diff --git a/lib/compatible_date.sh b/lib/compatible_date.sh
index e2f0ac3..fd3e469 100755
--- a/lib/compatible_date.sh
+++ b/lib/compatible_date.sh
@@ -200,3 +200,230 @@ dateTime_secs2canonical () {
 	echo $dateStr
 	return 0
 }
+
+#######################################################################
+# Compute the elapsed time (in secs) between two dateTime values.
+#
+# Usage: tspan dateTime1 dateTime2
+#
+# The arguments are given in "canonical dateTime string format"
+# as described above.
+#
+# If dateTime1 < dateTime2, the function returns a positive integer.
+# If dateTime1 > dateTime2, the function returns a negative integer.
+# If dateTime1 == dateTime2, the function returns zero.
+#######################################################################
+tspan () {
+
+	local dateTime1
+	local dateTime2
+	local secs1
+	local secs2
+	local dateTime1confirm
+	local dateTime2confirm
+	
+	# make sure there are two (and only two) command-line arguments
+	if [ $# -eq 2 ]; then
+		dateTime1="$1"
+		dateTime2="$2"
+	else
+		echo "ERROR: $FUNCNAME: incorrect number of arguments: $# (2 required)" >&2
+		return 2
+	fi
+	
+	# convert dateTime1 to seconds past the Epoch
+	secs1=$( dateTime_canonical2secs $dateTime1 )
+
+	# sanity check (for logging)
+	dateTime1confirm=$( dateTime_secs2canonical $secs1 )
+
+	# convert dateTime1 to seconds past the Epoch
+	secs2=$( dateTime_canonical2secs $dateTime2 )
+
+	# sanity check (for logging)
+	dateTime2confirm=$( dateTime_secs2canonical $secs2 )
+
+	# compute time difference (which may be negative)
+	echo $(( secs2 - secs1 ))
+
+	return 0
+}	
+
+#######################################################################
+# Given a time instant, compute the time interval (in secs) between 
+# the current time (NOW) and the time instant.
+#
+# Usage: secsUntil [-b begDateTime] [endDateTime]
+#
+# The arguments begDateTime and endDateTime are expected to be  
+# in "canonical dateTime string format" as described above.
+#
+# If the -b option is omitted, the function computes the time
+# interval between NOW and endDateTime. If the latter is omitted
+# on the command line, its value is taken from stdin.
+#
+# Presumably endDateTime is a time instant in the future but the 
+# function does not check this. If endDateTime is in the past, 
+# and option -b is omitted, the output of this function will be 
+# negative.
+#
+# If the -b option is present, the time interval between
+# begDateTime and endDateTime is computed. In this case,
+# the output will be positive if (and only if) endDateTime is 
+# chronologically later than begDateTime.
+#######################################################################
+secsUntil () {
+
+	local dateTime
+	local now
+	local d
+	
+	local opt
+	local OPTARG
+	local OPTIND
+	while getopts ":b:" opt; do
+		case $opt in
+			b)
+				now="$OPTARG"
+				;;
+			\?)
+				echo "ERROR: $FUNCNAME: Unrecognized option: -$OPTARG" >&2
+				return 2
+				;;
+			:)
+				echo "ERROR: $FUNCNAME: Option -$OPTARG requires an argument" >&2
+				return 2
+				;;
+		esac
+	done
+
+	# make sure there is at most one command-line argument
+	shift $(( OPTIND - 1 ))
+	if [ $# -eq 0 ]; then
+		# take input from stdin
+		dateTime=$( /bin/cat - )
+	elif [ $# -eq 1 ]; then
+		dateTime="$1"
+	else
+		echo "ERROR: $FUNCNAME: incorrect number of arguments: $# (0 or 1 required)" >&2
+		return 2
+	fi
+	
+	# compute NOW if necessary
+	if [ -z "$now" ]; then
+		# compute dateTime NOW
+		now=$( /bin/date -u +%Y-%m-%dT%TZ )
+	fi
+
+	# compute time until the given time instant
+	d=$( tspan "$now" "$dateTime" )
+	echo $d
+
+	return 0
+}	
+
+#######################################################################
+# Given a time instant, compute the time interval (in secs) between 
+# the time instant and the current time (NOW).
+#
+# Usage: secsSince [-e endDateTime] [begDateTime]
+#
+# The arguments begDateTime and endDateTime are expected to be  
+# in "canonical dateTime string format" as described above.
+#
+# If the -e option is omitted, the function computes the time
+# interval between begDateTime and NOW. If the former is omitted
+# on the command line, its value is taken from stdin.
+#
+# Presumably begDateTime is a time instant in the past but the 
+# function does not check this. If begDateTime is in the future, 
+# and option -e is omitted, the output of this function will be 
+# negative.
+#
+# If the -e option is present, the time interval between
+# begDateTime and endDateTime is computed. In this case,
+# the output will be positive if (and only if) endDateTime is 
+# chronologically later than begDateTime.
+#######################################################################
+secsSince () {
+
+	local dateTime
+	local now
+	local d
+	
+	local opt
+	local OPTARG
+	local OPTIND
+	while getopts ":e:" opt; do
+		case $opt in
+			e)
+				now="$OPTARG"
+				;;
+			\?)
+				echo "ERROR: $FUNCNAME: Unrecognized option: -$OPTARG" >&2
+				return 2
+				;;
+			:)
+				echo "ERROR: $FUNCNAME: Option -$OPTARG requires an argument" >&2
+				return 2
+				;;
+		esac
+	done
+
+	# make sure there is at most one command-line argument
+	shift $(( OPTIND - 1 ))
+	if [ $# -eq 0 ]; then
+		# take input from stdin
+		dateTime=$( /bin/cat - )
+	elif [ $# -eq 1 ]; then
+		dateTime="$1"
+	else
+		echo "ERROR: $FUNCNAME: incorrect number of arguments: $# (0 or 1 required)" >&2
+		return 2
+	fi
+	
+	# compute NOW if necessary
+	if [ -z "$now" ]; then
+		# compute dateTime NOW
+		now=$( /bin/date -u +%Y-%m-%dT%TZ )
+	fi
+
+	# compute time until invalid in secs
+	d=$( tspan $dateTime $now )
+	echo $d
+
+	return 0
+}	
+
+#######################################################################
+# Convert seconds into an ISO 8061 duration.
+#
+# Usage: secs2duration SECONDS
+#
+#######################################################################
+secs2duration () {
+
+	local days
+	local hours
+	local mins
+	local secs
+	
+	# make sure there is exactly one command-line argument
+	if [ $# -eq 1 ]; then
+		secs="$1"
+	else
+		echo "ERROR: $FUNCNAME: incorrect number of arguments: $# (1 required)" >&2
+		return 2
+	fi
+	
+	# convert seconds to days, hours, minutes, seconds
+	days=$(( secs/86400 ))
+	hours=$(( secs%86400/3600 ))
+	mins=$(( secs%3600/60 ))
+	secs=$(( secs%60 ))
+	
+	# an ISO 8601 duration
+	printf 'P%dDT%dH%dM%dS\n' $days $hours $mins $secs
+	
+	return
+}
\ No newline at end of file