Gabriele Cosmo
352 lines
10 KiB
C++
352 lines
10 KiB
C++
//
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// ********************************************************************
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// * License and Disclaimer *
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// * *
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// * The Geant4 software is copyright of the Copyright Holders of *
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// * the Geant4 Collaboration. It is provided under the terms and *
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// * conditions of the Geant4 Software License, included in the file *
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// * LICENSE and available at http://cern.ch/geant4/license . These *
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// * include a list of copyright holders. *
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// * *
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// * Neither the authors of this software system, nor their employing *
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// * institutes,nor the agencies providing financial support for this *
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// * work make any representation or warranty, express or implied, *
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// * regarding this software system or assume any liability for its *
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// * use. Please see the license in the file LICENSE and URL above *
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// * for the full disclaimer and the limitation of liability. *
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// * *
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// * This code implementation is the result of the scientific and *
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// * technical work of the GEANT4 collaboration. *
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// * By using, copying, modifying or distributing the software (or *
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// * any work based on the software) you agree to acknowledge its *
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// * use in resulting scientific publications, and indicate your *
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// * acceptance of all terms of the Geant4 Software license. *
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// ********************************************************************
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//
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// G4Log
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//
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// Class description:
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//
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// The basic idea is to exploit Pade polynomials.
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// A lot of ideas were inspired by the cephes math library
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// (by Stephen L. Moshier moshier@na-net.ornl.gov) as well as actual code.
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// The Cephes library can be found here: http://www.netlib.org/cephes/
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// Code and algorithms for G4Exp have been extracted and adapted for Geant4
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// from the original implementation in the VDT mathematical library
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// (https://svnweb.cern.ch/trac/vdt), version 0.3.7.
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// Original implementation created on: Jun 23, 2012
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// Author: Danilo Piparo, Thomas Hauth, Vincenzo Innocente
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//
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// --------------------------------------------------------------------
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/*
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* VDT is free software: you can redistribute it and/or modify
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* it under the terms of the GNU Lesser Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU Lesser Public License for more details.
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*
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* You should have received a copy of the GNU Lesser Public License
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* along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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// --------------------------------------------------------------------
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#ifndef G4Log_hh
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#define G4Log_hh 1
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#ifdef WIN32
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# define G4Log std::log
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#else
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# include "G4Types.hh"
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# include <cstdint>
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# include <limits>
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// local namespace for the constants/functions which are necessary only here
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//
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namespace G4LogConsts
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{
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const G4double LOG_UPPER_LIMIT = 1e307;
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const G4double LOG_LOWER_LIMIT = 0;
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const G4double SQRTH = 0.70710678118654752440;
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const G4float MAXNUMF = 3.4028234663852885981170418348451692544e38f;
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//----------------------------------------------------------------------------
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// Used to switch between different type of interpretations of the data
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// (64 bits)
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//
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union ieee754
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{
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ieee754()= default;
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ieee754(G4double thed) { d = thed; };
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ieee754(uint64_t thell) { ll = thell; };
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ieee754(G4float thef) { f[0] = thef; };
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ieee754(uint32_t thei) { i[0] = thei; };
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G4double d;
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G4float f[2];
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uint32_t i[2];
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uint64_t ll;
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uint16_t s[4];
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};
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inline G4double get_log_px(const G4double x)
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{
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const G4double PX1log = 1.01875663804580931796E-4;
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const G4double PX2log = 4.97494994976747001425E-1;
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const G4double PX3log = 4.70579119878881725854E0;
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const G4double PX4log = 1.44989225341610930846E1;
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const G4double PX5log = 1.79368678507819816313E1;
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const G4double PX6log = 7.70838733755885391666E0;
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G4double px = PX1log;
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px *= x;
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px += PX2log;
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px *= x;
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px += PX3log;
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px *= x;
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px += PX4log;
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px *= x;
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px += PX5log;
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px *= x;
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px += PX6log;
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return px;
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}
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inline G4double get_log_qx(const G4double x)
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{
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const G4double QX1log = 1.12873587189167450590E1;
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const G4double QX2log = 4.52279145837532221105E1;
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const G4double QX3log = 8.29875266912776603211E1;
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const G4double QX4log = 7.11544750618563894466E1;
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const G4double QX5log = 2.31251620126765340583E1;
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G4double qx = x;
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qx += QX1log;
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qx *= x;
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qx += QX2log;
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qx *= x;
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qx += QX3log;
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qx *= x;
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qx += QX4log;
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qx *= x;
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qx += QX5log;
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return qx;
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}
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//----------------------------------------------------------------------------
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// Converts a double to an unsigned long long
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//
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inline uint64_t dp2uint64(G4double x)
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{
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ieee754 tmp;
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tmp.d = x;
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return tmp.ll;
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}
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//----------------------------------------------------------------------------
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// Converts an unsigned long long to a double
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//
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inline G4double uint642dp(uint64_t ll)
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{
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ieee754 tmp;
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tmp.ll = ll;
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return tmp.d;
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}
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//----------------------------------------------------------------------------
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// Converts an int to a float
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//
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inline G4float uint322sp(G4int x)
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{
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ieee754 tmp;
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tmp.i[0] = x;
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return tmp.f[0];
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}
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//----------------------------------------------------------------------------
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// Converts a float to an int
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//
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inline uint32_t sp2uint32(G4float x)
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{
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ieee754 tmp;
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tmp.f[0] = x;
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return tmp.i[0];
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}
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//----------------------------------------------------------------------------
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/// Like frexp but vectorising and the exponent is a double.
