initial commit

1 files changed, 1377 insertions, 0 deletions

diff --git a/src/freetype/ftgrays.c b/src/freetype/ftgrays.c
new file mode 100644
index 0000000..afbe609
--- /dev/null
+++ b/src/freetype/ftgrays.c
@@ -0,0 +1,1377 @@
+/***************************************************************************/
+/*                                                                         */
+/*  ftgrays.c                                                              */
+/*                                                                         */
+/*    A new `perfect' anti-aliasing renderer (body).                       */
+/*                                                                         */
+/*  Copyright 2000-2018 by                                                 */
+/*  David Turner, Robert Wilhelm, and Werner Lemberg.                      */
+/*                                                                         */
+/*  This file is part of the FreeType project, and may only be used,       */
+/*  modified, and distributed under the terms of the FreeType project      */
+/*  license, LICENSE.TXT.  By continuing to use, modify, or distribute     */
+/*  this file you indicate that you have read the license and              */
+/*  understand and accept it fully.                                        */
+/*                                                                         */
+/***************************************************************************/
+
+  /*************************************************************************/
+  /*                                                                       */
+  /* This file can be compiled without the rest of the FreeType engine, by */
+  /* defining the STANDALONE_ macro when compiling it.  You also need to   */
+  /* put the files `ftgrays.h' and `ftimage.h' into the current            */
+  /* compilation directory.  Typically, you could do something like        */
+  /*                                                                       */
+  /* - copy `src/smooth/ftgrays.c' (this file) to your current directory   */
+  /*                                                                       */
+  /* - copy `include/freetype/ftimage.h' and `src/smooth/ftgrays.h' to the */
+  /*   same directory                                                      */
+  /*                                                                       */
+  /* - compile `ftgrays' with the STANDALONE_ macro defined, as in         */
+  /*                                                                       */
+  /*     cc -c -DSTANDALONE_ ftgrays.c                                     */
+  /*                                                                       */
+  /* The renderer can be initialized with a call to                        */
+  /* `ft_gray_raster.raster_new'; an anti-aliased bitmap can be generated  */
+  /* with a call to `ft_gray_raster.raster_render'.                        */
+  /*                                                                       */
+  /* See the comments and documentation in the file `ftimage.h' for more   */
+  /* details on how the raster works.                                      */
+  /*                                                                       */
+  /*************************************************************************/
+
+  /*************************************************************************/
+  /*                                                                       */
+  /* This is a new anti-aliasing scan-converter for FreeType 2.  The       */
+  /* algorithm used here is _very_ different from the one in the standard  */
+  /* `ftraster' module.  Actually, `ftgrays' computes the _exact_          */
+  /* coverage of the outline on each pixel cell.                           */
+  /*                                                                       */
+  /* It is based on ideas that I initially found in Raph Levien's          */
+  /* excellent LibArt graphics library (see http://www.levien.com/libart   */
+  /* for more information, though the web pages do not tell anything       */
+  /* about the renderer; you'll have to dive into the source code to       */
+  /* understand how it works).                                             */
+  /*                                                                       */
+  /* Note, however, that this is a _very_ different implementation         */
+  /* compared to Raph's.  Coverage information is stored in a very         */
+  /* different way, and I don't use sorted vector paths.  Also, it doesn't */
+  /* use floating point values.                                            */
+  /*                                                                       */
+  /* This renderer has the following advantages:                           */
+  /*                                                                       */
+  /* - It doesn't need an intermediate bitmap.  Instead, one can supply a  */
+  /*   callback function that will be called by the renderer to draw gray  */
