Network Working Group D. Mills
Request for Comments: 1589 University of Delaware
Category: Informational March 1994

A Kernel Model for Precision Timekeeping

Status of this Memo

This memo provides information for the Internet community. This memo
does not specify an Internet standard of any kind. Distribution of
this memo is unlimited.

Overview

This memorandum describes an engineering model which implements a
precision time-of-day function for a generic operating system. The
model is based on the principles of disciplined oscillators and
phase-lock loops (PLL) often found in the engineering literature. It
has been implemented in the Unix kernel for several workstations,
including those made by Sun Microsystems and Digital Equipment. The
model changes the way the system clock is adjusted in time and
frequency, as well as provides mechanisms to discipline its frequency
to an external precision timing source. The model incorporates a
generic system-call interface for use with the Network Time Protocol
(NTP) or similar time synchronization protocol. The NTP Version 3
daemon xntpd operates with this model to provide synchronization
limited in principle only by the accuracy and stability of the
external timing source.

This memorandum does not obsolete or update any RFC. It does not
propose a standard protocol, specification or algorithm. It is
intended to provoke comment, refinement and alternative
implementations. While a working knowledge of NTP is not required for
an understanding of the design principles or implementation of the
model, it may be helpful in understanding how the model behaves in a
fully functional timekeeping system. The architecture and design of
NTP is described in [1], while the current NTP Version 3 protocol
specification is given in RFC-1305 [2] and a subset of the protocol,
the Simple Network Time Protocol (SNTP), in RFC-1361 [4].

The model has been implemented in three Unix kernels for Sun
Microsystems and Digital Equipment workstations. In addition, for the
Digital machines the model provides improved precision to one
microsecond (us). Since these specific implementations involve
modifications to licensed code, they cannot be provided directly.
Inquiries should be directed to the manufacturer's representatives.
However, the engineering model for these implementations, including a

simulator with code segments almost identical to the implementations,
but not involving licensed code, is available via anonymous FTP from
host louie.udel.edu in the Directory pub/ntp and compressed tar
archive kernel.tar.Z. The NTP Version 3 distribution can be oBTained
via anonymous ftp from the same host and directory in the compressed
tar archive xntp3.3g.tar.Z, where the version number shown as 3.3g
may be adjusted for new versions as they occur.

1. IntrodUCtion

This memorandum describes a model and programming interface for
generic operating system software that manages the system clock and
timer functions. The model provides improved accuracy and stability
for most workstations and servers using the Network Time Protocol
(NTP) or similar time synchronization protocol. This memorandum
describes the principles of design and implementation of the model.
Related technical reports discuss the design approach, engineering
analysis and performance evaluation of the model as implemented in
Unix kernels for Sun Microsystems and Digital Equipment workstations.
The NTP Version 3 daemon xntpd operates with these implementations to
provide improved accuracy and stability, together with diminished
overhead in the operating system and network. In addition, the model
supports the use of external timing sources, such as precision
pulse-per-second (PPS) signals and the industry standard IRIG timing
signals. The NTP daemon automatically detects the presence of the new
features and utilizes them when available.

There are three prototype implementations of the model presented in
this memorandum, one each for the Sun Microsystems SPARCstation with
the SunOS 4.1.x kernel, Digital Equipment DECstation 5000 with the
Ultrix 4.x kernel and Digital Equipment 3000 AXP Alpha with the OSF/1
V1.x kernel. In addition, for the DECstation 5000/240 and 3000 AXP
Alpha machines, a special feature provides improved precision to 1 us
(Sun 4.1.x kernels already do provide 1-us precision). Other than
improving the system clock accuracy, stability and precision, these
implementations do not change the operation of existing Unix system
calls which manage the system clock, such as gettimeofday(),
settimeofday() and adjtime(); however, if the new features are in
use, the operations of gettimeofday() and adjtime() can be controlled
instead by new system calls ntp_gettime() and ntp_adjtime() as
described below.

A detailed description of the variables and algorithms is given in
the hope that similar functionality can be incorporated in Unix
kernels for other machines. The algorithms involve only minor changes
to the system clock and interval timer routines and include
interfaces for application programs to learn the system clock status
and certain statistics of the time synchronization process. Detailed

installation instructions are given in a specific README files
included in the kernel distributions.

In this memorandum, NTP Version 3 and the Unix implementation xntp3
are used as an example application of the new system calls for use by
a synchronization daemon. In principle, the new system calls can be
used by other protocols and implementations as well. Even in cases
where the local time is maintained by periodic exchanges of messages
at relatively long intervals, such as using the NIST Automated
Computer Time Service, the ability to precisely adjust the system
clock frequency simplifies the synchronization procedures and allows
the telephone call frequency to be considerably reduced.

2. Design Approach

While not strictly necessary for an understanding or implementation
of the model, it may be helpful to briefly describe how NTP operates
to control the system clock in a client workstation. As described in
[1], the NTP protocol exchanges timestamps with one or more peers
sharing a synchronization subnet to calculate the time offsets
between peer clocks and the local clock. These offsets are processed
by several algorithms which refine and combine the offsets to produce
an ensemble average, which is then used to adjust the local clock
time and frequency. The manner in which the local clock is adjusted
represents the main topic of this memorandum. The goal in the
enterprise is the most accurate and stable system clock possible with
the available kernel software and workstation hardware.

In order to understand how the new software works, it is useful to
review how most Unix kernels maintain the system time. In the Unix
design a hardware counter interrupts the kernel at a fixed rate: 100
Hz in the SunOS kernel, 256 Hz in the Ultrix kernel and 1024 Hz in
the OSF/1 kernel. Since the Ultrix timer interval (reciprocal of the
rate) does not evenly divide one second in microseconds, the Ultrix
kernel adds 64 microseconds once each second, so the timescale
consists of 255 advances of 3906 us plus one of 3970 us. Similarly,
the OSF/1 kernel adds 576 us once each second, so its timescale
consists of 1023 advances of 976 us plus one of 1552 us.

2.1. Mechanisms to Adjust Time and Frequency

In most Unix kernels it is possible to slew the system clock to a
new offset relative to the current time by using the adjtime()
system call. To do this the clock frequency is changed by adding
or subtracting a fixed amount (tickadj) at each timer interrupt
(tick) for a calculated number of ticks. Since this calculation
involves dividing the requested offset by tickadj, it is possible
to slew to a new offset with a precision only of tickadj, which is

usually in the neighborhood of 5 us, but sometimes much more. This
results in a roundoff error which can accumulate to an
unacceptable degree, so that special provisions must be made in
the clock adjustment procedures of the synchronization daemon.

In order to implement a frequency-discipline function, it is
necessary to provide time offset adjustments to the kernel at
regular adjustment intervals using the adjtime() system call. In
order to reduce the system clock jitter to the regime considered
in this memorandum, it is necessary that the adjustment interval
be relatively small, in the neighborhood of 1 s. However, the Unix
adjtime() implementation requires each offset adjustment to
complete before another one can be begun, which means that large
adjustments must be amortized in possibly many adjustment
intervals. The requirement to implement the adjustment interval
and compensate for roundoff error considerably complicates the
synchronizing daemon implementation.

In the new model this scheme is replaced by another that
represents the system clock as a multiple-Word, precision-time
variable in order to provide very precise clock adjustments. At
each timer interrupt a precisely calibrated quantity is added to
the kernel time variable and overflows propagated as required. The
quantity is computed as in the NTP local clock model described in
[3], which operates as an adaptive-parameter, first-order, type-II
phase-lock loop (PLL). In principle, this PLL design can provide
precision control of the system clock oscillator within 1 us and
frequency to within parts in 10^11. While precisions of this order
are surely well beyond the capabilities of the CPU clock
oscillator used in typical workstations, they are appropriate
using precision external oscillators as described below.

