Use existing constants where appropriate

src/FSharpExamples/MCMC.fsx

@@ -31,6 +31,7 @@
 #r "../../out/lib/Net40/MathNet.Numerics.dll"
 #r "../../out/lib/Net40/MathNet.Numerics.FSharp.dll"
 
+open MathNet.Numerics
 open MathNet.Numerics.Random
 open MathNet.Numerics.Statistics
 open MathNet.Numerics.Distributions
@@ -113,7 +114,7 @@ do
     let normal = new Normal(mean, stddev)
 
     /// Evaluates the log normal distribution.
-    let npdf x m s = -0.5*(x-m)*(x-m)/(s*s) - 0.5 * log(2.0 * System.Math.PI * s * s)
+    let npdf x m s = -0.5*(x-m)*(x-m)/(s*s) - 0.5 * log(Constants.Pi2 * s * s)
 
     /// Implements the rejection sampling procedure.
     let ms = new MetropolisHastingsSampler<float>( 0.1, (fun x -> log(normal.Density(x))),
@@ -144,7 +145,7 @@ do
     let normal = new Normal(mean, stddev)
 
     /// Evaluates the logarithm of the normal distribution function.
-    let npdf x m s = -0.5*(x-m)*(x-m)/(s*s) - 0.5 * log(2.0 * System.Math.PI * s * s)
+    let npdf x m s = -0.5*(x-m)*(x-m)/(s*s) - 0.5 * log(Constants.Pi2 * s * s)
 
     /// Samples from a mixture that is biased towards samples larger than x.
     let mixSample x =

src/Numerics/Distributions/Chi.cs

@@ -144,7 +144,7 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         public double Mean
         {
-            get { return Math.Sqrt(2)*(SpecialFunctions.Gamma((_dof + 1.0)/2.0)/SpecialFunctions.Gamma(_dof/2.0)); }
+            get { return Constants.Sqrt2*(SpecialFunctions.Gamma((_dof + 1.0)/2.0)/SpecialFunctions.Gamma(_dof/2.0)); }
         }
 
         /// <summary>

src/Numerics/Distributions/Laplace.cs

@@ -181,7 +181,7 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         public double StdDev
         {
-            get { return Math.Sqrt(2.0)*_scale; }
+            get { return Constants.Sqrt2*_scale; }
         }
 
         /// <summary>

src/Numerics/Distributions/Normal.cs

@@ -378,7 +378,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the inverse cumulative density at <paramref name="p"/>.</returns>
         public double InverseCumulativeDistribution(double p)
         {
-            return _mean - (_stdDev*Math.Sqrt(2.0)*SpecialFunctions.ErfcInv(2.0*p));
+            return _mean - (_stdDev*Constants.Sqrt2*SpecialFunctions.ErfcInv(2.0*p));
         }
 
         /// <summary>

src/Numerics/Distributions/Rayleigh.cs

@@ -171,7 +171,7 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         public double Entropy
         {
-            get { return 1.0 + Math.Log(_scale/Math.Sqrt(2)) + (Constants.EulerMascheroni/2.0); }
+            get { return 1.0 + Math.Log(_scale/Constants.Sqrt2) + (Constants.EulerMascheroni/2.0); }
         }
 
         /// <summary>

src/Numerics/Distributions/Stable.cs

@@ -237,7 +237,7 @@ namespace MathNet.Numerics.Distributions
             {
                 if (_alpha == 2)
                 {
-                    return Math.Sqrt(2.0)*_scale;
+                    return Constants.Sqrt2*_scale;
                 }
 
                 return Double.PositiveInfinity;
@@ -452,7 +452,7 @@ namespace MathNet.Numerics.Distributions
                 var summand = part1*Math.Tan(randTheta);
                 var subtrahend = beta*Math.Log(Constants.PiOver2*randW*Math.Cos(randTheta)/part1);
 
-                return location + scale*((2.0/Math.PI)*(summand - subtrahend));
+                return location + scale*Constants.TwoInvPi*(summand - subtrahend);
             }
         }
 

src/Numerics/LinearAlgebra/Complex/Factorization/UserQR.cs

@@ -152,7 +152,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex.Factorization
             if (row == a.RowCount - 1 || norm.Magnitude == 0)
             {
                 a.At(row, column, -u[0]);
-                u[0] = Math.Sqrt(2.0);
+                u[0] = Constants.Sqrt2;
                 return u;
             }
 

