/***************************************************************************/
/*                                                                         */
/*  ftgrays.c                                                              */
/*                                                                         */
/*    A new `perfect' anti-aliasing renderer (body).                       */
/*                                                                         */
/*  Copyright 2000-2003, 2005-2014 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 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.                                                           */
/*                                                                       */
/*************************************************************************/

#include "v_ft_raster.h"
#include "v_ft_math.h"

/* Auxiliary macros for token concatenation. */
#define SW_FT_ERR_XCAT(x, y) x##y
#define SW_FT_ERR_CAT(x, y) SW_FT_ERR_XCAT(x, y)

#define SW_FT_BEGIN_STMNT do {
#define SW_FT_END_STMNT \
    }                   \
    while (0)

#include <limits.h>
#include <setjmp.h>
#include <stddef.h>
#include <string.h>
#define SW_FT_UINT_MAX UINT_MAX
#define SW_FT_INT_MAX INT_MAX
#define SW_FT_ULONG_MAX ULONG_MAX
#define SW_FT_CHAR_BIT CHAR_BIT

#define ft_memset memset

#define ft_setjmp setjmp
#define ft_longjmp longjmp
#define ft_jmp_buf jmp_buf

typedef ptrdiff_t SW_FT_PtrDist;

#define ErrRaster_Invalid_Mode -2
#define ErrRaster_Invalid_Outline -1
#define ErrRaster_Invalid_Argument -3
#define ErrRaster_Memory_Overflow -4

#define SW_FT_BEGIN_HEADER
#define SW_FT_END_HEADER

/* This macro is used to indicate that a function parameter is unused. */
/* Its purpose is simply to reduce compiler warnings.  Note also that  */
/* simply defining it as `(void)x' doesn't avoid warnings with certain */
/* ANSI compilers (e.g. LCC).                                          */
#define SW_FT_UNUSED(x) (x) = (x)

#define SW_FT_THROW(e) SW_FT_ERR_CAT(ErrRaster_, e)

/* The size in bytes of the render pool used by the scan-line converter  */
/* to do all of its work.                                                */
#define SW_FT_RENDER_POOL_SIZE 16384L

typedef int (*SW_FT_Outline_MoveToFunc)(const SW_FT_Vector* to, void* user);

#define SW_FT_Outline_MoveTo_Func SW_FT_Outline_MoveToFunc

typedef int (*SW_FT_Outline_LineToFunc)(const SW_FT_Vector* to, void* user);

#define SW_FT_Outline_LineTo_Func SW_FT_Outline_LineToFunc

typedef int (*SW_FT_Outline_ConicToFunc)(const SW_FT_Vector* control,
                                         const SW_FT_Vector* to, void* user);

#define SW_FT_Outline_ConicTo_Func SW_FT_Outline_ConicToFunc

typedef int (*SW_FT_Outline_CubicToFunc)(const SW_FT_Vector* control1,
                                         const SW_FT_Vector* control2,
                                         const SW_FT_Vector* to, void* user);

#define SW_FT_Outline_CubicTo_Func SW_FT_Outline_CubicToFunc

typedef struct SW_FT_Outline_Funcs_ {
    SW_FT_Outline_MoveToFunc  move_to;
    SW_FT_Outline_LineToFunc  line_to;
    SW_FT_Outline_ConicToFunc conic_to;
    SW_FT_Outline_CubicToFunc cubic_to;

    int       shift;
    SW_FT_Pos delta;

} SW_FT_Outline_Funcs;

#define SW_FT_DEFINE_OUTLINE_FUNCS(class_, move_to_, line_to_, conic_to_,      \
                                   cubic_to_, shift_, delta_)                  \
    static const SW_FT_Outline_Funcs class_ = {move_to_,  line_to_, conic_to_, \
                                               cubic_to_, shift_,   delta_};

#define SW_FT_DEFINE_RASTER_FUNCS(class_, raster_new_, raster_reset_, \
                                  raster_render_, raster_done_)       \
    const SW_FT_Raster_Funcs class_ = {raster_new_, raster_reset_,    \
                                       raster_render_, raster_done_};

#ifndef SW_FT_MEM_SET
#define SW_FT_MEM_SET(d, s, c) ft_memset(d, s, c)
#endif

#ifndef SW_FT_MEM_ZERO
#define SW_FT_MEM_ZERO(dest, count) SW_FT_MEM_SET(dest, 0, count)
#endif