The PLL design is identical to the one originally implemented in
NTP and described in [3]. In this design the software daemon
simulates the PLL using the adjtime() system call; however, the
daemon implementation is considerably complicated by the
considerations described above. The modified kernel routines
implement the PLL in the kernel using precision time and frequency
representions, so that these complications are avoided. A new
system call ntp_adjtime() is called only as each new time update
is determined, which in NTP occurs at intervals of from 16 s to
1024 s. In addition, doing frequency compensation in the kernel
means that the system time runs true even if the daemon were to
cease operation or the network paths to the primary
synchronization source fail.

In the new model the new ntp_adjtime() operates in a way similar
to the original adjtime() system call, but does so independently

of adjtime(), which continues to operate in its traditional
fashion. When used with NTP, it is the design intent that
settimeofday() or adjtime() be used only for system time
adjustments greater than +-128 ms, although the dynamic range of
the new model is much larger at +-512 ms. It has been the Internet
experience that the need to change the system time in increments
greater than +-128 ms is extremely rare and is usually associated
with a hardware or software malfunction or system reboot.

The easiest way to set the time is with the settimeofday() system
call; however, this can under some conditions cause the clock to
jump backward. If this cannot be tolerated, adjtime() can be used
to slew the clock to the new value without running backward or
affecting the frequency discipline process. Once the system clock
has been set within +-128 ms, the ntp_adjtime() system call is
used to provide periodic updates including the time offset,
maximum error, estimated error and PLL time constant. With NTP the
update interval depends on the measured dispersion and time
constant; however, the scheme is quite forgiving and neither
moderate loss of updates nor variations in the update interval are
serious.

2.2 Daemon and Application Interface

Unix application programs can read the system clock using the
gettimeofday() system call, which returns only the system time and
timezone data. For some applications it is useful to know the
maximum error of the reported time due to all causes, including
clock reading errors, oscillator frequency errors and accumulated
latencies on the path to a primary synchronization source.
However, in the new model the PLL adjusts the system clock to
compensate for its intrinsic frequency error, so that the time
errors expected in normal operation will usually be much less than
the maximum error. The programming interface includes a new system
call ntp_gettime(), which returns the system time, as well as the
maximum error and estimated error. This interface is intended to
support applications that need such things, including distributed
file systems, multimedia teleconferencing and other real-time
applications. The programming interface also includes the new
system call ntp_adjtime() mentioned previously, which can be used
to read and write kernel variables for time and frequency
adjustment, PLL time constant, leap-second warning and related
data.

In addition, the kernel adjusts the maximum error to grow by an
amount equal to the oscillator frequency tolerance times the
elapsed time since the last update. The default engineering
parameters have been optimized for update intervals in the order

of 64 s. For other intervals the PLL time constant can be adjusted
to optimize the dynamic response over intervals of 16-1024 s.
Normally, this is automatically done by NTP. In any case, if
updates are suspended, the PLL coasts at the frequency last
determined, which usually results in errors increasing only to a
few tens of milliseconds over a day using room-temperature quartz
oscillators of typical modern workstations.

While any synchronization daemon can in principle be modified to
use the new system calls, the most likely will be users of the NTP
Version 3 daemon xntpd. The xntpd code determines whether the new
system calls are implemented and automatically reconfigures as
required. When implemented, the daemon reads the frequency offset
from a file and provides it and the initial time constant via
ntp_adjtime(). In subsequent calls to ntp_adjtime(), only the time
offset and time constant are affected. The daemon reads the
frequency from the kernel using ntp_adjtime() at intervals of
about one hour and writes it to a system file. This information is
recovered when the daemon is restarted after reboot, for example,
so the sometimes extensive training period to learn the frequency
separately for each system can be avoided.

2.3. Precision Clocks for DECstation 5000/240 and 3000 AXP Alpha

The stock microtime() routine in the Ultrix kernel returns system
time to the precision of the timer interrupt interval, which is in
the 1-4 ms range. However, in the DECstation 5000/240 and possibly
other machines of that family, there is an undocumented IOASIC
hardware register that counts system bus cycles at a rate of 25
MHz. The new microtime() routine for the Ultrix kernel uses this
register to interpolate system time between timer interrupts. This
results in a precision of 1 us for all time values obtained via
the gettimeofday() and ntp_gettime() system calls. For the Digital
Equipment 3000 AXP Alpha, the architecture provides a hardware
Process Cycle Counter and a machine instruction rpcc to read it.
This counter operates at the fundamental frequency of the CPU
clock or some submultiple of it, 133.333 MHz for the 3000/400 for
example. The new microtime() routine for the OSF/1 kernel uses
this counter in the same fashion as the Ultrix routine.

In both the Ultrix and OSF/1 kernels the gettimeofday() and
ntp_gettime() system call use the new microtime() routine, which
returns the actual interpolated value, but does not change the
kernel time variable. Therefore, other routines that Access the
kernel time variable directly and do not call either
gettimeofday(), ntp_gettime() or microtime() will continue their
present behavior. The microtime() feature is independent of other
features described here and is operative even if the kernel PLL or

new system calls have not been implemented.

The SunOS kernel already includes a system clock with 1-us
resolution; so, in principle, no microtime() routine is necessary.
An existing kernel routine uniqtime() implements this function,
but it is coded in the C language and is rather slow at 42-85 us
per call. A replacement microtime() routine coded in assembler
language is available in the NTP Version 3 distribution and is
much faster at about 3 us per call.

2.4. External Time and Frequency Discipline

The overall accuracy of a time synchronization subnet with respect
to Coordinated Universal Time (UTC) depends on the accuracy and
stability of the primary synchronization source, usually a radio
or satellite receiver, and the system clock oscillator of the
primary server. As discussed in [5], the traditional interface
using an RS232 protocol and serial port precludes the full
accuracy of the radio clock. In addition, the poor stability of
typical CPU clock oscillators limits the accuracy, whether or not
precision time sources are available. There are, however, several
ways in which the system clock accuracy and stability can be
improved to the degree limited only by the accuracy and stability
of the synchronization source and the jitter of the operating
system.

Many radio clocks produce special signals that can be used by
external equipment to precisely synchronize time and frequency.
Most produce a pulse-per-second (PPS) signal that can be read via
a modem-control lead of a serial port and some produce a special
IRIG signal that can be read directly by a bus peripheral, such as
the KSI/Odetics TPRO IRIG SBus interface, or indirectly via the
audio codec of some workstations, as described in [5]. In the NTP
Version 3 distribution, the PPS signal can be used to augment the
less precise ASCII serial timecode to improve accuracy to the
order of microseconds. Support is also included in the
distribution for the TPRO interface as well as the audio codec;
however, the latter requires a modified kernel audio driver
contained in the bsd_audio.tar.Z distribution in the same host and
directory as the NTP Version 3 distribution mentioned previously.

2.4.1. PPS Signal

The NTP Version 3 distribution includes a special ppsclock
module for the SunOS 4.1.x kernel that captures the PPS signal
presented via a modem-control lead of a serial port. Normally,
the ppsclock module produces a timestamp at each transition of
the PPS signal and provides it to the synchronization daemon

for integration with the serial ASCII timecode, also produced
by the radio clock. With the conventional PLL implementation in
either the daemon or the kernel as described above, the
accuracy of this scheme is limited by the intrinsic stability
of the CPU clock oscillator to a millisecond or two, depending
on environmental temperature variations.

The ppsclock module has been modified to in addition call a new
kernel routine hardpps() once each second. The kernel routine
compares the timestamp with a sample of the CPU clock
oscillator to develop a frequency offset estimate. This offset
is used to discipline the oscillator frequency, nominally to
within a few parts in 10^8, which is about two orders of
magnitude better than the undisciplined oscillator. The new
feature is conditionally compiled in the code described below
only if the PPS_SYNC option is used in the kernel configuration
file.

