type_t * pboxP, * pboxN;
        box_type_t box;

        pboxP = PIXREGION_RECTS(reg);
        box = *pboxP;
        box.y2 = pboxP[numRects-1].y2;
        pboxN = pboxP + 1;
        for (i = numRects; --i > 0; pboxP++, pboxN++)
        {
            if ((pboxN->x1 >= pboxN->x2) ||
                (pboxN->y1 >= pboxN->y2))
                return FALSE;
            if (pboxN->x1 < box.x1)
                box.x1 = pboxN->x1;
            if (pboxN->x2 > box.x2)
                box.x2 = pboxN->x2;
            if ((pboxN->y1 < pboxP->y1) ||
                ((pboxN->y1 == pboxP->y1) &&
                 ((pboxN->x1 < pboxP->x2) || (pboxN->y2 != pboxP->y2))))
                return FALSE;
        }
        return ((box.x1 == reg->extents.x1) &&
                (box.x2 == reg->extents.x2) &&
                (box.y1 == reg->extents.y1) &&
                (box.y2 == reg->extents.y2));
    }
}

PIXMAN_EXPORT pixman_bool_t
PREFIX(_init_rects) (region_type_t *region,
                     box_type_t *boxes, int count)
{
    int overlap;

    /* if it's 1, then we just want to set the extents, so call
     * the existing method. */
    if (count == 1) {
       PREFIX(_init_rect) (region,
                               boxes[0].x1,
                               boxes[0].y1,
                               boxes[0].x2 - boxes[0].x1,
                               boxes[0].y2 - boxes[0].y1);
       return TRUE;
    }

    PREFIX(_init) (region);

    /* if it's 0, don't call pixman_rect_alloc -- 0 rectangles is
     * a special case, and causing pixman_rect_alloc would cause
     * us to leak memory (because the 0-rect case should be the
     * static pixman_region_emptyData data).
     */
    if (count == 0)
        return TRUE;

    if (!pixman_rect_alloc(region, count))
        return FALSE;

    /* Copy in the rects */
    memcpy (PIXREGION_RECTS(region), boxes, sizeof(box_type_t) * count);
    region->data->numRects = count;

    /* Validate */
    region->extents.x1 = region->extents.x2 = 0;
    return validate (region, &overlap);
}