First import

[xorg_rtime.git] / xorg-server-1.4 / mi / miregion.c

/***********************************************************

Copyright 1987, 1988, 1989, 1998  The Open Group

Permission to use, copy, modify, distribute, and sell this software and its
documentation for any purpose is hereby granted without fee, provided that
the above copyright notice appear in all copies and that both that
copyright notice and this permission notice appear in supporting
documentation.

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL THE
OPEN GROUP BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN
AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

Except as contained in this notice, the name of The Open Group shall not be
used in advertising or otherwise to promote the sale, use or other dealings
in this Software without prior written authorization from The Open Group.
 

Copyright 1987, 1988, 1989 by 
Digital Equipment Corporation, Maynard, Massachusetts. 

                        All Rights Reserved

Permission to use, copy, modify, and distribute this software and its 
documentation for any purpose and without fee is hereby granted, 
provided that the above copyright notice appear in all copies and that
both that copyright notice and this permission notice appear in 
supporting documentation, and that the name of Digital not be
used in advertising or publicity pertaining to distribution of the
software without specific, written prior permission.  

DIGITAL DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, INCLUDING
ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS, IN NO EVENT SHALL
DIGITAL BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR
ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS,
WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION,
ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS
SOFTWARE.

******************************************************************/

/* The panoramix components contained the following notice */
/*****************************************************************

Copyright (c) 1991, 1997 Digital Equipment Corporation, Maynard, Massachusetts.

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software.

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
DIGITAL EQUIPMENT CORPORATION BE LIABLE FOR ANY CLAIM, DAMAGES, INCLUDING,
BUT NOT LIMITED TO CONSEQUENTIAL OR INCIDENTAL DAMAGES, OR OTHER LIABILITY,
WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR
IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

Except as contained in this notice, the name of Digital Equipment Corporation
shall not be used in advertising or otherwise to promote the sale, use or other
dealings in this Software without prior written authorization from Digital
Equipment Corporation.

******************************************************************/

#ifdef HAVE_DIX_CONFIG_H
#include <dix-config.h>
#endif

#include "regionstr.h"
#include <X11/Xprotostr.h>
#include <X11/Xfuncproto.h>
#include "gc.h"
#include "mi.h"
#include "mispans.h"
#include <pixman.h>

#undef assert
#ifdef DEBUG
#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(miValidRegion(reg))

/*
 * 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 miRegionValidate in order to support several speed improvements
 * to miValidateTree.  Bob Scheifler changed the representation to be more
 * compact when empty or a single rectangle, and did a bunch of gratuitous
 * reformatting.
 */

/*  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) )

#define xallocData(n) (RegDataPtr)xalloc(REGION_SZOF(n))
#define xfreeData(reg) if ((reg)->data && (reg)->data->size) xfree((reg)->data)

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

#define RECTALLOC(pReg,n) \
if (!(pReg)->data || (((pReg)->data->numRects + (n)) > (pReg)->data->size)) \
    if (!miRectAlloc(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 (!miRectAlloc(pReg, 1))                                      \
            return FALSE;                                               \
        pNextRect = REGION_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)) \
{                                                                        \
    RegDataPtr NewData;                                                  \
    NewData = (RegDataPtr)xrealloc((reg)->data, REGION_SZOF(numRects));  \
    if (NewData)                                                         \
    {                                                                    \
        NewData->size = (numRects);                                      \
        (reg)->data = NewData;                                           \
    }                                                                    \
}


_X_EXPORT BoxRec miEmptyBox = {0, 0, 0, 0};
_X_EXPORT RegDataRec miEmptyData = {0, 0};

RegDataRec  miBrokenData = {0, 0};
static RegionRec   miBrokenRegion = { { 0, 0, 0, 0 }, &miBrokenData };

extern void
InitRegions (void)
{
    pixman_region_set_static_pointers (&miEmptyBox, &miEmptyData, &miBrokenData);
}

/*****************************************************************
 *   RegionCreate(rect, size)
 *     This routine does a simple malloc to make a structure of
 *     REGION of "size" number of rectangles.
 *****************************************************************/

_X_EXPORT RegionPtr
miRegionCreate(rect, size)
    BoxPtr rect;
    int size;
{
    RegionPtr pReg;
   
    pReg = (RegionPtr)xalloc(sizeof(RegionRec));
    if (!pReg)
        return &miBrokenRegion;

    miRegionInit (pReg, rect, size);
    
    return(pReg);
}

_X_EXPORT void
miRegionDestroy(pReg)
    RegionPtr pReg;
{
    pixman_region_fini (pReg);
    if (pReg != &miBrokenRegion)
        xfree(pReg);
}

