26 Numerics library [numerics]

26.5 Random number generation [rand]

26.5.3 Random number engine class templates [rand.eng]

26.5.3.1 Class template linear_congruential_engine [rand.eng.lcong]

1

A linear_congruential_engine random number engine produces unsigned integer random numbers. The state xi of a linear_congruential_engine object x is of size 1 and consists of a single integer. The transition algorithm is a modular linear function of the form TA(xi) = (a · xi + c) mod m; the generation algorithm is GA(xi) = xi+1 .

template<class UIntType, UIntType a, UIntType c, UIntType m>
 class linear_congruential_engine{
public:
 // types
 typedef UIntType result_type;

 // engine characteristics
 static constexpr result_type multiplier = a;
 static constexpr result_type increment = c;
 static constexpr result_type modulus = m;
 static constexpr result_type min() { return c == 0u ? 1u: 0u; }
 static constexpr result_type max() { return m - 1u; }
 static constexpr result_type default_seed = 1u;

 // constructors and seeding functions
 explicit linear_congruential_engine(result_type s = default_seed);
 template<class Sseq> explicit linear_congruential_engine(Sseq& q);
 void seed(result_type s = default_seed);
 template<class Sseq> void seed(Sseq& q);

 // generating functions
 result_type operator()();
 void discard(unsigned long long z);
};
2

If the template parameter m is 0, the modulus m used throughout this section [rand.eng.lcong] is numeric_limits<result_type>::max() plus 1. [ Note: m need not be representable as a value of type result_type.  — end note ]

3

If the template parameter m is not 0, the following relations shall hold: a < m and c < m.

4

The textual representation consists of the value of xi.

explicit linear_congruential_engine(result_type s = default_seed);

5

Effects: Constructs a linear_congruential_engine object. If c mod m is 0 and s mod m is 0, sets the engine's state to 1, otherwise sets the engine's state to s mod m.

template<class Sseq> explicit linear_congruential_engine(Sseq& q);

6

Effects: Constructs a linear_congruential_engine object. With $ k = \left\lceil \frac{\log_2 m} {32} \right\rceil $ and a an array (or equivalent) of length k + 3, invokes q.generate(a+0, a+k+3) and then computes $ S = \left(\sum_{j=0}^{k-1}a_{j+3} \cdot 2^{32j} \right) \bmod m $. If c mod m is 0 and S is 0, sets the engine's state to 1, else sets the engine's state to S.