ntlib::mod_int< T, m > Class Template Reference

Class representing an element of a ring of integers modulo another positive integer. The modulus is provided at compile-time. More...

Public Member Functions
	mod_int () noexcept
	Default constructor. Initializes the value to zero.
	mod_int (T n) noexcept
	Construct a new element from a given value.
	operator T () const noexcept
	Returns the value.
mod_int &	operator++ () noexcept
	Prefix increment operator.
mod_int	operator++ (int) noexcept
	Postfix increment operator.
mod_int &	operator-- () noexcept
	Prefix decrement operator.
mod_int	operator-- (int) noexcept
	Postfix decrement operator.
mod_int &	operator+= (mod_int rhs) noexcept
	Compound plus operator for modular addition.
mod_int &	operator-= (mod_int rhs) noexcept
	Compound minus operator for modular subtraction.
mod_int &	operator*= (mod_int rhs) noexcept
	Compound times operator for modular multiplication.
mod_int	operator+ () const noexcept
	Unary plus operator. Does nothing.
mod_int	operator- () const noexcept
	Unary minus operator to negate value.
void	invert ()
	Inverts the value.

Friends
mod_int	operator+ (mod_int lhs, mod_int rhs) noexcept
	Plus operator for modular addition.
mod_int	operator- (mod_int lhs, mod_int rhs) noexcept
	Minus operator for modular subtraction.
mod_int	operator* (mod_int lhs, mod_int rhs) noexcept
	Times operator for modular multiplication.
bool	operator== (mod_int lhs, mod_int rhs) noexcept
	Equality comparison operator.

Detailed Description

template<Integer T, T m>
requires (m > 0)
class ntlib::mod_int< T, m >

Class representing an element of a ring of integers modulo another positive integer. The modulus is provided at compile-time.

Note

To avoid overflows, the type T must be able to hold

• \(2m\) for addition and subtraction,
• \(m^2\) for multiplication. This is ensured at compile-time. For this to work, T must provide std::numeric_limits<T>::max().

Template Parameters

T	An integer-like type.
m	The modulus.

Constructor & Destructor Documentation

mod_int()

template<Integer T, T m>

ntlib::mod_int< T, m >::mod_int ( T n )

inlineexplicitnoexcept

Construct a new element from a given value.

Parameters

n	The given value.

Member Function Documentation

invert()

template<Integer T, T m>

void ntlib::mod_int< T, m >::invert ( )

inline

Inverts the value.

Note

This requires that the current value is coprime to the modulus.

operator T()

template<Integer T, T m>

ntlib::mod_int< T, m >::operator T ( ) const

inlineexplicitnoexcept

Returns the value.

Returns

The value in the range \([0, m)\).

operator*=()

template<Integer T, T m>

mod_int & ntlib::mod_int< T, m >::operator*= ( mod_int< T, m > rhs )

inlinenoexcept

Compound times operator for modular multiplication.

Note

Contains a compile-time check to ensure that no overflow can occur.

Parameters

rhs	The second factor.

Returns

Reference to the result.

operator+()

template<Integer T, T m>

mod_int ntlib::mod_int< T, m >::operator+ ( ) const

inlinenoexcept

Unary plus operator. Does nothing.

Returns

The same instance as before.

operator++() [1/2]

template<Integer T, T m>

mod_int & ntlib::mod_int< T, m >::operator++ ( )

inlinenoexcept

Prefix increment operator.

Returns

Reference to the result (with new value).

operator++() [2/2]

template<Integer T, T m>

mod_int ntlib::mod_int< T, m >::operator++ ( int )

inlinenoexcept

Postfix increment operator.

Returns

The old value.

operator+=()

template<Integer T, T m>

mod_int & ntlib::mod_int< T, m >::operator+= ( mod_int< T, m > rhs )

inlinenoexcept

Compound plus operator for modular addition.

Note

Contains a compile-time check to ensure that no overflow can occur.

Parameters

rhs	The second summand.

Returns

Reference to the result.

operator-()

template<Integer T, T m>

mod_int ntlib::mod_int< T, m >::operator- ( ) const

inlinenoexcept

Unary minus operator to negate value.

Returns

The negated instance.

operator--() [1/2]

template<Integer T, T m>

mod_int & ntlib::mod_int< T, m >::operator-- ( )

inlinenoexcept

Prefix decrement operator.

Returns

Reference to the result (with the new value).

operator--() [2/2]

template<Integer T, T m>

mod_int ntlib::mod_int< T, m >::operator-- ( int )

inlinenoexcept

Postfix decrement operator.

Returns

The old value.

operator-=()

template<Integer T, T m>

mod_int & ntlib::mod_int< T, m >::operator-= ( mod_int< T, m > rhs )

inlinenoexcept

Compound minus operator for modular subtraction.

Note

Contains a compile-time check to ensure that no overflow can occur.

Parameters

rhs	The subtrahend.

Returns

Reference to the result.

Friends And Related Symbol Documentation

operator*

template<Integer T, T m>

mod_int operator* ( mod_int< T, m > lhs, mod_int< T, m > rhs )

friend

Times operator for modular multiplication.

Parameters

lhs	The first factor.
rhs	The second factor.

Returns

The product of lhs and rhs.

operator+

template<Integer T, T m>

mod_int operator+ ( mod_int< T, m > lhs, mod_int< T, m > rhs )

friend

Plus operator for modular addition.

Parameters

lhs	The first summand.
rhs	The second summand.

Returns

The sum of lhs and rhs.

operator-

template<Integer T, T m>

mod_int operator- ( mod_int< T, m > lhs, mod_int< T, m > rhs )

friend

Minus operator for modular subtraction.

Parameters

lhs	The minuend.
rhs	The subtrahend.

Returns

The difference of lhs and rhs.

operator==

template<Integer T, T m>

bool operator== ( mod_int< T, m > lhs, mod_int< T, m > rhs )

friend

Equality comparison operator.

Parameters

lhs	The first instance.
rhs	The second instance.

Returns

Whether lhs and rhs are equal.

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The documentation for this class was generated from the following file:

• modules/types/mod_int.cpp