#!/usr/bin/env python3
# -*- coding: utf-8 -*-

# ***************************************************************************
# *   Copyright (C) 2011, Paul Lutus                                        *
# *                                                                         *
# *   This program is free software; you can redistribute it and/or modify  *
# *   it under the terms of the GNU General Public License as published by  *
# *   the Free Software Foundation; either version 2 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 General Public License for more details.                          *
# *                                                                         *
# *   You should have received a copy of the GNU General Public License     *
# *   along with this program; if not, write to the                         *
# *   Free Software Foundation, Inc.,                                       *
# *   59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.             *
# ***************************************************************************

from math import *
import re

def f(y):
  return 2 * sqrt((2-y)*y)
  
def cff(y):
  if(y == 0): return 0
  s1 = sqrt(y)
  s2 = sqrt(-y+2)
  return pi + s2 * (y-1) * s1 - 2 * atan(s2/s1)

def num_int(f,ni,a,b):
  if(a == b): return 0
  nf = float(ni)
  r = b-a
  s = 0
  di = 1/nf
  for i in range(ni+1):
    x = i*di*r+a
    s += f(x)
  return s * r / nf
  
def gen_table(ni):
  nx = 10
  html = True
  print(('Samples: %d' % ni))
  for i in range(1,nx+1):
    x = i * 2 / float(nx)
    rcf = cff(x)
    rni = num_int(f,ni,0,x)
    out = '%.1f %.6f %.6f %+.6f%%' % (x,rcf,rni, 100 * ((rni-rcf)/rcf))
    if(html):
      out = '<tr>' + re.sub('(\S+)\s*','<td>\\1</td>',out) + '</tr>'
    print(out)

for n in range(2,5):
  gen_table(int(pow(10,n)))