[rand.eng.sub] (original) (raw)

29 Numerics library [numerics]

29.5 Random number generation [rand]

29.5.4 Random number engine class templates [rand.eng]

29.5.4.4 Class template subtract_with_carry_engine [rand.eng.sub]

A subtract_with_carry_engine random number engine produces unsigned integer random numbers.

The state xof a subtract_with_carry_engine object xis 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 xadditionally consists of an integer c(known as the carry) whose value is either 0 or 1.

The state transition is performed as follows:

• Set to .
  Set c to 1 if , otherwise set c to 0.

[Note 1:

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.

namespace std { template<class UIntType, size_t w, size_t s, size_t r> class subtract_with_carry_engine { public: using result_type = UIntType;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 uint_least32_t default_seed = 19780503u; subtract_with_carry_engine() : subtract_with_carry_engine(0u) {} explicit subtract_with_carry_engine(result_type value);template<class Sseq> explicit subtract_with_carry_engine(Sseq& q);void seed(result_type value = 0u);template<class Sseq> void seed(Sseq& q);friend bool operator==(const subtract_with_carry_engine& x,const subtract_with_carry_engine& y); result_type operator()();void discard(unsigned long long z);template<class charT, class traits> friend basic_ostream<charT, traits>& operator<<(basic_ostream<charT, traits>& os, const subtract_with_carry_engine& x);template<class charT, class traits> friend basic_istream<charT, traits>& operator>>(basic_istream<charT, traits>& is, subtract_with_carry_engine& x);};}

The following relations shall hold:0u < s,s < r,0 < w, andw <= 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: 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<uint_least32_t, 40014u, 0u, 2147483563u> e( value == 0u ? default_seed : static_cast<uint_least32_t>(value % 2147483563u));

Then, to set each , obtain new values from successive invocations of e.

Set to .

Complexity: Exactly invocations of e.

template<class Sseq> explicit subtract_with_carry_engine(Sseq& q);

Effects: 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.