ftcalc.c

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           ( ( al * ( ub & 0xFFFFU ) + 0x8000U ) >> 16 );
    }

    sa ^= sb,
    ua  = (FT_ULong)(( ua ^ sa ) - sa);

    return (FT_Long)ua;

#else /* 0 */

    FT_Long   s;
    FT_ULong  ua, ub;


    if ( a == 0 || b == 0x10000L )
      return a;

    s  = a; a = FT_ABS( a );
    s ^= b; b = FT_ABS( b );

    ua = (FT_ULong)a;
    ub = (FT_ULong)b;

    if ( ua <= 2048 && ub <= 1048576L )
      ua = ( ua * ub + 0x8000UL ) >> 16;
    else
    {
      FT_ULong  al = ua & 0xFFFFUL;


      ua = ( ua >> 16 ) * ub +  al * ( ub >> 16 ) +
           ( ( al * ( ub & 0xFFFFUL ) + 0x8000UL ) >> 16 );
    }

    return ( s < 0 ? -(FT_Long)ua : (FT_Long)ua );

#endif /* 0 */

  }


  /* documentation is in freetype.h */

  FT_EXPORT_DEF( FT_Long )
  FT_DivFix( FT_Long  a,
             FT_Long  b )
  {
    FT_Int32   s;
    FT_UInt32  q;


    s  = a; a = FT_ABS( a );
    s ^= b; b = FT_ABS( b );

    if ( b == 0 )
    {
      /* check for division by 0 */
      q = 0x7FFFFFFFL;
    }
    else if ( ( a >> 16 ) == 0 )
    {
      /* compute result directly */
      q = (FT_UInt32)( (a << 16) + (b >> 1) ) / (FT_UInt32)b;
    }
    else
    {
      /* we need more bits; we have to do it by hand */
      FT_Int64  temp, temp2;

      temp.hi  = (FT_Int32) (a >> 16);
      temp.lo  = (FT_UInt32)(a << 16);
      temp2.hi = 0;
      temp2.lo = (FT_UInt32)( b >> 1 );
      FT_Add64( &temp, &temp2, &temp );
      q = ft_div64by32( temp.hi, temp.lo, b );
    }

    return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q );
  }


#if 0

  /* documentation is in ftcalc.h */

  FT_EXPORT_DEF( void )
  FT_MulTo64( FT_Int32   x,
              FT_Int32   y,
              FT_Int64  *z )
  {
    FT_Int32  s;


    s  = x; x = FT_ABS( x );
    s ^= y; y = FT_ABS( y );

    ft_multo64( x, y, z );

    if ( s < 0 )
    {
      z->lo = (FT_UInt32)-(FT_Int32)z->lo;
      z->hi = ~z->hi + !( z->lo );
    }
  }


  /* apparently, the second version of this code is not compiled correctly */
  /* on Mac machines with the MPW C compiler..  tsk, tsk, tsk...           */

#if 1

  FT_EXPORT_DEF( FT_Int32 )
  FT_Div64by32( FT_Int64*  x,
                FT_Int32   y )
  {
    FT_Int32   s;
    FT_UInt32  q, r, i, lo;


    s  = x->hi;
    if ( s < 0 )
    {
      x->lo = (FT_UInt32)-(FT_Int32)x->lo;
      x->hi = ~x->hi + !x->lo;
    }
    s ^= y;  y = FT_ABS( y );

    /* Shortcut */
    if ( x->hi == 0 )
    {
      if ( y > 0 )
        q = x->lo / y;
      else
        q = 0x7FFFFFFFL;

      return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q );
    }

    r  = x->hi;
    lo = x->lo;

    if ( r >= (FT_UInt32)y ) /* we know y is to be treated as unsigned here */
      return ( s < 0 ? 0x80000001UL : 0x7FFFFFFFUL );
                             /* Return Max/Min Int32 if division overflow. */
                             /* This includes division by zero!            */
    q = 0;
    for ( i = 0; i < 32; i++ )
    {
      r <<= 1;
      q <<= 1;
      r  |= lo >> 31;

