p     = ( ONE_PIXEL - fx1 ) * ( y2 - y1 );
    first = ONE_PIXEL;
    incr  = 1;

    if ( dx < 0 )
    {
      p     = fx1 * ( y2 - y1 );
      first = 0;
      incr  = -1;
      dx    = -dx;
    }

    delta = (TCoord)( p / dx );
    mod   = (TCoord)( p % dx );
    if ( mod < 0 )
    {
      delta--;
      mod += (TCoord)dx;
    }

    ras.area  += (TArea)( fx1 + first ) * delta;
    ras.cover += delta;

    ex1 += incr;
    gray_set_cell( RAS_VAR_ ex1, ey );
    y1  += delta;

    if ( ex1 != ex2 )
    {
      p    = ONE_PIXEL * ( y2 - y1 + delta );
      lift = (TCoord)( p / dx );
      rem  = (TCoord)( p % dx );
      if ( rem < 0 )
      {
        lift--;
        rem += (TCoord)dx;
      }

      mod -= (int)dx;

      while ( ex1 != ex2 )
      {
        delta = lift;
        mod  += rem;
        if ( mod >= 0 )
        {
          mod -= (TCoord)dx;
          delta++;
        }

        ras.area  += (TArea)ONE_PIXEL * delta;
        ras.cover += delta;
        y1        += delta;
        ex1       += incr;
        gray_set_cell( RAS_VAR_ ex1, ey );
      }
    }

    delta      = y2 - y1;
    ras.area  += (TArea)( fx2 + ONE_PIXEL - first ) * delta;
    ras.cover += delta;
  }


  /*************************************************************************/
  /*                                                                       */
  /* Render a given line as a series of scanlines.                         */
  /*                                                                       */
  static void
  gray_render_line( RAS_ARG_ TPos  to_x,
                             TPos  to_y )
  {
    TCoord  ey1, ey2, fy1, fy2;
    TPos    dx, dy, x, x2;
    long    p, first;
    int     delta, rem, mod, lift, incr;


    ey1 = TRUNC( ras.last_ey );
    ey2 = TRUNC( to_y ); /* if (ey2 >= ras.max_ey) ey2 = ras.max_ey-1; */
    fy1 = (TCoord)( ras.y - ras.last_ey );
    fy2 = (TCoord)( to_y - SUBPIXELS( ey2 ) );

    dx = to_x - ras.x;
    dy = to_y - ras.y;

    /* XXX: we should do something about the trivial case where dx == 0, */
    /*      as it happens very often!                                    */

    /* perform vertical clipping */
    {
      TCoord  min, max;


      min = ey1;
      max = ey2;
      if ( ey1 > ey2 )
      {
        min = ey2;
        max = ey1;
      }
      if ( min >= ras.max_ey || max < ras.min_ey )
        goto End;
    }

    /* everything is on a single scanline */
    if ( ey1 == ey2 )
    {
      gray_render_scanline( RAS_VAR_ ey1, ras.x, fy1, to_x, fy2 );
      goto End;
    }

    /* vertical line - avoid calling gray_render_scanline */
    incr = 1;

    if ( dx == 0 )
    {
      TCoord  ex     = TRUNC( ras.x );
      TCoord  two_fx = (TCoord)( ( ras.x - SUBPIXELS( ex ) ) << 1 );
      TPos    area;


      first = ONE_PIXEL;
      if ( dy < 0 )
      {
        first = 0;
        incr  = -1;
      }

      delta      = (int)( first - fy1 );
      ras.area  += (TArea)two_fx * delta;
      ras.cover += delta;
      ey1       += incr;

      gray_set_cell( raster, ex, ey1 );

      delta = (int)( first + first - ONE_PIXEL );
      area  = (TArea)two_fx * delta;
      while ( ey1 != ey2 )
      {
        ras.area  += area;
        ras.cover += delta;
        ey1       += incr;
        gray_set_cell( raster, ex, ey1 );
      }

      delta      = (int)( fy2 - ONE_PIXEL + first );
      ras.area  += (TArea)two_fx * delta;
      ras.cover += delta;
      goto End;
    }

    /* ok, we have to render several scanlines */
    p     = ( ONE_PIXEL - fy1 ) * dx;
    first = ONE_PIXEL;
    incr  = 1;

    if ( dy < 0 )
    {
      p     = fy1 * dx;
      first = 0;
      incr  = -1;
      dy    = -dy;
    }

    delta = (int)( p / dy );
    mod   = (int)( p % dy );
    if ( mod < 0 )
    {
      delta--;
      mod += (TCoord)dy;
    }

    x = ras.x + delta;
    gray_render_scanline( RAS_VAR_ ey1, ras.x, fy1, x, (TCoord)first );

    ey1 += incr;
    gray_set_cell( RAS_VAR_ TRUNC( x ), ey1 );

    if ( ey1 != ey2 )
    {
      p     = ONE_PIXEL * dx;
      lift  = (int)( p / dy );
      rem   = (int)( p % dy );
      if ( rem < 0 )
      {
        lift--;
        rem += (int)dy;
      }
      mod -= (int)dy;

      while ( ey1 != ey2 )
      {
        delta = lift;
        mod  += rem;
        if ( mod >= 0 )
        {
          mod -= (int)dy;
          delta++;
        }

        x2 = x + delta;
        gray_render_scanline( RAS_VAR_ ey1, x,
                                       (TCoord)( ONE_PIXEL - first ), x2,
                                       (TCoord)first );
        x = x2;

        ey1 += incr;
        gray_set_cell( RAS_VAR_ TRUNC( x ), ey1 );
      }
    }

    gray_render_scanline( RAS_VAR_ ey1, x,
                                   (TCoord)( ONE_PIXEL - first ), to_x,
                                   fy2 );