_X_EXPORT void
miPrintRegion(rgn)
    RegionPtr rgn;
{
    int num, size;
    int i;
    BoxPtr rects;

    num = REGION_NUM_RECTS(rgn);
    size = REGION_SIZE(rgn);
    rects = REGION_RECTS(rgn);
    ErrorF("num: %d size: %d\n", num, size);
    ErrorF("extents: %d %d %d %d\n",
           rgn->extents.x1, rgn->extents.y1, rgn->extents.x2, rgn->extents.y2);
    for (i = 0; i < num; i++)
      ErrorF("%d %d %d %d \n",
             rects[i].x1, rects[i].y1, rects[i].x2, rects[i].y2);
    ErrorF("\n");
}

_X_EXPORT Bool
miRegionEqual(reg1, reg2)
    RegionPtr reg1;
    RegionPtr reg2;
{
    return pixman_region_equal (reg1, reg2);
}

#ifdef DEBUG
Bool
miValidRegion(reg)
    RegionPtr reg;
{
    int i, numRects;
    
    if ((reg->extents.x1 > reg->extents.x2) ||
        (reg->extents.y1 > reg->extents.y2))
        return FALSE;
    numRects = REGION_NUM_RECTS(reg);
    if (!numRects)
        return ((reg->extents.x1 == reg->extents.x2) &&
                (reg->extents.y1 == reg->extents.y2) &&
                (reg->data->size || (reg->data == &miEmptyData)));
    else if (numRects == 1)
        return (!reg->data);
    else
    {
        BoxPtr pboxP, pboxN;
        BoxRec box;
        
        pboxP = REGION_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));
    }
}
#endif /* DEBUG */

/*****************************************************************
 *   RegionInit(pReg, rect, size)
 *     Outer region rect is statically allocated.
 *****************************************************************/

_X_EXPORT void
miRegionInit(pReg, rect, size)
    RegionPtr pReg;
    BoxPtr rect;
    int size;
{
    if (rect)
        pixman_region_init_with_extents (pReg, rect);
    else
        pixman_region_init (pReg);
}

_X_EXPORT void
miRegionUninit(pReg)
    RegionPtr pReg;
{
    pixman_region_fini (pReg);
}

Bool
miRegionBreak (pReg)
    RegionPtr pReg;
{
    xfreeData (pReg);
    pReg->extents = miEmptyBox;
    pReg->data = &miBrokenData;
    return FALSE;
}

_X_EXPORT Bool
miRectAlloc(
    RegionPtr pRgn,
    int n)
{
    RegDataPtr  data;
    
    if (!pRgn->data)
    {
        n++;
        pRgn->data = xallocData(n);
        if (!pRgn->data)
            return miRegionBreak (pRgn);
        pRgn->data->numRects = 1;
        *REGION_BOXPTR(pRgn) = pRgn->extents;
    }
    else if (!pRgn->data->size)
    {
        pRgn->data = xallocData(n);
        if (!pRgn->data)
            return miRegionBreak (pRgn);
        pRgn->data->numRects = 0;
    }
    else
    {
        if (n == 1)
        {
            n = pRgn->data->numRects;
            if (n > 500) /* XXX pick numbers out of a hat */
                n = 250;
        }
        n += pRgn->data->numRects;
        data = (RegDataPtr)xrealloc(pRgn->data, REGION_SZOF(n));
        if (!data)
            return miRegionBreak (pRgn);
        pRgn->data = data;
    }
    pRgn->data->size = n;
    return TRUE;
}

_X_EXPORT Bool
miRegionCopy(dst, src)
    RegionPtr dst;
    RegionPtr src;
{
    return pixman_region_copy (dst, src);
}

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

/*-
 *-----------------------------------------------------------------------
 * miCoalesce --
 *      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 miRegionOp.
 *
 * 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.
 *          - pReg->data->numRects will be decreased.
 *
 *-----------------------------------------------------------------------
 */
_X_INLINE static int
miCoalesce (
    RegionPtr   pReg,           /* Region to coalesce                */
    int                 prevStart,      /* Index of start of previous band   */
    int                 curStart)       /* Index of start of current band    */
{
    BoxPtr      pPrevBox;       /* Current box in previous band      */
    BoxPtr      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 == pReg->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 = REGION_BOX(pReg, prevStart);
    pCurBox = REGION_BOX(pReg, 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;
    pReg->data->numRects -= numRects;
    do {
        pPrevBox--;
        pPrevBox->y2 = y2;
        numRects--;
    } while (numRects);
    return prevStart;
}


