Diversity, not for political reasons, but for survival


There are others who can write about this more eloquently than I can, but pulling your leaders from many walks of life across the spectrum of gender, race, nationality, and even age, is essential to your organization’s survival. Google knows it. So does Apple.

Physics labs contain, in my experience, a cult of old technology. They use outdated tools and outdated practices to write unreliable applications. It is very difficult to make the case for improvements because the appointed leaders are older men whose technology background is completely outdated. The problem is compounded when they continue to hire physicists who follow in these traditions, rather than hiring technology specialists to do the jobs they are trained for. Labs often hire someone with a PhD in physics and a research background to run their computer centers and write their software.

I would like to think that if the labs start putting more women and minorities into director roles, it will generate a more dynamic environment and we will start to see more modern ideas being put into place.

ARM64 Assembly with Swift and XCode

Here is a popular interview question:

Given an unsigned integer, how would you count the number of set bits (that is, bits = 1)?

This is otherwise known as a Hamming Weight, and there are clever tricks for solving this problem using only a few lines of C. You could also use a loop with shift and compare:

There is actually a single CPU instruction that implements this entire function:

CNT (vector)

Population count per byte.


CNT Vd.T, Vn.T

This is an instruction, in ARM64 Assembly (AArch64), that performs the population count operation in one line of code. A similar instruction exists in most CPU assembly languages. iPhones use ARM-family chips. For example, my iPhone 6 uses an Apple A8, a System-on-a-Chip (SoC) built around an ARM64 CPU.

This inspired me to write an iPhone app that utilizes the CNT instruction, which means I get to write a little bit of ARM assembly code and deploy it on the iPhone. The code is on Github. This is what the finished product looks like:

The app is written in Swift but uses C and Assembly for the bit-counting operation. Calling ARM64 functions from Swift is a lot like calling a C function from Swift, so I wrote a C popcount() function to use with the simulator (compiles into x86 assembly) and an ARM64 popcount() function to deploy on the iPhone itself. The function is defined in the two files popcount.c and popcount.s. They use the preprocessor flags #ifdef __arm64__ and ifndef __arm64__ to tell the compiler which code goes with which platform.

Both files utilize the same header to declare the function. You can create a header called popcount.h using the File menu. But this is a Swift project, so we need a bridging header to make the functions callable from Swift. A bridging header is created automatically if you carefully follow the prompts when creating a C file, but you can create one manually if need be.

A function written in assembly code comes with a lot of boilerplate code for setting up the stack, returning results, aligning memory, and much more. Fortunately, there is a way to get a working example that can be used as a kind of template. The compiler will show you generated assembly if you use the right options. Take this simple Swift function:

Compiling this code manually will show the assembly code generated by the swiftc compiler. I used this command: xcrun -sdk iphoneos swiftc -emit-assembly -target arm64-apple-ios11.0 SimpleFunction.swift. It produces a very large assembly file, not all of which needs to be replicated in the popcount.s code. The code starting at the function label and ending with the ret statement is useful, because we can use it to create our own function in assembly.

The addTwoNumbers function is actually contained in the assembly code labelled __T014SimpleFunction13addTwoNumbersS2i_SitF. The name has been mangled to make it unique and identifiable across potentially many compiled objects. The single line adds x0, x0, x1  actually contains the entire body of this simple function in one command. Here is a breakdown of the command:

  • adds is an opcode, a single basic instruction in assembly. Assembly opcodes typically perform a simple math operation on one of a few built-in variables. They may also move a word of data in or out of memory. This opcode adds two numbers together, respecting the sign bit.
  • x0 is the destination variable for the operation, where the results are written. These variables are called registers in assembly, and they live on the CPU outside of memory. There are only 31 general-purpose registers on modern ARM chips, so assembly programs spend a lot of code moving data between memory and these local registers.
  • x0, x1 are the source registers. The code that came before this command takes care of pulling the values off of the call stack (placed there by the calling function) and putting them into registers.

There are a lot of other ARM64 commands, and a lot of details needed to understand function calls. But I won’t need to dive this deep to complete my task.

I need to replace this adds command with cnt. The cnt command is actually part of the ARM64 SIMD instruction set, and uses a separate set of registers from the general-purpose x0-x31 registers. I need a three-line program: one line to move the function parameter into a SIMD register, one to perform the count, and one to move the result back to a GP register. These three lines accomplish this:

Breaking down the assembly syntax again:

