source: rtems/doc/user/clock.t @ 94eb1bb

@c
@c  COPYRIGHT (c) 1988-2008
@c  On-Line Applications Research Corporation (OAR).
@c  All rights reserved.

@chapter Clock Manager

@cindex clock

@section Introduction

The clock manager provides support for time of day
and other time related capabilities.  The directives provided by
the clock manager are:

@itemize @bullet
@item @code{@value{DIRPREFIX}clock_set} - Set date and time
@item @code{@value{DIRPREFIX}clock_get} - Get date and time information
@item @code{@value{DIRPREFIX}clock_get_tod} - Get date and time in TOD format
@item @code{@value{DIRPREFIX}clock_get_tod_timeval} - Get date and time in timeval format
@item @code{@value{DIRPREFIX}clock_get_seconds_since_epoch} - Get seconds since epoch 
@item @code{@value{DIRPREFIX}clock_get_ticks_per_second} - Get ticks per second
@item @code{@value{DIRPREFIX}clock_get_ticks_since_boot} - Get ticks since boot
@item @code{@value{DIRPREFIX}clock_get_uptime} - Get time since boot
@item @code{@value{DIRPREFIX}clock_get_uptime_timeval} - Get time since boot in timeval format
@item @code{@value{DIRPREFIX}clock_get_uptime_seconds} - Get seconds since boot
@item @code{@value{DIRPREFIX}clock_set_nanoseconds_extension} - Install the nanoseconds since last tick handler
@item @code{@value{DIRPREFIX}clock_tick} - Announce a clock tick
@end itemize

@section Background

@subsection Required Support

For the features provided by the clock manager to be
utilized, periodic timer interrupts are required.  Therefore, a
real-time clock or hardware timer is necessary to create the
timer interrupts.  The @code{@value{DIRPREFIX}clock_tick}
directive is normally called
by the timer ISR to announce to RTEMS that a system clock tick
has occurred.  Elapsed time is measured in ticks.  A tick is
defined to be an integral number of microseconds which is
specified by the user in the Configuration Table.

@subsection Time and Date Data Structures

The clock facilities of the clock manager operate
upon calendar time.  These directives utilize the following date
and time @value{STRUCTURE} for the native time and date format:


@ifset is-C
@findex rtems_time_of_day
@example
struct rtems_tod_control @{
  uint32_t year;   /* greater than 1987 */
  uint32_t month;  /* 1 - 12 */
  uint32_t day;    /* 1 - 31 */
  uint32_t hour;   /* 0 - 23 */
  uint32_t minute; /* 0 - 59 */
  uint32_t second; /* 0 - 59 */
  uint32_t ticks;  /* elapsed between seconds */
@};

typedef struct rtems_tod_control rtems_time_of_day;
@end example
@end ifset

@ifset is-Ada
@example
type Time_Of_Day is
   record
      Year    : RTEMS.Unsigned32; -- year, A.D.
      Month   : RTEMS.Unsigned32; -- month, 1 .. 12
      Day     : RTEMS.Unsigned32; -- day, 1 .. 31
      Hour    : RTEMS.Unsigned32; -- hour, 0 .. 23
      Minute  : RTEMS.Unsigned32; -- minute, 0 .. 59
      Second  : RTEMS.Unsigned32; -- second, 0 .. 59
      Ticks   : RTEMS.Unsigned32; -- elapsed ticks between seconds
   end record;
@end example
@end ifset


The native date and time format is the only format
supported when setting the system date and time using the
@code{@value{DIRPREFIX}clock_set} directive.  Some applications
expect to operate on a "UNIX-style" date and time data structure.  The 
@code{@value{DIRPREFIX}clock_get_tod_timeval} always returns
the date and time in @code{struct timeval} format.  The 
@code{@value{DIRPREFIX}clock_get} directive can optionally return
the current date and time in this format.  

The @code{struct timeval} data structure has two fields: @code{tv_sec}
and @code{tv_usec} which are seconds and microseconds, respectively.
The @code{tv_sec} field in this data structure is the number of seconds
since the POSIX epoch of January 1, 1970 but will never be prior to
the RTEMS epoch of January 1, 1988.

