G4Exp.hh

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//
// G4Exp
//
// Class description:
//
// The basic idea is to exploit Pade polynomials.
// A lot of ideas were inspired by the cephes math library
// (by Stephen L. Moshier moshier@na-net.ornl.gov) as well as actual code.
// The Cephes library can be found here:  http://www.netlib.org/cephes/
// Code and algorithms for G4Exp have been extracted and adapted for Geant4
// from the original implementation in the VDT mathematical library
// (https://svnweb.cern.ch/trac/vdt), version 0.3.7.
 
// Original implementation created on: Jun 23, 2012
// Authors: Danilo Piparo, Thomas Hauth, Vincenzo Innocente
//
// --------------------------------------------------------------------
/*
 * VDT is free software: you can redistribute it and/or modify
 * it under the terms of the GNU Lesser Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program 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 Lesser Public License for more details.
 *
 * You should have received a copy of the GNU Lesser Public License
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
 */
// --------------------------------------------------------------------
#ifndef G4Exp_hh
#define G4Exp_hh 1
 
#ifdef WIN32
 
#  define G4Exp std::exp
 
#else
 
#  include "G4Types.hh"
#  include "G4IEEE754.hh"
#  include <cstdint>
#  include <limits>
 
namespace G4ExpConsts
{
  const G4double EXP_LIMIT = 708;
 
  const G4double PX1exp = 1.26177193074810590878E-4;
  const G4double PX2exp = 3.02994407707441961300E-2;
  const G4double PX3exp = 9.99999999999999999910E-1;
  const G4double QX1exp = 3.00198505138664455042E-6;
  const G4double QX2exp = 2.52448340349684104192E-3;
  const G4double QX3exp = 2.27265548208155028766E-1;
  const G4double QX4exp = 2.00000000000000000009E0;
 
  const G4double LOG2E = 1.4426950408889634073599;  // 1/log(2)
 
  const G4float MAXLOGF = 88.72283905206835f;
  const G4float MINLOGF = -88.f;
 
  const G4float C1F = 0.693359375f;
  const G4float C2F = -2.12194440e-4f;
 
  const G4float PX1expf = 1.9875691500E-4f;
  const G4float PX2expf = 1.3981999507E-3f;
  const G4float PX3expf = 8.3334519073E-3f;
  const G4float PX4expf = 4.1665795894E-2f;
  const G4float PX5expf = 1.6666665459E-1f;
  const G4float PX6expf = 5.0000001201E-1f;
 
  const G4float LOG2EF = 1.44269504088896341f;
 
  //----------------------------------------------------------------------------
  /**
   * A vectorisable floor implementation, not only triggered by fast-math.
   * These functions do not distinguish between -0.0 and 0.0, so are not IEC6509
   * compliant for argument -0.0
   **/
  inline G4double fpfloor(const G4double x)
  {
    // no problem since exp is defined between -708 and 708. Int is enough for
    // it!
    int32_t ret = int32_t(x);
    ret -= (G4IEEE754::sp2uint32(x) >> 31);
    return ret;
  }
 
  //----------------------------------------------------------------------------
  /**
   * A vectorisable floor implementation, not only triggered by fast-math.
   * These functions do not distinguish between -0.0 and 0.0, so are not IEC6509
   * compliant for argument -0.0
   **/
  inline G4float fpfloor(const G4float x)
  {
    int32_t ret = int32_t(x);
    ret -= (G4IEEE754::sp2uint32(x) >> 31);
    return ret;
  }
}  // namespace G4ExpConsts
 
// Exp double precision --------------------------------------------------------
 
/// Exponential Function double precision
inline G4double G4Exp(G4double initial_x)
{
  G4double x  = initial_x;
  G4double px = G4ExpConsts::fpfloor(G4ExpConsts::LOG2E * x + 0.5);
 
  const int32_t n = int32_t(px);
 
  x -= px * 6.93145751953125E-1;
  x -= px * 1.42860682030941723212E-6;
 
  const G4double xx = x * x;
 
  // px = x * P(x**2).
  px = G4ExpConsts::PX1exp;
  px *= xx;
  px += G4ExpConsts::PX2exp;
  px *= xx;
  px += G4ExpConsts::PX3exp;
  px *= x;
 
  // Evaluate Q(x**2).
  G4double qx = G4ExpConsts::QX1exp;
  qx *= xx;
  qx += G4ExpConsts::QX2exp;
  qx *= xx;
  qx += G4ExpConsts::QX3exp;
  qx *= xx;
  qx += G4ExpConsts::QX4exp;
 
  // e**x = 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
  x = px / (qx - px);
  x = 1.0 + 2.0 * x;
 
  // Build 2^n in double.
  x *= G4IEEE754::uint642dp((((uint64_t) n) + 1023) << 52);
 
  if(initial_x > G4ExpConsts::EXP_LIMIT)
    x = std::numeric_limits<G4double>::infinity();
  if(initial_x < -G4ExpConsts::EXP_LIMIT)
    x = 0.;
 
  return x;
}
 
// Exp single precision --------------------------------------------------------
 
/// Exponential Function single precision
inline G4float G4Expf(G4float initial_x)
{
  G4float x = initial_x;
 
  G4float z =
    G4ExpConsts::fpfloor(G4ExpConsts::LOG2EF * x +
                         0.5f); /* std::floor() truncates toward -infinity. */
 
  x -= z * G4ExpConsts::C1F;
  x -= z * G4ExpConsts::C2F;
  const int32_t n = int32_t(z);
 
  const G4float x2 = x * x;
 
  z = x * G4ExpConsts::PX1expf;
  z += G4ExpConsts::PX2expf;
  z *= x;
  z += G4ExpConsts::PX3expf;
  z *= x;
  z += G4ExpConsts::PX4expf;
  z *= x;
  z += G4ExpConsts::PX5expf;
  z *= x;
  z += G4ExpConsts::PX6expf;
  z *= x2;
  z += x + 1.0f;
 
  /* multiply by power of 2 */
  z *= G4IEEE754::uint322sp((n + 0x7f) << 23);
 
  if(initial_x > G4ExpConsts::MAXLOGF)
    z = std::numeric_limits<G4float>::infinity();
  if(initial_x < G4ExpConsts::MINLOGF)
    z = 0.f;
 
  return z;
}
 
#endif /* WIN32 */
 
#endif