Update docs.

[pintos-anon] / doc / threads.texi

@node Project 1--Threads, Project 2--User Programs, Introduction, Top
@chapter Project 1: Threads

In this assignment, we give you a minimally functional thread system.
Your job is to extend the functionality of this system to gain a
better understanding of synchronization problems. Additionally, you
will use at least part of this increased functionality in future
assignments.

You will be working in primarily in the @file{threads} directory for
this assignment, with some work in the @file{devices} directory on the
side.  Compilation should be done in the @file{threads} directory.

@menu
* Understanding Threads::       
* Project 1 Code::              
* Debugging versus Testing::    
* Tips::                        
* Problem 1-1 Alarm Clock::     
* Problem 1-2 Join::            
* Problem 1-3 Priority Scheduling::  
* Problem 1-4 Advanced Scheduler::  
* Threads FAQ::                 
@end menu

@node Understanding Threads
@section Understanding Threads

The first step is to read and understand the initial thread system.
Pintos, by default, implements thread creation and thread completion,
a simple scheduler to switch between threads, and synchronization
primitives (semaphores, locks, and condition variables). 

However, there's a lot of magic going on in some of this code, so if
you haven't already compiled and run the base system, as described in
the introduction (@pxref{Introduction}), you should do so now.  You
can read through parts of the source code by hand to see what's going
on.  If you like, you can add calls to @code{printf()} almost
anywhere, then recompile and run to see what happens and in what
order.  You can also run the kernel in a debugger and set breakpoints
at interesting spots, single-step through code and examine data, and
so on.  @xref{i386-elf-gdb}, for more information.

When a thread is created, you are creating a new context to be
scheduled. You provide a function to be run in this context as an
argument to @code{thread_create()}. The first time the thread is
scheduled and runs, it will start from the beginning of that function
and execute it in the context. When that function returns, that thread
completes. Each thread, therefore, acts like a mini-program running
inside Pintos, with the function passed to @code{thread_create()}
acting like @code{main()}.

At any given time, Pintos is running exactly one thread, with the
others switched out.  The scheduler decides which thread to run next
when it needs to switch between them.  (If no thread is ready to run
at any given time, then the special ``idle'' thread runs.)  The
synchronization primitives are used to force context switches when one
thread needs to wait for another thread to do something.

The exact mechanics of a context switch are pretty gruesome and have
been provided for you in @file{threads/switch.S} (this is 80@var{x}86
assembly; don't worry about understanding it).  It involves saving the
state of the currently running thread and restoring the state of the
thread we're switching to.

Using the @command{gdb} debugger, slowly trace through a context
switch to see what happens (@pxref{i386-elf-gdb}).  You can set a
breakpoint on the @code{schedule()} function to start out, and then
single-step from there.  Be sure to keep track of each thread's
address and state, and what procedures are on the call stack for each
thread.  You will notice that when one thread calls
@code{switch_threads()}, another thread starts running, and the first
thing the new thread does is to return from
@code{switch_threads()}.  We realize this comment will seem cryptic to
you at this point, but you will understand threads once you understand
why the @code{switch_threads()} that gets called is different from the
@code{switch_threads()} that returns.  @c FIXME

@strong{Warning}: In Pintos, each thread is assigned a small,
fixed-size execution stack just under @w{4 kB} in size.  The kernel
does try to detect stack overflow, but it cannot always succeed.  You
ma cause bizarre problems, such as mysterious kernel panics, if you
declare large data structures as non-static local variables,
e.g. @samp{int buf[1000];}.  Alternatives to stack allocation include
the page allocator in @file{threads/palloc.c} and the block allocator
in @file{threads/malloc.c}.  Note that the page allocator doles out
@w{4 kB} chunks and that @code{malloc()} has a @w{2 kB} block size
limit.  If you need larger chunks, consider using a linked structure
instead.

@node Project 1 Code
@section Code

Here is a brief overview of the files in the @file{threads}
directory.  You will not need to modify most of this code, but the
hope is that presenting this overview will give you a start on what
code to look at.

@table @file
@item loader.S
@itemx loader.h
The kernel loader.  Assembles to 512 bytes of code and data that the
PC BIOS loads into memory and which in turn loads the kernel into
memory, does basic processor initialization, and jumps to the
beginning of the kernel.  You should not need to look at this code or
modify it.

