path: root/sys/libfont/font.c

#include <u.h>
#include <libn.h>
#include <libfont.h>

#define SAMPLE 8     /* should not be > 255 */ 

#define getshort(b)  getbytes((b), 2)
#define getint(b)    getbytes((b), 4)

// -----------------------------------------------------------------------
// internal types

typedef struct Buffer      Buffer;
typedef struct Edge        Edge;
typedef struct ActiveEdge  ActiveEdge;
typedef struct Point       Point;

struct Buffer
{
   uchar *data;
   int   cursor;
   int   size;
};

struct Edge {
   float x0, y0, x1,y1;
   int invert;
};

struct ActiveEdge
{
   struct ActiveEdge *next;
   float fx,fdx,fdy;
   float direction;
   float sy;
   float ey;
};

struct Point
{
   float x,y;
};

// -----------------------------------------------------------------------
// opaque external types

struct font·Info
{
    struct {
        void    *heap;
        union {
            mem·Allocator;
            mem·Allocator mal;
        };
    };

    uchar  *data;                     // pointer to .ttf file
    int    fontstart;                 // offset of start of font

    int numglyphs;                    // number of glyphs, needed for range checking

    int loca,head,glyf,hhea,hmtx,kern,gpos,svg; // table locations as offset from start of .ttf
    int index_map;                   // a cmap mapping for our chosen character encoding
    int indexToLocFormat;            // format needed to map from glyph index to glyph

    Buffer cff;                    // cff font data
    Buffer charstrings;            // the charstring index
    Buffer gsubrs;                 // global charstring subroutines index
    Buffer subrs;                  // private charstring subroutines index
    Buffer fontdicts;              // array of font dicts
    Buffer fdselect;               // map from glyph to fontdict
};

struct font·Bitmap
{
   int    w;
   int    h;
   int    stride;
   uchar *pixels;
}; 

typedef int test_oversample_pow2[(SAMPLE & (SAMPLE-1)) == 0 ? 1 : -1];

// -----------------------------------------------------------------------
// buffer helpers to parse data from file

static 
uchar 
getbyte(Buffer *b)
{
   if (b->cursor >= b->size)
      return 0;

   return b->data[b->cursor++];
}

static
uchar
peek(Buffer *b)
{
   if (b->cursor >= b->size)
      return 0;

   return b->data[b->cursor];
}

static 
void 
seek(Buffer *b, int o)
{
   assert(!(o > b->size || o < 0));
   b->cursor = (o > b->size || o < 0) ? b->size : o;
}

static 
void 
skip(Buffer *b, int o)
{
   seek(b, b->cursor + o);
}

static 
uint32 
getbytes(Buffer *b, int n)
{
   uint32 v;
   int i;
   assert(n >= 1 && n <= 4);

   v = 0;
   for (i = 0; i < n; i++)
      v = (v << 8) | getbyte(b);
   return v;
}

static 
Buffer 
makebuffer(void *p, uintptr size)
{
   Buffer r;
   assert(size < 0x40000000);

   r.data   = (uchar*) p;
   r.size   = (int)size;
   r.cursor = 0;

   return r;
}

static 
Buffer 
slice(Buffer *b, int o, int s)
{
   Buffer r = makebuffer(nil, 0);
   if (o < 0 || s < 0 || o > b->size || s > b->size - o) 
       return r;

   r.data = b->data + o;
   r.size = s;

   return r;
}

static 
Buffer 
cff_index(Buffer *b)
{
   int count, start, offsize;

   start = b->cursor;
   count = getshort(b);
   if (count) {
      offsize = getbyte(b);
      assert(offsize >= 1 && offsize <= 4);
      skip(b, offsize * count);
      skip(b, getbytes(b, offsize) - 1);
   }
   return slice(b, start, b->cursor - start);
}

static 
uint32 
cff_int(Buffer *b)
{
   int b0 = getbyte(b);
   if (b0 >= 32 && b0 <= 246)       return +b0 - 139;
   else if (b0 >= 247 && b0 <= 250) return +(b0 - 247)*256 + getbyte(b) + 108;
   else if (b0 >= 251 && b0 <= 254) return -(b0 - 251)*256 - getbyte(b) - 108;
   else if (b0 == 28)               return +getshort(b);
   else if (b0 == 29)               return +getint(b);

   panicf("unreachable");
   return 0;
}

static 
void 
skip_operand(Buffer *b) {
   int v, b0 = peek(b);
   assert(b0 >= 28);
   if (b0 == 30) {
      skip(b, 1);
      while (b->cursor < b->size) {
         v = getbyte(b);
         if ((v & 0xF) == 0xF || (v >> 4) == 0xF)
            break;
      }
   } else {
      cff_int(b);
   }
}

static 
Buffer 
dict_get(Buffer *b, int key)
{
   seek(b, 0);
   while (b->cursor < b->size) {
      int start = b->cursor, end, op;
      while (peek(b) >= 28)
         skip_operand(b);
      end = b->cursor;
      op = getbyte(b);
      if (op == 12)  op = getbyte(b) | 0x100;
      if (op == key) return slice(b, start, end-start);
   }
   return slice(b, 0, 0);
}

static 
void 
dict_get_ints(Buffer *b, int key, int outcount, uint32 *out)
{
   int i;
   Buffer operands = dict_get(b, key);
   for (i = 0; i < outcount && operands.cursor < operands.size; i++)
      out[i] = cff_int(&operands);
}

static 
int 
cff_index_count(Buffer *b)
{
   seek(b, 0);
   return getshort(b);
}

static 
Buffer 
cff_index_get(Buffer b, int i)
{
   int count, offsize, start, end;
   seek(&b, 0);
   count = getshort(&b);
   offsize = getbyte(&b);
   assert(i >= 0 && i < count);
   assert(offsize >= 1 && offsize <= 4);
   skip(&b, i*offsize);
   start = getbytes(&b, offsize);
   end = getbytes(&b, offsize);
   return slice(&b, 2+(count+1)*offsize+start, end - start);
}

// -----------------------------------------------------------------------
// accessors to parse data from file

/* 
 * on platforms that don't allow misaligned reads, if we want to allow
 * truetype fonts that aren't padded to alignment, define ALLOW_UNALIGNED_TRUETYPE
 */

#define ttBYTE(p)     (* (uchar *) (p))
#define ttCHAR(p)     (* (char *) (p))
#define ttFixed(p)    ttlong(p)

static ushort ttushort(uchar *p) { return p[0]*256 + p[1]; }
static short  ttshort(uchar *p)  { return p[0]*256 + p[1]; }
static uint32 ttulong(uchar *p)  { return (p[0]<<24) + (p[1]<<16) + (p[2]<<8) + p[3]; }
static int32  ttlong(uchar *p)   { return (p[0]<<24) + (p[1]<<16) + (p[2]<<8) + p[3]; }

#define ttf·tag4(p,c0,c1,c2,c3) ((p)[0] == (c0) && (p)[1] == (c1) && (p)[2] == (c2) && (p)[3] == (c3))
#define ttf·tag(p,str)           ttf·tag4(p,str[0],str[1],str[2],str[3])

static 
int 
isfont(uchar *font)
{
   // check the version number
   if (ttf·tag4(font, '1',0,0,0))  return 1; // TrueType 1
   if (ttf·tag(font, "typ1"))      return 1; // TrueType with type 1 font -- we don't support this!
   if (ttf·tag(font, "OTTO"))      return 1; // OpenType with CFF
   if (ttf·tag4(font, 0,1,0,0))    return 1; // OpenType 1.0
   if (ttf·tag(font, "true"))      return 1; // Apple specification for TrueType fonts

   return 0;
}

// @OPTIMIZE: binary search
static 
uint32 
find_table(uchar *data, uint32 offset, char *tag)
{
   int i;
   int32 ntab;    
   uint32 tabdir, loc; 

   ntab   = ttushort(data+offset+4); 
   tabdir = offset + 12;
   for (i=0; i < ntab; ++i) {
      loc = tabdir + 16*i;
      if (ttf·tag(data+loc+0, tag))
         return ttulong(data+loc+8);
   }
   return 0;
}

int
font·offsetfor(uchar *font_collection, int index)
{
   // if it's just a font, there's only one valid index
   if (isfont(font_collection))
      return index == 0 ? 0 : -1;

   // check if it's a TTC
   if (ttf·tag(font_collection, "ttcf")) {
      // version 1?
      if (ttulong(font_collection+4) == 0x00010000 || ttulong(font_collection+4) == 0x00020000) {
         int32 n = ttlong(font_collection+8);
         if (index >= n)
            return -1;
         return ttulong(font_collection+12+index*4);
      }
   }
   return -1;
}

int 
font·number(uchar *font_collection)
{
   // if it's just a font, there's only one valid font
   if (isfont(font_collection))
      return 1;

   // check if it's a TTC
   if (ttf·tag(font_collection, "ttcf")) {
      // version 1?
      if (ttulong(font_collection+4) == 0x00010000 || ttulong(font_collection+4) == 0x00020000) {
         return ttlong(font_collection+8);
      }
   }
   return 0;
}

static 
Buffer 
get_subrs(Buffer cff, Buffer fontdict)
{
   uint32 subrsoff = 0, private_loc[2] = { 0, 0 };
   Buffer pdict;
   dict_get_ints(&fontdict, 18, 2, private_loc);
   if (!private_loc[1] || !private_loc[0]) 
       return makebuffer(nil, 0);
   pdict = slice(&cff, private_loc[1], private_loc[0]);
   dict_get_ints(&pdict, 19, 1, &subrsoff);
   if (!subrsoff) 
       return makebuffer(nil, 0);
   seek(&cff, private_loc[1]+subrsoff);
   return cff_index(&cff);
}

// since most people won't use this, find this table the first time it's needed
static 
int 
get_svg(font·Info *info)
{
   uint32 t;
   if (info->svg < 0) {
      t = find_table(info->data, info->fontstart, "SVG ");
      if (t) {
         uint32 offset = ttulong(info->data + t + 2);
         info->svg = t + offset;
      } else {
         info->svg = 0;
      }
   }
   return info->svg;
}

static
int 
init(font·Info *info, uchar *data, int offset)
{
   uint32 cmap, t;
   int32 i, ntab;

   info->data      = data;
   info->fontstart = offset;
   info->cff       = makebuffer(nil, 0);

   cmap       = find_table(data, offset, "cmap"); // required
   info->loca = find_table(data, offset, "loca"); // required
   info->head = find_table(data, offset, "head"); // required
   info->glyf = find_table(data, offset, "glyf"); // required
   info->hhea = find_table(data, offset, "hhea"); // required
   info->hmtx = find_table(data, offset, "hmtx"); // required
   info->kern = find_table(data, offset, "kern"); // not required
   info->gpos = find_table(data, offset, "GPOS"); // not required

   if (!cmap || !info->head || !info->hhea || !info->hmtx)
      return 1;
   if (info->glyf) {
      // required for truetype
      if (!info->loca) 
          return 1;
   } else {
      // initialization for CFF / Type2 fonts (OTF)
      Buffer b, topdict, topdictidx;
      uint32 cstype = 2, charstrings = 0, fdarrayoff = 0, fdselectoff = 0;
      uint32 cff;

      cff = find_table(data, offset, "CFF ");
      if (!cff) 
          return 1;

      info->fontdicts = makebuffer(nil, 0);
      info->fdselect  = makebuffer(nil, 0);

      // @TODO this should use size from table (not 512MB)
      info->cff = makebuffer(data+cff, 512*1024*1024);
      b = info->cff;

      // read the header
      skip(&b, 2);
      seek(&b, getbyte(&b)); // hdrsize

      // @TODO the name INDEX could list multiple fonts,
      // but we just use the first one.
      cff_index(&b);  // name INDEX
      topdictidx = cff_index(&b);
      topdict = cff_index_get(topdictidx, 0);
      cff_index(&b);  // string INDEX
      info->gsubrs = cff_index(&b);

      dict_get_ints(&topdict, 17,         1, &charstrings);
      dict_get_ints(&topdict, 0x100 | 6,  1, &cstype);
      dict_get_ints(&topdict, 0x100 | 36, 1, &fdarrayoff);
      dict_get_ints(&topdict, 0x100 | 37, 1, &fdselectoff);
      info->subrs = get_subrs(b, topdict);

      // we only support Type 2 charstrings
      if (cstype != 2) 
          return 1;
      if (charstrings == 0) 
          return 1;

      if (fdarrayoff) {
         // looks like a CID font
         if (!fdselectoff) 
             return 1;
         seek(&b, fdarrayoff);
         info->fontdicts = cff_index(&b);
         info->fdselect = slice(&b, fdselectoff, b.size-fdselectoff);
      }

      seek(&b, charstrings);
      info->charstrings = cff_index(&b);
   }

   t = find_table(data, offset, "maxp");
   if (t)
      info->numglyphs = ttushort(data+t+4);
   else
      info->numglyphs = 0xffff;

   info->svg = -1;

   // find a cmap encoding table we understand *now* to avoid searching
   // later. (todo: could make this installable)
   // the same regardless of glyph.
   ntab = ttushort(data + cmap + 2);
   info->index_map = 0;
   for (i=0; i < ntab; ++i) {
      uint32 encoding_record = cmap + 4 + 8 * i;
      // find an encoding we understand:
      switch(ttushort(data+encoding_record)) {
        case font·platform_unicode:
            // Mac/iOS has these
            // all the encodingIDs are unicode, so we don't bother to check it
            info->index_map = cmap + ttulong(data+encoding_record+4);
            break;
        default:
            ;
      }
   }
   if (info->index_map == 0) {
      return 1;
   }

   info->indexToLocFormat = ttushort(data+info->head + 50);
   return 0;
}

font·Info *
font·make(uchar *file, int offset, mem·Allocator mem, void *heap)
{
    int err;
    font·Info *info;

    info = mem.alloc(heap, 1, sizeof(*info));
    info->mal  = mem;
    info->heap = heap;

    err  = init(info, file, offset);
    if (err) {
        mem.free(heap, info);
        info = nil;
    }

    return info;
}

void
font·free(font·Info *info)
{
    void *heap;
    mem·Allocator mem;

    heap = info->heap;
    mem  = info->mal;

    mem.free(heap, info);
}

int 
font·glyph_index(font·Info *info, int unicode_codepoint)
{
    uchar *data;
    ushort fmt;
    uint32 index_map;
    union {
        int32 bytes;
        struct {
            uint32 first;
            uint32 count;
        };
        struct {
            ushort segcount;
            ushort srchrange;
            ushort entrysel;
            ushort rangeshft;

            uint32 end;
            uint32 search;
        };
        struct {
            uint32 begg, begc, endc, ngroups;
            int32  low, mid, high;
        };
    } v;
 
    data       = info->data;
    index_map  = info->index_map;
 
    fmt = ttushort(data + index_map + 0);
    switch (fmt) {
    case 0: /* apple byte encoding */
       v.bytes = ttushort(data + index_map + 2);
       if (unicode_codepoint < v.bytes-6)
          return ttBYTE(data + index_map + 6 + unicode_codepoint);
       return 0;

    case 6:
       v.first = ttushort(data + index_map + 6);
       v.count = ttushort(data + index_map + 8);
       if ((uint32)unicode_codepoint >= v.first && (uint32)unicode_codepoint < v.first+v.count)
          return ttushort(data + index_map + 10 + (unicode_codepoint - v.first)*2);
       return 0;

    case 2:
       panicf("high-byte mapping for asian characters not implemented");
       return 0;

    case 4: /* standard mapping for windows fonts: binary search collection of ranges */
       v.segcount  = ttushort(data+index_map+6) >> 1;
       v.srchrange = ttushort(data+index_map+8) >> 1;
       v.entrysel  = ttushort(data+index_map+10);
       v.rangeshft = ttushort(data+index_map+12) >> 1;
 
