Is F# Math Really Faster than C#?

I ran across an article claiming that F# was about an order of magnitude faster at calculating a basic math algorithm. Can this be true?

Sigmoid in C#

public static float Sigmoid(float value) 
{
    return 1.0f / (1.0f + (float) Math.Exp(-value));
}
//csc -o -debug-
.method public static float32 Sigmoid(float32 'value') cil managed
{
    .maxstack 8
    L_0000: ldc.r8 1
    L_0009: ldc.r8 1
    L_0012: ldarg.0 
    L_0013: neg 
    L_0014: conv.r8 
    L_0015: call float64 [mscorlib]System.Math::Exp(float64)
    L_001a: add 
    L_001b: div 
    L_001c: conv.r4 
    L_001d: ret 
}

Sigmoid in F#

let Sigmoid value = 1.0f/(1.0f + exp(-value));
//fsc --debug- --optimize+
.method public static float32 Sigmoid(float32 'value') cil managed
{
    .maxstack 5
    .locals init (
        [0] float32 num)
    L_0000: ldc.r4 1
    L_0005: ldc.r4 1
    L_000a: ldarg.0 
    L_000b: neg 
    L_000c: stloc.0 
    L_000d: ldloc.0 
    L_000e: conv.r8 
    L_000f: call float64 [mscorlib]System.Math::Exp(float64)
    L_0014: conv.r4 
    L_0015: add 
    L_0016: div 
    L_0017: ret 
}

The IL generated is nearly the same. The F# version allocates a little less memory using float32 variables on the stack where C# uses float64 and generally manages with a smaller stack, but the basic math operations are the same. Can these differences make an order of magnitude performance difference? Short answer is no.

Benchmarks are Tricky

C# sigmoid algorithm benchmark

// (c) Rinat Abdullin
// http://abdullin.com/journal/2009/1/5/caching-activation-function-is-not-worth-it.html
// sigmoidcs.cs

using System;
using System.Diagnostics;

static class App
{
	const float Scale = 320.0f;
	const int Resolution = 2047;
	const float Min = -Resolution/Scale;
	const float Max = Resolution/Scale;

	static readonly float[] _lut = InitLut();

	static float[] InitLut()
	{
	  var lut =  new float[Resolution + 1];
	  for (int i = 0; i < Resolution + 1; i++)
	  {
	    lut[i] = (float) (1.0/(1.0 + Math.Exp(-i/Scale)));
	  }
	  return lut;
	}

	static float Sigmoid1(double value)
	{
	  return (float) (1.0/(1.0 + Math.Exp(-value)));
	}

	static float Sigmoid2(float value)
	{
	  if (value <= Min) return 0.0f;
	  if (value >= Max) return 1.0f;
	  var f = value*Scale;
	  if (value >= 0) return _lut[(int) (f + 0.5f)];
	  return 1.0f - _lut[(int) (0.5f - f)];
	}

	static float TestError()
	{
	  var emax = 0.0f;
	  for (var x = -10.0f; x < 10.0f; x += 0.000001f)
	  {
	    var v0 = Sigmoid1(x);
	    var v1 = Sigmoid2(x);

	    var e = Math.Abs(v1 - v0);
	    if (e > emax) emax = e;
	  }
	  return emax;
	}

	static double TestPerformancePlain()
	{
	  var sw = new Stopwatch();
	  sw.Start();
	  for (int i = 0; i < 10; i++)
	  {
	    for (float x = -5.0f; x < 5.0f; x += 0.000001f)
	    {
	      Sigmoid1(x);
	    }
	  }

	  return sw.Elapsed.TotalMilliseconds;
	}

	static double TestPerformanceOfLut()
	{
	  var sw = new Stopwatch();
	  sw.Start();
	  for (int i = 0; i < 10; i++)
	  {
	    for (float x = -5.0f; x < 5.0f; x += 0.000001f)
	    {
	      Sigmoid2(x);
	    }
	  }
	  return sw.Elapsed.TotalMilliseconds;
	}

	static void Main()
	{
	  var emax = TestError();
	  var t0 = TestPerformancePlain();
	  var t1 = TestPerformanceOfLut();