  End:
    ras.x       = to_x;
    ras.y       = to_y;
    ras.last_ey = SUBPIXELS( ey2 );
  }


  static void
  gray_split_conic( FT_Vector*  base )
  {
    TPos  a, b;


    base[4].x = base[2].x;
    b = base[1].x;
    a = base[3].x = ( base[2].x + b ) / 2;
    b = base[1].x = ( base[0].x + b ) / 2;
    base[2].x = ( a + b ) / 2;

    base[4].y = base[2].y;
    b = base[1].y;
    a = base[3].y = ( base[2].y + b ) / 2;
    b = base[1].y = ( base[0].y + b ) / 2;
    base[2].y = ( a + b ) / 2;
  }


  static void
  gray_render_conic( RAS_ARG_ const FT_Vector*  control,
                              const FT_Vector*  to )
  {
    TPos        dx, dy;
    int         top, level;
    int*        levels;
    FT_Vector*  arc;


    dx = DOWNSCALE( ras.x ) + to->x - ( control->x << 1 );
    if ( dx < 0 )
      dx = -dx;
    dy = DOWNSCALE( ras.y ) + to->y - ( control->y << 1 );
    if ( dy < 0 )
      dy = -dy;
    if ( dx < dy )
      dx = dy;

    level = 1;
    dx = dx / ras.conic_level;
    while ( dx > 0 )
    {
      dx >>= 2;
      level++;
    }

    /* a shortcut to speed things up */
    if ( level <= 1 )
    {
      /* we compute the mid-point directly in order to avoid */
      /* calling gray_split_conic()                          */
      TPos   to_x, to_y, mid_x, mid_y;


      to_x  = UPSCALE( to->x );
      to_y  = UPSCALE( to->y );
      mid_x = ( ras.x + to_x + 2 * UPSCALE( control->x ) ) / 4;
      mid_y = ( ras.y + to_y + 2 * UPSCALE( control->y ) ) / 4;

      gray_render_line( RAS_VAR_ mid_x, mid_y );
      gray_render_line( RAS_VAR_ to_x, to_y );
      return;
    }

    arc       = ras.bez_stack;
    levels    = ras.lev_stack;
    top       = 0;
    levels[0] = level;

    arc[0].x = UPSCALE( to->x );
    arc[0].y = UPSCALE( to->y );
    arc[1].x = UPSCALE( control->x );
    arc[1].y = UPSCALE( control->y );
    arc[2].x = ras.x;
    arc[2].y = ras.y;

    while ( top >= 0 )
    {
      level = levels[top];
      if ( level > 1 )
      {
        /* check that the arc crosses the current band */
        TPos  min, max, y;


        min = max = arc[0].y;

        y = arc[1].y;
        if ( y < min ) min = y;
        if ( y > max ) max = y;

        y = arc[2].y;
        if ( y < min ) min = y;
        if ( y > max ) max = y;

        if ( TRUNC( min ) >= ras.max_ey || TRUNC( max ) < ras.min_ey )
          goto Draw;

        gray_split_conic( arc );
        arc += 2;
        top++;
        levels[top] = levels[top - 1] = level - 1;
        continue;
      }

    Draw:
      {
        TPos  to_x, to_y, mid_x, mid_y;


        to_x  = arc[0].x;
        to_y  = arc[0].y;
        mid_x = ( ras.x + to_x + 2 * arc[1].x ) / 4;
        mid_y = ( ras.y + to_y + 2 * arc[1].y ) / 4;

        gray_render_line( RAS_VAR_ mid_x, mid_y );
        gray_render_line( RAS_VAR_ to_x, to_y );

        top--;
        arc -= 2;
      }
    }
    return;
  }


  static void
  gray_split_cubic( FT_Vector*  base )
  {
    TPos  a, b, c, d;


    base[6].x = base[3].x;
    c = base[1].x;
    d = base[2].x;
    base[1].x = a = ( base[0].x + c ) / 2;
    base[5].x = b = ( base[3].x + d ) / 2;
    c = ( c + d ) / 2;
    base[2].x = a = ( a + c ) / 2;
    base[4].x = b = ( b + c ) / 2;
    base[3].x = ( a + b ) / 2;

