/*
 * constants - implementation of different constants to arbitrary precision
 *
 * Copyright (C) 2013 Christoph Zurnieden
 *
 * constants is open software; you can redistribute it and/or modify it under
 * the terms of the version 2.1 of the GNU Lesser General Public License
 * as published by the Free Software Foundation.
 *
 * constants 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 General
 * Public License for more details.
 *
 * A copy of version 2.1 of the GNU Lesser General Public License is
 * distributed with calc under the filename COPYING-LGPL.  You should have
 * received a copy with calc; if not, write to Free Software Foundation, Inc.
 * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 *
 * @(#) $Revision: 30.3 $
 * @(#) $Id: constants.cal,v 30.3 2013/08/11 08:41:38 chongo Exp $
 * @(#) $Source: /usr/local/src/bin/calc/cal/RCS/constants.cal,v $
 *
 * Under source code control:	2013/08/11 01:31:28
 * File existed as early as:	2013
 */


static resource_debug_level;
resource_debug_level = config("resource_debug", 0);


static __CZ__euler_mascheroni = 0;
static __CZ__euler_mascheroni_prec = 0;


define e(){
  local k temp1 temp2 ret eps factor upperlimit prec;

  prec = digits(1/epsilon());
  if(__CZ__euler_mascheroni != 0 &&  __CZ__euler_mascheroni_prec >= prec)
    return __CZ__euler_mascheroni;
  if(prec<=20) return 2.718281828459045235360287471;
  if(prec<=1800){
    __CZ__euler_mascheroni = exp(1);
    __CZ__euler_mascheroni_prec = prec;
  }

  eps=epsilon(1e-20);
  factor = 1;
  k = 0;
  upperlimit = prec * ln(10);
  while(k<upperlimit){
    k += ln(factor);
    factor++;
  }
  epsilon(eps);
  temp1 = 0;
  ret   = 1;
  for(k=3;k<=factor;k++){
    temp2 = temp1;
    temp1 = ret;
    ret =  (k-1) *(temp1 + temp2);
  }

  ret = inverse( ret * inverse(factorial(factor) ) ) ;
  __CZ__euler_mascheroni = ret;
  __CZ__euler_mascheroni_prec = prec;
  return ret;
}


/* Lupas' series */
static __CZ__catalan = 0;
static __CZ__catalan_prec = 0;
define G(){
  local eps a s t n;
  eps = epsilon(epsilon()*1e-10);
  if(__CZ__catalan != 0 &&  __CZ__catalan >= log(1/eps))
    return __CZ__catalan;
  a = 1;
  s = 0;
  t = 1;
  n = 1;
  while(abs(t)> eps){
    a *= 32 * n^3 * (2*n-1);
    a /=((3-16*n+16*n^2)^2);
    t = a * (-1)^(n-1) * (40*n^2-24*n+3) / (n^3 * (2*n-1));
    s += t;
    n += 1;
  }
  s = s/64;
  __CZ__catalan = s;
  __CZ__catalan_prec = log(1/eps);
  epsilon(eps);
  return s;
}


config("resource_debug", resource_debug_level),;
if (config("resource_debug") & 3) {
    print "e()";
    print "G()";
}