@subsection Clock Tick and Timeslicing

@cindex timeslicing

Timeslicing is a task scheduling discipline in which
tasks of equal priority are executed for a specific period of
time before control of the CPU is passed to another task.  It is
also sometimes referred to as the automatic round-robin
scheduling algorithm.  The length of time allocated to each task
is known as the quantum or timeslice.

The system's timeslice is defined as an integral
number of ticks, and is specified in the Configuration Table.
The timeslice is defined for the entire system of tasks, but
timeslicing is enabled and disabled on a per task basis.

The @code{@value{DIRPREFIX}clock_tick}
directive implements timeslicing by
decrementing the running task's time-remaining counter when both
timeslicing and preemption are enabled.  If the task's timeslice
has expired, then that task will be preempted if there exists a
ready task of equal priority.

@subsection Delays

@cindex delays

A sleep timer allows a task to delay for a given
interval or up until a given time, and then wake and continue
execution.  This type of timer is created automatically by the
@code{@value{DIRPREFIX}task_wake_after}
and @code{@value{DIRPREFIX}task_wake_when} directives and, as a result,
does not have an RTEMS ID.  Once activated, a sleep timer cannot
be explicitly deleted.  Each task may activate one and only one
sleep timer at a time.

@subsection Timeouts

@cindex timeouts

Timeouts are a special type of timer automatically
created when the timeout option is used on the
@code{@value{DIRPREFIX}message_queue_receive},
@code{@value{DIRPREFIX}event_receive},
@code{@value{DIRPREFIX}semaphore_obtain} and
@code{@value{DIRPREFIX}region_get_segment} directives.  
Each task may have one and only one timeout active at a time.  
When a timeout expires, it unblocks the task with a timeout status code.

@section Operations

@subsection Announcing a Tick

RTEMS provides the @code{@value{DIRPREFIX}clock_tick} directive which is
called from the user's real-time clock ISR to inform RTEMS that
a tick has elapsed.  The tick frequency value, defined in
microseconds, is a configuration parameter found in the
Configuration Table.  RTEMS divides one million microseconds
(one second) by the number of microseconds per tick to determine
the number of calls to the
@code{@value{DIRPREFIX}clock_tick} directive per second.  The
frequency of @code{@value{DIRPREFIX}clock_tick}
calls determines the resolution
(granularity) for all time dependent RTEMS actions.  For
example, calling @code{@value{DIRPREFIX}clock_tick}
ten times per second yields a higher
resolution than calling @code{@value{DIRPREFIX}clock_tick}
two times per second.  The @code{@value{DIRPREFIX}clock_tick}
directive is responsible for maintaining both
calendar time and the dynamic set of timers.

@subsection Setting the Time

The @code{@value{DIRPREFIX}clock_set} directive allows a task or an ISR to
set the date and time maintained by RTEMS.  If setting the date
and time causes any outstanding timers to pass their deadline,
then the expired timers will be fired during the invocation of
the @code{@value{DIRPREFIX}clock_set} directive.

@subsection Obtaining the Time

The @code{@value{DIRPREFIX}clock_get} directive allows a task or an ISR to
obtain the current date and time or date and time related
information.  The current date and time can be returned in
either native or UNIX-style format.  Additionally, the
application can obtain date and time related information such as
the number of seconds since the RTEMS epoch, the number of ticks
since the executive was initialized, and the number of ticks per
second.  The information returned by the
@code{@value{DIRPREFIX}clock_get} directive is
dependent on the option selected by the caller.  This
is specified using one of the following constants
associated with the enumerated type
@code{@value{DIRPREFIX}clock_get_options}:

@findex rtems_clock_get_options 

@itemize @bullet
@item @code{@value{RPREFIX}CLOCK_GET_TOD} - obtain native style date and time

@item @code{@value{RPREFIX}CLOCK_GET_TIME_VALUE} - obtain UNIX-style
date and time

@item @code{@value{RPREFIX}CLOCK_GET_TICKS_SINCE_BOOT} - obtain number of ticks
since RTEMS was initialized

@item @code{@value{RPREFIX}CLOCK_GET_SECONDS_SINCE_EPOCH} - obtain number
of seconds since RTEMS epoch

@item @code{@value{RPREFIX}CLOCK_GET_TICKS_PER_SECOND} - obtain number of clock
ticks per second

@end itemize

Calendar time operations will return an error code if
invoked before the date and time have been set.

