2015-07-17 14:38:16 +00:00
|
|
|
ORANGEFS
|
|
|
|
========
|
|
|
|
|
|
|
|
OrangeFS is an LGPL userspace scale-out parallel storage system. It is ideal
|
|
|
|
for large storage problems faced by HPC, BigData, Streaming Video,
|
|
|
|
Genomics, Bioinformatics.
|
|
|
|
|
|
|
|
Orangefs, originally called PVFS, was first developed in 1993 by
|
|
|
|
Walt Ligon and Eric Blumer as a parallel file system for Parallel
|
|
|
|
Virtual Machine (PVM) as part of a NASA grant to study the I/O patterns
|
|
|
|
of parallel programs.
|
|
|
|
|
|
|
|
Orangefs features include:
|
|
|
|
|
|
|
|
* Distributes file data among multiple file servers
|
|
|
|
* Supports simultaneous access by multiple clients
|
|
|
|
* Stores file data and metadata on servers using local file system
|
|
|
|
and access methods
|
|
|
|
* Userspace implementation is easy to install and maintain
|
|
|
|
* Direct MPI support
|
|
|
|
* Stateless
|
|
|
|
|
|
|
|
|
|
|
|
MAILING LIST
|
|
|
|
============
|
|
|
|
|
|
|
|
http://beowulf-underground.org/mailman/listinfo/pvfs2-users
|
|
|
|
|
|
|
|
|
|
|
|
DOCUMENTATION
|
|
|
|
=============
|
|
|
|
|
|
|
|
http://www.orangefs.org/documentation/
|
|
|
|
|
|
|
|
|
|
|
|
USERSPACE FILESYSTEM SOURCE
|
|
|
|
===========================
|
|
|
|
|
|
|
|
http://www.orangefs.org/download
|
|
|
|
|
|
|
|
Orangefs versions prior to 2.9.3 would not be compatible with the
|
|
|
|
upstream version of the kernel client.
|
|
|
|
|
|
|
|
|
|
|
|
BUILDING THE USERSPACE FILESYSTEM ON A SINGLE SERVER
|
|
|
|
====================================================
|
|
|
|
|
|
|
|
When Orangefs is upstream, "--with-kernel" shouldn't be needed, but
|
|
|
|
until then the path to where the kernel with the Orangefs kernel client
|
|
|
|
patch was built is needed to ensure that pvfs2-client-core (the bridge
|
|
|
|
between kernel space and user space) will build properly. You can omit
|
|
|
|
--prefix if you don't care that things are sprinkled around in
|
|
|
|
/usr/local.
|
|
|
|
|
|
|
|
./configure --prefix=/opt/ofs --with-kernel=/path/to/orangefs/kernel
|
|
|
|
|
|
|
|
make
|
|
|
|
|
|
|
|
make install
|
|
|
|
|
|
|
|
Create an orangefs config file:
|
|
|
|
/opt/ofs/bin/pvfs2-genconfig /etc/pvfs2.conf
|
|
|
|
|
|
|
|
for "Enter hostnames", use the hostname, don't let it default to
|
|
|
|
localhost.
|
|
|
|
|
|
|
|
create a pvfs2tab file in /etc:
|
|
|
|
cat /etc/pvfs2tab
|
|
|
|
tcp://myhostname:3334/orangefs /mymountpoint pvfs2 defaults,noauto 0 0
|
|
|
|
|
|
|
|
create the mount point you specified in the tab file if needed:
|
|
|
|
mkdir /mymountpoint
|
|
|
|
|
|
|
|
bootstrap the server:
|
|
|
|
/opt/ofs/sbin/pvfs2-server /etc/pvfs2.conf -f
|
|
|
|
|
|
|
|
start the server:
|
|
|
|
/opt/osf/sbin/pvfs2-server /etc/pvfs2.conf
|
|
|
|
|
|
|
|
Now the server is running. At this point you might like to
|
|
|
|
prove things are working with:
|
|
|
|
|
|
|
|
/opt/osf/bin/pvfs2-ls /mymountpoint
|
|
|
|
|
|
|
|
You might not want to enforce selinux, it doesn't seem to matter by
|
|
|
|
linux 3.11...
|
|
|
|
|
|
|
|
If stuff seems to be working, turn on the client core:
|
|
|
|
/opt/osf/sbin/pvfs2-client -p /opt/osf/sbin/pvfs2-client-core
|
|
|
|
|
|
|
|
Mount your filesystem.
