G4Pow.hh

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//
// -------------------------------------------------------------------
//
// Class G4Pow
//
// Class description:
//
// Utility singleton class for the fast computation of log and pow
// functions. Integer argument should in the interval 0-512, no
// check is performed inside these methods for performance reasons.
// For factorial integer argument should be in the interval 0-170
// Computations with double arguments are fast for the interval
// 0.002-511.5 for all functions except exponent, which is computed 
// for the interval 0-84.4, standard library is used in the opposite case

// Author: Vladimir Ivanchenko
//
// Creation date: 23.05.2009
// -------------------------------------------------------------------

#ifndef G4Pow_h
#define G4Pow_h 1

#include "globals.hh"
#include "G4Log.hh"
#include "G4Exp.hh"
#include "G4DataVector.hh"

class G4Pow
{

  public:

    static G4Pow* GetInstance();
   ~G4Pow();

    // Fast computation of Z^1/3
    //
    inline G4double Z13(G4int Z) const;
           G4double A13(G4double A) const;

    // Fast computation of Z^2/3
    //
    inline G4double Z23(G4int Z) const;
    inline G4double A23(G4double A) const;

    // Fast computation of log(Z)
    //
    inline G4double logZ(G4int Z) const;
    inline G4double logA(G4double A) const;
    inline G4double logX(G4double x) const;

    // Fast computation of log10(Z)
    //
    inline G4double log10Z(G4int Z) const;
    inline G4double log10A(G4double A) const;

    // Fast computation of exp(X)
    //
    inline G4double expA(G4double A) const;

    // Fast computation of pow(Z,X)
    //
    inline G4double powZ(G4int Z, G4double y) const;
    inline G4double powA(G4double A, G4double y) const;
           G4double powN(G4double x, G4int n) const;

    // Fast factorial
    //
    inline G4double factorial(G4int Z) const;
    inline G4double logfactorial(G4int Z) const;

  private:

    G4Pow();

    G4double A13Low(const G4double, const bool) const;
    G4double A13High(const G4double, const bool) const;

    inline G4double logBase(G4double x) const;

    static G4Pow* fpInstance;

    const G4double onethird;
    const G4int    max2;

    G4double maxA;
    G4double maxLowA;
    G4double maxA2;
    G4double maxAexp;

    G4DataVector ener;
    G4DataVector logen;
    G4DataVector pz13;
    G4DataVector lowa13;
    G4DataVector lz;
    G4DataVector lz2;
    G4DataVector fexp;
    G4DataVector fact;
    G4DataVector logfact;
};

// -------------------------------------------------------------------

inline G4double G4Pow::Z13(G4int Z) const
{
  return pz13[Z];
}

inline G4double G4Pow::Z23(G4int Z) const
{
  G4double x = Z13(Z);
  return x*x;
}

inline G4double G4Pow::A23(G4double A) const
{
  G4double x = A13(A);
  return x*x;
}

inline G4double G4Pow::logZ(G4int Z) const
{
  return lz[Z];
}

inline G4double G4Pow::logBase(G4double a) const
{
  G4double res;
  if(a <= maxA2) 
  {
    G4int i = G4int(max2*(a - 1) + 0.5);
    if(i > max2) { i = max2; }
    G4double x = a/(G4double(i)/max2 + 1) - 1;
    res = lz2[i] + x*(1.0 - (0.5 - onethird*x)*x);
  }
  else if(a <= maxA)
  {
    G4int i = G4int(a + 0.5);
    G4double x = a/G4double(i) - 1;
    res = lz[i] + x*(1.0 - (0.5 - onethird*x)*x);
  }
  else
  {
    res = G4Log(a);
  }
  return res;
}

inline G4double G4Pow::logA(G4double A) const
{
  return (1.0 <= A ? logBase(A) : -logBase(1./A));
}

inline G4double G4Pow::logX(G4double x) const
{
  G4double res = 0.0;
  G4double a = (1.0 <= x) ? x : 1.0/x;

  if(a <= maxA) 
  {
    res = logBase(a);
  }
  else if(a <= ener[2])
  {
    res = logen[1] + logBase(a/ener[1]);
  }
  else if(a <= ener[3])
  {
    res = logen[2] + logBase(a/ener[2]);
  }
  else
  {
    res = G4Log(a);
  }

  if(1.0 > x) { res = -res; }
  return res;
}

inline G4double G4Pow::log10Z(G4int Z) const
{
  return lz[Z]/lz[10];
}

inline G4double G4Pow::log10A(G4double A) const
{
  return logX(A)/lz[10];
}

inline G4double G4Pow::expA(G4double A) const
{
  G4double res;
  G4double a = (0.0 <= A) ? A : -A;

  if(a <= maxAexp)
  {
    G4int i = G4int(2*a + 0.5);
    G4double x = a - i*0.5;
    res = fexp[i]*(1.0 + x*(1.0 + 0.5*(1.0 + onethird*x)*x));
  }
  else
  {
    res = G4Exp(a);
  }
  if(0.0 > A) { res = 1.0/res; }
  return res;
}

inline G4double G4Pow::powZ(G4int Z, G4double y) const
{
  return expA(y*lz[Z]);
}

inline G4double G4Pow::powA(G4double A, G4double y) const
{
  return (0.0 == A ? 0.0 : expA(y*logX(A)));
}

inline G4double G4Pow::factorial(G4int Z) const
{
  return fact[Z];
}

inline G4double G4Pow::logfactorial(G4int Z) const
{
  return logfact[Z];
}

// -------------------------------------------------------------------

#endif