@section Directives

This section details the clock manager's directives.
A subsection is dedicated to each of this manager's directives
and describes the calling sequence, related constants, usage,
and status codes.

@c
@c
@c
@page
@subsection CLOCK_SET - Set date and time

@subheading CALLING SEQUENCE:

@cindex set the time of day

@ifset is-C
@findex rtems_clock_set
@example
rtems_status_code rtems_clock_set(
  rtems_time_of_day *time_buffer
);
@end example
@end ifset

@ifset is-Ada
@example
procedure Clock_Set (
   Time_Buffer : in     RTEMS.Time_Of_Day;
   Result      :    out RTEMS.Status_Codes
);
@end example
@end ifset

@subheading DIRECTIVE STATUS CODES:
@code{@value{RPREFIX}SUCCESSFUL} - date and time set successfully@*
@code{@value{RPREFIX}INVALID_ADDRESS} - @code{time_buffer} is NULL@*
@code{@value{RPREFIX}INVALID_CLOCK} - invalid time of day

@subheading DESCRIPTION:

This directive sets the system date and time.  The
date, time, and ticks in the time_buffer @value{STRUCTURE} are all
range-checked, and an error is returned if any one is out of its
valid range.

@subheading NOTES:

Years before 1988 are invalid.

The system date and time are based on the configured
tick rate (number of microseconds in a tick).

Setting the time forward may cause a higher priority
task, blocked waiting on a specific time, to be made ready.  In
this case, the calling task will be preempted after the next
clock tick.

Re-initializing RTEMS causes the system date and time
to be reset to an uninitialized state.  Another call to
@code{@value{DIRPREFIX}clock_set} is required to re-initialize
the system date and time to application specific specifications.

@c
@c
@c
@page
@subsection CLOCK_GET - Get date and time information

@cindex obtain the time of day

@subheading CALLING SEQUENCE:

@ifset is-C
@findex rtems_clock_get
@example
rtems_status_code rtems_clock_get(
  rtems_clock_get_options  option,
  void                    *time_buffer
);
@end example
@end ifset

@ifset is-Ada
@example
procedure Clock_Get (
   Option      : in     RTEMS.Clock_Get_Options;
   Time_Buffer : in     RTEMS.Address;
   Result      :    out RTEMS.Status_Codes
);
@end example
@end ifset

@subheading DIRECTIVE STATUS CODES:
@code{@value{RPREFIX}SUCCESSFUL} - current time obtained successfully@*
@code{@value{RPREFIX}NOT_DEFINED} - system date and time is not set@*
@code{@value{RPREFIX}INVALID_ADDRESS} - @code{time_buffer} is NULL

@subheading DESCRIPTION:

This directive obtains the system date and time.  If
the caller is attempting to obtain the date and time (i.e.
option is set to either @code{@value{RPREFIX}CLOCK_GET_SECONDS_SINCE_EPOCH},
@code{@value{RPREFIX}CLOCK_GET_TOD}, or
@code{@value{RPREFIX}CLOCK_GET_TIME_VALUE}) and the date and time
has not been set with a previous call to
@code{@value{DIRPREFIX}clock_set}, then the
@code{@value{RPREFIX}NOT_DEFINED} status code is returned. 
The caller can always obtain the number of ticks per second (option is
@code{@value{RPREFIX}CLOCK_GET_TICKS_PER_SECOND}) and the number of
ticks since the executive was initialized option is
@code{@value{RPREFIX}CLOCK_GET_TICKS_SINCE_BOOT}).

The @code{option} argument may taken on any value of the enumerated
type @code{rtems_clock_get_options}.  The data type expected for
@code{time_buffer} is based on the value of @code{option} as
indicated below:

@findex rtems_clock_get_options 
@ifset is-C
@itemize @bullet
@item @code{@value{RPREFIX}CLOCK_GET_TOD} - (rtems_time_of_day *)

@item @code{@value{RPREFIX}CLOCK_GET_SECONDS_SINCE_EPOCH} - (rtems_interval *)

@item @code{@value{RPREFIX}CLOCK_GET_TICKS_SINCE_BOOT} - (rtems_interval *)

@item @code{@value{RPREFIX}CLOCK_GET_TICKS_PER_SECOND} - (rtems_interval *)

@item @code{@value{RPREFIX}CLOCK_GET_TIME_VALUE} - (struct timeval *)

