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/src/freetype/src/base/ftcalc.c

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C | 958 lines | 582 code | 258 blank | 118 comment | 108 complexity | 85091157b9f95f1a3ccc72b1a9049712 MD5 | raw file
  1/***************************************************************************/
  2/*                                                                         */
  3/*  ftcalc.c                                                               */
  4/*                                                                         */
  5/*    Arithmetic computations (body).                                      */
  6/*                                                                         */
  7/*  Copyright 1996-2006, 2008, 2012 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 >= 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 ( (FT_Int32)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 ( (FT_Int32)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 ( (FT_UInt32)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
563      temp.hi  = (FT_Int32) ( a >> 16 );
564      temp.lo  = (FT_UInt32)( a << 16 );
565      temp2.hi = 0;
566      temp2.lo = (FT_UInt32)( b >> 1 );
567      FT_Add64( &temp, &temp2, &temp );
568      q = ft_div64by32( temp.hi, temp.lo, (FT_Int32)b );
569    }
570
571    return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q );
572  }
573
574
575#if 0
576
577  /* documentation is in ftcalc.h */
578
579  FT_EXPORT_DEF( void )
580  FT_MulTo64( FT_Int32   x,
581              FT_Int32   y,
582              FT_Int64  *z )
583  {
584    FT_Int32  s;
585
586
587    s  = x; x = FT_ABS( x );
588    s ^= y; y = FT_ABS( y );
589
590    ft_multo64( x, y, z );
591
592    if ( s < 0 )
593    {
594      z->lo = (FT_UInt32)-(FT_Int32)z->lo;
595      z->hi = ~z->hi + !( z->lo );
596    }
597  }
598
599
600  /* apparently, the second version of this code is not compiled correctly */
601  /* on Mac machines with the MPW C compiler..  tsk, tsk, tsk...           */
602
603#if 1
604
605  FT_EXPORT_DEF( FT_Int32 )
606  FT_Div64by32( FT_Int64*  x,
607                FT_Int32   y )
608  {
609    FT_Int32   s;
610    FT_UInt32  q, r, i, lo;
611
612
613    s  = x->hi;
614    if ( s < 0 )
615    {
616      x->lo = (FT_UInt32)-(FT_Int32)x->lo;
617      x->hi = ~x->hi + !x->lo;
618    }
619    s ^= y;  y = FT_ABS( y );
620
621    /* Shortcut */
622    if ( x->hi == 0 )
623    {
624      if ( y > 0 )
625        q = x->lo / y;
626      else
627        q = 0x7FFFFFFFL;
628
629      return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q );
630    }
631
632    r  = x->hi;
633    lo = x->lo;
634
635    if ( r >= (FT_UInt32)y ) /* we know y is to be treated as unsigned here */
636      return ( s < 0 ? 0x80000001UL : 0x7FFFFFFFUL );
637                             /* Return Max/Min Int32 if division overflow. */
638                             /* This includes division by zero!            */
639    q = 0;
640    for ( i = 0; i < 32; i++ )
641    {
642      r <<= 1;
643      q <<= 1;
644      r  |= lo >> 31;
645
646      if ( r >= (FT_UInt32)y )
647      {
648        r -= y;
649        q |= 1;
650      }
651      lo <<= 1;
652    }
653
654    return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q );
655  }
656
657#else /* 0 */
658
659  FT_EXPORT_DEF( FT_Int32 )
660  FT_Div64by32( FT_Int64*  x,
661                FT_Int32   y )
