# 25 Numerics library [numerics]

## 25.6 Random number generation [rand]

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

#### 25.6.3.3 Class template subtract_­with_­carry_­engine[rand.eng.sub]

A subtract_­with_­carry_­engine random number engine produces unsigned integer random numbers.
The state x of a subtract_­with_­carry_­engine object x is of size , and consists of a sequence X of r integer values ; all subscripts applied to X are to be taken modulo r.
The state x additionally consists of an integer c (known as the carry) whose value is either 0 or 1.
The state transition is performed as follows:
• Let .
• Set to .
Set c to 1 if , otherwise set c to 0.
[Note
:
This algorithm corresponds to a modular linear function of the form , where b is of the form and .
end note
]
The generation algorithm is given by , where y is the value produced as a result of advancing the engine's state as described above.
template<class UIntType, size_t w, size_t s, size_t r>
class subtract_with_carry_engine {
public:
// types
using result_type = UIntType;

// engine characteristics
static constexpr size_t word_size = w;
static constexpr size_t short_lag = s;
static constexpr size_t long_lag = r;
static constexpr result_type min() { return 0; }
static constexpr result_type max() { return m−1; }
static constexpr result_type default_seed = 19780503u;

// constructors and seeding functions
subtract_with_carry_engine() : subtract_with_carry_engine(default_seed) {}
explicit subtract_with_carry_engine(result_type value);
template<class Sseq> explicit subtract_with_carry_engine(Sseq& q);
void seed(result_type value = default_seed);
template<class Sseq> void seed(Sseq& q);

// generating functions
result_type operator()();
};

The following relations shall hold: 0u < s, s < r, 0 < w, and w <= numeric_­limits<UIntType>::digits.
The textual representation consists of the values of , in that order, followed by c.
explicit subtract_with_carry_engine(result_type value); 
Effects: Constructs a subtract_­with_­carry_­engine object.
Sets the values of , in that order, as specified below.
If is then 0, sets c to 1; otherwise sets c to 0.
To set the values , first construct e, a linear_­congruential_­engine object, as if by the following definition:
linear_congruential_engine<result_type,
40014u,0u,2147483563u> e(value == 0u ? default_seed : value);

Then, to set each , obtain new values from successive invocations of e taken modulo .
Set to .
Complexity: Exactly invocations of e.
template<class Sseq> explicit subtract_with_carry_engine(Sseq& q); 
Effects: Constructs a subtract_­with_­carry_­engine object.
With and a an array (or equivalent) of length , invokes q.generate(, ) and then, iteratively for , sets to .
If is then 0, sets c to 1; otherwise sets c to 0.