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inline G4double getMantExponent(const G4double x, G4double& fe)
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{
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uint64_t n = dp2uint64(x);
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// Shift to the right up to the beginning of the exponent.
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// Then with a mask, cut off the sign bit
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uint64_t le = (n >> 52);
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// chop the head of the number: an int contains more than 11 bits (32)
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int32_t e =
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(int32_t)le; // This is important since sums on uint64_t do not vectorise
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fe = e - 1023;
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// This puts to 11 zeroes the exponent
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n &= 0x800FFFFFFFFFFFFFULL;
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// build a mask which is 0.5, i.e. an exponent equal to 1022
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// which means *2, see the above +1.
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const uint64_t p05 = 0x3FE0000000000000ULL; // dp2uint64(0.5);
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n |= p05;
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return uint642dp(n);
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}
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//----------------------------------------------------------------------------
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/// Like frexp but vectorising and the exponent is a float.
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inline G4float getMantExponentf(const G4float x, G4float& fe)
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{
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uint32_t n = sp2uint32(x);
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int32_t e = (n >> 23) - 127;
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fe = e;
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// fractional part
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const uint32_t p05f = 0x3f000000; // //sp2uint32(0.5);
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n &= 0x807fffff; // ~0x7f800000;
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n |= p05f;
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return uint322sp(n);
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}
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} // namespace G4LogConsts
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// Log double precision --------------------------------------------------------
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inline G4double G4Log(G4double x)
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{
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const G4double original_x = x;
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/* separate mantissa from exponent */
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G4double fe;
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x = G4LogConsts::getMantExponent(x, fe);
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// blending
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x > G4LogConsts::SQRTH ? fe += 1. : x += x;
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x -= 1.0;
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/* rational form */
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G4double px = G4LogConsts::get_log_px(x);
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// for the final formula
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const G4double x2 = x * x;
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px *= x;
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px *= x2;
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const G4double qx = G4LogConsts::get_log_qx(x);
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G4double res = px / qx;
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res -= fe * 2.121944400546905827679e-4;
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res -= 0.5 * x2;
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res = x + res;
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res += fe * 0.693359375;
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if(original_x > G4LogConsts::LOG_UPPER_LIMIT)
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res = std::numeric_limits<G4double>::infinity();
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if(original_x < G4LogConsts::LOG_LOWER_LIMIT) // THIS IS NAN!
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res = -std::numeric_limits<G4double>::quiet_NaN();
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return res;
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}
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// Log single precision --------------------------------------------------------
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namespace G4LogConsts
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{
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const G4float LOGF_UPPER_LIMIT = MAXNUMF;
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const G4float LOGF_LOWER_LIMIT = 0;
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const G4float PX1logf = 7.0376836292E-2f;
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const G4float PX2logf = -1.1514610310E-1f;
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const G4float PX3logf = 1.1676998740E-1f;
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const G4float PX4logf = -1.2420140846E-1f;
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const G4float PX5logf = 1.4249322787E-1f;
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const G4float PX6logf = -1.6668057665E-1f;
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const G4float PX7logf = 2.0000714765E-1f;
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const G4float PX8logf = -2.4999993993E-1f;
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const G4float PX9logf = 3.3333331174E-1f;
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inline G4float get_log_poly(const G4float x)
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{
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G4float y = x * PX1logf;
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y += PX2logf;
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y *= x;
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y += PX3logf;
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y *= x;
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y += PX4logf;
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y *= x;
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y += PX5logf;
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y *= x;
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y += PX6logf;
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y *= x;
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y += PX7logf;
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y *= x;
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y += PX8logf;
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y *= x;
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y += PX9logf;
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return y;
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}
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const G4float SQRTHF = 0.707106781186547524f;
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} // namespace G4LogConsts
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// Log single precision --------------------------------------------------------
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inline G4float G4Logf(G4float x)
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{
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const G4float original_x = x;
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G4float fe;
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x = G4LogConsts::getMantExponentf(x, fe);
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x > G4LogConsts::SQRTHF ? fe += 1.f : x += x;
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x -= 1.0f;
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const G4float x2 = x * x;
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G4float res = G4LogConsts::get_log_poly(x);
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res *= x2 * x;
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res += -2.12194440e-4f * fe;
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res += -0.5f * x2;
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res = x + res;
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res += 0.693359375f * fe;
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if(original_x > G4LogConsts::LOGF_UPPER_LIMIT)
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res = std::numeric_limits<G4float>::infinity();
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if(original_x < G4LogConsts::LOGF_LOWER_LIMIT)
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res = -std::numeric_limits<G4float>::quiet_NaN();
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return res;
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}
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//------------------------------------------------------------------------------
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void logv(const uint32_t size, G4double const* __restrict__ iarray,
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G4double* __restrict__ oarray);
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void G4Logv(const uint32_t size, G4double const* __restrict__ iarray,
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G4double* __restrict__ oarray);
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void logfv(const uint32_t size, G4float const* __restrict__ iarray,
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G4float* __restrict__ oarray);
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void G4Logfv(const uint32_t size, G4float const* __restrict__ iarray,
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G4float* __restrict__ oarray);
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#endif /* WIN32 */
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#endif /* LOG_H_ */
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