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

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

/*-
 *-----------------------------------------------------------------------
 * miAppendNonO --
 *      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:
 *      pReg->data->numRects is incremented and the rectangles overwritten
 *      with the rectangles we're passed.
 *
 *-----------------------------------------------------------------------
 */

_X_INLINE static Bool
miAppendNonO (
    RegionPtr   pReg,
    BoxPtr      r,
    BoxPtr      rEnd,
    int         y1,
    int         y2)
{
    BoxPtr      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(pReg, newRects);
    pNextRect = REGION_TOP(pReg);
    pReg->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 *)REGION_TOP(newReg),(char *)r,                   \
              newRects * sizeof(BoxRec));                               \
        newReg->data->numRects += newRects;                             \
    }                                                                   \
}

/*-
 *-----------------------------------------------------------------------
 * miRegionOp --
 *      Apply an operation to two regions. Called by miUnion, miInverse,
 *      miSubtract, miIntersect....  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 Bool (*OverlapProcPtr)(
    RegionPtr   pReg,
    BoxPtr      r1,
    BoxPtr      r1End,
    BoxPtr      r2,
    BoxPtr      r2End,
    short       y1,
    short       y2,
    Bool        *pOverlap);

static Bool
miRegionOp(
    RegionPtr       newReg,                 /* Place to store result         */
    RegionPtr       reg1,                   /* First region in operation     */
    RegionPtr       reg2,                   /* 2d region in operation        */
    OverlapProcPtr  overlapFunc,            /* Function to call for over-
                                             * lapping bands                 */
    Bool            appendNon1,             /* Append non-overlapping bands  */
                                            /* in region 1 ? */
    Bool            appendNon2,             /* Append non-overlapping bands  */
                                            /* in region 2 ? */
    Bool            *pOverlap)
{
    BoxPtr      r1;                 /* Pointer into first region     */
    BoxPtr      r2;                 /* Pointer into 2d region        */
    BoxPtr      r1End;              /* End of 1st region             */
    BoxPtr      r2End;              /* End of 2d region              */
    short       ybot;               /* Bottom of intersection        */
    short       ytop;               /* Top of intersection           */
    RegDataPtr  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                */
    BoxPtr      r1BandEnd;          /* End of current band in r1     */
    BoxPtr      r2BandEnd;          /* End of current band in r2     */
    short       top;                /* Top of non-overlapping band   */
    short       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 (REGION_NAR (reg1) || REGION_NAR(reg2))
        return miRegionBreak (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 = REGION_RECTS(reg1);
    newSize = REGION_NUM_RECTS(reg1);
    r1End = r1 + newSize;
    numRects = REGION_NUM_RECTS(reg2);
    r2 = REGION_RECTS(reg2);
    r2End = r2 + numRects;
    assert(r1 != r1End);
    assert(r2 != r2End);

    oldData = (RegDataPtr)NULL;
    if (((newReg == reg1) && (newSize > 1)) ||
        ((newReg == reg2) && (numRects > 1)))
    {
        oldData = newReg->data;
        newReg->data = &miEmptyData;
    }
    /* guess at new size */
    if (numRects > newSize)
        newSize = numRects;
    newSize <<= 1;
    if (!newReg->data)
        newReg->data = &miEmptyData;
    else if (newReg->data->size)
        newReg->data->numRects = 0;
    if (newSize > newReg->data->size)
        if (!miRectAlloc(newReg, newSize))
            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. miCoalesce, 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;
                    miAppendNonO(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;
                    miAppendNonO(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;
        miAppendNonO(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;
        miAppendNonO(newReg, r2, r2BandEnd, max(r2y1, ybot), r2->y2);
        Coalesce(newReg, prevBand, curBand);
        /* Append rest of boxes */
        AppendRegions(newReg, r2BandEnd, r2End);
    }

    if (oldData)
        xfree(oldData);

