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/src/compiler/android-ndk/jni/freetype/src/base/ftcalc.c

http://ftk.googlecode.com/
C | 957 lines | 582 code | 257 blank | 118 comment | 108 complexity | ea8c76f0cdee11b67a8dbf45a01695bd MD5 | raw file
  1/***************************************************************************/
  2/*                                                                         */
  3/*  ftcalc.c                                                               */
  4/*                                                                         */
  5/*    Arithmetic computations (body).                                      */
  6/*                                                                         */
  7/*  Copyright 1996-2001, 2002, 2003, 2004, 2005, 2006, 2008 by             */
  8/*  David Turner, Robert Wilhelm, and Werner Lemberg.                      */
  9/*                                                                         */
 10/*  This file is part of the FreeType project, and may only be used,       */
 11/*  modified, and distributed under the terms of the FreeType project      */
 12/*  license, LICENSE.TXT.  By continuing to use, modify, or distribute     */
 13/*  this file you indicate that you have read the license and              */
 14/*  understand and accept it fully.                                        */
 15/*                                                                         */
 16/***************************************************************************/
 17
 18  /*************************************************************************/
 19  /*                                                                       */
 20  /* Support for 1-complement arithmetic has been totally dropped in this  */
 21  /* release.  You can still write your own code if you need it.           */
 22  /*                                                                       */
 23  /*************************************************************************/
 24
 25  /*************************************************************************/
 26  /*                                                                       */
 27  /* Implementing basic computation routines.                              */
 28  /*                                                                       */
 29  /* FT_MulDiv(), FT_MulFix(), FT_DivFix(), FT_RoundFix(), FT_CeilFix(),   */
 30  /* and FT_FloorFix() are declared in freetype.h.                         */
 31  /*                                                                       */
 32  /*************************************************************************/
 33
 34
 35#include <ft2build.h>
 36#include FT_GLYPH_H
 37#include FT_INTERNAL_CALC_H
 38#include FT_INTERNAL_DEBUG_H
 39#include FT_INTERNAL_OBJECTS_H
 40
 41#ifdef FT_MULFIX_INLINED
 42#undef FT_MulFix
 43#endif
 44
 45/* we need to define a 64-bits data type here */
 46
 47#ifdef FT_LONG64
 48
 49  typedef FT_INT64  FT_Int64;
 50
 51#else
 52
 53  typedef struct  FT_Int64_
 54  {
 55    FT_UInt32  lo;
 56    FT_UInt32  hi;
 57
 58  } FT_Int64;
 59
 60#endif /* FT_LONG64 */
 61
 62
 63  /*************************************************************************/
 64  /*                                                                       */
 65  /* The macro FT_COMPONENT is used in trace mode.  It is an implicit      */
 66  /* parameter of the FT_TRACE() and FT_ERROR() macros, used to print/log  */
 67  /* messages during execution.                                            */
