Rework the email frequency calculation to account for gaps in runs

The previous code had some issues with respect to how we decided whether to
send an email.  The age used for calculating when the next mail should be
sent was saved as a float rather than an integer; since p-m runs never
happen exactly an integer number of days after upload, this results in a
cumulative error in the timing of the emails, that is further exacerbated if
a particular run is significantly delayed or if p-m infrastructure is down
for a period of time.

So instead, we now calculate the age at which the most recent email /should
have been sent/, and store that in our cache instead of the precise age.

There is still a bit of surprising behavior here due to the fact that we use
two different 'max_age' values for valid vs. invalid candidate packages: a
single package can, over the course of its stay in -proposed, move from
being an invalid candidate to being a valid candidate /and back again/
without ever migrating.  Such a package will switch back and forth between
two sets of calculations based on different starting offsets, causing the
ages at which the emails are sent to vary in a non-obvious fashion.
However, this will still obey the general principle of "email reminders of
decreasing frequency", so I think this is acceptable given that it is still
an overall improvement in predictability.

LP: #1671468

britney2/policies/email.py

@@ -1,6 +1,7 @@
 import os
 import re
 import json
+import math
 import socket
 import smtplib
 
@@ -12,7 +13,7 @@ from britney2.policies.policy import BasePolicy, PolicyVerdict
 
 
 # Recurring emails should never be more than this many days apart
-MAX_FREQUENCY = 30
+MAX_INTERVAL = 30
 
 API_PREFIX = 'https://api.launchpad.net/1.0/'
 USER = API_PREFIX + '~'
@@ -28,13 +29,13 @@ BOTS = {
 MESSAGE = """From: Ubuntu Release Team <noreply@canonical.com>
 To: {recipients}
 X-Proposed-Migration: notice
-Subject: [proposed-migration] {source_name} {version} stuck in {series}-proposed for {rounded_age} day{plural}.
+Subject: [proposed-migration] {source_name} {version} stuck in {series}-proposed for {age} day{plural}.
 
 Hi,
 
 {source_name} {version} needs attention.
 
-It has been stuck in {series}-proposed for {rounded_age} day{plural}.
+It has been stuck in {series}-proposed for {age} day{plural}.
 
 You either sponsored or uploaded this package, please investigate why it hasn't been approved for migration.
 
@@ -161,9 +162,8 @@ class EmailPolicy(BasePolicy, Rest):
         max_age = 5 if excuse.is_valid else 1
         series = self.options.series
         version = source_data_srcdist.version
-        age = excuse.daysold or 0
-        rounded_age = int(age)
-        plural = '' if rounded_age == 1 else 's'
+        age = int(excuse.daysold) or 0
+        plural = '' if age == 1 else 's'
         # an item is stuck if it's
         # - old enough
         # - not blocked
@@ -171,25 +171,35 @@ class EmailPolicy(BasePolicy, Rest):
         #   are still running)
         stuck = age >= max_age and 'block' not in excuse.reason and \
             excuse.current_policy_verdict != PolicyVerdict.REJECTED_TEMPORARILY
-
-        cached = self.cache.get(source_name, {}).get(version)
-        try:
-            emails, sent_age = cached
-            sent = (age - sent_age) < min(MAX_FREQUENCY, (age / 2.0) + 0.5)
-        except TypeError:
-            # This exception happens when source_name, version never seen before
-            emails = []
-            sent_age = 0
-            sent = False
         if self.dry_run:
             self.log("[email dry run] Considering: %s/%s: %s" %
                      (source_name, version, "stuck" if stuck else "not stuck"))
-            if stuck:
-                self.log("[email dry run] Age %d >= threshold %d: would email: %s" %
-                         (age, max_age, self.lp_get_emails(source_name, version)))
+        if not stuck:
+            return PolicyVerdict.PASS
+
+        cached = self.cache.get(source_name, {}).get(version)
+        try:
+            emails, last_sent = cached
+            # migration of older data
+            last_sent = int(last_sent)
+            if last_sent < max_age:
+                next_due = max_age
+            else:
+                next_due = int(math.pow(2,
+                                        int(math.log(last_sent - max_age + 1,
+                                                     2))+1) + last_sent)
+                if next_due - last_sent > MAX_INTERVAL:
+                    next_due = last_sent + MAX_INTERVAL
+        except TypeError:
+            # This exception happens when source_name, version never seen before
+            emails = []
+            next_due = max_age
+        if self.dry_run:
+            self.log("[email dry run] Age %d >= threshold %d: would email: %s" %
+                     (age, max_age, self.lp_get_emails(source_name, version)))
             # don't update the cache file in dry run mode; we'll see all output each time
             return PolicyVerdict.PASS
-        if stuck and not sent:
+        if age >= next_due:
             if not emails:
                 emails = self.lp_get_emails(source_name, version)
             if emails:
@@ -201,12 +211,12 @@ class EmailPolicy(BasePolicy, Rest):
                     server = smtplib.SMTP(self.email_host)
                     server.sendmail('noreply@canonical.com', emails, msg)
                     server.quit()
-                    sent_age = age
+                    # record the age at which the mail should have been sent
+                    self.emails_by_pkg[source_name][version] = (emails, next_due)
+                    self.save_state()
                 except socket.error as err:
                     self.log("Failed to send mail! Is SMTP server running?")
                     self.log(err)
-        self.emails_by_pkg[source_name][version] = (emails, sent_age)
-        self.save_state()
         return PolicyVerdict.PASS
 
     def save_state(self, britney=None):