id,summary,reporter,owner,description,type,status,milestone,component,version,severity,resolution,keywords,cc
8379,side_by_triangle foils scaled-epsilon for equality by comparing determinant against zero,Hubert Tong <hstong@…>,Barend Gehrels,"In boost/geometry/strategies/cartesian/side_by_triangle.hpp:

{{{#!cpp
/*    88*/              promoted_type const s 
/*    89*/                  = geometry::detail::determinant<promoted_type>
/*    90*/                      (
/*    91*/                          dx, dy, 
/*    92*/                          dpx, dpy
/*    93*/                      );
/*    94*/      
/*    95*/              promoted_type const zero = promoted_type();
/*    96*/              return math::equals(s, zero) ? 0 
/*    97*/                  : s > zero ? 1 
/*    98*/                  : -1;
}}}

The math::equals() interface implements, in boost/geometry/util/math.hpp, an equality comparison with an epsilon value—scaled by its arguments—when the common type is a floating-point type:

{{{#!cpp
/*    52*/          static inline bool apply(Type const& a, Type const& b)
/*    53*/          {
/*    54*/                      if (a == b)
/*    55*/                      {
/*    56*/                              return true;
/*    57*/                      }
/*    58*/
/*    59*/              // See http://www.parashift.com/c++-faq-lite/newbie.html#faq-29.17,
/*    60*/              // FUTURE: replace by some boost tool or boost::test::close_at_tolerance
/*    61*/              return std::abs(a - b) <= std::numeric_limits<Type>::epsilon() * get_max(std::abs(a), std::abs(b), 1.0);
}}}

The scaling performed by the math::equals() interface fails to reliably reflect the scale of the original inputs to the determinant calculation (dx, dy, dpx, dpy) through no fault of its own; it was not passed the appropriate information.

In particular,
{{{#!c
fma(x, y, -(x * y)); /* x*y - x*y */
}}}
is known to produce, on some platforms, the double value which is nearest to the round-off from (x * y). This round-off can legitimately be greater than DBL_EPSILON.

The determinant calculation in boost/geometry/arithmetic/determinant.hpp:
{{{#!cpp
/*    42*/              return rt(ux) * rt(vy) - rt(uy) * rt(vx);
}}}
is liable to hit similar behaviour.",Bugs,closed,Boost 1.58.0,geometry,Boost Development Trunk,Problem,fixed,,