Improve easter egg for 20 years of grml.org

Relevant changes:

1) Don't convert dates via date(1), but provide epoch seconds right away
2) Also use zsh's ${EPOCHSECONDS} instead of forking to date(1)
3) Display easter egg message with einfo iff we are within the birthday range
4) Don't display easter egg only on 2023-09-16 and one month later,
   but also in all the days in between (sigh :))
5) Don't display anything at all when booting with noeasteregg boot option
6) Have the easter egg appear randomly, with diminishing probability as
   you get farther from the actual birthday

Thanks: Christopher Bock and András Korn

autoconfig.functions

@@ -1993,18 +1993,9 @@ fi
 # }}}
 
 # {{{ Easteregg (for 20 years grml.org)
-config_easteregg() {
-  current_date=$(date +%Y-%m-%d)
-  birthday="2023-09-16"
-  one_month_later=$(date -d "${current_date} + 1 month" +%Y-%m-%d)
-
+display_easteregg() {
   einfo "You found the birthday easter egg!" ; eend 0
 
-  # nothing to be done if it's more than one month since $birthday
-  if ! [[ "${current_date}" == "${birthday}" || "${current_date}" == "${one_month_later}" ]]; then
-    return 0
-  fi
-
   if [[ -x /bin/toilet && -x /usr/games/lolcat ]] ; then
     visualize() { printf "%s\n" "$*" | toilet | /usr/games/lolcat ; }
   elif [[ -x /bin/toilet ]] ; then
@@ -2017,6 +2008,26 @@ config_easteregg() {
   visualize "20 years"
   visualize "grml.org"
 }
+
+config_easteregg() {
+  checkbootparam 'noeasteregg' && return 0
+
+  zmodload zsh/datetime 2>/dev/null || return 0
+  zmodload zsh/mathfunc 2>/dev/null || return 0
+
+  local birthday=1694822400            # := 2023-09-16 -> TZ=UTC date -d "2023-09-16" +%s
+  local one_month=$[24*30*3600]
+  local pi=3.14159265358979323846
+  local magic=$(( one_month/(pi/2) ))  # normalization factor, used to map the [birthday;birthday+-one_month] range onto [0;+-pi/2]
+
+  if [[ $(( abs(birthday-EPOCHSECONDS) )) -le $one_month ]] ; then
+    if [[ $(( rand48() )) -le $(( cos((birthday-EPOCHSECONDS)/magic) )) ]] ; then
+      display_easteregg
+    fi
+  fi
+
+  return 0
+}
 # }}}
 
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