WARNING! I know that F# is intended to be use in a very Functional way, however, my goal is to show its Imperative and OO language features, so it can be compared with other 19 OO languages. Said that, if you know how to do something on the examples below in a more Functional style you can add it in a comment :)
Here below a little program in F# that implements 2 classes (in fact, they are 3). There is the main class, called Fiborial (Fibo(nnacci)+(Facto)rial) that implements the Fibonacci and the Factorial algorithms in two ways, one Recursive (using recursion) and the other Imperative (using loops and states). The second class is just an instance class that does the same thing, but its there just to show the difference between static and instance classes, and finally the third one (which will not appear in other languages) is the Program class which has the static execution method "Main".
You can also find 3 more little examples at the bottom. One prints out the Factorial's Series and Fibonacci's Series, the second one just shows a class that mixes both: static and instance members, and finally the third one that uses different return types (including System.Numerics.BigInteger) for the Factorial method to compare the timing and result.
As with the previous posts, you can copy and paste the code below in your favorite IDE/Editor and start playing and learning with it. This little "working" program will teach you some more basics of the Programming Language.
There are some "comments" on the code added just to tell you what are or how are some features called. In case you want to review the theory, you can read my previous post, where I give a definition of each of the concepts mentioned on the code. You can find it here: http://carlosqt.blogspot.com/2011/01/new-series-factorial-and-fibonacci.html
In F# like in VB.NET there is a type called Module. An F# module is a grouping of F# code constructs such as types, values, function values, and code in do bindings. It is implemented as a common language runtime (CLR) class that has only static members. Normally I would only use the Module type as the first example, however, here I included both, an instance class with only Static Members and a second example using Module. The syntax for the members declaration varies so I wanted to include both even if we see a second example in the Mixing Instance and Static members program.
The Fiborial Program (using Type = Instance Class)
// Factorial and Fibonacci in F#
namespace FiborialFs
open System
open System.Collections.Generic
open System.Diagnostics
open System.Numerics
// Instance Class
// with all static members
type StaticFiborial() = class
// Static Field
static let mutable className:string = ""
// Static Constructor/Initializer(s)
static do className <- "Static Constructor"
static do printfn "%s" className
// Static Method - Factorial Recursive
// in F#: type bigint = BigInteger
static member public FactorialR(n:int) : bigint =
if n = 1 then
bigint(1)
else
bigint(n) * StaticFiborial.FactorialR(n-1)
// Static Method - Factorial Imperative
static member public FactorialI(n:int) : bigint =
let mutable res:bigint = bigint(1)
for i = n downto 1 do
res <- res * bigint(i)
res
// Static Method - Fibonacci Recursive
static member public FibonacciR(n:int) : int64 =
if (n < 2) then
int64(1)
else
StaticFiborial.FibonacciR(n - 1) + StaticFiborial.FibonacciR(n - 2)
// Static Method - Fibonacci Imperative
static member public FibonacciI(n:int) : int64 =
let mutable pre:int64 = int64(1)
let mutable cur:int64 = int64(1)
let mutable tmp:int64 = int64(0)
for i = 2 to n do
tmp <- cur + pre
pre <- cur
cur <- tmp
cur
// Static Method - Benchmarking Algorithms
static member public BenchmarkAlgorithm(algorithm:int, values:list<int>) =
let timer = new Stopwatch()
let mutable i:int = 1
let mutable testValue:int = 1
let mutable facTimeResult:bigint = bigint(0)
let mutable fibTimeResult:int64 = int64(0)
// "if-elif-else" Flow Control Statement
if algorithm = 1 then
printfn "\nFactorial Imperative:"
// "For to" Loop Statement
for i = 1 to values.Length - 1 do
testValue <- values.Item(i)
// Taking Time
timer.Start()
facTimeResult <- StaticFiborial.FactorialI(testValue)
timer.Stop()
// Getting Time
printfn " (%s) = %s" (testValue.ToString()) (timer.Elapsed.ToString())
elif algorithm = 2 then
printfn "\nFactorial Recursive:"
// "While" Loop Statement
while i < values.Length - 1 do
testValue <- values.Item(i)
// Taking Time
timer.Start()
facTimeResult <- StaticFiborial.FactorialR(testValue)
timer.Stop()
// Getting Time
printfn " (%s) = %s" (testValue.ToString()) (timer.Elapsed.ToString())
i <- i + 1
elif algorithm = 3 then
printfn "\nFibonacci Imperative:"
// "For in" Loop Statement
for item in values do
testValue <- item
// Taking Time
timer.Start();
fibTimeResult <- StaticFiborial.FibonacciI(testValue)
timer.Stop();
// Getting Time
printfn " (%s) = %s" (testValue.ToString()) (timer.Elapsed.ToString())
elif algorithm = 4 then
printfn "\nFibonacci Recursive:"
// "For in" Loop Statement
for item in values do
testValue <- item
// Taking Time
timer.Start();
fibTimeResult <- StaticFiborial.FibonacciR(testValue)
timer.Stop();
// Getting Time
printfn " (%s) = %s" (testValue.ToString()) (timer.Elapsed.ToString())
else
printfn "DONG!"