662  {
663    FT_Int32   s;
664    FT_UInt32  q;
665
666
667    s  = x->hi;
668    if ( s < 0 )
669    {
670      x->lo = (FT_UInt32)-(FT_Int32)x->lo;
671      x->hi = ~x->hi + !x->lo;
672    }
673    s ^= y;  y = FT_ABS( y );
674
675    /* Shortcut */
676    if ( x->hi == 0 )
677    {
678      if ( y > 0 )
679        q = ( x->lo + ( y >> 1 ) ) / y;
680      else
681        q = 0x7FFFFFFFL;
682
683      return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q );
684    }
685
686    q = ft_div64by32( x->hi, x->lo, y );
687
688    return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q );
689  }
690
691#endif /* 0 */
692
693#endif /* 0 */
694
695
696#endif /* FT_LONG64 */
697
698
699  /* documentation is in ftglyph.h */
700
701  FT_EXPORT_DEF( void )
702  FT_Matrix_Multiply( const FT_Matrix*  a,
703                      FT_Matrix        *b )
704  {
705    FT_Fixed  xx, xy, yx, yy;
706
707
708    if ( !a || !b )
709      return;
710
711    xx = FT_MulFix( a->xx, b->xx ) + FT_MulFix( a->xy, b->yx );
712    xy = FT_MulFix( a->xx, b->xy ) + FT_MulFix( a->xy, b->yy );
713    yx = FT_MulFix( a->yx, b->xx ) + FT_MulFix( a->yy, b->yx );
714    yy = FT_MulFix( a->yx, b->xy ) + FT_MulFix( a->yy, b->yy );
715
716    b->xx = xx;  b->xy = xy;
717    b->yx = yx;  b->yy = yy;
718  }
719
720
721  /* documentation is in ftglyph.h */
722
723  FT_EXPORT_DEF( FT_Error )
724  FT_Matrix_Invert( FT_Matrix*  matrix )
725  {
726    FT_Pos  delta, xx, yy;
727
728
729    if ( !matrix )
730      return FT_Err_Invalid_Argument;
731
732    /* compute discriminant */
733    delta = FT_MulFix( matrix->xx, matrix->yy ) -
734            FT_MulFix( matrix->xy, matrix->yx );
735
736    if ( !delta )
737      return FT_Err_Invalid_Argument;  /* matrix can't be inverted */
738
739    matrix->xy = - FT_DivFix( matrix->xy, delta );
740    matrix->yx = - FT_DivFix( matrix->yx, delta );
741
742    xx = matrix->xx;
743    yy = matrix->yy;
744
745    matrix->xx = FT_DivFix( yy, delta );
746    matrix->yy = FT_DivFix( xx, delta );
747
748    return FT_Err_Ok;
749  }
750
751
752  /* documentation is in ftcalc.h */
753
754  FT_BASE_DEF( void )
755  FT_Matrix_Multiply_Scaled( const FT_Matrix*  a,
756                             FT_Matrix        *b,
757                             FT_Long           scaling )
758  {
759    FT_Fixed  xx, xy, yx, yy;
760
761    FT_Long   val = 0x10000L * scaling;
762
763
764    if ( !a || !b )
765      return;
766
767    xx = FT_MulDiv( a->xx, b->xx, val ) + FT_MulDiv( a->xy, b->yx, val );
768    xy = FT_MulDiv( a->xx, b->xy, val ) + FT_MulDiv( a->xy, b->yy, val );
769    yx = FT_MulDiv( a->yx, b->xx, val ) + FT_MulDiv( a->yy, b->yx, val );
770    yy = FT_MulDiv( a->yx, b->xy, val ) + FT_MulDiv( a->yy, b->yy, val );
771
772    b->xx = xx;  b->xy = xy;
773    b->yx = yx;  b->yy = yy;
774  }
775
776
777  /* documentation is in ftcalc.h */
778
779  FT_BASE_DEF( void )
780  FT_Vector_Transform_Scaled( FT_Vector*        vector,
781                              const FT_Matrix*  matrix,
782                              FT_Long           scaling )
783  {
784    FT_Pos   xz, yz;
785
786    FT_Long  val = 0x10000L * scaling;
787
788
789    if ( !vector || !matrix )
790      return;
791
792    xz = FT_MulDiv( vector->x, matrix->xx, val ) +
793         FT_MulDiv( vector->y, matrix->xy, val );
794
795    yz = FT_MulDiv( vector->x, matrix->yx, val ) +
796         FT_MulDiv( vector->y, matrix->yy, val );