|
|
|
|
mount -t pvfs2 tcp://myhostname:3334/orangefs /mymountpoint
|
|
|
|
|
|
|
|
|
|
|
|
OPTIONS
|
|
|
|
=======
|
|
|
|
|
|
|
|
The following mount options are accepted:
|
|
|
|
|
|
|
|
acl
|
|
|
|
Allow the use of Access Control Lists on files and directories.
|
|
|
|
|
|
|
|
intr
|
|
|
|
Some operations between the kernel client and the user space
|
|
|
|
filesystem can be interruptible, such as changes in debug levels
|
|
|
|
and the setting of tunable parameters.
|
|
|
|
|
|
|
|
local_lock
|
|
|
|
Enable posix locking from the perspective of "this" kernel. The
|
|
|
|
default file_operations lock action is to return ENOSYS. Posix
|
|
|
|
locking kicks in if the filesystem is mounted with -o local_lock.
|
|
|
|
Distributed locking is being worked on for the future.
|
|
|
|
|
|
|
|
|
|
|
|
DEBUGGING
|
|
|
|
=========
|
|
|
|
|
2016-01-13 19:28:13 +00:00
|
|
|
If you want the debug (GOSSIP) statements in a particular
|
2015-07-17 14:38:16 +00:00
|
|
|
source file (inode.c for example) go to syslog:
|
|
|
|
|
|
|
|
echo inode > /sys/kernel/debug/orangefs/kernel-debug
|
|
|
|
|
|
|
|
No debugging (the default):
|
|
|
|
|
|
|
|
echo none > /sys/kernel/debug/orangefs/kernel-debug
|
|
|
|
|
|
|
|
Debugging from several source files:
|
|
|
|
|
|
|
|
echo inode,dir > /sys/kernel/debug/orangefs/kernel-debug
|
|
|
|
|
|
|
|
All debugging:
|
|
|
|
|
|
|
|
echo all > /sys/kernel/debug/orangefs/kernel-debug
|
|
|
|
|
|
|
|
Get a list of all debugging keywords:
|
|
|
|
|
|
|
|
cat /sys/kernel/debug/orangefs/debug-help
|
2016-01-13 19:28:13 +00:00
|
|
|
|
|
|
|
|
|
|
|
PROTOCOL BETWEEN KERNEL MODULE AND USERSPACE
|
|
|
|
============================================
|
|
|
|
|
|
|
|
Orangefs is a user space filesystem and an associated kernel module.
|
|
|
|
We'll just refer to the user space part of Orangefs as "userspace"
|
|
|
|
from here on out. Orangefs descends from PVFS, and userspace code
|
|
|
|
still uses PVFS for function and variable names. Userspace typedefs
|
|
|
|
many of the important structures. Function and variable names in
|
|
|
|
the kernel module have been transitioned to "orangefs", and The Linux
|
|
|
|
Coding Style avoids typedefs, so kernel module structures that
|
|
|
|
correspond to userspace structures are not typedefed.
|
|
|
|
|
|
|
|
The kernel module implements a pseudo device that userspace
|
|
|
|
can read from and write to. Userspace can also manipulate the
|
|
|
|
kernel module through the pseudo device with ioctl.
|
|
|
|
|
|
|
|
THE BUFMAP:
|
|
|
|
|
|
|
|
At startup userspace allocates two page-size-aligned (posix_memalign)
|
|
|
|
mlocked memory buffers, one is used for IO and one is used for readdir
|
|
|
|
operations. The IO buffer is 41943040 bytes and the readdir buffer is
|
|
|
|
4194304 bytes. Each buffer contains logical chunks, or partitions, and
|
|
|
|
a pointer to each buffer is added to its own PVFS_dev_map_desc structure
|
|
|
|
which also describes its total size, as well as the size and number of
|
|
|
|
the partitions.
|
|
|
|
|
|
|
|
A pointer to the IO buffer's PVFS_dev_map_desc structure is sent to a
|
|
|
|
mapping routine in the kernel module with an ioctl. The structure is
|
|
|
|
copied from user space to kernel space with copy_from_user and is used
|
|
|
|
to initialize the kernel module's "bufmap" (struct orangefs_bufmap), which
|
|
|
|
then contains:
|
|
|
|
|
|
|
|
* refcnt - a reference counter
|
|
|
|
* desc_size - PVFS2_BUFMAP_DEFAULT_DESC_SIZE (4194304) - the IO buffer's
|
|
|
|
partition size, which represents the filesystem's block size and
|
|
|
|
is used for s_blocksize in super blocks.
