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Branched from the monolithic repo, Qt master branch, at commit
896db169ea224deb96c59ce8af800d019de63f12

1 files changed, 953 insertions, 0 deletions

diff --git a/src/3rdparty/freetype/src/base/ftcalc.c b/src/3rdparty/freetype/src/base/ftcalc.c
new file mode 100644
index 0000000000..04295a6931
--- /dev/null
+++ b/src/3rdparty/freetype/src/base/ftcalc.c
@@ -0,0 +1,953 @@
+/***************************************************************************/
+/*                                                                         */
+/*  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_ULong  val, root, newroot, mask;
+
+
+    root = 0;
+    mask = 0x40000000L;
+    val  = (FT_ULong)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;
+
+
+    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( a, b, &temp );
+
+      temp2.hi = 0;
+      temp2.lo = (FT_UInt32)(c >> 1);
+      FT_Add64( &temp, &temp2, &temp );
+      a = ft_div64by32( temp.hi, temp.lo, 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( a, b, &temp );
+      a = ft_div64by32( temp.hi, temp.lo, 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;
+
+
+    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 */