    base[6].y = base[3].y;
    c = base[1].y;
    d = base[2].y;
    base[1].y = a = ( base[0].y + c ) / 2;
    base[5].y = b = ( base[3].y + d ) / 2;
    c = ( c + d ) / 2;
    base[2].y = a = ( a + c ) / 2;
    base[4].y = b = ( b + c ) / 2;
    base[3].y = ( a + b ) / 2;
  }


  static void
  gray_render_cubic( RAS_ARG_ const FT_Vector*  control1,
                              const FT_Vector*  control2,
                              const FT_Vector*  to )
  {
    TPos        dx, dy, da, db;
    int         top, level;
    int*        levels;
    FT_Vector*  arc;


    dx = DOWNSCALE( ras.x ) + to->x - ( control1->x << 1 );
    if ( dx < 0 )
      dx = -dx;
    dy = DOWNSCALE( ras.y ) + to->y - ( control1->y << 1 );
    if ( dy < 0 )
      dy = -dy;
    if ( dx < dy )
      dx = dy;
    da = dx;

    dx = DOWNSCALE( ras.x ) + to->x - 3 * ( control1->x + control2->x );
    if ( dx < 0 )
      dx = -dx;
    dy = DOWNSCALE( ras.y ) + to->y - 3 * ( control1->x + control2->y );
    if ( dy < 0 )
      dy = -dy;
    if ( dx < dy )
      dx = dy;
    db = dx;

    level = 1;
    da    = da / ras.cubic_level;
    db    = db / ras.conic_level;
    while ( da > 0 || db > 0 )
    {
      da >>= 2;
      db >>= 3;
      level++;
    }

    if ( level <= 1 )
    {
      TPos   to_x, to_y, mid_x, mid_y;


      to_x  = UPSCALE( to->x );
      to_y  = UPSCALE( to->y );
      mid_x = ( ras.x + to_x +
                3 * UPSCALE( control1->x + control2->x ) ) / 8;
      mid_y = ( ras.y + to_y +
                3 * UPSCALE( control1->y + control2->y ) ) / 8;

      gray_render_line( RAS_VAR_ mid_x, mid_y );
      gray_render_line( RAS_VAR_ to_x, to_y );
      return;
    }

    arc      = ras.bez_stack;
    arc[0].x = UPSCALE( to->x );
    arc[0].y = UPSCALE( to->y );
    arc[1].x = UPSCALE( control2->x );
    arc[1].y = UPSCALE( control2->y );
    arc[2].x = UPSCALE( control1->x );
    arc[2].y = UPSCALE( control1->y );
    arc[3].x = ras.x;
    arc[3].y = ras.y;

    levels    = ras.lev_stack;
    top       = 0;
    levels[0] = level;

    while ( top >= 0 )
    {
      level = levels[top];
      if ( level > 1 )
      {
        /* check that the arc crosses the current band */
        TPos  min, max, y;


        min = max = arc[0].y;
        y = arc[1].y;
        if ( y < min ) min = y;
        if ( y > max ) max = y;
        y = arc[2].y;
        if ( y < min ) min = y;
        if ( y > max ) max = y;
        y = arc[3].y;
        if ( y < min ) min = y;
        if ( y > max ) max = y;
        if ( TRUNC( min ) >= ras.max_ey || TRUNC( max ) < 0 )
          goto Draw;
        gray_split_cubic( arc );
        arc += 3;
        top ++;
        levels[top] = levels[top - 1] = level - 1;
        continue;
      }

    Draw:
      {
        TPos  to_x, to_y, mid_x, mid_y;


        to_x  = arc[0].x;
        to_y  = arc[0].y;
        mid_x = ( ras.x + to_x + 3 * ( arc[1].x + arc[2].x ) ) / 8;
        mid_y = ( ras.y + to_y + 3 * ( arc[1].y + arc[2].y ) ) / 8;

        gray_render_line( RAS_VAR_ mid_x, mid_y );
        gray_render_line( RAS_VAR_ to_x, to_y );
        top --;
        arc -= 3;
      }
    }
    return;
  }


  /* a macro comparing two cell pointers.  Returns true if a <= b. */
#if 1

#define PACK( a )          ( ( (long)(a)->y << 16 ) + (a)->x )
#define LESS_THAN( a, b )  ( PACK( a ) < PACK( b ) )

#else /* 1 */

#define LESS_THAN( a, b )  ( (a)->y < (b)->y || \
                             ( (a)->y == (b)->y && (a)->x < (b)->x ) )

#endif /* 1 */

#define SWAP_CELLS( a, b, temp )  do             \
                                  {              \
                                    temp = *(a); \
                                    *(a) = *(b); \
                                    *(b) = temp; \
                                  } while ( 0 )
#define DEBUG_SORT
#define QUICK_SORT

#ifdef SHELL_SORT

  /* a simple shell sort algorithm that works directly on our */
  /* cells table                                              */
  static void
  gray_shell_sort ( PCell  cells,
                    int    count )
  {
    PCell  i, j, limit = cells + count;
    TCell  temp;
    int    gap;


    /* compute initial gap */
    for ( gap = 0; ++gap < count; gap *= 3 )
      ;

    while ( gap /= 3 )
    {
      for ( i = cells + gap; i < limit; i++ )