      if ( r >= (FT_UInt32)y )
      {
        r -= y;
        q |= 1;
      }
      lo <<= 1;
    }

    return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q );
  }

#else /* 0 */

  FT_EXPORT_DEF( FT_Int32 )
  FT_Div64by32( FT_Int64*  x,
                FT_Int32   y )
  {
    FT_Int32   s;
    FT_UInt32  q;


    s  = x->hi;
    if ( s < 0 )
    {
      x->lo = (FT_UInt32)-(FT_Int32)x->lo;
      x->hi = ~x->hi + !x->lo;
    }
    s ^= y;  y = FT_ABS( y );

    /* Shortcut */
    if ( x->hi == 0 )
    {
      if ( y > 0 )
        q = ( x->lo + ( y >> 1 ) ) / y;
      else
        q = 0x7FFFFFFFL;

      return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q );
    }

    q = ft_div64by32( x->hi, x->lo, y );

    return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q );
  }

#endif /* 0 */

#endif /* 0 */


#endif /* FT_LONG64 */


  /* documentation is in ftglyph.h */

  FT_EXPORT_DEF( void )
  FT_Matrix_Multiply( const FT_Matrix*  a,
                      FT_Matrix        *b )
  {
    FT_Fixed  xx, xy, yx, yy;


    if ( !a || !b )
      return;

    xx = FT_MulFix( a->xx, b->xx ) + FT_MulFix( a->xy, b->yx );
    xy = FT_MulFix( a->xx, b->xy ) + FT_MulFix( a->xy, b->yy );
    yx = FT_MulFix( a->yx, b->xx ) + FT_MulFix( a->yy, b->yx );
    yy = FT_MulFix( a->yx, b->xy ) + FT_MulFix( a->yy, b->yy );

    b->xx = xx;  b->xy = xy;
    b->yx = yx;  b->yy = yy;
  }


  /* documentation is in ftglyph.h */

  FT_EXPORT_DEF( FT_Error )
  FT_Matrix_Invert( FT_Matrix*  matrix )
  {
    FT_Pos  delta, xx, yy;


    if ( !matrix )
      return FT_Err_Invalid_Argument;

    /* compute discriminant */
    delta = FT_MulFix( matrix->xx, matrix->yy ) -
            FT_MulFix( matrix->xy, matrix->yx );

    if ( !delta )
      return FT_Err_Invalid_Argument;  /* matrix can't be inverted */

    matrix->xy = - FT_DivFix( matrix->xy, delta );
    matrix->yx = - FT_DivFix( matrix->yx, delta );

    xx = matrix->xx;
    yy = matrix->yy;

    matrix->xx = FT_DivFix( yy, delta );
    matrix->yy = FT_DivFix( xx, delta );

    return FT_Err_Ok;
  }


  /* documentation is in ftcalc.h */

  FT_BASE_DEF( void )
  FT_Matrix_Multiply_Scaled( const FT_Matrix*  a,
                             FT_Matrix        *b,
                             FT_Long           scaling )
  {
    FT_Fixed  xx, xy, yx, yy;

    FT_Long   val = 0x10000L * scaling;


    if ( !a || !b )
      return;

    xx = FT_MulDiv( a->xx, b->xx, val ) + FT_MulDiv( a->xy, b->yx, val );
    xy = FT_MulDiv( a->xx, b->xy, val ) + FT_MulDiv( a->xy, b->yy, val );
    yx = FT_MulDiv( a->yx, b->xx, val ) + FT_MulDiv( a->yy, b->yx, val );
    yy = FT_MulDiv( a->yx, b->xy, val ) + FT_MulDiv( a->yy, b->yy, val );

    b->xx = xx;  b->xy = xy;
    b->yx = yx;  b->yy = yy;
  }


  /* documentation is in ftcalc.h */

  FT_BASE_DEF( void )
  FT_Vector_Transform_Scaled( FT_Vector*        vector,
                              const FT_Matrix*  matrix,
                              FT_Long           scaling )
  {
    FT_Pos   xz, yz;