    if (!(numRects = newReg->data->numRects))
    {
        xfreeData(newReg);
        newReg->data = &miEmptyData;
    }
    else if (numRects == 1)
    {
        newReg->extents = *REGION_BOXPTR(newReg);
        xfreeData(newReg);
        newReg->data = (RegDataPtr)NULL;
    }
    else
    {
        DOWNSIZE(newReg, numRects);
    }

    return TRUE;
}

/*-
 *-----------------------------------------------------------------------
 * miSetExtents --
 *      Reset the extents of a region to what they should be. Called by
 *      miSubtract and miIntersect as they can't figure it out along the
 *      way or do so easily, as miUnion can.
 *
 * Results:
 *      None.
 *
 * Side Effects:
 *      The region's 'extents' structure is overwritten.
 *
 *-----------------------------------------------------------------------
 */
static void
miSetExtents (RegionPtr pReg)
{
    BoxPtr pBox, pBoxEnd;

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

    pBox = REGION_BOXPTR(pReg);
    pBoxEnd = REGION_END(pReg);

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

    assert(pReg->extents.y1 < pReg->extents.y2);
    while (pBox <= pBoxEnd) {
        if (pBox->x1 < pReg->extents.x1)
            pReg->extents.x1 = pBox->x1;
        if (pBox->x2 > pReg->extents.x2)
            pReg->extents.x2 = pBox->x2;
        pBox++;
    };

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

/*======================================================================
 *          Region Intersection
 *====================================================================*/
/*-
 *-----------------------------------------------------------------------
 * miIntersectO --
 *      Handle an overlapping band for miIntersect.
 *
 * Results:
 *      TRUE if successful.
 *
 * Side Effects:
 *      Rectangles may be added to the region.
 *
 *-----------------------------------------------------------------------
 */
/*ARGSUSED*/
_X_EXPORT Bool
miIntersect(newReg, reg1, reg2)
    RegionPtr   newReg;     /* destination Region */
    RegionPtr   reg1;
    RegionPtr   reg2;       /* source regions     */
{
    return pixman_region_intersect (newReg, reg1, reg2);
}

#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(pReg, pNextRect, x1, y1, x2, y2);               \
        x1 = r->x1;                                             \
        x2 = r->x2;                                             \
    }                                                           \
    r++;                                                        \
}

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

/*-
 *-----------------------------------------------------------------------
 * miUnionO --
 *      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:
 *      pReg is overwritten.
 *      pOverlap is set to TRUE if any boxes overlap.
 *
 *-----------------------------------------------------------------------
 */
static Bool
miUnionO (
    RegionPtr   pReg,
    BoxPtr      r1,
    BoxPtr      r1End,
    BoxPtr      r2,
    BoxPtr      r2End,
    short       y1,
    short       y2,
    Bool        *pOverlap)
{
    BoxPtr     pNextRect;
    int        x1;     /* left and right side of current union */
    int        x2;

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

    pNextRect = REGION_TOP(pReg);

    /* 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(pReg, pNextRect, x1, y1, x2, y2);

    return TRUE;
}

_X_EXPORT Bool 
miUnion(newReg, reg1, reg2)
    RegionPtr           newReg;                  /* destination Region */
    RegionPtr   reg1;
    RegionPtr   reg2;             /* source regions     */
{
    return pixman_region_union (newReg, reg1, reg2);
}

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

/*-
 *-----------------------------------------------------------------------
 * miRegionAppend --
 * 
 *      "Append" the rgn rectangles onto the end of dstrgn, maintaining
 *      knowledge of YX-banding when it's easy.  Otherwise, dstrgn just
 *      becomes a non-y-x-banded random collection of rectangles, and not
 *      yet a true region.  After a sequence of appends, the caller must
 *      call miRegionValidate to ensure that a valid region is constructed.
 *
 * Results:
 *      TRUE if successful.
 *
 * Side Effects:
 *      dstrgn is modified if rgn has rectangles.
 *
 */
_X_EXPORT Bool
miRegionAppend(dstrgn, rgn)
    RegionPtr dstrgn;
    RegionPtr rgn;
{
    int numRects, dnumRects, size;
    BoxPtr new, old;
    Bool prepend;

    if (REGION_NAR(rgn))
        return miRegionBreak (dstrgn);
    
    if (!rgn->data && (dstrgn->data == &miEmptyData))
    {
        dstrgn->extents = rgn->extents;
        dstrgn->data = (RegDataPtr)NULL;
        return TRUE;
    }

