misc/libfreetype/src/base/ftcalc.c
changeset 9431 0f5961910e27
parent 9357 a501f5ec7b34
parent 9429 7a97a554ac80
child 9433 f0a8ac191839
--- a/misc/libfreetype/src/base/ftcalc.c	Tue Jul 16 11:14:27 2013 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,957 +0,0 @@
-/***************************************************************************/
-/*                                                                         */
-/*  ftcalc.c                                                               */
-/*                                                                         */
-/*    Arithmetic computations (body).                                      */
-/*                                                                         */
-/*  Copyright 1996-2001, 2002, 2003, 2004, 2005, 2006, 2008 by             */
-/*  David Turner, Robert Wilhelm, and Werner Lemberg.                      */
-/*                                                                         */
-/*  This file is part of the FreeType project, and may only be used,       */
-/*  modified, and distributed under the terms of the FreeType project      */
-/*  license, LICENSE.TXT.  By continuing to use, modify, or distribute     */
-/*  this file you indicate that you have read the license and              */
-/*  understand and accept it fully.                                        */
-/*                                                                         */
-/***************************************************************************/
-
-  /*************************************************************************/
-  /*                                                                       */
-  /* Support for 1-complement arithmetic has been totally dropped in this  */
-  /* release.  You can still write your own code if you need it.           */
-  /*                                                                       */
-  /*************************************************************************/
-
-  /*************************************************************************/
-  /*                                                                       */
-  /* Implementing basic computation routines.                              */
-  /*                                                                       */
-  /* FT_MulDiv(), FT_MulFix(), FT_DivFix(), FT_RoundFix(), FT_CeilFix(),   */
-  /* and FT_FloorFix() are declared in freetype.h.                         */
-  /*                                                                       */
-  /*************************************************************************/
-
-
-#include <ft2build.h>
-#include FT_GLYPH_H
-#include FT_INTERNAL_CALC_H
-#include FT_INTERNAL_DEBUG_H
-#include FT_INTERNAL_OBJECTS_H
-
-#ifdef FT_MULFIX_INLINED
-#undef FT_MulFix
-#endif
-
-/* we need to define a 64-bits data type here */
-
-#ifdef FT_LONG64
-
-  typedef FT_INT64  FT_Int64;
-
-#else
-
-  typedef struct  FT_Int64_
-  {
-    FT_UInt32  lo;
-    FT_UInt32  hi;
-
-  } FT_Int64;
-
-#endif /* FT_LONG64 */
-
-
-  /*************************************************************************/
-  /*                                                                       */
-  /* The macro FT_COMPONENT is used in trace mode.  It is an implicit      */
-  /* parameter of the FT_TRACE() and FT_ERROR() macros, used to print/log  */
-  /* messages during execution.                                            */