+  /*   spans on any target surface.  You can thus do direct composition on */
+  /*   any kind of bitmap, provided that you give the renderer the right   */
+  /*   callback.                                                           */
+  /*                                                                       */
+  /* - A perfect anti-aliaser, i.e., it computes the _exact_ coverage on   */
+  /*   each pixel cell.                                                    */
+  /*                                                                       */
+  /* - It performs a single pass on the outline (the `standard' FT2        */
+  /*   renderer makes two passes).                                         */
+  /*                                                                       */
+  /* - It can easily be modified to render to _any_ number of gray levels  */
+  /*   cheaply.                                                            */
+  /*                                                                       */
+  /* - For small (< 20) pixel sizes, it is faster than the standard        */
+  /*   renderer.                                                           */
+  /*                                                                       */
+  /*************************************************************************/
+
+
+  /*************************************************************************/
+  /*                                                                       */
+  /* The macro FT_COMPONENT is used in trace mode.  It is an implicit      */
+  /* parameter of the FT_TRACE() and FT_ERROR() macros, used to print/log  */
+  /* messages during execution.                                            */
+  /*                                                                       */
+#undef  FT_COMPONENT
+#define FT_COMPONENT  trace_smooth
+
+
+#include "ft2build.h"
+#include "ftgrays.h"
+#include FT_INTERNAL_OBJECTS_H
+#include FT_INTERNAL_DEBUG_H
+#include FT_INTERNAL_CALC_H
+#include FT_OUTLINE_H
+
+#include "ftsmerrs.h"
+
+#define Smooth_Err_Invalid_Mode     Smooth_Err_Cannot_Render_Glyph
+#define Smooth_Err_Memory_Overflow  Smooth_Err_Out_Of_Memory
+#define ErrRaster_Memory_Overflow   Smooth_Err_Out_Of_Memory
+
+
+  /* as usual, for the speed hungry :-) */
+
+#undef RAS_ARG
+#undef RAS_ARG_
+#undef RAS_VAR
+#undef RAS_VAR_
+
+#ifndef FT_STATIC_RASTER
+
+#define RAS_ARG   gray_PWorker  worker
+#define RAS_ARG_  gray_PWorker  worker,
+
+#define RAS_VAR   worker
+#define RAS_VAR_  worker,
+
+#else /* FT_STATIC_RASTER */
+
+#define RAS_ARG   void
+#define RAS_ARG_  /* empty */
+#define RAS_VAR   /* empty */
+#define RAS_VAR_  /* empty */
+
+#endif /* FT_STATIC_RASTER */
+
+
+  /* must be at least 6 bits! */
+#define PIXEL_BITS  8
+
+#undef FLOOR
+#undef CEILING
+#undef TRUNC
+#undef SCALED
+
+#define ONE_PIXEL       ( 1 << PIXEL_BITS )
+#define TRUNC( x )      ( (TCoord)( (x) >> PIXEL_BITS ) )
+#define SUBPIXELS( x )  ( (TPos)(x) * ONE_PIXEL )
+#define FLOOR( x )      ( (x) & -ONE_PIXEL )
+#define CEILING( x )    ( ( (x) + ONE_PIXEL - 1 ) & -ONE_PIXEL )
+#define ROUND( x )      ( ( (x) + ONE_PIXEL / 2 ) & -ONE_PIXEL )
+
+#if PIXEL_BITS >= 6
+#define UPSCALE( x )    ( (x) * ( ONE_PIXEL >> 6 ) )
+#define DOWNSCALE( x )  ( (x) >> ( PIXEL_BITS - 6 ) )
+#else
+#define UPSCALE( x )    ( (x) >> ( 6 - PIXEL_BITS ) )
+#define DOWNSCALE( x )  ( (x) * ( 64 >> PIXEL_BITS ) )
+#endif
+
+
+  /* Compute `dividend / divisor' and return both its quotient and     */
+  /* remainder, cast to a specific type.  This macro also ensures that */
+  /* the remainder is always positive.  We use the remainder to keep   */
+  /* track of accumulating errors and compensate for them.             */
+#define FT_DIV_MOD( type, dividend, divisor, quotient, remainder ) \
+  FT_BEGIN_STMNT                                                   \
+    (quotient)  = (type)( (dividend) / (divisor) );                \
+    (remainder) = (type)( (dividend) % (divisor) );                \
+    if ( (remainder) < 0 )                                         \
+    {                                                              \
+      (quotient)--;                                                \
+      (remainder) += (type)(divisor);                              \
+    }                                                              \
+  FT_END_STMNT
+
+#ifdef  __arm__
+  /* Work around a bug specific to GCC which make the compiler fail to */
+  /* optimize a division and modulo operation on the same parameters   */
+  /* into a single call to `__aeabi_idivmod'.  See                     */
+  /*                                                                   */
+  /*  https://gcc.gnu.org/bugzilla/show_bug.cgi?id=43721               */
+#undef FT_DIV_MOD
+#define FT_DIV_MOD( type, dividend, divisor, quotient, remainder ) \
+  FT_BEGIN_STMNT                                                   \
+    (quotient)  = (type)( (dividend) / (divisor) );                \
+    (remainder) = (type)( (dividend) - (quotient) * (divisor) );   \
+    if ( (remainder) < 0 )                                         \