 68  /*                                                                       */
 69#undef  FT_COMPONENT
 70#define FT_COMPONENT  trace_calc
 71
 72
 73  /* The following three functions are available regardless of whether */
 74  /* FT_LONG64 is defined.                                             */
 75
 76  /* documentation is in freetype.h */
 77
 78  FT_EXPORT_DEF( FT_Fixed )
 79  FT_RoundFix( FT_Fixed  a )
 80  {
 81    return ( a >= 0 ) ?   ( a + 0x8000L ) & ~0xFFFFL
 82                      : -((-a + 0x8000L ) & ~0xFFFFL );
 83  }
 84
 85
 86  /* documentation is in freetype.h */
 87
 88  FT_EXPORT_DEF( FT_Fixed )
 89  FT_CeilFix( FT_Fixed  a )
 90  {
 91    return ( a >= 0 ) ?   ( a + 0xFFFFL ) & ~0xFFFFL
 92                      : -((-a + 0xFFFFL ) & ~0xFFFFL );
 93  }
 94
 95
 96  /* documentation is in freetype.h */
 97
 98  FT_EXPORT_DEF( FT_Fixed )
 99  FT_FloorFix( FT_Fixed  a )
100  {
101    return ( a >= 0 ) ?   a & ~0xFFFFL
102                      : -((-a) & ~0xFFFFL );
103  }
104
105
106#ifdef FT_CONFIG_OPTION_OLD_INTERNALS
107
108  /* documentation is in ftcalc.h */
109
110  FT_EXPORT_DEF( FT_Int32 )
111  FT_Sqrt32( FT_Int32  x )
112  {
113    FT_UInt32  val, root, newroot, mask;
114
115
116    root = 0;
117    mask = (FT_UInt32)0x40000000UL;
118    val  = (FT_UInt32)x;
119
120    do
121    {
122      newroot = root + mask;
123      if ( newroot <= val )
124      {
125        val -= newroot;
126        root = newroot + mask;
127      }
128
129      root >>= 1;
130      mask >>= 2;
131
132    } while ( mask != 0 );
133
134    return root;
135  }
136
137#endif /* FT_CONFIG_OPTION_OLD_INTERNALS */
138
139
140#ifdef FT_LONG64
141
142
143  /* documentation is in freetype.h */
144
145  FT_EXPORT_DEF( FT_Long )
146  FT_MulDiv( FT_Long  a,
147             FT_Long  b,
148             FT_Long  c )
149  {
150    FT_Int   s;
151    FT_Long  d;
152
153
154    s = 1;
155    if ( a < 0 ) { a = -a; s = -1; }
156    if ( b < 0 ) { b = -b; s = -s; }
157    if ( c < 0 ) { c = -c; s = -s; }
158
159    d = (FT_Long)( c > 0 ? ( (FT_Int64)a * b + ( c >> 1 ) ) / c
160                         : 0x7FFFFFFFL );
161
162    return ( s > 0 ) ? d : -d;
163  }
164
165
166#ifdef TT_USE_BYTECODE_INTERPRETER
167
168  /* documentation is in ftcalc.h */
169
170  FT_BASE_DEF( FT_Long )
171  FT_MulDiv_No_Round( FT_Long  a,
172                      FT_Long  b,
173                      FT_Long  c )
174  {
175    FT_Int   s;
176    FT_Long  d;
177
178
179    s = 1;
180    if ( a < 0 ) { a = -a; s = -1; }
181    if ( b < 0 ) { b = -b; s = -s; }
182    if ( c < 0 ) { c = -c; s = -s; }
183
184    d = (FT_Long)( c > 0 ? (FT_Int64)a * b / c
185                         : 0x7FFFFFFFL );
186
187    return ( s > 0 ) ? d : -d;
188  }
189
190#endif /* TT_USE_BYTECODE_INTERPRETER */
191
192
193  /* documentation is in freetype.h */
194
195  FT_EXPORT_DEF( FT_Long )
196  FT_MulFix( FT_Long  a,
197             FT_Long  b )
198  {
199#ifdef FT_MULFIX_ASSEMBLER
200
201    return FT_MULFIX_ASSEMBLER( a, b );
202
203#else
204
205    FT_Int   s = 1;
206    FT_Long  c;
207
208
209    if ( a < 0 )
210    {
211      a = -a;
212      s = -1;
213    }
214
215    if ( b < 0 )
216    {
217      b = -b;
218      s = -s;
219    }
220
221    c = (FT_Long)( ( (FT_Int64)a * b + 0x8000L ) >> 16 );
222
223    return ( s > 0 ) ? c : -c;
224
225#endif /* FT_MULFIX_ASSEMBLER */
226  }
227
228
229  /* documentation is in freetype.h */
230
231  FT_EXPORT_DEF( FT_Long )
232  FT_DivFix( FT_Long  a,
233             FT_Long  b )