end
// Instance Class
type InstanceFiborial() = class
// Instance Field
let mutable className:string = ""
// Instance Constructor/Initializer(s)
do className <- "Instance Constructor"
do printfn "%s" className
// Instance Method - Factorial Recursive
member public self.FactorialR(n:int) : bigint =
// Calling Static Method
StaticFiborial.FactorialR(n)
// Instance Method - Factorial Imperative
member public self.FactorialI(n:int) : bigint =
// Calling Static Method
StaticFiborial.FactorialI(n)
// Instance Method - Fibonacci Recursive
member public self.FibonacciR(n:int) : int64 =
// Calling Static Method
StaticFiborial.FibonacciR(n)
// Instance Method - Factorial Imperative
member public self.FibonacciI(n:int) : int64 =
// Calling Static Method
StaticFiborial.FibonacciI(n);
end
module Program =
//printfn "%s" (Fiborial.FactorialR(40).ToString())
printfn "\nStatic Class"
// Calling Instance Class with Static Methods
// No instantiation needed. Calling method directly from the class
printfn "FacImp(5) = {%s}" (StaticFiborial.FactorialI(5).ToString())
printfn "FacRec(5) = {%s}" (StaticFiborial.FactorialR(5).ToString())
printfn "FibImp(11)= {%s}" (StaticFiborial.FibonacciI(11).ToString())
printfn "FibRec(11)= {%s}" (StaticFiborial.FibonacciR(11).ToString())
printfn "\nInstance Class"
// Calling Instance Class and Methods
// Need to instantiate before using. Calling method from instantiated object
let ff:InstanceFiborial = new InstanceFiborial()
Console.WriteLine("FacImp(5) = {0}", ff.FactorialI(5))
Console.WriteLine("FacRec(5) = {0}", ff.FactorialR(5))
Console.WriteLine("FibImp(11)= {0}", ff.FibonacciI(11))
Console.WriteLine("FibRec(11)= {0}", ff.FibonacciR(11))
// Create a (generic) list of integer values to test
// From 5 to 50 by 5
let values = [5..5..50]
// Benchmarking Fibonacci
// 1 = Factorial Imperative
StaticFiborial.BenchmarkAlgorithm(1, values);
// 2 = Factorial Recursive
StaticFiborial.BenchmarkAlgorithm(2, values);
// Benchmarking Factorial
// 3 = Fibonacci Imperative
StaticFiborial.BenchmarkAlgorithm(3, values);
// 4 = Fibonacci Recursive
StaticFiborial.BenchmarkAlgorithm(4, values);
// Stop and Exit
let i = Console.Read()
And the Output is:
Humm, looks like Fibonnaci's algorithm implemented using recursion is definitively more complex than the others 3 right? I will grab these results for this and each of the upcoming posts to prepare a comparison of time execution between all the programming languages, then we will be able to talk about the algorithm's complexity as well.
