Ada and Rust are the only two pragmatic languages that are still growing in a healthy way that meet the Steelman language requirements (created by US DoD circa 1978).

Crucial in the Steelman requirements were:

A general, flexible design that adapts to satisfy the needs of embedded computer applications.

Reliability. The language should aid the design and development of reliable programs.

Ease of maintainability. Code should be readable and programming decisions explicit.

Easy to produce efficient code with. Inefficient constructs should be easily identifiable.

No unnecessary complexity. Semantic structure should be consistent and minimize the number of concepts.

Easy to implement the language specification. All features should be easy to understand.

Machine independence. The language shall not be bound to any hardware or OS details.

Complete definition. All parts of the language shall be fully and unambiguously defined.

As I’ve been spending a lot of time with Arm hardware lately as my primary desktop and server platform I missed using my secure messenger app of choice. I was able to cook up builds for both armv7l/armhf/GNU Linux (32-bit) and arm64/aarch64/GNU Linux (64-bit).

These are unofficial but fully working builds of Signal Desktop for Linux on Arm processors. Enjoy !

Here are some initial thoughts on Rust in the almost two years since I last looked at it along with some implementations of merge and quick sort. (These are just my opinions so please don’t panic !)

1. Cargo is awesome for managing package dependencies and building projects.
2. Rust is a very nice systems programming language that supports a functional style of programming. Much easier to work with than C/C++ with very near the same performance in many cases.
3. Strong static inferred type system !
4. The authors have not neglected the rich and varied history of programming language theory while trying to be very pragmatic about the design and usefulness of the language.

Let’s look at implementing some popular sorting algorithms. First … quick sort.
I won’t be pedantic here by explaining the quick sort algorithm but an elegant and performant implementation is ~20 LOC. Not bad for a systems level programming language.

pub fn quicksort_rec(nums: Vec) -> Vec {
return match nums.len() {
cnt if cnt <= 1 => nums,
cnt => {
let mut left = Vec::new();
let mut right = Vec::new();
let pivot = nums[0];
for i in 1..cnt {
match nums[i] {
num if num < pivot => left.push(num),
num => right.push(num),
}
}
let mut left_sorted = quicksort_rec(left);
let mut right_sorted = quicksort_rec(right);
left_sorted.push(pivot);
left_sorted.append(&mut right_sorted);
return left_sorted;
},
};
}

An implementation of merge sort is a bit longer at ~35 LOC.

fn merge(mut left: Vec, mut right: Vec) -> Vec {
let mut merged = Vec::new();
while !left.is_empty() && !right.is_empty() {
if left.last() >= right.last() {
merged.push(left.pop().unwrap());
} else {
merged.push(right.pop().unwrap());
}
}
while !left.is_empty() {
merged.push(left.pop().unwrap());
}
while !right.is_empty() {
merged.push(right.pop().unwrap());
}
merged.reverse();
return merged;
}
pub fn mergesort_rec(nums: Vec) -> Vec {
return match nums.len() {
cnt if cnt <= 1 => nums,
cnt => {
let mut left = Vec::new();
let mut right = Vec::new();
let middle = cnt / 2;
for i in (0..middle).rev() { left.push(nums[i]); }
for i in (middle..cnt).rev() { right.push(nums[i]); }
left = mergesort_rec(left);
right = mergesort_rec(right);
return merge(left, right);
},
};
}

Lastly, here are the timings for my very CPU under-powered laptop …

A few months back I took a look at Elixir. More recently I’ve been exploring F# and I’m very pleased with the experience so far. Here is the ring probabilities algorithm implemented using F#. It’s unlikely that I will ever use Elixir again because having a powerful static type system provided by F# at my disposal is just too good.

let rec calcStateProbs (prob: float, i: int,
currProbs: float [], newProbs: float []) =
if i < 0 then
newProbs
else
let maxIndex = currProbs.Length-1
// Match prev, next probs based on the fact that this is a
// ring structure.
let (prevProb, nextProb) =
match i with
| i when i = maxIndex -> (currProbs.[i-1], currProbs.[0])
| 0 -> (currProbs.[maxIndex], currProbs.[i+1])
| _ -> (currProbs.[i-1], currProbs.[i+1])
let newProb = prob * prevProb + (1.0 - prob) * nextProb
Array.set newProbs i newProb
calcStateProbs(prob, i-1, currProbs, newProbs)
let calcRingProbs parsedArgs =
// Probs at S = 0.
// Make certain that we are positioned at only start location.
// e.g. P(Start Node) = 1
let startProbs =
Array.concat [ [| 1.0 |] ; [| for _ in 1 .. parsedArgs.nodes - 1 -> 0.0 |] ]
let endProbs =
List.fold (fun probs _ ->
calcStateProbs(parsedArgs.probability, probs.Length-1,
probs, Array.create probs.Length 0.0))
startProbs [1..parsedArgs.states]
endProbs

Here’s the code.
No promises this time but I may follow this sequential version up with a parallelized version.