@item kernel.lds.S
The linker script used to link the kernel.  Sets the load address of
the kernel and arranges for @file{start.S} to be at the very beginning
of the kernel image.  Again, you should not need to look at this code
or modify it, but it's here in case you're curious.

@item start.S
Jumps to @code{main()}.

@item init.c
@itemx init.h
Kernel initialization, including @code{main()}, the kernel's ``main
program.''  You should look over @code{main()} at least to see what
gets initialized.

@item thread.c
@itemx thread.h
Basic thread support.  Much of your work will take place in these
files.  @file{thread.h} defines @code{struct thread}, which you will
modify in the first three projects.

@item switch.S
@itemx switch.h
Assembly language routine for switching threads.  Already discussed
above.

@item palloc.c
@itemx palloc.h
Page allocator, which hands out system memory one 4 kB page at a time.

@item malloc.c
@itemx malloc.h
A very simple implementation of @code{malloc()} and @code{free()} for
the kernel.  The largest block that can be allocated is 2 kB.

@item interrupt.c
@itemx interrupt.h
Basic interrupt handling and functions for turning interrupts on and
off.

@item intr-stubs.pl
@itemx intr-stubs.h
A Perl program that outputs assembly for low-level interrupt handling.

@item synch.c
@itemx synch.h
Basic synchronization primitives: semaphores, locks, and condition
variables.  You will need to use these for synchronization through all
four projects.

@item test.c
@itemx test.h
Test code.  For project 1, you will replace this file with your test
cases.

@item io.h
Functions for I/O port access.  This is mostly used by source code in
the @file{devices} directory that you won't have to touch.

@item mmu.h
Functions and macros related to memory management, including page
directories and page tables.  This will be more important to you in
project 3.  For now, you can ignore it.
@end table

FIXME devices and lib directories?

@node Debugging versus Testing
@section Debugging versus Testing

When you're debugging code, it's useful to be able to be able to run a
program twice and have it do exactly the same thing.  On second and
later runs, you can make new observations without having to discard or
verify your old observations.  This property is called
``reproducibility.''  The simulator we use, Bochs, can be set up for
reproducibility.  If you use the Bochs configuration files we provide,
which specify @samp{ips: @var{n}} where @var{n} is a number of
simulated instructions per second, your simulations can be
reproducible.

Of course, a simulation can only be reproducible from one run to the
next if its input is the same each time.  For simulating an entire
computer, as we do, this means that every part of the computer must be
the same.  For example, you must use the same disks, the same version
of Bochs, and you must not hit any keys on the keyboard (because you
could not be sure to hit them at exactly the same point each time)
during the runs.

While reproducibility is useful for debugging, it is a problem for
testing thread synchronization, an important part of this project.  In
particular, when Bochs is set up for reproducibility, timer interrupts
will come at perfectly reproducible points, and therefore so will
thread switches.  That means that running the same test several times
doesn't give you any greater confidence in your code's correctness
than does running it only once.

So, to make your code easier to test, we've added a feature to Bochs
that makes timer interrupts come at random intervals, but in a
perfectly predictable way.  In particular, if you invoke
@command{pintos} with the option @option{-j @var{seed}}, timer
interrupts will come at irregularly spaced intervals.  Within a single
@var{seed} value, execution will still be reproducible, but timer
behavior will change as @var{seed} is varied.  Thus, for the highest
degree of confidence you should test your code with many seed values.

@node Tips
@section Tips

There should be no busy-waiting in any of your solutions to this
assignment.  Furthermore, resist the temptation to directly disable
interrupts in your solution by calling @code{intr_disable()} or
@code{intr_set_level()}, although you may find doing so to be useful
while debugging.  Instead, use semaphores, locks and condition
variables to solve synchronization problems.  Hint: read the comments
in @file{threads/synch.h} if you're unsure what synchronization
primitives may be used in what situations.

Given some designs of some problems, there may be one or two instances
in which it is appropriate to directly change the interrupt levels
instead of relying on the given synchroniztion primitives.  This must
be justified in your @file{DESIGNDOC} file.  If you're not sure you're
justified, ask!