       // do a binary search of the segments
       v.end    = index_map + 14;
       v.search = v.end;
 
       if (unicode_codepoint > 0xffff)
          return 0;
 
       // they lie from endCount .. endCount + segCount
       // but searchRange is the nearest power of two, so...
       if (unicode_codepoint >= ttushort(data + v.search + v.rangeshft*2))
          v.search += v.rangeshft*2;
 
       // now decrement to bias correctly to find smallest
       v.search -= 2;
       while (v.entrysel) {
          ushort end;
          v.srchrange >>= 1;
          end = ttushort(data + v.search + v.srchrange*2);
          if (unicode_codepoint > end)
             v.search += v.srchrange*2;
          --v.entrysel;
       }
       v.search += 2;
 
       {
          ushort offset, start;
          ushort item = (ushort) ((v.search - v.end) >> 1);
 
          assert(unicode_codepoint <= ttushort(data + v.end+ 2*item));
          start = ttushort(data + index_map + 14 + v.segcount*2 + 2 + 2*item);
          if (unicode_codepoint < start)
             return 0;
 
          offset = ttushort(data + index_map + 14 + v.segcount*6 + 2 + 2*item);
          if (offset == 0)
             return (ushort) (unicode_codepoint + ttshort(data + index_map + 14 + v.segcount*4 + 2 + 2*item));
 
          return ttushort(data + offset + (unicode_codepoint-start)*2 + index_map + 14 + v.segcount*6 + 2 + 2*item);
       }

    case 12: case 13:
       v.ngroups = ttulong(data+index_map+12);
       v.low = 0; v.high = (int32)v.ngroups;
       // Binary search the right group.
       while (v.low < v.high) {
          v.mid  = v.low + ((v.high-v.low) >> 1); // rounds down, so low <= mid < high
          v.begc = ttulong(data+index_map+16+v.mid*12);
          v.endc = ttulong(data+index_map+16+v.mid*12+4);
          if ((uint32)unicode_codepoint < v.begc)
             v.high = v.mid;
          else if ((uint32) unicode_codepoint > v.endc)
             v.low = v.mid+1;
          else {
             v.begg = ttulong(data+index_map+16+v.mid*12+8);
             if (fmt == 12)
                return v.begg + unicode_codepoint-v.begc;
             else // fmt == 13
                return v.begg;
          }
       }
       return 0; // not found

    default:
        ;
    }

    // @TODO
    assert(0);
    return 0;
}

int 
font·code_shape(font·Info *info, int unicode_codepoint, font·Vertex **verts)
{
   return font·glyph_shape(info, font·glyph_index(info, unicode_codepoint), verts);
}

static
void 
setvertex(font·Vertex *v, uchar type, int32 x, int32 y, int32 cx, int32 cy)
{
   v->type = type;
   v->x    = (short) x;
   v->y    = (short) y;
   v->cx   = (short) cx;
   v->cy   = (short) cy;
}

static 
int 
glyph_offset(font·Info *info, int glyph_index)
{
   int g1,g2;

   assert(!info->cff.size);

   if (glyph_index >= info->numglyphs) return -1; // glyph index out of range
   if (info->indexToLocFormat >= 2)    return -1; // unknown index->glyph map format

   if (info->indexToLocFormat == 0) {
      g1 = info->glyf + ttushort(info->data + info->loca + glyph_index * 2) * 2;
      g2 = info->glyf + ttushort(info->data + info->loca + glyph_index * 2 + 2) * 2;
   } else {
      g1 = info->glyf + ttulong (info->data + info->loca + glyph_index * 4);
      g2 = info->glyf + ttulong (info->data + info->loca + glyph_index * 4 + 4);
   }

   return (g1==g2) ? -1 : g1; // if length is 0, return -1
}

static int glyph_info_t2(font·Info *info, int glyph_index, int *x0, int *y0, int *x1, int *y1);

int 
font·glyph_box(font·Info *info, int glyph_index, int *x0, int *y0, int *x1, int *y1)
{
   if (info->cff.size) {
      glyph_info_t2(info, glyph_index, x0, y0, x1, y1);
   } else {
      int g = glyph_offset(info, glyph_index);
      if (g < 0) return 0;

      if (x0) *x0 = ttshort(info->data + g + 2);
      if (y0) *y0 = ttshort(info->data + g + 4);
      if (x1) *x1 = ttshort(info->data + g + 6);
      if (y1) *y1 = ttshort(info->data + g + 8);
   }
   return 1;
}

int 
font·code_box(font·Info *info, int codepoint, int *x0, int *y0, int *x1, int *y1)
{
   return font·glyph_box(info, font·glyph_index(info,codepoint), x0,y0,x1,y1);
}

int 
font·glyph_empty(font·Info *info, int glyph_index)
{
   int g;
   short numc;

   if (info->cff.size)
      return glyph_info_t2(info, glyph_index, nil, nil, nil, nil) == 0;

   g = glyph_offset(info, glyph_index);
   if (g < 0) 
       return 1;

   numc = ttshort(info->data + g);
   return numc == 0;
}

static 
int 
close_shape(font·Vertex *verts, int num_verts, int was_off, int start_off,
    int32 sx, int32 sy, int32 scx, int32 scy, int32 cx, int32 cy)
{
   if (start_off) {
      if (was_off)
         setvertex(&verts[num_verts++], font·Vcurve, (cx+scx)>>1, (cy+scy)>>1, cx,cy);
      setvertex(&verts[num_verts++], font·Vcurve, sx,sy,scx,scy);
   } else {
      if (was_off)
         setvertex(&verts[num_verts++], font·Vcurve,sx,sy,cx,cy);
      else
         setvertex(&verts[num_verts++], font·Vline,sx,sy,0,0);
   }
   return num_verts;
}

static 
int 
glyph_shape_tt(font·Info *info, int glyph_index, font·Vertex **pverts)
{
   short numc;
   uchar *contourend;
   uchar *data = info->data;
   font·Vertex *verts = nil;
   int num_verts = 0;
   int g = glyph_offset(info, glyph_index);

   *pverts = nil;

   if (g < 0) 
       return 0;

   numc = ttshort(data + g);

   if (numc > 0) {
      uchar flags=0, flagcount;
      int32 ins, i,j=0,m,n, next_move, was_off=0, off, start_off=0;
      int32 x,y,cx,cy,sx,sy,scx,scy;

      uchar *points;
      contourend = (data + g + 10);
      ins = ttushort(data + g + 10 + numc * 2);
      points = data + g + 10 + numc * 2 + 2 + ins;

      n = 1+ttushort(contourend + numc*2-2);

      m     = n + 2*numc;  // a loose bound on how many verts we might need
      verts = info->alloc(info->heap, m, sizeof(verts[0]));
      if (verts == 0)
         return 0;

      next_move = 0;
      flagcount = 0;

      // in first pass, we load uninterpreted data into the allocated array
      // above, shifted to the end of the array so we won't overwrite it when
      // we create our final data starting from the front

      off = m - n; // starting offset for uninterpreted data, regardless of how m ends up being calculated

      // first load flags

      for (i=0; i < n; ++i) {
         if (flagcount == 0) {
            flags = *points++;
            if (flags & 8)
               flagcount = *points++;
         } else
            --flagcount;
         verts[off+i].type = flags;
      }

      // now load x coordinates
      x=0;
      for (i=0; i < n; ++i) {
         flags = verts[off+i].type;
         if (flags & 2) {
            short dx = *points++;
            x += (flags & 16) ? dx : -dx; // ???
         } else {
            if (!(flags & 16)) {
               x = x + (short)(points[0]*256 + points[1]);
               points += 2;
            }
         }
         verts[off+i].x = (short)x;
      }

      // now load y coordinates
      y=0;
      for (i=0; i < n; ++i) {
         flags = verts[off+i].type;
         if (flags & 4) {
            short dy = *points++;
            y += (flags & 32) ? dy : -dy; // ???
         } else {
            if (!(flags & 32)) {
               y = y + (short) (points[0]*256 + points[1]);
               points += 2;
            }
         }
         verts[off+i].y = (short)y;
      }

      // now convert them to our format
      num_verts=0;
      sx = sy = cx = cy = scx = scy = 0;
      for (i=0; i < n; ++i) {
         flags = verts[off+i].type;
         x     = (short)verts[off+i].x;
         y     = (short)verts[off+i].y;

         if (next_move == i) {
            if (i != 0)
               num_verts = close_shape(verts, num_verts, was_off, start_off, sx,sy,scx,scy,cx,cy);

            // now start the new one
            start_off = !(flags & 1);
            if (start_off) {
               // if we start off with an off-curve point, then when we need to find a point on the curve
               // where we can start, and we need to save some state for when we wraparound.
               scx = x;
               scy = y;
               if (!(verts[off+i+1].type & 1)) {
                  // next point is also a curve point, so interpolate an on-point curve
                  sx = (x + (int32) verts[off+i+1].x) >> 1;
                  sy = (y + (int32) verts[off+i+1].y) >> 1;
               } else {
                  // otherwise just use the next point as our start point
                  sx = (int32) verts[off+i+1].x;
                  sy = (int32) verts[off+i+1].y;
                  ++i; // we're using point i+1 as the starting point, so skip it
               }
            } else {
               sx = x;
               sy = y;
            }
            setvertex(&verts[num_verts++], font·Vmove,sx,sy,0,0);
            was_off   = 0;
            next_move = 1 + ttushort(contourend+j*2);
            ++j;
         } else {
            if (!(flags & 1)) { // if it's a curve
               if (was_off) // two off-curve control points in a row means interpolate an on-curve midpoint
                  setvertex(&verts[num_verts++], font·Vcurve, (cx+x)>>1, (cy+y)>>1, cx, cy);
               cx = x;
               cy = y;
               was_off = 1;
            } else {
               if (was_off)
                  setvertex(&verts[num_verts++], font·Vcurve, x,y, cx, cy);
               else
                  setvertex(&verts[num_verts++], font·Vline, x,y,0,0);
               was_off = 0;
            }
         }
      }
      num_verts = close_shape(verts, num_verts, was_off, start_off, sx, sy, scx, scy, cx, cy);
   } else if (numc < 0) {
      // Compound shapes.
      int more = 1;
      uchar *comp = data + g + 10;
      num_verts = 0;
      verts = 0;
      while (more) {
         ushort flags, gidx;
         int comp_num_verts = 0, i;
         font·Vertex *comp_verts = 0, *tmp = 0;
         float mtx[6] = {1,0,0,1,0,0}, m, n;

         flags = ttshort(comp); comp+=2;
         gidx = ttshort(comp); comp+=2;

         if (flags & 2) { // XY values
            if (flags & 1) { // shorts
               mtx[4] = ttshort(comp); comp+=2;
               mtx[5] = ttshort(comp); comp+=2;
            } else {
               mtx[4] = ttCHAR(comp); comp+=1;
               mtx[5] = ttCHAR(comp); comp+=1;
            }
         }
         else {
            // @TODO handle matching point
            assert(0);
         }
         if (flags & (1<<3)) { // WE_HAVE_A_SCALE
            mtx[0] = mtx[3] = ttshort(comp)/16384.0f; comp+=2;
            mtx[1] = mtx[2] = 0;
         } else if (flags & (1<<6)) { // WE_HAVE_AN_X_AND_YSCALE
            mtx[0] = ttshort(comp)/16384.0f; comp+=2;
            mtx[1] = mtx[2] = 0;
            mtx[3] = ttshort(comp)/16384.0f; comp+=2;
         } else if (flags & (1<<7)) { // WE_HAVE_A_TWO_BY_TWO
            mtx[0] = ttshort(comp)/16384.0f; comp+=2;
            mtx[1] = ttshort(comp)/16384.0f; comp+=2;
            mtx[2] = ttshort(comp)/16384.0f; comp+=2;
            mtx[3] = ttshort(comp)/16384.0f; comp+=2;
         }

         // Find transformation scales.
         m = (float) sqrt(mtx[0]*mtx[0] + mtx[1]*mtx[1]);
         n = (float) sqrt(mtx[2]*mtx[2] + mtx[3]*mtx[3]);

         // Get indexed glyph.
         comp_num_verts = font·glyph_shape(info, gidx, &comp_verts);
         if (comp_num_verts > 0) {
            // Transform verts.
            for (i = 0; i < comp_num_verts; ++i) {
               font·Vertex* v = &comp_verts[i];
               short x,y;
               x=v->x; y=v->y;
               v->x = (short)(m * (mtx[0]*x + mtx[2]*y + mtx[4]));
               v->y = (short)(n * (mtx[1]*x + mtx[3]*y + mtx[5]));
               x=v->cx; y=v->cy;
               v->cx = (short)(m * (mtx[0]*x + mtx[2]*y + mtx[4]));
               v->cy = (short)(n * (mtx[1]*x + mtx[3]*y + mtx[5]));
            }
            // Append verts.
            tmp = info->alloc(info->heap, num_verts+comp_num_verts, sizeof(font·Vertex));
            if (!tmp) {
               if (verts)      info->free(info->heap, verts);
               if (comp_verts) info->free(info->heap, comp_verts);
               return 0;
            }
            if (num_verts > 0) 
                memcpy(tmp, verts, num_verts*sizeof(font·Vertex));

            memcpy(tmp+num_verts, comp_verts, comp_num_verts*sizeof(font·Vertex));

            if (verts) 
                info->free(info->heap, verts);

            verts = tmp;
            info->free(info->heap, comp_verts);
            num_verts += comp_num_verts;
         }
         // More components ?
         more = flags & (1<<5);
      }
   }    

