#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...