# 28 Numerics library [numerics]

## 28.5 Random number generation [rand]

### 28.5.4 Random number engine class templates [rand.eng]

#### 28.5.4.2 Class template linear_congruential_engine[rand.eng.lcong]

A linear_congruential_engine random number engine produces unsigned integer random numbers.
The state x 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 ; the generation algorithm is .
namespace std { template<class UIntType, UIntType a, UIntType c, UIntType m> class linear_congruential_engine { public: // types using result_type = UIntType; // 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 linear_congruential_engine() : linear_congruential_engine(default_seed) {} explicit linear_congruential_engine(result_type s); template<class Sseq> explicit linear_congruential_engine(Sseq& q); void seed(result_type s = default_seed); template<class Sseq> void seed(Sseq& q); // equality operators friend bool operator==(const linear_congruential_engine& x, const linear_congruential_engine& y); // generating functions result_type operator()(); void discard(unsigned long long z); // inserters and extractors template<class charT, class traits> friend basic_ostream<charT, traits>& operator<<(basic_ostream<charT, traits>& os, const linear_congruential_engine& x); template<class charT, class traits> friend basic_istream<charT, traits>& operator>>(basic_istream<charT, traits>& is, linear_congruential_engine& x); }; }
If the template parameter m is 0, the modulus m used throughout [rand.eng.lcong] is numeric_limits<result_type>​::​max() plus 1.
[Note 1:
m need not be representable as a value of type result_type.
— end note]
If the template parameter m is not 0, the following relations shall hold: a < m and c < m.
The textual representation consists of the value of x.
```explicit linear_congruential_engine(result_type s); ```
Effects: If is 0 and is 0, sets the engine's state to 1, otherwise sets the engine's state to .
```template<class Sseq> explicit linear_congruential_engine(Sseq& q); ```
Effects: With and a an array (or equivalent) of length , invokes q.generate(, ) and then computes .
If is 0 and S is 0, sets the engine's state to 1, else sets the engine's state to S.