+    {                                                              \
+      (quotient)--;                                                \
+      (remainder) += (type)(divisor);                              \
+    }                                                              \
+  FT_END_STMNT
+#endif /* __arm__ */
+
+
+  /* These macros speed up repetitive divisions by replacing them */
+  /* with multiplications and right shifts.                       */
+#define FT_UDIVPREP( c, b )                                        \
+  long  b ## _r = c ? (long)( FT_ULONG_MAX >> PIXEL_BITS ) / ( b ) \
+                    : 0
+#define FT_UDIV( a, b )                                        \
+  ( ( (unsigned long)( a ) * (unsigned long)( b ## _r ) ) >>   \
+    ( sizeof( long ) * FT_CHAR_BIT - PIXEL_BITS ) )
+
+
+  /*************************************************************************/
+  /*                                                                       */
+  /*   TYPE DEFINITIONS                                                    */
+  /*                                                                       */
+
+  /* don't change the following types to FT_Int or FT_Pos, since we might */
+  /* need to define them to "float" or "double" when experimenting with   */
+  /* new algorithms                                                       */
+
+  typedef long  TPos;     /* subpixel coordinate               */
+  typedef int   TCoord;   /* integer scanline/pixel coordinate */
+  typedef int   TArea;    /* cell areas, coordinate products   */
+
+
+  typedef struct TCell_*  PCell;
+
+  typedef struct  TCell_
+  {
+    TCoord  x;     /* same with gray_TWorker.ex    */
+    TCoord  cover; /* same with gray_TWorker.cover */
+    TArea   area;
+    PCell   next;
+
+  } TCell;
+
+  typedef struct TPixmap_
+  {
+    unsigned char*  origin;  /* pixmap origin at the bottom-left */
+    int             pitch;   /* pitch to go down one row */
+
+  } TPixmap;
+
+  /* maximum number of gray cells in the buffer */
+#if FT_RENDER_POOL_SIZE > 2048
+#define FT_MAX_GRAY_POOL  ( FT_RENDER_POOL_SIZE / sizeof ( TCell ) )
+#else
+#define FT_MAX_GRAY_POOL  ( 2048 / sizeof ( TCell ) )
+#endif
+
+
+#if defined( _MSC_VER )      /* Visual C++ (and Intel C++) */
+  /* We disable the warning `structure was padded due to   */
+  /* __declspec(align())' in order to compile cleanly with */
+  /* the maximum level of warnings.                        */
+#pragma warning( push )
+#pragma warning( disable : 4324 )
+#endif /* _MSC_VER */
+
+  typedef struct  gray_TWorker_
+  {
+    ft_jmp_buf  jump_buffer;
+
+    TCoord  ex, ey;
+    TCoord  min_ex, max_ex;
+    TCoord  min_ey, max_ey;
+
+    TArea   area;
+    TCoord  cover;
+    int     invalid;
+
+    PCell*      ycells;
+    PCell       cells;
+    FT_PtrDist  max_cells;
+    FT_PtrDist  num_cells;
+
+    TPos    x,  y;
+
+    FT_Outline  outline;
+    TPixmap     target;
+
+    FT_Raster_Span_Func  render_span;
+    void*                render_span_data;
+
+  } gray_TWorker, *gray_PWorker;
+
+#if defined( _MSC_VER )
+#pragma warning( pop )
+#endif
+
+
+#ifndef FT_STATIC_RASTER
+#define ras  (*worker)
+#else
+  static gray_TWorker  ras;
+#endif
+
+
+#ifdef FT_DEBUG_LEVEL_TRACE
+
+  /* to be called while in the debugger --                                */
+  /* this function causes a compiler warning since it is unused otherwise */
+  static void
+  gray_dump_cells( RAS_ARG )
+  {
+    int  y;
+
+
+    for ( y = ras.min_ey; y < ras.max_ey; y++ )
+    {
+      PCell  cell = ras.ycells[y - ras.min_ey];
+
+
+      printf( "%3d:", y );
+
+      for ( ; cell != NULL; cell = cell->next )
+        printf( " (%3d, c:%4d, a:%6d)",
+                cell->x, cell->cover, cell->area );
+      printf( "\n" );
+    }
+  }
+
+#endif /* FT_DEBUG_LEVEL_TRACE */
+
+
+  /*************************************************************************/
+  /*                                                                       */
+  /* Record the current cell in the table.                                 */
+  /*                                                                       */
+  static void
+  gray_record_cell( RAS_ARG )
+  {
+    PCell  *pcell, cell;
+    TCoord  x = ras.ex;
+
+
+    pcell = &ras.ycells[ras.ey - ras.min_ey];
+    for (;;)
+    {
+      cell = *pcell;
+      if ( !cell || cell->x > x )
+        break;
+
+      if ( cell->x == x )
+        goto Found;
+
+      pcell = &cell->next;
+    }
+
+    if ( ras.num_cells >= ras.max_cells )
+      ft_longjmp( ras.jump_buffer, 1 );
+
+    /* insert new cell */
+    cell        = ras.cells + ras.num_cells++;
+    cell->x     = x;
+    cell->area  = ras.area;
+    cell->cover = ras.cover;
+
+    cell->next  = *pcell;
+    *pcell      = cell;
+
+    return;
+
+  Found:
+    /* update old cell */
+    cell->area  += ras.area;
+    cell->cover += ras.cover;
+  }
+
+
+  /*************************************************************************/
+  /*                                                                       */
+  /* Set the current cell to a new position.                               */