234  {
235    FT_Int32   s;
236    FT_UInt32  q;
237
238    s = 1;
239    if ( a < 0 ) { a = -a; s = -1; }
240    if ( b < 0 ) { b = -b; s = -s; }
241
242    if ( b == 0 )
243      /* check for division by 0 */
244      q = 0x7FFFFFFFL;
245    else
246      /* compute result directly */
247      q = (FT_UInt32)( ( ( (FT_Int64)a << 16 ) + ( b >> 1 ) ) / b );
248
249    return ( s < 0 ? -(FT_Long)q : (FT_Long)q );
250  }
251
252
253#else /* !FT_LONG64 */
254
255
256  static void
257  ft_multo64( FT_UInt32  x,
258              FT_UInt32  y,
259              FT_Int64  *z )
260  {
261    FT_UInt32  lo1, hi1, lo2, hi2, lo, hi, i1, i2;
262
263
264    lo1 = x & 0x0000FFFFU;  hi1 = x >> 16;
265    lo2 = y & 0x0000FFFFU;  hi2 = y >> 16;
266
267    lo = lo1 * lo2;
268    i1 = lo1 * hi2;
269    i2 = lo2 * hi1;
270    hi = hi1 * hi2;
271
272    /* Check carry overflow of i1 + i2 */
273    i1 += i2;
274    hi += (FT_UInt32)( i1 < i2 ) << 16;
275
276    hi += i1 >> 16;
277    i1  = i1 << 16;
278
279    /* Check carry overflow of i1 + lo */
280    lo += i1;
281    hi += ( lo < i1 );
282
283    z->lo = lo;
284    z->hi = hi;
285  }
286
287
288  static FT_UInt32
289  ft_div64by32( FT_UInt32  hi,
290                FT_UInt32  lo,
291                FT_UInt32  y )
292  {
293    FT_UInt32  r, q;
294    FT_Int     i;
295
296
297    q = 0;
298    r = hi;
299
300    if ( r >= y )
301      return (FT_UInt32)0x7FFFFFFFL;
302
303    i = 32;
304    do
305    {
306      r <<= 1;
307      q <<= 1;
308      r  |= lo >> 31;
309
310      if ( r >= (FT_UInt32)y )
311      {
312        r -= y;
313        q |= 1;
314      }
315      lo <<= 1;
316    } while ( --i );
317
318    return q;
319  }
320
321
322  static void
323  FT_Add64( FT_Int64*  x,
324            FT_Int64*  y,
325            FT_Int64  *z )
326  {
327    register FT_UInt32  lo, hi;
328
329
330    lo = x->lo + y->lo;
331    hi = x->hi + y->hi + ( lo < x->lo );
332
333    z->lo = lo;
334    z->hi = hi;
335  }
336
337
338  /* documentation is in freetype.h */
339
340  /* The FT_MulDiv function has been optimized thanks to ideas from      */
341  /* Graham Asher.  The trick is to optimize computation when everything */
342  /* fits within 32-bits (a rather common case).                         */
343  /*                                                                     */
344  /*  we compute 'a*b+c/2', then divide it by 'c'. (positive values)     */
345  /*                                                                     */
346  /*  46340 is FLOOR(SQRT(2^31-1)).                                      */
347  /*                                                                     */
348  /*  if ( a <= 46340 && b <= 46340 ) then ( a*b <= 0x7FFEA810 )         */
349  /*                                                                     */
350  /*  0x7FFFFFFF - 0x7FFEA810 = 0x157F0                                  */
351  /*                                                                     */
352  /*  if ( c < 0x157F0*2 ) then ( a*b+c/2 <= 0x7FFFFFFF )                */
353  /*                                                                     */
354  /*  and 2*0x157F0 = 176096                                             */
355  /*                                                                     */
356
357  FT_EXPORT_DEF( FT_Long )
358  FT_MulDiv( FT_Long  a,
359             FT_Long  b,
360             FT_Long  c )
361  {
362    long  s;
363
364
365    /* XXX: this function does not allow 64-bit arguments */
366    if ( a == 0 || b == c )
