std::seed_seq::generate(3)

NAME
std::seed_seq::generate - std::seed_seq::generate

Synopsis
   template< class RandomIt > (since C++11)
   void generate( RandomIt begin, RandomIt end );
   Fills the range [begin, end) with unsigned integer values i, 0 ≤ i < 232
   , based on the data originally provided in the constructor of this seed_seq. The
   produced values are distributed over the entire 32-bit range even if the initial
   values were strongly biased.
   The following algorithm is used (adapted from the initialization sequence of the
   Mersenne Twister generator by Makoto Matsumoto and Takuji Nishimura, incorporating
   the improvements made by Mutsuo Saito in 2007)
     * If begin == end, do nothing. Otherwise,
     * First, set each element of the output range to the value 0x8b8b8b8b
     * Transform the elements of the output range according to the following algorithm:
   For k = 0,..., m-1
   where m=max(s+1, n)
   and n=end-begin
   and s=v.size()
   and v is the private container holding the values originally provided by the
   constructor of this seed_seq object,
    1. begin[k+p] += r1
    2. begin[k+q] += r2
    3. begin[k] = r2,
   where p=(n-t)/2
   and q=p+t
   and t=(n >= 623) ? 11 : (n >= 68) ? 7 : (n >= 39) ? 5 : (n >= 7) ? 3 : (n - 1) / 2
   and r1=1664525 * T(begin[k]^begin[k+p]^begin[k−1])
   and T(x) = x ^ (x >> 27)
   and r2=r1+s if k==0, r2=r1 + k%n + v[k-1] if 0<k<=s, r2=r1 + k%n if k>s.
   For k = m,..., m+n-1,
    1. begin[k+p] ^= r3
    2. begin[k+q] ^= r4
    3. begin[k]=r4
   where r3 = 1566083941 * T(begin[k]+begin[k+p]+begin[k-1])
   and r4=r3 - k%n
   where all calculations are performed modulo 232
   and where the indexing of the output range (begin[x]) is taken modulo n.

Parameters
                mutable random-access iterators whose
   begin, end - std::iterator_traits<>::value_type is an unsigned integer type suitable
                for storing 32-bit values

Type requirements
   -
   RandomIt must meet the requirements of LegacyRandomAccessIterator.

Return value
   none, the results are written to the [begin, end) range.

Exceptions
   Only throws if the operations on begin and end throw.

Example
// Run this code
 #include <algorithm>
 #include <cassert>
 #include <cstdint>
 #include <iostream>
 #include <random>
 // Prototyping the main part of std::seed_seq...
 struct seed_seq {
     std::vector<std::uint32_t> v;
     seed_seq(std::initializer_list<std::uint32_t> const il) : v{il} {}
     template <typename RandomIt>
     void generate(RandomIt first, RandomIt last) {
         if (first == last)
             return;
         //
         // Assuming v = {1,2,3,4,5} and distance(first, last) == 10.
         //
         // Step 1: fill with 0x8b8b8b8b
         // seeds = {2341178251, 2341178251, 2341178251, 2341178251, 2341178251,
         // 2341178251, 2341178251, 2341178251, 2341178251, 2341178251 }
         //
         std::fill(first, last, 0x8b8b8b8b);
         //
         // Step 2:
         // n = 10, s = 5, t = 3, p = 3, q = 6, m = 10
         //
         const std::uint32_t n = last - first;
         const std::uint32_t s = v.size();
         const std::uint32_t t = (n < 7) ? (n - 1) / 2
                        : (n < 39) ? 3
                        : (n < 68) ? 5
                        : (n < 623) ? 7
                        : 11;
         const std::uint32_t p = (n - t) / 2;
         const std::uint32_t q = p + t;
         const std::uint32_t m = std::max(s + 1, n);
         //
         // First iteration, k = 0; r1 = 1371501266, r2 = 1371501271
         //
         // seeds = {1371501271, 2341178251, 2341178251, 3712679517, 2341178251,
         // 2341178251, 3712679522, 2341178251, 2341178251, 2341178251 }
         //
         // Iterations from k = 1 to k = 5 (r2 = r1 + k%n + v[k-1])
         //
         // r1 = 2786190137, 3204727651, 4173325571, 1979226628, 401983366
         // r2 = 2786190139, 3204727655, 4173325577, 1979226636, 401983376
         //
         // seeds = {3350727907, 3188173515, 3204727655, 4173325577, 1979226636,
         // 401983376, 3591037797, 2811627722, 1652921976, 2219536532 }
         //
         // Iterations from k = 6 to k = 9 (r2 = r1 + k%n)
         //
         // r1 = 2718637909, 1378394210, 2297813071, 1608643617
         // r2 = 2718637915, 1378394217, 2297813079, 1608643626
         //
         // seeds = { 434154821, 1191019290, 3237041891, 1256752498, 4277039715,
         // 2010627002, 2718637915, 1378394217, 2297813079, 1608643626 }
         //
         auto begin_mod = [first, n](std::uint32_t u) -> decltype(*first)& {
             return first[u % n]; // i.e. begin[x] is taken modulo n
         };
         auto T = [](std::uint32_t x) { return x ^ (x >> 27); };
         for (std::uint32_t k = 0, r1, r2; k < m; ++k) {
             r1 = 1664525 * T(begin_mod(k) ^ begin_mod(k + p) ^ begin_mod(k - 1));
             r2 = (k == 0) ? r1 + s
                : (k <= s) ? r1 + k % n + v[k - 1]
                : r1 + k % n;
             begin_mod(k + p) += r1;
             begin_mod(k + q) += r2;
             begin_mod(k) = r2;
         }
         //
         // Step 3
         // iterations from k = 10 to k = 19, using ^= to modify the output
         //
         // r1 = 1615303485, 3210438310, 893477041, 2884072672, 1918321961,
         // r2 = 1615303485, 3210438309, 893477039, 2884072669, 1918321957
         //
         // seeds = { 303093272, 3210438309, 893477039, 2884072669, 1918321957,
         // 1117182731, 1772877958, 2669970405, 3182737656, 4094066935 }
         //
         // r1 = 423054846, 46783064, 3904109085, 1534123446, 1495905687
         // r2 = 423054841, 46783058, 3904109078, 1534123438, 1495905678
         //
         // seeds = { 4204997637, 4246533866, 1856049002, 1129615051, 690460811,
         // 1075771511, 46783058, 3904109078, 1534123438, 1495905678 }
         //
         for (std::uint32_t k = m, r3, r4; k < m + n; ++k) {
             r3 = 1566083941 * T(begin_mod(k) + begin_mod(k+p) + begin_mod(k-1));
             r4 = r3 - k%n;
             begin_mod(k+p) ^= r3;
             begin_mod(k+q) ^= r4;
             begin_mod(k) = r4;
         }
     }
 };
 int main()
 {
     const auto input = std::initializer_list<std::uint32_t>{1,2,3,4,5};
     const auto output_size = 10;
     // using std version of seed_seq
     std::seed_seq seq(input);
     std::vector<std::uint32_t> seeds(output_size);
     seq.generate(seeds.begin(), seeds.end());
     for(const std::uint32_t n : seeds) {
         std::cout << n << '\n';
     }
     // using custom version of seed_seq
     seed_seq seq2(input);
     std::vector<std::uint32_t> seeds2(output_size);
     seq2.generate(seeds2.begin(), seeds2.end());
     assert(seeds == seeds2);
 }

Output:
 4204997637
 4246533866
 1856049002
 1129615051
 690460811
 1075771511
 46783058
 3904109078
 1534123438
 1495905678