I’ve been hearing more about Elixir lately so I thought I’d take it for a spin.

“Elixir is a functional, meta-programming aware language built on top of the Erlang VM. It is a dynamic language that focuses on tooling to leverage Erlang’s abilities to build concurrent, distributed and fault-tolerant applications with hot code upgrades.”

I’ve never really spent any time with Erlang but always been curious about it and the fact that it’s one of the best kept ‘secrets’ in many startups these days. I’ve heard for years how easy it is to ‘scale out’ compared with many other languages and platforms.

Joe Armstrong, the creator of Erlang, wrote a post about Elixir in which he seemed to really like it except for some minor things. This got me even more curious so I decided to write some code that seemed like it could benefit from the features provided by Elixir for easily making suitable algorithms parallelizable.

Let’s talk about Ring probabilities. Let’s say we had a cluster of N nodes in a ring topology. We then might have some code that requires S steps to be run and each subsequent step is run on a node to the right of the previous node with some probability P.
In the initial state (S=0) the probability of some piece of code running on node A is P=1.
At the next step (S=1) the probability of the step running on a node to the right in the ring is P and the probability of the step running on a node to the left is 1-P.

Here is an example with some crude ascii diagrams to visually represent this :

Initial node probablity for 5 node ring at S=0 is P=1 for starting node.
N = 5 (nodes)
For S = 0 (initial state)
1 - P = 0.5βββββββββββββββββ P = 0.5
Counter-clockwise Clockwise
+-----+
|βP =β|
+----------+β1.0β+----------+
|ββββββββββ+-----+ββββββββββ|
+--+--+βββββββββββββββββββββ+--+--+
|β0.0 |βββββββββββββββββββββ|β0.0β|
+--+--+βββββββββββββββββββββ+--+--+
|βββββββββββββββββββββββββββ|
|βββββββββββββββββββββββββββ|
|ββ+-----+βββββββββ+-----+ββ|
+--+β0.0 +---------+β0.0β+--+
+-----+βββββββββ+-----+
Node probablities for the same 5 node ring after 2 state transitions
N = 5 (nodes)
S = 2
1 - P = 0.5βββββββββββββββββ P = 0.5
Counter-clockwiseβ Clockwise
+-----+
|βP =β|
+----------+β0.5β+-------------+
|ββββββ β +-----+ββ ββ βββββ β|
+--+--+βββββββββ βββββββββββ β +--+--+
|β0.0 |βββββββ βββββββββββ βββ |β0.0β|
+--+--+ββββββ βββββββββββ ββββ +--+--+
|β βββββββββββ ββββββββββββββ |
| ββ βββββββββββββββββββββββββ |
|ββ+------+βββββββββ+-------+ββ|
+--+β0.25 +---------+β0.25β +--+
+------+βββββββββ+-------+

Let’s first write the sequential version of the algorithm to calculate the ring probabilities. The parallel version will be handled in the next post. Data types in Elixir are pretty basic at this point with Elixir still having not reached 1.0. I decided to use an array to represent the ring in anticipation of later parallelizing the algorithm. A list seemed unsuitable for this due to access times being linear and that a parallel map across the structure would most likely be required. For a sequential version it’s interesting that a list is the fastest data structure to use in combination with recursion and pattern matching but I’ll get into that in the next post.
For now let’s get back to implementing a sequential version with an array and the map function …

Elixir doesn’t have an array or vector type (yet ?). I’m not going to comment on this. Instead we will use Erlang’s array type. Dipping into Erlang libraries from Elixir is pretty trivial so it’s no big deal other than Elixir’s parameter conventions for function calls is the reverse of Erlang’s and this can be a little annoying.

