std::mersenne_twister_engine(3)

NAME
std::mersenne_twister_engine - std::mersenne_twister_engine

Synopsis
   Defined in header <random>
   template<
   class UIntType,
   std::size_t w, std::size_t n, std::size_t m, std::size_t r,
   UIntType a, std::size_t u, UIntType d, std::size_t s, (since C++11)
   UIntType b, std::size_t t,
   UIntType c, std::size_t l, UIntType f
   > class mersenne_twister_engine;
   mersenne_twister_engine is a random number engine based on Mersenne Twister
   algorithm. It produces high quality unsigned integer random numbers of type UIntType
   on the interval \(\scriptsize {[0,2^w)}\)[0, 2w
   ).
   The following type aliases define the random number engine with two commonly used
   parameter sets:
   Defined in header <random>
   Type Definition
                     std::mersenne_twister_engine<std::uint_fast32_t, 32, 624, 397, 31,
                     0x9908b0df, 11,
   mt19937(C++11) 0xffffffff, 7,
                     0x9d2c5680, 15,
                     0xefc60000, 18, 1812433253>
                     32-bit Mersenne Twister by Matsumoto and Nishimura, 1998
                     std::mersenne_twister_engine<std::uint_fast64_t, 64, 312, 156, 31,
                     0xb5026f5aa96619e9, 29,
   mt19937_64(C++11) 0x5555555555555555, 17,
                     0x71d67fffeda60000, 37,
                     0xfff7eee000000000, 43, 6364136223846793005>
                     64-bit Mersenne Twister by Matsumoto and Nishimura, 2000

Template parameters
              The result type generated by the generator. The effect is undefined if
   UIntType - this is not one of unsigned short, unsigned int, unsigned long, or
              unsigned long long.
   w - the power of two that determines the range of values generated by the
              engine
   n - the degree of recurrence
   m - the middle word, an offset used in the recurrence relation defining the
              series x, 1 ≤ m < n
   r - the number of bits of the lower bit-mask, 0 ≤ r ≤ w - 1, also known
              as the twist value
   a - the conditional xor-mask, i.e. the coefficients of the rational normal
              form twist matrix
   u - 1st component of the bit-scrambling (tempering) matrix
   d - 2nd component of the bit-scrambling (tempering) matrix
   s - 3rd component of the bit-scrambling (tempering) matrix
   b - 4th component of the bit-scrambling (tempering) matrix
   t - 5th component of the bit-scrambling (tempering) matrix
   c - 6th component of the bit-scrambling (tempering) matrix
   l - 7th component of the bit-scrambling (tempering) matrix
   f - the initialization multiplier
   The following relations shall hold:
   0 < m <= n,
   2 < w,
   r <= w,
   u <= w,
   s <= w,
   t <= w,
   l <= w,
   w <= std::numeric_limits<UIntType>::digits,
   a <= 2^w-1,
   b <= 2^w-1,
   c <= 2^w-1,
   d <= 2^w-1, and
   f <= 2^w-1 (a^b denotes a to the power of b)

Member types
   Member type Definition
   result_type(C++11) The integral type, UIntType, generated by the engine. Results are
                      undefined if this is not an unsigned integral type.

Member functions

Construction and Seeding
   constructor constructs the engine
   (C++11) (public member function)
   seed sets the current state of the engine
   (C++11) (public member function)

Generation
   operator() advances the engine's state and returns the generated value
   (C++11) (public member function)
   discard advances the engine's state by a specified amount
   (C++11) (public member function)

Characteristics
   min gets the smallest possible value in the output range
   [static] (C++11) (public static member function)
   max gets the largest possible value in the output range
   [static] (C++11) (public static member function)

Non-member functions
   operator== compares the internal states of two pseudo-random number
   operator!= engines
   (C++11) (function)
   (C++11)(removed in C++20)
   operator<< performs stream input and output on pseudo-random number
   operator>> engine
   (C++11) (function template)

Member constants
   constexpr size_t word_size the template parameter w, determines the range of
   [static] (C++11) values generated by the engine.
                        (public static member constant)
   constexpr size_t state_size the template parameter n. The engine state is n
   [static] (C++11) values of UIntType
                        (public static member constant)
   constexpr size_t shift_size the template parameter m
   [static] (C++11) (public static member constant)
   constexpr size_t mask_bits the template parameter r, also known as the twist
   [static] (C++11) value.
                        (public static member constant)
   constexpr UIntType xor_mask the template parameter a, the conditional xor-mask.
   [static] (C++11) (public static member constant)
   constexpr size_t tempering_u the template parameter u, first component of the
   [static] (C++11) bit-scrambling (tempering) matrix
                        (public static member constant)
   constexpr UIntType tempering_d the template parameter d, second component of the
   [static] (C++11) bit-scrambling (tempering) matrix
                        (public static member constant)
   constexpr size_t tempering_s the template parameter s, third component of the
   [static] (C++11) bit-scrambling (tempering) matrix
                        (public static member constant)
   constexpr UIntType tempering_b the template parameter b, fourth component of the
   [static] (C++11) bit-scrambling (tempering) matrix
                        (public static member constant)
   constexpr size_t tempering_t the template parameter t, fifth component of the
   [static] (C++11) bit-scrambling (tempering) matrix
                        (public static member constant)
   constexpr UIntType tempering_c the template parameter c, sixth component of the
   [static] (C++11) bit-scrambling (tempering) matrix
                        (public static member constant)
   constexpr size_t tempering_l the template parameter l, seventh component of the
   [static] (C++11) bit-scrambling (tempering) matrix
                        (public static member constant)
   constexpr UIntType the template parameter f
   initialization_multiplier (public static member constant)
   [static] (C++11)
   constexpr UIntType default_seed the constant value 5489u
   [static] (C++11) (public static member constant)

Notes
   The Nth consecutive invocation of a default-constructed engine is required to
   produce the following value:
                      N The random engine type The value to produce
                    10000 std::mt19937 4123659995
                    10000 std::mt19937_64 9981545732273789042 // Run this code
 #include <random>
 #include <cassert>
 int main()
 {
     std::mt19937 gen32;
     std::mt19937_64 gen64;
     for (auto n{1}; n != 10'000; gen32(), gen64(), ++n);
     assert(gen32() == 4'123'659'995 and
            gen64() == 9'981'545'732'273'789'042ULL);
 }