|
|
|
|
* desc_count - PVFS2_BUFMAP_DEFAULT_DESC_COUNT (10) - the number of
|
|
|
|
partitions in the IO buffer.
|
|
|
|
* desc_shift - log2(desc_size), used for s_blocksize_bits in super blocks.
|
|
|
|
* total_size - the total size of the IO buffer.
|
|
|
|
* page_count - the number of 4096 byte pages in the IO buffer.
|
|
|
|
* page_array - a pointer to page_count * (sizeof(struct page*)) bytes
|
|
|
|
of kcalloced memory. This memory is used as an array of pointers
|
|
|
|
to each of the pages in the IO buffer through a call to get_user_pages.
|
|
|
|
* desc_array - a pointer to desc_count * (sizeof(struct orangefs_bufmap_desc))
|
|
|
|
bytes of kcalloced memory. This memory is further intialized:
|
|
|
|
|
|
|
|
user_desc is the kernel's copy of the IO buffer's ORANGEFS_dev_map_desc
|
|
|
|
structure. user_desc->ptr points to the IO buffer.
|
|
|
|
|
|
|
|
pages_per_desc = bufmap->desc_size / PAGE_SIZE
|
|
|
|
offset = 0
|
|
|
|
|
|
|
|
bufmap->desc_array[0].page_array = &bufmap->page_array[offset]
|
|
|
|
bufmap->desc_array[0].array_count = pages_per_desc = 1024
|
|
|
|
bufmap->desc_array[0].uaddr = (user_desc->ptr) + (0 * 1024 * 4096)
|
|
|
|
offset += 1024
|
|
|
|
.
|
|
|
|
.
|
|
|
|
.
|
|
|
|
bufmap->desc_array[9].page_array = &bufmap->page_array[offset]
|
|
|
|
bufmap->desc_array[9].array_count = pages_per_desc = 1024
|
|
|
|
bufmap->desc_array[9].uaddr = (user_desc->ptr) +
|
|
|
|
(9 * 1024 * 4096)
|
|
|
|
offset += 1024
|
|
|
|
|
|
|
|
* buffer_index_array - a desc_count sized array of ints, used to
|
|
|
|
indicate which of the IO buffer's partitions are available to use.
|
|
|
|
* buffer_index_lock - a spinlock to protect buffer_index_array during update.
|
|
|
|
* readdir_index_array - a five (ORANGEFS_READDIR_DEFAULT_DESC_COUNT) element
|
|
|
|
int array used to indicate which of the readdir buffer's partitions are
|
|
|
|
available to use.
|
|
|
|
* readdir_index_lock - a spinlock to protect readdir_index_array during
|
|
|
|
update.
|
|
|
|
|
|
|
|
OPERATIONS:
|
|
|
|
|
|
|
|
The kernel module builds an "op" (struct orangefs_kernel_op_s) when it
|
|
|
|
needs to communicate with userspace. Part of the op contains the "upcall"
|
|
|
|
which expresses the request to userspace. Part of the op eventually
|
|
|
|
contains the "downcall" which expresses the results of the request.
|
|
|
|
|
|
|
|
The slab allocator is used to keep a cache of op structures handy.
|
|
|
|
|
2016-02-26 19:39:08 +00:00
|
|
|
At init time the kernel module defines and initializes a request list
|
|
|
|
and an in_progress hash table to keep track of all the ops that are
|
|
|
|
in flight at any given time.
|
|
|
|
|
|
|
|
Ops are stateful:
|
|
|
|
|
|
|
|
* unknown - op was just initialized
|
|
|
|
* waiting - op is on request_list (upward bound)
|
|
|
|
* inprogr - op is in progress (waiting for downcall)
|
|
|
|
* serviced - op has matching downcall; ok
|
|
|
|
* purged - op has to start a timer since client-core
|
|
|
|
exited uncleanly before servicing op
|
|
|
|
* given up - submitter has given up waiting for it
|
|
|
|
|
|
|
|
When some arbitrary userspace program needs to perform a
|
|
|
|
filesystem operation on Orangefs (readdir, I/O, create, whatever)
|
|
|
|
an op structure is initialized and tagged with a distinguishing ID
|
|
|
|
number. The upcall part of the op is filled out, and the op is
|
|
|
|
passed to the "service_operation" function.