Let’s look at the function for calculating the node probabilities given a direction change probability, number of nodes and state count :

def calc_ring_probs(p, n, s)
when is_float(p) and p >= 0 and p <= 1 and
is_integer(n) and n > 0 and
is_integer(s) and s >= 0 do
# Probs at S = 0.
# Certain that we are positioned at only start location.
# e.g. P(Start Node) = 1
initial_probs = :array.new [size: n, fixed: true, default: 0.0]
initial_probs = :array.set 0, 1.0, initial_probs
final_probs = initial_probs
IO.puts "Calculating ring node probabilities where P=#{p} N=#{n} S=#{s} ...\n"
# If we are moving beyond the initial state then do the calculation ...
if s > 0 do
# ... through all the states ...
final_probs =
reduce 1..s,
initial_probs,
fn (_, new_probs) -> calc_state_probs(p, new_probs) end
end
final_probs
end

The first thing you might notice at the beginning of calc_ring_probs are the guard clauses (when …) after the function parameter definition. This is a nice way of ensuring some pre-conditions are met for the function to return meaningful results.
We check that the probability parameter is a float within the range 0.0 -> 1.0, we also make sure that there are more than zero nodes and this must be an integer and that the state is either zero or more and also an integer.
Next the initial probabilities are created using an Erlang array. If the state required is not the initial state (S=0) then we reduce for the number of states and calculate the probabilities of the ring at each state(calc_state_probs) until we reach the final state.

Now let’s look at the implementation of calc_state_probs.

def calc_state_probs(p, prev_probs)
when is_float(p) and p >= 0 and p <= 1 do
sz = :array.size(prev_probs)
:array.map fn(i, _) ->
prev_i = if i == 0 do sz - 1 else i - 1 end
prev_prob = :array.get(prev_i, prev_probs)
next_i = if i == sz - 1 do 0 else i + 1 end
next_prob = :array.get(next_i, prev_probs)
p * prev_prob + (1 - p) * next_prob
end, prev_probs
end

The function takes the probability P and an array of the previous probabilities. We determine the previous and next node probability indexes based on the current index. If the current index is the first or last index in the array then the previous index is the last and the next index is the first, respectively. We calculate the current index using the respective probability P or 1-P and the previous and next node probabilities.

That’s really all there is to the sequential version.

On a macbook air a 1,000,000 node ring over 10 state changes takes ~7.4 seconds.

My reluctance with Elixir is that it’s a strong dynamically typed language. This is much the same issue I’ve had with Erlang. There are ways to work around this. One way is using a static analysis tool. Read this for more info. Apparently success types are a way to correctly infer types in Erlang. I can’t say that I’m convinced, my own experience has shown that any production system that needs to scale at least requires something like type-hinting. I might be wrong and in fact I hope I am because I like what I’ve seen regarding Elixir and heard about the Erlang VM for building distributed systems.

In the next post we’ll re-write the code to make it run concurrently and also look at how a sequential version of the algorithm using recursion, pattern matching and lists is an order of magnitude faster than the sequential version using arrays in this post.
The sequential recursive version may even be faster than a concurrent version depending on how many cores your machine has ;-)

Popular interest in Clojure has rapidly increased over the last few years since 2008, almost to the level of Java (the language) today, which has dropped off significantly.Β (At least according to Google web trends.)
In contrast, popular interest in Common Lisp seems to have dropped off steadily since 2004.

I used “java language” instead of “java” because it is ambiguous enough to mean the language, framework, JVM, the island or the coffee.

In practice the O-notation approach to algorithmic analysis can often be quite misleading. Quick Sort vs. Merge Sort is a great example. Quick Sort is classified as time quadratic O(nΒ²) and Merge Sort as time log-linear O(n log n) according to O-notation. In practice however, Quick Sort often performs twice as fast as Merge Sort and is also far more space efficient. As many folks know this has to do with the typical inputs of these algorithms inΒ practice.Β Most engineers I know would still argue that Merge Sort is a better solution and apparently Robert has had the same argumentative response even though he is an expert in the field. In the lecture he kindly says the following : “… Such people usually don’t program much and shouldn’t be recommending what practitioners do”.

There are many more numerous examples of where practical application does not align with the use of O-notation.Β Also, detailed analysis of algorithmic performance just takes too long to be useful inΒ practice most of the time. So what other options do we have ?

There is a better way. An emerging science called “Analytic Combinatorics” pioneered by Robert Sedgewick and the late Philippe Flajolet over the past 30 years with the first (and only) text appearing in 2009 calledΒ Analytic Combinatorics. This approach is based on the scientific method and provides an accurate and more efficient way to determine the performance of algorithms(and classify them correctly). It even makes it possible to reason about an algorithms’ performance based on real-world input. It also allows for the generation of random data for a particular structure or structures, among other benefits.

“[Sedgewick and Flajolet] are not only worldwide leaders of the field, they also are masters of exposition. I am sure that every serious computer scientist will find this book rewarding in many ways.”Β βFrom the Foreword byΒ Donald E. Knuth