kernel_ftc3.h

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    Protect_FPU_rounding<false> Protection(CGAL_FE_TONEAREST);
    return collinearC3(
		px.exact(),
		py.exact(),
		pz.exact(),
		qx.exact(),
		qy.exact(),
		qz.exact(),
		rx.exact(),
		ry.exact(),
		rz.exact());
  }
}

template < class CT, class ET, bool Protected, class Cache >
/* CGAL_KERNEL_MEDIUM_INLINE */
Orientation
orientationC3(
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &px,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &py,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &pz,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &qx,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &qy,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &qz,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &rx,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &ry,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &rz,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &sx,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &sy,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &sz)
{
  try
  {
    CGAL_PROFILER("IA orientationC3 calls");
    Protect_FPU_rounding<Protected> Protection;
    return orientationC3(
		px.interval(),
		py.interval(),
		pz.interval(),
		qx.interval(),
		qy.interval(),
		qz.interval(),
		rx.interval(),
		ry.interval(),
		rz.interval(),
		sx.interval(),
		sy.interval(),
		sz.interval());
  } 
  catch (Interval_nt_advanced::unsafe_comparison)
  {
    CGAL_PROFILER("IA orientationC3 failures");
    Protect_FPU_rounding<!Protected> Protection(CGAL_FE_TONEAREST);
    return orientationC3(
		px.exact(),
		py.exact(),
		pz.exact(),
		qx.exact(),
		qy.exact(),
		qz.exact(),
		rx.exact(),
		ry.exact(),
		rz.exact(),
		sx.exact(),
		sy.exact(),
		sz.exact());
  }
}

template < class ET >
/* CGAL_KERNEL_MEDIUM_INLINE */
Orientation
orientationC3(
    const Lazy_exact_nt<ET> &px,
    const Lazy_exact_nt<ET> &py,
    const Lazy_exact_nt<ET> &pz,
    const Lazy_exact_nt<ET> &qx,
    const Lazy_exact_nt<ET> &qy,
    const Lazy_exact_nt<ET> &qz,
    const Lazy_exact_nt<ET> &rx,
    const Lazy_exact_nt<ET> &ry,
    const Lazy_exact_nt<ET> &rz,
    const Lazy_exact_nt<ET> &sx,
    const Lazy_exact_nt<ET> &sy,
    const Lazy_exact_nt<ET> &sz)
{
  try
  {
    CGAL_PROFILER("Lazy IA orientationC3 calls");
    Protect_FPU_rounding<true> Protection;
    return orientationC3(
		px.interval(),
		py.interval(),
		pz.interval(),
		qx.interval(),
		qy.interval(),
		qz.interval(),
		rx.interval(),
		ry.interval(),
		rz.interval(),
		sx.interval(),
		sy.interval(),
		sz.interval());
  } 
  catch (Interval_nt_advanced::unsafe_comparison)
  {
    CGAL_PROFILER("Lazy IA orientationC3 failures");
    Protect_FPU_rounding<false> Protection(CGAL_FE_TONEAREST);
    return orientationC3(
		px.exact(),
		py.exact(),
		pz.exact(),
		qx.exact(),
		qy.exact(),
		qz.exact(),
		rx.exact(),
		ry.exact(),
		rz.exact(),
		sx.exact(),
		sy.exact(),
		sz.exact());
  }
}

template < class CT, class ET, bool Protected, class Cache >
/* inline */
Angle
angleC3(
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &px,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &py,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &pz,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &qx,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &qy,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &qz,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &rx,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &ry,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &rz)
{
  try
  {
    CGAL_PROFILER("IA angleC3 calls");
    Protect_FPU_rounding<Protected> Protection;
    return angleC3(
		px.interval(),
		py.interval(),
		pz.interval(),
		qx.interval(),
		qy.interval(),
		qz.interval(),
		rx.interval(),
		ry.interval(),
		rz.interval());
  } 
  catch (Interval_nt_advanced::unsafe_comparison)
  {
    CGAL_PROFILER("IA angleC3 failures");
    Protect_FPU_rounding<!Protected> Protection(CGAL_FE_TONEAREST);
    return angleC3(
		px.exact(),
		py.exact(),
		pz.exact(),
		qx.exact(),
		qy.exact(),
		qz.exact(),
		rx.exact(),
		ry.exact(),
		rz.exact());
  }
}

