package com.ignatieff.zeta;

import java.math.BigDecimal;
import java.math.MathContext;
import java.math.RoundingMode;
import java.util.Scanner;

public class Main {

    private static BigDecimal PI;
    private static BigDecimal PiPow;
    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        int rounds = s.radix();
        int x=3;
        do{
            System.out.print("Calculate Zeta(s), where s = ");
            try{
            x=Integer.parseInt(s.nextLine());}catch(Exception e){}
        }while(x==s.radix());
        do{
            System.out.print("Precision (digits): ");
            try{
            rounds=Integer.parseInt(s.nextLine());}catch(Exception e){}
        }while(rounds==s.radix());

        MathContext mc = new MathContext(rounds+20, RoundingMode.HALF_UP);
        System.out.println("Calculating PI to " + rounds + " decimal places...");
        PI = Pi.pi(rounds);


        //The digit d affected by zeta iteration i, is: d = log10(i^3)
        BigDecimal p = new BigDecimal(10).pow(rounds);
        BigDecimal root = Zeta.cuberoot(p, 100, mc);
        long r = root.round(new MathContext(1)).longValue();
        System.out.println("Approximating the riemann zeta function to " + rounds + " decimals ("+r+" rounds).\n");
        BigDecimal zeta = Zeta.zeta(x, r, mc);
        System.out.println("Finding best match...");
        BigDecimal smallestDev = new BigDecimal(Integer.MAX_VALUE);
        BigDecimal val = new BigDecimal(0);
        int bestMatch = -1;
        int pi = 1;
        for(int P=0;P<51;P++){
            PiPow = PI.pow(P);
            for(int i=0;i<5000;i++){
            BigDecimal exact = PiPow.divide(new BigDecimal(i+1),mc);
            BigDecimal testDev = (zeta.subtract(exact,mc)).abs();
            if(testDev.compareTo(smallestDev) == -1){
                bestMatch=i;
                smallestDev=testDev;
                val = exact;
                pi=P;
            }
            }}

        smallestDev = smallestDev.setScale(rounds, RoundingMode.CEILING);
        zeta = zeta.setScale(rounds, RoundingMode.CEILING);
        val = val.setScale(rounds, RoundingMode.CEILING);

        System.out.println("The best approximation is (Pi^"+pi+")/"+(bestMatch+1)+" - with a deviation of " + smallestDev.toString());
        System.out.println("    - Zeta("+x+") = " + zeta.toString());
        System.out.println("    - (Pi^"+pi+")/"+(bestMatch+1)+" = " +val);
    }

}