    numRects = REGION_NUM_RECTS(rgn);
    if (!numRects)
        return TRUE;
    prepend = FALSE;
    size = numRects;
    dnumRects = REGION_NUM_RECTS(dstrgn);
    if (!dnumRects && (size < 200))
        size = 200; /* XXX pick numbers out of a hat */
    RECTALLOC(dstrgn, size);
    old = REGION_RECTS(rgn);
    if (!dnumRects)
        dstrgn->extents = rgn->extents;
    else if (dstrgn->extents.x2 > dstrgn->extents.x1)
    {
        BoxPtr first, last;

        first = old;
        last = REGION_BOXPTR(dstrgn) + (dnumRects - 1);
        if ((first->y1 > last->y2) ||
            ((first->y1 == last->y1) && (first->y2 == last->y2) &&
             (first->x1 > last->x2)))
        {
            if (rgn->extents.x1 < dstrgn->extents.x1)
                dstrgn->extents.x1 = rgn->extents.x1;
            if (rgn->extents.x2 > dstrgn->extents.x2)
                dstrgn->extents.x2 = rgn->extents.x2;
            dstrgn->extents.y2 = rgn->extents.y2;
        }
        else
        {
            first = REGION_BOXPTR(dstrgn);
            last = old + (numRects - 1);
            if ((first->y1 > last->y2) ||
                ((first->y1 == last->y1) && (first->y2 == last->y2) &&
                 (first->x1 > last->x2)))
            {
                prepend = TRUE;
                if (rgn->extents.x1 < dstrgn->extents.x1)
                    dstrgn->extents.x1 = rgn->extents.x1;
                if (rgn->extents.x2 > dstrgn->extents.x2)
                    dstrgn->extents.x2 = rgn->extents.x2;
                dstrgn->extents.y1 = rgn->extents.y1;
            }
            else
                dstrgn->extents.x2 = dstrgn->extents.x1;
        }
    }
    if (prepend)
    {
        new = REGION_BOX(dstrgn, numRects);
        if (dnumRects == 1)
            *new = *REGION_BOXPTR(dstrgn);
        else
            memmove((char *)new,(char *)REGION_BOXPTR(dstrgn), 
                  dnumRects * sizeof(BoxRec));
        new = REGION_BOXPTR(dstrgn);
    }
    else
        new = REGION_BOXPTR(dstrgn) + dnumRects;
    if (numRects == 1)
        *new = *old;
    else
        memmove((char *)new, (char *)old, numRects * sizeof(BoxRec));
    dstrgn->data->numRects += numRects;
    return TRUE;
}

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

static void
QuickSortRects(
    BoxRec     rects[],
    int        numRects)
{
    int y1;
    int x1;
    int        i, j;
    BoxPtr     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);
}

/*-
 *-----------------------------------------------------------------------
 * miRegionValidate --
 * 
 *      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 tranformation (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
 *              miUnion.  Maximize the work each miUnion call does by using
 *              a binary merge.
 *
 *-----------------------------------------------------------------------
 */

_X_EXPORT Bool
miRegionValidate(badreg, pOverlap)
    RegionPtr badreg;
    Bool *pOverlap;
{
    /* Descriptor for regions under construction  in Step 2. */
    typedef struct {
        RegionRec   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]                                */
    RegionPtr  reg;        /* ri[j].reg                     */
    BoxPtr      box;        /* Current box in rects                 */
    BoxPtr      riBox;      /* Last box in ri[j].reg                */
    RegionPtr  hreg;       /* ri[j_half].reg                        */
    Bool                ret = TRUE;

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

    /* Step 1: Sort the rects array into ascending (y1, x1) order */
    QuickSortRects(REGION_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 *) xalloc(4 * sizeof(RegionInfo));
    if (!ri)
        return miRegionBreak (badreg);
    sizeRI = 4;
    numRI = 1;
    ri[0].prevBand = 0;
    ri[0].curBand = 0;
    ri[0].reg = *badreg;
    box = REGION_BOXPTR(&ri[0].reg);
    ri[0].reg.extents = *box;
    ri[0].reg.data->numRects = 1;

