/*
Written by Reginald Ford
Computes the integral from 0 to endPt
of exp(t), which is exp(t).
Serves as a template for writing solvers
*/
#include <iostream>
#include <cmath>
#include <stdlib.h>
#include "pstools.h"

using namespace std;


#define MAXORDER 170
#define NUMEQS 1
//c[NUMEQS][order+1]
double c[1][MAXORDER];


void step(double stepSize, int order)
{
  //build the coefficients
  for(int i=0;i<=order;i++)
  {
    double oip1 = 1.0/(i+1.0);//over i+1
    c[0][i+1] = oip1*c[0][i];
  }
  //evaluate the polynomials, and set new initial conditions
  for(int i=0;i<NUMEQS;i++)
    c[i][0]=polyval(c[i],stepSize,order);
  
  //record your initial conditions
  cout<<c[0][0]<<endl;
}

int main(int numArgs,char **argv)
{
  int order = 0;
  double endPt,stepSize;
  
  if(numArgs != 4)
  {
    cout<<"Provide arguments:\n";
    cout<<argv[0]<<" (order) (inverse stepSize) (endPt) \n";
    return 0;
  }
  else
  {
    order = atoi(argv[1]);
    stepSize = 1.0/atoi(argv[2]);
    endPt = atoi(argv[3]);
    if(order>MAXORDER)
      cout<<"Order is above MAXORDER: "<<MAXORDER;
    cout<<"order: "<<order<<" stepsize: "<<stepSize<<endl;
  }
  //initial conditions (t=0)
  c[0][0] = 1;
  
  //stepping. make sure that endPt is a multiple of stepSize
  if(endPt < 0)
    stepSize*=-1.0;
  int numSteps = abs(endPt/stepSize);
  
  for(int s=1;s<=numSteps;s++)
  {
    step(stepSize, order);
  }
  
  if(numSteps*stepSize < endPt)
    step(endPt - numSteps*stepSize,order);
 
  return 0;
}