5. Real Life Examples¶
Let’s pretend that your Internet service provider (ISP) advertises your maximum downstream as 50Mbps (50 Megabits per second)1 and you want to know how fast that is in Megabytes per second? bitmath can do that for you easily. We can calculate this as such:
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>>> from bitmath import * >>> downstream = Mib(50) >>> print downstream.to_MB() MB(6.25)
This tells us that if our ISP advertises 50Mbps we can expect to see download rates of over 6MB/sec.
- Assuming your ISP follows the common industry practice of using SI (base-10) units to describe file sizes/rates
In 2001 Apple® announced the iPod™. Their headline statement boasting:
”... iPod stores up to 1,000 CD-quality songs on its super-thin 5 GB hard drive, ...”
OK. That’s pretty simple to work backwards: capacity of disk drive divided by number of songs equals the average size of a song. Which in this case is:
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>>> song_size = GB(5) / 1000 >>> print song_size 0.005GB
Or, using best_prefix, (line 2) to generate a more human-readable form:
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>>> song_size = GB(5) / 1000 >>> print song_size.best_prefix() 5.0MB
That’s great, if you have normal radio-length songs. But how many of our favorite jam-band’s 15-30+ minute-long songs could we fit on this iPod? Let’s pretend we did the math and the average audio file worked out to be 18.6 MiB (19.5 MB) large.
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>>> ipod_capacity = GB(5) >>> bootleg_size = MB(19.5) >>> print ipod_capacity / bootleg_size 256.41025641
The result on line 4 tells tells us that we could fit 256 average-quality songs on our iPod.
In a Python script or interpreter we may wish to print out file sizes in something other than bytes (which is what os.path.getsize returns). We can use bitmath to do that too:
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>>> import os >>> from bitmath import * >>> these_files = os.listdir('.') >>> for f in these_files: ... f_size = Byte(os.path.getsize(f)) ... print "%s - %s" % (f, f_size.to_KiB()) test_basic_math.py - 3.048828125 KiB __init__.py - 0.1181640625 KiB test_representation.py - 0.744140625 KiB test_to_Type_conversion.py - 2.2119140625 KiB
Alternatively, we could simplify things and use bitmath.getsize() to read the file size directly into a bitmath object:
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>>> import os >>> import bitmath >>> these_files = os.listdir('.') >>> for f in these_files: ... print "%s - %s" % (f, bitmath.getsize(f)) test_basic_math.py - 3.048828125 KiB __init__.py - 0.1181640625 KiB test_representation.py - 0.744140625 KiB test_to_Type_conversion.py - 2.2119140625 KiB
- Instance Formatting
- How to print results in a prettier format
Say we’re doing some Linux Kernel TCP performance tuning. For optimum speeds we need to calculate our BDP, or Bandwidth Delay Product. For this we need to calculate certain values to set some kernel tuning parameters to. The point of this tuning is to send the most data we can during a measured round-trip-time without sending more than can be processed. To accomplish this we are resizing our kernel read/write networking/socket buffers.
We will see two ways of doing this. The tedious manual way, and the way with bitmath.
Core Networking Values
- net.core.rmem_max - Bytes - Single Value - Default receive buffer size
- net.core.wmem_max - Bytes - Single Value - Default write buffer size
System-Wide Memory Limits
- net.ipv4.tcp_mem - Pages - Three Value Vector - The max field of the parameter is the number of memory pages allowed for queueing by all TCP sockets.
Per-socket buffer sizes must not exceed the core networking buffer sizes.
- net.ipv4.tcp_rmem - Bytes - Three Field Vector - The max field sets the size of the TCP receive buffer
- net.ipv4.tcp_wmem - Bytes - Three Field Vector - As above, but for the write buffer
We would normally calculate the optimal BDP and related values following this approach:
- Measure the latency, or round trip time (RTT, measured in milliseconds), between the host we’re tuning and our target remote host
- Measure/identify our network transfer rate
- Calculate the BDP (multiply transfer rate by rtt)
- Obtain our current kernel settings
- Adjust settings as necessary
But for the sake brevity we’ll be working out of an example scenario with a pre-defined RTT and transfer rate.