While all parts of this assignment are required if you intend to earn
full credit on this project, keep in mind that Problem 1-2 (Join) will
be needed for future assignments, so you'll want to get this one
right.  We don't give out solutions, so you're stuck with your Join
code for the whole quarter.  Problem 1-1 (Alarm Clock) could be very
handy, but not strictly required in the future.  The upshot of all
this is that you should focus heavily on making sure that your
implementation of @code{thread_join()} works correctly, since if it's
broken, you will need to fix it for future assignments.  The other
parts can be turned off in the future if you find you can't make them
work quite right.

Also keep in mind that Problem 1-4 (the MLFQS) builds on the features you
implement in Problem 1-3, so to avoid unnecessary code duplication, it
would be a good idea to divide up the work among your team members
such that you have Problem 1-3 fully working before you begin to tackle
Problem 1-4.

@node Problem 1-1 Alarm Clock
@section Problem 1-1: Alarm Clock

Improve the implementation of the timer device defined in
@file{devices/timer.c} by reimplementing @code{timer_sleep()}.
Threads call @code{timer_sleep(@var{x})} to suspend execution until
time has advanced by at least @w{@var{x} timer ticks}.  This is
useful for threads that operate in real-time, for example, for
blinking the cursor once per second.  There is no requirement that
threads start running immediately after waking up; just put them on
the ready queue after they have waited for approximately the right
amount of time.

A working implementation of this function is provided.  However, the
version provided is poor, because it ``busy waits,'' that is, it spins
in a tight loop checking the current time until the current time has
advanced far enough.  This is undesirable because it wastes time that
could potentially be used more profitably by another thread.  Your
solution should not busy wait.

The argument to @code{timer_sleep()} is expressed in timer ticks, not
in milliseconds or some other unit.

@node Problem 1-2 Join
@section Problem 1-2: Join

Implement @code{thread_join(tid_t)} in @file{threads/thread.c}.  There
is already a prototype for it in @file{threads/thread.h}, which you
should not change.  This function causes the currently running thread
to block until the thread whose thread id is passed as an argument
exits.  If A is the running thread and B is the argument, then we say
that ``A joins B'' in this case.

Incidentally, we don't use @code{struct thread *} as
@file{thread_join()}'s parameter type because a thread pointer is not
unique over time.  That is, when a thread dies, its memory may be,
whether immediately or much later, reused for another thread.  If
thread A over time had two children B and C that were stored at the
same address, then @code{thread_join(@r{B})} and
@code{thread_join(@r{C})} would be ambiguous.  Introducing a thread id
or @dfn{tid}, represented by type @code{tid_t}, that is intentionally
unique over time solves the problem.  The provided code uses an
@code{int} for @code{tid_t}, but you may decide you prefer to use some
other type.

The model for @code{thread_join()} is the @command{wait} system call
in Unix-like systems.  (Try reading the manpages.)  That system call
can only be used by a parent process to wait for a child's death.  You
should implement @code{thread_join()} to have the same restriction.
That is, a thread may only join its immediate children.

A thread need not ever be joined.  Your solution should properly free
all of a thread's resources, including its @code{struct thread},
whether it is ever joined or not, and regardless of whether the child
exits before or after its parent.  That is, a thread should be freed
exactly once in all cases.

Joining a given thread is idempotent.  That is, joining a thread T
multiple times is equivalent to joining it once, because T has already
exited at the time of the later joins.  Thus, joins on T after the
first should return immediately.

Calling @code{thread_join()} on an thread that is not the caller's
child should cause the caller to return immediately.

Consider all the ways a join can occur: nested joins (A joins B when B
is joined on C), multiple joins (A joins B, then A joins C), and so
on.  Does your join work if @code{thread_join()} is called on a thread
that has not yet been scheduled for the first time?  You should handle
all of these cases.  Write test code that demonstrates the cases your
join works for.  Don't overdo the output volume, please!

Be careful to program this function correctly.  You will need its
functionality for project 2.

Once you've implemented @code{thread_join()}, define
@code{THREAD_JOIN_IMPLEMENTED} in @file{constants.h}.
@xref{Conditional Compilation}, for more information.

@node Problem 1-3 Priority Scheduling
@section Problem 1-3: Priority Scheduling

Implement priority scheduling in Pintos.  Priority scheduling is a key
building block for real-time systems.  Implement functions
@code{thread_set_priority()} to set the priority of the running thread
and @code{thread_get_priority()} to get the running thread's priority.
(A thread can examine and modify only its own priority.)  There are
already prototypes for these functions in @file{threads/thread.h},
which you should not change.