The Fiborial Program (using Module = Static Class)
// Factorial and Fibonacci in F#
namespace FiborialFs
open System
open System.Collections.Generic
open System.Diagnostics
open System.Numerics
// Static Class
module StaticFiborial =
// Static Field
let mutable className:string = ""
// Static Constructor/Initializer(s)
do className <- "Static Constructor"
do printfn "%s" className
// Static Method - Factorial Recursive
// in F#: type bigint = BigInteger
let rec FactorialR(n:int) : bigint =
if n = 1 then
bigint(1)
else
bigint(n) * FactorialR(n-1)
// Static Method - Factorial Imperative
let public FactorialI(n:int) : bigint =
let mutable res:bigint = bigint(1)
for i = n downto 1 do
res <- res * bigint(i)
res
// Static Method - Fibonacci Recursive
let rec FibonacciR(n:int) : int64 =
if (n < 2) then
int64(1)
else
FibonacciR(n - 1) + FibonacciR(n - 2)
// Static Method - Fibonacci Imperative
let public FibonacciI(n:int) : int64 =
let mutable pre:int64 = int64(1)
let mutable cur:int64 = int64(1)
let mutable tmp:int64 = int64(0)
for i = 2 to n do
tmp <- cur + pre
pre <- cur
cur <- tmp
cur
// Static Method - Benchmarking Algorithms
let public BenchmarkAlgorithm(algorithm:int, values:list<int>) =
let timer = new Stopwatch()
let mutable i:int = 1
let mutable testValue:int = 1
let mutable facTimeResult:bigint = bigint(0)
let mutable fibTimeResult:int64 = int64(0)
// "if-elif-else" Flow Control Statement
if algorithm = 1 then
printfn "\nFactorial Imperative:"
// "For to" Loop Statement
for i = 1 to values.Length - 1 do
testValue <- values.Item(i)
// Taking Time
timer.Start()
facTimeResult <- FactorialI(testValue)
timer.Stop()
// Getting Time
printfn " (%s) = %s" (testValue.ToString()) (timer.Elapsed.ToString())
elif algorithm = 2 then
printfn "\nFactorial Recursive:"
// "While" Loop Statement
while i < values.Length - 1 do
testValue <- values.Item(i)
// Taking Time
timer.Start()
facTimeResult <- FactorialR(testValue)
timer.Stop()
// Getting Time
printfn " (%s) = %s" (testValue.ToString()) (timer.Elapsed.ToString())
i <- i + 1
elif algorithm = 3 then
printfn "\nFibonacci Imperative:"
// "For in" Loop Statement
for item in values do
testValue <- item
// Taking Time
timer.Start();
fibTimeResult <- FibonacciI(testValue)
timer.Stop();
// Getting Time
printfn " (%s) = %s" (testValue.ToString()) (timer.Elapsed.ToString())
elif algorithm = 4 then
printfn "\nFibonacci Recursive:"
// "For in" Loop Statement
for item in values do
testValue <- item
// Taking Time
timer.Start();
fibTimeResult <- FibonacciR(testValue)
timer.Stop();
// Getting Time
printfn " (%s) = %s" (testValue.ToString()) (timer.Elapsed.ToString())
else
printfn "DONG!"
module Program =
//printfn "%s" (Fiborial.FactorialR(40).ToString())
printfn "\nStatic Class"
// Calling Instance Class with Static Methods
// No instantiation needed. Calling method directly from the class
printfn "FacImp(5) = {%s}" (StaticFiborial.FactorialI(5).ToString())
printfn "FacRec(5) = {%s}" (StaticFiborial.FactorialR(5).ToString())
printfn "FibImp(11)= {%s}" (StaticFiborial.FibonacciI(11).ToString())
printfn "FibRec(11)= {%s}" (StaticFiborial.FibonacciR(11).ToString())
// Create a (generic) list of integer values to test
// From 5 to 50 by 5
let values = [5..5..50]
// Benchmarking Fibonacci
// 1 = Factorial Imperative
StaticFiborial.BenchmarkAlgorithm(1, values);
// 2 = Factorial Recursive
StaticFiborial.BenchmarkAlgorithm(2, values);
// Benchmarking Factorial
// 3 = Fibonacci Imperative
StaticFiborial.BenchmarkAlgorithm(3, values);
// 4 = Fibonacci Recursive
StaticFiborial.BenchmarkAlgorithm(4, values);
// Stop and Exit
let i = Console.Read()
And the Output is:
Printing the Factorial and Fibonacci Series
// Factorial and Fibonacci in F#
namespace FiborialSeries
open System
open System.Text
open System.Numerics
// Static Class
module Fiborial =
// We first define the Factorial and Fibonacci methods
// so we can use them after in the Series methods
let rec Factorial(n:int) : bigint =
if n = 1 then
bigint(1)
else
bigint(n) * Factorial(n-1)
let rec Fibonacci(n:int) : int64 =
if (n < 2) then
int64(1)
else
Fibonacci(n - 1) + Fibonacci(n - 2)
// Using a StringBuilder as a list of string elements
let public GetFactorialSeries(n:int): string =
// Create the String that will hold the list
let mutable series:StringBuilder = StringBuilder()
// We begin by concatenating the number you want to calculate
// in the following format: "!# ="
ignore (series.Append("!"))
