Iterators, LINQ deferred execution and prime numbers computation

There is something
that I am proud of. In my book Practical .NET2 and C#2 I presented the
concept of deferred execution and deferred execution is a central concept in LINQ
in-memory querying. The C# team made deferred execution easy to implement
thanks to the concept of iterators introduced
with C#2.

 

At that time of C#2, 2 years ago, the
community was wondering why the hell the C# team invested so much in such a
tricky compiler artifact, that is basically only useful to save you a dozen
lines of code when you implement your own collection classes. But thanks to the
Wesner Moise thoughts in its blog, I realized that iterators are a good way to implement some funny stuff such
as some pipeline patterns. This is illustrated by the example 47 of the Chapter
14

 

Here is this example:

 

using System.Collections.Generic;

class Program
{

   static public IEnumerable<int> PipelineIntRange(int
begin, int end) {

      System.Diagnostics.Debug.Assert(begin < end);

      for (int i = begin; i <= end; i++) {

         System.Console.WriteLine(“Yield:” + i);

         yield return i;

      }

   }

   static public IEnumerable<int> PipelineMultiply(int
factor,

                                               IEnumerable<int>
input) {

      foreach (int i in input)

         yield return i * factor;

   }

   static public IEnumerable<int> PipelineFilterModulo(int
modulo,

                                               IEnumerable<int>
input) {

      foreach (int i in input)

         if (i
% modulo == 0)

            yield
return i;

   }

   static public IEnumerable<int> PipelineJoin(IEnumerable<int> input1,

                                               IEnumerable<int>
input2) {

      foreach (int i in input1)

         yield return i;

      foreach (int i in input2)

         yield return i;

   }

   static void Main() {

      IEnumerable<int> pipeline = PipelineJoin(

         PipelineIntRange(-4, -2),
PipelineFilterModulo(3,

                                     
PipelineMultiply(2,

                                     
PipelineIntRange(1, 10))));

      System.Console.WriteLine(“Begin foreach:” + i);

      foreach (int i in pipeline)

         System.Console.WriteLine(i);

   }

}

 

This program outputs:

 

Begin
foreach:


Yield:1
Yield:2
Yield:3
6
Yield:4
Yield:5
Yield:6
12
Yield:7
Yield:8
Yield:9
18
Yield:10
Yield:-4

-4
Yield:-3
-3
Yield:-2
-2 

 

Here is a small explanation
why the pipeline output the sequence  6 12 18
-4 -3 -2:

 

PipelineIntRange(1,10)    1 
2  3  4 
5  6  7 
8  9  10

PipelineMultiply(2)       2 
4  6  8  10
12 14 16 18 20

PipelineFilterModulo(3)         6       
12       18

PipelineIntRange(-4, -2)                                -4 -3 -2  

PipelineJoin                    6        12       18    -4 -3 -2

 

What is funny is the
way we obtain the sequence. The order the Console.WriteLine() we put into the program are executed shows
2 tricky things:

 

  • First, no computation
    happen before the foreach() instruction. The pipeline object actually
    represents a tree of pipeline node objects.

 

  • Second, each integer
    goes through all chain pipeline nodes (except if a node discard it) before the next integer is treated.

 

This is deferred
execution!

 

Now, it is
easy to rewrite this example with C#3 extension methods to make the code more LINQ
compliant:

 

 

using System.Collections.Generic;

static class
Program {

   static public IEnumerable<int>
PipelineIntRange(int begin, int end) {

      System.Diagnostics.Debug.Assert(begin
< end);

      for (int i = begin; i <= end; i++) {

         System.Console.WriteLine(“Yield:” + i);

         yield return i;

      }

   }

   static public IEnumerable<int>
PipelineMultiply(

                                               this IEnumerable<int>
input
,

                                               int factor) {

      foreach (int i in input)

         yield return i * factor;

   }

   static public IEnumerable<int>
PipelineFilterModulo(

                                               this IEnumerable<int>
input
,

                                               int modulo) {

      foreach (int i in input)

         if (i
% modulo == 0)

            yield
return i;

   }

   static public IEnumerable<int>
PipelineJoinWith(

                                               this
IEnumerable<int> input1
,

                                              
IEnumerable<int> input2) {

      foreach (int i in input1)

         yield return i;

      foreach (int i in input2)

         yield return i;

   }

   static void Main() {

     
IEnumerable<int> pipeline =

        
PipelineIntRange(1, 10)

        
.PipelineMultiply(2)

        
.PipelineFilterModulo(3)

        
.PipelineJoinWith(PipelineIntRange(-4, -2));

 

      foreach (int i in pipeline)

         System.Console.WriteLine(i);

   }

}

 

This time, the way the
pipeline object is defined makes it much more look alike a LINQ query.

 

 

 

More fun with prime number computation!

 

The example 50 of the
Chapter 14
is even more fun.

 

This time, the deal
is to chain iterators to compute prime numbers. This is possible thanks to an
easy algorithm to compute prime numbers named Sieve of Erathostène. The following schema shows how the algorithm
works:

 

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
|

 
3   5   7  
9    11    13   
15    17 | 3 is prime, 

                                        |
4,6,8,10,12,14,16,18 and

                                        | 20
are multiples of 2.

                                        |

     
5   7        11  
 13          17 | 5 is prime, 9 and 21

                                        | are
multiples of 3.

                                       

         
7        11    13         
17 | 7 is prime, the list doesn’t

                                        |
contain any multiple of 5.

                                       

                   11   
13          17 | 11 is prime, the
list doesn’t

                                        |
contain any multiple of 7.