+  /*                                                                       */
+  static void
+  gray_set_cell( RAS_ARG_ TCoord  ex,
+                          TCoord  ey )
+  {
+    /* Move the cell pointer to a new position.  We set the `invalid'      */
+    /* flag to indicate that the cell isn't part of those we're interested */
+    /* in during the render phase.  This means that:                       */
+    /*                                                                     */
+    /* . the new vertical position must be within min_ey..max_ey-1.        */
+    /* . the new horizontal position must be strictly less than max_ex     */
+    /*                                                                     */
+    /* Note that if a cell is to the left of the clipping region, it is    */
+    /* actually set to the (min_ex-1) horizontal position.                 */
+
+    if ( ex < ras.min_ex )
+      ex = ras.min_ex - 1;
+
+    /* record the current one if it is valid and substantial */
+    if ( !ras.invalid && ( ras.area || ras.cover ) )
+      gray_record_cell( RAS_VAR );
+
+    ras.area  = 0;
+    ras.cover = 0;
+    ras.ex    = ex;
+    ras.ey    = ey;
+
+    ras.invalid = ( ey >= ras.max_ey || ey < ras.min_ey ||
+                    ex >= ras.max_ex );
+  }
+
+
+#ifndef FT_LONG64
+
+  /*************************************************************************/
+  /*                                                                       */
+  /* Render a scanline as one or more cells.                               */
+  /*                                                                       */
+  static void
+  gray_render_scanline( RAS_ARG_ TCoord  ey,
+                                 TPos    x1,
+                                 TCoord  y1,
+                                 TPos    x2,
+                                 TCoord  y2 )
+  {
+    TCoord  ex1, ex2, fx1, fx2, first, dy, delta, mod;
+    TPos    p, dx;
+    int     incr;
+
+
+    ex1 = TRUNC( x1 );
+    ex2 = TRUNC( x2 );
+
+    /* trivial case.  Happens often */
+    if ( y1 == y2 )
+    {
+      gray_set_cell( RAS_VAR_ ex2, ey );
+      return;
+    }
+
+    fx1   = (TCoord)( x1 - SUBPIXELS( ex1 ) );
+    fx2   = (TCoord)( x2 - SUBPIXELS( ex2 ) );
+
+    /* everything is located in a single cell.  That is easy! */
+    /*                                                        */
+    if ( ex1 == ex2 )
+      goto End;
+
+    /* ok, we'll have to render a run of adjacent cells on the same */
+    /* scanline...                                                  */
+    /*                                                              */
+    dx = x2 - x1;
+    dy = y2 - y1;
+
+    if ( dx > 0 )
+    {
+      p     = ( ONE_PIXEL - fx1 ) * dy;
+      first = ONE_PIXEL;
+      incr  = 1;
+    }
+    else
+    {
+      p     = fx1 * dy;
+      first = 0;
+      incr  = -1;
+      dx    = -dx;
+    }
+
+    FT_DIV_MOD( TCoord, p, dx, delta, mod );
+
+    ras.area  += (TArea)( ( fx1 + first ) * delta );
+    ras.cover += delta;
+    y1        += delta;
+    ex1       += incr;
+    gray_set_cell( RAS_VAR_ ex1, ey );
+
+    if ( ex1 != ex2 )
+    {
+      TCoord  lift, rem;
+
+
+      p = ONE_PIXEL * dy;
+      FT_DIV_MOD( TCoord, p, dx, lift, rem );
+
+      do
+      {
+        delta = lift;
+        mod  += rem;
+        if ( mod >= (TCoord)dx )
+        {
+          mod -= (TCoord)dx;
+          delta++;
+        }
+
+        ras.area  += (TArea)( ONE_PIXEL * delta );
+        ras.cover += delta;
+        y1        += delta;
+        ex1       += incr;
+        gray_set_cell( RAS_VAR_ ex1, ey );
+      } while ( ex1 != ex2 );
+    }
+
+    fx1 = ONE_PIXEL - first;
+
+  End:
+    dy = y2 - y1;
+
+    ras.area  += (TArea)( ( fx1 + fx2 ) * dy );
+    ras.cover += dy;
+  }
+
+
+  /*************************************************************************/
+  /*                                                                       */
+  /* 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, first, delta, mod;
+    TPos    p, dx, dy, x, x2;
+    int     incr;
+
+
+    ey1 = TRUNC( ras.y );
+    ey2 = TRUNC( to_y );     /* if (ey2 >= ras.max_ey) ey2 = ras.max_ey-1; */
+
+    /* perform vertical clipping */
+    if ( ( ey1 >= ras.max_ey && ey2 >= ras.max_ey ) ||
+         ( ey1 <  ras.min_ey && ey2 <  ras.min_ey ) )
+      goto End;
+
+    fy1 = (TCoord)( ras.y - SUBPIXELS( ey1 ) );
+    fy2 = (TCoord)( to_y - SUBPIXELS( ey2 ) );
+
+    /* everything is on a single scanline */
+    if ( ey1 == ey2 )
+    {
+      gray_render_scanline( RAS_VAR_ ey1, ras.x, fy1, to_x, fy2 );
+      goto End;
+    }
+
+    dx = to_x - ras.x;
+    dy = to_y - ras.y;
+
+    /* vertical line - avoid calling gray_render_scanline */
+    if ( dx == 0 )
+    {
+      TCoord  ex     = TRUNC( ras.x );
+      TCoord  two_fx = (TCoord)( ( ras.x - SUBPIXELS( ex ) ) << 1 );
+      TArea   area;
+
+
+      if ( dy > 0)
+      {
+        first = ONE_PIXEL;
+        incr  = 1;
+      }
+      else
+      {
+        first = 0;
+        incr  = -1;
+      }
+
+      delta      = first - fy1;
+      ras.area  += (TArea)two_fx * delta;
+      ras.cover += delta;
