# 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)

Generate unbiased seeds by filling the output range `[`begin`,` end`)` with 32-bit unsigned integer values, based on the (possibly biased) seeds stored in `v`.

- If begin == end is true, does nothing.
- Otherwise, generates seeds by the generation algorithm described below.

If std::iterator_traits <RandomIt>::value_type is not an unsigned integer type, or its width is less than 32, the program is ill-formed.

If `RandomIt` does not meet the requirements of LegacyRandomAccessIterator, or it is not mutable, the behavior is undefined.

### Generation algorithm

Given the following values and operations:

Value | Definition
z | `v`﻿.size()
n | end - begin
m | std::max (z + 1, n)
t | (n >= 623) ? 11 : (n >= 68) ? 7 : (n >= 39) ? 5 : (n >= 7) ? 3 : (n - 1) / 2
p | (n - t) / 2
q | p + t
Operation | Definition
\(\scriptsize \mathsf{xor} \)xor | built-in bitwise XOR
\(\scriptsize \mathsf{rshift} \)rshift | built-in bitwise right-shift
\(\scriptsize T(x) \)T(x) | \(\scriptsize x\ \mathsf{xor}\ (x\ \mathsf{rshift}\ 27) \)x xor (x rshift 27)

The generation algorithm consists of the following steps, where \(\scriptsize S_i \)Si denotes begin[i % n], \(\scriptsize V_i \)Vi denotes `v`﻿[i]:

1) Set each element of the output range to the value 0x8b8b8b8b.
2) For each integer k in `[`​0​`,` m`)`, performs the following operations in order:
1) Let \(\scriptsize r_1 \)r1 be \(\scriptsize 1664525 \cdot T(S_k\ \mathsf{xor}\ S_{k+p}\ \mathsf{xor}\ S_{k-1}) \)1664525·T(Sk xor Sk+p xor Sk-1).
2) Let \(\scriptsize r_2 \)r2 be \(\scriptsize r_1 + j \)r1+j, where \(\scriptsize j \)j is:

- \(\scriptsize z \)z, if \(\scriptsize k=0 \)k=0
- \(\scriptsize (k \mod n)+V_{k-1} \)(k mod n)+Vk-1, if \(\scriptsize 0<k⩽z \)0<k⩽z
- \(\scriptsize k \mod n \)k mod n, if \(\scriptsize z<k \)z<k

3) Set \(\scriptsize S_{k+p} \)Sk+p to \(\scriptsize (S_{k+p}+r_1) \mod 2^{32} \)(Sk+p+r1) mod 232
.
4) Set \(\scriptsize S_{k+q} \)Sk+q to \(\scriptsize (S_{k+q}+r_2) \mod 2^{32} \)(Sk+q+r2) mod 232
.
5) Set \(\scriptsize S_k \)Sk to \(\scriptsize r_2 \mod 2^{32} \)r2 mod 232
.
3) For each integer k in `[`m`,` m + n`)`, performs the following operations in order:
1) Let \(\scriptsize r_3 \)r3 be \(\scriptsize 1566083941 \cdot T(S_k+S_{k+p}+S_{k-1}) \)1566083941·T(Sk+Sk+p+Sk-1).
2) Let \(\scriptsize r_4 \)r4 be \(\scriptsize r_3-(k \mod n) \)r3-(k mod n).
3) Set \(\scriptsize S_{k+p} \)Sk+p to \(\scriptsize (S_{k+p}\ \mathsf{xor}\ r_3) \mod 2^{32} \)(Sk+p xor r3) mod 232
.
4) Set \(\scriptsize S_{k+q} \)Sk+q to \(\scriptsize (S_{k+q}\ \mathsf{xor}\ r_4) \mod 2^{32} \)(Sk+q xor r4) mod 232
.
5) Set \(\scriptsize S_k \)Sk to \(\scriptsize r_4 \mod 2^{32} \)r4 mod 232
.

### Parameters

begin, end | - | the iterators denoting the output range

### Exceptions

Only throws the exceptions thrown by the `RandomIt` operations on begin and end.

### Notes

The generation algorithm is 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.

### 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

### Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

DR | Applied to | Behavior as published | Correct behavior
--- | --- | --- | ---
LWG 2180 | C++11 | `seed_seq::generate` is non-throwing | it may throw exceptions

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