ftcalc.c

Qt/Embedded是一个多平台的C++图形用户界面应用程序框架

  /*                                                                       */
  /* <Description>                                                         */
  /*    A very simple function used to perform the computation             */
  /*    `(a*b)/0x10000' with maximum accuracy.  Most of the time, this is  */
  /*    used to multiply a given value by a 16.16 fixed float factor.      */
  /*                                                                       */
  /* <Input>                                                               */
  /*    a :: The first multiplier.                                         */
  /*    b :: The second multiplier.  Use a 16.16 factor here whenever      */
  /*         possible (see note below).                                    */
  /*                                                                       */
  /* <Return>                                                              */
  /*    The result of `(a*b)/0x10000'.                                     */
  /*                                                                       */
  /* <Note>                                                                */
  /*    The optimization for FT_MulFix() is different.  We could simply be */
  /*    happy by applying the same principles as with FT_MulDiv(), because */
  /*                                                                       */
  /*      c = 0x10000 < 176096                                             */
  /*                                                                       */
  /*    However, in most cases, we have a `b' with a value around 0x10000  */
  /*    which is greater than 46340.                                       */
  /*                                                                       */
  /*    According to some testing, most cases have `a' < 2048, so a good   */
  /*    idea is to use bounds like 2048 and 1048576 (=floor((2^31-1)/2048) */
  /*    for `a' and `b', respectively.                                     */
  /*                                                                       */
  EXPORT_FUNC
  FT_Long  FT_MulFix( FT_Long  a,
                      FT_Long  b )
  {
    FT_Long   s;


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

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

    if ( a <= 2048 && b <= 1048576L )
    {
      a = ( a*b + 0x8000 ) >> 16;
    }
    else
    {
      FT_Long  al = a & 0xFFFF;


      a = (a >> 16)*b + al*(b >> 16) + ( al*(b & 0xFFFF) >> 16 );
    }

    return ( s < 0 ? -a : a );
  }


  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    FT_DivFix                                                          */
  /*                                                                       */
  /* <Description>                                                         */
  /*    A very simple function used to perform the computation             */
  /*    `(a*0x10000)/b' with maximum accuracy.  Most of the time, this is  */
  /*    used to divide  a given value by a 16.16 fixed float factor.       */
  /*                                                                       */
  /* <Input>                                                               */
  /*    a :: The first multiplier.                                         */
  /*    b :: The second multiplier.  Use a 16.16 factor here whenever      */
  /*         possible (see note below).                                    */
  /*                                                                       */
  /* <Return>                                                              */
  /*    The result of `(a*0x10000)/b'.                                     */
  /*                                                                       */
  /* <Note>                                                                */
  /*    The optimization for FT_DivFix() is simple: If (a << 16) fits in   */
  /*    32 bits, then the division is computed directly.  Otherwise, we    */
  /*    use a specialized version of the old FT_MulDiv64().                */
  /*                                                                       */
  EXPORT_FUNC
  FT_Long  FT_DivFix( FT_Long  a,
                      FT_Long  b )
  {
    FT_Int32   s;
    FT_Word32  q;


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

    if ( b == 0 )
      /* check for divide by 0 */
      q = 0x7FFFFFFF;

    else if ( (a >> 16) == 0 )
    {
      /* compute result directly */
      q = (FT_Word32)(a << 16) / (FT_Word32)b;
    }
    else
    {
      /* we need more bits, we'll have to do it by hand */
      FT_Word32  c;


      q  = ( a / b ) << 16;
      c  = a % b;

      /* we must compute C*0x10000/B; we simply shift C and B so */
      /* C becomes smaller than 16 bits                          */
      while ( c >> 16 )
      {
        c >>= 1;
        b <<= 1;
      }

      q += ( c << 16 ) / b;
    }

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


  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    FT_Add64                                                           */
  /*                                                                       */
  /* <Description>                                                         */
  /*    Add two Int64 values.                                              */
  /*                                                                       */
  /* <Input>                                                               */
  /*    x :: A pointer to the first value to be added.                     */
  /*    y :: A pointer to the second value to be added.                    */
  /*                                                                       */
  /* <Output>                                                              */
  /*    z :: A pointer to the result of `x + y'.                           */
  /*                                                                       */
  /* <Note>                                                                */
  /*    Will be wrapped by the ADD_64() macro.                             */
  /*                                                                       */
  BASE_FUNC
  void  FT_Add64( FT_Int64*  x,
                  FT_Int64*  y,
                  FT_Int64*  z )
  {
    register FT_Word32  lo, hi;