   *pverts = verts;
   return num_verts;
}

typedef struct
{
   int bounds;
   int started;
   float first_x, first_y;
   float x, y;
   int32 min_x, max_x, min_y, max_y;

   font·Vertex *pverts;
   int num_verts;
} csctx;

#define CSCTX_INIT(bounds) {bounds,0, 0,0, 0,0, 0,0,0,0, nil, 0}

static 
void 
track_vertex(csctx *c, int32 x, int32 y)
{
   if (x > c->max_x || !c->started) c->max_x = x;
   if (y > c->max_y || !c->started) c->max_y = y;
   if (x < c->min_x || !c->started) c->min_x = x;
   if (y < c->min_y || !c->started) c->min_y = y;
   c->started = 1;
}

static 
void 
csctx_v(csctx *c, uchar type, int32 x, int32 y, int32 cx, int32 cy, int32 cx1, int32 cy1)
{
   if (c->bounds) {
      track_vertex(c, x, y);
      if (type == font·Vcubic) {
         track_vertex(c, cx, cy);
         track_vertex(c, cx1, cy1);
      }
   } else {
      setvertex(&c->pverts[c->num_verts], type, x, y, cx, cy);
      c->pverts[c->num_verts].cx1 = (short) cx1;
      c->pverts[c->num_verts].cy1 = (short) cy1;
   }
   c->num_verts++;
}

static 
void 
csctx_close_shape(csctx *ctx)
{
   if (ctx->first_x != ctx->x || ctx->first_y != ctx->y)
      csctx_v(ctx, font·Vline, (int)ctx->first_x, (int)ctx->first_y, 0, 0, 0, 0);
}

static 
void 
csctx_rmove_to(csctx *ctx, float dx, float dy)
{
   csctx_close_shape(ctx);
   ctx->first_x = ctx->x = ctx->x + dx;
   ctx->first_y = ctx->y = ctx->y + dy;
   csctx_v(ctx, font·Vmove, (int)ctx->x, (int)ctx->y, 0, 0, 0, 0);
}

static 
void 
csctx_rline_to(csctx *ctx, float dx, float dy)
{
   ctx->x += dx;
   ctx->y += dy;
   csctx_v(ctx, font·Vline, (int)ctx->x, (int)ctx->y, 0, 0, 0, 0);
}

static 
void 
csctx_rccurve_to(csctx *ctx, float dx1, float dy1, float dx2, float dy2, float dx3, float dy3)
{
   float cx1 = ctx->x + dx1;
   float cy1 = ctx->y + dy1;
   float cx2 = cx1 + dx2;
   float cy2 = cy1 + dy2;
   ctx->x = cx2 + dx3;
   ctx->y = cy2 + dy3;
   csctx_v(ctx, font·Vcubic, (int)ctx->x, (int)ctx->y, (int)cx1, (int)cy1, (int)cx2, (int)cy2);
}

static 
Buffer 
get_subr(Buffer idx, int n)
{
   int count = cff_index_count(&idx);
   int bias = 107;
   if (count >= 33900)
      bias = 32768;
   else if (count >= 1240)
      bias = 1131;
   n += bias;
   if (n < 0 || n >= count)
      return makebuffer(nil, 0);
   return cff_index_get(idx, n);
}

static 
Buffer 
cid_get_glyph_subrs(font·Info *info, int glyph_index)
{
   Buffer fdselect = info->fdselect;
   int nranges, start, end, v, fmt, fdselector = -1, i;

   seek(&fdselect, 0);
   fmt = getbyte(&fdselect);
   if (fmt == 0) {
      // untested
      skip(&fdselect, glyph_index);
      fdselector = getbyte(&fdselect);
   } else if (fmt == 3) {
      nranges = getshort(&fdselect);
      start = getshort(&fdselect);
      for (i = 0; i < nranges; i++) {
         v = getbyte(&fdselect);
         end = getshort(&fdselect);
         if (glyph_index >= start && glyph_index < end) {
            fdselector = v;
            break;
         }
         start = end;
      }
   }
   if (fdselector == -1) makebuffer(nil, 0);
   return get_subrs(info->cff, cff_index_get(info->fontdicts, fdselector));
}

static 
int 
run_charstring(font·Info *info, int glyph_index, csctx *c)
{
   int in_header = 1, maskbits = 0, subr_stack_height = 0, sp = 0, v, i, b0;
   int has_subrs = 0, clear_stack;
   float s[48];
   Buffer subr_stack[10], subrs = info->subrs, b;
   float f;

   // this currently ignores the initial width value, which isn't needed if we have hmtx
   b = cff_index_get(info->charstrings, glyph_index);
   while (b.cursor < b.size) {
      i = 0;
      clear_stack = 1;
      b0 = getbyte(&b);
      switch (b0) {
      // @TODO implement hinting
      case 0x13: // hintmask
      case 0x14: // cntrmask
         if (in_header)
            maskbits += (sp / 2); // implicit "vstem"
         in_header = 0;
         skip(&b, (maskbits + 7) / 8);
         break;

      case 0x01: // hstem
      case 0x03: // vstem
      case 0x12: // hstemhm
      case 0x17: // vstemhm
         maskbits += (sp / 2);
         break;

      case 0x15: // rmoveto
         in_header = 0;
         if (sp < 2) {
             errorf("rmoveto stack");
             return 0;
         }
         csctx_rmove_to(c, s[sp-2], s[sp-1]);
         break;
      case 0x04: // vmoveto
         in_header = 0;
         if (sp < 1) {
             errorf("vmoveto stack");
             return 0; 
         }
         csctx_rmove_to(c, 0, s[sp-1]);
         break;
      case 0x16: // hmoveto
         in_header = 0;
         if (sp < 1) {
             errorf("hmoveto stack");
             return 0;
         }
         csctx_rmove_to(c, s[sp-1], 0);
         break;

      case 0x05: // rlineto
         if (sp < 2) {
             errorf("rlineto stack");
             return 0;
         }
         for (; i + 1 < sp; i += 2)
            csctx_rline_to(c, s[i], s[i+1]);
         break;

      // hlineto/vlineto and vhcurveto/hvcurveto alternate horizontal and vertical
      // starting from a different place.

      case 0x07: // vlineto
         if (sp < 1) {
             errorf("vlineto stack");
             return 0;
         }
         goto vlineto;
      case 0x06: // hlineto
         if (sp < 1) {
             errorf("hlineto stack");
             return 0;
         }
         for (;;) {
            if (i >= sp) break;
            csctx_rline_to(c, s[i], 0);
            i++;
      vlineto:
            if (i >= sp) break;
            csctx_rline_to(c, 0, s[i]);
            i++;
         }
         break;

      case 0x1F: // hvcurveto
         if (sp < 4) {
             errorf("hvcurveto stack");
             return 0;
         }
         goto hvcurveto;
      case 0x1E: // vhcurveto
         if (sp < 4) {
             errorf("vhcurveto stack");
             return 0;
         }
         for (;;) {
            if (i + 3 >= sp) break;
            csctx_rccurve_to(c, 0, s[i], s[i+1], s[i+2], s[i+3], (sp - i == 5) ? s[i + 4] : 0.0f);
            i += 4;
      hvcurveto:
            if (i + 3 >= sp) break;
            csctx_rccurve_to(c, s[i], 0, s[i+1], s[i+2], (sp - i == 5) ? s[i+4] : 0.0f, s[i+3]);
            i += 4;
         }
         break;

      case 0x08: // rrcurveto
         if (sp < 6) {
             errorf("rcurveline stack");
             return 0;
         }
         for (; i + 5 < sp; i += 6)
            csctx_rccurve_to(c, s[i], s[i+1], s[i+2], s[i+3], s[i+4], s[i+5]);
         break;

      case 0x18: // rcurveline
         if (sp < 8) {
             errorf("rcurveline stack");
             return 0;
         }
         for (; i + 5 < sp - 2; i += 6)
            csctx_rccurve_to(c, s[i], s[i+1], s[i+2], s[i+3], s[i+4], s[i+5]);
         if (i + 1 >= sp) {
             errorf("rcurveline stack");
             return 0;
         }
         csctx_rline_to(c, s[i], s[i+1]);
         break;

      case 0x19: // rlinecurve
         if (sp < 8) {
             errorf("rlinecurve stack");
             return 0;
         }
         for (; i + 1 < sp - 6; i += 2)
            csctx_rline_to(c, s[i], s[i+1]);
         if (i + 5 >= sp) {
             errorf("rlinecurve stack");
             return 0;
         }
         csctx_rccurve_to(c, s[i], s[i+1], s[i+2], s[i+3], s[i+4], s[i+5]);
         break;

      case 0x1A: // vvcurveto
      case 0x1B: // hhcurveto
         if (sp < 4) {
             errorf("(vv|hh)curveto stack");
             return 0;
         }
         f = 0.0;
         if (sp & 1) { f = s[i]; i++; }
         for (; i + 3 < sp; i += 4) {
            if (b0 == 0x1B)
               csctx_rccurve_to(c, s[i], f, s[i+1], s[i+2], s[i+3], 0.0);
            else
               csctx_rccurve_to(c, f, s[i], s[i+1], s[i+2], 0.0, s[i+3]);
            f = 0.0;
         }
         break;

      case 0x0A: // callsubr
         if (!has_subrs) {
            if (info->fdselect.size)
               subrs = cid_get_glyph_subrs(info, glyph_index);
            has_subrs = 1;
         }
         // fallthrough
      case 0x1D: // callgsubr
         if (sp < 1) {
             errorf("call(g|)subr stack");
             return 0;
         }
         v = (int) s[--sp];
         if (subr_stack_height >= 10) {
             errorf("recursion limit");
             return 0;
         }
         subr_stack[subr_stack_height++] = b;
         b = get_subr(b0 == 0x0A ? subrs : info->gsubrs, v);
         if (b.size == 0) {
             errorf("subr not found");
             return 0;
         }
         b.cursor = 0;
         clear_stack = 0;
         break;

      case 0x0B: // return
         if (subr_stack_height <= 0) {
             errorf("return outside subr");
             return 0;
         }
         b = subr_stack[--subr_stack_height];
         clear_stack = 0;
         break;

      case 0x0E: // endchar
         csctx_close_shape(c);
         return 1;

      case 0x0C: { // two-byte escape
         float dx1, dx2, dx3, dx4, dx5, dx6, dy1, dy2, dy3, dy4, dy5, dy6;
         float dx, dy;
         int b1 = getbyte(&b);
         switch (b1) {
         // @TODO These "flex" implementations ignore the flex-depth and resolution,
         // and always draw beziers.
         case 0x22: // hflex
            if (sp < 7) {
                errorf("hflex stack");
                return 0;
            }
            dx1 = s[0];
            dx2 = s[1];
            dy2 = s[2];
            dx3 = s[3];
            dx4 = s[4];
            dx5 = s[5];
            dx6 = s[6];
            csctx_rccurve_to(c, dx1, 0, dx2, dy2, dx3, 0);
            csctx_rccurve_to(c, dx4, 0, dx5, -dy2, dx6, 0);
            break;

         case 0x23: // flex
            if (sp < 13) {
                errorf("flex stack");
                return 0;
            }
            dx1 = s[0];
            dy1 = s[1];
            dx2 = s[2];
            dy2 = s[3];
            dx3 = s[4];
            dy3 = s[5];
            dx4 = s[6];
            dy4 = s[7];
            dx5 = s[8];
            dy5 = s[9];
            dx6 = s[10];
            dy6 = s[11];
            //fd is s[12]
            csctx_rccurve_to(c, dx1, dy1, dx2, dy2, dx3, dy3);
            csctx_rccurve_to(c, dx4, dy4, dx5, dy5, dx6, dy6);
            break;

         case 0x24: // hflex1
            if (sp < 9) {
                errorf("hflex1 stack");
                return 0;
            }
            dx1 = s[0];
            dy1 = s[1];
            dx2 = s[2];
            dy2 = s[3];
            dx3 = s[4];
            dx4 = s[5];
            dx5 = s[6];
            dy5 = s[7];
            dx6 = s[8];
            csctx_rccurve_to(c, dx1, dy1, dx2, dy2, dx3, 0);
            csctx_rccurve_to(c, dx4, 0, dx5, dy5, dx6, -(dy1+dy2+dy5));
            break;

         case 0x25: // flex1
            if (sp < 11) {
                errorf("flex1 stack");
                return 0;
            }
            dx1 = s[0];
            dy1 = s[1];
            dx2 = s[2];
            dy2 = s[3];
            dx3 = s[4];
            dy3 = s[5];
            dx4 = s[6];
            dy4 = s[7];
            dx5 = s[8];
            dy5 = s[9];
            dx6 = dy6 = s[10];
            dx = dx1+dx2+dx3+dx4+dx5;
            dy = dy1+dy2+dy3+dy4+dy5;
            if (fabs(dx) > fabs(dy))
               dy6 = -dy;
            else
               dx6 = -dx;
            csctx_rccurve_to(c, dx1, dy1, dx2, dy2, dx3, dy3);
            csctx_rccurve_to(c, dx4, dy4, dx5, dy5, dx6, dy6);
            break;

         default:
            panicf("unimplemented");
            return 0;
         }
      } break;

      default:
         if (b0 != 255 && b0 != 28 && (b0 < 32 || b0 > 254)) {
            errorf("reserved operator");
            return 0;
         }

         // push immediate
         if (b0 == 255) {
            f = (float)(int32)getint(&b) / 0x10000;
         } else {
            skip(&b, -1);
            f = (float)(short)cff_int(&b);
         }
         if (sp >= 48) {
             errorf("push stack overflow");
             return 0;
         }
         s[sp++] = f;
         clear_stack = 0;
         break;
      }
      if (clear_stack) sp = 0;
   }

   errorf("no endchar");
   return 0;

