[rand.eng] (original) (raw)
26 Numerics library [numerics]
26.6 Random number generation [rand]
26.6.3 Random number engine class templates [rand.eng]
Each type instantiated from a class template specified in this subclause [rand.eng]meets the requirements of a random number engine type.
Except where specified otherwise, the complexity of each function specified in this subclause [rand.eng]is constant.
Except where specified otherwise, no function described in this subclause [rand.eng]throws an exception.
Every function described in this subclause [rand.eng]that has a function parameter q of type Sseq&for a template type parameter named Sseqthat is different from type seed_seqthrows what and when the invocation of q.generate throws.
Descriptions are provided in this subclause [rand.eng]only for engine operations that are not described in [rand.req.eng]or for operations where there is additional semantic information.
In particular, declarations for copy constructors, for copy assignment operators, for streaming operators, and for equality and inequality operators are not shown in the synopses.
Each template specified in this subclause [rand.eng]requires one or more relationships, involving the value(s) of its non-type template parameter(s), to hold.
A program instantiating any of these templates is ill-formed if any such required relationship fails to hold.
For every random number engine and for every random number engine adaptor Xdefined in this subclause ([rand.eng]) and in subclause [rand.adapt]:
- if the constructor
template explicit X(Sseq& q);
is called with a type Sseq that does not qualify as a seed sequence, then this constructor shall not participate in overload resolution; - if the member function
template void seed(Sseq& q);
is called with a type Sseq that does not qualify as a seed sequence, then this function shall not participate in overload resolution.
The extent to which an implementation determines that a type cannot be a seed sequence is unspecified, except that as a minimum a type shall not qualify as a seed sequence if it is implicitly convertible to X::result_type.
26.6.3.1 Class template linear_congruential_engine [rand.eng.lcong]
A linear_congruential_engine random number engine produces unsigned integer random numbers.
The state xof a linear_congruential_engine object xis of size 1and consists of a single integer.
The transition algorithmis a modular linear function of the form; the generation algorithmis .
template<class UIntType, UIntType a, UIntType c, UIntType m> class linear_congruential_engine { public:
using result_type = UIntType;
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;
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);
result_type operator()();
void discard(unsigned long long z);};
If the template parameterm is 0, the modulus mused throughout this subclause [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 parameterm is not 0, the following relations shall hold:a < mandc < m.
The textual representationconsists of the value of x.
explicit linear_congruential_engine(result_type s);
Effects: If is 0 and is 0, sets the engine's state to 1, otherwise sets the engine's state to .
template<class Sseq> explicit linear_congruential_engine(Sseq& q);
Effects: With and a an array (or equivalent) of length , invokes q.generate(, ) and then computes.
If is 0 and S is 0, sets the engine's state to 1, else sets the engine's state to S.
26.6.3.2 Class template mersenne_twister_engine [rand.eng.mers]
A mersenne_twister_engine random number engine243produces unsigned integer random numbers in the closed interval .
Thestatexof a mersenne_twister_engine object xis of size nand consists of a sequence Xof n values of the type delivered by x; all subscripts applied to X are to be taken modulo n.
The transition algorithmemploys a twisted generalized feedback shift register defined by shift values n and m, a twist value r, and a conditional xor-mask a.
To improve the uniformity of the result, the bits of the raw shift register are additionally tempered(i.e., scrambled) according to a bit-scrambling matrix defined by values u, d, s, b, t, c, and ℓ.
The state transition is performed as follows:
- Concatenate the upper bits of with the lower r bits of to obtain an unsigned integer value Y.
- With , set to.
The sequence X is initialized with the help of an initialization multiplier f.
The generation algorithm determines the unsigned integer values as follows, then delivers as its result:
- Let .
- Let .
- Let .
- Let .
template<class UIntType, size_t w, size_t n, size_t m, size_t r, UIntType a, size_t u, UIntType d, size_t s, UIntType b, size_t t, UIntType c, size_t l, UIntType f> class mersenne_twister_engine { public:
using result_type = UIntType;
static constexpr size_t word_size = w;
static constexpr size_t state_size = n;
static constexpr size_t shift_size = m;
static constexpr size_t mask_bits = r;
static constexpr UIntType xor_mask = a;
static constexpr size_t tempering_u = u;
static constexpr UIntType tempering_d = d;
static constexpr size_t tempering_s = s;
static constexpr UIntType tempering_b = b;
static constexpr size_t tempering_t = t;
static constexpr UIntType tempering_c = c;
static constexpr size_t tempering_l = l;
static constexpr UIntType initialization_multiplier = f;
static constexpr result_type min() { return 0; }
static constexpr result_type max() { return ; }
static constexpr result_type default_seed = 5489u;
mersenne_twister_engine() : mersenne_twister_engine(default_seed) {}
explicit mersenne_twister_engine(result_type value);
template<class Sseq> explicit mersenne_twister_engine(Sseq& q);
void seed(result_type value = default_seed);
template<class Sseq> void seed(Sseq& q);
result_type operator()();
void discard(unsigned long long z);};
The following relations shall hold:0 < m,m <= n,2u < w,r <= w,u <= w,s <= w,t <= w,l <= w,w <= numeric_limits<UIntType>::digits,a <= (1u<<w) - 1u,b <= (1u<<w) - 1u,c <= (1u<<w) - 1u,d <= (1u<<w) - 1u, andf <= (1u<<w) - 1u.
The textual representationof xconsists of the values of , in that order.
explicit mersenne_twister_engine(result_type value);
Effects:Sets to .
Then, iteratively for , sets to
template<class Sseq> explicit mersenne_twister_engine(Sseq& q);
Effects: With and a an array (or equivalent) of length , invokes q.generate(, ) and then, iteratively for , sets to .
Finally, if the most significant bits of are zero, and if each of the other resulting is 0, changes to .
26.6.3.3 Class template subtract_with_carry_engine [rand.eng.sub]
A subtract_with_carry_engine random number engine produces unsigned integer random numbers.
The state 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 transitionis 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 algorithmis 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:
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 result_type default_seed = 19780503u;
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);
result_type operator()();
void discard(unsigned long long z);};
The following relations shall hold:0u < s,s < r,0 < w, andw <= numeric_limits<UIntType>::digits.
The textual representationconsists 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<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: 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.