+      ey1       += incr;
+
+      gray_set_cell( RAS_VAR_ ex, ey1 );
+
+      delta = first + first - ONE_PIXEL;
+      area  = (TArea)two_fx * delta;
+      while ( ey1 != ey2 )
+      {
+        ras.area  += area;
+        ras.cover += delta;
+        ey1       += incr;
+
+        gray_set_cell( RAS_VAR_ ex, ey1 );
+      }
+
+      delta      = fy2 - ONE_PIXEL + first;
+      ras.area  += (TArea)two_fx * delta;
+      ras.cover += delta;
+
+      goto End;
+    }
+
+    /* ok, we have to render several scanlines */
+    if ( dy > 0)
+    {
+      p     = ( ONE_PIXEL - fy1 ) * dx;
+      first = ONE_PIXEL;
+      incr  = 1;
+    }
+    else
+    {
+      p     = fy1 * dx;
+      first = 0;
+      incr  = -1;
+      dy    = -dy;
+    }
+
+    FT_DIV_MOD( TCoord, p, dy, delta, mod );
+
+    x = ras.x + delta;
+    gray_render_scanline( RAS_VAR_ ey1, ras.x, fy1, x, first );
+
+    ey1 += incr;
+    gray_set_cell( RAS_VAR_ TRUNC( x ), ey1 );
+
+    if ( ey1 != ey2 )
+    {
+      TCoord  lift, rem;
+
+
+      p    = ONE_PIXEL * dx;
+      FT_DIV_MOD( TCoord, p, dy, lift, rem );
+
+      do
+      {
+        delta = lift;
+        mod  += rem;
+        if ( mod >= (TCoord)dy )
+        {
+          mod -= (TCoord)dy;
+          delta++;
+        }
+
+        x2 = x + delta;
+        gray_render_scanline( RAS_VAR_ ey1,
+                                       x, ONE_PIXEL - first,
+                                       x2, first );
+        x = x2;
+
+        ey1 += incr;
+        gray_set_cell( RAS_VAR_ TRUNC( x ), ey1 );
+      } while ( ey1 != ey2 );
+    }
+
+    gray_render_scanline( RAS_VAR_ ey1,
+                                   x, ONE_PIXEL - first,
+                                   to_x, fy2 );
+
+  End:
+    ras.x       = to_x;
+    ras.y       = to_y;
+  }
+
+#else
+
+  /*************************************************************************/
+  /*                                                                       */
+  /* Render a straight line across multiple cells in any direction.        */
+  /*                                                                       */
+  static void
+  gray_render_line( RAS_ARG_ TPos  to_x,
+                             TPos  to_y )
+  {
+    TPos    dx, dy, fx1, fy1, fx2, fy2;
+    TCoord  ex1, ex2, ey1, ey2;
+
+
+    ey1 = TRUNC( ras.y );
+    ey2 = TRUNC( to_y );
+
+    /* perform vertical clipping */
+    if ( ( ey1 >= ras.max_ey && ey2 >= ras.max_ey ) ||
+         ( ey1 <  ras.min_ey && ey2 <  ras.min_ey ) )
+      goto End;
+
+    ex1 = TRUNC( ras.x );
+    ex2 = TRUNC( to_x );
+
+    fx1 = ras.x - SUBPIXELS( ex1 );
+    fy1 = ras.y - SUBPIXELS( ey1 );
+
+    dx = to_x - ras.x;
+    dy = to_y - ras.y;
+
+    if ( ex1 == ex2 && ey1 == ey2 )       /* inside one cell */
+      ;
+    else if ( dy == 0 ) /* ex1 != ex2 */  /* any horizontal line */
+    {
+      ex1 = ex2;
+      gray_set_cell( RAS_VAR_ ex1, ey1 );
+    }
+    else if ( dx == 0 )
+    {
+      if ( dy > 0 )                       /* vertical line up */
+        do
+        {
+          fy2 = ONE_PIXEL;
+          ras.cover += ( fy2 - fy1 );
+          ras.area  += ( fy2 - fy1 ) * fx1 * 2;
+          fy1 = 0;
+          ey1++;
+          gray_set_cell( RAS_VAR_ ex1, ey1 );
+        } while ( ey1 != ey2 );
+      else                                /* vertical line down */
+        do
+        {
+          fy2 = 0;
+          ras.cover += ( fy2 - fy1 );
+          ras.area  += ( fy2 - fy1 ) * fx1 * 2;
+          fy1 = ONE_PIXEL;
+          ey1--;
+          gray_set_cell( RAS_VAR_ ex1, ey1 );
+        } while ( ey1 != ey2 );
+    }
+    else                                  /* any other line */
+    {
+      TPos  prod = dx * fy1 - dy * fx1;
+      FT_UDIVPREP( ex1 != ex2, dx );
+      FT_UDIVPREP( ey1 != ey2, dy );
+
+
+      /* The fundamental value `prod' determines which side and the  */
+      /* exact coordinate where the line exits current cell.  It is  */
+      /* also easily updated when moving from one cell to the next.  */
+      do
+      {
+        if      ( prod                                   <= 0 &&
+                  prod - dx * ONE_PIXEL                  >  0 ) /* left */
+        {
+          fx2 = 0;
+          fy2 = (TPos)FT_UDIV( -prod, -dx );
+          prod -= dy * ONE_PIXEL;
+          ras.cover += ( fy2 - fy1 );
+          ras.area  += ( fy2 - fy1 ) * ( fx1 + fx2 );
+          fx1 = ONE_PIXEL;
+          fy1 = fy2;
+          ex1--;
+        }
+        else if ( prod - dx * ONE_PIXEL                  <= 0 &&
+                  prod - dx * ONE_PIXEL + dy * ONE_PIXEL >  0 ) /* up */
+        {
+          prod -= dx * ONE_PIXEL;
+          fx2 = (TPos)FT_UDIV( -prod, dy );
+          fy2 = ONE_PIXEL;
+          ras.cover += ( fy2 - fy1 );
+          ras.area  += ( fy2 - fy1 ) * ( fx1 + fx2 );
+          fx1 = fx2;
+          fy1 = 0;
+          ey1++;
+        }
+        else if ( prod - dx * ONE_PIXEL + dy * ONE_PIXEL <= 0 &&
+                  prod                  + dy * ONE_PIXEL >= 0 ) /* right */
+        {
+          prod += dy * ONE_PIXEL;
+          fx2 = ONE_PIXEL;
+          fy2 = (TPos)FT_UDIV( prod, dx );