When using the PPS signal to adjust the time, there is a
problem with the SunOS implementation which is very delicate to
fix. The Sun serial port interrupt routine operates at
interrupt priority level 12, while the timer interrupt routine
operates at priority 10. Thus, it is possible that the PPS
signal interrupt can occur during the timer interrupt routine,
with result that a tick increment can be missed and the
returned time early by one tick. It may happen that, if the CPU
clock oscillator is within a few ppm of the PPS oscillator,
this condition can persist for two or more successive PPS
interrupts. A useful workaround has been to use a median filter
to process the PPS sample offsets. In this filter the sample
offsets in a window of 20 samples are sorted by offset and the
six highest and six lowest outlyers discarded. The average of
the eight samples remaining becomes the output of the filter.

The problem is not nearly so serious when using the PPS signal
to discipline the frequency of the CPU clock oscillator. In
this case the quantity of interest is the contents of the
microseconds counter only, which does not depend on the kernel
time variable.

2.4.2. External Clocks

It is possible to replace the system clock function with an
external bus peripheral. The TPRO device mentioned previously
can be used to provide IRIG-synchronized time with a precision
of 1 us. A driver for this device tprotime.c and header file
tpro.h are included in the kernel.tar.Z distribution mentioned
previously. Using this device the system clock is read directly

from the interface; however, the device does not record the
year, so special provisions have to be made to obtain the year
from the kernel time variable and initialize the driver
accordingly. This feature is conditionally compiled in the code
described below only if the EXT_CLOCK option is used in the
kernel configuration file.

While the system clock function is provided directly by the
microtime() routine in the driver, the kernel time variable
must be disciplined as well, since not all system timing
functions use the microtime() routine. This is done by
measuring the difference between the microtime() clock and
kernel time variable and using the difference to adjust the
kernel PLL as if the adjustment were provided by an external
peer and NTP.

A good deal of error checking is done in the TPRO driver, since
the system clock is vulnerable to a misbehaving radio clock,
IRIG signal source, interface cables and TPRO device itself.
Unfortunately, there is no easy way to utilize the extensive
diversity and redundancy capabilities available in the NTP
synchronization daemon. In order to avoid disruptions that
might occur if the TPRO time is far different from the kernel
time variable, the latter is used instead of the former if the
difference between the two exceeds 1000 s; presumably in that
case operator intervention is required.

2.4.3. External Oscillators

Even if a source of PPS or IRIG signals is not available, it is
still possible to improve the stability of the system clock
through the use of a specialized bus peripheral. In order to
explore the benefits of such an approach, a special SBus
peripheral caled HIGHBALL has been constructed. The device
includes a pair of 32-bit hardware counters in Unix timeval
format, together with a precision, oven-controlled quartz
oscillator with a stability of a few parts in 10^9. A driver
for this device hightime.c and header file high.h are included
in the kernel.tar.Z distribution mentioned previously. This
feature is conditionally compiled in the code described below
only if the EXT_CLOCK and HIGHBALL options are used in the
kernel configuration file.

Unlike the external clock case, where the system clock function
is provided directly by the microtime() routine in the driver,
the HIGHBALL counter offsets with respect to UTC must be
provided first. This is done using the ordinary kernel PLL,
but controlling the counter offsets directly, rather than the

kernel time variable. At first, this might seem to defeat the
purpose of the design, since the jitter and wander of the
synchronization source will affect the counter offsets and thus
the accuracy of the time. However, the jitter is much reduced
by the PLL and the wander is small, especially if using a radio
clock or another primary server disciplined in the same way.
In practice, the scheme works to reduce the incidental wander
to a few parts in 10^8, or about the same as using the PPS
signal.

As in the previous case, the kernel time variable must be
disciplined as well, since not all system timing functions use
the microtime() routine. However, the kernel PLL cannot be used
for this, since it is already in use providing offsets for the
HIGHBALL counters. Therefore, a special correction is
calculated from the difference between the microtime() clock
and the kernel time variable and used to adjust the kernel time
variable at the next timer interrupt. This somewhat roundabout
approach is necessary in order that the adjustment does not
cause the kernel time variable to jump backwards and possibly
lose or duplicate a timer event.

2.5 Other Features

It is a design feature of the NTP architecture that the system
clocks in a synchronization subnet are to read the same or nearly
the same values before during and after a leap-second event, as
declared by national standards bodies. The new model is designed
to implement the leap event upon command by an ntp_adjtime()
argument. The intricate and sometimes arcane details of the model
and implementation are discussed in [3] and [5]. Further details
are given in the technical summary later in this memorandum.

3. Technical Summary

In order to more fully understand the workings of the model, a stand-
alone simulator kern.c and header file timex.h are included in the
kernel.tar.Z distribution mentioned previously. In addition, a
complete C program kern_ntptime.c which implements the ntp_gettime()
and ntp_adjtime() functions is provided, but with the vendor-specific
argument-passing code deleted. Since the distribution is somewhat
large, due to copious comments and ornamentation, it is impractical
to include a listing of these programs in this memorandum. In any
case, implementors may choose to snip portions of the simulator for
use in new kernel designs, but, due to formatting conventions, this
would be difficult if included in this memorandum.

The kern.c program is an implementation of an adaptive-parameter,
first-order, type-II phase-lock loop. The system clock is implemented
using a set of variables and algorithms defined in the simulator and
driven by explicit offsets generated by a driver program also
included in the program. The algorithms include code fragments almost
identical to those in the machine-specific kernel implementations and
operate in the same way, but the operations can be understood
separately from any licensed source code into which these fragments
may be integrated. The code fragments themselves are not derived from
any licensed code. The following discussion assumes that the
simulator code is available for inspection.

3.1. PLL Simulation

The simulator operates in conformance with the analytical model
described in [3]. The main() program operates as a driver for the
fragments hardupdate(), hardclock(), second_overflow(), hardpps()
and microtime(), although not all functions implemented in these
fragments are simulated. The program simulates the PLL at each
timer interrupt and prints a summary of critical program variables
at each time update.

There are three defined options in the kernel configuration file
specific to each implementation. The PPS_SYNC option provides
support for a pulse-per-second (PPS) signal, which is used to
discipline the frequency of the CPU clock oscillator. The
EXT_CLOCK option provides support for an external kernel-readable
clock, such as the KSI/Odetics TPRO IRIG interface or HIGHBALL
precision oscillator, both for the SBus. The TPRO option provides
support for the former, while the HIGHBALL option provides support
for the latter. External clocks are implemented as the microtime()
clock driver, with the specific source code selected by the kernel
configuration file.

3.1.1. The hardupdate() Fragment

The hardupdate() fragment is called by ntp_adjtime() as each
update is computed to adjust the system clock phase and
frequency. Note that the time constant is in units of powers of
two, so that multiplies can be done by simple shifts. The phase
variable is computed as the offset divided by the time
constant. Then, the time since the last update is computed and
clamped to a maximum (for robustness) and to zero if
initializing. The offset is multiplied (sorry about the ugly
multiply) by the result and divided by the square of the time
constant and then added to the frequency variable. Note that
all shifts are assumed to be positive and that a shift of a
signed quantity to the right requires a little dance.

With the defines given, the maximum time offset is determined
by the size in bits of the long type (32 or 64) less the
SHIFT_UPDATE scale factor (12) or at least 20 bits (signed).
The scale factor is chosen so that there is no loss of
significance in later steps, which may involve a right shift up
to SHIFT_UPDATE bits. This results in a time adjustment range
over +-512 ms. Since time_constant must be greater than or
equal to zero, the maximum frequency offset is determined by
the SHIFT_USEC scale factor (16) or at least 16 bits (signed).
This results in a frequency adjustment range over +-31,500 ppm.

