Extra: integration with pybind11

Warning

The functionality described in this section is experimental, and it may be subject to API changes in future versions.

New in version 0.6.

#include <mp++/extra/pybind11.hpp>

The mp++/extra/pybind11.hpp header provides facilities to seamlessly translate mp++ multiprecision objects to/from Python in pybind11 modules. pybind11 is a C++11 library that, similarly to the older Boost.Python library, allows to use C++ functions and classes from Python.

The API for the pybind11 integration currently includes a single function in the mppp_pybind11 namespace:

void mppp_pybind11::init()

Initialisation function for the pybind11 integration.

This function should be called in the definition of a pybind11 extension module, right after the PYBIND11_MODULE() invocation.

Note

Do not forget to invoke the mppp_pybind11::init() function! Failure to do so will result in unpredictable runtime errors.

Including the mp++/extra/pybind11.hpp header and invoking the mppp_pybind11::init() function will register custom type casters that will automatically translate to/from Python mp++ objects used as arguments and return values in functions exposed from C++. The translation rules are the following:

If the mpmath library is not installed, the translations for real128 and real will be disabled at runtime.

Let’s take a look at an example of a pybind11 module enabling automatic translation of mp++ objects:

#include <mp++/mp++.hpp>
#include <mp++/extra/pybind11.hpp>

#include <string>
#include <unordered_map>
#include <vector>

#include <pybind11/pybind11.h>
#include <pybind11/stl.h>

// A couple of functions accepting and returning C++ containers.
template <typename T>
static inline std::vector<T> test_vector(const std::vector<T> &v)
{
    return v;
}

template <typename T>
static inline std::unordered_map<std::string, T> test_unordered_map(const std::unordered_map<std::string, T> &um)
{
    return um;
}

PYBIND11_MODULE(pybind11_test_01, m)
{
    // Init the pybind11 integration for this module.
    mppp_pybind11::init();

    // Expose a few functions testing the automatic translation of mp++ objects.
    // -------------------------------------------------------------------------

    m.def("test_int1_conversion", [](const mppp::integer<1> &n) { return n; });

    m.def("test_rat1_conversion", [](const mppp::rational<1> &q) { return q; });

    m.def("test_real_conversion", [](const mppp::real &r) { return r; });
    m.def("test_real_conversion", [](const mppp::real &r, ::mpfr_prec_t prec) { return mppp::real{r, prec}; });

    m.def("test_real128_conversion", [](const mppp::real128 &r) { return r; });

    m.def("test_overload", [](const mppp::integer<1> &n) { return n; });
    m.def("test_overload", [](const mppp::rational<1> &q) { return q; });
    m.def("test_overload", [](const mppp::real128 &r) { return r; });
    m.def("test_overload", [](const mppp::real &r) { return r; });

    m.def("test_vector_conversion", test_vector<mppp::integer<1>>);
    m.def("test_vector_conversion", test_vector<mppp::rational<1>>);
    m.def("test_vector_conversion", test_vector<mppp::real128>);
    m.def("test_vector_conversion", test_vector<mppp::real>);

    m.def("test_unordered_map_conversion", test_unordered_map<mppp::integer<1>>);
    m.def("test_unordered_map_conversion", test_unordered_map<mppp::rational<1>>);
    m.def("test_unordered_map_conversion", test_unordered_map<mppp::real128>);
    m.def("test_unordered_map_conversion", test_unordered_map<mppp::real>);

    m.def("test_zero_division_error", []() { return mppp::integer<1>{1} / 0; });
}

Note that we have exposed functions which just return a copy of their input parameter. This will allow us to verify that the automatic translation between mp++ and Python objects works as intended. Now, assuming that we have built the code above into a Python extension called pybind11_test_01 (see the pybind11 documentation for details), we can try to call the exposed functions from Python:

>>> import pybind11_test_01 as p
>>> from fractions import Fraction as F
>>> p.test_int1_conversion(42)
42
>>> p.test_int1_conversion(-1)
-1
>>> p.test_rat1_conversion(F(3, 4))
Fraction(3, 4)
>>> p.test_rat1_conversion(F(-1, 2))
Fraction(-1, 2)

Indeed, the Python objects passed as arguments to the exposed functions are correctly translated to mp++ objects before being passed to the C++ functions, and the mp++ return values are correctly translated back to the original Python objects.

