// test_Big_math.java  generate Pi, e to 100 fraction bits (error<1/2^100)
//                and test a few other functiond sqrt, sin, cos, atan, exp 
// compile and run  javac -cp . Big_math.java
//                  javac -cp . test_Big_math.java
//                  java  -cp . test_Big_math

import java.math.BigDecimal;

public class test_Big_math
{
  Big_math B = new Big_math(); //  B.  for  Big_math  functions 
  BigDecimal natural_e;  
  BigDecimal pi;
  BigDecimal epsilon;
  BigDecimal tmp;
  BigDecimal two = new BigDecimal(2.0);
  BigDecimal half = new BigDecimal("0.5");
  int prec  = 100; // digits
                   // precision in bits = about 3.32 precision in digits

  public test_Big_math() // constructor
  {
    System.out.println("test_Big_math running");
    natural_e = B.naturalE(prec); // precision
    System.out.println("natural_e="+natural_e);
    epsilon = half.pow(prec);
    System.out.println("epsilon="+epsilon);
    pi = B.Npi();
    System.out.println("pi="+pi);

    System.out.println("test exp");
    BigDecimal e1 = B.exp(new BigDecimal("1"));
    BigDecimal e2 = B.exp(new BigDecimal("2"));
    BigDecimal diff = e1.subtract(B.sqrt(e2));
    System.out.println("     e="+natural_e);
    System.out.println("exp(1)="+e1);
    System.out.println("     err e-exp(1)="+natural_e.subtract(e1));
    System.out.println("exp(2)="+e2);
    System.out.println("exp(1)-sqrt(exp(2))="+diff);
    System.out.println("exp(.001)="+B.exp(new BigDecimal("0.001")));
    System.out.println("exp(100)="+B.exp(new BigDecimal("100")));
    System.out.println();

    // test atan
    System.out.println("test atan, compute Pi");
    BigDecimal a1 = B.atan(new BigDecimal("1"));
    BigDecimal ep1 = B.epsilon.add(new BigDecimal("1"));
    BigDecimal b1  = (new BigDecimal("2")).subtract((B.sqrt(
                      new BigDecimal("3"))));
    b1 = b1.setScale(prec,BigDecimal.ROUND_DOWN);
    BigDecimal a2 = B.atan(ep1.divide(B.sqrt(new BigDecimal("3")),BigDecimal.ROUND_DOWN));
    BigDecimal a3 = B.atan(b1);
    BigDecimal b2 = ((new BigDecimal("2")).multiply(B.sqrt(b1))).subtract(
                      new BigDecimal("1"));
    b2 = b2.setScale(prec,BigDecimal.ROUND_DOWN);
    b2 = b2.divide(b1, BigDecimal.ROUND_DOWN);
    BigDecimal a4 = B.atan(b2);
    System.out.println("atan(1)="+a1);
    System.out.println("atan(1/sqrt(3))="+a2);
    System.out.println("atan(2-sqrt(3))="+a3);
    System.out.println("atan(b2)="+a4);
    System.out.println("Pi  4*a1="+a1.multiply(new BigDecimal("4")));
    System.out.println("Pi  6*a2="+a2.multiply(new BigDecimal("6")));
    System.out.println("Pi 12*a3="+a3.multiply(new BigDecimal("12")));
    BigDecimal pi4 = a4.multiply(new BigDecimal("24"));
    System.out.println("Pi 24*a4="+pi4);
    System.out.println("     err npi-Pi24="+pi.subtract(pi4));
    System.out.println();

    // test sin
    System.out.println("test sin");
    BigDecimal pid2 = pi.divide(new BigDecimal("2"));
    BigDecimal sin50 = B.sin((pi.multiply(new BigDecimal("50")).add(pid2)));
    System.out.println("sin(50pi+pi/2)= 1 ="+sin50);
    BigDecimal sin50n = B.sin((pi.multiply(new BigDecimal("-50")).subtract(
                               pid2)));
    System.out.println("sin(-50pi-pi/2)= -1 ="+sin50n);
    System.out.println(" ");

    System.out.println("end test_Big_math");
  }

  public static void main (String[] args)
  {
    new test_Big_math();
  }
} // end  test_Big_math.java