ENH: 'Math' namespace for mathematical functions

- centralises existing functions (erfInv, incGamma*, invIncGamma*).
  Provides a location for additional functions in the future.

- adjusted existing models to use these functions
  (e.g. distributionModels::normal)

src/OpenFOAM/primitives/functions/Math/MathFunctions.H

@@ -0,0 +1,122 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2021 OpenCFD Ltd.
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+    for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
+
+Namespace
+    Foam::Math
+
+Description
+    A namespace for various mathematical functions.
+
+    Reference:
+    \verbatim
+        Inverse error function (tag:W):
+            Winitzki, S. (2008).
+            A handy approximation for the error function and its inverse.
+            A lecture note obtained through private communication.
+            URL:https://sites.google.com/site/winitzki/sergei-winitzkis-files
+            (Retrieved on: 16 Feb 2021).
+
+        Incomplete gamma functions (tag:DM):
+            DiDonato, A. R., & Morris Jr, A. H. (1986).
+            Computation of the incomplete gamma
+            function ratios and their inverse.
+            ACM Transactions on Mathematical Software (TOMS), 12(4), 377-393.
+            DOI:10.1145/22721.23109
+    \endverbatim
+
+Note
+  - The algorithm in \c invIncGamma is described in (DM:Sec. 4).
+  - The algorithm in \c incGammaRatio_Q is described in (DM:Sec. 3).
+  - The accuracy parameter \c IND is set to a value of 1.
+
+SourceFiles
+    erfInv.C
+    incGamma.C
+    invIncGamma.C
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef MathFunctions_H
+#define MathFunctions_H
+
+#include "scalar.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+/*---------------------------------------------------------------------------*\
+                        Namespace Math Declaration
+\*---------------------------------------------------------------------------*/
+
+namespace Math
+{
+
+//- Inverse error function of a real-number argument
+//  \param y Real-number argument at which to evaluate. Domain: (-1, 1)
+//  \return The inverse of error function of y
+scalar erfInv(const scalar y);
+
+
+// Incomplete gamma functions
+
+//- Inverse of regularised lower incomplete gamma function
+//  \param a Real-number argument. Domain: (0, infty]
+//  \param P Real-number argument. Domain: [0,1]
+scalar invIncGamma(const scalar a, const scalar P);
+
+//- Regularised upper incomplete gamma function
+//  \param a Real-number argument. Domain: (0, infty]
+//  \param x Real-number argument. Domain: [0, infty]
+scalar incGammaRatio_Q(const scalar a, const scalar x);
+
+//- Regularised lower incomplete gamma function
+//  \param a Real-number argument. Domain: (0, infty]
+//  \param x Real-number argument. Domain: [0, infty]
+scalar incGammaRatio_P(const scalar a, const scalar x);
+
+//- Upper incomplete gamma function
+//  \param a Real-number argument. Domain: (0, infty]
+//  \param x Real-number argument. Domain: [0, infty]
+scalar incGamma_Q(const scalar a, const scalar x);
+
+//- Lower incomplete gamma function
+//  \param a Real-number argument. Domain: (0, infty]
+//  \param x Real-number argument. Domain: [0, infty]
+scalar incGamma_P(const scalar a, const scalar x);
+
+
+} // End namespace Math
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //