std::seed_seq::generate

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) $ $T(x)$	$x xor (x rshift 27)$

The generation algorithm consists of the following steps, where $\scriptsize S_i $ $S i$ denotes begin[i % n], $\scriptsize V_i $ $V i$ 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

r 1

be

1664525\cdotT(S k xor S k+p xor S k-1)

.

2) Let

r 2

be

r 1 +j

, where

j

is:

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

3) Set

S k+p

to

(S k+p +r 1) mod 2 32

.

4) Set

S k+q

to

(S k+q +r 2) mod 2 32

.

5) Set

S k

to

r 2 mod 2 32

.

3) For each integer k in [m, m + n), performs the following operations in order:

1) Let

r 3

be

1566083941\cdotT(S k +S k+p +S k-1)

.

2) Let

r 4

be

r 3 -(k mod n)

.

3) Set

S k+p

to

(S k+p xor r 3) mod 2 32

.

4) Set

S k+q

to

(S k+q xor r 4) mod 2 32

.

5) Set

S k

to

r 4 mod 2 32

.

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:

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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Member functions
seed_seq::seed_seq
seed_seq::generate
seed_seq::size
seed_seq::param

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