}

static 
int 
glyph_shape_t2(font·Info *info, int glyph_index, font·Vertex **pverts)
{
    // runs the charstring twice, once to count and once to output (to avoid realloc)
    csctx count_ctx  = CSCTX_INIT(1);
    csctx output_ctx = CSCTX_INIT(0);

    if (run_charstring(info, glyph_index, &count_ctx)) {
       *pverts = info->alloc(info->heap, count_ctx.num_verts, sizeof(font·Vertex));
       output_ctx.pverts = *pverts;
       if (run_charstring(info, glyph_index, &output_ctx)) {
          assert(output_ctx.num_verts == count_ctx.num_verts);
          return output_ctx.num_verts;
       }
    }

    *pverts = nil;
    return 0;
}

static 
int 
glyph_info_t2(font·Info *info, int glyph_index, int *x0, int *y0, int *x1, int *y1)
{
 
    csctx c = CSCTX_INIT(1);
    int r = run_charstring(info, glyph_index, &c);
    if (x0) *x0 = r ? c.min_x : 0;
    if (y0) *y0 = r ? c.min_y : 0;
    if (x1) *x1 = r ? c.max_x : 0;
    if (y1) *y1 = r ? c.max_y : 0;
 
    return r ? c.num_verts : 0;
}

int 
font·glyph_shape(font·Info *info, int glyph_index, font·Vertex **pverts)
{
    if (!info->cff.size)
       return glyph_shape_tt(info, glyph_index, pverts);
    else
       return glyph_shape_t2(info, glyph_index, pverts);
}

void 
font·glyph_hmetrics(font·Info *info, int glyph_index, int *adv, int *lsb)
{
    ushort n;
 
    n = ttushort(info->data+info->hhea + 34);
    if (glyph_index < n) {
       if (adv) *adv = ttshort(info->data + info->hmtx + 4*glyph_index);
       if (lsb) *lsb = ttshort(info->data + info->hmtx + 4*glyph_index + 2);
    } else {
       if (adv) *adv = ttshort(info->data + info->hmtx + 4*(n-1));
       if (lsb) *lsb = ttshort(info->data + info->hmtx + 4*n + 2*(glyph_index - n));
    }
}

int 
font·kerntablen(font·Info *info)
{
   uchar *data = info->data + info->kern;

   // we only look at the first table. it must be 'horizontal' and format 0.
   if (!info->kern)
      return 0;
   if (ttushort(data+2) < 1) // number of tables, need at least 1
      return 0;
   if (ttushort(data+8) != 1) // horizontal flag must be set in format
      return 0;

   return ttushort(data+10);
}

int 
font·kerntab(font·Info *info, font·TabElt* table, int table_length)
{
   uchar *data = info->data + info->kern;
   int k, length;

   // we only look at the first table. it must be 'horizontal' and format 0.
   if (!info->kern)
      return 0;
   if (ttushort(data+2) < 1) // number of tables, need at least 1
      return 0;
   if (ttushort(data+8) != 1) // horizontal flag must be set in format
      return 0;

   length = ttushort(data+10);
   if (table_length < length)
      length = table_length;

   for (k = 0; k < length; k++)
   {
      table[k].glyph1 = ttushort(data+18+(k*6));
      table[k].glyph2 = ttushort(data+20+(k*6));
      table[k].advance = ttshort(data+22+(k*6));
   }

   return length;
}

static 
int  
glyph_kernadvance(font·Info *info, int glyph1, int glyph2)
{
   uchar *data = info->data + info->kern;
   uint32 needle, straw;
   int l, r, m;

   // we only look at the first table. it must be 'horizontal' and format 0.
   if (!info->kern)
      return 0;
   if (ttushort(data+2) < 1) // number of tables, need at least 1
      return 0;
   if (ttushort(data+8) != 1) // horizontal flag must be set in format
      return 0;

   l = 0;
   r = ttushort(data+10) - 1;
   needle = glyph1 << 16 | glyph2;
   while (l <= r) {
      m = (l + r) >> 1;
      straw = ttulong(data+18+(m*6)); // note: unaligned read
      if (needle < straw)
         r = m - 1;
      else if (needle > straw)
         l = m + 1;
      else
         return ttshort(data+22+(m*6));
   }
   return 0;
}

static 
int32  
coverage_index(uchar *coverageTable, int glyph)
{
    ushort coverageFormat = ttushort(coverageTable);
    switch(coverageFormat) {
        case 1: {
            ushort glyphCount = ttushort(coverageTable + 2);

            // Binary search.
            int32 l=0, r=glyphCount-1, m;
            int straw, needle=glyph;
            while (l <= r) {
                uchar *glyphArray = coverageTable + 4;
                ushort glyphID;
                m = (l + r) >> 1;
                glyphID = ttushort(glyphArray + 2 * m);
                straw = glyphID;
                if (needle < straw)
                    r = m - 1;
                else if (needle > straw)
                    l = m + 1;
                else {
                     return m;
                }
            }
        } break;

        case 2: {
            ushort rangeCount = ttushort(coverageTable + 2);
            uchar *rangeArray = coverageTable + 4;

            // Binary search.
            int32 l=0, r=rangeCount-1, m;
            int strawStart, strawEnd, needle=glyph;
            while (l <= r) {
                uchar *rangeRecord;
                m = (l + r) >> 1;
                rangeRecord = rangeArray + 6 * m;
                strawStart = ttushort(rangeRecord);
                strawEnd = ttushort(rangeRecord + 2);
                if (needle < strawStart)
                    r = m - 1;
                else if (needle > strawEnd)
                    l = m + 1;
                else {
                    ushort startCoverageIndex = ttushort(rangeRecord + 4);
                    return startCoverageIndex + glyph - strawStart;
                }
            }
        } break;

        default: {
            // There are no other cases.
            assert(0);
        } break;
    }

    return -1;
}

static 
int32  
glyph_class(uchar *classDefTable, int glyph)
{
    ushort classDefFormat = ttushort(classDefTable);
    switch(classDefFormat)
    {
        case 1: {
            ushort startGlyphID = ttushort(classDefTable + 2);
            ushort glyphCount = ttushort(classDefTable + 4);
            uchar *classDef1ValueArray = classDefTable + 6;

            if (glyph >= startGlyphID && glyph < startGlyphID + glyphCount)
                return (int32)ttushort(classDef1ValueArray + 2 * (glyph - startGlyphID));

            classDefTable = classDef1ValueArray + 2 * glyphCount;
        } break;

        case 2: {
            ushort classRangeCount = ttushort(classDefTable + 2);
            uchar *classRangeRecords = classDefTable + 4;

            // Binary search.
            int32 l=0, r=classRangeCount-1, m;
            int strawStart, strawEnd, needle=glyph;
            while (l <= r) {
                uchar *classRangeRecord;
                m = (l + r) >> 1;
                classRangeRecord = classRangeRecords + 6 * m;
                strawStart = ttushort(classRangeRecord);
                strawEnd = ttushort(classRangeRecord + 2);
                if (needle < strawStart)
                    r = m - 1;
                else if (needle > strawEnd)
                    l = m + 1;
                else
                    return (int32)ttushort(classRangeRecord + 4);
            }

            classDefTable = classRangeRecords + 6 * classRangeCount;
        } break;

        default: {
            // There are no other cases.
            assert(0);
        } break;
    }

    return -1;
}

static 
int32  
glyph_gposadvance(font·Info *info, int glyph1, int glyph2)
{
    ushort lookupListOffset;
    uchar *lookupList;
    ushort lookupCount;
    uchar *data;
    int32 i;

    if (!info->gpos) return 0;

    data = info->data + info->gpos;

    if (ttushort(data+0) != 1) return 0; // Major version 1
    if (ttushort(data+2) != 0) return 0; // Minor version 0

    lookupListOffset = ttushort(data+8);
    lookupList = data + lookupListOffset;
    lookupCount = ttushort(lookupList);

    for (i=0; i<lookupCount; ++i) {
        ushort lookupOffset = ttushort(lookupList + 2 + 2 * i);
        uchar *lookupTable = lookupList + lookupOffset;

        ushort lookupType = ttushort(lookupTable);
        ushort subTableCount = ttushort(lookupTable + 4);
        uchar *subTableOffsets = lookupTable + 6;
        switch(lookupType) {
            case 2: { // Pair Adjustment Positioning Subtable
                int32 sti;
                for (sti=0; sti<subTableCount; sti++) {
                    ushort subtableOffset = ttushort(subTableOffsets + 2 * sti);
                    uchar *table = lookupTable + subtableOffset;
                    ushort posFormat = ttushort(table);
                    ushort coverageOffset = ttushort(table + 2);
                    int32 coverageIndex = coverage_index(table + coverageOffset, glyph1);
                    if (coverageIndex == -1) continue;

                    switch (posFormat) {
                        case 1: {
                            int32 l, r, m;
                            int straw, needle;
                            ushort valueFormat1 = ttushort(table + 4);
                            ushort valueFormat2 = ttushort(table + 6);
                            int32 valueRecordPairSizeInBytes = 2;
                            ushort pairSetCount = ttushort(table + 8);
                            ushort pairPosOffset = ttushort(table + 10 + 2 * coverageIndex);
                            uchar *pairValueTable = table + pairPosOffset;
                            ushort pairValueCount = ttushort(pairValueTable);
                            uchar *pairValueArray = pairValueTable + 2;
                            // TODO: Support more formats.
                            if (valueFormat1 != 4) return 0;
                            if (valueFormat2 != 0) return 0;

                            assert(coverageIndex < pairSetCount);

                            needle=glyph2;
                            r=pairValueCount-1;
                            l=0;

                            // Binary search.
                            while (l <= r) {
                                ushort secondGlyph;
                                uchar *pairValue;
                                m = (l + r) >> 1;
                                pairValue = pairValueArray + (2 + valueRecordPairSizeInBytes) * m;
                                secondGlyph = ttushort(pairValue);
                                straw = secondGlyph;
                                if (needle < straw)
                                    r = m - 1;
                                else if (needle > straw)
                                    l = m + 1;
                                else {
                                    short xAdvance = ttshort(pairValue + 2);
                                    return xAdvance;
                                }
                            }
                        } break;

                        case 2: {
                            ushort valueFormat1 = ttushort(table + 4);
                            ushort valueFormat2 = ttushort(table + 6);

                            ushort classDef1Offset = ttushort(table + 8);
                            ushort classDef2Offset = ttushort(table + 10);
                            int glyph1class = glyph_class(table + classDef1Offset, glyph1);
                            int glyph2class = glyph_class(table + classDef2Offset, glyph2);

                            ushort class1Count = ttushort(table + 12);
                            ushort class2Count = ttushort(table + 14);
                            assert(glyph1class < class1Count);
                            assert(glyph2class < class2Count);

                            // TODO: Support more formats.
                            if (valueFormat1 != 4) return 0;
                            if (valueFormat2 != 0) return 0;

                            if (glyph1class >= 0 && glyph1class < class1Count && glyph2class >= 0 && glyph2class < class2Count) {
                                uchar *class1Records = table + 16;
                                uchar *class2Records = class1Records + 2 * (glyph1class * class2Count);
                                short xAdvance = ttshort(class2Records + 2 * glyph2class);
                                return xAdvance;
                            }
                        } break;

                        default: {
                            // There are no other cases.
                            assert(0);
                            break;
                        };
                    }
                }
                break;
            };

            default:
                // TODO: Implement other stuff.
                break;
        }
    }

    return 0;
}

int  
font·glyph_kernadvance(font·Info *info, int g1, int g2)
{
   int xAdvance = 0;

   if (info->gpos)
      xAdvance += glyph_gposadvance(info, g1, g2);
   else if (info->kern)
      xAdvance += glyph_kernadvance(info, g1, g2);

   return xAdvance;
}

int  
font·code_kernadvance(font·Info *info, int ch1, int ch2)
{
   if (!info->kern && !info->gpos) // if no kerning table, don't waste time looking up both codepoint->glyphs
      return 0;
   return font·glyph_kernadvance(info, font·glyph_index(info,ch1), font·glyph_index(info,ch2));
}

void 
font·code_hmetrics(font·Info *info, int codepoint, int *advanceWidth, int *lsb)
{
   font·glyph_hmetrics(info, font·glyph_index(info,codepoint), advanceWidth, lsb);
}

void 
font·vmetrics(font·Info *info, int *ascent, int *descent, int *lineGap)
{
   if (ascent ) *ascent  = ttshort(info->data+info->hhea + 4);
   if (descent) *descent = ttshort(info->data+info->hhea + 6);
   if (lineGap) *lineGap = ttshort(info->data+info->hhea + 8);
}

void 
font·bbox(font·Info *info, int *x0, int *y0, int *x1, int *y1)
{
   *x0 = ttshort(info->data + info->head + 36);
   *y0 = ttshort(info->data + info->head + 38);
   *x1 = ttshort(info->data + info->head + 40);
   *y1 = ttshort(info->data + info->head + 42);
}

float 
font·scaleheightto(font·Info *info, float height)
{
   int fheight = ttshort(info->data + info->hhea + 4) - ttshort(info->data + info->hhea + 6);
   return (float) height / fheight;
}

float 
font·scaleheighttoem(font·Info *info, float pixels)
{
   int unitsPerEm = ttushort(info->data + info->head + 18);
   return pixels / unitsPerEm;
}

void 
font·freeshape(font·Info *info, font·Vertex *v)
{
   info->free(info->heap, v);
}

static 
uchar *
find_svg(font·Info *info, int gl)
{
   int i;
   uchar *data = info->data;
   uchar *svg_doc_list = data + get_svg((font·Info *) info);

   int numEntries = ttushort(svg_doc_list);
   uchar *svg_docs = svg_doc_list + 2;

   for(i=0; i<numEntries; i++) {
      uchar *svg_doc = svg_docs + (12 * i);
      if ((gl >= ttushort(svg_doc)) && (gl <= ttushort(svg_doc + 2)))
         return svg_doc;
   }
   return 0;
}

int 
font·glyph_svg(font·Info *info, int gl, char **svg)
{
   uchar *data = info->data;
   uchar *svg_doc;

   if (info->svg == 0)
      return 0;

   svg_doc = find_svg(info, gl);
   if (svg_doc != nil) {
      *svg = (char *) data + info->svg + ttulong(svg_doc + 4);
      return ttulong(svg_doc + 8);
   } else {
      return 0;
   }
}

int 
font·code_svg(font·Info *info, int unicode_codepoint, char **svg)
{
   return font·glyph_svg(info, font·glyph_index(info, unicode_codepoint), svg);
}