-  /*                                                                       */
-#undef  FT_COMPONENT
-#define FT_COMPONENT  trace_calc
-
-
-  /* The following three functions are available regardless of whether */
-  /* FT_LONG64 is defined.                                             */
-
-  /* documentation is in freetype.h */
-
-  FT_EXPORT_DEF( FT_Fixed )
-  FT_RoundFix( FT_Fixed  a )
-  {
-    return ( a >= 0 ) ?   ( a + 0x8000L ) & ~0xFFFFL
-                      : -((-a + 0x8000L ) & ~0xFFFFL );
-  }
-
-
-  /* documentation is in freetype.h */
-
-  FT_EXPORT_DEF( FT_Fixed )
-  FT_CeilFix( FT_Fixed  a )
-  {
-    return ( a >= 0 ) ?   ( a + 0xFFFFL ) & ~0xFFFFL
-                      : -((-a + 0xFFFFL ) & ~0xFFFFL );
-  }
-
-
-  /* documentation is in freetype.h */
-
-  FT_EXPORT_DEF( FT_Fixed )
-  FT_FloorFix( FT_Fixed  a )
-  {
-    return ( a >= 0 ) ?   a & ~0xFFFFL
-                      : -((-a) & ~0xFFFFL );
-  }
-
-
-#ifdef FT_CONFIG_OPTION_OLD_INTERNALS
-
-  /* documentation is in ftcalc.h */
-
-  FT_EXPORT_DEF( FT_Int32 )
-  FT_Sqrt32( FT_Int32  x )
-  {
-    FT_UInt32  val, root, newroot, mask;
-
-
-    root = 0;
-    mask = (FT_UInt32)0x40000000UL;
-    val  = (FT_UInt32)x;
-
-    do
-    {
-      newroot = root + mask;
-      if ( newroot <= val )
-      {
-        val -= newroot;
-        root = newroot + mask;
-      }
-
-      root >>= 1;
-      mask >>= 2;
-
-    } while ( mask != 0 );
-
-    return root;
-  }
-
-#endif /* FT_CONFIG_OPTION_OLD_INTERNALS */
-
-
-#ifdef FT_LONG64
-
-
-  /* documentation is in freetype.h */
-
-  FT_EXPORT_DEF( FT_Long )
-  FT_MulDiv( FT_Long  a,
-             FT_Long  b,
-             FT_Long  c )
-  {
-    FT_Int   s;
-    FT_Long  d;
-
-
-    s = 1;
-    if ( a < 0 ) { a = -a; s = -1; }
-    if ( b < 0 ) { b = -b; s = -s; }
-    if ( c < 0 ) { c = -c; s = -s; }
-
-    d = (FT_Long)( c > 0 ? ( (FT_Int64)a * b + ( c >> 1 ) ) / c
-                         : 0x7FFFFFFFL );
-
-    return ( s > 0 ) ? d : -d;
-  }
-
-
-#ifdef TT_USE_BYTECODE_INTERPRETER
-
-  /* documentation is in ftcalc.h */
-
-  FT_BASE_DEF( FT_Long )
-  FT_MulDiv_No_Round( FT_Long  a,
-                      FT_Long  b,
-                      FT_Long  c )
-  {
-    FT_Int   s;
-    FT_Long  d;
-
-
-    s = 1;
-    if ( a < 0 ) { a = -a; s = -1; }
-    if ( b < 0 ) { b = -b; s = -s; }
-    if ( c < 0 ) { c = -c; s = -s; }
-
-    d = (FT_Long)( c > 0 ? (FT_Int64)a * b / c
-                         : 0x7FFFFFFFL );
-
-    return ( s > 0 ) ? d : -d;
-  }
-
-#endif /* TT_USE_BYTECODE_INTERPRETER */
-
-
-  /* documentation is in freetype.h */
-
-  FT_EXPORT_DEF( FT_Long )
-  FT_MulFix( FT_Long  a,
-             FT_Long  b )
-  {
-#ifdef FT_MULFIX_ASSEMBLER
-
-    return FT_MULFIX_ASSEMBLER( a, b );
-
-#else
-
-    FT_Int   s = 1;
-    FT_Long  c;
-
-
-    if ( a < 0 )
-    {
-      a = -a;
-      s = -1;
-    }
-
-    if ( b < 0 )
-    {
-      b = -b;
-      s = -s;
-    }
-
-    c = (FT_Long)( ( (FT_Int64)a * b + 0x8000L ) >> 16 );
-
-    return ( s > 0 ) ? c : -c;
-
-#endif /* FT_MULFIX_ASSEMBLER */
-  }
-
-
-  /* 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 = 1;
-    if ( a < 0 ) { a = -a; s = -1; }
-    if ( b < 0 ) { b = -b; s = -s; }
-
-    if ( b == 0 )
-      /* check for division by 0 */
-      q = 0x7FFFFFFFL;
-    else
-      /* compute result directly */
-      q = (FT_UInt32)( ( ( (FT_Int64)a << 16 ) + ( b >> 1 ) ) / b );
-
-    return ( s < 0 ? -(FT_Long)q : (FT_Long)q );
-  }
-
-
-#else /* !FT_LONG64 */