Thread priority ranges from @code{PRI_MIN} (0) to @code{PRI_MAX} (59).
The initial thread priority is passed as an argument to
@code{thread_create()}.  If there's no reason to choose another
priority, use @code{PRI_DEFAULT} (29).  The @code{PRI_} macros are
defined in @file{threads/thread.h}, and you should not change their
values.

When a thread is added to the ready list that has a higher priority
than the currently running thread, the current thread should
immediately yield the processor to the new thread.  Similarly, when
threads are waiting for a lock, semaphore or condition variable, the
highest priority waiting thread should be woken up first.  A thread's
priority may be set at any time, including while the thread is waiting
on a lock, semaphore, or condition variable.

One issue with priority scheduling is ``priority inversion'': if a
high priority thread needs to wait for a low priority thread (for
instance, for a lock held by a low priority thread, or in
@code{thread_join()} for a thread to complete), and a middle priority
thread is on the ready list, then the high priority thread will never
get the CPU because the low priority thread will not get any CPU time.
A partial fix for this problem is to have the waiting thread
``donate'' its priority to the low priority thread while it is holding
the lock, then recall the donation once it has acquired the lock.
Implement this fix.

You will need to account for all different orders that priority
donation and inversion can occur.  Be sure to handle multiple
donations, in which multiple priorities are donated to a thread.  You
must also handle nested donation: given high, medium, and low priority
threads H, M, and L, respectively, if H is waiting on a lock that M
holds and M is waiting on a lock that L holds, then both M and L
should be boosted to H's priority.

You only need to implement priority donation when a thread is waiting
for a lock held by a lower-priority thread.  You do not need to
implement this fix for semaphores, condition variables or joins.
However, you do need to implement priority scheduling in all cases.

@node Problem 1-4 Advanced Scheduler
@section Problem 1-4: Advanced Scheduler

Implement Solaris's multilevel feedback queue scheduler (MLFQS) to
reduce the average response time for running jobs on your system.
@xref{Multilevel Feedback Scheduling}, for a detailed description of
the MLFQS requirements.

Demonstrate that your scheduling algorithm reduces response time
relative to the original Pintos scheduling algorithm (round robin) for
at least one workload of your own design (i.e.@: in addition to the
provided test).

You may assume a static priority for this problem. It is not necessary
to ``re-donate'' a thread's priority if it changes (although you are
free to do so).

You must write your code so that we can turn the MLFQS on and off at
compile time.  By default, it must be off, but we must be able to turn
it on by inserting the line @code{#define MLFQS 1} in
@file{constants.h}.  @xref{Conditional Compilation}, for details.

@node Threads FAQ
@section FAQ

@enumerate 1
@item General FAQs

@enumerate 1
@item
@b{I am adding a new @file{.h} or @file{.c} file.  How do I fix the
@file{Makefile}s?}@anchor{Adding c or h Files}

To add a @file{.c} file, edit the top-level @file{Makefile.build}.
You'll want to add your file to variable @samp{@var{dir}_SRC}, where
@var{dir} is the directory where you added the file.  For this
project, that means you should add it to @code{threads_SRC}, or
possibly @code{devices_SRC} if you put in the @file{devices}
directory.  Then run @code{make}.  If your new file doesn't get
compiled, run @code{make clean} and then try again.

When you modify the top-level @file{Makefile.build}, the modified
version should be automatically copied to
@file{threads/build/Makefile} when you re-run make.  The opposite is
not true, so any changes will be lost the next time you run @code{make
clean} from the @file{threads} directory.  Therefore, you should
prefer to edit @file{Makefile.build} (unless your changes are meant to
be truly temporary).

There is no need to edit the @file{Makefile}s to add a @file{.h} file.

@item
@b{How do I write my test cases?}

Test cases should be replacements for the existing @file{test.c}
file.  Put them in a @file{threads/testcases} directory.
@xref{TESTCASE}, for more information.

@item
@b{Why can't I disable interrupts?}

Turning off interrupts should only be done for short amounts of time,
or else you end up losing important things such as disk or input
events.  Turning off interrupts also increases the interrupt handling
latency, which can make a machine feel sluggish if taken too far.
Therefore, in general, setting the interrupt level should be used
sparingly.  Also, any synchronization problem can be easily solved by
turning interrupts off, since while interrupts are off, there is no
concurrency, so there's no possibility for race condition.