367      return a;
368
369    s  = a; a = FT_ABS( a );
370    s ^= b; b = FT_ABS( b );
371    s ^= c; c = FT_ABS( c );
372
373    if ( a <= 46340L && b <= 46340L && c <= 176095L && c > 0 )
374      a = ( a * b + ( c >> 1 ) ) / c;
375
376    else if ( c > 0 )
377    {
378      FT_Int64  temp, temp2;
379
380
381      ft_multo64( (FT_Int32)a, (FT_Int32)b, &temp );
382
383      temp2.hi = 0;
384      temp2.lo = (FT_UInt32)(c >> 1);
385      FT_Add64( &temp, &temp2, &temp );
386      a = ft_div64by32( temp.hi, temp.lo, (FT_Int32)c );
387    }
388    else
389      a = 0x7FFFFFFFL;
390
391    return ( s < 0 ? -a : a );
392  }
393
394
395#ifdef TT_USE_BYTECODE_INTERPRETER
396
397  FT_BASE_DEF( FT_Long )
398  FT_MulDiv_No_Round( FT_Long  a,
399                      FT_Long  b,
400                      FT_Long  c )
401  {
402    long  s;
403
404
405    if ( a == 0 || b == c )
406      return a;
407
408    s  = a; a = FT_ABS( a );
409    s ^= b; b = FT_ABS( b );
410    s ^= c; c = FT_ABS( c );
411
412    if ( a <= 46340L && b <= 46340L && c > 0 )
413      a = a * b / c;
414
415    else if ( c > 0 )
416    {
417      FT_Int64  temp;
418
419
420      ft_multo64( (FT_Int32)a, (FT_Int32)b, &temp );
421      a = ft_div64by32( temp.hi, temp.lo, (FT_Int32)c );
422    }
423    else
424      a = 0x7FFFFFFFL;
425
426    return ( s < 0 ? -a : a );
427  }
428
429#endif /* TT_USE_BYTECODE_INTERPRETER */
430
431
432  /* documentation is in freetype.h */
433
434  FT_EXPORT_DEF( FT_Long )
435  FT_MulFix( FT_Long  a,
436             FT_Long  b )
437  {
438#ifdef FT_MULFIX_ASSEMBLER
439
440    return FT_MULFIX_ASSEMBLER( a, b );
441
442#elif 0
443
444    /*
445     *  This code is nonportable.  See comment below.
446     *
447     *  However, on a platform where right-shift of a signed quantity fills
448     *  the leftmost bits by copying the sign bit, it might be faster.
449     */
450
451    FT_Long   sa, sb;
452    FT_ULong  ua, ub;
453
454
455    if ( a == 0 || b == 0x10000L )
456      return a;
457
458    /*
459     *  This is a clever way of converting a signed number `a' into its
460     *  absolute value (stored back into `a') and its sign.  The sign is
461     *  stored in `sa'; 0 means `a' was positive or zero, and -1 means `a'
462     *  was negative.  (Similarly for `b' and `sb').
463     *
464     *  Unfortunately, it doesn't work (at least not portably).
465     *
466     *  It makes the assumption that right-shift on a negative signed value
467     *  fills the leftmost bits by copying the sign bit.  This is wrong. 
468     *  According to K&R 2nd ed, section `A7.8 Shift Operators' on page 206,
469     *  the result of right-shift of a negative signed value is
470     *  implementation-defined.  At least one implementation fills the
471     *  leftmost bits with 0s (i.e., it is exactly the same as an unsigned
472     *  right shift).  This means that when `a' is negative, `sa' ends up
473     *  with the value 1 rather than -1.  After that, everything else goes
474     *  wrong.
475     */
476    sa = ( a >> ( sizeof ( a ) * 8 - 1 ) );
477    a  = ( a ^ sa ) - sa;
478    sb = ( b >> ( sizeof ( b ) * 8 - 1 ) );
479    b  = ( b ^ sb ) - sb;
480
481    ua = (FT_ULong)a;
482    ub = (FT_ULong)b;
483
484    if ( ua <= 2048 && ub <= 1048576L )
485      ua = ( ua * ub + 0x8000U ) >> 16;
486    else
487    {
488      FT_ULong  al = ua & 0xFFFFU;
489
490
491      ua = ( ua >> 16 ) * ub +  al * ( ub >> 16 ) +
492           ( ( al * ( ub & 0xFFFFU ) + 0x8000U ) >> 16 );
493    }
494
495    sa ^= sb,