In the addition step, the value of offset * mtemp is not
greater than MAXPHASE * MAXSEC = 31 bits (signed), which will
not overflow a long add on a 32-bit machine. There could be a
loss of precision due to the right shift of up to 12 bits,
since time_constant is bounded at 6. This results in a net
worst-case frequency resolution of about .063 ppm, which is not
significant for most quartz oscillators. The worst case could
be realized only if the NTP peer misbehaves according to the
protocol specification.

The time_offset value is clamped upon entry. The time_phase
variable is an accumulator, so is clamped to the tolerance on
every call. This helps to damp transients before the oscillator
frequency has been determined, as well as to satisfy the
correctness assertions if the time synchronization protocol or
implementation misbehaves.

3.1.2. The hardclock() Fragment

The hardclock() fragment is inserted in the hardware timer
interrupt routine at the point the system clock is to be
incremented. Previous to this fragment the time_update variable
has been initialized to the value computed by the adjtime()
system call in the stock Unix kernel, normally plus/minus the
tickadj value, which is usually in the order of 5 us. The
time_phase variable, which represents the instantaneous phase
of the system clock, is advanced by time_adj, which is
calculated in the second_overflow() fragment described below.
If the value of time_phase exceeds 1 us in scaled units,
time_update is increased by the (signed) excess and time_phase
retains the residue.

Except in the case of an external oscillator such as the
HIGHBALL interface, the hardclock() fragment advances the
system clock by the value of tick plus time_update. However, in
the case of an external oscillator, the system clock is
obtained directly from the interface and time_update used to

discipline that interface instead. However, the system clock
must still be disciplined as explained previously, so the value
of clock_cpu computed by the second_overflow() fragment is used
instead.

3.1.3. The second_overflow() Fragment

The second_overflow() fragment is inserted at the point where
the microseconds field of the system time variable is being
checked for overflow. Upon overflow the maximum error
time_maxerror is increased by time_tolerance to reflect the
maximum time offset due to oscillator frequency error. Then,
the increment time_adj to advance the kernel time variable is
calculated from the (scaled) time_offset and time_freq
variables updated at the last call to the hardclock() fragment.

The phase adjustment is calculated as a (signed) fraction of
the time_offset remaining, where the fraction is added to
time_adj, then subtracted from time_offset. This technique
provides a rapid convergence when offsets are high, together
with good resolution when offsets are low. The frequency
adjustment is the sum of the (scaled) time_freq variable, an
adjustment necessary when the tick interval does not evenly
divide one second fixtick and PPS frequency adjustment pps_ybar
(if configured).

The scheme of approximating exact multiply/divide operations
with shifts produces good results, except when an exact
calculation is required, such as when the PPS signal is being
used to discipling the CPU clock oscillator frequency, as
described below. As long as the actual oscillator frequency is
a power of two in seconds, no correction is required. However,
in the SunOS kernel the clock frequency is 100 Hz, which
results in an error factor of 0.78. In this case the code
increases time_adj by a factor of 1.25, which results in an
overall error less than three percent.

On rollover of the day, the leap-second state machine described
below determines whether a second is to be inserted or deleted
in the timescale. The microtime() routine insures that the
reported time is always monotonically increasing.

3.1.4. The hardpps() Fragment

The hardpps() fragment is operative only if the PPS_SYNC option
is specified in the kernel configuration file. It is called
from the serial port driver or equivalent interface at the on-
time transition of the PPS signal. The fragment operates as a

first-order, type-I frequency-lock loop (FLL) controlled by the
difference between the frequency represented by the pps_ybar
variable and the frequency of the hardware clock oscillator.

In order to avoid calling the microtime() routine more than
once for each PPS transition, the interface requires the
calling program to capture the system time and hardware counter
contents at the on-time transition of the PPS signal and
provide a pointer to the timestamp (Unix timeval) and counter
contents as arguments to the hardpps() call. The hardware
counter contents can be determined by saving the microseconds
field of the system time, calling the microtime() routine, and
subtracting the saved value. If a counter overflow has occured
during the process, the resulting microseconds value will be
negative, in which case the caller adds 1000000 to normalize
the microseconds field.

The frequency of the hardware oscillator can be determined from
the difference in hardware counter readings at the beginning
and end of the calibration interval divided by the duration of
the interval. However, the oscillator frequency tolerance, as
much as 100 ppm, may cause the difference to exceed the tick
value, creating an ambiguity. In order to avoid this ambiguity,
the hardware counter value at the beginning of the interval is
increased by the current pps_ybar value once each second, but
computed modulo the tick value. At the end of the interval, the
difference between this value and the value computed from the
hardware counter is used as a control signal sample for the
FLL.

Control signal samples which exceed the frequency tolerance are
discarded, as well as samples resulting from excessive interval
duration jitter. Surviving samples are then processed by a
three-stage median filter. The signal which drives the FLL is
derived from the median sample, while the average of
differences between the other two samples is used as a measure
of dispersion. If the dispersion is below the threshold
pps_dispmax, the median is used to correct the pps_ybar value
with a weight expressed as a shift PPS_AVG (2). In addition to
the averaging function, pps_disp is increased by the amount
pps_dispinc once each second. The result is that, should the
dispersion be exceptionally high, or if the PPS signal fails
for some reason, the pps_disp will eventually exceed
pps_dispmax and raise an alarm.

Initially, an approximate value for pps_ybar is not known, so
the duration of the calibration interval must be kept small to
avoid overflowing the tick. The time difference at the end of

the calibration interval is measured. If greater than a
fraction tick/4, the interval is reduced by half. If less than
this fraction for four successive calibration intervals, the
interval is doubled. This design automatically adapts to
nominal jitter in the PPS signal, as well as the value of tick.
The duration of the calibration interval is set by the
pps_shift variable as a shift in powers of two. The minimum
value PPS_SHIFT (2) is chosen so that with the highest CPU
oscillator frequency 1024 Hz and frequency tolerance 100 ppm
the tick will not overflow. The maximum value PPS_SHIFTMAX (8)
is chosen such that the maximum averaging time is about 1000 s
as determined by measurements of Allan variance [5].

Should the PPS signal fail, the current frequency estimate
pps_ybar continues to be used, so the nominal frequency remains
correct subject only to the instability of the undisciplined
oscillator. The procedure to save and restore the frequency
estimate works as follows. When setting the frequency from a
file, the time_freq value is set as the file value minus the
pps_ybar value; when retrieving the frequency, the two values
are added before saving in the file. This scheme provides a
seamless interface should the PPS signal fail or the kernel
configuration change. Note that the frequency discipline is
active whether or not the synchronization daemon is active.
Since all Unix systems take some time after reboot to build a
running system, usually by that time the discipline process has
already settled down and the initial transients due to
frequency discipline have damped out.

3.1.4. External Clock Interface

The external clock driver interface is implemented with two
routines, microtime(), which returns the current clock time,
and clock_set(), which furnishes the apparent system time
derived from the kernel time variable. The latter routine is
called only when the clock is set using the settimeofday()
system call, but can be called from within the driver, such as
when the year rolls over, for example.

In the stock SunOS kernel and modified Ultrix and OSF/1
kernels, the microtime() routine returns the kernel time
variable plus an interpolation between timer interrupts based
on the contents of a hardware counter. In the case of an
external clock, such as described above, the system clock is
read directly from the hardware clock registers. Examples of
external clock drivers are in the tprotime.c and hightime.c
routines included in the kernel.tar.Z distribution.

The external clock routines return a status code which
indicates whether the clock is operating correctly and the
nature of the problem, if not. The return code is interpreted
by the ntp_gettime() system call, which transitions the status
state machine to the TIME_ERR state if an error code is
returned. This is the only error checking implemented for the
external clock in the present version of the code.

