text: /***************************************************************************/
  /*                                                                         */
  /*  ftcalc.c                                                               */
  /*                                                                         */
  /*    Arithmetic computations (body).                                      */
  /*                                                                         */
  /*  Copyright 1996-2001, 2002, 2003, 2004, 2005, 2006 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_INTERNAL_CALC_H
  #include FT_INTERNAL_DEBUG_H
  #include FT_INTERNAL_OBJECTS_H
  
  
  /* 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 )
    {
      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 ;
    }
  
  
    /* 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 )
    {
      /* use inline assembly to speed up things a bit */
  
  #if defined( __GNUC__ ) && defined( i386 )
  
      FT_Long  result;
  
  
      __asm__ __volatile__ (
        "imul  %%edx\n"
        "movl  %%edx, %%ecx\n"
        "sarl  $31, %%ecx\n"
        "addl  $0x8000, %%ecx\n"
        "addl  %%ecx, %%eax\n"
        "adcl  $0, %%edx\n"
        "shrl  $16, %%eax\n"
        "shll  $16, %%edx\n"
        "addl  %%edx, %%eax\n"
        "mov   %%eax, %0\n"
        : "=r"(result)
        : "a"(a), "d"(b)
        : "%ecx"
      );
      return result;
  
  #elif 1
  
      FT_Long   sa, sb;
      FT_ULong  ua, ub;
  
  
      if ( a == 0 || b == 0x10000L )
        return a;
  
      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 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 */
  