Support dynamic evaluation of synchronous replication quorum

[TarantoolBot]

Support dynamic evaluation of synchronous replication quorum

Product: Tarantool
Since: 2.5.3, 2.6.2, 2.7.1
Audience/target:
Root document:

• https://www.tarantool.io/en/doc/latest/reference/configuration/#cfg-replication-replication-synchro-quorum
• (possibly) https://www.tarantool.io/en/doc/latest/book/replication/repl_leader_elect/
• (possibly) https://www.tarantool.io/en/doc/latest/book/replication/repl_sync/
  SME: @ cyrillos
  Peer reviewer: @

Details

Setting replication_synchro_quorum option to an explicit integer
value was introduced rather for simplicity sake mostly. For example
if the cluster's size is not a constant value and new replicas are
connected in dynamically then an administrator might need to increase
the option by hands or by some other external tool.

Instead one can use a dynamic evaluation of a quorum value via formal
representation using symbol N as a current number of registered replicas
in a cluster.

For example, the canonical definition for a quorum (that is, majority
of members in a set) of N replicas is N/2+1. For such configuration
define

box.cfg {replication_synchro_quorum = "N/2+1"}

The formal statement allows to provide a flexible configuration but keep
in mind that only canonical quorum (and bigger values, say N for all
replicas) guarantees data reliability and various weird forms such as
N/3+1 while allowed may lead to unexpected results.
Requested by @cyrillos in tarantool/tarantool@14fa5fd.

See other details in the issue comments below.

[Totktonada]

The division gives an integral result? The rounding is to a lower integral number / to zero / to a nearest integral value?

Or, if the division is floating point / exact decimal, whether the result of expression is rounded? If so, how exactly?

[cyrillos]

It simply returns the formula evaluated, we don't even care much what exactly a user has passed. The result is treated as an integer number.
tarantool/tarantool@14fa5fd#diff-fc276b44b551b4eac3431c9433d4bc881790ddd7df76226d7579f80da7798f6eR566

[cyrillos]

If result is out of range the error is returned

	if (quorum <= 0 || quorum >= VCLOCK_MAX) {
		const char *msg =
			tt_sprintf("the formula is evaluated "
				   "to the quorum %d for replica "
				   "number %d, which is out of range "
				   "[%d;%d]",
				   quorum, nr_replicas, 1, VCLOCK_MAX - 1);
		diag_set(ClientError, ER_CFG,
			 "replication_synchro_quorum", msg);
		return -1;
	}