template < class ET >
/* inline */
Angle
angleC3(
    const Lazy_exact_nt<ET> &px,
    const Lazy_exact_nt<ET> &py,
    const Lazy_exact_nt<ET> &pz,
    const Lazy_exact_nt<ET> &qx,
    const Lazy_exact_nt<ET> &qy,
    const Lazy_exact_nt<ET> &qz,
    const Lazy_exact_nt<ET> &rx,
    const Lazy_exact_nt<ET> &ry,
    const Lazy_exact_nt<ET> &rz)
{
  try
  {
    CGAL_PROFILER("Lazy IA angleC3 calls");
    Protect_FPU_rounding<true> Protection;
    return angleC3(
		px.interval(),
		py.interval(),
		pz.interval(),
		qx.interval(),
		qy.interval(),
		qz.interval(),
		rx.interval(),
		ry.interval(),
		rz.interval());
  } 
  catch (Interval_nt_advanced::unsafe_comparison)
  {
    CGAL_PROFILER("Lazy IA angleC3 failures");
    Protect_FPU_rounding<false> Protection(CGAL_FE_TONEAREST);
    return angleC3(
		px.exact(),
		py.exact(),
		pz.exact(),
		qx.exact(),
		qy.exact(),
		qz.exact(),
		rx.exact(),
		ry.exact(),
		rz.exact());
  }
}

template < class CT, class ET, bool Protected, class Cache >
/* CGAL_KERNEL_LARGE_INLINE */
Bounded_side
coplanar_side_of_bounded_circleC3(
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &px,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &py,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &pz,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &qx,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &qy,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &qz,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &rx,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &ry,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &rz,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &tx,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &ty,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &tz)
{
  try
  {
    CGAL_PROFILER("IA coplanar_side_of_bounded_circleC3 calls");
    Protect_FPU_rounding<Protected> Protection;
    return coplanar_side_of_bounded_circleC3(
		px.interval(),
		py.interval(),
		pz.interval(),
		qx.interval(),
		qy.interval(),
		qz.interval(),
		rx.interval(),
		ry.interval(),
		rz.interval(),
		tx.interval(),
		ty.interval(),
		tz.interval());
  } 
  catch (Interval_nt_advanced::unsafe_comparison)
  {
    CGAL_PROFILER("IA coplanar_side_of_bounded_circleC3 failures");
    Protect_FPU_rounding<!Protected> Protection(CGAL_FE_TONEAREST);
    return coplanar_side_of_bounded_circleC3(
		px.exact(),
		py.exact(),
		pz.exact(),
		qx.exact(),
		qy.exact(),
		qz.exact(),
		rx.exact(),
		ry.exact(),
		rz.exact(),
		tx.exact(),
		ty.exact(),
		tz.exact());
  }
}

template < class ET >
/* CGAL_KERNEL_LARGE_INLINE */
Bounded_side
coplanar_side_of_bounded_circleC3(
    const Lazy_exact_nt<ET> &px,
    const Lazy_exact_nt<ET> &py,
    const Lazy_exact_nt<ET> &pz,
    const Lazy_exact_nt<ET> &qx,
    const Lazy_exact_nt<ET> &qy,
    const Lazy_exact_nt<ET> &qz,
    const Lazy_exact_nt<ET> &rx,
    const Lazy_exact_nt<ET> &ry,
    const Lazy_exact_nt<ET> &rz,
    const Lazy_exact_nt<ET> &tx,
    const Lazy_exact_nt<ET> &ty,
    const Lazy_exact_nt<ET> &tz)
{
  try
  {
    CGAL_PROFILER("Lazy IA coplanar_side_of_bounded_circleC3 calls");
    Protect_FPU_rounding<true> Protection;
    return coplanar_side_of_bounded_circleC3(
		px.interval(),
		py.interval(),
		pz.interval(),
		qx.interval(),
		qy.interval(),
		qz.interval(),
		rx.interval(),
		ry.interval(),
		rz.interval(),
		tx.interval(),
		ty.interval(),
		tz.interval());
  } 
  catch (Interval_nt_advanced::unsafe_comparison)
  {
    CGAL_PROFILER("Lazy IA coplanar_side_of_bounded_circleC3 failures");
    Protect_FPU_rounding<false> Protection(CGAL_FE_TONEAREST);
    return coplanar_side_of_bounded_circleC3(
		px.exact(),
		py.exact(),
		pz.exact(),
		qx.exact(),
		qy.exact(),
		qz.exact(),
		rx.exact(),
		ry.exact(),
		rz.exact(),
		tx.exact(),
		ty.exact(),
		tz.exact());
  }
}