@end itemize
@end ifset

@ifset is-Ada
@itemize @bullet
@item @code{@value{RPREFIX}Clock_Get_TOD} - Address of an variable of
type RTEMS.Time_Of_Day

@item @code{@value{RPREFIX}Clock_Get_Seconds_Since_Epoch} - Address of an
variable of type RTEMS.Interval

@item @code{@value{RPREFIX}Clock_Get_Ticks_Since_Boot} - Address of an
variable of type RTEMS.Interval

@item @code{@value{RPREFIX}Clock_Get_Ticks_Per_Second} - Address of an
variable of type RTEMS.Interval

@item @code{@value{RPREFIX}Clock_Get_Time_Value} - Address of an variable of
type RTEMS.Clock_Time_Value

@end itemize
@end ifset

@subheading NOTES:

This directive is callable from an ISR.

This directive will not cause the running task to be
preempted.  Re-initializing RTEMS causes the system date and
time to be reset to an uninitialized state.  Another call to
@code{@value{DIRPREFIX}clock_set} is required to re-initialize the
system date and time to application specific specifications.

@c
@c
@c
@page
@subsection CLOCK_GET_TOD - Get date and time in TOD format

@cindex obtain the time of day

@subheading CALLING SEQUENCE:

@ifset is-C
@findex rtems_clock_get_tod
@example
rtems_status_code rtems_clock_get_tod(
  rtems_time_of_day *time_buffer
);
@end example
@end ifset

@ifset is-Ada
@example
procedure Clock_Get_TOD (
   Time_Buffer : in     RTEMS.Time_Of_Day;
   Result      :    out RTEMS.Status_Codes
);
@end example
@end ifset

@subheading DIRECTIVE STATUS CODES:
@code{@value{RPREFIX}SUCCESSFUL} - current time obtained successfully@*
@code{@value{RPREFIX}NOT_DEFINED} - system date and time is not set@*
@code{@value{RPREFIX}INVALID_ADDRESS} - @code{time_buffer} is NULL

@subheading DESCRIPTION:

This directive obtains the system date and time.  If the date and time
has not been set with a previous call to
@code{@value{DIRPREFIX}clock_set}, then the
@code{@value{RPREFIX}NOT_DEFINED} status code is returned. 

@subheading NOTES:

This directive is callable from an ISR.

This directive will not cause the running task to be
preempted.  Re-initializing RTEMS causes the system date and
time to be reset to an uninitialized state.  Another call to
@code{@value{DIRPREFIX}clock_set} is required to re-initialize the
system date and time to application specific specifications.

@c
@c
@c
@page
@subsection CLOCK_GET_TOD_TIMEVAL - Get date and time in timeval format

@cindex obtain the time of day

@subheading CALLING SEQUENCE:

@ifset is-C
@findex rtems_clock_get_tod_timeval
@example
rtems_status_code rtems_clock_get_tod(
  struct timeval  *time
);
@end example
@end ifset

@ifset is-Ada
@example
procedure Clock_Get_TOD_Timeval (
   Time   : in     RTEMS.Timeval;
   Result :    out RTEMS.Status_Codes
);
@end example
@end ifset

@subheading DIRECTIVE STATUS CODES:
@code{@value{RPREFIX}SUCCESSFUL} - current time obtained successfully@*
@code{@value{RPREFIX}NOT_DEFINED} - system date and time is not set@*
@code{@value{RPREFIX}INVALID_ADDRESS} - @code{time} is NULL

@subheading DESCRIPTION:

This directive obtains the system date and time in POSIX
@code{struct timeval} format.  If the date and time
has not been set with a previous call to
@code{@value{DIRPREFIX}clock_set}, then the
@code{@value{RPREFIX}NOT_DEFINED} status code is returned. 

@subheading NOTES:

This directive is callable from an ISR.

This directive will not cause the running task to be
preempted.  Re-initializing RTEMS causes the system date and
time to be reset to an uninitialized state.  Another call to
@code{@value{DIRPREFIX}clock_set} is required to re-initialize the
system date and time to application specific specifications.