+          ras.cover += ( fy2 - fy1 );
+          ras.area  += ( fy2 - fy1 ) * ( fx1 + fx2 );
+          fx1 = 0;
+          fy1 = fy2;
+          ex1++;
+        }
+        else /* ( prod                  + dy * ONE_PIXEL <  0 &&
+                  prod                                   >  0 )    down */
+        {
+          fx2 = (TPos)FT_UDIV( prod, -dy );
+          fy2 = 0;
+          prod += dx * ONE_PIXEL;
+          ras.cover += ( fy2 - fy1 );
+          ras.area  += ( fy2 - fy1 ) * ( fx1 + fx2 );
+          fx1 = fx2;
+          fy1 = ONE_PIXEL;
+          ey1--;
+        }
+
+        gray_set_cell( RAS_VAR_ ex1, ey1 );
+      } while ( ex1 != ex2 || ey1 != ey2 );
+    }
+
+    fx2 = to_x - SUBPIXELS( ex2 );
+    fy2 = to_y - SUBPIXELS( ey2 );
+
+    ras.cover += ( fy2 - fy1 );
+    ras.area  += ( fy2 - fy1 ) * ( fx1 + fx2 );
+
+  End:
+    ras.x       = to_x;
+    ras.y       = to_y;
+  }
+
+#endif
+
+  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 )
+  {
+    FT_Vector   bez_stack[16 * 2 + 1];  /* enough to accommodate bisections */
+    FT_Vector*  arc = bez_stack;
+    TPos        dx, dy;
+    int         draw, split;
+
+
+    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;
+
+    /* short-cut the arc that crosses the current band */
+    if ( ( TRUNC( arc[0].y ) >= ras.max_ey &&
+           TRUNC( arc[1].y ) >= ras.max_ey &&
+           TRUNC( arc[2].y ) >= ras.max_ey ) ||
+         ( TRUNC( arc[0].y ) <  ras.min_ey &&
+           TRUNC( arc[1].y ) <  ras.min_ey &&
+           TRUNC( arc[2].y ) <  ras.min_ey ) )
+    {
+      ras.x = arc[0].x;
+      ras.y = arc[0].y;
+      return;
+    }
+
+    dx = FT_ABS( arc[2].x + arc[0].x - 2 * arc[1].x );
+    dy = FT_ABS( arc[2].y + arc[0].y - 2 * arc[1].y );
+    if ( dx < dy )
+      dx = dy;
+
+    /* We can calculate the number of necessary bisections because  */
+    /* each bisection predictably reduces deviation exactly 4-fold. */
+    /* Even 32-bit deviation would vanish after 16 bisections.      */
+    draw = 1;
+    while ( dx > ONE_PIXEL / 4 )
+    {
+      dx   >>= 2;
+      draw <<= 1;
+    }
+
+    /* We use decrement counter to count the total number of segments */
+    /* to draw starting from 2^level. Before each draw we split as    */
+    /* many times as there are trailing zeros in the counter.         */
+    do
+    {
+      split = 1;
+      while ( ( draw & split ) == 0 )
+      {
+        gray_split_conic( arc );
+        arc += 2;
+        split <<= 1;
+      }
+
+      gray_render_line( RAS_VAR_ arc[0].x, arc[0].y );
+      arc -= 2;
+
+    } while ( --draw );
+  }
+
+
+  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 )
+  {
+    FT_Vector   bez_stack[16 * 3 + 1];  /* enough to accommodate bisections */
+    FT_Vector*  arc = bez_stack;
+    TPos        dx, dy, dx_, dy_;
+    TPos        dx1, dy1, dx2, dy2;
+    TPos        L, s, s_limit;
+
+
+    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;
+
+    /* short-cut the arc that crosses the current band */
+    if ( ( TRUNC( arc[0].y ) >= ras.max_ey &&
+           TRUNC( arc[1].y ) >= ras.max_ey &&
+           TRUNC( arc[2].y ) >= ras.max_ey &&
+           TRUNC( arc[3].y ) >= ras.max_ey ) ||
+         ( TRUNC( arc[0].y ) <  ras.min_ey &&
+           TRUNC( arc[1].y ) <  ras.min_ey &&
+           TRUNC( arc[2].y ) <  ras.min_ey &&
+           TRUNC( arc[3].y ) <  ras.min_ey ) )
+    {
+      ras.x = arc[0].x;
+      ras.y = arc[0].y;
+      return;
+    }
+
+    for (;;)
+    {
+      /* Decide whether to split or draw. See `Rapid Termination          */
+      /* Evaluation for Recursive Subdivision of Bezier Curves' by Thomas */
+      /* F. Hain, at                                                      */
+      /* http://www.cis.southalabama.edu/~hain/general/Publications/Bezier/Camera-ready%20CISST02%202.pdf */
+
+      /* dx and dy are x and y components of the P0-P3 chord vector. */
+      dx = dx_ = arc[3].x - arc[0].x;
+      dy = dy_ = arc[3].y - arc[0].y;
+
+      L = FT_HYPOT( dx_, dy_ );
+
+      /* Avoid possible arithmetic overflow below by splitting. */
+      if ( L > 32767 )
+        goto Split;
+
+      /* Max deviation may be as much as (s/L) * 3/4 (if Hain's v = 1). */
+      s_limit = L * (TPos)( ONE_PIXEL / 6 );
+
+      /* s is L * the perpendicular distance from P1 to the line P0-P3. */
+      dx1 = arc[1].x - arc[0].x;
+      dy1 = arc[1].y - arc[0].y;
+      s = FT_ABS( SUB_LONG( MUL_LONG( dy, dx1 ), MUL_LONG( dx, dy1 ) ) );
+
+      if ( s > s_limit )
+        goto Split;
+
+      /* s is L * the perpendicular distance from P2 to the line P0-P3. */
+      dx2 = arc[2].x - arc[0].x;
+      dy2 = arc[2].y - arc[0].y;
+      s = FT_ABS( SUB_LONG( MUL_LONG( dy, dx2 ), MUL_LONG( dx, dy2 ) ) );
+
+      if ( s > s_limit )
+        goto Split;
+
+      /* Split super curvy segments where the off points are so far
+         from the chord that the angles P0-P1-P3 or P0-P2-P3 become
+         acute as detected by appropriate dot products. */
+      if ( dx1 * ( dx1 - dx ) + dy1 * ( dy1 - dy ) > 0 ||
+           dx2 * ( dx2 - dx ) + dy2 * ( dy2 - dy ) > 0 )
