real.cpp

/*
**  CXSC is a C++ library for eXtended Scientific Computing (V 2.5.4)
**
**  Copyright (C) 1990-2000 Institut fuer Angewandte Mathematik,
**                          Universitaet Karlsruhe, Germany
**            (C) 2000-2014 Wiss. Rechnen/Softwaretechnologie
**                          Universitaet Wuppertal, Germany   
**
**  This library is free software; you can redistribute it and/or
**  modify it under the terms of the GNU Library General Public
**  License as published by the Free Software Foundation; either
**  version 2 of the License, or (at your option) any later version.
**
**  This library 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
**  Library General Public License for more details.
**
**  You should have received a copy of the GNU Library General Public
**  License along with this library; if not, write to the Free
**  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
*/

/* CVS $Id: real.cpp,v 1.28 2014/01/30 17:23:48 cxsc Exp $ */

#include "real.hpp"
#include "ioflags.hpp"

namespace cxsc {

//----------------------------------------------------------------------------
// MakeHexReal - erstellt aus den binaer angegebenen Einzelteilen einer
//               IEEE 64-bit Gleitkommazahl eine solche, hierbei ist
//                 sign         Flag 'zu erzeugener real ist negativ'
//                 expo         Exponent (11 Bit 0x000 - 0x7FF)
//                 manthigh     obere  20 Bit der Mantisse (Bit 32 - 53)
//                 mantlow      untere 32 Bit der Mantisse (Bit  0 - 31)
//
//             - die Mantisse ist normalisiert dargestellt, d.h.
//               implizit wird noch ein Bit 1 als Vorkommastelle
//               vorangestellt.
//               Eine Ausnahme bilden die Zahlen mit Exponent = 0,
//               oder Exponent = 0x7FF (alle Exponentenbits = 1)
//
const real& MakeHexReal(int sign, unsigned int expo, a_btyp manthigh, a_btyp mantlow)
{
  static real a;
  ((a_btyp*)&a)[LOWREAL]   = mantlow,
  ((a_btyp*)&a)[HIGHREAL]  = manthigh & 0xFFFFFL,
  ((a_btyp*)&a)[HIGHREAL] |= ((a_btyp) (expo & 0x7FF)) << 20,
  ((a_btyp*)&a)[HIGHREAL] |= (sign ? 0x80000000L : 0x00000000);
  return a;
}

const real MinReal      = MakeHexReal(0, 0x001, 0x00000L, 0x00000000L);
const real minreal      = MakeHexReal(0, 0x000, 0x00000L, 0x00000001L);
// Blomquist, 26.09.02; minreal = smallest positive real number.
const real MaxReal      = MakeHexReal(0, 0x7FE, 0xFFFFFL, 0xFFFFFFFFL);
const real Infinity     = MakeHexReal(0, 0x7FF, 0x00000L, 0x00000000L);
const real SignalingNaN = MakeHexReal(1, 0x7FF, 0x80000L, 0x00000000L);
const real QuietNaN     = MakeHexReal(0, 0x7FF, 0x00000L, 0x00000001L);
const real Epsilon      = power(2,-53);
const real Factor       = power(2, 27) + 1;


// The following constants are roundet to the nearest machine nunmber:

const real Pi_real = 7074237752028440.0 / 2251799813685248.0;  // Pi
const real Pi2_real = 7074237752028440.0/1125899906842624.0;   // 2*Pi
const real Pi3_real = 5305678314021330.0/562949953421312.0;    // 3*Pi
const real Pid2_real = 7074237752028440.0/4503599627370496.0;  // Pi/2
const real Pid3_real = 4716158501352294.0/4503599627370496.0;  // Pi/3
const real Pid4_real = 7074237752028440.0/9007199254740992.0;  // Pi/4
const real Pir_real = 5734161139222659.0/18014398509481984.0;  // 1/Pi
const real Pi2r_real = 5734161139222659.0/36028797018963968.0; // 1/(2*Pi)
const real Pip2_real = 5556093337880030.0/562949953421312.0;   // Pi^2
const real SqrtPi_real = 7982422502469483.0/4503599627370496.0;// sqrt(Pi)
const real Sqrt2Pi_real = 5644425081792262.0/2251799813685248.0; // sqrt(2Pi)
const real SqrtPir_real = 5081767996463981.0/9007199254740992.0; // 1/sqrt(Pi)
const real Sqrt2Pir_real = 7186705221432913.0/18014398509481984.0; // 1/sqrt(2Pi)
const real Sqrt2_real = 6369051672525773.0/4503599627370496.0; // sqrt(2)
const real Sqrt5_real = 5035177455121576.0 / 2251799813685248.0; // sqrt(5)
const real Sqrt7_real = 5957702309312746.0 / 2251799813685248.0; // sqrt(7)
const real Sqrt2r_real = 6369051672525773.0/9007199254740992.0;// 1/sqrt(2)
const real Sqrt3_real = 7800463371553962.0/4503599627370496.0; // sqrt(3)
const real Sqrt3d2_real = 7800463371553962.0/9007199254740992.0;  // sqrt(3)/2
const real Sqrt3r_real = 5200308914369308.0/9007199254740992.0;// 1/sqrt(3)
const real Ln2_real = 6243314768165359.0 / 9007199254740992.0; // ln(2)
const real Ln2r_real = 6497320848556798.0 / 4503599627370496.0; // 1/ln(2)
const real Ln10_real = 5184960683398422.0 / 2251799813685248.0; // ln(10)
const real Ln10r_real = 7823553867474190.0/18014398509481984.0; // 1/ln(10)
const real LnPi_real = 5155405087351229.0 / 4503599627370496.0; // ln(Pi)
const real Ln2Pi_real = 8277062471433909.0/4503599627370496.0;  // ln(2Pi)
const real E_real = 6121026514868073.0 / 2251799813685248.0;    // e
const real Er_real = 6627126856707896.0 / 18014398509481984.0;  // 1/e
const real Ep2_real = 8319337573440942.0 / 1125899906842624.0;  // e^2
const real Ep2r_real = 4875967449235916.0/36028797018963968.0;  // 1/e^2
const real EpPi_real = 6513525919879994.0/281474976710656.0;    // e^(Pi)
const real Ep2Pi_real = 4710234414611993.0/8796093022208.0;     // e^(2Pi)
const real EpPid2_real = 5416116035097439.0/1125899906842624.0; // e^(Pi/2)
const real EpPid4_real = 4938827609611434.0/2251799813685248.0; // e^(Pi/4)

} // namespace cxsc