# std::seed_seq::generate

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< cpp‎ | numeric‎ | random‎ | seed seq

template< class RandomIt > void generate( RandomIt begin, RandomIt end ); |  | (since C++11)

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

begin, end | - | mutable random-access iterators whose 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

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