    FT_Long  val = 0x10000L * scaling;


    if ( !vector || !matrix )
      return;

    xz = FT_MulDiv( vector->x, matrix->xx, val ) +
         FT_MulDiv( vector->y, matrix->xy, val );

    yz = FT_MulDiv( vector->x, matrix->yx, val ) +
         FT_MulDiv( vector->y, matrix->yy, val );

    vector->x = xz;
    vector->y = yz;
  }


  /* documentation is in ftcalc.h */

  FT_BASE_DEF( FT_Int32 )
  FT_SqrtFixed( FT_Int32  x )
  {
    FT_UInt32  root, rem_hi, rem_lo, test_div;
    FT_Int     count;


    root = 0;

    if ( x > 0 )
    {
      rem_hi = 0;
      rem_lo = x;
      count  = 24;
      do
      {
        rem_hi   = ( rem_hi << 2 ) | ( rem_lo >> 30 );
        rem_lo <<= 2;
        root   <<= 1;
        test_div = ( root << 1 ) + 1;

        if ( rem_hi >= test_div )
        {
          rem_hi -= test_div;
          root   += 1;
        }
      } while ( --count );
    }

    return (FT_Int32)root;
  }


  /* documentation is in ftcalc.h */

  FT_BASE_DEF( FT_Int )
  ft_corner_orientation( FT_Pos  in_x,
                         FT_Pos  in_y,
                         FT_Pos  out_x,
                         FT_Pos  out_y )
  {
    FT_Int  result;


    /* deal with the trivial cases quickly */
    if ( in_y == 0 )
    {
      if ( in_x >= 0 )
        result = out_y;
      else
        result = -out_y;
    }
    else if ( in_x == 0 )
    {
      if ( in_y >= 0 )
        result = -out_x;
      else
        result = out_x;
    }
    else if ( out_y == 0 )
    {
      if ( out_x >= 0 )
        result = in_y;
      else
        result = -in_y;
    }
    else if ( out_x == 0 )
    {
      if ( out_y >= 0 )
        result = -in_x;
      else
        result =  in_x;
    }
    else /* general case */
    {
#ifdef FT_LONG64

      FT_Int64  delta = (FT_Int64)in_x * out_y - (FT_Int64)in_y * out_x;


      if ( delta == 0 )
        result = 0;
      else
        result = 1 - 2 * ( delta < 0 );

#else

      FT_Int64  z1, z2;


      ft_multo64( in_x, out_y, &z1 );
      ft_multo64( in_y, out_x, &z2 );

      if ( z1.hi > z2.hi )
        result = +1;
      else if ( z1.hi < z2.hi )
        result = -1;
      else if ( z1.lo > z2.lo )
        result = +1;
      else if ( z1.lo < z2.lo )
        result = -1;
      else
        result = 0;

#endif
    }

    return result;
  }


  /* documentation is in ftcalc.h */

  FT_BASE_DEF( FT_Int )
  ft_corner_is_flat( FT_Pos  in_x,
                     FT_Pos  in_y,
                     FT_Pos  out_x,
                     FT_Pos  out_y )
  {
    FT_Pos  ax = in_x;
    FT_Pos  ay = in_y;

    FT_Pos  d_in, d_out, d_corner;


    if ( ax < 0 )
      ax = -ax;
    if ( ay < 0 )
      ay = -ay;
    d_in = ax + ay;

    ax = out_x;
    if ( ax < 0 )
      ax = -ax;
    ay = out_y;
    if ( ay < 0 )
      ay = -ay;
    d_out = ax + ay;

    ax = out_x + in_x;
    if ( ax < 0 )
      ax = -ax;
    ay = out_y + in_y;
    if ( ay < 0 )
      ay = -ay;
    d_corner = ax + ay;

    return ( d_in + d_out - d_corner ) < ( d_corner >> 4 );
  }


/* END */