-
-
-  static void
-  ft_multo64( FT_UInt32  x,
-              FT_UInt32  y,
-              FT_Int64  *z )
-  {
-    FT_UInt32  lo1, hi1, lo2, hi2, lo, hi, i1, i2;
-
-
-    lo1 = x & 0x0000FFFFU;  hi1 = x >> 16;
-    lo2 = y & 0x0000FFFFU;  hi2 = y >> 16;
-
-    lo = lo1 * lo2;
-    i1 = lo1 * hi2;
-    i2 = lo2 * hi1;
-    hi = hi1 * hi2;
-
-    /* Check carry overflow of i1 + i2 */
-    i1 += i2;
-    hi += (FT_UInt32)( i1 < i2 ) << 16;
-
-    hi += i1 >> 16;
-    i1  = i1 << 16;
-
-    /* Check carry overflow of i1 + lo */
-    lo += i1;
-    hi += ( lo < i1 );
-
-    z->lo = lo;
-    z->hi = hi;
-  }
-
-
-  static FT_UInt32
-  ft_div64by32( FT_UInt32  hi,
-                FT_UInt32  lo,
-                FT_UInt32  y )
-  {
-    FT_UInt32  r, q;
-    FT_Int     i;
-
-
-    q = 0;
-    r = hi;
-
-    if ( r >= y )
-      return (FT_UInt32)0x7FFFFFFFL;
-
-    i = 32;
-    do
-    {
-      r <<= 1;
-      q <<= 1;
-      r  |= lo >> 31;
-
-      if ( r >= (FT_UInt32)y )
-      {
-        r -= y;
-        q |= 1;
-      }
-      lo <<= 1;
-    } while ( --i );
-
-    return q;
-  }
-
-
-  static void
-  FT_Add64( FT_Int64*  x,
-            FT_Int64*  y,
-            FT_Int64  *z )
-  {
-    register FT_UInt32  lo, hi;
-
-
-    lo = x->lo + y->lo;
-    hi = x->hi + y->hi + ( lo < x->lo );
-
-    z->lo = lo;
-    z->hi = hi;
-  }
-
-
-  /* documentation is in freetype.h */
-
-  /* The FT_MulDiv function has been optimized thanks to ideas from      */
-  /* Graham Asher.  The trick is to optimize computation when everything */
-  /* fits within 32-bits (a rather common case).                         */
-  /*                                                                     */
-  /*  we compute 'a*b+c/2', then divide it by 'c'. (positive values)     */
-  /*                                                                     */
-  /*  46340 is FLOOR(SQRT(2^31-1)).                                      */
-  /*                                                                     */
-  /*  if ( a <= 46340 && b <= 46340 ) then ( a*b <= 0x7FFEA810 )         */
-  /*                                                                     */
-  /*  0x7FFFFFFF - 0x7FFEA810 = 0x157F0                                  */
-  /*                                                                     */
-  /*  if ( c < 0x157F0*2 ) then ( a*b+c/2 <= 0x7FFFFFFF )                */
-  /*                                                                     */
-  /*  and 2*0x157F0 = 176096                                             */
-  /*                                                                     */
-
-  FT_EXPORT_DEF( FT_Long )
-  FT_MulDiv( FT_Long  a,
-             FT_Long  b,
-             FT_Long  c )
-  {
-    long  s;
-
-
-    /* XXX: this function does not allow 64-bit arguments */
-    if ( a == 0 || b == c )
-      return a;
-
-    s  = a; a = FT_ABS( a );
-    s ^= b; b = FT_ABS( b );
-    s ^= c; c = FT_ABS( c );
-
-    if ( a <= 46340L && b <= 46340L && c <= 176095L && c > 0 )
-      a = ( a * b + ( c >> 1 ) ) / c;
-
-    else if ( c > 0 )
-    {
-      FT_Int64  temp, temp2;
-
-
-      ft_multo64( (FT_Int32)a, (FT_Int32)b, &temp );
-
-      temp2.hi = 0;
-      temp2.lo = (FT_UInt32)(c >> 1);
-      FT_Add64( &temp, &temp2, &temp );
-      a = ft_div64by32( temp.hi, temp.lo, (FT_Int32)c );
-    }
-    else
-      a = 0x7FFFFFFFL;
-
-    return ( s < 0 ? -a : a );
-  }
-
-
-#ifdef TT_USE_BYTECODE_INTERPRETER
-
-  FT_BASE_DEF( FT_Long )