    lo = x->lo + y->lo;
    hi = x->hi + y->hi + ( lo < x->lo );

    z->lo = lo;
    z->hi = hi;
  }


  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    FT_MulTo64                                                         */
  /*                                                                       */
  /* <Description>                                                         */
  /*    Multiplies two Int32 integers.  Returns a Int64 integer.           */
  /*                                                                       */
  /* <Input>                                                               */
  /*    x :: The first multiplier.                                         */
  /*    y :: The second multiplier.                                        */
  /*                                                                       */
  /* <Output>                                                              */
  /*    z :: A pointer to the result of `x * y'.                           */
  /*                                                                       */
  /* <Note>                                                                */
  /*    Will be wrapped by the MUL_64() macro.                             */
  /*                                                                       */
  BASE_FUNC
  void  FT_MulTo64( FT_Int32   x,
                    FT_Int32   y,
                    FT_Int64*  z )
  {
    FT_Int32   s;


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

    {
      FT_Word32  lo1, hi1, lo2, hi2, lo, hi, i1, i2;


      lo1 = x & 0x0000FFFF;  hi1 = x >> 16;
      lo2 = y & 0x0000FFFF;  hi2 = y >> 16;

      lo = lo1 * lo2;
      i1 = lo1 * hi2;
      i2 = lo2 * hi1;
      hi = hi1 * hi2;

      /* Check carry overflow of i1 + i2 */
      i1 += i2;
      if ( i1 < i2 )
        hi += 1L << 16;

      hi += i1 >> 16;
      i1  = i1 << 16;

      /* Check carry overflow of i1 + lo */
      lo += i1;
      hi += (lo < i1);

      z->lo = lo;
      z->hi = hi;
    }

    if ( s < 0 )
    {
      z->lo = (FT_Word32)-(FT_Int32)z->lo;
      z->hi = ~z->hi + !(z->lo);
    }
  }


  /*************************************************************************/
  /*                                                                       */
  /* <Function>                                                            */
  /*    FT_Div64by32                                                       */
  /*                                                                       */
  /* <Description>                                                         */
  /*    Divides an Int64 value by an Int32 value.  Returns an Int32        */
  /*    integer.                                                           */
  /*                                                                       */
  /* <Input>                                                               */
  /*    x :: A pointer to the dividend.                                    */
  /*    y :: The divisor.                                                  */
  /*                                                                       */
  /* <Return>                                                              */
  /*    The result of `x / y'.                                             */
  /*                                                                       */
  /* <Note>                                                                */
  /*    Will be wrapped by the DIV_64() macro.                             */
  /*                                                                       */
  BASE_FUNC
  FT_Int32  FT_Div64by32( FT_Int64*  x,
                          FT_Int32   y )
  {
    FT_Int32   s;
    FT_Word32  q, r, i, lo;


    s  = x->hi;
    if ( s < 0 )
    {
      x->lo = (FT_Word32)-(FT_Int32)x->lo;
      x->hi = ~x->hi + !(x->lo);
    }
    s ^= y;  y = ABS( y );

    /* Shortcut */
    if ( x->hi == 0 )
    {
      q = x->lo / y;
      return ( s < 0 ) ? -(FT_Int32)q : (FT_Int32)q;
    }

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

    if ( r >= (FT_Word32)y ) /* we know y is to be treated as unsigned here */
      return ( s < 0 ) ? 0x80000001L : 0x7FFFFFFFL;
                            /* Return Max/Min Int32 if divide overflow. */
                            /* This includes division by zero!          */
    q = 0;
    for ( i = 0; i < 32; i++ )
    {
      r <<= 1;
      q <<= 1;
      r  |= lo >> 31;

      if ( r >= (FT_Word32)y )
      {
        r -= y;
        q |= 1;
      }
      lo <<= 1;
    }

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


#endif /* LONG64 */


/* END */