/* as usual, for the speed hungry :-) */

#undef RAS_ARG
#undef RAS_ARG_
#undef RAS_VAR
#undef RAS_VAR_

#ifndef SW_FT_STATIC_RASTER

#define RAS_ARG gray_PWorker worker
#define RAS_ARG_ gray_PWorker worker,

#define RAS_VAR worker
#define RAS_VAR_ worker,

#else /* SW_FT_STATIC_RASTER */

#define RAS_ARG  /* empty */
#define RAS_ARG_ /* empty */
#define RAS_VAR  /* empty */
#define RAS_VAR_ /* empty */

#endif /* SW_FT_STATIC_RASTER */

/* must be at least 6 bits! */
#define PIXEL_BITS 8

#undef FLOOR
#undef CEILING
#undef TRUNC
#undef SCALED

#define ONE_PIXEL (1L << PIXEL_BITS)
#define PIXEL_MASK (-1L << PIXEL_BITS)
#define TRUNC(x) ((TCoord)((x) >> PIXEL_BITS))
#define SUBPIXELS(x) ((TPos)(x) << PIXEL_BITS)
#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) << (PIXEL_BITS - 6))
#define DOWNSCALE(x) ((x) >> (PIXEL_BITS - 6))
#else
#define UPSCALE(x) ((x) >> (6 - PIXEL_BITS))
#define DOWNSCALE(x) ((x) << (6 - 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.                                 */
#define SW_FT_DIV_MOD(type, dividend, divisor, quotient, remainder) \
    SW_FT_BEGIN_STMNT(quotient) = (type)((dividend) / (divisor));   \
    (remainder) = (type)((dividend) % (divisor));                   \
    if ((remainder) < 0) {                                          \
        (quotient)--;                                               \
        (remainder) += (type)(divisor);                             \
    }                                                               \
    SW_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                     */
/*                                                                   */
/*  http://gcc.gnu.org/bugzilla/show_bug.cgi?id=43721                */
#undef SW_FT_DIV_MOD
#define SW_FT_DIV_MOD(type, dividend, divisor, quotient, remainder) \
    SW_FT_BEGIN_STMNT(quotient) = (type)((dividend) / (divisor));   \
    (remainder) = (type)((dividend) - (quotient) * (divisor));      \
    if ((remainder) < 0) {                                          \
        (quotient)--;                                               \
        (remainder) += (type)(divisor);                             \
    }                                                               \
    SW_FT_END_STMNT
#endif /* __arm__ */

/* These macros speed up repetitive divisions by replacing them */
/* with multiplications and right shifts.                       */
#define SW_FT_UDIVPREP(b) \
    long b##_r = (long)(SW_FT_ULONG_MAX >> PIXEL_BITS) / (b)
#define SW_FT_UDIV(a, b)                              \
    (((unsigned long)(a) * (unsigned long)(b##_r)) >> \
     (sizeof(long) * SW_FT_CHAR_BIT - PIXEL_BITS))

/*************************************************************************/
/*                                                                       */
/*   TYPE DEFINITIONS                                                    */
/*                                                                       */

/* don't change the following types to SW_FT_Int or SW_FT_Pos, since we might */
/* need to define them to "float" or "double" when experimenting with   */
/* new algorithms                                                       */

typedef long TCoord; /* integer scanline/pixel coordinate */
typedef long TPos;   /* sub-pixel coordinate              */

/* determine the type used to store cell areas.  This normally takes at */
/* least PIXEL_BITS*2 + 1 bits.  On 16-bit systems, we need to use      */
/* `long' instead of `int', otherwise bad things happen                 */

#if PIXEL_BITS <= 7

typedef int TArea;

#else /* PIXEL_BITS >= 8 */

/* approximately determine the size of integers using an ANSI-C header */
#if SW_FT_UINT_MAX == 0xFFFFU
typedef long        TArea;
#else
typedef int TArea;
#endif

#endif /* PIXEL_BITS >= 8 */

/* maximum number of gray spans in a call to the span callback */
#define SW_FT_MAX_GRAY_SPANS 256

typedef struct TCell_* PCell;

typedef struct TCell_ {
    TPos   x;     /* same with gray_TWorker.ex    */
    TCoord cover; /* same with gray_TWorker.cover */
    TArea  area;
    PCell  next;

} TCell;

#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_ {
    TCoord ex, ey;
    TPos   min_ex, max_ex;
    TPos   min_ey, max_ey;
    TPos   count_ex, count_ey;

    TArea  area;
    TCoord cover;
    int    invalid;