|
|
|
|
|
|
|
|
Service_operation changes the op's state to "waiting", puts
|
|
|
|
it on the request list, and signals the Orangefs file_operations.poll
|
|
|
|
function through a wait queue. Userspace is polling the pseudo-device
|
|
|
|
and thus becomes aware of the upcall request that needs to be read.
|
|
|
|
|
|
|
|
When the Orangefs file_operations.read function is triggered, the
|
|
|
|
request list is searched for an op that seems ready-to-process.
|
|
|
|
The op is removed from the request list. The tag from the op and
|
|
|
|
the filled-out upcall struct are copy_to_user'ed back to userspace.
|
|
|
|
|
|
|
|
If any of these (and some additional protocol) copy_to_users fail,
|
|
|
|
the op's state is set to "waiting" and the op is added back to
|
|
|
|
the request list. Otherwise, the op's state is changed to "in progress",
|
|
|
|
and the op is hashed on its tag and put onto the end of a list in the
|
|
|
|
in_progress hash table at the index the tag hashed to.
|
|
|
|
|
|
|
|
When userspace has assembled the response to the upcall, it
|
|
|
|
writes the response, which includes the distinguishing tag, back to
|
|
|
|
the pseudo device in a series of io_vecs. This triggers the Orangefs
|
|
|
|
file_operations.write_iter function to find the op with the associated
|
|
|
|
tag and remove it from the in_progress hash table. As long as the op's
|
|
|
|
state is not "canceled" or "given up", its state is set to "serviced".
|
|
|
|
The file_operations.write_iter function returns to the waiting vfs,
|
|
|
|
and back to service_operation through wait_for_matching_downcall.
|
|
|
|
|
|
|
|
Service operation returns to its caller with the op's downcall
|
|
|
|
part (the response to the upcall) filled out.
|
|
|
|
|
|
|
|
The "client-core" is the bridge between the kernel module and
|
|
|
|
userspace. The client-core is a daemon. The client-core has an
|
|
|
|
associated watchdog daemon. If the client-core is ever signaled
|
|
|
|
to die, the watchdog daemon restarts the client-core. Even though
|
|
|
|
the client-core is restarted "right away", there is a period of
|
|
|
|
time during such an event that the client-core is dead. A dead client-core
|
|
|
|
can't be triggered by the Orangefs file_operations.poll function.
|
|
|
|
Ops that pass through service_operation during a "dead spell" can timeout
|
|
|
|
on the wait queue and one attempt is made to recycle them. Obviously,
|
|
|
|
if the client-core stays dead too long, the arbitrary userspace processes
|
|
|
|
trying to use Orangefs will be negatively affected. Waiting ops
|
|
|
|
that can't be serviced will be removed from the request list and
|
2016-08-01 18:01:40 +00:00
|
|
|
have their states set to "given up". In-progress ops that can't
|
2016-02-26 19:39:08 +00:00
|
|
|
be serviced will be removed from the in_progress hash table and
|
|
|
|
have their states set to "given up".
|
|
|
|
|
|
|
|
Readdir and I/O ops are atypical with respect to their payloads.
|
2016-01-13 19:28:13 +00:00
|
|
|
|
|
|
|
- readdir ops use the smaller of the two pre-allocated pre-partitioned
|
|
|
|
memory buffers. The readdir buffer is only available to userspace.
|
|
|
|
The kernel module obtains an index to a free partition before launching
|
|
|
|
a readdir op. Userspace deposits the results into the indexed partition
|
|
|
|
and then writes them to back to the pvfs device.
|
|
|
|
|
|
|
|
- io (read and write) ops use the larger of the two pre-allocated
|
|
|
|
pre-partitioned memory buffers. The IO buffer is accessible from
|
|
|
|
both userspace and the kernel module. The kernel module obtains an
|
|
|
|
index to a free partition before launching an io op. The kernel module
|
|
|
|
deposits write data into the indexed partition, to be consumed
|
|
|
|
directly by userspace. Userspace deposits the results of read
|
|
|
|
requests into the indexed partition, to be consumed directly
|
|
|
|
by the kernel module.
