5. Real Life Examples

5.1. Download Speeds

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:

>>> from bitmath import *

>>> downstream = Mib(50)

>>> print downstream.to_MB()


This tells us that if our ISP advertises 50Mbps we can expect to see download rates of over 6MB/sec.

  1. Assuming your ISP follows the common industry practice of using SI (base-10) units to describe file sizes/rates

5.2. Calculating how many files fit on a device

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:

>>> song_size = GB(5) / 1000
>>> print song_size

Or, using best_prefix, (line 2) to generate a more human-readable form:

>>> song_size = GB(5) / 1000
>>> print song_size.best_prefix()

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.

>>> ipod_capacity = GB(5)
>>> bootleg_size = MB(19.5)
>>> print ipod_capacity / bootleg_size

The result on line 4 tells tells us that we could fit 256 average-quality songs on our iPod.

5.3. Printing Human-Readable File Sizes in Python

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:

>>> 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 - 3.048828125KiB
__init__.py - 0.1181640625KiB
test_representation.py - 0.744140625KiB
test_to_Type_conversion.py - 2.2119140625KiB

See also

Instance Formatting
How to print results in a prettier format

5.4. Calculating Linux BDP and TCP Window Scaling

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.

5.4.1. The Hard Way

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 Buffers

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:

  1. Measure the latency, or round trip time (RTT, measured in milliseconds), between the host we’re tuning and our target remote host
  2. Measure/identify our network transfer rate
  3. Calculate the BDP (multiply transfer rate by rtt)
  4. Obtain our current kernel settings
  5. 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)

Calculate Manually

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:

>>> from bitmath import GB

>>> tx = 1/8.0

>>> rtt = 0.199 * 10**-3

>>> bdp = (GB(tx * rtt)).to_Byte()

>>> print bdp.to_KiB()



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()

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()

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


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()


>>> print sys_buffer.to_GiB()


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.