    /* 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 = REGION_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);
                    *REGION_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);
                *REGION_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)
        {
            /* Oops, allocate space for new region information */
            sizeRI <<= 1;
            rit = (RegionInfo *) xrealloc(ri, sizeRI * sizeof(RegionInfo));
            if (!rit)
                goto bail;
            ri = rit;
            rit = &ri[numRI];
        }
        numRI++;
        rit->prevBand = 0;
        rit->curBand = 0;
        rit->reg.extents = *box;
        rit->reg.data = (RegDataPtr)NULL;
        if (!miRectAlloc(&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 = REGION_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 */
        {
            xfreeData(reg);
            reg->data = (RegDataPtr)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 (!miRegionOp(reg, reg, hreg, miUnionO, 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;
            xfreeData(hreg);
        }
        numRI -= half;
    }
    *badreg = ri[0].reg;
    xfree(ri);
    good(badreg);
    return ret;
bail:
    for (i = 0; i < numRI; i++)
        xfreeData(&ri[i].reg);
    xfree (ri);
    return miRegionBreak (badreg);
}

_X_EXPORT RegionPtr
miRectsToRegion(nrects, prect, ctype)
    int                 nrects;
    xRectangle          *prect;
    int                 ctype;
{
    
    RegionPtr           pRgn;
    RegDataPtr          pData;
    BoxPtr              pBox;
    int                 i;
    int                 x1, y1, x2, y2;

    pRgn = miRegionCreate(NullBox, 0);
    if (REGION_NAR (pRgn))
        return pRgn;
    if (!nrects)
        return pRgn;
    if (nrects == 1)
    {
        x1 = prect->x;
        y1 = prect->y;
        if ((x2 = x1 + (int) prect->width) > MAXSHORT)
            x2 = MAXSHORT;
        if ((y2 = y1 + (int) prect->height) > MAXSHORT)
            y2 = MAXSHORT;
        if (x1 != x2 && y1 != y2)
        {
            pRgn->extents.x1 = x1;
            pRgn->extents.y1 = y1;
            pRgn->extents.x2 = x2;
            pRgn->extents.y2 = y2;
            pRgn->data = (RegDataPtr)NULL;
        }
        return pRgn;
    }
    pData = xallocData(nrects);
    if (!pData)
    {
        miRegionBreak (pRgn);
        return pRgn;
    }
    pBox = (BoxPtr) (pData + 1);
    for (i = nrects; --i >= 0; prect++)
    {
        x1 = prect->x;
        y1 = prect->y;
        if ((x2 = x1 + (int) prect->width) > MAXSHORT)
            x2 = MAXSHORT;
        if ((y2 = y1 + (int) prect->height) > MAXSHORT)
            y2 = MAXSHORT;
        if (x1 != x2 && y1 != y2)
        {
            pBox->x1 = x1;
            pBox->y1 = y1;
            pBox->x2 = x2;
            pBox->y2 = y2;
            pBox++;
        }
    }
    if (pBox != (BoxPtr) (pData + 1))
    {
        pData->size = nrects;
        pData->numRects = pBox - (BoxPtr) (pData + 1);
        pRgn->data = pData;
        if (ctype != CT_YXBANDED)
        {
            Bool overlap; /* result ignored */
            pRgn->extents.x1 = pRgn->extents.x2 = 0;
            miRegionValidate(pRgn, &overlap);
        }
        else
            miSetExtents(pRgn);
        good(pRgn);
    }
    else
    {
        xfree (pData);
    }
    return pRgn;
}

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


/*-
 *-----------------------------------------------------------------------
 * miSubtractO --
 *      Overlapping band subtraction. x1 is the left-most point not yet
 *      checked.
 *
 * Results:
 *      TRUE if successful.
 *
 * Side Effects:
 *      pReg may have rectangles added to it.
 *
 *-----------------------------------------------------------------------
 */
/*ARGSUSED*/

/*-
 *-----------------------------------------------------------------------
 * miSubtract --
 *      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.
 *
 *-----------------------------------------------------------------------
 */
_X_EXPORT Bool
miSubtract(regD, regM, regS)
    RegionPtr   regD;               
    RegionPtr   regM;
    RegionPtr   regS;          
{
    return pixman_region_subtract (regD, regM, regS);
}

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

/*-
 *-----------------------------------------------------------------------
 * miInverse --
 *      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.
 *
 *-----------------------------------------------------------------------
 */
_X_EXPORT Bool
miInverse(newReg, reg1, invRect)
    RegionPtr     newReg;       /* Destination region */
    RegionPtr     reg1;         /* Region to invert */
    BoxPtr        invRect;      /* Bounding box for inversion */
{
    return pixman_region_inverse (newReg, reg1, invRect);
}
_X_EXPORT int
miRectIn(region, prect)
    RegionPtr  region;
    BoxPtr     prect;
{
    return pixman_region_contains_rectangle (region, prect);
}