|
|
|
|
|
|
|
|
Responses to kernel requests are all packaged in pvfs2_downcall_t
|
|
|
|
structs. Besides a few other members, pvfs2_downcall_t contains a
|
|
|
|
union of structs, each of which is associated with a particular
|
|
|
|
response type.
|
|
|
|
|
|
|
|
The several members outside of the union are:
|
|
|
|
- int32_t type - type of operation.
|
|
|
|
- int32_t status - return code for the operation.
|
|
|
|
- int64_t trailer_size - 0 unless readdir operation.
|
|
|
|
- char *trailer_buf - initialized to NULL, used during readdir operations.
|
|
|
|
|
|
|
|
The appropriate member inside the union is filled out for any
|
|
|
|
particular response.
|
|
|
|
|
|
|
|
PVFS2_VFS_OP_FILE_IO
|
|
|
|
fill a pvfs2_io_response_t
|
|
|
|
|
|
|
|
PVFS2_VFS_OP_LOOKUP
|
|
|
|
fill a PVFS_object_kref
|
|
|
|
|
|
|
|
PVFS2_VFS_OP_CREATE
|
|
|
|
fill a PVFS_object_kref
|
|
|
|
|
|
|
|
PVFS2_VFS_OP_SYMLINK
|
|
|
|
fill a PVFS_object_kref
|
|
|
|
|
|
|
|
PVFS2_VFS_OP_GETATTR
|
|
|
|
fill in a PVFS_sys_attr_s (tons of stuff the kernel doesn't need)
|
|
|
|
fill in a string with the link target when the object is a symlink.
|
|
|
|
|
|
|
|
PVFS2_VFS_OP_MKDIR
|
|
|
|
fill a PVFS_object_kref
|
|
|
|
|
|
|
|
PVFS2_VFS_OP_STATFS
|
|
|
|
fill a pvfs2_statfs_response_t with useless info <g>. It is hard for
|
|
|
|
us to know, in a timely fashion, these statistics about our
|
2016-08-01 18:01:40 +00:00
|
|
|
distributed network filesystem.
|
2016-01-13 19:28:13 +00:00
|
|
|
|
|
|
|
PVFS2_VFS_OP_FS_MOUNT
|
|
|
|
fill a pvfs2_fs_mount_response_t which is just like a PVFS_object_kref
|
|
|
|
except its members are in a different order and "__pad1" is replaced
|
|
|
|
with "id".
|
|
|
|
|
|
|
|
PVFS2_VFS_OP_GETXATTR
|
|
|
|
fill a pvfs2_getxattr_response_t
|
|
|
|
|
|
|
|
PVFS2_VFS_OP_LISTXATTR
|
|
|
|
fill a pvfs2_listxattr_response_t
|
|
|
|
|
|
|
|
PVFS2_VFS_OP_PARAM
|
|
|
|
fill a pvfs2_param_response_t
|
|
|
|
|
|
|
|
PVFS2_VFS_OP_PERF_COUNT
|
|
|
|
fill a pvfs2_perf_count_response_t
|
|
|
|
|
|
|
|
PVFS2_VFS_OP_FSKEY
|
|
|
|
file a pvfs2_fs_key_response_t
|
|
|
|
|
|
|
|
PVFS2_VFS_OP_READDIR
|
|
|
|
jamb everything needed to represent a pvfs2_readdir_response_t into
|
|
|
|
the readdir buffer descriptor specified in the upcall.
|
|
|
|
|
2016-02-26 19:39:08 +00:00
|
|
|
Userspace uses writev() on /dev/pvfs2-req to pass responses to the requests
|
2016-01-13 19:28:13 +00:00
|
|
|
made by the kernel side.
|
|
|
|
|
|
|
|
A buffer_list containing:
|
|
|
|
- a pointer to the prepared response to the request from the
|
|
|
|
kernel (struct pvfs2_downcall_t).
|
|
|
|
- and also, in the case of a readdir request, a pointer to a
|
|
|
|
buffer containing descriptors for the objects in the target
|
|
|
|
directory.
|
|
|
|
... is sent to the function (PINT_dev_write_list) which performs
|
|
|
|
the writev.