	  Console.WriteLine("Max detected deviation using LUT: {0}", emax);
	  Console.WriteLine("10^7 iterations using Sigmoid1() took {0} ms", t0);
	  Console.WriteLine("10^7 iterations using Sigmoid2() took {0} ms", t1);
	}
}

F# sigmoid algorithm benchmark

// (c) Rinat Abdullin
// http://abdullin.com/journal/2009/1/6/f-has-better-performance-than-c-in-math.html
// sigmoidfs.fs

#light

let Scale = 320.0f;
let Resolution = 2047;

let Min = -single(Resolution)/Scale;
let Max = single(Resolution)/Scale;

let range step a b =
  let count = int((b-a)/step);
  seq { for i in 0 .. count -> single(i)*step + a };

let lut = [| 
  for x in 0 .. Resolution ->
    single(1.0/(1.0 +  exp(-double(x)/double(Scale))))
  |]

let sigmoid1 value = 1.0f/(1.0f + exp(-value));

let sigmoid2 v = 
  if (v <= Min) then 0.0f;
  elif (v>= Max) then 1.0f;
  else
    let f = v * Scale;
    if (v>0.0f) then lut.[int (f + 0.5f)]
    else 1.0f - lut.[int(0.5f - f)];

let getError f = 
  let test = range 0.00001f -10.0f 10.0f;
  let errors = seq { 
    for v in test -> 
      abs(sigmoid1(single(v)) - f(single(v)))
  }
  Seq.max errors;

open System.Diagnostics;

let test f = 
  let sw = Stopwatch.StartNew(); 
  let mutable m = 0.0f;
  let result = 
    for t in 1 .. 10 do
      for x in 1 .. 1000000 do
        m <- f(single(x)/100000.0f-5.0f);
  sw.Elapsed.TotalMilliseconds;

printf "Max deviation is %f\n" (getError sigmoid2)
printf "10^7 iterations using sigmoid1: %f ms\n" (test sigmoid1)
printf "10^7 iterations using sigmoid2: %f ms\n" (test sigmoid2)
PS> csc -o -debug- .\sigmoidcs.cs
Microsoft (R) Visual C# 2010 Compiler version 4.0.30319.1
Copyright (C) Microsoft Corporation. All rights reserved.

PS> fsc --debug- --optimize+  .\sigmoidfs.fs
Microsoft (R) F# 2.0 Compiler build 4.0.30319.1
Copyright (c) Microsoft Corporation. All Rights Reserved.
PS> .\sigmoidcs.exe
Max detected deviation using LUT: 0.001663984
10^7 iterations using Sigmoid1() took 2644.5935 ms
10^7 iterations using Sigmoid2() took 510.9379 ms
PS> .\sigmoidfs.exe
Max deviation is 0.001664
10^7 iterations using sigmoid1: 403.974300 ms
10^7 iterations using sigmoid2: 124.520100 ms

Wow. That’s 404ms for F# and 2,656 for C#. That’s a huge difference. Why?

We already established that the IL for the Sigmoid1() algorithm above compiles to very similar IL. What else could be different?

fsharp-test-func

Wait a minute.

let result = 
    for t in 1 .. 10 do
      for x in 1 .. 1000000 do
        m <- f(single(x)/100000.0f-5.0f);

The F# loop is not equivalent to the C# version. In the F# version the counter is an int and the C# version the counter is a float. (Also the F# version is passing a delegate to the test function.)

for (int i = 0; i < 10; i++)
{
	for (float x = -5.0f; x < 5.0f; x += 0.000001f)
	{
		Sigmoid1(x);
	}
}

Does that int counter thing make a big difference.

using System;
using System.Diagnostics;

static class App
{
	static float Sigmoid1(double value)
	{
	  return (float) (1.0/(1.0 + Math.Exp(-value)));
	}

	static double TestPerformancePlain()
	{
		var sw = new Stopwatch();
		sw.Start();
		float num = 0f;
		for (int i = 0; i < 10; i++)
		{
			for (int j = 1; j < 1000001; j++)
			{
				num = Sigmoid1((((float) j) / 100000f) - 5f);
			}
		}  
		return sw.Elapsed.TotalMilliseconds;
	}

	static void Main()
	{
	  var t0 = TestPerformancePlain();
	  Console.WriteLine("10^7 iterations using Sigmoid1() took {0} ms", t0);
	}
}
PS> csc -o -debug- .\sigmoid-counter.cs
Microsoft (R) Visual C# 2010 Compiler version 4.0.30319.1
Copyright (C) Microsoft Corporation. All rights reserved.