- We have an average network transfer rate of 1Gb/sec (where Gb is the SI unit for Gigabits, not Gibibytes: GiB)
- Our latency (RTT) is 0.199ms (milliseconds)
Lets calculate the BDP now. Because the kernel parameters expect values in units of bytes and pages we’ll have to convert our transfer rate of 1Gb/sec into B/s (Gigabits/second to Bytes/second):
- Convert 1Gb into an equivalent byte based unit
Remember 1 Byte = 8 Bits:
tx_rate_GB = 1/8 = 0.125
Our equivalent transfer rate is 0.125GB/sec.
- Convert our RTT from milliseconds into seconds
Remember 1ms = 10-3s:
window_seconds = 0.199 * 10^-3 = 0.000199
Our equivalent RTT window is 0.000199s
- Next we multiply the transfer rate by the length of our RTT window (in seconds)
(The unit analysis for this is GB/s * s leaving us with GB)
BDP = rx_rate_GB * window_seconds = 0.125 * 0.000199 = 0.000024875
Our BDP is 0.000024875GB.
- Convert 0.000024875GB to bytes:
Remember 1GB = 109B
BDP_bytes = 0.000024875 * 10^9 = 24875.0
Our BDP is 24875 bytes (or about 24.3KiB)
5.4.2. The bitmath way¶
All of this math can be done much quicker (and with greater accuracy) using the bitmath library. Let’s see how:
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>>> from bitmath import GB >>> tx = 1/8.0 >>> rtt = 0.199 * 10**-3 >>> bdp = (GB(tx * rtt)).to_Byte() >>> print bdp.to_KiB() KiB(24.2919921875)
To avoid integer rounding during division, don’t forget to divide by 8.0 rather than 8
We could shorten that even further:
>>> print (GB((1/8.0) * (0.199 * 10**-3))).to_Byte() 24875.0Byte
Get the current kernel parameters
Important to note is that the per-socket buffer sizes must not exceed the core network buffer sizes. Lets fetch our current core buffer sizes:
$ sysctl net.core.rmem_max net.core.wmem_max net.core.rmem_max = 212992 net.core.wmem_max = 212992
Recall, these values are in bytes. What are they in KiB?
>>> print Byte(212992).to_KiB() KiB(208.0)
This means our core networking buffer sizes are set to 208KiB each. Now let’s check our current per-socket buffer sizes:
$ sysctl net.ipv4.tcp_rmem net.ipv4.tcp_wmem net.ipv4.tcp_rmem = 4096 87380 6291456 net.ipv4.tcp_wmem = 4096 16384 4194304
Let’s double-check that our buffer sizes aren’t already out of wack (per-socket should be <= networking core)
>>> net_core_max = KiB(bytes=212992) >>> ipv4_tcp_rmem_max = KiB(bytes=6291456) >>> ipv4_tcp_rmem_max > net_core_max True
It appears that my buffers aren’t sized appropriately. We’ll fix that when we set the tunable parameters.
Finally, how large is the entire system TCP buffer?
$ sysctl net.ipv4.tcp_mem net.ipv4.tcp_mem = 280632 374176 561264
Our max system TCP buffer size is set to 561264. Recall that this parameter is measured in memory pages. Most of the time your page size is 4096 bytes, but you can check by running the command: getconf PAGESIZE. To convert the system TCP buffer size (561264) into a byte-based unit, we’ll multiply it by our pagesize (4096):
>>> sys_pages = 561264 >>> page_size = 4096 >>> sys_buffer = Byte(sys_pages * page_size) >>> print sys_buffer.to_MiB() 2192.4375MiB >>> print sys_buffer.to_GiB() 2.14105224609GiB
The system max TCP buffer size is about 2.14GiB.
In review, we discovered the following:
- Our core network buffer size is insufficient (212992), we’ll set it higher
- Our current per-socket buffer sizes are 6291456 and 4194304
And we calculated the following:
- Our ideal max per-socket buffer size is 24875 bytes
- Our ideal default per-socket buffer size (half the max): 12437
Finally: Set the new kernel parameters
Set the core-network buffer sizes:
$ sudo sysctl net.core.rmem_max=24875 net.core.wmem_max=24875 net.core.rmem_max = 4235 net.core.wmem_max = 4235
Set the per-socket buffer sizes:
$ sudo sysctl net.ipv4.tcp_rmem="4096 12437 24875" net.ipv4.tcp_wmem="4096 12437 24875" net.ipv4.tcp_rmem = 4096 12437 24875 net.ipv4.tcp_wmem = 4096 12437 24875
And it’s done! Testing this is left as an exercise for the reader. Note that in my experience this is less useful on wireless connections.