[rand.eng.lcong]

# 29 Numerics library [[numerics]](./#numerics)

## 29.5 Random number generation [[rand]](rand#eng.lcong)

### 29.5.4 Random number engine class templates [[rand.eng]](rand.eng#lcong)

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

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L2670)

A linear_congruential_engine random number engine
produces unsigned integer random numbers[.](#1.sentence-1)

The state xi of a linear_congruential_engine object x is of size 1 and consists of a single integer[.](#1.sentence-2)

The transition algorithm
is a modular linear function of the formTA(xi)=(aâ‹xi+c)modm;
the generation algorithm
is GA(xi)=xi+1[.](#1.sentence-3)

[🔗](#lib:linear_congruential_engine_)

namespace std {template<class UIntType, UIntType a, UIntType c, UIntType m>class linear_congruential_engine {public:// typesusing result_type = UIntType; // engine characteristicsstatic 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 operatorsfriend 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 extractorstemplate<class charT, class traits>friend basic_ostream<charT, traits>&operator<<(basic_ostream<charT, traits>& os, // hostedconst linear_congruential_engine& x); template<class charT, class traits>friend basic_istream<charT, traits>&operator>>(basic_istream<charT, traits>& is, // hosted linear_congruential_engine& x); };}

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L2729)

If the template parameterm is 0,
the modulus m used throughout [rand.eng.lcong]
is numeric_limits<result_type>​::​max() plus 1[.](#2.sentence-1)

[*Note [1](#note-1)*:

m need not be representable
 as a value of type result_type[.](#2.sentence-2)

— *end note*]

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L2740)

If the template parameterm is not 0,
the following relations shall hold: a < m and c < m[.](#3.sentence-1)

[4](#4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L2748)

The textual representation
consists of
the value of xi[.](#4.sentence-1)

[🔗](#lib:linear_congruential_engine,constructor)

`explicit linear_congruential_engine(result_type s);
`

[5](#5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L2759)

*Effects*: If cmodm is 0 and smodm is 0,
 sets the engine's state to 1,
 otherwise sets the engine's state to smodm[.](#5.sentence-1)

[🔗](#lib:linear_congruential_engine,constructor_)

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

[6](#6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L2772)

*Effects*: 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=(∑k−1j=0aj+3â‹232j)modm[.](#6.sentence-1)

If cmodm is 0 and S is 0,
 sets the engine's state to 1,
 else sets the engine's state
 to S[.](#6.sentence-2)