PS> ./sigmoid-counter
10^7 iterations using Sigmoid1() took 431.6634 ms

Yup C# just executed that Sigmoid1() test in 431ms. Recall that F# was 404ms.

The other difference was that the F# code was passing a delegate of FsharpFunc<float,float> rather than making a method call. Lets try the same thing in C# using a Lambda expression to create an anonymous Func<float,float> delegate.

using System;
using System.Diagnostics;

static class App
{
	static double Test(Func<float,float> f)
	{
		var sw = new Stopwatch();
		sw.Start();
		float num = 0f;
		for (int i = 0; i < 10; i++)
		{
			for (int j = 1; j < 1000001; j++)
			{
		   		num = f((((float) j) / 100000f) - 5f);
			}
		}  
		return sw.Elapsed.TotalMilliseconds;
	}

	static void Main()
	{
	  var t0 = Test( x => { return (float) (1.0/(1.0 + Math.Exp(-x))); } );
	  Console.WriteLine("10^7 iterations using Sigmoid1() took {0} ms", t0);
	}
}
PS> ./sigmoid-counter
10^7 iterations using Sigmoid1() took 431.6634 ms
PS> csc -o -debug- .\sigmoid-lambda.cs
Microsoft (R) Visual C# 2010 Compiler version 4.0.30319.1
Copyright (C) Microsoft Corporation. All rights reserved.

PS> .\sigmoid-lambda.exe
10^7 iterations using Sigmoid1() took 275.1087 ms

Now C# is 130ms faster than F#.

For what it’s worth the C version of the Sigmoid1() benchmark executes in 166ms on my machine using CL 16 x64 on my machine.

  • C: 166ms
  • C# (delegate): 275ms
  • C# (method): 431ms
  • C# (method, float counter): 2,656ms
  • F#: 404ms
  • So, what have we learned?

  • Never, ever use a float as a counter in a for loop in C#.
  • Invoking a delegate in the CLR is slightly faster than a normal method invocation.
  • It’s very easy to measure something other than what you intended when benchmarking.
  • In as much as this little test means anything, C# and F# have similar performance. C is still faster.
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2 Responses to Is F# Math Really Faster than C#?

  1. Pingback: Let Result | More More Pics

  2. Mohit says:

    Interesting!
    Though, it is plausible that use of int over float in a for loop may speed up the execution. But I didn’t thought delegate would come into affect too. From what I know, the most important field in a delegate is _methodPtr that points to the actual method (may it be an anonymous method), so I am thinking that when we use delegate instead of method we are somehow accessing direct memory in a way, though by managed code. Am I thinking right?
    Because, I don’t think other fields (_target and _invocationList) have any role in this.
    I would like to know one thing though, would this use of delegates over function only useful in this particular scenario or it would be useful in every long running compute bound task?
    Say for example, we have

    int sum = 0
    for (int i=0; i<100000000; i++)
    sum += i;

    (I know a formula can be used here, but that's not the point), here we have a long running compute bound operation, is there any way use of delegate might decrease the time it takes to compute? What about IO bases operation? What about the combination?

    Say we have a table with 2 columns, ID and name, (ID being primary key)
    and SQLCommand cmd = "SELECT ID, Name FROM [table]"
    as ID is primary key, the data is on leaf, so no further lookups necessary. But when we read it like
    SQLDataReader rdr = cmd.ExecuteReader();
    List names = new List();
    while (rdr.read())
    {
    names.add(rdr.GetString(1));
    }
    // close reader and connection

    here, we have io bases operation, as datareader is reading, also compute based because of adding to the list (names), is there anyway delegates could be useful here? May be speed up the process by a few milliseconds?

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