                         13          17 | 13 is prime, the list doesn’t

                                        |
contain any multiple of 11.

                                       

                                     17 | 17 is
prime, the list doesn’t

                                        |
contain any multiple of 13.

Here is the code:

 

using System;

using System.Collections.Generic;

class Program
{

   static public IEnumerable<int> PipelineIntRange( int
begin, int end ) {

      System.Diagnostics.Debug.Assert( begin < end );

      for ( int i = begin; i <= end; i++ )

         yield return i;

   }

   static public IEnumerable<int>
PipelinePrime( IEnumerable<int> input ) {

      using ( IEnumerator<int>
e = input.GetEnumerator() ) {

         e.MoveNext();

         int
prime = e.Current;

         // The first
number of the list is a prime.

         Console.WriteLine(
prime );

         if (
prime != 0 ) {

            while
( e.MoveNext() ) {

               //
Remove all multiple of the found prime.

               if
( e.Current % prime != 0 )

                  yield
return e.Current;

            }

         }

      }

   }

   const int N = 100;

   static void Main() {

      // Apply the
approximation of Gauss/de la Vallée Poussin

      // to get the number of iterators.

      int
N_PRIME = (int)Math.Floor(
((double)N)/Math.Log(N)
);

 

      // Build a
pipeline of N_PRIME PipelineIntegerRange chained with

      // a
PipelineIntegerRange. Each call to PipelinePrime yield an

      // iterator
object that we store.

      List<IEnumerable<int>>
list = new List<IEnumerable<int>>();

      list.Add(PipelinePrime( PipelineIntRange(
2, N ) ) );

      for( int i=1 ; i<N_PRIME ;
i++ )

         list.Add( PipelinePrime(list[i-1]) );

 

      // Cascade the
computation among iterators by yielding every

      // numbers
between 2 and N.

      foreach (
int i in
list[N_PRIME-1] );

   }

}     

 

 

Here also it is
possible to make the example more clear thanks to C#3 extension methods. This
time we don’t need a list anymore and we are directly chaining filters:

 

using System;

using System.Collections.Generic;

static class
Program {

   static public IEnumerable<int> PipelineIntRange( int
begin, int end ) {

      System.Diagnostics.Debug.Assert( begin < end );

      for ( int i = begin; i <= end; i++ )

         yield return i;

   }

   static public IEnumerable<int> PipelinePrime(

       this IEnumerable<int> input ) {

      using ( IEnumerator<int>
e = input.GetEnumerator() ) {

         e.MoveNext();

         int
prime = e.Current;

         // The first
number of the list is a prime.

         Console.WriteLine(
prime );

         if (
prime != 0 ) {

            while
( e.MoveNext() ) {

               //
Remove all multiple of the found prime.

               if
( e.Current % prime != 0 )

                  yield
return e.Current;

            }

         }

      }

   }

   const int N = 100;

   static void Main() {

      // Apply the
approximation of Gauss/de la Vallée Poussin

      // to get the number of iterators.

      int
N_PRIME = (int)Math.Floor(
((double)N)/Math.Log(N)
);

 

      // Build a
pipeline of N_PRIME PipelineIntegerRange chained with

      // a
PipelineIntegerRange. Each call to PipelinePrime yield an

      // iterator
object that we store.

      IEnumerable<int> pipeline = PipelineIntRange(2,N);

 

      for( int i=1 ;
i<N_PRIME ; i++ )

         pipeline
= pipeline.PipelinePrime();

 

      // Cascade the
computation among iterators by yielding every

      // numbers
between 2 and N.

      foreach (
int i in
pipeline);

   }

}     

 

This example is a good
start for understanding how to build LINQ queries dynamically.

 

In case you want to dig more in iterators under the hood, the entire
section of my book I wrote about iterators is available as an article here. I explain what the C# compiler
is doing under the hood to mimic the notion of co-routine.  There is also another tricky example that
shows how iterators can be used to model the notion of continuation.

 

Apart dealing with
NDepend development I enjoy being a trainer on .NET, C# and also doin design and quality consultancy with NDepend. It is an excellent way to keep contact with real developers
that have real problems that can be solved with tools such as NDepend. I am
working closely with a bank with thousands of developers that is migrating most of its legacy to .NET. Hence, students I cop with
are motivated developers with a solid background in C++ and Java. Thanks
to LINQ I am now happy to show that things like iterators, co-routine or
closures and more are not just advanced geeky things but are in fact a dramatic
weapon to make code more expressive. This makes the Java guys, generally reluctant to
learning .NET, more open minded about what a multi-language platform bring to
the mainstream development. Some could say that Ruby was the initial starter but nobody can deny that LINQ is really really elegant.

 

Also I would like to
precise that I had the chance to proof-read a great book about LINQ  (LINQ in Action, Manning Publications) co-written
by my friend Fabrice Marguerie. I plan to review the book soon. For now I can’t say much more than Go buy it! Fabrice and its 2 colleagues just made an awesome work at explaining new C#3 stuff, LINQ concepts, LINQ use
cases (in-memory querying, LINQ2SQL, LINQ2XML…), LINQ under the hood tricky
things, the multiple ways to extend LINQ for your own needs and best practices to use LINQ.

 

 

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  • http://s.thainua2GMAIL.COM subhash

    Dear
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  • http://linq-book.com Fabrice

    Thanks for the reference and for the work you did during proof-reading.

    I’d like to point out that the chapter that covers deferred query execution is available as a free download. You can find it at http://manning.com/marguerie where you’ll be able to learn more about the book and find two more free chapters!