496    ua  = (FT_ULong)(( ua ^ sa ) - sa);
497
498    return (FT_Long)ua;
499
500#else /* 0 */
501
502    FT_Long   s;
503    FT_ULong  ua, ub;
504
505
506    if ( a == 0 || b == 0x10000L )
507      return a;
508
509    s  = a; a = FT_ABS( a );
510    s ^= b; b = FT_ABS( b );
511
512    ua = (FT_ULong)a;
513    ub = (FT_ULong)b;
514
515    if ( ua <= 2048 && ub <= 1048576L )
516      ua = ( ua * ub + 0x8000UL ) >> 16;
517    else
518    {
519      FT_ULong  al = ua & 0xFFFFUL;
520
521
522      ua = ( ua >> 16 ) * ub +  al * ( ub >> 16 ) +
523           ( ( al * ( ub & 0xFFFFUL ) + 0x8000UL ) >> 16 );
524    }
525
526    return ( s < 0 ? -(FT_Long)ua : (FT_Long)ua );
527
528#endif /* 0 */
529
530  }
531
532
533  /* documentation is in freetype.h */
534
535  FT_EXPORT_DEF( FT_Long )
536  FT_DivFix( FT_Long  a,
537             FT_Long  b )
538  {
539    FT_Int32   s;
540    FT_UInt32  q;
541
542
543    /* XXX: this function does not allow 64-bit arguments */
544    s  = (FT_Int32)a; a = FT_ABS( a );
545    s ^= (FT_Int32)b; b = FT_ABS( b );
546
547    if ( b == 0 )
548    {
549      /* check for division by 0 */
550      q = (FT_UInt32)0x7FFFFFFFL;
551    }
552    else if ( ( a >> 16 ) == 0 )
553    {
554      /* compute result directly */
555      q = (FT_UInt32)( (a << 16) + (b >> 1) ) / (FT_UInt32)b;
556    }
557    else
558    {
559      /* we need more bits; we have to do it by hand */
560      FT_Int64  temp, temp2;
561
562      temp.hi  = (FT_Int32) (a >> 16);
563      temp.lo  = (FT_UInt32)(a << 16);
564      temp2.hi = 0;
565      temp2.lo = (FT_UInt32)( b >> 1 );
566      FT_Add64( &temp, &temp2, &temp );
567      q = ft_div64by32( temp.hi, temp.lo, (FT_Int32)b );
568    }
569
570    return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q );
571  }
572
573
574#if 0
575
576  /* documentation is in ftcalc.h */
577
578  FT_EXPORT_DEF( void )
579  FT_MulTo64( FT_Int32   x,
580              FT_Int32   y,
581              FT_Int64  *z )
582  {
583    FT_Int32  s;
584
585
586    s  = x; x = FT_ABS( x );
587    s ^= y; y = FT_ABS( y );
588
589    ft_multo64( x, y, z );
590
591    if ( s < 0 )
592    {
593      z->lo = (FT_UInt32)-(FT_Int32)z->lo;
594      z->hi = ~z->hi + !( z->lo );
595    }
596  }
597
598
599  /* apparently, the second version of this code is not compiled correctly */
600  /* on Mac machines with the MPW C compiler..  tsk, tsk, tsk...           */
601
602#if 1
603
604  FT_EXPORT_DEF( FT_Int32 )
605  FT_Div64by32( FT_Int64*  x,
606                FT_Int32   y )
607  {
608    FT_Int32   s;
609    FT_UInt32  q, r, i, lo;
610
611
612    s  = x->hi;
613    if ( s < 0 )
614    {
615      x->lo = (FT_UInt32)-(FT_Int32)x->lo;
616      x->hi = ~x->hi + !x->lo;
617    }
618    s ^= y;  y = FT_ABS( y );
619
620    /* Shortcut */
621    if ( x->hi == 0 )
622    {
623      if ( y > 0 )
624        q = x->lo / y;
625      else
626        q = 0x7FFFFFFFL;
627
628      return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q );
629    }
630
631    r  = x->hi;
632    lo = x->lo;
633
634    if ( r >= (FT_UInt32)y ) /* we know y is to be treated as unsigned here */
635      return ( s < 0 ? 0x80000001UL : 0x7FFFFFFFUL );
636                             /* Return Max/Min Int32 if division overflow. */
637                             /* This includes division by zero!            */
638    q = 0;
639    for ( i = 0; i < 32; i++ )
640    {
641      r <<= 1;
642      q <<= 1;
643      r  |= lo >> 31;
644
645      if ( r >= (FT_UInt32)y )
646      {
647        r -= y;
648        q |= 1;
649      }
650      lo <<= 1;