// -----------------------------------------------------------------------
// antialiasing software rasterizer

void 
font·glyph_bitmapbox_subpixel(font·Info *font, int glyph, float scale_x, float scale_y,float shift_x, float shift_y, int *ix0, int *iy0, int *ix1, int *iy1)
{
   int x0=0,y0=0,x1,y1;
   if (!font·glyph_box(font, glyph, &x0,&y0,&x1,&y1)) {
      // e.g. space character
      if (ix0) *ix0 = 0;
      if (iy0) *iy0 = 0;
      if (ix1) *ix1 = 0;
      if (iy1) *iy1 = 0;
   } else {
      // move to integral bboxes (treating pixels as little squares, what pixels get touched)?
      if (ix0) *ix0 = (int)floor( x0 * scale_x + shift_x);
      if (iy0) *iy0 = (int)floor(-y1 * scale_y + shift_y);
      if (ix1) *ix1 = (int)ceil( x1 * scale_x + shift_x);
      if (iy1) *iy1 = (int)ceil(-y0 * scale_y + shift_y);
   }
}

void 
font·glyph_bitmapbox(font·Info *font, int glyph, float scale_x, float scale_y, int *ix0, int *iy0, int *ix1, int *iy1)
{
   font·glyph_bitmapbox_subpixel(font, glyph, scale_x, scale_y,0.0f,0.0f, ix0, iy0, ix1, iy1);
}

void 
font·code_bitmapbox_subpixel(font·Info *font, int codepoint, float scale_x, float scale_y, float shift_x, float shift_y, int *ix0, int *iy0, int *ix1, int *iy1)
{
   font·glyph_bitmapbox_subpixel(font, font·glyph_index(font,codepoint), scale_x, scale_y, shift_x, shift_y, ix0, iy0, ix1, iy1);
}

void 
font·code_bitmapbox(font·Info *font, int codepoint, float scale_x, float scale_y, int *ix0, int *iy0, int *ix1, int *iy1)
{
   font·code_bitmapbox_subpixel(font, codepoint, scale_x, scale_y, 0.0f, 0.0f, ix0, iy0, ix1, iy1);
}

// ------------------------------------------------------------------------
//  Rasterizer

typedef struct hheap_chunk
{
   struct hheap_chunk *next;
} hheap_chunk;

typedef struct hheap
{
   struct hheap_chunk *head;
   void   *first_free;
   int    nrem;
} hheap;

static 
void *
hheap_alloc(hheap *hh, uintptr size, mem·Allocator mem, void *heap)
{
    int   n;
    void *p;
    if (hh->first_free) {
       p = hh->first_free;
       hh->first_free = * (void **) p;
       return p;
    } else {
       if (hh->nrem == 0) {
          n = (size < 32 ? 2000 : size < 128 ? 800 : 100);
          hheap_chunk *c = mem.alloc(heap, 1, sizeof(hheap_chunk) + size * n);
          if (c == nil)
             return nil;

          c->next = hh->head;
          hh->head = c;
          hh->nrem = n;
       }
       --hh->nrem;
       return (char *)(hh->head) + sizeof(hheap_chunk) + size * hh->nrem;
    }
}

static 
void 
hheap_free(hheap *hh, void *p)
{
   *(void **) p = hh->first_free;
   hh->first_free = p;
}

static 
void 
hheap_cleanup(hheap *hh, mem·Allocator mem, void *heap)
{
   hheap_chunk *c = hh->head;
   while (c) {
      hheap_chunk *n = c->next;
      mem.free(heap, c);
      c = n;
   }
}

static 
ActiveEdge *
new_active(hheap *hh, Edge *e, int off_x, float start_point, mem·Allocator mem, void *heap)
{
   ActiveEdge *z = (ActiveEdge *) hheap_alloc(hh, sizeof(*z), mem, heap);
   float dxdy = (e->x1 - e->x0) / (e->y1 - e->y0);
   assert(z != nil);
   //assert(e->y0 <= start_point);
   if (!z) 
       return z;
   z->fdx = dxdy;
   z->fdy = dxdy != 0.0f ? (1.0f/dxdy) : 0.0f;
   z->fx = e->x0 + dxdy * (start_point - e->y0);
   z->fx -= off_x;
   z->direction = e->invert ? 1.0f : -1.0f;
   z->sy = e->y0;
   z->ey = e->y1;
   z->next = 0;
   return z;
}

// the edge passed in here does not cross the vertical line at x or the vertical line at x+1
// (i.e. it has already been clipped to those)
static 
void 
handle_clipped_edge(float *scanline, int x, ActiveEdge *e, float x0, float y0, float x1, float y1)
{
   if (y0 == y1) return;
   assert(y0 < y1);
   assert(e->sy <= e->ey);
   if (y0 > e->ey) return;
   if (y1 < e->sy) return;
   if (y0 < e->sy) {
      x0 += (x1-x0) * (e->sy - y0) / (y1-y0);
      y0 = e->sy;
   }
   if (y1 > e->ey) {
      x1 += (x1-x0) * (e->ey - y1) / (y1-y0);
      y1 = e->ey;
   }

   if (x0 == x)
      assert(x1 <= x+1);
   else if (x0 == x+1)
      assert(x1 >= x);
   else if (x0 <= x)
      assert(x1 <= x);
   else if (x0 >= x+1)
      assert(x1 >= x+1);
   else
      assert(x1 >= x && x1 <= x+1);

   if (x0 <= x && x1 <= x)
      scanline[x] += e->direction * (y1-y0);
   else if (x0 >= x+1 && x1 >= x+1)
      ;
   else {
      assert(x0 >= x && x0 <= x+1 && x1 >= x && x1 <= x+1);
      scanline[x] += e->direction * (y1-y0) * (1-((x0-x)+(x1-x))/2); // coverage = 1 - average x position
   }
}

static 
void 
fill_active_edges_new(float *scanline, float *scanline_fill, int len, ActiveEdge *e, float y_top)
{
   float y_bottom = y_top+1;

   while (e) {
      // brute force every pixel

      // compute intersection points with top & bottom
      assert(e->ey >= y_top);

      if (e->fdx == 0) {
         float x0 = e->fx;
         if (x0 < len) {
            if (x0 >= 0) {
               handle_clipped_edge(scanline,(int) x0,e, x0,y_top, x0,y_bottom);
               handle_clipped_edge(scanline_fill-1,(int) x0+1,e, x0,y_top, x0,y_bottom);
            } else {
               handle_clipped_edge(scanline_fill-1,0,e, x0,y_top, x0,y_bottom);
            }
         }
      } else {
         float x0 = e->fx;
         float dx = e->fdx;
         float xb = x0 + dx;
         float x_top, x_bottom;
         float sy0,sy1;
         float dy = e->fdy;
         assert(e->sy <= y_bottom && e->ey >= y_top);

         // compute endpoints of line segment clipped to this scanline (if the
         // line segment starts on this scanline. x0 is the intersection of the
         // line with y_top, but that may be off the line segment.
         if (e->sy > y_top) {
            x_top = x0 + dx * (e->sy - y_top);
            sy0 = e->sy;
         } else {
            x_top = x0;
            sy0 = y_top;
         }
         if (e->ey < y_bottom) {
            x_bottom = x0 + dx * (e->ey - y_top);
            sy1 = e->ey;
         } else {
            x_bottom = xb;
            sy1 = y_bottom;
         }

         if (x_top >= 0 && x_bottom >= 0 && x_top < len && x_bottom < len) {
            // from here on, we don't have to range check x values

            if ((int) x_top == (int) x_bottom) {
               float height;
               // simple case, only spans one pixel
               int x = (int) x_top;
               height = sy1 - sy0;
               assert(x >= 0 && x < len);
               scanline[x] += e->direction * (1-((x_top - x) + (x_bottom-x))/2)  * height;
               scanline_fill[x] += e->direction * height; // everything right of this pixel is filled
            } else {
               int x,x1,x2;
               float y_crossing, step, sign, area;
               // covers 2+ pixels
               if (x_top > x_bottom) {
                  // flip scanline vertically; signed area is the same
                  float t;
                  sy0 = y_bottom - (sy0 - y_top);
                  sy1 = y_bottom - (sy1 - y_top);
                  t = sy0, sy0 = sy1, sy1 = t;
                  t = x_bottom, x_bottom = x_top, x_top = t;
                  dx = -dx;
                  dy = -dy;
                  t = x0, x0 = xb, xb = t;
               }

               x1 = (int) x_top;
               x2 = (int) x_bottom;
               // compute intersection with y axis at x1+1
               y_crossing = (x1+1 - x0) * dy + y_top;

               sign = e->direction;
               // area of the rectangle covered from y0..y_crossing
               area = sign * (y_crossing-sy0);
               // area of the triangle (x_top,y0), (x+1,y0), (x+1,y_crossing)
               scanline[x1] += area * (1-((x_top - x1)+(x1+1-x1))/2);

               step = sign * dy;
               for (x = x1+1; x < x2; ++x) {
                  scanline[x] += area + step/2;
                  area += step;
               }
               y_crossing += dy * (x2 - (x1+1));

               assert(fabs(area) <= 1.01f);

               scanline[x2] += area + sign * (1-((x2-x2)+(x_bottom-x2))/2) * (sy1-y_crossing);

               scanline_fill[x2] += sign * (sy1-sy0);
            }
         } else {
            // if edge goes outside of box we're drawing, we require
            // clipping logic. since this does not match the intended use
            // of this library, we use a different, very slow brute
            // force implementation
            int x;
            for (x=0; x < len; ++x) {
               // cases:
               //
               // there can be up to two intersections with the pixel. any intersection
               // with left or right edges can be handled by splitting into two (or three)
               // regions. intersections with top & bottom do not necessitate case-wise logic.
               //
               // the old way of doing this found the intersections with the left & right edges,
               // then used some simple logic to produce up to three segments in sorted order
               // from top-to-bottom. however, this had a problem: if an x edge was epsilon
               // across the x border, then the corresponding y position might not be distinct
               // from the other y segment, and it might ignored as an empty segment. to avoid
               // that, we need to explicitly produce segments based on x positions.

               // rename variables to clearly-defined pairs
               float y0 = y_top;
               float x1 = (float) (x);
               float x2 = (float) (x+1);
               float x3 = xb;
               float y3 = y_bottom;

               // x = e->x + e->dx * (y-y_top)
               // (y-y_top) = (x - e->x) / e->dx
               // y = (x - e->x) / e->dx + y_top
               float y1 = (x - x0) / dx + y_top;
               float y2 = (x+1 - x0) / dx + y_top;

               if (x0 < x1 && x3 > x2) {         // three segments descending down-right
                  handle_clipped_edge(scanline,x,e, x0,y0, x1,y1);
                  handle_clipped_edge(scanline,x,e, x1,y1, x2,y2);
                  handle_clipped_edge(scanline,x,e, x2,y2, x3,y3);
               } else if (x3 < x1 && x0 > x2) {  // three segments descending down-left
                  handle_clipped_edge(scanline,x,e, x0,y0, x2,y2);
                  handle_clipped_edge(scanline,x,e, x2,y2, x1,y1);
                  handle_clipped_edge(scanline,x,e, x1,y1, x3,y3);
               } else if (x0 < x1 && x3 > x1) {  // two segments across x, down-right
                  handle_clipped_edge(scanline,x,e, x0,y0, x1,y1);
                  handle_clipped_edge(scanline,x,e, x1,y1, x3,y3);
               } else if (x3 < x1 && x0 > x1) {  // two segments across x, down-left
                  handle_clipped_edge(scanline,x,e, x0,y0, x1,y1);
                  handle_clipped_edge(scanline,x,e, x1,y1, x3,y3);
               } else if (x0 < x2 && x3 > x2) {  // two segments across x+1, down-right
                  handle_clipped_edge(scanline,x,e, x0,y0, x2,y2);
                  handle_clipped_edge(scanline,x,e, x2,y2, x3,y3);
               } else if (x3 < x2 && x0 > x2) {  // two segments across x+1, down-left
                  handle_clipped_edge(scanline,x,e, x0,y0, x2,y2);
                  handle_clipped_edge(scanline,x,e, x2,y2, x3,y3);
               } else {  // one segment
                  handle_clipped_edge(scanline,x,e, x0,y0, x3,y3);
               }
            }
         }
      }
      e = e->next;
   }
}

// directly AA rasterize edges w/o supersampling
static 
void 
rasterize_sorted_edges(font·Bitmap *result, Edge *e, int n, int vsubsample, int off_x, int off_y, mem·Allocator mem, void *heap)
{
   hheap hh = { 0 };
   ActiveEdge *active = nil;
   int y,j=0, i;
   float scanline_data[129], *scanline, *scanline2;

   if (result->w > 64)
      scanline = mem.alloc(heap, (result->w*2+1), sizeof(float));
   else
      scanline = scanline_data;

   scanline2 = scanline + result->w;

   y = off_y;
   e[n].y0 = (float) (off_y + result->h) + 1;

   while (j < result->h) {
      // find center of pixel for this scanline
      float scan_y_top    = y + 0.0f;
      float scan_y_bottom = y + 1.0f;
      ActiveEdge **step = &active;

      memset(scanline , 0, result->w*sizeof(scanline[0]));
      memset(scanline2, 0, (result->w+1)*sizeof(scanline[0]));

      // update all active edges;
      // remove all active edges that terminate before the top of this scanline
      while (*step) {
         ActiveEdge * z = *step;
         if (z->ey <= scan_y_top) {
            *step = z->next; // delete from list
            assert(z->direction);
            z->direction = 0;
            hheap_free(&hh, z);
         } else {
            step = &((*step)->next); // advance through list
         }
      }

      // insert all edges that start before the bottom of this scanline
      while (e->y0 <= scan_y_bottom) {
         if (e->y0 != e->y1) {
            ActiveEdge *z = new_active(&hh, e, off_x, scan_y_top, mem, heap);
            if (z != nil) {
               if (j == 0 && off_y != 0) {
                  if (z->ey < scan_y_top) {
                     // this can happen due to subpixel positioning and some kind of fp rounding error i think
                     z->ey = scan_y_top;
                  }
               }
               assert(z->ey >= scan_y_top); // if we get really unlucky a tiny bit of an edge can be out of bounds
               // insert at front
               z->next = active;
               active = z;
            }
         }
         ++e;
      }

