How is the weighted fractional uptime of a Tor relay calculated?

Question

How is the weighted fractional uptime of a Tor relay calculated?

Arma's "The lifecycle of a new relay" post mentions this statistic but does not describe it in detail:

Directory authorities assign the Guard flag to relays based on three characteristics: "bandwidth" (they need to have a large enough consensus weight), "weighted fractional uptime" (they need to be working most of the time), and "time known" (to make attacks more expensive, we don't want to give the Guard flag to relays that haven't been around a while first).

Answer 1

As described in Tor spec:

To calculate weighted fractional uptime:

compute the fraction of time that the router is up in any given day, weighting so that downtime and uptime in the past counts less.

A node is 'familiar' if 1/8 of all active nodes have appeared more recently than it, OR it has been around for a few weeks.

Answer 2

Here's how I explained requirements for the Guard flag, including weighted fractional uptime, in the tech report An Analysis of Tor Relay Stability in June 2011:

"A router is a possible ‘Guard’ [if it is ‘familiar’,] if its Weighted Fractional Uptime is at least the median for ‘familiar’ active routers [or its Weighted Fractional Uptime is at least 98 %], and if its [advertised] bandwidth is at least median [of all active routers] or at least 250KB/s. [...] A node is ‘familiar’ if 1/8 of all active nodes have appeared more recently than it, or it has been around for [a weighted time of 8 days]."

[...]

The WFU metric measures the fraction of uptime of a relay in the past. [...] WFU values are discounted by factor 0.95 every 12 hours [...] including the current uptime session.