src/Numerics/LinearAlgebra/Complex32/Factorization/UserQR.cs

@@ -147,7 +147,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization
             if (row == a.RowCount - 1 || norm.Magnitude == 0)
             {
                 a.At(row, column, -u[0]);
-                u[0] = (float)Math.Sqrt(2.0);
+                u[0] = (float)Constants.Sqrt2;
                 return u;
             }
 

src/Numerics/LinearAlgebra/Double/Factorization/UserQR.cs

@@ -146,7 +146,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
             if (row == a.RowCount - 1 || norm == 0)
             {
                 a.At(row, column, -u[0]);
-                u[0] = Math.Sqrt(2.0);
+                u[0] = Constants.Sqrt2;
                 return u;
             }
 

src/Numerics/LinearAlgebra/Single/Factorization/UserQR.cs

@@ -145,7 +145,7 @@ namespace MathNet.Numerics.LinearAlgebra.Single.Factorization
             if (row == a.RowCount - 1 || norm == 0)
             {
                 a.At(row, column, -u[0]);
-                u[0] = (float)Math.Sqrt(2.0);
+                u[0] = (float)Constants.Sqrt2;
                 return u;
             }
 

src/Numerics/Providers/LinearAlgebra/ManagedLinearAlgebraProvider.Double.cs

@@ -1720,7 +1720,7 @@ namespace MathNet.Numerics.Providers.LinearAlgebra
             if (row == rowCount - 1 || norm == 0)
             {
                 a[index] = -work[tmp];
-                work[tmp] = Math.Sqrt(2.0);
+                work[tmp] = Constants.Sqrt2;
                 return;
             }
 

src/Numerics/Providers/LinearAlgebra/ManagedLinearAlgebraProvider.Single.cs

@@ -1721,7 +1721,7 @@ namespace MathNet.Numerics.Providers.LinearAlgebra
             if (row == rowCount - 1 || norm == 0)
             {
                 a[index] = -work[tmp];
-                work[tmp] = (float) Math.Sqrt(2.0);
+                work[tmp] = (float) Constants.Sqrt2;
                 return;
             }
 

src/Numerics/Trigonometry.cs

@@ -473,7 +473,7 @@ namespace MathNet.Numerics
         {
             if (value.IsZero())
             {
-                return Math.PI / 2.0;
+                return Constants.PiOver2;
             }
 
             var inv = Complex.ImaginaryOne / value;

src/UnitTests/DistributionTests/Continuous/ChiTests.cs

@@ -124,7 +124,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         public void ValidateMean(double dof)
         {
             var n = new Chi(dof);
-            Assert.AreEqual(Math.Sqrt(2) * (SpecialFunctions.Gamma((dof + 1.0) / 2.0) / SpecialFunctions.Gamma(dof / 2.0)), n.Mean);
+            Assert.AreEqual(Constants.Sqrt2 * (SpecialFunctions.Gamma((dof + 1.0) / 2.0) / SpecialFunctions.Gamma(dof / 2.0)), n.Mean);
         }
 
         /// <summary>

src/UnitTests/DistributionTests/Continuous/LaplaceTests.cs

@@ -192,7 +192,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         public void ValidateStdDev(double location, double scale)
         {
             var n = new Laplace(location, scale);
-            Assert.AreEqual(Math.Sqrt(2.0) * scale, n.StdDev);
+            Assert.AreEqual(Constants.Sqrt2 * scale, n.StdDev);
         }
 
         /// <summary>

src/UnitTests/DistributionTests/Continuous/RayleighTests.cs

@@ -167,7 +167,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         public void ValidateEntropy(double scale)
         {
             var n = new Rayleigh(scale);
-            Assert.AreEqual(1.0 + Math.Log(scale / Math.Sqrt(2)) + (Constants.EulerMascheroni / 2.0), n.Entropy);
+            Assert.AreEqual(1.0 + Math.Log(scale / Constants.Sqrt2) + (Constants.EulerMascheroni / 2.0), n.Entropy);
         }
 
         /// <summary>

src/UnitTests/StatisticsTests/MCMCTests/UnivariateHybridMCTest.cs

@@ -141,7 +141,7 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests.McmcTests
             double deviationRation = Math.Pow(stats.StandardDeviation/sdv, 2);
 
             //Approximating chi-square with normal distribution. (Degree of freedom is large)
-            double deviationConvergence = 3*Math.Sqrt(2)/Math.Sqrt(effective);
+            double deviationConvergence = 3*Constants.Sqrt2/Math.Sqrt(effective);
             Assert.AreEqual(deviationRation, 1, deviationConvergence, "Standard Deivation");
         }
     }