Difference does not work reliable for double precision

[MauriceHubain]

This is a follow up ticket for #1288.

Adapting your test code from that ticket with a new data set, we get wrong results for double and long double precision:

#include <boost/geometry.hpp>
#include <boost/geometry/geometries/geometries.hpp>
#include <iostream>
#include <iomanip>

namespace bg = boost::geometry;

template <typename T>
void test_Difference_B83673_1_MP()
{
  using point_t = bg::model::point<T, 2, bg::cs::cartesian>;
  using polygon_t = bg::model::polygon<point_t, false, false>;
  using mp_t = bg::model::multi_polygon<polygon_t>;

  mp_t poly1;
  bg::read_wkt("MULTIPOLYGON(((1.2549999979079400 0.85000000411847698, -1.2550000020920500 0.84999999897038103, -1.2549999999999999 -0.85000000102961903, 1.2549999999999999 -0.84999999999999998)))", poly1);
  bg::correct(poly1);

  mp_t poly2;
  bg::read_wkt("MULTIPOLYGON(((-0.87500000000000000 -0.84999999999999998, -0.87500000000000000 -0.070000000000000201, -1.2549999999999999 -0.070000000000000201, -1.2549999999999999 -0.84999999999999998)))", poly2);
  bg::correct(poly2);

  mp_t diff, inters;
  bg::difference(poly1, poly2, diff);
  bg::intersection(poly1, poly2, inters);

  std::cout << std::setprecision(12) << std::boolalpha;
  std::cout
    << "Type: " << typeid(T).name()
    << " a: " << bg::area(poly1)
    << " b: " << bg::area(poly2)
    << " diff: " << bg::area(diff)
    << " ints: " << bg::area(inters)
    << " a-b: " << bg::area(poly1) - bg::area(poly2)
    << " d+i " << bg::area(diff) + bg::area(inters)
    << " validity diff: " << bg::is_valid(diff)
    << " ints: " << bg::is_valid(inters)
    << std::endl;
}

template <typename T>
void test_Difference_B83673_1_P()
{
  using point_t = bg::model::point<T, 2, bg::cs::cartesian>;
  using polygon_t = bg::model::polygon<point_t, false, false>;
  using mp_t = bg::model::multi_polygon<polygon_t>;

  mp_t poly1;
  bg::read_wkt("MULTIPOLYGON(((1.2549999979079400 0.85000000411847698, -1.2550000020920500 0.84999999897038103, -1.2549999999999999 -0.85000000102961903, 1.2549999999999999 -0.84999999999999998)))", poly1);
  bg::correct(poly1);

  polygon_t poly2;
  bg::read_wkt("POLYGON((-0.87500000000000000 -0.84999999999999998, -0.87500000000000000 -0.070000000000000201, -1.2549999999999999 -0.070000000000000201, -1.2549999999999999 -0.84999999999999998))", poly2);
  bg::correct(poly2);

  mp_t diff, inters;
  bg::difference(poly1, poly2, diff);
  bg::intersection(poly1, poly2, inters);

  std::cout << std::setprecision(12) << std::boolalpha;
  std::cout
    << "Type: " << typeid(T).name()
    << " a: " << bg::area(poly1)
    << " b: " << bg::area(poly2)
    << " diff: " << bg::area(diff)
    << " ints: " << bg::area(inters)
    << " a-b: " << bg::area(poly1) - bg::area(poly2)
    << " d+i " << bg::area(diff) + bg::area(inters)
    << " validity diff: " << bg::is_valid(diff)
    << " ints: " << bg::is_valid(inters)
    << std::endl;
}

int main() 
{
  test_Difference_B83673_1_MP<float>();
  test_Difference_B83673_1_MP<double>();
  test_Difference_B83673_1_MP<long double>();
  std::cout << std::endl;

  test_Difference_B83673_1_P<float>();
  test_Difference_B83673_1_P<double>();
  test_Difference_B83673_1_P<long double>();
  std::cout << std::endl;
}

Output:
Type: float a: 4.26700010347 b: 0.296400005227 diff: 3.97060009825 ints: 0.296400005227 a-b: 3.97060009825 d+i 4.26700010347 validity diff: true ints: true
Type: double a: 4.26700000517 b: 0.2964 diff: 0 ints: 0.2964 a-b: 3.97060000517 d+i 0.2964 validity diff: true ints: true
Type: long double a: 4.26700000517 b: 0.2964 diff: 0 ints: 0.2964 a-b: 3.97060000517 d+i 0.2964 validity diff: true ints: true

Type: float a: 4.26700010347 b: 0.296400005227 diff: 3.97060009825 ints: 0.296400005227 a-b: 3.97060009825 d+i 4.26700010347 validity diff: true ints: true
Type: double a: 4.26700000517 b: 0.2964 diff: 0 ints: 0.2964 a-b: 3.97060000517 d+i 0.2964 validity diff: true ints: true
Type: long double a: 4.26700000517 b: 0.2964 diff: 0 ints: 0.2964 a-b: 3.97060000517 d+i 0.2964 validity diff: true ints: true

[barendgehrels]

This is indeed also wrong and now is wrong for both multi and poly.
Thanks for the report.
It is not yet fixed by my concept fix for #1293 and #1294 and #1295