      // now process all active edges
      if (active)
         fill_active_edges_new(scanline, scanline2+1, result->w, active, scan_y_top);

      {
         float sum = 0;
         for (i=0; i < result->w; ++i) {
            float k;
            int m;
            sum += scanline2[i];
            k = scanline[i] + sum;
            k = (float) fabs(k)*255 + 0.5f;
            m = (int) k;
            if (m > 255) m = 255;
            result->pixels[j*result->stride + i] = (uchar) m;
         }
      }
      // advance all the edges
      step = &active;
      while (*step) {
         ActiveEdge *z = *step;
         z->fx += z->fdx; // advance to position for current scanline
         step = &((*step)->next); // advance through list
      }

      ++y;
      ++j;
   }

   hheap_cleanup(&hh, mem, heap);

   if (scanline != scanline_data)
      mem.free(heap, scanline);
}

#define CMP_Y0(a,b)  ((a)->y0 < (b)->y0)

static 
void 
sort_edges_ins_sort(Edge *p, int n)
{
   int i,j;
   for (i=1; i < n; ++i) {
      Edge t = p[i], *a = &t;
      j = i;
      while (j > 0) {
         Edge *b = &p[j-1];
         int c = CMP_Y0(a,b);
         if (!c) break;
         p[j] = p[j-1];
         --j;
      }
      if (i != j)
         p[j] = t;
   }
}

static 
void 
sort_edges_quicksort(Edge *p, int n)
{
   /* threshold for transitioning to insertion sort */
   while (n > 12) {
      Edge t;
      int c01,c12,c,m,i,j;

      /* compute median of three */
      m = n >> 1;
      c01 = CMP_Y0(&p[0],&p[m]);
      c12 = CMP_Y0(&p[m],&p[n-1]);
      /* if 0 >= mid >= end, or 0 < mid < end, then use mid */
      if (c01 != c12) {
         /* otherwise, we'll need to swap something else to middle */
         int z;
         c = CMP_Y0(&p[0],&p[n-1]);
         /* 0>mid && mid<n:  0>n => n; 0<n => 0 */
         /* 0<mid && mid>n:  0>n => 0; 0<n => n */
         z = (c == c12) ? 0 : n-1;
         t = p[z];
         p[z] = p[m];
         p[m] = t;
      }
      /* now p[m] is the median-of-three */
      /* swap it to the beginning so it won't move around */
      t = p[0];
      p[0] = p[m];
      p[m] = t;

      /* partition loop */
      i=1;
      j=n-1;
      for(;;) {
         /* handling of equality is crucial here */
         /* for sentinels & efficiency with duplicates */
         for (;;++i) {
            if (!CMP_Y0(&p[i], &p[0])) 
                break;
         }
         for (;;--j) {
            if (!CMP_Y0(&p[0], &p[j])) 
                break;
         }
         /* make sure we haven't crossed */
         if (i >= j) 
             break;
         t = p[i];
         p[i] = p[j];
         p[j] = t;

         ++i;
         --j;
      }
      /* recurse on smaller side, iterate on larger */
      if (j < (n-i)) {
         sort_edges_quicksort(p,j);
         p = p+i;
         n = n-i;
      } else {
         sort_edges_quicksort(p+i, n-i);
         n = j;
      }
   }
}

static 
void 
sort_edges(Edge *p, int n)
{
   sort_edges_quicksort(p, n);
   sort_edges_ins_sort(p, n);
}

static 
void 
rasterize_points(font·Bitmap *result, Point *pts, int *wcount, int windings, float scale_x, float scale_y, float shift_x, float shift_y, int off_x, int off_y, int invert, mem·Allocator mem, void *heap)
{
   float y_scale_inv = invert ? -scale_y : scale_y;
   Edge *e;
   int n,i,j,k,m;
   int vsubsample = 1;
   // vsubsample should divide 255 evenly; otherwise we won't reach full opacity

   // now we have to blow out the windings into explicit edge lists
   n = 0;
   for (i=0; i < windings; ++i)
      n += wcount[i];

   e = mem.alloc(heap, n+1, sizeof(*e)); // add an extra one as a sentinel
   if (e == 0) 
       return;
   n = 0;

   m=0;
   for (i=0; i < windings; ++i) {
      Point *p = pts + m;
      m += wcount[i];
      j = wcount[i]-1;
      for (k=0; k < wcount[i]; j=k++) {
         int a=k,b=j;
         // skip the Edge if horizontal
         if (p[j].y == p[k].y)
            continue;
         // add edge from j to k to the list
         e[n].invert = 0;
         if (invert ? p[j].y > p[k].y : p[j].y < p[k].y) {
            e[n].invert = 1;
            a=j,b=k;
         }
         e[n].x0 =  p[a].x * scale_x + shift_x;
         e[n].y0 = (p[a].y * y_scale_inv + shift_y) * vsubsample;
         e[n].x1 =  p[b].x * scale_x + shift_x;
         e[n].y1 = (p[b].y * y_scale_inv + shift_y) * vsubsample;
         ++n;
      }
   }

   // now sort the edges by their highest point (should snap to integer, and then by x)
   sort_edges(e, n);

   // now, traverse the scanlines and find the intersections on each scanline, use xor winding rule
   rasterize_sorted_edges(result, e, n, vsubsample, off_x, off_y, mem, heap);

   mem.free(heap, e);
}

static 
void 
add_point(Point *points, int n, float x, float y)
{
   if (!points) 
       return; // during first pass, it's unallocated

   points[n].x = x;
   points[n].y = y;
}

// tessellate until threshold p is happy... @TODO warped to compensate for non-linear stretching
static 
int 
tesselate_curve(Point *points, int *num_points, float x0, float y0, float x1, float y1, float x2, float y2, float objspace_flatness_squared, int n)
{
   // midpoint
   float mx = (x0 + 2*x1 + x2)/4;
   float my = (y0 + 2*y1 + y2)/4;
   // versus directly drawn line
   float dx = (x0+x2)/2 - mx;
   float dy = (y0+y2)/2 - my;
   if (n > 16) // 65536 segments on one curve better be enough!
      return 1;
   if (dx*dx+dy*dy > objspace_flatness_squared) { // half-pixel error allowed... need to be smaller if AA
      tesselate_curve(points, num_points, x0,y0, (x0+x1)/2.0f,(y0+y1)/2.0f, mx,my, objspace_flatness_squared,n+1);
      tesselate_curve(points, num_points, mx,my, (x1+x2)/2.0f,(y1+y2)/2.0f, x2,y2, objspace_flatness_squared,n+1);
   } else {
      add_point(points, *num_points,x2,y2);
      *num_points = *num_points+1;
   }
   return 1;
}

static 
void 
tesselate_cubic(Point *points, int *num_points, float x0, float y0, float x1, float y1, float x2, float y2, float x3, float y3, float objspace_flatness_squared, int n)
{
   // @TODO this "flatness" calculation is just made-up nonsense that seems to work well enough
   float dx0 = x1-x0;
   float dy0 = y1-y0;
   float dx1 = x2-x1;
   float dy1 = y2-y1;
   float dx2 = x3-x2;
   float dy2 = y3-y2;
   float dx = x3-x0;
   float dy = y3-y0;
   float longlen  = (float) (sqrt(dx0*dx0+dy0*dy0)+sqrt(dx1*dx1+dy1*dy1)+sqrt(dx2*dx2+dy2*dy2));
   float shortlen = (float) sqrt(dx*dx+dy*dy);
   float flatness_squared = longlen*longlen-shortlen*shortlen;

   if (n > 16) // 65536 segments on one curve better be enough!
      return;

   if (flatness_squared > objspace_flatness_squared) {
      float x01 = (x0+x1)/2;
      float y01 = (y0+y1)/2;
      float x12 = (x1+x2)/2;
      float y12 = (y1+y2)/2;
      float x23 = (x2+x3)/2;
      float y23 = (y2+y3)/2;

      float xa = (x01+x12)/2;
      float ya = (y01+y12)/2;
      float xb = (x12+x23)/2;
      float yb = (y12+y23)/2;

      float mx = (xa+xb)/2;
      float my = (ya+yb)/2;

      tesselate_cubic(points, num_points, x0,y0, x01,y01, xa,ya, mx,my, objspace_flatness_squared,n+1);
      tesselate_cubic(points, num_points, mx,my, xb,yb, x23,y23, x3,y3, objspace_flatness_squared,n+1);
   } else {
      add_point(points, *num_points,x3,y3);
      *num_points = *num_points+1;
   }
}

// returns number of contours
static 
Point *
flatten(font·Vertex *verts, int num_verts, float objspace_flatness, int **contour_lengths, int *num_contours, mem·Allocator mem, void *heap)
{
   Point *points=0;
   int num_points=0;

   float objspace_flatness_squared = objspace_flatness * objspace_flatness;
   int i,n=0,start=0, pass;

   // count how many "moves" there are to get the contour count
   for (i=0; i < num_verts; ++i)
      if (verts[i].type == font·Vmove)
         ++n;

   *num_contours = n;
   if (n == 0) 
       return 0;

   *contour_lengths = mem.alloc(heap, n, sizeof(**contour_lengths));

   if (*contour_lengths == 0) {
      *num_contours = 0;
      return 0;
   }

   // make two passes through the points so we don't need to realloc
   for (pass=0; pass < 2; ++pass) {
      float x=0,y=0;
      if (pass == 1) {
         points = mem.alloc(heap, num_points, sizeof(points[0]));
         if (!points)
             goto error;
      }
      num_points = 0;
      n= -1;
      for (i=0; i < num_verts; ++i) {
         switch (verts[i].type) {
            case font·Vmove:
               // start the next contour
               if (n >= 0)
                  (*contour_lengths)[n] = num_points - start;
               ++n;
               start = num_points;

               x = verts[i].x, y = verts[i].y;
               add_point(points, num_points++, x,y);
               break;
            case font·Vline:
               x = verts[i].x, y = verts[i].y;
               add_point(points, num_points++, x, y);
               break;
            case font·Vcurve:
               tesselate_curve(points, &num_points, x,y,
                                        verts[i].cx, verts[i].cy,
                                        verts[i].x,  verts[i].y,
                                        objspace_flatness_squared, 0);
               x = verts[i].x, y = verts[i].y;
               break;
            case font·Vcubic:
               tesselate_cubic(points, &num_points, x,y,
                                        verts[i].cx, verts[i].cy,
                                        verts[i].cx1, verts[i].cy1,
                                        verts[i].x,  verts[i].y,
                                        objspace_flatness_squared, 0);
               x = verts[i].x, y = verts[i].y;
               break;
         }
      }
      (*contour_lengths)[n] = num_points - start;
   }
   return points;

error:
   mem.free(heap, points);
   mem.free(heap, *contour_lengths);
   *contour_lengths = nil;
   *num_contours    = 0;
   return nil;
}

static
void
rasterize(font·Bitmap *result, float flatness_in_pixels, font·Vertex *verts, int num_verts, float scale_x, float scale_y, float shift_x, float shift_y, int x_off, int y_off, int invert, mem·Allocator mal, void *heap)
{
   float scale            = (scale_x > scale_y) ? scale_y : scale_x;
   int winding_count      = 0;
   int *winding_lengths   = nil;
   Point *windings = flatten(verts, num_verts, flatness_in_pixels / scale, &winding_lengths, &winding_count, mal, heap);
   if (windings) {
      rasterize_points(result, windings, winding_lengths, winding_count, scale_x, scale_y, shift_x, shift_y, x_off, y_off, invert, mal, heap);
      mal.free(heap, windings);
      mal.free(heap, winding_lengths);
   }
}

void 
font·freebitmap(font·Info *info, uchar *bm)
{
   info->free(info->heap, bm);
}

uchar *
font·glyph_makebitmap_subpixel(font·Info *info, float scale_x, float scale_y, float shift_x, float shift_y, int glyph, int *width, int *height, int *xoff, int *yoff)
{
   int ix0,iy0,ix1,iy1;
   font·Bitmap gbm;
   font·Vertex *verts;
   int num_verts = font·glyph_shape(info, glyph, &verts);

   if (scale_x == 0) scale_x = scale_y;
   if (scale_y == 0) {
      if (scale_x == 0) {
         info->free(info->heap, verts);
         return nil;
      }
      scale_y = scale_x;
   }

   font·glyph_bitmapbox_subpixel(info, glyph, scale_x, scale_y, shift_x, shift_y, &ix0,&iy0,&ix1,&iy1);