@c
@c
@c
@page
@subsection CLOCK_GET_SECONDS_SINCE_EPOCH - Get seconds since epoch

@cindex obtain seconds since epoch

@subheading CALLING SEQUENCE:

@ifset is-C
@findex rtems_clock_get_seconds_since_epoch
@example
rtems_status_code rtems_clock_get_seconds_since_epoch(
  rtems_interval *the_interval
);
@end example
@end ifset

@ifset is-Ada
@example
procedure Clock_Get_Seconds_Since_Epoch(
   The_Interval :    out RTEMS.Interval;
   Result       :    out RTEMS.Status_Codes
);
@end example
@end ifset

@subheading DIRECTIVE STATUS CODES:
@code{@value{RPREFIX}SUCCESSFUL} - current time obtained successfully@*
@code{@value{RPREFIX}NOT_DEFINED} - system date and time is not set@*
@code{@value{RPREFIX}INVALID_ADDRESS} - @code{the_interval} is NULL

@subheading DESCRIPTION:

This directive returns the number of seconds since the RTEMS
epoch and the current system date and time.  If the date and time
has not been set with a previous call to
@code{@value{DIRPREFIX}clock_set}, then the
@code{@value{RPREFIX}NOT_DEFINED} status code is returned. 

@subheading NOTES:

This directive is callable from an ISR.

This directive will not cause the running task to be
preempted.  Re-initializing RTEMS causes the system date and
time to be reset to an uninitialized state.  Another call to
@code{@value{DIRPREFIX}clock_set} is required to re-initialize the
system date and time to application specific specifications.

@c
@c
@c
@page
@subsection CLOCK_GET_TICKS_PER_SECOND - Get ticks per second

@cindex obtain seconds since epoch

@subheading CALLING SEQUENCE:

@ifset is-C
@findex rtems_clock_get_ticks_per_second
@example
rtems_interval rtems_clock_get_ticks_per_second(void);
@end example
@end ifset

@ifset is-Ada
@example
function Clock_Get_Ticks_Per_Seconds
return RTEMS.Interval;
@end example
@end ifset

@subheading DIRECTIVE STATUS CODES:
NONE

@subheading DESCRIPTION:

This directive returns the number of clock ticks per second.  This
is strictly based upon the microseconds per clock tick that the
application has configured.

@subheading NOTES:

This directive is callable from an ISR.

This directive will not cause the running task to be
preempted.  Re-initializing RTEMS causes the system date and
time to be reset to an uninitialized state.  Another call to
@code{@value{DIRPREFIX}clock_set} is required to re-initialize the
system date and time to application specific specifications.

@c
@c
@c
@page
@subsection CLOCK_GET_TICKS_SINCE_BOOT - Get ticks since boot

@cindex obtain ticks since boot

@subheading CALLING SEQUENCE:

@ifset is-C
@findex rtems_clock_get_ticks_since_boot
@example
rtems_interval rtems_clock_get_ticks_since_boot(void);
@end example
@end ifset

@ifset is-Ada
@example
function Clock_Get_Ticks_Since_Boot
return RTEMS.Interval;
@end example
@end ifset

@subheading DIRECTIVE STATUS CODES:
NONE

@subheading DESCRIPTION:

This directive returns the number of clock ticks that have elapsed
since the system was booted.  This is the historical measure of uptime
in an RTEMS system.  The newer service
@code{@value{DIRPREFIX}clock_get_uptime} is another and potentially
more accurate way of obtaining similar information.

@subheading NOTES:

This directive is callable from an ISR.

This directive will not cause the running task to be
preempted.  Re-initializing RTEMS causes the system date and
time to be reset to an uninitialized state.  Another call to
@code{@value{DIRPREFIX}clock_set} is required to re-initialize the
system date and time to application specific specifications.

This directive simply returns the number of times the dirivective
@code{@value{DIRPREFIX}clock_tick} has been invoked since the 
system was booted.

@c
@c
@c
@page
@subsection CLOCK_GET_UPTIME - Get the time since boot

@cindex clock get uptime
@cindex uptime

@subheading CALLING SEQUENCE:

@ifset is-C
@findex rtems_clock_get_uptime
@example
rtems_status_code rtems_clock_get_uptime(
  struct timespec *uptime
);
@end example
@end ifset

@ifset is-Ada
@example
procedure Clock_Get_Uptime (
   Uptime :    out RTEMS.Timespec;
   Result :    out RTEMS.Status_Codes
);
@end example
@end ifset

@subheading DIRECTIVE STATUS CODES:
@code{@value{RPREFIX}SUCCESSFUL} - clock tick processed successfully@*
@code{@value{RPREFIX}INVALID_ADDRESS} - @code{time_buffer} is NULL

@subheading DESCRIPTION:

This directive returns the seconds and nanoseconds since the
system was booted.  If the BSP supports nanosecond clock
accuracy, the time reported will probably be different on every
call.