    PCell         cells;
    SW_FT_PtrDist max_cells;
    SW_FT_PtrDist num_cells;

    TPos x, y;

    SW_FT_Vector bez_stack[32 * 3 + 1];
    int          lev_stack[32];

    SW_FT_Outline outline;
    SW_FT_BBox    clip_box;

    int           bound_left;
    int           bound_top;
    int           bound_right;
    int           bound_bottom;

    SW_FT_Span gray_spans[SW_FT_MAX_GRAY_SPANS];
    int        num_gray_spans;

    SW_FT_Raster_Span_Func render_span;
    void*                  render_span_data;

    int band_size;
    int band_shoot;

    ft_jmp_buf jump_buffer;

    void* buffer;
    long  buffer_size;

    PCell* ycells;
    TPos   ycount;

} gray_TWorker, *gray_PWorker;

#if defined(_MSC_VER)
#pragma warning(pop)
#endif

#ifndef SW_FT_STATIC_RASTER
#define ras (*worker)
#else
static gray_TWorker ras;
#endif

typedef struct gray_TRaster_ {
    void* memory;

} gray_TRaster, *gray_PRaster;

/*************************************************************************/
/*                                                                       */
/* Initialize the cells table.                                           */
/*                                                                       */
static void gray_init_cells(RAS_ARG_ void* buffer, long byte_size)
{
    ras.buffer = buffer;
    ras.buffer_size = byte_size;

    ras.ycells = (PCell*)buffer;
    ras.cells = NULL;
    ras.max_cells = 0;
    ras.num_cells = 0;
    ras.area = 0;
    ras.cover = 0;
    ras.invalid = 1;

    ras.bound_left = INT_MAX;
    ras.bound_top = INT_MAX;
    ras.bound_right = INT_MIN;
    ras.bound_bottom = INT_MIN;
}

/*************************************************************************/
/*                                                                       */
/* Compute the outline bounding box.                                     */
/*                                                                       */
static void gray_compute_cbox(RAS_ARG)
{
    SW_FT_Outline* outline = &ras.outline;
    SW_FT_Vector*  vec = outline->points;
    SW_FT_Vector*  limit = vec + outline->n_points;

    if (outline->n_points <= 0) {
        ras.min_ex = ras.max_ex = 0;
        ras.min_ey = ras.max_ey = 0;
        return;
    }

    ras.min_ex = ras.max_ex = vec->x;
    ras.min_ey = ras.max_ey = vec->y;

    vec++;

    for (; vec < limit; vec++) {
        TPos x = vec->x;
        TPos y = vec->y;

        if (x < ras.min_ex) ras.min_ex = x;
        if (x > ras.max_ex) ras.max_ex = x;
        if (y < ras.min_ey) ras.min_ey = y;
        if (y > ras.max_ey) ras.max_ey = y;
    }

    /* truncate the bounding box to integer pixels */
    ras.min_ex = ras.min_ex >> 6;
    ras.min_ey = ras.min_ey >> 6;
    ras.max_ex = (ras.max_ex + 63) >> 6;
    ras.max_ey = (ras.max_ey + 63) >> 6;
}

/*************************************************************************/
/*                                                                       */
/* Record the current cell in the table.                                 */
/*                                                                       */
static PCell gray_find_cell(RAS_ARG)
{
    PCell *pcell, cell;
    TPos   x = ras.ex;

    if (x > ras.count_ex) x = ras.count_ex;

    pcell = &ras.ycells[ras.ey];
    for (;;) {
        cell = *pcell;
        if (cell == NULL || cell->x > x) break;

        if (cell->x == x) goto Exit;

        pcell = &cell->next;
    }

    if (ras.num_cells >= ras.max_cells) ft_longjmp(ras.jump_buffer, 1);

    cell = ras.cells + ras.num_cells++;
    cell->x = x;
    cell->area = 0;
    cell->cover = 0;

    cell->next = *pcell;
    *pcell = cell;

Exit:
    return cell;
}

static void gray_record_cell(RAS_ARG)
{
    if (ras.area | ras.cover) {
        PCell cell = gray_find_cell(RAS_VAR);

        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.                 */

    /* All cells that are on the left of the clipping region go to the */
    /* min_ex - 1 horizontal position.                                 */
    ey -= ras.min_ey;

    if (ex > ras.max_ex) ex = ras.max_ex;

    ex -= ras.min_ex;
    if (ex < 0) ex = -1;

