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Showing content from https://en.cppreference.com/w/cpp/language/../numeric/random/linear_congruential_engine.html below:

std::linear_congruential_engine - cppreference.com

std::linear_congruential_engine template< class UIntType, UIntType a, UIntType c, UIntType m > class linear_congruential_engine; (since C++11)

linear_congruential_engine is a random number engine based on Linear congruential generator (LCG).

[edit] Template parameters UIntType - The result type generated by the generator. The effect is undefined if this is not one of unsigned short, unsigned int, unsigned long, or unsigned long long. a - the multiplier term c - the increment term m - the modulus term

When m is not zero, if a >= m or c >= m is true, the program is ill-formed.

[edit] Generator properties

The size of the states of linear_congruential_engine is 1, each of them consists of a single integer.

The actual modulus \(\scriptsize m_0\)m0 is defined as follows:

If m is not zero, \(\scriptsize m_0\)m0 is m.
If m is zero, \(\scriptsize m_0\)m0 is the value of std::numeric_limits<result_type>::max() plus 1 (which means \(\scriptsize m_0\)m0 need not be representable as result_type).

The transition algorithm of linear_congruential_engine is \(\scriptsize TA(x_i) = (a \cdot x_i + c)\mod m_0\)TA(xi) = (aÂ·xi+c) mod m0.

The generation algorithm of linear_congruential_engine is \(\scriptsize GA(x_i) = (a \cdot x_i + c)\mod m_0\)GA(xi) = (aÂ·xi+c) mod m0.

The pseudo-random number generated with the current state is also the successor state.

[edit] Predefined specializations

The following specializations define the random number engine with two commonly used parameter sets:

Type Definition minstd_rand0 (C++11) std::linear_congruential_engine<std::uint_fast32_t,
16807, 0, 2147483647>

Discovered in 1969 by Lewis, Goodman and Miller, adopted as "Minimal standard" in 1988 by Park and Miller[edit]

minstd_rand (C++11)

std::linear_congruential_engine<std::uint_fast32_t,
48271, 0, 2147483647>
Newer "Minimum standard", recommended by Park, Miller, and Stockmeyer in 1993[edit]

[edit] Nested types Type Definition result_type UIntType [edit] Data members

constexpr UIntType multiplier

[static]

a
(public static member constant)

constexpr UIntType increment

[static]

c
(public static member constant)

constexpr UIntType modulus

[static]

m
(public static member constant)

constexpr UIntType default_seed

[static]

1u
(public static member constant) [edit] Member functions Construction and Seeding constructs the engine
(public member function) [edit] sets the current state of the engine
(public member function) [edit] Generation advances the engine's state and returns the generated value
(public member function) [edit] advances the engine's state by a specified amount
(public member function) [edit] Characteristics gets the smallest possible value in the output range
(public static member function) [edit] gets the largest possible value in the output range
(public static member function) [edit] [edit] Non-member functions [edit] Example

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