# Phillip Trelford's Array

## POKE 36879,255

Chances are that if you are habitually applying C-style Micro-Optimization tricks when coding C#, like moving variable declarations out of loops, you are probably:

1. Prematurely optimizing
2. Doing it completely wrong

To demonstrate the point lets start by ignoring that there is a perfectly good Array.Reverse function in the framework and write our own:

```static void Reverse1<T>(T[] xs)
{
for (int i = 0; i < xs.Length / 2; i++)
{
T x = xs[i];
xs[i] = xs[xs.Length - 1 - i];
xs[xs.Length - 1 - i] = x;
}
}```

Now micro-optimize by taking the temp declaration out of the loop:

```static void Reverse2<T>(T[] xs)
{
T x;
for (int i = 0; i < xs.Length / 2; i++)
{
x = xs[i];
xs[i] = xs[xs.Length - 1 - i];
xs[xs.Length - 1 - i] = x;
}
}```

The IL (byte code) generated for both implementations is identical in both release and debug builds. If you don’t believe me then check it for yourself by using the ildasm tool.

Another micro-optimization would be to store a copy of the array length in a local variable:

```static void Reverse3<T>(T[] xs)
{
int len = xs.Length;
for (int i = 0; i < len / 2; i++)
{
T x = xs[i];
xs[i] = xs[len - 1 - i];
xs[len - 1 - i] = x;
}
}```

This does actually result in the generation of different IL code, however IL generation is only part of the story. The difference in execution time between these implementations is negligible. The reason is that the IL code is just-in-time (JIT) compiled to machine code before execution and this compilation step will apply further optimizations.

Premature optimization is wrong on so many levels:

• the optimization was probably unnecessary anyway
• code can become less readable for no tangible benefit
• you’re double guessing 2 compilation steps
• you’re probably not even considering high level optimizations

Pareto principle

The Sad Tragedy of Micro-Optimization Theater

Micro-Optimization and Meatballs

Micro-optimization tips to increase performance

F# lets you define your own operators, and like a man with a new hammer hunting for nails :) I’ve found an application of F# custom operators for sorting multiple columns:

`let inline (|?) a b = if a = 0 then b else a`

Lets start by trying to sort the table position of the current top 5 of English Football’s Premier League (compiled on 2010-01-21):

 Team Played Goal Difference Points Arsenal 22 34 48 Chelsea 21 34 48 Man Utd 22 30 47 Spurs 22 18 38 Man City 21 12 38

Lets say we represent the table as an array of tuples:

```let table = [|
("Arsenal", 22, 34, 48)
("Chelsea", 21, 34, 48)
("Spurs",   22, 18, 38)
("Man City",21, 12, 38)
("Man Utd", 22, 30, 47)
|] ```

If we could just sort on points, and wanted to sort the array in place, we could write:

`do  Array.Sort(table, fun (_,_,_,a) (_,_,_,b) -> b - a)   `

But as we can see from the table, some of the teams have the same points, so we need to order on points and goal difference. In the case of Arsenal and Chelsea at the top of the table, they not only have the same points, they have the same goal difference. In this situation the custom is to sort alphabetically (lucky for you if your team starts with the letter ‘A’).

The sort function must now apply secondary sorting criteria if the first expression gives zero:

```do  Array.Sort(table, fun a b ->
let nameA, _, gdA, pointsA = a
let nameB, _, gdB, pointsB = b
let points = pointsB - pointsA
let gd = gdB - gdA
let names = String.Compare(nameA, nameB)
if points <> 0 then points
else if gd <> 0 then gd
else names
)  ```

Now the custom operator introduced at the start of the article really captures it:

```do  Array.Sort(table, fun a b ->
let nameA, _, gdA, pointsA = a
let nameB, _, gdB, pointsB = b
pointsB - pointsA |? gdB - gdA |? String.Compare(nameA, nameB)
)  ```

The beauty of using the custom operator here, say over a function, is operators can be placed between expressions so can be used to compose the sort.

Finally, there are however a couple of other ways to hammer this nail:

• sort by mapping the table entry tuple
• using LINQ OrderBy and ThenBy

Mapping the table entry is easy on the eye but it does require the generation of temporary tuples and a new array:

`do  table |> Array.sortBy (fun (name,_,gd,points) -> -points,-gd,name) `

Using LINQ is also pretty easy on the eye but requires the generation of a new sequence:

```do  table.OrderByDescending(fun (_,_,_,p) -> p)
.ThenByDescending(fun (_,_,gd,_) -> gd)
.ThenBy(fun (name,_,_,_) -> name)```

PS If you are looking for a similar pattern in C#, Jon Skeet shows a similar (but more verbose) way of composing sort expressions using the ?? operator in his C# in Depth book.

PPS Tomas Petricek has a nice article with some sample use of custom operators in F#. Coincidentally he has just authored a book with Mr Skeet on Functional Programming.

PPPS For clarity I should point out that I am a Man Utd supporter, so the timing for this article could be seen as somewhat unfortunate.

Since I first posted an F# solution to Left-Truncatable Primes, C# and Haskell have entered the frame, and although this is not a good problem for a serious comparison of languages, I think it is still interesting.

So lets start at the beginning, Dominic Penfold initially posed the problem and gave an efficient algorithm implemented in C++ (39 lines):