    /* are we moving to a different cell ? */
    if (ex != ras.ex || ey != ras.ey) {
        /* record the current one if it is valid */
        if (!ras.invalid) gray_record_cell(RAS_VAR);

        ras.area = 0;
        ras.cover = 0;
        ras.ex = ex;
        ras.ey = ey;
    }

    ras.invalid =
        ((unsigned)ey >= (unsigned)ras.count_ey || ex >= ras.count_ex);
}

/*************************************************************************/
/*                                                                       */
/* Start a new contour at a given cell.                                  */
/*                                                                       */
static void gray_start_cell(RAS_ARG_ TCoord ex, TCoord ey)
{
    if (ex > ras.max_ex) ex = (TCoord)(ras.max_ex);

    if (ex < ras.min_ex) ex = (TCoord)(ras.min_ex - 1);

    ras.area = 0;
    ras.cover = 0;
    ras.ex = ex - ras.min_ex;
    ras.ey = ey - ras.min_ey;
    ras.invalid = 0;

    gray_set_cell(RAS_VAR_ ex, ey);
}

/*************************************************************************/
/*                                                                       */
/* 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;

    ex1 = TRUNC(ras.x);
    ex2 = TRUNC(to_x);
    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;

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

    fx1 = ras.x - SUBPIXELS(ex1);
    fy1 = ras.y - SUBPIXELS(ey1);

    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 */
    {
        TArea prod = dx * fy1 - dy * fx1;
        SW_FT_UDIVPREP(dx);
        SW_FT_UDIVPREP(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)SW_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)SW_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)SW_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)SW_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;
}

static void gray_split_conic(SW_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 SW_FT_Vector* control,
                              const SW_FT_Vector*          to)
{
    TPos          dx, dy;
    TPos          min, max, y;
    int           top, level;
    int*          levels;
    SW_FT_Vector* arc;

    levels = ras.lev_stack;

    arc = ras.bez_stack;
    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;
    top = 0;

    dx = SW_FT_ABS(arc[2].x + arc[0].x - 2 * arc[1].x);
    dy = SW_FT_ABS(arc[2].y + arc[0].y - 2 * arc[1].y);
    if (dx < dy) dx = dy;

    if (dx < ONE_PIXEL / 4) goto Draw;

    /* short-cut the arc that crosses the current band */
    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;

    level = 0;
    do {
        dx >>= 2;
        level++;
    } while (dx > ONE_PIXEL / 4);

    levels[0] = level;

    do {
        level = levels[top];
        if (level > 0) {
            gray_split_conic(arc);
            arc += 2;
            top++;
            levels[top] = levels[top - 1] = level - 1;
            continue;
        }

    Draw:
        gray_render_line(RAS_VAR_ arc[0].x, arc[0].y);
        top--;
        arc -= 2;

    } while (top >= 0);
}

static void gray_split_cubic(SW_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 SW_FT_Vector* control1,
                              const SW_FT_Vector*          control2,
                              const SW_FT_Vector*          to)
{
    SW_FT_Vector* arc;
    TPos          min, max, y;

    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;

    /* Short-cut the arc that crosses the current band. */
    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) < ras.min_ey) goto Draw;

    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
         */

        {
            TPos dx, dy, dx_, dy_;
            TPos dx1, dy1, dx2, dy2;
            TPos L, s, s_limit;

            /* 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 = SW_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 = SW_FT_ABS(dy * dx1 - 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 = SW_FT_ABS(dy * dx2 - 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;

            /* No reason to split. */
            goto Draw;
        }

    Split:
        gray_split_cubic(arc);
        arc += 3;
        continue;

    Draw:
        gray_render_line(RAS_VAR_ arc[0].x, arc[0].y);

        if (arc == ras.bez_stack) return;

        arc -= 3;
    }
}

static int gray_move_to(const SW_FT_Vector* to, gray_PWorker worker)
{
    TPos x, y;

    /* record current cell, if any */
    if (!ras.invalid) gray_record_cell(RAS_VAR);

    /* start to a new position */
    x = UPSCALE(to->x);
    y = UPSCALE(to->y);

    gray_start_cell(RAS_VAR_ TRUNC(x), TRUNC(y));

    worker->x = x;
    worker->y = y;
    return 0;
}

static int gray_line_to(const SW_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 SW_FT_Vector* control, const SW_FT_Vector* to,
                         gray_PWorker worker)
{
    gray_render_conic(RAS_VAR_ control, to);
    return 0;
}

static int gray_cubic_to(const SW_FT_Vector* control1,
                         const SW_FT_Vector* control2, const SW_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, TPos area, TCoord acount)
{
    int coverage;