template < class CT, class ET, bool Protected, class Cache >
/* CGAL_KERNEL_MEDIUM_INLINE */
bool
equal_directionC3(
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &dx1,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &dy1,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &dz1,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &dx2,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &dy2,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &dz2)
{
  try
  {
    CGAL_PROFILER("IA equal_directionC3 calls");
    Protect_FPU_rounding<Protected> Protection;
    return equal_directionC3(
		dx1.interval(),
		dy1.interval(),
		dz1.interval(),
		dx2.interval(),
		dy2.interval(),
		dz2.interval());
  } 
  catch (Interval_nt_advanced::unsafe_comparison)
  {
    CGAL_PROFILER("IA equal_directionC3 failures");
    Protect_FPU_rounding<!Protected> Protection(CGAL_FE_TONEAREST);
    return equal_directionC3(
		dx1.exact(),
		dy1.exact(),
		dz1.exact(),
		dx2.exact(),
		dy2.exact(),
		dz2.exact());
  }
}

template < class ET >
/* CGAL_KERNEL_MEDIUM_INLINE */
bool
equal_directionC3(
    const Lazy_exact_nt<ET> &dx1,
    const Lazy_exact_nt<ET> &dy1,
    const Lazy_exact_nt<ET> &dz1,
    const Lazy_exact_nt<ET> &dx2,
    const Lazy_exact_nt<ET> &dy2,
    const Lazy_exact_nt<ET> &dz2)
{
  try
  {
    CGAL_PROFILER("Lazy IA equal_directionC3 calls");
    Protect_FPU_rounding<true> Protection;
    return equal_directionC3(
		dx1.interval(),
		dy1.interval(),
		dz1.interval(),
		dx2.interval(),
		dy2.interval(),
		dz2.interval());
  } 
  catch (Interval_nt_advanced::unsafe_comparison)
  {
    CGAL_PROFILER("Lazy IA equal_directionC3 failures");
    Protect_FPU_rounding<false> Protection(CGAL_FE_TONEAREST);
    return equal_directionC3(
		dx1.exact(),
		dy1.exact(),
		dz1.exact(),
		dx2.exact(),
		dy2.exact(),
		dz2.exact());
  }
}

template < class CT, class ET, bool Protected, class Cache >
/* CGAL_KERNEL_MEDIUM_INLINE */
bool
equal_planeC3(
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &ha,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &hb,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &hc,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &hd,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &pa,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &pb,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &pc,
    const Filtered_exact <CT, ET, Dynamic, Protected, Cache> &pd)
{
  try
  {
    CGAL_PROFILER("IA equal_planeC3 calls");
    Protect_FPU_rounding<Protected> Protection;
    return equal_planeC3(
		ha.interval(),
		hb.interval(),
		hc.interval(),
		hd.interval(),
		pa.interval(),
		pb.interval(),
		pc.interval(),
		pd.interval());
  } 
  catch (Interval_nt_advanced::unsafe_comparison)
  {
    CGAL_PROFILER("IA equal_planeC3 failures");
    Protect_FPU_rounding<!Protected> Protection(CGAL_FE_TONEAREST);
    return equal_planeC3(
		ha.exact(),
		hb.exact(),
		hc.exact(),
		hd.exact(),
		pa.exact(),
		pb.exact(),
		pc.exact(),
		pd.exact());
  }
}

template < class ET >
/* CGAL_KERNEL_MEDIUM_INLINE */
bool
equal_planeC3(