G4Pow.hh

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//
// G4Pow
//
// Class description:
//
// Utility singleton class for the fast computation of log and pow
// functions. Integer argument should be 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, 23.05.2009
// --------------------------------------------------------------------
#ifndef G4Pow_hh
#define G4Pow_hh 1
 
#include "G4DataVector.hh"
#include "G4Exp.hh"
#include "G4Log.hh"
#include "globals.hh"
 
class G4Pow
{
 public:
  static G4Pow* GetInstance();
  ~G4Pow() = default;
 
  // 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 G4bool) const;
  G4double A13High(const G4double, const G4bool) const;
 
  inline G4double logBase(G4double x) const;
 
  static G4Pow* fpInstance;
 
  const G4double onethird = 1.0 / 3.0;
  const G4int max2        = 5;
 
  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 methods implementation
// -----------------------------
 
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