651    }
652
653    return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q );
654  }
655
656#else /* 0 */
657
658  FT_EXPORT_DEF( FT_Int32 )
659  FT_Div64by32( FT_Int64*  x,
660                FT_Int32   y )
661  {
662    FT_Int32   s;
663    FT_UInt32  q;
664
665
666    s  = x->hi;
667    if ( s < 0 )
668    {
669      x->lo = (FT_UInt32)-(FT_Int32)x->lo;
670      x->hi = ~x->hi + !x->lo;
671    }
672    s ^= y;  y = FT_ABS( y );
673
674    /* Shortcut */
675    if ( x->hi == 0 )
676    {
677      if ( y > 0 )
678        q = ( x->lo + ( y >> 1 ) ) / y;
679      else
680        q = 0x7FFFFFFFL;
681
682      return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q );
683    }
684
685    q = ft_div64by32( x->hi, x->lo, y );
686
687    return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q );
688  }
689
690#endif /* 0 */
691
692#endif /* 0 */
693
694
695#endif /* FT_LONG64 */
696
697
698  /* documentation is in ftglyph.h */
699
700  FT_EXPORT_DEF( void )
701  FT_Matrix_Multiply( const FT_Matrix*  a,
702                      FT_Matrix        *b )
703  {
704    FT_Fixed  xx, xy, yx, yy;
705
706
707    if ( !a || !b )
708      return;
709
710    xx = FT_MulFix( a->xx, b->xx ) + FT_MulFix( a->xy, b->yx );
711    xy = FT_MulFix( a->xx, b->xy ) + FT_MulFix( a->xy, b->yy );
712    yx = FT_MulFix( a->yx, b->xx ) + FT_MulFix( a->yy, b->yx );
713    yy = FT_MulFix( a->yx, b->xy ) + FT_MulFix( a->yy, b->yy );
714
715    b->xx = xx;  b->xy = xy;
716    b->yx = yx;  b->yy = yy;
717  }
718
719
720  /* documentation is in ftglyph.h */
721
722  FT_EXPORT_DEF( FT_Error )
723  FT_Matrix_Invert( FT_Matrix*  matrix )
724  {
725    FT_Pos  delta, xx, yy;
726
727
728    if ( !matrix )
729      return FT_Err_Invalid_Argument;
730
731    /* compute discriminant */
732    delta = FT_MulFix( matrix->xx, matrix->yy ) -
733            FT_MulFix( matrix->xy, matrix->yx );
734
735    if ( !delta )
736      return FT_Err_Invalid_Argument;  /* matrix can't be inverted */
737
738    matrix->xy = - FT_DivFix( matrix->xy, delta );
739    matrix->yx = - FT_DivFix( matrix->yx, delta );
740
741    xx = matrix->xx;
742    yy = matrix->yy;
743
744    matrix->xx = FT_DivFix( yy, delta );
745    matrix->yy = FT_DivFix( xx, delta );
746
747    return FT_Err_Ok;
748  }
749
750
751  /* documentation is in ftcalc.h */
752
753  FT_BASE_DEF( void )
754  FT_Matrix_Multiply_Scaled( const FT_Matrix*  a,
755                             FT_Matrix        *b,
756                             FT_Long           scaling )
757  {
758    FT_Fixed  xx, xy, yx, yy;
759
760    FT_Long   val = 0x10000L * scaling;
761
762
763    if ( !a || !b )
764      return;
765
766    xx = FT_MulDiv( a->xx, b->xx, val ) + FT_MulDiv( a->xy, b->yx, val );
767    xy = FT_MulDiv( a->xx, b->xy, val ) + FT_MulDiv( a->xy, b->yy, val );
768    yx = FT_MulDiv( a->yx, b->xx, val ) + FT_MulDiv( a->yy, b->yx, val );
769    yy = FT_MulDiv( a->yx, b->xy, val ) + FT_MulDiv( a->yy, b->yy, val );
770
771    b->xx = xx;  b->xy = xy;
772    b->yx = yx;  b->yy = yy;
773  }
774
775
776  /* documentation is in ftcalc.h */
777
778  FT_BASE_DEF( void )
779  FT_Vector_Transform_Scaled( FT_Vector*        vector,
780                              const FT_Matrix*  matrix,
781                              FT_Long           scaling )
782  {
783    FT_Pos   xz, yz;
784
785    FT_Long  val = 0x10000L * scaling;
786
787
788    if ( !vector || !matrix )
789      return;
790
791    xz = FT_MulDiv( vector->x, matrix->xx, val ) +
792         FT_MulDiv( vector->y, matrix->xy, val );