+        goto Split;
+
+      gray_render_line( RAS_VAR_ arc[0].x, arc[0].y );
+
+      if ( arc == bez_stack )
+        return;
+
+      arc -= 3;
+      continue;
+
+    Split:
+      gray_split_cubic( arc );
+      arc += 3;
+    }
+  }
+
+
+  static int
+  gray_move_to( const FT_Vector*  to,
+                gray_PWorker      worker )
+  {
+    TPos  x, y;
+
+
+    /* start to a new position */
+    x = UPSCALE( to->x );
+    y = UPSCALE( to->y );
+
+    gray_set_cell( RAS_VAR_ TRUNC( x ), TRUNC( y ) );
+
+    ras.x = x;
+    ras.y = y;
+    return 0;
+  }
+
+
+  static int
+  gray_line_to( const FT_Vector*  to,
+                gray_PWorker      worker )
+  {
+    gray_render_line( RAS_VAR_ UPSCALE( to->x ), UPSCALE( to->y ) );
+    return 0;
+  }
+
+
+  static int
+  gray_conic_to( const FT_Vector*  control,
+                 const FT_Vector*  to,
+                 gray_PWorker      worker )
+  {
+    gray_render_conic( RAS_VAR_ control, to );
+    return 0;
+  }
+
+
+  static int
+  gray_cubic_to( const FT_Vector*  control1,
+                 const FT_Vector*  control2,
+                 const FT_Vector*  to,
+                 gray_PWorker      worker )
+  {
+    gray_render_cubic( RAS_VAR_ control1, control2, to );
+    return 0;
+  }
+
+
+  static void
+  gray_hline( RAS_ARG_ TCoord  x,
+                       TCoord  y,
+                       TArea   coverage,
+                       TCoord  acount )
+  {
+    /* scale the coverage from 0..(ONE_PIXEL*ONE_PIXEL*2) to 0..256  */
+    coverage >>= PIXEL_BITS * 2 + 1 - 8;
+    if ( coverage < 0 )
+      coverage = -coverage - 1;
+
+    /* compute the line's coverage depending on the outline fill rule */
+    if ( ras.outline.flags & FT_OUTLINE_EVEN_ODD_FILL )
+    {
+      coverage &= 511;
+
+      if ( coverage >= 256 )
+        coverage = 511 - coverage;
+    }
+    else
+    {
+      /* normal non-zero winding rule */
+      if ( coverage >= 256 )
+        coverage = 255;
+    }
+
+    if ( ras.render_span )  /* for FT_RASTER_FLAG_DIRECT only */
+    {
+      FT_Span  span;
+
+
+      span.x        = (short)x;
+      span.len      = (unsigned short)acount;
+      span.coverage = (unsigned char)coverage;
+
+      ras.render_span( y, 1, &span, ras.render_span_data );
+    }
+    else
+    {
+      unsigned char*  q = ras.target.origin - ras.target.pitch * y + x;
+      unsigned char   c = (unsigned char)coverage;
+
+
+      /* For small-spans it is faster to do it by ourselves than
+       * calling `memset'.  This is mainly due to the cost of the
+       * function call.
+       */
+      switch ( acount )
+      {
+      case 7: *q++ = c;
+      case 6: *q++ = c;
+      case 5: *q++ = c;
+      case 4: *q++ = c;
+      case 3: *q++ = c;
+      case 2: *q++ = c;
+      case 1: *q   = c;
+      case 0: break;
+      default:
+        FT_MEM_SET( q, c, acount );
+      }
+    }
+  }
+
+
+  static void
+  gray_sweep( RAS_ARG )
+  {
+    int  y;
+
+
+    for ( y = ras.min_ey; y < ras.max_ey; y++ )
+    {
+      PCell   cell  = ras.ycells[y - ras.min_ey];
+      TCoord  x     = ras.min_ex;
+      TArea   cover = 0;
+      TArea   area;
+
+
+      for ( ; cell != NULL; cell = cell->next )
+      {
+        if ( cover != 0 && cell->x > x )
+          gray_hline( RAS_VAR_ x, y, cover, cell->x - x );
+
+        cover += (TArea)cell->cover * ( ONE_PIXEL * 2 );
+        area   = cover - cell->area;
+
+        if ( area != 0 && cell->x >= ras.min_ex )
+          gray_hline( RAS_VAR_ cell->x, y, area, 1 );
+
+        x = cell->x + 1;
+      }
+
+      if ( cover != 0 )
+        gray_hline( RAS_VAR_ x, y, cover, ras.max_ex - x );
+    }
+  }
+
+
+  FT_DEFINE_OUTLINE_FUNCS(
+    func_interface,
+
+    (FT_Outline_MoveTo_Func) gray_move_to,   /* move_to  */
+    (FT_Outline_LineTo_Func) gray_line_to,   /* line_to  */
+    (FT_Outline_ConicTo_Func)gray_conic_to,  /* conic_to */
+    (FT_Outline_CubicTo_Func)gray_cubic_to,  /* cubic_to */
+
+    0,                                       /* shift    */
+    0                                        /* delta    */
+  )
+
+
+  static int
+  gray_convert_glyph_inner( RAS_ARG )
+  {
+
+    volatile int  error = 0;
+
+    if ( ft_setjmp( ras.jump_buffer ) == 0 )
+    {
+      error = FT_Outline_Decompose( &ras.outline, &func_interface, &ras );
+      if ( !ras.invalid )
+        gray_record_cell( RAS_VAR );
+
+      FT_TRACE7(( "band [%d..%d]: %d cell%s\n",
+                  ras.min_ey,
+                  ras.max_ey,
+                  ras.num_cells,
+                  ras.num_cells == 1 ? "" : "s" ));
+    }
+    else
+    {
+      error = FT_THROW( Memory_Overflow );
+
+      FT_TRACE7(( "band [%d..%d]: to be bisected\n",
+                  ras.min_ey, ras.max_ey ));
+    }
+
+    return error;
+  }
+
+
+  static int
+  gray_convert_glyph( RAS_ARG )
+  {
+    const TCoord  yMin = ras.min_ey;
+    const TCoord  yMax = ras.max_ey;
+    const TCoord  xMin = ras.min_ex;
+    const TCoord  xMax = ras.max_ex;
+
+    TCell    buffer[FT_MAX_GRAY_POOL];
+    size_t   height = (size_t)( yMax - yMin );
+    size_t   n = FT_MAX_GRAY_POOL / 8;
+    TCoord   y;
