[ET Trac] #2925: overflow in rat<int64> in Arith

[Roland Haas]

#2925: overflow in rat<int64> in Arith

 Reporter: Roland Haas
   Status: new
Milestone: 
  Version: 
     Type: bug
 Priority: minor
Component: 

Comment (by Roland Haas):

Following up on the discussion, one can do the multiplication manually:

```
// TODO: need special code to handle the case if a or b is int64_min since -int64_min > int64_max (https://en.cppreference.com/w/cpp/numeric/math/abs#Notes)
int64_t save_mult(int64_t a, int64_t b) {
  uint64_t abs_a = std::abs(a);
  uint64_t abs_b = std::abs(b);
  auto upper = [](uint64_t x) -> uint32_t { return (x >> 32) & 0xffffffffu; };
  auto lower = [](uint64_t x) -> uint32_t { return (x >> 0) & 0xffffffffu; };
  assert(upper(abs_a) * upper(abs_b) == 0);
  assert(upper(upper(abs_a) * lower(abs_b)) == 0);
  assert(upper(lower(abs_a) * upper(abs_b)) == 0);
  // so far: no overflow for uint64_t, now check that we are not exceeding int64_max (~ 1/2 of uint64_max)
  assert(abs_a * abs_b <= std::numeric_limits<int64_t>::max());
  return a*b;
}
```

this does require knowing the bit-width at compile though (so is difficult with the templated `rational`) and has to handle corner cases.

--
Ticket URL: https://bitbucket.org/einsteintoolkit/tickets/issues/2925/overflow-in-rat-in-arith
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