6. Real Life Examples

6.1. 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:

>>> import bitmath
>>> downstream = bitmath.Mb(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

6.2. 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)
0.005GB

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

>>> 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.

>>> 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.

6.2.1. Using Real Device Capacity 

Rather than hard-coding a device size, we can query the actual free space on any mounted filesystem with bitmath.query_capacity() and feed that directly into the same calculation.

bitmath.query_capacity() returns a Capacity named tuple with total, used, and free fields. By default (bestprefix=True) each field is already normalized to a human-readable prefix (e.g. GiB). Pass bestprefix=False to get raw bitmath.Byte instances instead. It requires no elevated privileges and works cross-platform.

>>> import bitmath
>>> cap = bitmath.query_capacity("/")
>>> print(cap.free)
93.08 GiB

Now we can ask: how many 4.7 GB DVD images fit in that free space?

>>> dvd = bitmath.GB(4.7)
>>> count, remainder = divmod(cap.free, dvd)
>>> print(int(count), "DVDs,", remainder.best_prefix(), "left over")
19 DVDs, 3.262 GiB left over

Floor division (//) and modulo (%) work the same way if you only need one value:

>>> print(int(cap.free // dvd), "DVDs fit")
19 DVDs fit
>>> print((cap.free % dvd).best_prefix(), "remaining")
3.262 GiB remaining

6.3. 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 - 3.048828125 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:

>>> 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

6.4. 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.

6.4.1. 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:

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.

Scenario

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)

6.4.2. 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

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

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

>>> print(bdp.to_KiB())

KiB(24.2919921875)

We could shorten that even further:

>>> print((GB((1/8) * (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 = 24875
net.core.wmem_max = 24875

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.

6.5. Creating Download Progress Bars 

For a self-contained, copy-paste example of a progress bar that displays transfer speed using bitmath, see progressbar2 in the Integration Examples chapter.

6.6. Reading a Devices Storage Capacity 

Important

Superuser (root/admin) privileges are required to allow bitmath.query_device_capacity() to make system calls to read a devices capacity. Use of this function on a device the user does not have access to will result in run-time errors.

Using bitmath.query_device_capacity() we can read the size of a storage device or a partition on a device.

Examples of supported devices include:

Standard Hard Drives/External Drives
Filesystem Partitions
Loop Devices
LVM Logical Volumes
Encrypted LUKS Volumes
iSCSI Devices

Usage is fairly straight-forward. Create an open file handle of the device you want to read the capacity of and then create a bitmath object with the query_device_capacity function. Here’s an example where we read the capacity of device sda, the first device on the example system.

>>> with open('/dev/sda', 'r') as fh:
...     sda_capacity = bitmath.query_device_capacity(fh)
>>> print(sda_capacity.best_prefix())
238.474937439 GiB

6. Real Life Examples

6.4.2. The bitmath way

6.4.2. The `bitmath` way