29 Numerics library [numerics]

29.6 Random number generation [rand]

29.6.3 Random number engine class templates [rand.eng]

29.6.3.3 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:

  1. a)Let .

  2. b)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 ; }
    static constexpr result_type default_seed = 19780503u;

    // constructors and seeding functions
    explicit subtract_with_carry_engine(result_type value = default_seed);
    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()();
    void discard(unsigned long long z);
  };

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 = default_seed);

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.