ignore (series.Append(n))
ignore (series.Append(" = "))
// We iterate backwards through the elements of the series
for i = n downto 1 do
// and append it to the list
ignore (series.Append(i))
if i > 1 then
ignore (series.Append(" * "))
else
ignore (series.Append(" = "))
// Get the result from the Factorial Method
// and append it to the end of the list
ignore (series.Append(Factorial(n)))
// return the list as a string
series.ToString()
// Using a StringBuilder as a list of string elements
let public GetFibonnaciSeries(n:int): string =
// Create the String that will hold the list
let mutable series:StringBuilder = StringBuilder()
// We begin by concatenating the first 3 values which
// are always constant
ignore (series.Append("0, 1, 1"))
// Then we calculate the Fibonacci of each element
// and add append it to the list
for i = 2 to n do
if i < n then
ignore (series.Append(", "))
else
ignore (series.Append(" = "))
ignore (series.Append(Fibonacci(i)))
// return the list as string
series.ToString()
module Program =
// Printing Factorial Series
printfn ""
printfn "%s" (Fiborial.GetFactorialSeries(5))
printfn "%s" (Fiborial.GetFactorialSeries(7))
printfn "%s" (Fiborial.GetFactorialSeries(9))
printfn "%s" (Fiborial.GetFactorialSeries(11))
printfn "%s" (Fiborial.GetFactorialSeries(40))
// Printing Fibonacci Series
printfn ""
printfn "%s" (Fiborial.GetFibonnaciSeries(5))
printfn "%s" (Fiborial.GetFibonnaciSeries(7))
printfn "%s" (Fiborial.GetFibonnaciSeries(9))
printfn "%s" (Fiborial.GetFibonnaciSeries(11))
printfn "%s" (Fiborial.GetFibonnaciSeries(40))
And the Output is:
Mixing Instance and Static Members in the same Class
We can also define instance classes that have both, instance and static members such as: fields, properties, constructors, methods, etc. However, we cannot do that if the type is a Module because Module = Static Class and remember the features mentioned in the previous post:
The main features of a static class are:
- They only contain static members.
- They cannot be instantiated.
- They are sealed.
- They cannot contain Instance Constructors
namespace FiborialExtrasFs2
open System
// Instance Classes can have both: static and instance members.
// However, Modules (Static Classes) only allow static members to be defined.
// Instance Class
type Fiborial() = class
// Instance Field
let mutable instanceCount:int = 0
// Instance Constructor/Initializer(s)
do instanceCount <- 0
do printfn "\nInstance Constructor %s" (instanceCount.ToString())
// Static Field
static let mutable staticCount:int = 0
// Static Constructor/Initializer(s)
static do staticCount <- 0
static do printfn "\nStatic Constructor %s" (Fiborial.StaticCount.ToString())
//static do printfn "\nInstance Constructor {%s}" (staticCount.ToString())
// Instance Read-Only Property
member public this.InstanceCount
with get() = instanceCount
// Static Read-Only Property
// Remeber that Properties are Methods to the CLR, so, you can also
// define static properties for static fields.