-  FT_MulDiv_No_Round( FT_Long  a,
-                      FT_Long  b,
-                      FT_Long  c )
-  {
-    long  s;
-
-
-    if ( a == 0 || b == c )
-      return a;
-
-    s  = a; a = FT_ABS( a );
-    s ^= b; b = FT_ABS( b );
-    s ^= c; c = FT_ABS( c );
-
-    if ( a <= 46340L && b <= 46340L && c > 0 )
-      a = a * b / c;
-
-    else if ( c > 0 )
-    {
-      FT_Int64  temp;
-
-
-      ft_multo64( (FT_Int32)a, (FT_Int32)b, &temp );
-      a = ft_div64by32( temp.hi, temp.lo, (FT_Int32)c );
-    }
-    else
-      a = 0x7FFFFFFFL;
-
-    return ( s < 0 ? -a : a );
-  }
-
-#endif /* TT_USE_BYTECODE_INTERPRETER */
-
-
-  /* documentation is in freetype.h */
-
-  FT_EXPORT_DEF( FT_Long )
-  FT_MulFix( FT_Long  a,
-             FT_Long  b )
-  {
-#ifdef FT_MULFIX_ASSEMBLER
-
-    return FT_MULFIX_ASSEMBLER( a, b );
-
-#elif 0
-
-    /*
-     *  This code is nonportable.  See comment below.
-     *
-     *  However, on a platform where right-shift of a signed quantity fills
-     *  the leftmost bits by copying the sign bit, it might be faster.
-     */
-
-    FT_Long   sa, sb;
-    FT_ULong  ua, ub;
-
-
-    if ( a == 0 || b == 0x10000L )
-      return a;
-
-    /*
-     *  This is a clever way of converting a signed number `a' into its
-     *  absolute value (stored back into `a') and its sign.  The sign is
-     *  stored in `sa'; 0 means `a' was positive or zero, and -1 means `a'
-     *  was negative.  (Similarly for `b' and `sb').
-     *
-     *  Unfortunately, it doesn't work (at least not portably).
-     *
-     *  It makes the assumption that right-shift on a negative signed value
-     *  fills the leftmost bits by copying the sign bit.  This is wrong. 
-     *  According to K&R 2nd ed, section `A7.8 Shift Operators' on page 206,
-     *  the result of right-shift of a negative signed value is
-     *  implementation-defined.  At least one implementation fills the
-     *  leftmost bits with 0s (i.e., it is exactly the same as an unsigned
-     *  right shift).  This means that when `a' is negative, `sa' ends up
-     *  with the value 1 rather than -1.  After that, everything else goes
-     *  wrong.
-     */
-    sa = ( a >> ( sizeof ( a ) * 8 - 1 ) );
-    a  = ( a ^ sa ) - sa;
-    sb = ( b >> ( sizeof ( b ) * 8 - 1 ) );
-    b  = ( b ^ sb ) - sb;
-
-    ua = (FT_ULong)a;
-    ub = (FT_ULong)b;
-
-    if ( ua <= 2048 && ub <= 1048576L )
-      ua = ( ua * ub + 0x8000U ) >> 16;
-    else
-    {
-      FT_ULong  al = ua & 0xFFFFU;
-
-
-      ua = ( ua >> 16 ) * ub +  al * ( ub >> 16 ) +
-           ( ( 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;
-
-
-    /* XXX: this function does not allow 64-bit arguments */
-    s  = (FT_Int32)a; a = FT_ABS( a );
-    s ^= (FT_Int32)b; b = FT_ABS( b );
-
-    if ( b == 0 )
-    {
-      /* check for division by 0 */
-      q = (FT_UInt32)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, (FT_Int32)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_Long  result; /* avoid overflow on 16-bit system */
-
-
-    /* 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;
-
-
-      /* XXX: this function does not allow 64-bit arguments */
-      ft_multo64( (FT_Int32)in_x, (FT_Int32)out_y, &z1 );
-      ft_multo64( (FT_Int32)in_y, (FT_Int32)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
-    }
-
-    /* XXX: only the sign of return value, +1/0/-1 must be used */
-    return (FT_Int)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 */