/***************************************************************************/

/*                                                                         */

/*  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 */