static member public StaticCount
with get() = staticCount
// Instance Method
member public this.Factorial(n:int) =
instanceCount <- instanceCount + 1
printfn "\nFactorial(%s)" (instanceCount.ToString())
// Static Method
static member public Fibonacci(n:int) =
staticCount <- staticCount + 1
printfn "\nFibonacci(%s)" (Fiborial.StaticCount.ToString())
end
module Program =
// Calling Static Constructor and Methods
// No need to instantiate
Fiborial.Fibonacci(5)
// Calling Instance Constructor and Methods
// Instance required
let fib:Fiborial = new Fiborial()
fib.Factorial(5)
Fiborial.Fibonacci(15)
fib.Factorial(5)
// Calling Instance Constructor and Methods
// for a second object
let fib2:Fiborial = new Fiborial()
fib2.Factorial(5);
printfn ""
// Calling Static Property
printfn "Static Count = %s" (Fiborial.StaticCount.ToString())
// Calling Instance Property of object 1 and 2
printfn "Instance 1 Count = %s" (fib.InstanceCount.ToString())
printfn "Instance 2 Count = %s" (fib2.InstanceCount.ToString())
And the Output is:
Factorial using System.Int64, System.Double, System.Numerics.BigInteger (bigint)
The Factorial of numbers over 20 are massive!
For instance: !40 = 815915283247897734345611269596115894272000000000!
Because of this, the previous version of this program was giving the "wrong" result
!40 = -70609262346240000 when using "long" (System.Int64) type, but it was not until I did the Fiborial version in VB.NET that I realized about this faulty code, because instead of giving me a wrong value, VB.NET execution thrown an Overflow Exception when using the "Long" (System.Int64) type.
My first idea was to use ulong and ULong, but both failed for "big" numbers. I then used Double (double floating point) type and got no more exception/wrong result. The result of the factorial was now correct !40 = 1.1962222086548E+56, but still I wanted to show the Integer value of it, so I did some research and found that there is a new System.Numerics.BigInteger class in the .NET Framework 4.0. Adding the reference to the project and using this new class as the return type of the Factorial methods, I was able to get the result I was expecting.
!40 = 815915283247897734345611269596115894272000000000
What I also found was that using different types change the time the algorithm takes to finish:
System.Int64 < System.Double < System.Numerics.BigInteger
Almost by double!
To illustrate what I just "tried" to say, lets have a look at the following code and the output we get.
open System
open System.Diagnostics
open System.Numerics
// Long Factorial
let rec FactorialInt64(n:int): int64 =
match n with
| 1 -> int64(1)
| n -> int64(n) * FactorialInt64(n - 1)
// Double Factorial
let rec FactorialDouble(n:int): double =
match n with
| 1 -> double(1)
| n -> double(n) * FactorialDouble(n - 1)
// BigInteger Factorial
let rec FactorialBigInteger(n:int): bigint =
match n with
| 1 -> bigint(1)
| n -> bigint(n) * FactorialBigInteger(n - 1)
let timer:Stopwatch = new Stopwatch()
let mutable facIntResult:int64 = int64(0)
let mutable facDblResult:double = double(0)
let mutable facBigResult:bigint = bigint(0)
let mutable i:int = 0
let values:list<int> = [5..5..50]
printfn "\nFactorial using Int64"
// Benchmark Factorial using Int64
for i in values do
timer.Start();
facIntResult <- FactorialInt64(i)
timer.Stop();
printfn "(%d) = %s : %s" i (timer.Elapsed.ToString()) (facIntResult.ToString())
printfn "\nFactorial using Double"
// Benchmark Factorial using Double
for i in values do
timer.Start();
facDblResult <- FactorialDouble(i)
timer.Stop();
printfn "(%d) = %s : %s" i (timer.Elapsed.ToString()) (facDblResult.ToString())
printfn "\nFactorial using BigInteger"
// Benchmark Factorial using Double
for i in values do
timer.Start();
facBigResult <- FactorialBigInteger(i)
timer.Stop();
printfn "(%d) = %s : %s" i (timer.Elapsed.ToString()) (facBigResult.ToString())
NOTE: you DONT need to manually add a reference to the System.Numerics.dll assembly to your project because F# already adds it for you. In fact you don't need to use BigInteger, but bigint which is a type bigint = BigInteger.
And the Output is:
Posts
let fibonacci = Seq.unfold (fun (x, y) -> Some(x, (y, x + y))) (0I,1I)
ReplyDeletelet factorial n = let m = bigint n in [1 .. n] |> Seq.reduce ( * )
that factorial should be:
ReplyDeletelet factorial n = [1I .. (bigint n)] |> Seq.reduce ( * )
Thanks Daniel
ReplyDeleteI will add a section with examples people give in the comments to compare time and syntax.