    /* compute the coverage line's coverage, depending on the    */
    /* outline fill rule                                         */
    /*                                                           */
    /* the coverage percentage is area/(PIXEL_BITS*PIXEL_BITS*2) */
    /*                                                           */
    coverage = (int)(area >> (PIXEL_BITS * 2 + 1 - 8));
    /* use range 0..256 */
    if (coverage < 0) coverage = -coverage;

    if (ras.outline.flags & SW_FT_OUTLINE_EVEN_ODD_FILL) {
        coverage &= 511;

        if (coverage > 256)
            coverage = 512 - coverage;
        else if (coverage == 256)
            coverage = 255;
    } else {
        /* normal non-zero winding rule */
        if (coverage >= 256) coverage = 255;
    }

    y += (TCoord)ras.min_ey;
    x += (TCoord)ras.min_ex;

    /* SW_FT_Span.x is a 16-bit short, so limit our coordinates appropriately */
    if (x >= 32767) x = 32767;

    /* SW_FT_Span.y is an integer, so limit our coordinates appropriately */
    if (y >= SW_FT_INT_MAX) y = SW_FT_INT_MAX;

    if (coverage) {
        SW_FT_Span* span;
        int         count;

        // update bounding box.
        if (x < ras.bound_left) ras.bound_left = x;
        if (y < ras.bound_top) ras.bound_top = y;
        if (y > ras.bound_bottom) ras.bound_bottom = y;
        if (x + acount > ras.bound_right) ras.bound_right = x + acount;

        /* see whether we can add this span to the current list */
        count = ras.num_gray_spans;
        span = ras.gray_spans + count - 1;
        if (count > 0 && span->y == y && (int)span->x + span->len == (int)x &&
            span->coverage == coverage) {
            span->len = (unsigned short)(span->len + acount);
            return;
        }

        if (count >= SW_FT_MAX_GRAY_SPANS) {
            if (ras.render_span && count > 0)
                ras.render_span(count, ras.gray_spans, ras.render_span_data);

#ifdef DEBUG_GRAYS

            if (1) {
                int n;

                fprintf(stderr, "count = %3d ", count);
                span = ras.gray_spans;
                for (n = 0; n < count; n++, span++)
                    fprintf(stderr, "[%d , %d..%d] : %d ", span->y, span->x,
                            span->x + span->len - 1, span->coverage);
                fprintf(stderr, "\n");
            }

#endif /* DEBUG_GRAYS */

            ras.num_gray_spans = 0;

            span = ras.gray_spans;
        } else
            span++;

        /* add a gray span to the current list */
        span->x = (short)x;
        span->y = (short)y;
        span->len = (unsigned short)acount;
        span->coverage = (unsigned char)coverage;

        ras.num_gray_spans++;
    }
}

static void gray_sweep(RAS_ARG)
{
    int yindex;

    if (ras.num_cells == 0) return;

    ras.num_gray_spans = 0;

    for (yindex = 0; yindex < ras.ycount; yindex++) {
        PCell  cell = ras.ycells[yindex];
        TCoord cover = 0;
        TCoord x = 0;

        for (; cell != NULL; cell = cell->next) {
            TPos area;

            if (cell->x > x && cover != 0)
                gray_hline(RAS_VAR_ x, yindex, cover * (ONE_PIXEL * 2),
                           cell->x - x);

            cover += cell->cover;
            area = cover * (ONE_PIXEL * 2) - cell->area;

            if (area != 0 && cell->x >= 0)
                gray_hline(RAS_VAR_ cell->x, yindex, area, 1);

            x = cell->x + 1;
        }

        if (cover != 0)
            gray_hline(RAS_VAR_ x, yindex, cover * (ONE_PIXEL * 2),
                       ras.count_ex - x);
    }

    if (ras.render_span && ras.num_gray_spans > 0)
        ras.render_span(ras.num_gray_spans, ras.gray_spans,
                        ras.render_span_data);
}

/*************************************************************************/
/*                                                                       */
/*  The following function should only compile in stand-alone mode,      */
/*  i.e., when building this component without the rest of FreeType.     */
/*                                                                       */
/*************************************************************************/

