All of the non-member integer operations are overloaded for the fundamental (built-in) integer types in <boost/multiprecision/integer.hpp>. Where these operations require a temporary increase in precision (such as for powm), then if no fundamental (built-in) type is available, a cpp_int of appropriate precision will be used.

Some of these functions are trivial, others use compiler intrinsics (where available) to ensure optimal evaluation.

The overloaded functions are:

template <class Integer, class I2>
Integer& multiply(Integer& result, const I2& a, const I2& b);

Multiplies two I2 values, to produce a wider Integer result.

Returns result = a * b without overflow or loss of precision in the multiplication.

template <class Integer, class I2>
Integer& add(Integer& result, const I2& a, const I2& b);

Adds two I2 values, to produce a wider Integer result.

Returns result = a + b without overflow or loss of precision in the addition.

template <class Integer, class I2>
Integer& subtract(Integer& result, const I2& a, const I2& b);

Subtracts two I2 values, to produce a wider Integer result.

Returns result = a - b without overflow or loss of precision in the subtraction.

template <class Integer>
Integer powm(const Integer& b, const Integer& p, const Integer& m);

Returns b^p % m.

template <class Integer>
void divide_qr(const Integer& x, const Integer& y, Integer& q, Integer& r);

Sets q = x / y and r = x % y.

template <class Integer1, class Integer2>
Integer2 integer_modulus(const Integer1& x, Integer2 val);

Returns x % val;

template <class Integer>
unsigned lsb(const Integer& x);

Returns the (zero-based) index of the least significant bit of x.

Throws a std::domain_error if x <= 0.

template <class Integer>
unsigned msb(const Integer& x);

Returns the (zero-based) index of the most significant bit of x.

Throws a std::domain_error if x <= 0.

template <class Integer>
bool bit_test(const Integer& val, unsigned index);

Returns true if bit index is set in val.

template <class Integer>
Integer& bit_set(Integer& val, unsigned index);

Sets the index bit in val.

template <class Integer>
Integer& bit_unset(Integer& val, unsigned index);

Unsets the index bit in val.

template <class Integer>
Integer& bit_flip(Integer& val, unsigned index);

Flips the index bit in val.

template <class Integer>
Integer sqrt(const Integer& x);
template <class Integer>
Integer sqrt(const Integer& x, Integer& r);

Returns the integer square root s of x and sets r to the remainder x - s².

template <class Engine>
bool miller_rabin_test(const number-or-expression-template-type& n, unsigned trials, Engine& gen);
bool miller_rabin_test(const number-or-expression-template-type& n, unsigned trials);

The regular Miller-Rabin functions in <boost/multiprecision/miller_rabin.hpp> are defined in terms of the above generic operations, and so function equally well for fundamental (built-in) types and multiprecision types.