  • dup duplicates an element (copies it). We are copying from a general-purpose register, x0, into a specialized SIMD register, v0.2d.
  • v0.2d is a 128-bit SIMD register. x0 is a 64-bit register, so the .2d modifier instructs the assembler to duplicate x0 and put the two 64-bit copies into v0. This isn’t necessary for our purpose, but it is useful for other algorithms.
  • cnt executes the population count, replacing the bit pattern with the number counted. For example, 01101101 would become 00000101 (101=5, because there were five bits set in the data before the operation).
  • v0.16b indicates the same register as before, except this time the SIMD register is being divided into 16 lanes, each 1-byte in size. Each of the 16 8-bit lanes inside the vector is treated as a separate register and they are all executed in parallel. Vector instructions like to perform one operation on many pieces of data in parallel, hence SIMD: Same Instruction, Multiple Data elements.
  • fmov moves data between registers again, this time putting the results back in x0. The f here actually makes this a floating-point instruction, because FP and SIMD instructions share the same registers in ARM64. But it doesn’t make this a floating-point number.
  • v0.d[1] is once again the same SIMD register, but with a different way of splitting up the data elements. The indicates that a double-word (64 bits) is being copied out of element 1 of the SIMD register. This puts the results into our GP register.

Note: CNT only works in 8-bit chunks due to hardware limitations (more bits = more wires = less room to implement other features). If I wanted to support values larger than 255, I could add an addv command, which adds the 8-bit chunks together. There are many more ARM topics I have not explored.

The resulting assembly code reports the population count, and the Swift code displays the results to the user:

If you’re new to assembly language, it is worth noting some oddities of the assembly language environment. Assembly language gives you complete low-level control over the behavior of your CPU, but this means that understanding the details of CPU architecture is essential to writing efficient assembly. Instructions that rely on shared resources can create delays. Memory loads take several instruction cycles to complete.

Compilers are pretty good at allocating registers and scheduling instructions. It may be worth writing code in C and using the generated assembly as a starting point to see how it can be done. There is a lot more to writing effective assembly than just knowing the syntax of the language.

You can find lots of resources for learning ARM64 assembly. A crash course in ARM64 assembly might be a good place to start, and the ARMv8 Instruction Set Overview is both authoritative and exhaustive. Github member Richard Ross has written an entire iOS app in assembly.

You can practice ARM64 using QEMU, which, although it requires a lot of effort to set up, will let you analyze assembly instructions one-by-one as the execute.

Swift BigInteger?

I recently ran across the need for a large integer in Swift – something that needs more than the 64 bits provided by Int64. This is not the first time. I have played around with Swift Decimal in the past (NSDecimal, NSDecimalNumber) only to find they come up short in precisely representing a rational number. Python, for example, makes it trivial to find the Nth decimal place of any rational number by storing the repeating decimal pattern under the hood and making that info available to you.

This poor substitute of mine only supports the binary OR and POPULATION operations and has no string representation. But it worked for what I needed.


The Gap

So I’ve been silent here for the better part of a year, and I just wanted to say why: I made  a major career change and started a new job. I write Android apps for a tech company here in Williamsburg, VA now. The job is great, but I have been very busy. I intend to continue posting about iOS, Math, Python, AI, Databases, and now Android.


Heapsort, because I haven’t posted in a while

This is heapsort in a Swift playground. I needed a stable sort, so naturally I wrote an… unstable sort.

Of course, you can just use sort() or sorted(), but if you are inclined to roll your own, the Swifty way to do it is to create an extension. Note that an Array extension with a Generic Where Clause is needed to make element comparisons > < == work.

On to writing mergesort (stable).


Matrix Operations in Swift

I recently completed 10 Days of Statistics on HackerRank. Yay!

In the process, I needed some matrix operations for a medium-difficulty problem. And here they are, code style be damned :

That’s the identity matrix popping out at the end, which validates my implementation.

But what’s this? A 60-line method? Uncle Bob would not be pleased.

Comments should not take the place of good variable/method names. Those section comments give clues as to where my methods should be :

Better. Uncle Bob would be proud (or give me credit for trying, anyway).

One more thing : Thanks to StackOverflow user Alexander, I have an even better way to express that pivot loop :

iOS Williamsburg – Swift Basics

Do you want to learn Swift syntax, have fun, and meet an enthusiastic group of developers? Come by the Williamsburg Library at 515 Scotland Street, Williamsburg, VA, on Saturday, August 12, 2017. We will be going over Swift basics. We have many experienced developers who are eager to share tips and help newcomers.

iOS development basics.

Saturday, Aug 12, 2017, 10:00 AM

Location details are available to members only.

11 Members Attending

Room c

Check out this Meetup →

I hope to see you there!

iOS Swift Developers in Williamsburg, VA

Get together to meet, discuss our plans for future meet ups and learn some Swift

Saturday, Jul 22, 2017, 10:00 AM

Williamsburg Library
515 Scotland Street Williamsburg, VA

7 Members Attending

Bring your laptop, we can go over the basics of swift and see where everyone is skills wise.

Check out this Meetup →


If you are near the Williamsburg Library on Scotland St. this Saturday, July 22 2017, at 10AM, and you have an interest in iOS development using the Swift programming language, please stop by. I will be giving a presentation on language basics and the development environment. We have a diverse group of enthusiasts with newbies and app store veterans alike.