/* TranslateRegion(pReg, x, y)
   translates in place
*/

_X_EXPORT void
miTranslateRegion(pReg, x, y)
    RegionPtr pReg;
    int x;
    int y;
{
    pixman_region_translate (pReg, x, y);
}

_X_EXPORT void
miRegionReset(pReg, pBox)
    RegionPtr pReg;
    BoxPtr pBox;
{
    pixman_region_reset (pReg, pBox);
}

_X_EXPORT Bool
miPointInRegion(pReg, x, y, box)
    RegionPtr pReg;
    int x, y;
    BoxPtr box;     /* "return" value */
{
    return pixman_region_contains_point (pReg, x, y, box);
}

_X_EXPORT Bool
miRegionNotEmpty(pReg)
    RegionPtr pReg;
{
    return pixman_region_not_empty (pReg);
}

Bool
miRegionBroken(RegionPtr pReg)
{
    good(pReg);
    return (REGION_NAR(pReg));
}

_X_EXPORT void
miRegionEmpty(pReg)
    RegionPtr pReg;
{
    good(pReg);
    xfreeData(pReg);
    pReg->extents.x2 = pReg->extents.x1;
    pReg->extents.y2 = pReg->extents.y1;
    pReg->data = &miEmptyData;
}

_X_EXPORT BoxPtr
miRegionExtents(pReg)
    RegionPtr pReg;
{
    good(pReg);
    return(&pReg->extents);
}

#define ExchangeSpans(a, b)                                 \
{                                                           \
    DDXPointRec tpt;                                        \
    int         tw;                                         \
                                                            \
    tpt = spans[a]; spans[a] = spans[b]; spans[b] = tpt;    \
    tw = widths[a]; widths[a] = widths[b]; widths[b] = tw;  \
}

/* ||| I should apply the merge sort code to rectangle sorting above, and see
   if mapping time can be improved.  But right now I've been at work 12 hours,
   so forget it.
*/

static void QuickSortSpans(
    DDXPointRec spans[],
    int         widths[],
    int         numSpans)
{
    int     y;
    int     i, j, m;
    DDXPointPtr    r;

    /* Always called with numSpans > 1 */
    /* Sorts only by y, doesn't bother to sort by x */

    do
    {
        if (numSpans < 9)
        {
            /* Do insertion sort */
            int yprev;

            yprev = spans[0].y;
            i = 1;
            do
            { /* while i != numSpans */
                y = spans[i].y;
                if (yprev > y)
                {
                    /* spans[i] is out of order.  Move into proper location. */
                    DDXPointRec tpt;
                    int     tw, k;

                    for (j = 0; y >= spans[j].y; j++) {}
                    tpt = spans[i];
                    tw  = widths[i];
                    for (k = i; k != j; k--)
                    {
                        spans[k] = spans[k-1];
                        widths[k] = widths[k-1];
                    }
                    spans[j] = tpt;
                    widths[j] = tw;
                    y = spans[i].y;
                } /* if out of order */
                yprev = y;
                i++;
            } while (i != numSpans);
            return;
        }

        /* Choose partition element, stick in location 0 */
        m = numSpans / 2;
        if (spans[m].y > spans[0].y)            ExchangeSpans(m, 0);
        if (spans[m].y > spans[numSpans-1].y)   ExchangeSpans(m, numSpans-1);
        if (spans[m].y > spans[0].y)            ExchangeSpans(m, 0);
        y = spans[0].y;

        /* Partition array */
        i = 0;
        j = numSpans;
        do
        {
            r = &(spans[i]);
            do
            {
                r++;
                i++;
            } while (i != numSpans && r->y < y);
            r = &(spans[j]);
            do
            {
                r--;
                j--;
            } while (y < r->y);
            if (i < j)
                ExchangeSpans(i, j);
        } while (i < j);

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

        /* Recurse */
        if (numSpans-j-1 > 1)
            QuickSortSpans(&spans[j+1], &widths[j+1], numSpans-j-1);
        numSpans = j;
    } while (numSpans > 1);
}