The simulator has been used to check the PLL operation over the
design envelope of +-512 ms in time error and +-100 ppm in
frequency error. This confirms that no overflows occur and that
the loop initially converges in about 15 minutes for timer
interrupt rates from 50 Hz to 1024 Hz. The loop has a normal
overshoot of a few percent and a final convergence time of several
hours, depending on the initial time and frequency error.

3.2. Leap Seconds

It does not seem generally useful in the user application
interface to provide additional details private to the kernel and
synchronization protocol, such as stratum, reference identifier,
reference timestamp and so forth. It would in principle be
possible for the application to independently evaluate the quality
of time and project into the future how long this time might be
"valid." However, to do that properly would duplicate the
functionality of the synchronization protocol and require
knowledge of many mundane details of the platform architecture,
such as the subnet configuration, reachability status and related
variables. For the curious, the ntp_adjtime() system call can be
used to reveal some of these mysteries.

However, the user application may need to know whether a leap
second is scheduled, since this might affect interval calculations
spanning the event. A leap-warning condition is determined by the
synchronization protocol (if remotely synchronized), by the
timecode receiver (if available), or by the operator (if awake).
This condition is set by the synchronization daemon on the day the
leap second is to occur (30 June or 31 December, as announced) by
specifying in a ntp_adjtime() system call a clock status of either
TIME_DEL, if a second is to be deleted, or TIME_INS, if a second
is to be inserted. Note that, on all occasions since the inception
of the leap-second scheme, there has never been a deletion
occasion, nor is there likely to be one in future. If the value is
TIME_DEL, the kernel adds one second to the system time
immediately following second 23:59:58 and resets the clock status
to TIME_OK. If the value is TIME_INS, the kernel subtracts one
second from the system time immediately following second 23:59:59
and resets the clock status to TIME_OOP, in effect causing system

time to repeat second 59. Immediately following the repeated
second, the kernel resets the clock status to TIME_OK.

Depending upon the system call implementation, the reported time
during a leap second may repeat (with the TIME_OOP return code set
to advertise that fact) or be monotonically adjusted until system
time "catches up" to reported time. With the latter scheme the
reported time will be correct before and shortly after the leap
second (depending on the number of microtime() calls during the
leap second), but freeze or slowly advance during the leap second
itself. However, Most programs will probably use the ctime()
library routine to convert from timeval (seconds, microseconds)
format to tm format (seconds, minutes,...). If this routine is
modified to use the ntp_gettime() system call and inspect the
return code, it could simply report the leap second as second 60.

3.3. Clock Status State Machine

The various options possible with the system clock model described
in this memorandum require a careful examination of the state
transitions, status indications and recovery procedures should a
crucial signal or interface fail. In this section is presented a
prototype state machine designed to support leap second insertion
and deletion, as well as reveal various kinds of errors in the
synchronization process. The states of this machine are decoded as
follows:

TIME_OK If an external clock is present, it is working properly
and the system clock is derived from it. If no external
clock is present, the synchronization daemon is working
properly and the system clock is synchronized to a radio
clock or one or more peers.

TIME_INS An insertion of one second in the system clock has been
declared following the last second of the current day,
but has not yet been executed.

TIME_DEL A deletion of the last second of the current day has
been declared, but not yet executed.

TIME_OOP An insertion of one second in the system clock has been
declared following the last second of the current day.
The second is in progress, but not yet completed.
Library conversion routines should interpret this second
as 23:59:60.

TIME_BAD Either (a) the synchronization daemon has declared the
protocol is not working properly, (b) all sources of
outside synchronization have been lost or (c) an
external clock is present and it has just become
operational following a non-operational condition.

TIME_ERR An external clock is present, but is in a non-
operational condition.

In all except the TIME_ERR state the system clock is derived from
either an external clock, if present, or the kernel time variable,
if not. In the TIME_ERR state the external clock is present, but
not working properly, so the system clock may be derived from the
kernel time variable. The following diagram indicates the normal
transitions of the state machine. Not all valid transitions are
shown.

+--------+ +--------+ +--------+ +--------+

TIME_BAD---->TIME_OK <----TIME_OOP<----TIME_INS

+--------+ +--------+ +--------+ +--------+
A A


+--------+ +--------+

TIME_ERR TIME_DEL

+--------+ +--------+

The state machine makes a transition once each second at an
instant where the microseconds field of the kernel time variable
overflows and one second is added to the seconds field. However,
this condition is checked at each timer interrupt, which may not
exactly coincide with the actual instant of overflow. This may
lead to some interesting anomalies, such as a status indication of
a leap second in progress (TIME_OOP) when actually the leap second
had already expired.

The following state transitions are executed automatically by the
kernel:

any state -> TIME_ERR This transition occurs when an external
clock is present and an attempt is made to
read it when in a non-operational
condition.

TIME_INS -> TIME_OOP This transition occurs immediately
following second 86,400 of the current day
when an insert-second event has been
declared.

TIME_OOP -> TIME_OK This transition occurs immediately
following second 86,401 of the current
day; that is, one second after entry to
the TIME_OOP state.

TIME_DEL -> TIME_OK This transition occurs immediately
following second 86,399 of the current day
when a delete-second event has been
declared.

The following state transitions are executed by specific
ntp_adjtime() system calls:

TIME_OK -> TIME_INS This transition occurs as the result of a
ntp_adjtime() system call to declare an
insert-second event.

TIME_OK -> TIME_DEL This transition occurs as the result of a
ntp_adjtime() system call to declare a
delete-second event.

any state -> TIME_BAD This transition occurs as the result of a
ntp_adjtime() system call to declare loss
of all sources of synchronization or in
other cases of error.

The following table summarizes the actions just before, during and
just after a leap-second event. Each line in the table shows the
UTC and NTP times at the beginning of the second. The left column
shows the behavior when no leap event is to occur. In the middle
column the state machine is in TIME_INS at the end of UTC second
23:59:59 and the NTP time has just reached 400. The NTP time is
set back one second to 399 and the machine enters TIME_OOP. At the
end of the repeated second the machine enters TIME_OK and the UTC
and NTP times are again in correspondence. In the right column the
state machine is in TIME_DEL at the end of UTC second 23:59:58 and
the NTP time has just reached 399. The NTP time is incremented,
the machine enters TIME_OK and both UTC and NTP times are again in
correspondence.

No Leap Leap Insert Leap Delete
UTC NTP UTC NTP UTC NTP
---------------------------------------------
23:59:58398 23:59:58398 23:59:58398

23:59:59399 23:59:59399 00:00:00400

00:00:00400 23:59:60399 00:00:01401

00:00:01401 00:00:00400 00:00:02402

00:00:02402 00:00:01401 00:00:03403


To determine local midnight without fuss, the kernel code simply
finds the residue of the time.tv_sec (or time.tv_sec + 1) value
mod 86,400, but this requires a messy divide. Probably a better
way to do this is to initialize an auxiliary counter in the
settimeofday() routine using an ugly divide and increment the
counter at the same time the time.tv_sec is incremented in the
timer interrupt routine. For future embellishment.

4. Programming Model and Interfaces

This section describes the programming model for the synchronization
daemon and user application programs. The ideas are based on
suggestions from Jeff Mogul and Philip Gladstone and a similar
interface designed by the latter. It is important to point out that
the functionality of the original Unix adjtime() system call is
preserved, so that the modified kernel will work as the unmodified
one, should the new features not be in use. In this case the
ntp_adjtime() system call can still be used to read and write kernel
variables that might be used by a synchronization daemon other than
NTP, for example.

4.1. The ntp_gettime() System Call

The syntax and semantics of the ntp_gettime() call are given in
the following fragment of the timex.h header file. This file is
identical, except for the SHIFT_HZ define, in the SunOS, Ultrix
and OSF/1 kernel distributions. (The SHIFT_HZ define represents
the logarithm to the base 2 of the clock oscillator frequency
specific to each system type.) Note that the timex.h file calls
the syscall.h system header file, which must be modified to define
the SYS_ntp_gettime system call specific to each system type. The
kernel distributions include directions on how to do this.