/*************************************************************************/
/*                                                                       */
/* <Function>                                                            */
/*    SW_FT_Outline_Decompose                                               */
/*                                                                       */
/* <Description>                                                         */
/*    Walk over an outline's structure to decompose it into individual   */
/*    segments and Bézier arcs.  This function is also able to emit      */
/*    `move to' and `close to' operations to indicate the start and end  */
/*    of new contours in the outline.                                    */
/*                                                                       */
/* <Input>                                                               */
/*    outline        :: A pointer to the source target.                  */
/*                                                                       */
/*    func_interface :: A table of `emitters', i.e., function pointers   */
/*                      called during decomposition to indicate path     */
/*                      operations.                                      */
/*                                                                       */
/* <InOut>                                                               */
/*    user           :: A typeless pointer which is passed to each       */
/*                      emitter during the decomposition.  It can be     */
/*                      used to store the state during the               */
/*                      decomposition.                                   */
/*                                                                       */
/* <Return>                                                              */
/*    Error code.  0 means success.                                      */
/*                                                                       */
static int SW_FT_Outline_Decompose(const SW_FT_Outline*       outline,
                                   const SW_FT_Outline_Funcs* func_interface,
                                   void*                      user)
{
#undef SCALED
#define SCALED(x) (((x) << shift) - delta)

    SW_FT_Vector v_last;
    SW_FT_Vector v_control;
    SW_FT_Vector v_start;

    SW_FT_Vector* point;
    SW_FT_Vector* limit;
    char*         tags;

    int error;

    int  n;     /* index of contour in outline     */
    int  first; /* index of first point in contour */
    char tag;   /* current point's state           */

    int  shift;
    TPos delta;

    if (!outline || !func_interface) return SW_FT_THROW(Invalid_Argument);

    shift = func_interface->shift;
    delta = func_interface->delta;
    first = 0;

    for (n = 0; n < outline->n_contours; n++) {
        int last; /* index of last point in contour */

        last = outline->contours[n];
        if (last < 0) goto Invalid_Outline;
        limit = outline->points + last;

        v_start = outline->points[first];
        v_start.x = SCALED(v_start.x);
        v_start.y = SCALED(v_start.y);

        v_last = outline->points[last];
        v_last.x = SCALED(v_last.x);
        v_last.y = SCALED(v_last.y);

        v_control = v_start;

        point = outline->points + first;
        tags = outline->tags + first;
        tag = SW_FT_CURVE_TAG(tags[0]);

        /* A contour cannot start with a cubic control point! */
        if (tag == SW_FT_CURVE_TAG_CUBIC) goto Invalid_Outline;

        /* check first point to determine origin */
        if (tag == SW_FT_CURVE_TAG_CONIC) {
            /* first point is conic control.  Yes, this happens. */
            if (SW_FT_CURVE_TAG(outline->tags[last]) == SW_FT_CURVE_TAG_ON) {
                /* start at last point if it is on the curve */
                v_start = v_last;
                limit--;
            } else {
                /* if both first and last points are conic,         */
                /* start at their middle and record its position    */
                /* for closure                                      */
                v_start.x = (v_start.x + v_last.x) / 2;
                v_start.y = (v_start.y + v_last.y) / 2;
            }
            point--;
            tags--;
        }

        error = func_interface->move_to(&v_start, user);
        if (error) goto Exit;

        while (point < limit) {
            point++;
            tags++;

            tag = SW_FT_CURVE_TAG(tags[0]);
            switch (tag) {
            case SW_FT_CURVE_TAG_ON: /* emit a single line_to */
            {
                SW_FT_Vector vec;

                vec.x = SCALED(point->x);
                vec.y = SCALED(point->y);

                error = func_interface->line_to(&vec, user);
                if (error) goto Exit;
                continue;
            }

            case SW_FT_CURVE_TAG_CONIC: /* consume conic arcs */
                v_control.x = SCALED(point->x);
                v_control.y = SCALED(point->y);

            Do_Conic:
                if (point < limit) {
                    SW_FT_Vector vec;
                    SW_FT_Vector v_middle;

                    point++;
                    tags++;
                    tag = SW_FT_CURVE_TAG(tags[0]);

                    vec.x = SCALED(point->x);
                    vec.y = SCALED(point->y);

                    if (tag == SW_FT_CURVE_TAG_ON) {
                        error =
                            func_interface->conic_to(&v_control, &vec, user);
                        if (error) goto Exit;
                        continue;
                    }

                    if (tag != SW_FT_CURVE_TAG_CONIC) goto Invalid_Outline;

                    v_middle.x = (v_control.x + vec.x) / 2;
                    v_middle.y = (v_control.y + vec.y) / 2;

                    error =
                        func_interface->conic_to(&v_control, &v_middle, user);
                    if (error) goto Exit;