To make sure you understand concurrency well, we are discouraging you
from taking this shortcut at all in your solution.  If you are unable
to solve a particular synchronization problem with semaphores, locks,
or conditions, or think that they are inadequate for a particular
reason, you may turn to disabling interrupts.  If you want to do this,
we require in your design document a complete justification and
scenario (i.e.@: exact sequence of events) to show why interrupt
manipulation is the best solution.  If you are unsure, the TAs can
help you determine if you are using interrupts too haphazardly.  We
want to emphasize that there are only limited cases where this is
appropriate.

You might find @file{devices/intq.h} and its users to be an
inspiration or source of rationale.

@item
@b{Where might interrupt-level manipulation be appropriate?}

You might find it necessary in some solutions to the Alarm problem.

You might want it at one small point for the priority scheduling
problem.  Note that it is not required to use interrupts for these
problems.  There are other, equally correct solutions that do not
require interrupt manipulation.  However, if you do manipulate
interrupts and @strong{correctly and fully document it} in your design
document, we will allow limited use of interrupt disabling.

@item
@b{What does ``warning: no previous prototype for `@var{function}''
mean?}

It means that you defined a non-@code{static} function without
preceding it by a prototype.  Because non-@code{static} functions are
intended for use by other @file{.c} files, for safety they should be
prototyped in a header file included before their definition.  To fix
the problem, add a prototype in a header file that you include, or, if
the function isn't actually used by other @file{.c} files, make it
@code{static}.
@end enumerate

@item Alarm Clock FAQs

@enumerate 1
@item
@b{Why can't I use most synchronization primitives in an interrupt
handler?}

As you've discovered, you cannot sleep in an external interrupt
handler.  Since many lock, semaphore, and condition variable functions
attempt to sleep, you won't be able to call those in
@code{timer_interrupt()}.  You may still use those that never sleep.

Having said that, you need to make sure that global data does not get
updated by multiple threads simultaneously executing
@code{timer_sleep()}.  Here are some pieces of information to think
about:

@enumerate a
@item
Interrupts are turned off while @code{timer_interrupt()} runs.  This
means that @code{timer_interrupt()} will not be interrupted by a
thread running in @code{timer_sleep()}.

@item
A thread in @code{timer_sleep()}, however, can be interrupted by a
call to @code{timer_interrupt()}, except when that thread has turned
off interrupts.

@item
Examples of synchronization mechanisms have been presented in lecture.
Going over these examples should help you understand when each type is
useful or needed.
@end enumerate

@item
@b{What about timer overflow due to the fact that times are defined as
integers? Do I need to check for that?}

Don't worry about the possibility of timer values overflowing.  Timer
values are expressed as signed 63-bit numbers, which at 100 ticks per
second should be good for almost 2,924,712,087 years.
@end enumerate

@item Join FAQs

@enumerate 1
@item
@b{Am I correct to assume that once a thread is deleted, it is no
longer accessible by the parent (i.e.@: the parent can't call
@code{thread_join(child)})?}

A parent joining a child that has completed should be handled
gracefully and should act as a no-op.
@end enumerate

@item Priority Scheduling FAQs

@enumerate 1
@item
@b{Doesn't the priority scheduling lead to starvation? Or do I have to
implement some sort of aging?}

It is true that strict priority scheduling can lead to starvation
because thread may not run if a higher-priority thread is runnable.
In this problem, don't worry about starvation or any sort of aging
technique.  Problem 4 will introduce a mechanism for dynamically
changing thread priorities.

This sort of scheduling is valuable in real-time systems because it
offers the programmer more control over which jobs get processing
time.  High priorities are generally reserved for time-critical
tasks. It's not ``fair,'' but it addresses other concerns not
applicable to a general-purpose operating system.

@item
@b{After a lock has been released, does the program need to switch to
the highest priority thread that needs the lock (assuming that its
priority is higher than that of the current thread)?}

When a lock is released, the highest priority thread waiting for that
lock should be unblocked and put on the ready to run list.  The
scheduler should then run the highest priority thread on the ready
list.