/*
* This header file defines the Network Time Protocol (NTP)
* interfaces for user and daemon application programs. These are
* implemented using private system calls and data structures and
* require specific kernel support.
*
* NAME
* ntp_gettime - NTP user application interface
*
* SYNOPSIS
* #include <sys/timex.h>
*
* int system call(SYS_ntp_gettime, tptr)
*
* int SYS_ntp_gettime defined in syscall.h header file
* struct ntptimeval *tptr pointer to ntptimeval structure
*
* NTP user interface - used to read kernel clock values
* Note: maximum error = NTP synch distance = dispersion + delay /
* 2
* estimated error = NTP dispersion.
*/
struct ntptimeval {
struct timeval time; /* current time */
long maxerror; /* maximum error (us) */
long esterror; /* estimated error (us) */
};

The ntp_gettime() system call returns three values in the
ntptimeval structure: the current time in unix timeval format plus
the maximum and estimated errors in microseconds. While the 32-bit
long data type limits the error quantities to something more than
an hour, in practice this is not significant, since the protocol
itself will declare an unsynchronized condition well below that
limit. In the NTP Version 3 specification, if the protocol
computes either of these values in excess of 16 seconds, they are
clamped to that value and the system clock declared
unsynchronized.

Following is a detailed description of the ntptimeval structure
members.

struct timeval time; /* current time */

This member returns the current system time, expressed as a
Unix timeval structure. The timeval structure consists of two
32-bit words; the first returns the number of seconds past 1
January 1970, while the second returns the number of
microseconds.

long maxerror; /* maximum error (us) */

This member returns the time_maxerror kernel variable in
microseconds. See the entry for this variable in section 5 for
additional information.

long esterror; /* estimated error (us) */

This member returns the time_esterror kernel variable in
microseconds. See the entry for this variable in section 5 for
additional information.

4.2. The ntp_adjtime() System Call

The syntax and semantics of the ntp_adjtime() call are given in
the following fragment of the timex.h header file. Note that, as
in the ntp_gettime() system call, the syscall.h system header file
must be modified to define the SYS_ntp_adjtime system call
specific to each system type.

/*
* NAME
* ntp_adjtime - NTP daemon application interface
*
* SYNOPSIS
* #include <sys/timex.h>
*
* int system call(SYS_ntp_adjtime, mode, tptr)
*
* int SYS_ntp_adjtime defined in syscall.h header file
* struct timex *tptr pointer to timex structure
*
* NTP daemon interface - used to discipline kernel clock
* oscillator
*/
struct timex {
int mode; /* mode selector */
long offset; /* time offset (us) */
long frequency; /* frequency offset (scaled ppm) */
long maxerror; /* maximum error (us) */
long esterror; /* estimated error (us) */
int status; /* clock command/status */
long time_constant; /* pll time constant */
long precision; /* clock precision (us) (read only)
*/
long tolerance; /* clock frequency tolerance (scaled
* ppm) (read only) */
/*
* The following read-only structure members are implemented
* only if the PPS signal discipline is configured in the
* kernel.
*/
long ybar; /* frequency estimate (scaled ppm) */
long disp; /* dispersion estimate (scaled ppm)
*/
int shift; /* interval duration (s) (shift) */
long calcnt; /* calibration intervals */
long jitcnt; /* jitter limit exceeded */
long discnt; /* dispersion limit exceeded */
};

The ntp_adjtime() system call is used to read and write certain
time-related kernel variables summarized in this and subsequent
sections. Writing these variables can only be done in superuser
mode. To write a variable, the mode structure member is set with
one or more bits, one of which is assigned each of the following
variables in turn. The current values for all variables are
returned in any case; therefore, a mode argument of zero means to
return these values without changing anything.

Following is a description of the timex structure members.

int mode; /* mode selector */

This is a bit-coded variable selecting one or more structure
members, with one bit assigned each member. If a bit is set,
the value of the associated member variable is copied to the
corresponding kernel variable; if not, the member is ignored.
The bits are assigned as given in the following fragment of the
timex.h header file. Note that the precision and tolerance are
determined by the kernel and cannot be changed by
ntp_adjtime().

/*
* Mode codes (timex.mode)
*/
#define ADJ_OFFSET 0x0001 /* time offset */
#define ADJ_FREQUENCY 0x0002 /* frequency offset */
#define ADJ_MAXERROR 0x0004 /* maximum time error */
#define ADJ_ESTERROR 0x0008 /* estimated time error */
#define ADJ_STATUS 0x0010 /* clock status */
#define ADJ_TIMECONST 0x0020 /* pll time constant */

long offset; /* time offset (us) */

If selected, this member replaces the value of the time_offset
kernel variable in microseconds. The absolute value must be
less than MAXPHASE microseconds defined in the timex.h header
file. See the entry for this variable in section 5 for
additional information.

If within range and the PPS signal and/or external oscillator
are configured and operating properly, the clock status is
automatically set to TIME_OK.

long time_constant; /* pll time constant */

If selected, this member replaces the value of the
time_constant kernel variable. The value must be between zero
and MAXTC defined in the timex.h header file. See the entry for
this variable in section 5 for additional information.

long frequency; /* frequency offset (scaled ppm) */

If selected, this member replaces the value of the
time_frequency kernel variable. The value is in ppm, with the
integer part in the high order 16 bits and fraction in the low
order 16 bits. The absolute value must be in the range less
than MAXFREQ ppm defined in the timex.h header file. See the
entry for this variable in section 5 for additional
information.

long maxerror; /* maximum error (us) */

If selected, this member replaces the value of the
time_maxerror kernel variable in microseconds. See the entry
for this variable in section 5 for additional information.

long esterror; /* estimated error (us) */

If selected, this member replaces the value of the
time_esterror kernel variable in microseconds. See the entry
for this variable in section 5 for additional information.

int status; /* clock command/status */

If selected, this member replaces the value of the time_status
kernel variable. See the entry for this variable in section 5
for additional information.

In order to set this variable by ntp_adjtime(), either (a) the
current clock status must be TIME_OK or (b) the member value is
TIME_BAD; that is, the ntp_adjtime() call can always set the
clock to the unsynchronized state or, if the clock is running
correctly, can set it to any state. In any case, the
ntp_adjtime() call always returns the current state in this
member, so the caller can determine whether or not the request
succeeded.

long time_constant; /* pll time constant */

If selected, this member replaces the value of the
time_constant kernel variable. The value must be between zero
and MAXTC defined in the timex.h header file. See the entry for
this variable in section 5 for additional information.

long precision; /* clock precision (us) (read only) */

This member returns the time_precision kernel variable in
microseconds. The variable can be written only by the kernel.
See the entry for this variable in section 5 for additional
information.

long tolerance; /* clock frequency tolerance (scaled ppm)
*/

This member returns the time_tolerance kernel variable in
microseconds. The variable can be written only by the kernel.
See the entry for this variable in section 5 for additional
information.

long ybar; /* frequency estimate (scaled ppm) */

This member returns the pps_ybar kernel variable in
microseconds. The variable can be written only by the kernel.
See the entry for this variable in section 5 for additional
information.

long disp; /* dispersion estimate (scaled ppm) */

This member returns the pps_disp kernel variable in
microseconds. The variable can be written only by the kernel.
See the entry for this variable in section 5 for additional
information.

int shift; /* interval duration (s) (shift) */

This member returns the pps_shift kernel variable in
microseconds. The variable can be written only by the kernel.
See the entry for this variable in section 5 for additional
information.

long calcnt; /* calibration intervals */

This member returns the pps_calcnt kernel variable in
microseconds. The variable can be written only by the kernel.
See the entry for this variable in section 5 for additional
information.

long jitcnt; /* jitter limit exceeded */

This member returns the pps_jittcnt kernel variable in
microseconds. The variable can be written only by the kernel.
See the entry for this variable in section 5 for additional
information.

long discnt; /* dispersion limit exceeded */

This member returns the pps_discnt kernel variable in
microseconds. The variable can be written only by the kernel.
See the entry for this variable in section 5 for additional
information.

