Safe Numerics |
For many years, Boost has included a library to represent and operate
on rational
numbers. Its well crafted, has good documentation and is well
maintained. Using the rational library is as easy as construction an
instance with the expression rational r(n, d)
where n and d are
integers of the same type. From then on it can be used pretty much as any
other number. Reading the documentation with safe integers in mind one
finds
Limited-precision integer types [such as
int
] may raise issues with the range sizes of their allowable negative values and positive values. If the negative range is larger, then the extremely-negative numbers will not have an additive inverse in the positive range, making them unusable as denominator values since they cannot be normalized to positive values (unless the user is lucky enough that the input components are not relatively prime pre-normalization).
Which hints of trouble. Examination of the code reveals which suggest that care has been taken implement operations so as to avoid overflows, catch divide by zero, etc. But the code itself doesn't seem to consistently implement this idea. So we make a small demo program:
#include <iostream> #include <limits> #include <boost/rational.hpp> #include <boost/safe_numerics/safe_integer.hpp> int main(int, const char *[]){ // simple demo of rational library const boost::rational<int> r {1, 2}; std::cout << "r = " << r << std::endl; const boost::rational<int> q {-2, 4}; std::cout << "q = " << q << std::endl; // display the product std::cout << "r * q = " << r * q << std::endl; // problem: rational doesn't handle integer overflow well const boost::rational<int> c {1, INT_MAX}; std::cout << "c = " << c << std::endl; const boost::rational<int> d {1, 2}; std::cout << "d = " << d << std::endl; // display the product - wrong answer std::cout << "c * d = " << c * d << std::endl; // solution: use safe integer in rational definition using safe_rational = boost::rational< boost::safe_numerics::safe<int> >; // use rationals created with safe_t const safe_rational sc {1, INT_MAX}; std::cout << "c = " << sc << std::endl; const safe_rational sd {1, 2}; std::cout << "d = " << sd << std::endl; std::cout << "c * d = "; try { // multiply them. This will overflow std::cout << sc * sd << std::endl; } catch (std::exception const& e) { // catch exception due to multiplication overflow std::cout << e.what() << std::endl; } return 0; }
which produces the following output
r = 1/2 q = -1/2 r * q = -1/4 c = 1/2147483647 d = 1/2 c * d = 1/-2 c = 1/2147483647 d = 1/2 c * d = multiplication overflow: positive overflow error
The rational library
documentation is quite specific as to the type
requirements placed on the underlying type. Turns out the our own definition of an integer type
fulfills (actually surpasses) these requirements. So we have reason to hope
that we can use safe<int>
as the underlying type to
create what we might call a "safe_rational
". This we have done
in the above example where we demonstrate how to compose the rational
library with the safe numerics library in order to create what amounts to a
safe_rational library - all without writing a line of code! Still, things
are not perfect. Since the rational numbers
library implements its own checking for divide by zero by throwing
an exception, the safe numerics code for handling this - included exception
policy will not be respected. To summarize:
In some cases safe types can be used as template parameters to other types to inject the concept of "no erroneous results" into the target type.
Such composition is not guaranteed to work. The target type must be reviewed in some detail.