@item
@b{If a thread calls @code{thread_yield()} and then it turns out that
it has higher priority than any other threads, does the high-priority
thread continue running?}

Yes.  If there is a single highest-priority thread, it continues
running until it blocks or finishes, even if it calls
@code{thread_yield()}.

@item
@b{If the highest priority thread is added to the ready to run list it
should start execution immediately.  Is it immediate enough if I
wait until next timer interrupt occurs?}

The highest priority thread should run as soon as it is runnable,
preempting whatever thread is currently running.

@item
@b{What happens to the priority of the donating thread?  Do the priorities
get swapped?}

No.  Priority donation only changes the priority of the low-priority
thread.  The donating thread's priority stays unchanged.  Also note
that priorities aren't additive: if thread A (with priority 5) donates
to thread B (with priority 3), then B's new priority is 5, not 8.

@item 
@b{Can a thread's priority be changed while it is sitting on the ready
queue?}

Yes.  Consider this case: low-priority thread L currently has a lock
that high-priority thread H wants.  H donates its priority to L (the
lock holder).  L finishes with the lock, and then loses the CPU and is
moved to the ready queue.  Now L's old priority is restored while it
is in the ready queue.

@item
@b{Can a thread's priority change while it is sitting on the queue of a
semaphore?}

Yes.  Same scenario as above except L gets blocked waiting on a new
lock when H restores its priority.

@item
@b{Why is pubtest3's FIFO test skipping some threads! I know my scheduler
is round-robin'ing them like it's supposed to!  Our output is like this:}

@example
Thread 0 goes.
Thread 2 goes.
Thread 3 goes.
Thread 4 goes.
Thread 0 goes.
Thread 1 goes.
Thread 2 goes.
Thread 3 goes.
Thread 4 goes.
@end example

@noindent @b{which repeats 5 times and then}

@example
Thread 1 goes.
Thread 1 goes.
Thread 1 goes.
Thread 1 goes.
Thread 1 goes.
@end example

This happens because context switches are being invoked by the test
when it explicitly calls @code{thread_yield()}.  However, the time
slice timer is still alive and so, every tick (by default), thread 1
gets switched out (caused by @code{timer_interrupt()} calling
@code{intr_yield_on_return()}) before it gets a chance to run its
mainline.  It is by coincidence that Thread 1 is the one that gets
skipped in our example.  If we use a different jitter value, the same
behavior is seen where a thread gets started and switched out
completely.

Solution: Increase the value of @code{TIME_SLICE} in
@file{devices/timer.c} to a very high value, such as 10000, to see
that the threads will round-robin if they aren't interrupted.

@item
@b{What happens when a thread is added to the ready list which has
higher priority than the currently running thread?}

The correct behavior is to immediately yield the processor.  Your
solution must act this way.

@item
@b{What should @code{thread_get_priority()} return in a thread while
its priority has been increased by a donation?}

The higher (donated) priority.
@end enumerate

@item Advanced Scheduler FAQs

@enumerate 1
@item
@b{What is the interval between timer interrupts?}

Timer interrupts occur @code{TIMER_FREQ} times per second.  You can
adjust this value by editing @file{devices/timer.h}.  The default is
100 Hz.

You can also adjust the number of timer ticks per time slice by
modifying @code{TIME_SLICE} in @file{devices/timer.c}.

@item
@b{Do I have to modify the dispatch table?}

No, although you are allowed to. It is possible to complete
this problem (i.e.@: demonstrate response time improvement)
without doing so.

@item
@b{When the scheduler changes the priority of a thread, how does this
affect priority donation?}

Short (official) answer: Don't worry about it. Your priority donation
code may assume static priority assignment.

Longer (unofficial) opinion: If you wish to take this into account,
however, your design may end up being ``cleaner.''  You have
considerable freedom in what actually takes place. I believe what
makes the most sense is for scheduler changes to affect the
``original'' (non-donated) priority.  This change may actually be
masked by the donated priority.  Priority changes should only
propagate with donations, not ``backwards'' from donees to donors.

@item
@b{What is meant by ``static priority''?}

Once thread A has donated its priority to thread B, if thread A's
priority changes (due to the scheduler) while the donation still
exists, you do not have to change thread B's donated priority.
However, you are free to do so.

@item
@b{Do I have to make my dispatch table user-configurable?}

No.  Hard-coding the dispatch table values is fine.
@end enumerate
@end enumerate