Let’s try with some floating-point objects:

>>> from mpmath import mpf, mp
>>> p.test_real_conversion(mpf("1.1"))
mpf('1.1000000000000001')

The default precision in mpmath is 53 (double-precision), and indeed the conversion between mpf on the Python side and real on the C++ side is done with 53 bits of precision. We can increase the precision to 200 bits and verify that the value is correctly preserved and translated:

>>> mp.prec = 200
>>> p.test_real_conversion(mpf("1.1"))
mpf('1.1000000000000000000000000000000000000000000000000000000000002')

If the precision is set exactly to 113, mpf objects can be converted to real128:

>>> mp.prec = 113
>>> p.test_real128_conversion(mpf("1.1"))
mpf('1.10000000000000000000000000000000008')
>>> mp.prec = 114
>>> p.test_real128_conversion(mpf("1.1"))
Traceback (most recent call last):
     ...
TypeError: test_real128_conversion(): incompatible function arguments. The following argument types are supported:
    1. (arg0: mppp::real128) -> mppp::real128

A real128 will be successfully converted to an mpf iff the current mpmath working precision is exactly 113. A real will be successfully converted to an mpf iff its precision is not greater than the current mpmath working precision:

>>> mp.prec = 53;
>>> p.test_real_conversion(mpf("1.1"), 100)
Traceback (most recent call last):
     ...
ValueError: Cannot convert the real 1.1000000000000000888178419700125 to an mpf: the precision of the real (100) is greater than the current mpf precision (53). Please increase the current mpf precision to at least 100 in order to avoid this error
>>> mp.prec = 100;
>>> p.test_real_conversion(mpf("1.1"), 100)
mpf('1.1000000000000000000000000000003')

Overloaded functions are supported as well:

>>> p.test_overload(-2)
-2
>>> p.test_overload(F(6, 7))
Fraction(6, 7)
>>> p.test_overload(mpf("1.3"))
mpf('1.2999999999999999999999999999994')

Note that, due to the fact that mpf arguments can be converted both to real128 and real, overloads with real128 arguments should be exposed before overloads with real arguments (otherwise, the real overload will always be preferred).

There’s an important caveat to keep in mind when translating to/from real128. The IEEE 754 quadruple precision format, implemented by real128, has a limited exponent range. The value \(2^{-30000}\), for instance, becomes simply zero in quadruple precision, and \(2^{30000}\) becomes \(+\infty\):

>>> mp.prec = 113
>>> p.test_real128_conversion(mpf(2)**-30000)
mpf('0.0')
>>> p.test_real128_conversion(mpf(2)**30000)
mpf('+inf')

In mpmath, however, \(2^{-30000}\) and \(2^{30000}\) are correctly computed to quadruple precision:

>>> mpf(2)**-30000
mpf('1.25930254358409145729153078521520406e-9031')
>>> mpf(2)**30000
mpf('7.94090351913296032413251784349270251e+9030')

This happens because mpmath features a much larger (practically unlimited) range for the value of the exponent. As a consequence, a conversion from mpf to real128 will not preserve the exact value if the absolute value of the exponent is too large.

We can verify that the conversion between mp++ and Python works transparently when containers are involved:

>>> p.test_vector_conversion([1, 2, 3])
[1, 2, 3]
>>> p.test_vector_conversion([F(1), F(1, 2), F(1, 3)])
[Fraction(1, 1), Fraction(1, 2), Fraction(1, 3)]
>>> p.test_vector_conversion([mpf(1), mpf(2), mpf(3)])
[mpf('1.0'), mpf('2.0'), mpf('3.0')]
>>> p.test_unordered_map_conversion({'a': 1, 'b': 3})
{'a': 1, 'b': 3}
>>> p.test_unordered_map_conversion({'a': F(1, 2), 'b': F(1, 3)})
{'a': Fraction(1, 2), 'b': Fraction(1, 3)}
>>> p.test_unordered_map_conversion({'a': mpf(1), 'b': mpf(3)})
{'a': mpf('1.0'), 'b': mpf('3.0')}

Finally, the pybind11 integration utilities will automatically translate mp++ exceptions thrown from C++ code into corresponding Python exceptions. Here is an example where mp++’s zero_division_error exception is translated to Python’s ZeroDivisionError exception:

>>> p.test_zero_division_error()
Traceback (most recent call last):
     ...
ZeroDivisionError: Integer division by zero