Provides utilities to help with mathematics. More...

Modules
	Mathematical Constants
	Defines mathematical constants commonly in use.

Classes
struct	gears::math::uintx< Bits, Digit, Digits >
	Multi-precision unsigned integer. More...

Functions
template<typename T >
T	gears::math::fibonacci (T number)
	Calculates the nth fibonacci number. More...

template<typename T >
constexpr T	gears::math::factorial (const T &number)
	Calculates the Nth factorial. More...

template<typename T >
constexpr T	gears::math::gcd (const T &x, const T &y)
	Calculates the greatest common divisor. More...

template<typename T >
T	gears::math::mod_pow (T base, T exponent, const T &modulus)
	Calculates the modular exponentiation. More...

template<typename T >
T	gears::math::sum_of_divisors (const T &number) noexcept
	Calculates the sum of divisors function. More...

template<typename T >
bool	gears::math::is_prime (const T &number) noexcept
	Checks if a number is prime. More...

template<typename T >
constexpr T	gears::math::abs (T t)
	Calculates the absolute value of a number. More...

template<typename Container , typename Value = typename Container::value_type>
void	gears::math::primes (Value limit, Container &cont)
	Generates primes using a modified Sieve of Eratosthenes. More...

template<typename Container , typename Integral >
void	gears::math::pythagorean_triples (Integral limit, Container &cont)
	Generates Pythagorean triples. More...

template<typename T , typename U , typename... Args>
constexpr std::common_type< T, U, Args...>::type	gears::math::min (T &&t, U &&u, Args &&...args)
	Calculates the minimum value of a list of numbers. More...

template<typename T , typename U , typename... Args>
constexpr std::common_type< T, U, Args...>::type	gears::math::max (T &&t, U &&u, Args &&...args)
	Calculates the maximum value of a list of numbers. More...

Detailed Description

This module provides an implementation of common mathematical algorithms and an infinite precision integer.

Example usage:

#include <gears/math.hpp>
#include <iostream>
namespace math = gears::math;
// needed to use _x user defined literal
using namespace gears::math::operators;
int main() {
    auto lhs = 9384721983748274812387232191827321_x;
    auto rhs = 2937189237182973865769137697362736_x;
    std::cout << (lhs * rhs) << '\n';
    std::cout << math::factorial(10) << '\n';
}

Output

27564704404619880556797005156529364384954680388538087951954412110256
3628800

Function Documentation

template<typename T >

constexpr T gears::math::abs ( T t )

Calculates the absolute value of a number. This uses the incredibly naive implementation and should only be used for its constexpr status, which the function in <cmath> lacks.

Parameters

t	The number to make positive.

Returns: The absolute value of a number.

Definition at line 191 of file algorithm.hpp.

template<typename T >

constexpr T gears::math::factorial ( const T & number )

Calculates the Nth factorial. The internal implementation uses the naive recursion way of doing it in order to preserve C++11 constexpr status.

Parameters

number Which factorial to calculate.

Returns: Nth factorial number.

Definition at line 69 of file algorithm.hpp.

template<typename T >

T gears::math::fibonacci ( T number )

inline

Calculates the nth fibonacci number. The internal implementation does not use the naive recursion.

Parameters

number Which fibonacci number to calculate.

Returns: Nth fibonacci number.

Definition at line 40 of file algorithm.hpp.

template<typename T >

constexpr T gears::math::gcd	(	const T &	x,
		const T &	y
	)

Calculates the greatest common divisor between two numbers. Uses Euclid's algorithm to compute it.

Parameters

x	Left hand side.
y	Right hand side.

Returns: The greatest common divisor between the numbers.

Definition at line 84 of file algorithm.hpp.

template<typename T >

bool gears::math::is_prime ( const T & number )

inlinenoexcept

Checks if a number is prime using the AKS primality test. This function is pretty slow for numbers that are relatively large.

Parameters

number Number to test for primality.

Returns: true is number is prime, false otherwise.

Definition at line 147 of file algorithm.hpp.

template<typename T , typename U , typename... Args>

constexpr std::common_type<T, U, Args...>::type gears::math::max	(	T &&	t,
		U &&	u,
		Args &&...	args
	)

Calculates the maximum value of a list of numbers. It is recommended to not mix different types when using this function as it will promote types and make it unsafe.

Parameters

t	First type to compare against.
u	Second type to compare against.
args	Other types to compare against.

Returns: The maximum value of the list of numbers.

Definition at line 248 of file algorithm.hpp.

template<typename T , typename U , typename... Args>

constexpr std::common_type<T, U, Args...>::type gears::math::min	(	T &&	t,
		U &&	u,
		Args &&...	args
	)

Calculates the minimum value of a list of numbers. It is recommended to not mix different types when using this function as it will promote types and make it unsafe.

Parameters

t	First type to compare against.
u	Second type to compare against.
args	Other types to compare against.

Returns: The minimum value of the list of numbers.

Definition at line 219 of file algorithm.hpp.

template<typename T >

T gears::math::mod_pow	(	T	base,
		T	exponent,
		const T &	modulus
	)

inline

Calculates the modular exponentiation. That is, it computes essentially (base ** exponent) % modulus where ** denotes exponentiation. All numbers provided must be positive.

Parameters

base	The base number of the formula.
exponent	The exponent number of the formula.
modulus	The modulo number of the formula.

Returns: (base ** exponent) % modulus.

Definition at line 102 of file algorithm.hpp.

template<typename Container , typename Value = typename Container::value_type>

void gears::math::primes	(	Value	limit,
		Container &	cont
	)

inline

Generates primes using a modified Sieve of Eratosthenes. The function will generate primes up to the limit provided. e.g. if limit is 100, then the last prime generated would be 97. The container must have an integral value_type for best results. Currently this function only works on containers that provide the push_back function. This might be changed in the future. The first two primes (2 and 3) are always provided regardless of the limit given.

Parameters

limit	The upper limit of primes to generate.
cont	The container to insert the primes to.

Definition at line 47 of file generator.hpp.

template<typename Container , typename Integral >

void gears::math::pythagorean_triples	(	Integral	limit,
		Container &	cont
	)

inline

Generates Pythagorean triples and puts the results into a container provided. The results are added to the container as if calling:

cont.emplace_back(x, y, z)

Parameters

limit	The upper limit of Pythagorean triples to generate.
cont	The container to emplace the Pythagorean triples.

Definition at line 92 of file generator.hpp.

template<typename T >

T gears::math::sum_of_divisors ( const T & number )

inlinenoexcept

Calculates the sum of divisors of a given integer. For example, the divisors for the number 12 are 1, 2, 3, 4, 6, and 12. The sum of these numbers is 28. So sum_of_divisors(12) would return 28.

Parameters

number The number to take the sum of divisors for.

Returns: The sum of the number's divisors.

Definition at line 128 of file algorithm.hpp.

Modules

Classes

Functions

Detailed Description

Function Documentation