                    v_control = vec;
                    goto Do_Conic;
                }

                error = func_interface->conic_to(&v_control, &v_start, user);
                goto Close;

            default: /* SW_FT_CURVE_TAG_CUBIC */
            {
                SW_FT_Vector vec1, vec2;

                if (point + 1 > limit ||
                    SW_FT_CURVE_TAG(tags[1]) != SW_FT_CURVE_TAG_CUBIC)
                    goto Invalid_Outline;

                point += 2;
                tags += 2;

                vec1.x = SCALED(point[-2].x);
                vec1.y = SCALED(point[-2].y);

                vec2.x = SCALED(point[-1].x);
                vec2.y = SCALED(point[-1].y);

                if (point <= limit) {
                    SW_FT_Vector vec;

                    vec.x = SCALED(point->x);
                    vec.y = SCALED(point->y);

                    error = func_interface->cubic_to(&vec1, &vec2, &vec, user);
                    if (error) goto Exit;
                    continue;
                }

                error = func_interface->cubic_to(&vec1, &vec2, &v_start, user);
                goto Close;
            }
            }
        }

        /* close the contour with a line segment */
        error = func_interface->line_to(&v_start, user);

    Close:
        if (error) goto Exit;

        first = last + 1;
    }

    return 0;

Exit:
    return error;

Invalid_Outline:
    return SW_FT_THROW(Invalid_Outline);
}

typedef struct gray_TBand_ {
    TPos min, max;

} gray_TBand;

SW_FT_DEFINE_OUTLINE_FUNCS(func_interface,
                           (SW_FT_Outline_MoveTo_Func)gray_move_to,
                           (SW_FT_Outline_LineTo_Func)gray_line_to,
                           (SW_FT_Outline_ConicTo_Func)gray_conic_to,
                           (SW_FT_Outline_CubicTo_Func)gray_cubic_to, 0, 0)

static int gray_convert_glyph_inner(RAS_ARG)
{
    volatile int error = 0;

    if (ft_setjmp(ras.jump_buffer) == 0) {
        error = SW_FT_Outline_Decompose(&ras.outline, &func_interface, &ras);
        if (!ras.invalid) gray_record_cell(RAS_VAR);
    } else
        error = SW_FT_THROW(Memory_Overflow);

    return error;
}

static int gray_convert_glyph(RAS_ARG)
{
    gray_TBand bands[40];
    gray_TBand* volatile band;
    int volatile n, num_bands;
    TPos volatile min, max, max_y;
    SW_FT_BBox* clip;

    /* Set up state in the raster object */
    gray_compute_cbox(RAS_VAR);

    /* clip to target bitmap, exit if nothing to do */
    clip = &ras.clip_box;

    if (ras.max_ex <= clip->xMin || ras.min_ex >= clip->xMax ||
        ras.max_ey <= clip->yMin || ras.min_ey >= clip->yMax)
        return 0;

    if (ras.min_ex < clip->xMin) ras.min_ex = clip->xMin;
    if (ras.min_ey < clip->yMin) ras.min_ey = clip->yMin;

    if (ras.max_ex > clip->xMax) ras.max_ex = clip->xMax;
    if (ras.max_ey > clip->yMax) ras.max_ey = clip->yMax;

    ras.count_ex = ras.max_ex - ras.min_ex;
    ras.count_ey = ras.max_ey - ras.min_ey;

    /* set up vertical bands */
    num_bands = (int)((ras.max_ey - ras.min_ey) / ras.band_size);
    if (num_bands == 0) num_bands = 1;
    if (num_bands >= 39) num_bands = 39;

    ras.band_shoot = 0;

    min = ras.min_ey;
    max_y = ras.max_ey;

    for (n = 0; n < num_bands; n++, min = max) {
        max = min + ras.band_size;
        if (n == num_bands - 1 || max > max_y) max = max_y;

        bands[0].min = min;
        bands[0].max = max;
        band = bands;

        while (band >= bands) {
            TPos bottom, top, middle;
            int  error;

