# 29 Numerics library [numerics]

## 29.6 Random number generation [rand]

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

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

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)=(axi+c)modm; the generation algorithm is GA(xi)=xi+1.

```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
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()();
};```

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]

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 xi.

```explicit linear_congruential_engine(result_type s = default_seed); ```

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

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

Effects: Constructs a linear_­congruential_­engine object. With k=log2m32 and a an array (or equivalent) of length k+3, invokes q.generate(a+0, a+k+3) and then computes S=(k1j=0aj+3232j)modm. If cmodm is 0 and S is 0, sets the engine's state to 1, else sets the engine's state to S.