+    TCoord   bands[32];  /* enough to accommodate bisections */
+    TCoord*  band;
+
+
+    /* set up vertical bands */
+    if ( height > n )
+    {
+      /* two divisions rounded up */
+      n       = ( height + n - 1 ) / n;
+      height  = ( height + n - 1 ) / n;
+    }
+
+    /* memory management */
+    n = ( height * sizeof ( PCell ) + sizeof ( TCell ) - 1 ) / sizeof ( TCell );
+
+    ras.cells     = buffer + n;
+    ras.max_cells = (FT_PtrDist)( FT_MAX_GRAY_POOL - n );
+    ras.ycells    = (PCell*)buffer;
+
+    for ( y = yMin; y < yMax; )
+    {
+      ras.min_ey = y;
+      y         += height;
+      ras.max_ey = FT_MIN( y, yMax );
+
+      band    = bands;
+      band[1] = xMin;
+      band[0] = xMax;
+
+      do
+      {
+        TCoord  width = band[0] - band[1];
+        int     error;
+
+
+        FT_MEM_ZERO( ras.ycells, height * sizeof ( PCell ) );
+
+        ras.num_cells = 0;
+        ras.invalid   = 1;
+        ras.min_ex    = band[1];
+        ras.max_ex    = band[0];
+
+        error = gray_convert_glyph_inner( RAS_VAR );
+
+        if ( !error )
+        {
+          gray_sweep( RAS_VAR );
+          band--;
+          continue;
+        }
+        else if ( error != ErrRaster_Memory_Overflow )
+          return 1;
+
+        /* render pool overflow; we will reduce the render band by half */
+        width >>= 1;
+
+        /* this should never happen even with tiny rendering pool */
+        if ( width == 0 )
+        {
+          FT_TRACE7(( "gray_convert_glyph: rotten glyph\n" ));
+          return 1;
+        }
+
+        band++;
+        band[1]  = band[0];
+        band[0] += width;
+      } while ( band >= bands );
+    }
+
+    return 0;
+  }
+
+
+  static int
+  gray_raster_render( const FT_Raster_Params*  params )
+  {
+    const FT_Outline*  outline    = (const FT_Outline*)params->source;
+    const FT_Bitmap*   target_map = params->target;
+    FT_BBox            cbox, clip;
+
+#ifndef FT_STATIC_RASTER
+    gray_TWorker  worker[1];
+#endif
+
+    /* this version does not support monochrome rendering */
+    if ( !( params->flags & FT_RASTER_FLAG_AA ) )
+      return FT_THROW( Invalid_Mode );
+
+    if ( !outline )
+      return FT_THROW( Invalid_Outline );
+
+    /* return immediately if the outline is empty */
+    if ( outline->n_points == 0 || outline->n_contours <= 0 )
+      return 0;
+
+    if ( !outline->contours || !outline->points )
+      return FT_THROW( Invalid_Outline );
+
+    if ( outline->n_points !=
+           outline->contours[outline->n_contours - 1] + 1 )
+      return FT_THROW( Invalid_Outline );
+
+    ras.outline = *outline;
+
+    if ( params->flags & FT_RASTER_FLAG_DIRECT )
+    {
+      if ( !params->gray_spans )
+        return 0;
+
+      ras.render_span      = (FT_Raster_Span_Func)params->gray_spans;
+      ras.render_span_data = params->user;
+    }
+    else
+    {
+      /* if direct mode is not set, we must have a target bitmap */
+      if ( !target_map )
+        return FT_THROW( Invalid_Argument );
+
+      /* nothing to do */
+      if ( !target_map->width || !target_map->rows )
+        return 0;
+
+      if ( !target_map->buffer )
+        return FT_THROW( Invalid_Argument );
+
+      if ( target_map->pitch < 0 )
+        ras.target.origin = target_map->buffer;
+      else
+        ras.target.origin = target_map->buffer
+              + ( target_map->rows - 1 ) * (unsigned int)target_map->pitch;
+
+      ras.target.pitch = target_map->pitch;
+
+      ras.render_span      = (FT_Raster_Span_Func)NULL;
+      ras.render_span_data = NULL;
+    }
+
+    FT_Outline_Get_CBox( outline, &cbox );
+
+    /* reject too large outline coordinates */
+    if ( cbox.xMin < -0x1000000L || cbox.xMax > 0x1000000L ||
+         cbox.yMin < -0x1000000L || cbox.yMax > 0x1000000L )
+      return FT_THROW( Invalid_Outline );
+
+    /* truncate the bounding box to integer pixels */
+    cbox.xMin = cbox.xMin >> 6;
+    cbox.yMin = cbox.yMin >> 6;
+    cbox.xMax = ( cbox.xMax + 63 ) >> 6;
+    cbox.yMax = ( cbox.yMax + 63 ) >> 6;
+
+    /* compute clipping box */
+    if ( !( params->flags & FT_RASTER_FLAG_DIRECT ) )
+    {
+      /* compute clip box from target pixmap */
+      clip.xMin = 0;
+      clip.yMin = 0;
+      clip.xMax = (FT_Pos)target_map->width;
+      clip.yMax = (FT_Pos)target_map->rows;
+    }
+    else if ( params->flags & FT_RASTER_FLAG_CLIP )
+      clip = params->clip_box;
+    else
+    {
+      clip.xMin = -32768L;
+      clip.yMin = -32768L;
+      clip.xMax =  32767L;
+      clip.yMax =  32767L;
+    }
+
+    /* clip to target bitmap, exit if nothing to do */
+    ras.min_ex = FT_MAX( cbox.xMin, clip.xMin );
+    ras.min_ey = FT_MAX( cbox.yMin, clip.yMin );
+    ras.max_ex = FT_MIN( cbox.xMax, clip.xMax );
+    ras.max_ey = FT_MIN( cbox.yMax, clip.yMax );
+
+    if ( ras.max_ex <= ras.min_ex || ras.max_ey <= ras.min_ey )
+      return 0;
+
+    return gray_convert_glyph( RAS_VAR );
+  }
+
+
+  FT_DEFINE_RASTER_FUNCS(
+    ft_grays_raster,
+
+    (FT_Raster_Render_Func)  gray_raster_render    /* raster_render   */
+  )
+
+
+/* END */
+
+
+/* Local Variables: */
+/* coding: utf-8    */
+/* End:             */