#define NextBand()                                                  \
{                                                                   \
    clipy1 = pboxBandStart->y1;                                     \
    clipy2 = pboxBandStart->y2;                                     \
    pboxBandEnd = pboxBandStart + 1;                                \
    while (pboxBandEnd != pboxLast && pboxBandEnd->y1 == clipy1) {  \
        pboxBandEnd++;                                              \
    }                                                               \
    for (; ppt != pptLast && ppt->y < clipy1; ppt++, pwidth++) {} \
}

/*
    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.
*/

_X_EXPORT int
miClipSpans(
    RegionPtr   prgnDst,
    DDXPointPtr ppt,
    int         *pwidth,
    int         nspans,
    DDXPointPtr pptNew,
    int         *pwidthNew,
    int         fSorted)
{
    DDXPointPtr pptLast;
    int *pwidthNewStart;        /* the vengeance of Xerox! */
    int y, x1, x2;
    int numRects;

    good(prgnDst);
    pptLast = ppt + nspans;
    pwidthNewStart = pwidthNew;

    if (!prgnDst->data)
    {
        /* Do special fast code with clip boundaries in registers(?) */
        /* It doesn't pay much to make use of fSorted in this case, 
           so we lump everything together. */

        int clipx1, clipx2, clipy1, clipy2;

        clipx1 = prgnDst->extents.x1;
        clipy1 = prgnDst->extents.y1;
        clipx2 = prgnDst->extents.x2;
        clipy2 = prgnDst->extents.y2;
            
        for (; ppt != pptLast; ppt++, pwidth++)
        {
            y = ppt->y;
            x1 = ppt->x;
            if (clipy1 <= y && y < clipy2)
            {
                x2 = x1 + *pwidth;
                if (x1 < clipx1)    x1 = clipx1;
                if (x2 > clipx2)    x2 = clipx2;
                if (x1 < x2)
                {
                    /* part of span in clip rectangle */
                    pptNew->x = x1;
                    pptNew->y = y;
                    *pwidthNew = x2 - x1;
                    pptNew++;
                    pwidthNew++;
                }
            }
        } /* end for */

    }
    else if ((numRects = prgnDst->data->numRects))
    {
        /* Have to clip against many boxes */
        BoxPtr pboxBandStart, pboxBandEnd;
        BoxPtr pbox;
        BoxPtr pboxLast;
        int clipy1, clipy2;

        /* In this case, taking advantage of sorted spans gains more than
           the sorting costs. */
        if ((! fSorted) && (nspans > 1))
            QuickSortSpans(ppt, pwidth, nspans);

        pboxBandStart = REGION_BOXPTR(prgnDst);
        pboxLast = pboxBandStart + numRects;
    
        NextBand();

        for (; ppt != pptLast; )
        {
            y = ppt->y;
            if (y < clipy2)
            {
                /* span is in the current band */
                pbox = pboxBandStart;
                x1 = ppt->x;
                x2 = x1 + *pwidth;
                do
                { /* For each box in band */
                    int newx1, newx2;

                    newx1 = x1;
                    newx2 = x2;
                    if (newx1 < pbox->x1)   newx1 = pbox->x1;
                    if (newx2 > pbox->x2)   newx2 = pbox->x2;
                    if (newx1 < newx2)
                    {
                        /* Part of span in clip rectangle */
                        pptNew->x = newx1;
                        pptNew->y = y;
                        *pwidthNew = newx2 - newx1;
                        pptNew++;
                        pwidthNew++;
                    }
                    pbox++;
                } while (pbox != pboxBandEnd);
                ppt++;
                pwidth++;
            }
            else
            {
                /* Move to next band, adjust ppt as needed */
                pboxBandStart = pboxBandEnd;
                if (pboxBandStart == pboxLast)
                    break; /* We're completely done */
                NextBand();
            }
        }
    }
    return (pwidthNew - pwidthNewStart);
}

/* find the band in a region with the most rectangles */
_X_EXPORT int
miFindMaxBand(prgn)
    RegionPtr prgn;
{
    int nbox;
    BoxPtr pbox;
    int nThisBand;
    int nMaxBand = 0;
    short yThisBand;

    good(prgn);
    nbox = REGION_NUM_RECTS(prgn);
    pbox = REGION_RECTS(prgn);

    while(nbox > 0)
    {
        yThisBand = pbox->y1;
        nThisBand = 0;
        while((nbox > 0) && (pbox->y1 == yThisBand))
        {
            nbox--;
            pbox++;
            nThisBand++;
        }
        if (nThisBand > nMaxBand)
            nMaxBand = nThisBand;
    }
    return (nMaxBand);
}