   // now we get the size
   gbm.w = (ix1 - ix0);
   gbm.h = (iy1 - iy0);
   gbm.pixels = nil; // in case we error

   if (width ) *width  = gbm.w;
   if (height) *height = gbm.h;
   if (xoff  ) *xoff   = ix0;
   if (yoff  ) *yoff   = iy0;

   if (gbm.w && gbm.h) {
      gbm.pixels = info->alloc(info->heap, 1, gbm.h*gbm.w);
      if (gbm.pixels) {
         gbm.stride = gbm.w;

         rasterize(&gbm, 0.35f, verts, num_verts, scale_x, scale_y, shift_x, shift_y, ix0, iy0, 1, info->mal, info->heap);
      }
   }
   info->free(info->heap, verts);
   return gbm.pixels;
}

uchar *
font·glyph_makebitmap(font·Info *info, float scale_x, float scale_y, int glyph, int *width, int *height, int *xoff, int *yoff)
{
   return font·glyph_makebitmap_subpixel(info, scale_x, scale_y, 0.0f, 0.0f, glyph, width, height, xoff, yoff);
}

void 
font·glyph_fillbitmap_subpixel(font·Info *info, uchar *output, int out_w, int out_h, int out_stride, float scale_x, float scale_y, float shift_x, float shift_y, int glyph)
{
   int ix0,iy0;
   font·Vertex *verts;
   int num_verts = font·glyph_shape(info, glyph, &verts);
   font·Bitmap gbm;

   font·glyph_bitmapbox_subpixel(info, glyph, scale_x, scale_y, shift_x, shift_y, &ix0,&iy0,0,0);
   gbm.pixels = output;
   gbm.w = out_w;
   gbm.h = out_h;
   gbm.stride = out_stride;

   if (gbm.w && gbm.h)
      rasterize(&gbm, 0.35f, verts, num_verts, scale_x, scale_y, shift_x, shift_y, ix0,iy0, 1, info->mal, info->heap);

   info->free(info->heap, verts);
}

void 
font·glyph_fillbitmap(font·Info *info, unsigned char *output, int out_w, int out_h, int out_stride, float scale_x, float scale_y, int glyph)
{
   font·glyph_fillbitmap_subpixel(info, output, out_w, out_h, out_stride, scale_x, scale_y, 0.0f, 0.0f, glyph);
}

uchar *
font·code_makebitmap_subpixel(font·Info *info, float scale_x, float scale_y, float shift_x, float shift_y, int codepoint, int *width, int *height, int *xoff, int *yoff)
{
   return font·glyph_makebitmap_subpixel(info, scale_x, scale_y,shift_x,shift_y, font·glyph_index(info,codepoint), width,height,xoff,yoff);
}

void 
font·code_fillbitmap_subpixel_prefilter(font·Info *info, unsigned char *output, int out_w, int out_h, int out_stride, float scale_x, float scale_y, float shift_x, float shift_y, int oversample_x, int oversample_y, float *sub_x, float *sub_y, int codepoint)
{
   font·glyph_fillbitmap_subpixel_prefilter(info, output, out_w, out_h, out_stride, scale_x, scale_y, shift_x, shift_y, oversample_x, oversample_y, sub_x, sub_y, font·glyph_index(info,codepoint));
}

void 
font·code_fillbitmap_subpixel(font·Info *info, unsigned char *output, int out_w, int out_h, int out_stride, float scale_x, float scale_y, float shift_x, float shift_y, int codepoint)
{
   font·glyph_fillbitmap_subpixel(info, output, out_w, out_h, out_stride, scale_x, scale_y, shift_x, shift_y, font·glyph_index(info, codepoint));
}

uchar *
font·code_makebitmap(font·Info *info, float scale_x, float scale_y, int codepoint, int *width, int *height, int *xoff, int *yoff)
{
   return font·code_makebitmap_subpixel(info, scale_x, scale_y, 0.0f,0.0f, codepoint, width,height,xoff,yoff);
}

void 
font·code_fillbitmap(font·Info *info, unsigned char *output, int out_w, int out_h, int out_stride, float scale_x, float scale_y, int codepoint)
{
   font·code_fillbitmap_subpixel(info, output, out_w, out_h, out_stride, scale_x, scale_y, 0.0f,0.0f, codepoint);
}

#define OVERMASK (SAMPLE-1)

static 
void 
h_prefilter(uchar *pixels, int w, int h, int stride_in_bytes, unsigned int kernel_width)
{
   uchar buffer[SAMPLE];
   int safe_w = w - kernel_width;
   int j;
   memset(buffer, 0, SAMPLE);
   for (j=0; j < h; ++j) {
      int i;
      unsigned int total;
      memset(buffer, 0, kernel_width);

      total = 0;

      // make kernel_width a constant in common cases so compiler can optimize out the divide
      switch (kernel_width) {
         case 2:
            for (i=0; i <= safe_w; ++i) {
               total += pixels[i] - buffer[i & OVERMASK];
               buffer[(i+kernel_width) & OVERMASK] = pixels[i];
               pixels[i] = (uchar) (total / 2);
            }
            break;
         case 3:
            for (i=0; i <= safe_w; ++i) {
               total += pixels[i] - buffer[i & OVERMASK];
               buffer[(i+kernel_width) & OVERMASK] = pixels[i];
               pixels[i] = (uchar) (total / 3);
            }
            break;
         case 4:
            for (i=0; i <= safe_w; ++i) {
               total += pixels[i] - buffer[i & OVERMASK];
               buffer[(i+kernel_width) & OVERMASK] = pixels[i];
               pixels[i] = (uchar) (total / 4);
            }
            break;
         case 5:
            for (i=0; i <= safe_w; ++i) {
               total += pixels[i] - buffer[i & OVERMASK];
               buffer[(i+kernel_width) & OVERMASK] = pixels[i];
               pixels[i] = (uchar) (total / 5);
            }
            break;
         default:
            for (i=0; i <= safe_w; ++i) {
               total += pixels[i] - buffer[i & OVERMASK];
               buffer[(i+kernel_width) & OVERMASK] = pixels[i];
               pixels[i] = (uchar) (total / kernel_width);
            }
            break;
      }

      for (; i < w; ++i) {
         assert(pixels[i] == 0);
         total -= buffer[i & OVERMASK];
         pixels[i] = (uchar) (total / kernel_width);
      }

      pixels += stride_in_bytes;
   }
}

static 
void 
v_prefilter(uchar *pixels, int w, int h, int stride_in_bytes, unsigned int kernel_width)
{
   uchar buffer[SAMPLE];
   int safe_h = h - kernel_width;
   int j;
   memset(buffer, 0, SAMPLE); 
   for (j=0; j < w; ++j) {
      int i;
      unsigned int total;
      memset(buffer, 0, kernel_width);

      total = 0;

      // make kernel_width a constant in common cases so compiler can optimize out the divide
      switch (kernel_width) {
         case 2:
            for (i=0; i <= safe_h; ++i) {
               total += pixels[i*stride_in_bytes] - buffer[i & OVERMASK];
               buffer[(i+kernel_width) & OVERMASK] = pixels[i*stride_in_bytes];
               pixels[i*stride_in_bytes] = (uchar) (total / 2);
            }
            break;
         case 3:
            for (i=0; i <= safe_h; ++i) {
               total += pixels[i*stride_in_bytes] - buffer[i & OVERMASK];
               buffer[(i+kernel_width) & OVERMASK] = pixels[i*stride_in_bytes];
               pixels[i*stride_in_bytes] = (uchar) (total / 3);
            }
            break;
         case 4:
            for (i=0; i <= safe_h; ++i) {
               total += pixels[i*stride_in_bytes] - buffer[i & OVERMASK];
               buffer[(i+kernel_width) & OVERMASK] = pixels[i*stride_in_bytes];
               pixels[i*stride_in_bytes] = (uchar) (total / 4);
            }
            break;
         case 5:
            for (i=0; i <= safe_h; ++i) {
               total += pixels[i*stride_in_bytes] - buffer[i & OVERMASK];
               buffer[(i+kernel_width) & OVERMASK] = pixels[i*stride_in_bytes];
               pixels[i*stride_in_bytes] = (uchar) (total / 5);
            }
            break;
         default:
            for (i=0; i <= safe_h; ++i) {
               total += pixels[i*stride_in_bytes] - buffer[i & OVERMASK];
               buffer[(i+kernel_width) & OVERMASK] = pixels[i*stride_in_bytes];
               pixels[i*stride_in_bytes] = (uchar) (total / kernel_width);
            }
            break;
      }

      for (; i < h; ++i) {
         assert(pixels[i*stride_in_bytes] == 0);
         total -= buffer[i & OVERMASK];
         pixels[i*stride_in_bytes] = (uchar) (total / kernel_width);
      }

      pixels += 1;
   }
}

static 
float 
oversample_shift(int oversample)
{
   if (!oversample)
      return 0.0f;

   // The prefilter is a box filter of width "oversample",
   // which shifts phase by (oversample - 1)/2 pixels in
   // oversampled space. We want to shift in the opposite
   // direction to counter this.
   return (float)-(oversample - 1) / (2.0f * (float)oversample);
}

// rects array must be big enough to accommodate all characters in the given ranges
void 
font·glyph_fillbitmap_subpixel_prefilter(font·Info *info, uchar *output, int out_w, int out_h, int out_stride, float scale_x, float scale_y, float shift_x, float shift_y, int prefilter_x, int prefilter_y, float *sub_x, float *sub_y, int glyph)
{
   font·glyph_fillbitmap_subpixel(info,
                                 output,
                                 out_w - (prefilter_x - 1),
                                 out_h - (prefilter_y - 1),
                                 out_stride,
                                 scale_x,
                                 scale_y,
                                 shift_x,
                                 shift_y,
                                 glyph);

   if (prefilter_x > 1)
      h_prefilter(output, out_w, out_h, out_stride, prefilter_x);

   if (prefilter_y > 1)
      v_prefilter(output, out_w, out_h, out_stride, prefilter_y);

   *sub_x = oversample_shift(prefilter_x);
   *sub_y = oversample_shift(prefilter_y);
}

void 
font·scaledvmetrics(uchar *fontdata, int index, float size, float *ascent, float *descent, float *lineGap)
{
   int i_ascent, i_descent, i_lineGap;
   float scale;
   font·Info info;
   init(&info, fontdata, font·offsetfor(fontdata, index));
   scale = size > 0 ? font·scaleheightto(&info, size) : font·scaleheighttoem(&info, -size);
   font·vmetrics(&info, &i_ascent, &i_descent, &i_lineGap);
   *ascent  = (float) i_ascent  * scale;
   *descent = (float) i_descent * scale;
   *lineGap = (float) i_lineGap * scale;
}

// -----------------------------------------------------------------------
// sdf computation

static 
int 
ray_intersect_bezier(float orig[2], float ray[2], float q0[2], float q1[2], float q2[2], float hits[2][2])
{
   float q0perp = q0[1]*ray[0] - q0[0]*ray[1];
   float q1perp = q1[1]*ray[0] - q1[0]*ray[1];
   float q2perp = q2[1]*ray[0] - q2[0]*ray[1];
   float roperp = orig[1]*ray[0] - orig[0]*ray[1];

   float a = q0perp - 2*q1perp + q2perp;
   float b = q1perp - q0perp;
   float c = q0perp - roperp;

   float s0 = 0., s1 = 0.;
   int num_s = 0;

   if (a != 0.0) {
      float discr = b*b - a*c;
      if (discr > 0.0) {
         float rcpna = -1 / a;
         float d = (float) sqrt(discr);
         s0 = (b+d) * rcpna;
         s1 = (b-d) * rcpna;
         if (s0 >= 0.0 && s0 <= 1.0)
            num_s = 1;
         if (d > 0.0 && s1 >= 0.0 && s1 <= 1.0) {
            if (num_s == 0) s0 = s1;
            ++num_s;
         }
      }
   } else {
      // 2*b*s + c = 0
      // s = -c / (2*b)
      s0 = c / (-2 * b);
      if (s0 >= 0.0 && s0 <= 1.0)
         num_s = 1;
   }

   if (num_s == 0)
      return 0;
   else {
      float rcp_len2 = 1 / (ray[0]*ray[0] + ray[1]*ray[1]);
      float rayn_x = ray[0] * rcp_len2, rayn_y = ray[1] * rcp_len2;

      float q0d =   q0[0]*rayn_x +   q0[1]*rayn_y;
      float q1d =   q1[0]*rayn_x +   q1[1]*rayn_y;
      float q2d =   q2[0]*rayn_x +   q2[1]*rayn_y;
      float rod = orig[0]*rayn_x + orig[1]*rayn_y;

      float q10d = q1d - q0d;
      float q20d = q2d - q0d;
      float q0rd = q0d - rod;

      hits[0][0] = q0rd + s0*(2.0f - 2.0f*s0)*q10d + s0*s0*q20d;
      hits[0][1] = a*s0+b;

      if (num_s > 1) {
         hits[1][0] = q0rd + s1*(2.0f - 2.0f*s1)*q10d + s1*s1*q20d;
         hits[1][1] = a*s1+b;
         return 2;
      } else {
         return 1;
      }
   }
}

static 
int 
equal(float *a, float *b)
{
   return (a[0] == b[0] && a[1] == b[1]);
}

static 
int 
compute_crossings_x(float x, float y, int nverts, font·Vertex *verts)
{
   int i;
   float orig[2], ray[2] = { 1, 0 };
   float y_frac;
   int winding = 0;

   orig[0] = x;
   orig[1] = y;

   // make sure y never passes through a vertex of the shape
   y_frac = (float) fmod(y, 1.0f);
   if (y_frac < 0.01f)
      y += 0.01f;
   else if (y_frac > 0.99f)
      y -= 0.01f;
   orig[1] = y;

   // test a ray from (-infinity,y) to (x,y)
   for (i=0; i < nverts; ++i) {
      if (verts[i].type == font·Vline) {
         int x0 = (int) verts[i-1].x, y0 = (int) verts[i-1].y;
         int x1 = (int) verts[i  ].x, y1 = (int) verts[i  ].y;
         if (y > MIN(y0,y1) && y < MAX(y0,y1) && x > MIN(x0,x1)) {
            float x_inter = (y - y0) / (y1 - y0) * (x1-x0) + x0;
            if (x_inter < x)
               winding += (y0 < y1) ? 1 : -1;
         }
      }
      if (verts[i].type == font·Vcurve) {
         int x0 = (int) verts[i-1].x , y0 = (int) verts[i-1].y ;
         int x1 = (int) verts[i  ].cx, y1 = (int) verts[i  ].cy;
         int x2 = (int) verts[i  ].x , y2 = (int) verts[i  ].y ;
         int ax = MIN(x0,MIN(x1,x2)), ay = MIN(y0,MIN(y1,y2));
         int by = MAX(y0,MAX(y1,y2));
         if (y > ay && y < by && x > ax) {
            float q0[2],q1[2],q2[2];
            float hits[2][2];
            q0[0] = (float)x0;
            q0[1] = (float)y0;
            q1[0] = (float)x1;
            q1[1] = (float)y1;
            q2[0] = (float)x2;
            q2[1] = (float)y2;
            if (equal(q0,q1) || equal(q1,q2)) {
               x0 = (int)verts[i-1].x;
               y0 = (int)verts[i-1].y;
               x1 = (int)verts[i  ].x;
               y1 = (int)verts[i  ].y;
               if (y > MIN(y0,y1) && y < MAX(y0,y1) && x > MIN(x0,x1)) {
                  float x_inter = (y - y0) / (y1 - y0) * (x1-x0) + x0;
                  if (x_inter < x)
                     winding += (y0 < y1) ? 1 : -1;
               }
            } else {
               int num_hits = ray_intersect_bezier(orig, ray, q0, q1, q2, hits);
               if (num_hits >= 1)
                  if (hits[0][0] < 0)
                     winding += (hits[0][1] < 0 ? -1 : 1);
               if (num_hits >= 2)
                  if (hits[1][0] < 0)
                     winding += (hits[1][1] < 0 ? -1 : 1);
            }
         }
      }
   }
   return winding;
}

static 
float 
cuberoot(float x)
{
   if (x<0)
      return -(float) pow(-x,1.0f/3.0f);
   else
      return  (float) pow( x,1.0f/3.0f);
}