4.3. Command/Status Codes

The kernel routines use the system clock status variable
time_status, which records whether the clock is synchronized,
waiting for a leap second, etc. The value of this variable is
returned as the result code by both the ntp_gettime() and
ntp_adjtime() system calls. In addition, it can be explicitly read
and written using the ntp_adjtime() system call, but can be
written only in superuser mode. Values presently defined in the
timex.h header file are as follows:

/*
* Clock command/status codes (timex.status)
*/
#define TIME_OK 0 /* clock synchronized */
#define TIME_INS 1 /* insert leap second */
#define TIME_DEL 2 /* delete leap second */
#define TIME_OOP 3 /* leap second in progress */
#define TIME_BAD 4 /* kernel clock not synchronized */
#define TIME_ERR 5 /* external oscillator not
synchronized */

A detailed description of these codes as used by the leap-second
state machine is given later in this memorandum. In case of a
negative result code, the kernel has intercepted an invalid
address or (in case of the ntp_adjtime() system call), a superuser
violation.

5. Kernel Variables

This section contains a list of kernel variables and a detailed
description of their function, initial value, scaling and limits.

5.1. Interface Variables

The following variables are read and set by the ntp_adjtime()
system call. Additional automatic variables are used as
temporaries as described in the code fragments.

int time_status = TIME_BAD;

This variable controls the state machine used to insert or
delete leap seconds and show the status of the timekeeping
system, PPS signal and external oscillator, if configured.

long time_offset = 0;

This variable is used by the PLL to adjust the system time in
small increments. It is scaled by (1 << SHIFT_UPDATE) (12) in
microseconds. The maximum value that can be represented is
about +-512 ms and the minimum value or precision is a few
parts in 10^10 s.

long time_constant = 0; /* pll time constant */

This variable determines the bandwidth or "stiffness" of the
PLL. The value is used as a shift between zero and MAXTC (6),
with the effective PLL time constant equal to a multiple of (1
<< time_constant) in seconds. For room-temperature quartz
oscillator the recommended default value is 2, which
corresponds to a PLL time constant of about 900 s and a maximum
update interval of about 64 s. The maximum update interval
scales directly with the time constant, so that at the maximum
time constant of 6, the update interval can be as large as 1024
s.

Values of time_constant between zero and 2 can be used if quick
convergence is necessary; values between 2 and 6 can be used to
reduce network load, but at a modest cost in accuracy. Values
above 6 are appropriate only if an external oscillator is
present.

long time_tolerance = MAXFREQ; /* frequency tolerance (ppm) */

This variable represents the maximum frequency error or
tolerance in ppm of the particular CPU clock oscillator and is
a property of the architecture; however, in principle it could
change as result of the presence of external discipline
signals, for instance. It is expressed as a positive number
greater than zero in parts-per-million (ppm).

The recommended value of MAXFREQ is 200 ppm is appropriate for
room-temperature quartz oscillators used in typical
workstations. However, it can change due to the operating
condition of the PPS signal and/or external oscillator. With
either the PPS signal or external oscillator, the recommended
value for MAXFREQ is 100 ppm.

long time_precision = 1000000 / HZ; /* clock precision (us) */

This variable represents the maximum error in reading the
system clock in microseconds. It is usually based on the number
of microseconds between timer interrupts, 10000 us for the
SunOS kernel, 3906 us for the Ultrix kernel, 976 us for the
OSF/1 kernel. However, in cases where the time can be
interpolated between timer interrupts with microsecond
resolution, such as in the unmodified SunOS kernel and modified
Ultrix and OSF/1 kernels, the precision is specified as 1 us.
In cases where a PPS signal or external oscillator is
available, the precision can depend on the operating condition
of the signal or oscillator. This variable is determined by the
kernel for use by the synchronization daemon, but is otherwise
not used by the kernel.

long time_maxerror = MAXPHASE; /* maximum error */

This variable establishes the maximum error of the indicated
time relative to the primary synchronization source in
microseconds. For NTP, the value is initialized by a
ntp_adjtime() call to the synchronization distance, which is
equal to the root dispersion plus one-half the root delay. It
is increased by a small amount (time_tolerance) each second to
reflect the clock frequency tolerance. This variable is
computed by the synchronization daemon and the kernel, but is
otherwise not used by the kernel.

long time_esterror = MAXPHASE; /* estimated error */

This variable establishes the expected error of the indicated
time relative to the primary synchronization source in
microseconds. For NTP, the value is determined as the root
dispersion, which represents the best estimate of the actual
error of the system clock based on its past behavior, together
with observations of multiple clocks within the peer group.
This variable is computed by the synchronization daemon and
returned in system calls, but is otherwise not used by the
kernel.

5.2. Phase-Lock Loop Variables

The following variables establish the state of the PLL and the
residual time and frequency offset of the system clock. Additional
automatic variables are used as temporaries as described in the
code fragments.

long time_phase = 0; /* phase offset (scaled us) */

The time_phase variable represents the phase of the kernel time
variable at each tick of the clock. This variable is scaled by
(1 << SHIFT_SCALE) (23) in microseconds, giving a maximum
adjustment of about +-256 us/tick and a resolution less than
one part in 10^12.

long time_offset = 0; /* time offset (scaled us) */

The time_offset variable represents the time offset of the CPU
clock oscillator. It is recalculated as each update to the
system clock is received via the hardupdate() routine and at
each second in the seconds_overflow routine. This variable is
scaled by (1 << SHIFT_UPDATE) (12) in microseconds, giving a
maximum adjustment of about +-512 ms and a resolution of a few
parts in 10^10 s.

long time_freq = 0; /* frequency offset (scaled ppm) */

The time_freq variable represents the frequency offset of the
CPU clock oscillator. It is recalculated as each update to the
system clock is received via the hardupdate() routine. It can
also be set via ntp_adjtime() from a value stored in a file
when the synchronization daemon is first started. It can be
retrieved via ntp_adjtime() and written to the file about once
per hour by the daemon. The time_freq variable is scaled by (1
<< SHIFT_KF) (16) ppm, giving it a maximum value well in excess
of the limit of +-256 ppm imposed by other constraints. The
precision of this representation (frequency resolution) is
parts in 10^11, which is adequate for all but the best external
oscillators.

time_adj = 0; /* tick adjust (scaled 1 / HZ) */

The time_adj variable is the adjustment added to the value of
tick at each timer interrupt. It is computed once each second
from the time_offset, time_freq and, if the PPS signal is
present, the ps_ybar variable once each second.

long time_reftime = 0; /* time at last adjustment (s) */

This variable is the seconds portion of the system time on the
last update received by the hardupdate() routine. It is used to
compute the time_freq variable as the time since the last
update increases.

int fixtick = 1000000 % HZ; /* amortization factor */

In the Ultrix and OSF/1 kernels, the interval between timer
interrupts does not evenly divide the number of microseconds in
the second. In order that the clock runs at a precise rate, it
is necessary to introduce an amortization factor into the local
timescale. In the original Unix code, the value of fixtick is
amortized once each second, introducing an additional source of
jitter; in the new model the value is amortized at each tick of
the system clock, reducing the jitter by the reciprocal of the
clock oscillator frequency. This is not a new kernel variable,
but a new use of an existing kernel variable.