|
|
|
|
|
|
|
|
PINT_dev_write_list has a local iovec array: struct iovec io_array[10];
|
|
|
|
|
|
|
|
The first four elements of io_array are initialized like this for all
|
|
|
|
responses:
|
|
|
|
|
|
|
|
io_array[0].iov_base = address of local variable "proto_ver" (int32_t)
|
|
|
|
io_array[0].iov_len = sizeof(int32_t)
|
|
|
|
|
|
|
|
io_array[1].iov_base = address of global variable "pdev_magic" (int32_t)
|
|
|
|
io_array[1].iov_len = sizeof(int32_t)
|
2016-08-01 18:01:40 +00:00
|
|
|
|
2016-01-13 19:28:13 +00:00
|
|
|
io_array[2].iov_base = address of parameter "tag" (PVFS_id_gen_t)
|
|
|
|
io_array[2].iov_len = sizeof(int64_t)
|
|
|
|
|
|
|
|
io_array[3].iov_base = address of out_downcall member (pvfs2_downcall_t)
|
|
|
|
of global variable vfs_request (vfs_request_t)
|
|
|
|
io_array[3].iov_len = sizeof(pvfs2_downcall_t)
|
|
|
|
|
|
|
|
Readdir responses initialize the fifth element io_array like this:
|
|
|
|
|
|
|
|
io_array[4].iov_base = contents of member trailer_buf (char *)
|
|
|
|
from out_downcall member of global variable
|
|
|
|
vfs_request
|
|
|
|
io_array[4].iov_len = contents of member trailer_size (PVFS_size)
|
|
|
|
from out_downcall member of global variable
|
|
|
|
vfs_request
|
2016-08-01 18:01:40 +00:00
|
|
|
|
|
|
|
Orangefs exploits the dcache in order to avoid sending redundant
|
|
|
|
requests to userspace. We keep object inode attributes up-to-date with
|
|
|
|
orangefs_inode_getattr. Orangefs_inode_getattr uses two arguments to
|
|
|
|
help it decide whether or not to update an inode: "new" and "bypass".
|
|
|
|
Orangefs keeps private data in an object's inode that includes a short
|
|
|
|
timeout value, getattr_time, which allows any iteration of
|
|
|
|
orangefs_inode_getattr to know how long it has been since the inode was
|
|
|
|
updated. When the object is not new (new == 0) and the bypass flag is not
|
|
|
|
set (bypass == 0) orangefs_inode_getattr returns without updating the inode
|
|
|
|
if getattr_time has not timed out. Getattr_time is updated each time the
|
|
|
|
inode is updated.
|
|
|
|
|
|
|
|
Creation of a new object (file, dir, sym-link) includes the evaluation of
|
|
|
|
its pathname, resulting in a negative directory entry for the object.
|
|
|
|
A new inode is allocated and associated with the dentry, turning it from
|
|
|
|
a negative dentry into a "productive full member of society". Orangefs
|
|
|
|
obtains the new inode from Linux with new_inode() and associates
|
|
|
|
the inode with the dentry by sending the pair back to Linux with
|
|
|
|
d_instantiate().
|
|
|
|
|
|
|
|
The evaluation of a pathname for an object resolves to its corresponding
|
|
|
|
dentry. If there is no corresponding dentry, one is created for it in
|
|
|
|
the dcache. Whenever a dentry is modified or verified Orangefs stores a
|
|
|
|
short timeout value in the dentry's d_time, and the dentry will be trusted
|
|
|
|
for that amount of time. Orangefs is a network filesystem, and objects
|
|
|
|
can potentially change out-of-band with any particular Orangefs kernel module
|
|
|
|
instance, so trusting a dentry is risky. The alternative to trusting
|
|
|
|
dentries is to always obtain the needed information from userspace - at
|
|
|
|
least a trip to the client-core, maybe to the servers. Obtaining information
|
|
|
|
from a dentry is cheap, obtaining it from userspace is relatively expensive,
|
|
|
|
hence the motivation to use the dentry when possible.
|
|
|
|
|
|
|
|
The timeout values d_time and getattr_time are jiffy based, and the
|
|
|
|
code is designed to avoid the jiffy-wrap problem:
|
|
|
|
|
|
|
|
"In general, if the clock may have wrapped around more than once, there
|
|
|
|
is no way to tell how much time has elapsed. However, if the times t1
|
|
|
|
and t2 are known to be fairly close, we can reliably compute the
|
|
|
|
difference in a way that takes into account the possibility that the
|
|
|
|
clock may have wrapped between times."
|
|
|
|
|
|
|
|
from course notes by instructor Andy Wang
|
2016-01-13 19:28:13 +00:00
|
|
|
|