            {
                PCell cells_max;
                int   yindex;
                long  cell_start, cell_end, cell_mod;

                ras.ycells = (PCell*)ras.buffer;
                ras.ycount = band->max - band->min;

                cell_start = sizeof(PCell) * ras.ycount;
                cell_mod = cell_start % sizeof(TCell);
                if (cell_mod > 0) cell_start += sizeof(TCell) - cell_mod;

                cell_end = ras.buffer_size;
                cell_end -= cell_end % sizeof(TCell);

                cells_max = (PCell)((char*)ras.buffer + cell_end);
                ras.cells = (PCell)((char*)ras.buffer + cell_start);
                if (ras.cells >= cells_max) goto ReduceBands;

                ras.max_cells = cells_max - ras.cells;
                if (ras.max_cells < 2) goto ReduceBands;

                for (yindex = 0; yindex < ras.ycount; yindex++)
                    ras.ycells[yindex] = NULL;
            }

            ras.num_cells = 0;
            ras.invalid = 1;
            ras.min_ey = band->min;
            ras.max_ey = band->max;
            ras.count_ey = band->max - band->min;

            error = gray_convert_glyph_inner(RAS_VAR);

            if (!error) {
                gray_sweep(RAS_VAR);
                band--;
                continue;
            } else if (error != ErrRaster_Memory_Overflow)
                return 1;

        ReduceBands:
            /* render pool overflow; we will reduce the render band by half */
            bottom = band->min;
            top = band->max;
            middle = bottom + ((top - bottom) >> 1);

            /* This is too complex for a single scanline; there must */
            /* be some problems.                                     */
            if (middle == bottom) {
                return 1;
            }

            if (bottom - top >= ras.band_size) ras.band_shoot++;

            band[1].min = bottom;
            band[1].max = middle;
            band[0].min = middle;
            band[0].max = top;
            band++;
        }
    }

    if (ras.band_shoot > 8 && ras.band_size > 16)
        ras.band_size = ras.band_size / 2;

    return 0;
}

static int gray_raster_render(gray_PRaster               raster,
                              const SW_FT_Raster_Params* params)
{
    SW_FT_UNUSED(raster);
    const SW_FT_Outline* outline = (const SW_FT_Outline*)params->source;

    gray_TWorker worker[1];

    TCell buffer[SW_FT_RENDER_POOL_SIZE / sizeof(TCell)];
    long  buffer_size = sizeof(buffer);
    int   band_size = (int)(buffer_size / (long)(sizeof(TCell) * 8));

    if (!outline) return SW_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 SW_FT_THROW(Invalid_Outline);

    if (outline->n_points != outline->contours[outline->n_contours - 1] + 1)
        return SW_FT_THROW(Invalid_Outline);

    /* this version does not support monochrome rendering */
    if (!(params->flags & SW_FT_RASTER_FLAG_AA))
        return SW_FT_THROW(Invalid_Mode);

    if (params->flags & SW_FT_RASTER_FLAG_CLIP)
        ras.clip_box = params->clip_box;
    else {
        ras.clip_box.xMin = -32768L;
        ras.clip_box.yMin = -32768L;
        ras.clip_box.xMax = 32767L;
        ras.clip_box.yMax = 32767L;
    }

    gray_init_cells(RAS_VAR_ buffer, buffer_size);

    ras.outline = *outline;
    ras.num_cells = 0;
    ras.invalid = 1;
    ras.band_size = band_size;
    ras.num_gray_spans = 0;

    ras.render_span = (SW_FT_Raster_Span_Func)params->gray_spans;
    ras.render_span_data = params->user;

    gray_convert_glyph(RAS_VAR);
    params->bbox_cb(ras.bound_left, ras.bound_top,
                    ras.bound_right - ras.bound_left,
                    ras.bound_bottom - ras.bound_top + 1, params->user);
    return 1;
}

/**** RASTER OBJECT CREATION: In stand-alone mode, we simply use *****/
/****                         a static object.                   *****/

static int gray_raster_new(SW_FT_Raster* araster)
{
    static gray_TRaster the_raster;

    *araster = (SW_FT_Raster)&the_raster;
    SW_FT_MEM_ZERO(&the_raster, sizeof(the_raster));

    return 0;
}

static void gray_raster_done(SW_FT_Raster raster)
{
    /* nothing */
    SW_FT_UNUSED(raster);
}

static void gray_raster_reset(SW_FT_Raster raster, char* pool_base,
                              long pool_size)
{
    SW_FT_UNUSED(raster);
    SW_FT_UNUSED(pool_base);
    SW_FT_UNUSED(pool_size);
}

SW_FT_DEFINE_RASTER_FUNCS(sw_ft_grays_raster,

                          (SW_FT_Raster_New_Func)gray_raster_new,
                          (SW_FT_Raster_Reset_Func)gray_raster_reset,
                          (SW_FT_Raster_Render_Func)gray_raster_render,
                          (SW_FT_Raster_Done_Func)gray_raster_done)

/* END */