```bool IsPrime(int num)
{
int sqrt = 1 + sqrtf(num);
for (int i=2; i<sqrt; i++)
{
if (num % i == 0)
return false;
}
return true;
}

int NthLeftTruncatablePrime(int target)
{
std::vector<int> PrimeRoots;
PrimeRoots.push_back(2);
PrimeRoots.push_back(3);
PrimeRoots.push_back(5);
PrimeRoots.push_back(7);
int start = 0;
int tens = 10;
while(true)
{
int end = PrimeRoots.size();
for (int i=1; i<10; i++)
{
for (int pos = start; pos< end; pos++)
{
int newprime = tens * i + PrimeRoots[pos];
if (IsPrime(newprime))
{
PrimeRoots.push_back(newprime);
if (PrimeRoots.size()==target)
return newprime;
}
}
}
start = end;
tens *= 10;
}
}```

Performance was considerably faster when 32-bit integers were switched for 64-bit integers.

The C++ code is very easily converted into C# (35 lines):

```static bool IsPrime(int num)
{
int sqrt = 1 + (int ) System.Math.Sqrt(num);
blue">for (int i = 2; i < sqrt; i++)
{
if (num % i == 0)
return false;
}
return true;
}

static int NthLeftTruncatedPrime(int target)
{
var primeRoots = new List<int>() { 2, 3, 5, 7};
int start = 0;
int tens = 10;
while (true)
{
int end = primeRoots.Count;
for (int i = 1; i < 10; i++)
{
for (int pos = start; pos < end; pos++)
{
int newprime = tens * i + primeRoots[pos];
if (IsPrime(newprime))
{
if (primeRoots.Count == target)
return newprime;
}
}
}
start = end;
tens *= 10;
}
}```

Conversion to F# is only slightly trickier as there is no equivalent return statement, but similar behavior can be accomplished using yield (30 lines):

```let IsPrime n =
if n = 1 then false
else
let max = n |> float |> sqrt |> int
let rec Test = function
| x when x > max -> true
| x -> if (n % x) = 0 then false else Test (x+1)
Test 2

let NthLeftTruncatablePrime n =
let oneDigitPrimes = [2;3;5;7]
seq {
let primes = ref oneDigitPrimes
for tens = 1 to 8 do
let acc = ref []
for i=1 to 9 do
let newPrime = i * pown 10 tens
let primes' = ref !primes
while (!primes').Length > 0 do
let x = newPrime+(!primes').Head
if IsPrime x then
acc := x :: !acc
yield x
primes' := (!primes').Tail
done
done
primes := !acc |> List.rev
done
}
|> Seq.append oneDigitPrimes
|> Seq.nth (n-1)```

The extra overhead of generating a sequence can be avoided using instead recursion (25 lines including IsPrime function):

```let NthLeftTruncatablePrime index =
let rec Find digit factor primes primes' count acc =
match digit, primes' with
| 10, _ ->
let primes = List.rev acc
Find 1 (10*factor) primes primes count []
| _, [] ->
Find (digit+1) factor primes primes count acc
| _, prime::tail ->
let k = (digit * factor) + prime
let count, acc =
if IsPrime k then count+1, k::acc else count, acc
if count = index then k
else Find digit factor primes tail count acc
let primes = [2;3;5;7]
if index <= 4 then List.nth primes (index-1)
else Find 1 10 primes primes 4 []```

Later Matt Curran (coincidentally another ex-games developer) got in on the act with a Haskell version (17 lines including a comment – although the lines are a little dense):

```isPrime :: Int -> Bool
isPrime 1 = False
isPrime x = null \$ take 1 [n | n <- [2..upperBound x], 0 == mod x n]
where
upperBound = floor . sqrt . fromIntegral

-- list of all left truncatable primes
ltps :: [Int]
ltps = ps 1 [0]
where
ps _ []      = []
ps m prevMag = thisMag ++ (ps (m*10) thisMag)
where
thisMag = primes [x*m | x <- [1..9]] prevMag
where
primes [] _ = []
primes (m:mgs) bases =
(filter isPrime [m+x | x <- bases]) ++ (primes mgs bases)```

Results Breakdown by language

 Language Lines of code Performance(ms) C++ 39 5.213 C# 35 5.332 F# sequence 30 14.075 F# recursive 25 5.412 Haskell 17 ?

Note: the time is to generate the 1000th prime, and the same computer was used for all tests, as was release mode. Haskell time coming soon.

LeftTruncatablePrime.cpp (1.45 kb)

LeftTruncatablePrime.cs (1.58 kb)

LeftTruncatablePrime_seq.fs (1.53 kb)

LeftTruncatablePrime_rec.fs (1.36 kb)

This article has been translated to Serbo-Croatian language by WHGeeks .