package bigdecimal;
import java.math.BigDecimal;
import java.math.BigInteger;
public class Main {
public static BigDecimal bigRoot(BigDecimal number, int n, int scale, int roundingMode) {//开n次方，保留scale位小数
boolean negate = false;
if (n < 0)
throw new ArithmeticException();
if (number.compareTo(BigDecimal.ZERO) < 0) {
if (n % 2 == 0)
throw new ArithmeticException();
else {
number = number.negate();
negate = true;
}
}
BigDecimal root;
if (n == 0)
root = BigDecimal.ONE;
else if (n == 1)
root = number;
else {
final BigInteger N = BigInteger.valueOf(n);
final BigInteger N2 = BigInteger.TEN.pow(n);
final BigInteger N3 = BigInteger.TEN.pow(n - 1);
final BigInteger NINE = BigInteger.valueOf(9);
BigInteger[] C = new BigInteger[n + 1];
for (int i = 0; i <= n; i++) {
C[i] = combination(n, i);
}
BigInteger integer = number.toBigInteger();
String strInt = integer.toString();
int lenInt = strInt.length();
for (int i = lenInt % n; i < n && i > 0; i++)
strInt = "0" + strInt;
lenInt = (lenInt + n - 1) / n * n;
BigDecimal fraction = number.subtract(number.setScale(0, BigDecimal.ROUND_DOWN));
int lenFrac = (fraction.scale() + n - 1) / n * n;
fraction = fraction.movePointRight(lenFrac);
String strFrac = fraction.toPlainString();
for (int i = strFrac.length(); i < lenFrac; i++)
strFrac = "0" + strFrac;
BigInteger res = BigInteger.ZERO;
BigInteger rem = BigInteger.ZERO;
for (int i = 0; i < lenInt / n; i++) {
rem = rem.multiply(N2);
BigInteger temp = new BigInteger(strInt.substring(i * n, i * n + n));
rem = rem.add(temp);
BigInteger j;
if (res.compareTo(BigInteger.ZERO) != 0)
j = rem.divide(res.pow(n - 1).multiply(N).multiply(N3));
else
j = NINE;
BigInteger test = BigInteger.ZERO;
temp = res.multiply(BigInteger.TEN);
while (j.compareTo(BigInteger.ZERO) >= 0) {
//test = res.multiply(BigInteger.TEN);
//test = ((test.add(j)).pow(n)).subtract(test.pow(n));
test = BigInteger.ZERO;
if (j.compareTo(BigInteger.ZERO) > 0)
for (int k = 1; k <= n; k++)
test = test.add(j.pow(k).multiply(C[k]).multiply(temp.pow(n - k)));
if (test.compareTo(rem) <= 0)
break;
j = j.subtract(BigInteger.ONE);
}
rem = rem.subtract(test);
res = res.multiply(BigInteger.TEN);
res = res.add(j);
}
for (int i = 0; i <= scale; i++) {
rem = rem.multiply(N2);
if (i < lenFrac / n) {
BigInteger temp = new BigInteger(strFrac.substring(i * n, i * n + n));
rem = rem.add(temp);
}
BigInteger j;
if (res.compareTo(BigInteger.ZERO) != 0) {
j = rem.divide(res.pow(n - 1).multiply(N).multiply(N3));
}
else
j = NINE;
BigInteger test = BigInteger.ZERO;
BigInteger temp = res.multiply(BigInteger.TEN);
while (j.compareTo(BigInteger.ZERO) >= 0) {
//test = res.multiply(BigInteger.TEN);
//test = ((test.add(j)).pow(n)).subtract(test.pow(n));
test = BigInteger.ZERO;
if (j.compareTo(BigInteger.ZERO) > 0)
for (int k = 1; k <= n; k++)
test = test.add(j.pow(k).multiply(C[k]).multiply(temp.pow(n - k)));
if (test.compareTo(rem) <= 0)
break;
j = j.subtract(BigInteger.ONE);
}
rem = rem.subtract(test);
res = res.multiply(BigInteger.TEN);
res = res.add(j);
}
root = new BigDecimal(res).movePointLeft(scale + 1);
if (negate)
root = root.negate();
}
return root.setScale(scale, roundingMode);
}
public static BigInteger combination(int n, int k) {
if (k > n || n < 0 || k < 0)
return BigInteger.ZERO;
if (k > n / 2)
return combination(n, n - k);
BigInteger N1 = BigInteger.ONE;
BigInteger N2 = BigInteger.ONE;
BigInteger N = BigInteger.valueOf(n);
BigInteger K = BigInteger.valueOf(k);
for (int i = 0; i < k; i++) {
N1 = N1.multiply(N);
N2 = N2.multiply(K);
N = N.subtract(BigInteger.ONE);
K = K.subtract(BigInteger.ONE);
}
return N1.divide(N2);
}
public static void main(String args[]) {
BigDecimal num = new BigDecimal("1000.0001");
long time;
time= System.nanoTime();
BigDecimal root = bigRoot(num, 3, 1000, BigDecimal.ROUND_HALF_UP);//开3次方，保留1000位小数。
time = System.nanoTime() - time;
System.out.println("开方结果:"+root);
System.out.println("root的3次方:"+root.pow(3).setScale(2, BigDecimal.ROUND_HALF_UP));
System.out.println("原来的数:"+num);
System.out.println("运行时间:"+time);
}
}