793
794    yz = FT_MulDiv( vector->x, matrix->yx, val ) +
795         FT_MulDiv( vector->y, matrix->yy, val );
796
797    vector->x = xz;
798    vector->y = yz;
799  }
800
801
802  /* documentation is in ftcalc.h */
803
804  FT_BASE_DEF( FT_Int32 )
805  FT_SqrtFixed( FT_Int32  x )
806  {
807    FT_UInt32  root, rem_hi, rem_lo, test_div;
808    FT_Int     count;
809
810
811    root = 0;
812
813    if ( x > 0 )
814    {
815      rem_hi = 0;
816      rem_lo = x;
817      count  = 24;
818      do
819      {
820        rem_hi   = ( rem_hi << 2 ) | ( rem_lo >> 30 );
821        rem_lo <<= 2;
822        root   <<= 1;
823        test_div = ( root << 1 ) + 1;
824
825        if ( rem_hi >= test_div )
826        {
827          rem_hi -= test_div;
828          root   += 1;
829        }
830      } while ( --count );
831    }
832
833    return (FT_Int32)root;
834  }
835
836
837  /* documentation is in ftcalc.h */
838
839  FT_BASE_DEF( FT_Int )
840  ft_corner_orientation( FT_Pos  in_x,
841                         FT_Pos  in_y,
842                         FT_Pos  out_x,
843                         FT_Pos  out_y )
844  {
845    FT_Long  result; /* avoid overflow on 16-bit system */
846
847
848    /* deal with the trivial cases quickly */
849    if ( in_y == 0 )
850    {
851      if ( in_x >= 0 )
852        result = out_y;
853      else
854        result = -out_y;
855    }
856    else if ( in_x == 0 )
857    {
858      if ( in_y >= 0 )
859        result = -out_x;
860      else
861        result = out_x;
862    }
863    else if ( out_y == 0 )
864    {
865      if ( out_x >= 0 )
866        result = in_y;
867      else
868        result = -in_y;
869    }
870    else if ( out_x == 0 )
871    {
872      if ( out_y >= 0 )
873        result = -in_x;
874      else
875        result =  in_x;
876    }
877    else /* general case */
878    {
879#ifdef FT_LONG64
880
881      FT_Int64  delta = (FT_Int64)in_x * out_y - (FT_Int64)in_y * out_x;
882
883
884      if ( delta == 0 )
885        result = 0;
886      else
887        result = 1 - 2 * ( delta < 0 );
888
889#else
890
891      FT_Int64  z1, z2;
892
893
894      /* XXX: this function does not allow 64-bit arguments */
895      ft_multo64( (FT_Int32)in_x, (FT_Int32)out_y, &z1 );
896      ft_multo64( (FT_Int32)in_y, (FT_Int32)out_x, &z2 );
897
898      if ( z1.hi > z2.hi )
899        result = +1;
900      else if ( z1.hi < z2.hi )
901        result = -1;
902      else if ( z1.lo > z2.lo )
903        result = +1;
904      else if ( z1.lo < z2.lo )
905        result = -1;
906      else
907        result = 0;
908
909#endif
910    }
911
912    /* XXX: only the sign of return value, +1/0/-1 must be used */
913    return (FT_Int)result;
914  }
915
916
917  /* documentation is in ftcalc.h */
918
919  FT_BASE_DEF( FT_Int )
920  ft_corner_is_flat( FT_Pos  in_x,
921                     FT_Pos  in_y,
922                     FT_Pos  out_x,
923                     FT_Pos  out_y )
924  {
925    FT_Pos  ax = in_x;
926    FT_Pos  ay = in_y;
927
928    FT_Pos  d_in, d_out, d_corner;
929
930
931    if ( ax < 0 )
932      ax = -ax;
933    if ( ay < 0 )
934      ay = -ay;
935    d_in = ax + ay;
936
937    ax = out_x;
938    if ( ax < 0 )
939      ax = -ax;
940    ay = out_y;
941    if ( ay < 0 )
942      ay = -ay;
943    d_out = ax + ay;
944
945    ax = out_x + in_x;
946    if ( ax < 0 )
947      ax = -ax;
948    ay = out_y + in_y;
949    if ( ay < 0 )
950      ay = -ay;
951    d_corner = ax + ay;
952
953    return ( d_in + d_out - d_corner ) < ( d_corner >> 4 );
954  }
955
956
957/* END */