797
798    vector->x = xz;
799    vector->y = yz;
800  }
801
802
803  /* documentation is in ftcalc.h */
804
805  FT_BASE_DEF( FT_Int32 )
806  FT_SqrtFixed( FT_Int32  x )
807  {
808    FT_UInt32  root, rem_hi, rem_lo, test_div;
809    FT_Int     count;
810
811
812    root = 0;
813
814    if ( x > 0 )
815    {
816      rem_hi = 0;
817      rem_lo = x;
818      count  = 24;
819      do
820      {
821        rem_hi   = ( rem_hi << 2 ) | ( rem_lo >> 30 );
822        rem_lo <<= 2;
823        root   <<= 1;
824        test_div = ( root << 1 ) + 1;
825
826        if ( rem_hi >= test_div )
827        {
828          rem_hi -= test_div;
829          root   += 1;
830        }
831      } while ( --count );
832    }
833
834    return (FT_Int32)root;
835  }
836
837
838  /* documentation is in ftcalc.h */
839
840  FT_BASE_DEF( FT_Int )
841  ft_corner_orientation( FT_Pos  in_x,
842                         FT_Pos  in_y,
843                         FT_Pos  out_x,
844                         FT_Pos  out_y )
845  {
846    FT_Long  result; /* avoid overflow on 16-bit system */
847
848
849    /* deal with the trivial cases quickly */
850    if ( in_y == 0 )
851    {
852      if ( in_x >= 0 )
853        result = out_y;
854      else
855        result = -out_y;
856    }
857    else if ( in_x == 0 )
858    {
859      if ( in_y >= 0 )
860        result = -out_x;
861      else
862        result = out_x;
863    }
864    else if ( out_y == 0 )
865    {
866      if ( out_x >= 0 )
867        result = in_y;
868      else
869        result = -in_y;
870    }
871    else if ( out_x == 0 )
872    {
873      if ( out_y >= 0 )
874        result = -in_x;
875      else
876        result =  in_x;
877    }
878    else /* general case */
879    {
880#ifdef FT_LONG64
881
882      FT_Int64  delta = (FT_Int64)in_x * out_y - (FT_Int64)in_y * out_x;
883
884
885      if ( delta == 0 )
886        result = 0;
887      else
888        result = 1 - 2 * ( delta < 0 );
889
890#else
891
892      FT_Int64  z1, z2;
893
894
895      /* XXX: this function does not allow 64-bit arguments */
896      ft_multo64( (FT_Int32)in_x, (FT_Int32)out_y, &z1 );
897      ft_multo64( (FT_Int32)in_y, (FT_Int32)out_x, &z2 );
898
899      if ( z1.hi > z2.hi )
900        result = +1;
901      else if ( z1.hi < z2.hi )
902        result = -1;
903      else if ( z1.lo > z2.lo )
904        result = +1;
905      else if ( z1.lo < z2.lo )
906        result = -1;
907      else
908        result = 0;
909
910#endif
911    }
912
913    /* XXX: only the sign of return value, +1/0/-1 must be used */
914    return (FT_Int)result;
915  }
916
917
918  /* documentation is in ftcalc.h */
919
920  FT_BASE_DEF( FT_Int )
921  ft_corner_is_flat( FT_Pos  in_x,
922                     FT_Pos  in_y,
923                     FT_Pos  out_x,
924                     FT_Pos  out_y )
925  {
926    FT_Pos  ax = in_x;
927    FT_Pos  ay = in_y;
928
929    FT_Pos  d_in, d_out, d_corner;
930
931
932    if ( ax < 0 )
933      ax = -ax;
934    if ( ay < 0 )
935      ay = -ay;
936    d_in = ax + ay;
937
938    ax = out_x;
939    if ( ax < 0 )
940      ax = -ax;
941    ay = out_y;
942    if ( ay < 0 )
943      ay = -ay;
944    d_out = ax + ay;
945
946    ax = out_x + in_x;
947    if ( ax < 0 )
948      ax = -ax;
949    ay = out_y + in_y;
950    if ( ay < 0 )
951      ay = -ay;
952    d_corner = ax + ay;
953
954    return ( d_in + d_out - d_corner ) < ( d_corner >> 4 );
955  }
956
957
958/* END */