// x^3 + c*x^2 + b*x + a = 0
static 
int 
solve_cubic(float a, float b, float c, float *r)
{
	float s = -a / 3;
	float p = b - a*a / 3;
	float q = a * (2*a*a - 9*b) / 27 + c;
    float p3 = p*p*p;
	float d = q*q + 4*p3 / 27;
	if (d >= 0) {
		float z = (float) sqrt(d);
		float u = (-q + z) / 2;
		float v = (-q - z) / 2;
		u = cuberoot(u);
		v = cuberoot(v);
		r[0] = s + u + v;
		return 1;
	} else {
	   float u = (float) sqrt(-p/3);
	   float v = (float) acos(-sqrt(-27/p3) * q / 2) / 3; // p3 must be negative, since d is negative
	   float m = (float) cos(v);
       float n = (float) cos(v-3.141592/2)*1.732050808f;
	   r[0] = s + u * 2 * m;
	   r[1] = s - u * (m + n);
	   r[2] = s - u * (m - n);

   	return 3;
   }
}

uchar * 
font·glyph_sdf(font·Info *info, float scale, int glyph, int padding, uchar onedge_value, float pixel_dist_scale, int *width, int *height, int *xoff, int *yoff)
{
   float scale_x = scale, scale_y = scale;
   int ix0,iy0,ix1,iy1;
   int w,h;
   uchar *data;

   if (scale == 0) return nil;

   font·glyph_bitmapbox_subpixel(info, glyph, scale, scale, 0.0f,0.0f, &ix0,&iy0,&ix1,&iy1);

   // if empty, return nil
   if (ix0 == ix1 || iy0 == iy1)
      return nil;

   ix0 -= padding;
   iy0 -= padding;
   ix1 += padding;
   iy1 += padding;

   w = (ix1 - ix0);
   h = (iy1 - iy0);

   if (width ) *width  = w;
   if (height) *height = h;
   if (xoff  ) *xoff   = ix0;
   if (yoff  ) *yoff   = iy0;

   // invert for y-downwards bitmaps
   scale_y = -scale_y;

   {
      int x,y,i,j;
      float *precompute;
      font·Vertex *verts;
      int num_verts = font·glyph_shape(info, glyph, &verts);
      data = info->alloc(info->heap, 1, w * h);
      precompute = info->alloc(info->heap, num_verts, sizeof(float));

      for (i=0,j=num_verts-1; i < num_verts; j=i++) {
         if (verts[i].type == font·Vline) {
            float x0 = verts[i].x*scale_x, y0 = verts[i].y*scale_y;
            float x1 = verts[j].x*scale_x, y1 = verts[j].y*scale_y;
            float dist = (float) sqrt((x1-x0)*(x1-x0) + (y1-y0)*(y1-y0));
            precompute[i] = (dist == 0) ? 0.0f : 1.0f / dist;
         } else if (verts[i].type == font·Vcurve) {
            float x2 = verts[j].x *scale_x, y2 = verts[j].y *scale_y;
            float x1 = verts[i].cx*scale_x, y1 = verts[i].cy*scale_y;
            float x0 = verts[i].x *scale_x, y0 = verts[i].y *scale_y;
            float bx = x0 - 2*x1 + x2, by = y0 - 2*y1 + y2;
            float len2 = bx*bx + by*by;
            if (len2 != 0.0f)
               precompute[i] = 1.0f / (bx*bx + by*by);
            else
               precompute[i] = 0.0f;
         } else
            precompute[i] = 0.0f;
      }

      for (y=iy0; y < iy1; ++y) {
         for (x=ix0; x < ix1; ++x) {
            float val;
            float min_dist = 999999.0f;
            float sx = (float) x + 0.5f;
            float sy = (float) y + 0.5f;
            float x_gspace = (sx / scale_x);
            float y_gspace = (sy / scale_y);

            int winding = compute_crossings_x(x_gspace, y_gspace, num_verts, verts); // @OPTIMIZE: this could just be a rasterization, but needs to be line vs. non-tesselated curves so a new path

            for (i=0; i < num_verts; ++i) {
               float x0 = verts[i].x*scale_x, y0 = verts[i].y*scale_y;

               // check against every point here rather than inside line/curve primitives -- @TODO: wrong if multiple 'moves' in a row produce a garbage point, and given culling, probably more efficient to do within line/curve
               float dist2 = (x0-sx)*(x0-sx) + (y0-sy)*(y0-sy);
               if (dist2 < min_dist*min_dist)
                  min_dist = (float)sqrt(dist2);

               if (verts[i].type == font·Vline) {
                  float x1 = verts[i-1].x*scale_x, y1 = verts[i-1].y*scale_y;

                  // coarse culling against bbox
                  //if (sx > MIN(x0,x1)-min_dist && sx < MAX(x0,x1)+min_dist &&
                  //    sy > MIN(y0,y1)-min_dist && sy < MAX(y0,y1)+min_dist)
                  float dist = (float) fabs((x1-x0)*(y0-sy) - (y1-y0)*(x0-sx)) * precompute[i];
                  assert(i != 0);
                  if (dist < min_dist) {
                     // check position along line
                     // x' = x0 + t*(x1-x0), y' = y0 + t*(y1-y0)
                     // minimize (x'-sx)*(x'-sx)+(y'-sy)*(y'-sy)
                     float dx = x1-x0, dy = y1-y0;
                     float px = x0-sx, py = y0-sy;
                     // minimize (px+t*dx)^2 + (py+t*dy)^2 = px*px + 2*px*dx*t + t^2*dx*dx + py*py + 2*py*dy*t + t^2*dy*dy
                     // derivative: 2*px*dx + 2*py*dy + (2*dx*dx+2*dy*dy)*t, set to 0 and solve
                     float t = -(px*dx + py*dy) / (dx*dx + dy*dy);
                     if (t >= 0.0f && t <= 1.0f)
                        min_dist = dist;
                  }
               } else if (verts[i].type == font·Vcurve) {
                  float x2 = verts[i-1].x *scale_x, y2 = verts[i-1].y *scale_y;
                  float x1 = verts[i  ].cx*scale_x, y1 = verts[i  ].cy*scale_y;
                  float box_x0 = MIN(MIN(x0,x1),x2);
                  float box_y0 = MIN(MIN(y0,y1),y2);
                  float box_x1 = MAX(MAX(x0,x1),x2);
                  float box_y1 = MAX(MAX(y0,y1),y2);
                  // coarse culling against bbox to avoid computing cubic unnecessarily
                  if (sx > box_x0-min_dist && sx < box_x1+min_dist && sy > box_y0-min_dist && sy < box_y1+min_dist) {
                     int num=0;
                     float ax = x1-x0, ay = y1-y0;
                     float bx = x0 - 2*x1 + x2, by = y0 - 2*y1 + y2;
                     float mx = x0 - sx, my = y0 - sy;
                     float res[3],px,py,t,it;
                     float a_inv = precompute[i];
                     if (a_inv == 0.0) { // if a_inv is 0, it's 2nd degree so use quadratic formula
                        float a = 3*(ax*bx + ay*by);
                        float b = 2*(ax*ax + ay*ay) + (mx*bx+my*by);
                        float c = mx*ax+my*ay;
                        if (a == 0.0) { // if a is 0, it's linear
                           if (b != 0.0) {
                              res[num++] = -c/b;
                           }
                        } else {
                           float discriminant = b*b - 4*a*c;
                           if (discriminant < 0)
                              num = 0;
                           else {
                              float root = (float) sqrt(discriminant);
                              res[0] = (-b - root)/(2*a);
                              res[1] = (-b + root)/(2*a);
                              num = 2; // don't bother distinguishing 1-solution case, as code below will still work
                           }
                        }
                     } else {
                        float b = 3*(ax*bx + ay*by) * a_inv; // could precompute this as it doesn't depend on sample point
                        float c = (2*(ax*ax + ay*ay) + (mx*bx+my*by)) * a_inv;
                        float d = (mx*ax+my*ay) * a_inv;
                        num = solve_cubic(b, c, d, res);
                     }
                     if (num >= 1 && res[0] >= 0.0f && res[0] <= 1.0f) {
                        t = res[0], it = 1.0f - t;
                        px = it*it*x0 + 2*t*it*x1 + t*t*x2;
                        py = it*it*y0 + 2*t*it*y1 + t*t*y2;
                        dist2 = (px-sx)*(px-sx) + (py-sy)*(py-sy);
                        if (dist2 < min_dist * min_dist)
                           min_dist = (float) sqrt(dist2);
                     }
                     if (num >= 2 && res[1] >= 0.0f && res[1] <= 1.0f) {
                        t = res[1], it = 1.0f - t;
                        px = it*it*x0 + 2*t*it*x1 + t*t*x2;
                        py = it*it*y0 + 2*t*it*y1 + t*t*y2;
                        dist2 = (px-sx)*(px-sx) + (py-sy)*(py-sy);
                        if (dist2 < min_dist * min_dist)
                           min_dist = (float) sqrt(dist2);
                     }
                     if (num >= 3 && res[2] >= 0.0f && res[2] <= 1.0f) {
                        t = res[2], it = 1.0f - t;
                        px = it*it*x0 + 2*t*it*x1 + t*t*x2;
                        py = it*it*y0 + 2*t*it*y1 + t*t*y2;
                        dist2 = (px-sx)*(px-sx) + (py-sy)*(py-sy);
                        if (dist2 < min_dist * min_dist)
                           min_dist = (float) sqrt(dist2);
                     }
                  }
               }
            }
            if (winding == 0)
               min_dist = -min_dist;  // if outside the shape, value is negative
            val = onedge_value + pixel_dist_scale * min_dist;
            if (val < 0)
               val = 0;
            else if (val > 255)
               val = 255;
            data[(y-iy0)*w+(x-ix0)] = (uchar) val;
         }
      }
      info->free(info->heap,precompute);
      info->free(info->heap, verts);
   }
   return data;
}

uchar * 
font·code_sdf(font·Info *info, float scale, int codepoint, int padding, uchar onedge_value, float pixel_dist_scale, int *width, int *height, int *xoff, int *yoff)
{
   return font·glyph_sdf(info, scale, font·glyph_index(info, codepoint), padding, onedge_value, pixel_dist_scale, width, height, xoff, yoff);
}

void 
font·freesdf(font·Info* info, uchar *bitmap)
{
   info->free(info->heap, bitmap);
}

char*
font·name(font·Info *font, int *length, int platformID, int encodingID, int languageID, int nameID)
{
   int32 i,count,stringOffset;
   uchar *fc = font->data;
   uint32 offset = font->fontstart;
   uint32 nm = find_table(fc, offset, "name");
   if (!nm) return nil;

   count = ttushort(fc+nm+2);
   stringOffset = nm + ttushort(fc+nm+4);
   for (i=0; i < count; ++i) {
      uint32 loc = nm + 6 + 12 * i;
      if (platformID == ttushort(fc+loc+0) && encodingID == ttushort(fc+loc+2)
          && languageID == ttushort(fc+loc+4) && nameID == ttushort(fc+loc+6)) {
         *length = ttushort(fc+loc+8);
         return (char *) (fc+stringOffset+ttushort(fc+loc+10));
      }
   }
   return nil;
}

#if 0
static 
int 
matchpair(uchar *fc, uint32 nm, uchar *name, int32 nlen, int32 target_id, int32 next_id)
{
   int32 i;
   int32 count = ttushort(fc+nm+2);
   int32 stringOffset = nm + ttushort(fc+nm+4);

   for (i=0; i < count; ++i) {
      uint32 loc = nm + 6 + 12 * i;
      int32 id = ttushort(fc+loc+6);
      if (id == target_id) {
         // find the encoding
         int32 platform = ttushort(fc+loc+0), encoding = ttushort(fc+loc+2), language = ttushort(fc+loc+4);

         // is this a Unicode encoding?
         if (platform == 0 || (platform == 3 && encoding == 1) || (platform == 3 && encoding == 10)) {
            int32 slen = ttushort(fc+loc+8);
            int32 off = ttushort(fc+loc+10);

            // check if there's a prefix match
            int32 matchlen = CompareUTF8toUTF16_bigendian_prefix(name, nlen, fc+stringOffset+off,slen);
            if (matchlen >= 0) {
               // check for target_id+1 immediately following, with same encoding & language
               if (i+1 < count && ttushort(fc+loc+12+6) == next_id && ttushort(fc+loc+12) == platform && ttushort(fc+loc+12+2) == encoding && ttushort(fc+loc+12+4) == language) {
                  slen = ttushort(fc+loc+12+8);
                  off = ttushort(fc+loc+12+10);
                  if (slen == 0) {
                     if (matchlen == nlen)
                        return 1;
                  } else if (matchlen < nlen && name[matchlen] == ' ') {
                     ++matchlen;
                     if (font·CompareUTF8toUTF16_bigendian((char*) (name+matchlen), nlen-matchlen, (char*)(fc+stringOffset+off),slen))
                        return 1;
                  }
               } else {
                  // if nothing immediately following
                  if (matchlen == nlen)
                     return 1;
               }
            }
         }

         // @TODO handle other encodings
      }
   }
   return 0;
}

static 
int 
matches(uchar *fc, uint32 offset, uchar *name, int32 flags)
{
   int32 nlen = (int32) strlen((char *) name);
   uint32 nm, hd;
   if (!isfont(fc+offset)) 
       return 0;

   // check italics/bold/underline flags in macStyle...
   if (flags) {
      hd = find_table(fc, offset, "head");
      if ((ttushort(fc+hd+44) & 7) != (flags & 7)) return 0;
   }

   nm = find_table(fc, offset, "name");
   if (!nm) return 0;

   if (flags) {
      // if we checked the macStyle flags, then just check the family and ignore the subfamily
      if (matchpair(fc, nm, name, nlen, 16, -1))  return 1;
      if (matchpair(fc, nm, name, nlen,  1, -1))  return 1;
      if (matchpair(fc, nm, name, nlen,  3, -1))  return 1;
   } else {
      if (matchpair(fc, nm, name, nlen, 16, 17))  return 1;
      if (matchpair(fc, nm, name, nlen,  1,  2))  return 1;
      if (matchpair(fc, nm, name, nlen,  3, -1))  return 1;
   }

   return 0;
}

int 
font·findmatch(uchar *font_collection, char *name_utf8, int32 flags)
{
   int32 i;
   for (i=0;;++i) {
      int32 off = font·offsetfor(font_collection, i);
      if (off < 0) return off;
      if (matches((uchar *) font_collection, off, (uchar*) name_utf8, flags))
         return off;
   }
}
#endif