@subheading NOTES:

This directive may be called from an ISR.

@c
@c
@c
@page
@subsection CLOCK_GET_UPTIME_TIMEVAL - Get the time since boot in timeval format

@cindex clock get uptime
@cindex uptime

@subheading CALLING SEQUENCE:

@ifset is-C
@findex rtems_clock_get_uptime_timeval
@example
void rtems_clock_get_uptime_timeval(
  struct timeval *uptime
);
@end example
@end ifset

@subheading DIRECTIVE STATUS CODES:

NONE

@subheading DESCRIPTION:

This directive returns the seconds and microseconds since the
system was booted.  If the BSP supports nanosecond clock
accuracy, the time reported will probably be different on every
call.

@subheading NOTES:

This directive may be called from an ISR.

@c
@c
@c
@page
@subsection CLOCK_GET_UPTIME_SECONDS - Get the seconds since boot

@cindex clock get uptime
@cindex uptime

@subheading CALLING SEQUENCE:

@ifset is-C
@findex rtems_clock_get_uptime_seconds
@example
time_t rtems_clock_get_uptime_seconds(void);
@end example
@end ifset

@subheading DIRECTIVE STATUS CODES:

The system uptime in seconds.

@subheading DESCRIPTION:

This directive returns the seconds since the system was booted.

@subheading NOTES:

This directive may be called from an ISR.

@c
@c
@c
@page
@subsection CLOCK_SET_NANOSECONDS_EXTENSION - Install the nanoseconds since last tick handler

@cindex clock set nanoseconds extension
@cindex nanoseconds extension
@cindex nanoseconds time accuracy

@subheading CALLING SEQUENCE:

@ifset is-C
@findex rtems_clock_set_nanoseconds_extension
@example
rtems_status_code rtems_clock_set_nanoseconds_extension(
  rtems_nanoseconds_extension_routine routine
);
@end example
@end ifset

@ifset is-Ada
@example
NOT SUPPORTED FROM Ada BINDING
@end example
@end ifset

@subheading DIRECTIVE STATUS CODES:
@code{@value{RPREFIX}SUCCESSFUL} - clock tick processed successfully@*
@code{@value{RPREFIX}INVALID_ADDRESS} - @code{time_buffer} is NULL

@subheading DESCRIPTION:

This directive is used by the Clock device driver to install the 
@code{routine} which will be invoked by the internal RTEMS method used to
obtain a highly accurate time of day.  It is usually called during
the initialization of the driver.

When the @code{routine} is invoked, it will determine the number of
nanoseconds which have elapsed since the last invocation of
the @code{@value{DIRPREFIX}clock_tick} directive.  It should do
this as quickly as possible with as little impact as possible
on the device used as a clock source.

@subheading NOTES:

This directive may be called from an ISR.

This directive is called as part of every service to obtain the 
current date and time as well as timestamps.

@c
@c
@c
@page
@subsection CLOCK_TICK - Announce a clock tick

@cindex clock tick

@subheading CALLING SEQUENCE:

@ifset is-C
@findex rtems_clock_tick
@example
rtems_status_code rtems_clock_tick( void );
@end example
@end ifset

@ifset is-Ada
@example
procedure Clock_Tick (
   Result :    out RTEMS.Status_Codes
);
@end example
@end ifset

@subheading DIRECTIVE STATUS CODES:
@code{@value{RPREFIX}SUCCESSFUL} - clock tick processed successfully

@subheading DESCRIPTION:

This directive announces to RTEMS that a system clock
tick has occurred.  The directive is usually called from the
timer interrupt ISR of the local processor.  This directive
maintains the system date and time, decrements timers for
delayed tasks, timeouts, rate monotonic periods, and implements
timeslicing.

@subheading NOTES:

This directive is typically called from an ISR.

The @code{microseconds_per_tick} and @code{ticks_per_timeslice}
parameters in the Configuration Table contain the number of
microseconds per tick and number of ticks per timeslice,
respectively.