5.3. Pulse-per-second (PPS) Frequency-Lock Loop Variables

The following variables are used only if a pulse-per-second (PPS)
signal is available and connected via a modem-control lead, such
as produced by the optional ppsclock feature incorporated in the
serial port driver. They establish the design parameters of the
PPS frequency-lock loop used to discipline the CPU clock
oscillator to an external PPS signal. Additional automatic
variables are used as temporaries as described in the code
fragments.

long pps_usec; /* microseconds at last pps */

The pps_usec variable is latched from a high resolution counter
or external oscillator at each PPS interrupt. In determining
this value, only the hardware counter contents are used, not
the contents plus the kernel time variable, as returned by the
microtime() routine.

long pps_ybar = 0; /* pps frequency offset estimate */

The pps_ybar variable is the average CPU clock oscillator
frequency offset relative to the PPS disciplining signal. It is
scaled in the same units as the time_freq variable.

pps_disp = MAXFREQ; /* dispersion estimate (scaled ppm) */

The pps_disp variable represents the average sample dispersion
measured over the last three samples. It is scaled in the same
units as the time_freq variable.

pps_dispmax = MAXFREQ / 2; /* dispersion threshold */

The pps_dispmax variable is used as a dispersion threshold. If
pps_disp is less than this threshold, the median sample is used
to update the pps_ybar estimate; if not, the sample is
discarded.

pps_dispinc = MAXFREQ >> (PPS_SHIFT + 4); /* pps dispersion
increment/sec */

The pps_dispinc variable is the increment to add to pps_disp
once each second. It is computed such that, if no PPS samples
have arrived for several calibration intervals, the value of
pps_disp will exceed the pps_dispmax threshold and raise an
alarm.

int pps_mf[] = {0, 0, 0}; /* pps median filter */

The pps-mf[] array is used as a median filter to detect and
discard jitter in the PPS signal.

int pps_count = 0; /* pps calibrate interval counter */

The pps_count variable measures the length of the calibration
interval used to calculate the frequency. It normally counts
from zero to the value 1 << pps_shift.

pps_shift = PPS_SHIFT; /* interval duration (s) (shift) */

The pps_shift variable determines the duration of the
calibration interval, 1 << pps_shift s.

pps_intcnt = 0; /* intervals at current duration */

The pps_intcnt variable counts the number of calibration
intervals at the current interval duration. It is reset to zero
after four intervals and when the interval duration is changed.

long pps_calcnt = 0; /* calibration intervals */

The pps_calcnt variable counts the number of calibration
intervals.

long pps_jitcnt = 0; /* jitter limit exceeded */

The pps_jitcnt variable counts the number of resets due to
excessive jitter or frequency offset. These resets are
usually due to excessive noise in the PPS signal or
interface.

long pps_discnt = 0; /* dispersion limit exceeded */

The pps_discnt variable counts the number of calibration
intervals where the dispersion is above the pps_dispmax
limit. These resets are usually due to excessive frequency
wander in the PPS signal source.

5.4. External Oscillator Variables

The following variables are used only if an external oscillator
(HIGHBALL or TPRO) is present. Additional automatic variables are
used as temporaries as described in the code fragments.

int clock_count = 0; /* CPU clock counter */

The clock_count variable counts the seconds between adjustments
to the kernel time variable to discipline it to the external
clock.

struct timeval clock_offset; /* HIGHBALL clock offset */

The clock_offset variable defines the offset between system
time and the HIGHBALL counters.

long clock_cpu = 0; /* CPU clock adjust */

The clock_cpu variable contains the offset between the system
clock and the HIGHBALL clock for use in disciplining the kernel
time variable.

6. Architecture Constants

Following is a list of the important architecture constants that
establish the response and stability of the PLL and provide maximum
bounds on behavior in order to satisfy correctness assertions made in
the protocol specification. Additional definitions are given in the
timex.h header file.

6.1. Phase-lock loop (PLL) definitions

The following defines establish the performance envelope of the
PLL. They establish the maximum phase error (MAXPHASE), maximum
frequency error (MAXFREQ), minimum interval between updates
(MINSEC) and maximum interval between updates (MAXSEC). The intent
of these bounds is to force the PLL to operate within predefined
limits in order to satisfy correctness assertions of the
synchronization protocol. An excursion which exceeds these bounds
is clamped to the bound and operation proceeds normally. In
practice, this can occur only if something has failed or is
operating out of tolerance, but otherwise the PLL continues to
operate in a stable mode.

MAXPHASE must be set greater than or equal to CLOCK.MAX (128 ms),
as defined in the NTP specification. CLOCK.MAX establishes the
maximum time offset allowed before the system time is reset,

rather than incrementally adjusted. Here, the maximum offset is
clamped to MAXPHASE only in order to prevent overflow errors due
to defective programming.

MAXFREQ reflects the manufacturing frequency tolerance of the CPU
oscillator plus the maximum slew rate allowed by the protocol. It
should be set to at least the intrinsic frequency tolerance of the
oscillator plus 100 ppm for vernier frequency adjustments. If the
kernel frequency discipline code is installed (PPS_SYNC), the CPU
oscillator frequency is disciplined to an external source,
presumably with negligible frequency error.

#define MAXPHASE 512000 /* max phase error (us) */
#ifdef PPS_SYNC
#define MAXFREQ 100 /* max frequency error (ppm) */
#else
#define MAXFREQ 200 /* max frequency error (ppm) */
#endif /* PPS_SYNC */
#define MINSEC 16 /* min interval between updates (s)
*/
#define MAXSEC 1200 /* max interval between updates (s)
*/

6.2. Pulse-per-second (PPS) Frequency-lock Loop (FLL) Definitions

The following defines and declarations are used only if a pulse-
per-second (PPS) signal is available and connected via a modem-
control lead, such as produced by the optional ppsclock feature
incorporated in the serial port driver. They establish the design
parameters of the frequency-lock loop (FLL) used to discipline the
CPU clock oscillator to the PPS oscillator.

PPS_AVG is the averaging constant used to update the FLL from
frequency samples measured for each calibration interval.
PPS_SHIFT and PPS_SHIFTMAX are the minimum and maximem,
respectively, of the calibration interval represented as a power
of two. The PPS_DISPINC is the initial increment to pps_disp at
each second.

#define PPS_AVG 2 /* pps averaging constant (shift) */
#define PPS_SHIFT 2 /* min interval duration (s) (shift)
*/
#define PPS_SHIFTMAX 6 /* max interval duration (s) (shift)
*/
#define PPS_DISPINC 0 /* dispersion increment (us/s) */

6.3. External Oscillator Definitions

The following definitions and declarations are used only if an
external oscillator (HIGHBALL or TPRO) is configured on the
system.

#define CLOCK_INTERVAL 30 /* CPU clock update interval (s) */

7. References

[1] Mills, D., "Internet time synchronization: the Network Time
Protocol", IEEE Trans. Communications COM-39, 10 (October 1991),
1482- 1493. Also in: Yang, Z., and T.A. Marsland (Eds.). Global
States and Time in Distributed Systems, IEEE Press, Los Alamitos,
CA, 91-102.

[2] Mills, D., "Network Time Protocol (Version 3) specification,
implementation and analysis", RFC1305, University of Delaware,
March 1992, 113 pp.

[3] Mills, D., "Modelling and analysis of computer network clocks",
Electrical Engineering Department Report 92-5-2, University of
Delaware, May 1992, 29 pp.

[4] Mills, D., "Simple Network Time Protocol (SNTP)", RFC1361,
University of Delaware, August 1992, 10 pp.

[5] Mills, D., "Precision synchronizatin of computer network clocks",
Electrical Engineering Department Report 93-11-1, University of
Delaware, November 1993, 66 pp.

Security Considerations

Security issues are not discussed in this memo.

Author's Address

David L. Mills
Electrical Engineering Department
University of Delaware
Newark, DE 19716

Phone: (302) 831-8247
EMail: mills@udel.edu