How to properly initialize a C++11 std::seed_seq - c++

Question

I have a C++11 program that needs to create several independent random generators, for use by different threads in a parallel computation. These generators should be initialized with different seed values so that they all produce different pseudo-random sequences.
I see that there's a std::seed_seq class that seems to be meant for this purpose, but it's not clear what's the right way to construct one. The examples I've seen, such as the one on cppreference.com, initialize it with a handful of integer constants hard-coded in the program:
std::seed_seq seq{1,2,3,4,5};
I doubt that's actually a recommended best practice, so I'm wondering what is the recommended practice. In particular:
Since a seed_seq can be initialized with an arbitrary number of integers, what's the significance of the length of its initializer list? If I want to produce seeds for 100 random generators, do I need to initialize my seed_seq with 100 integers?
If the length of the initializer list doesn't have to match the number of seeds I intend to generate, is it OK to initialize a seed_seq with just one integer and then use it to produce a large number of seeds?
How about initializing with no integers, i.e. using the default constructor? (This means I'd get the same seeds every time, of course.)
If it's OK to construct a seed_seq from a single integer and then generate lots of seeds from it, what's the benefit of using seed_seq instead of an ordinary random generator? Why not just construct a std::mt19937 from that single integer and use that to produce seed values for other generators?

Answer 1

The trouble with using a fixed sequence like that is that you get the same sequence of seeds out of it, much the same as if you had called srand(42) at the start of your program: it generates identical sequences.
The C++11 standard states (in section 26.5.7.1 Class seed_seq):
A seed sequence is an object that consumes a sequence of integer-valued data and produces a requested number of unsigned integer values i, 0 i < 232, based on the consumed data.
[Note: Such an object provides a mechanism to avoid replication of streams of random variates. This can be useful, for example, in applications requiring large numbers of random number engines. —end note]
It also states how those integers are turned into seeds in paragraph 8 of that section, in such a way that the distribution of those seeds is acceptable even if the integer input items are very similar. So you can probably think of it as a pseudo-random number generator for seed values.
A larger number of items will provide more "randomness" in the seed values, provided they have some randomness themselves. Using constants as input is a bad idea for this reason.
What I tend to do is very similar to the way you normally randomise one generator, with srand (time (0)). In other words:
#include <random>
#include <cstdint>
#include <ctime>
#include <iostream>
int main()
{
std::seed_seq seq{time(0)};
std::vector<std::uint32_t> seeds(10);
seq.generate(seeds.begin(), seeds.end());
for (std::uint32_t n : seeds) {
std::cout << n << '\n';
}
}
If you have multiple sources of randomness, such as a value read from /dev/random under Linux, or a white noise generator of some description, or the average number of milliseconds between keypresses the last time a user ran this program, you could use those as extra inputs:
std::seed_seq seq{time(0), valFromDevRandom(), getWhiteNoise(), avgMillis()};
but I doubt constants are the way to go, since they add no randomness to the equation.

Answer 2

According The C++11 standard (in section 26.5.7.1.8），seed_seq can generate a sequence which is likely generated by a hash function, uniformly and randomly in the range.
I try to answer the below questions:
Q1 "Since a seed_seq can be initialized with an arbitrary number of integers, what's the significance of the length of its initializer list? If I want to produce seeds for 100 random generators, do I need to initialize my seed_seq with 100 integers?"
A1. You needn't initialize seed_seq with a lot integers. Even seed_seq initialized by one random integer, the generated sequence keep the randomness. But you initialize seed_seq with more integers and in the wider range, The generated sequence is more hardly "collide" by attackers.
Q2. "If the length of the initializer list doesn't have to match the number of seeds I intend to generate, is it OK to initialize a seed_seq with just one integer and then use it to produce a large number of seeds?"
A2. Yes, it is OK to initialize a seed_seq with just one integer if you don't need cryptographically secure level.
Q3. "How about initializing with no integers, i.e. using the default constructor? (This means I'd get the same seeds every time, of course.)"
A3. You will get the identical sequences by the default constructed seed_seq runs more. Thus it will became a security hole.
Q4. "If it's OK to construct a seed_seq from a single integer and then generate lots of seeds from it, what's the benefit of using seed_seq instead of an ordinary random generator? Why not just construct a std::mt19937 from that single integer and use that to produce seed values for other generators?"
A4. seed_seq is a light-weight algorithm, only iterates the filled sequence 3 times. I guess you can use other random generator instead of seed_seq.