1
Check Primes
public boolean isPrime(int number){
for(int i=2; i
else b = b – a;
}
Return a;
}
}
Calculate Pi to a certain number of digits (from Week-3 examples)
public class Pi {
private static final long serialVersionUID = 227L;
/** constants used in pi computation */
private static final BigDecimal FOUR = BigDecimal.valueOf(4);
/** rounding mode to use during pi computation */
private static final int roundingMode = BigDecimal.ROUND_HALF_EVEN;
/** digits of precision after the decimal point */
private final int digits;
/**
* Construct a task to calculate pi to the specified
* precision.
*/
public Pi(int digits) {
this.digits = digits;
}
/**
* Calculate pi.
*/
public BigDecimal execute() {
return computePi(digits);
}
/**
* Compute the value of pi to the specified number of
* digits after the decimal point. The value is
* computed using Machin’s formula:
*
* pi/4 = 4*arctan(1/5) – arctan(1/239)
*
* and a power series expansion of arctan(x) to
* sufficient precision.
*/
public static BigDecimal computePi(int digits) {
int scale = digits + 5;
BigDecimal arctan1_5 = arctan(5, scale);
BigDecimal arctan1_239 = arctan(239, scale);
BigDecimal pi = arctan1_5.multiply(FOUR).subtract(arctan1_239).multiply(FOUR);
return pi.setScale(digits, BigDecimal.ROUND_HALF_UP);
}
/**
* Compute the value, in radians, of the arctangent of
* the inverse of the supplied integer to the specified
* number of digits after the decimal point. The value
2
* is computed using the power series expansion for the
* arc tangent:
*
* arctan(x) = x – (x^3)/3 + (x^5)/5 – (x^7)/7 +(x^9)/9 …
*/
public static BigDecimal arctan(int inverseX, int scale)
{
BigDecimal result, numer, term;
BigDecimal invX = BigDecimal.valueOf(inverseX);
BigDecimal invX2 = BigDecimal.valueOf(inverseX * inverseX);
numer = BigDecimal.ONE.divide(invX, scale, roundingMode);
result = numer;
int i = 1;
do {
numer = numer.divide(invX2, scale, roundingMode);
int denom = 2 * i + 1;
term = numer.divide(BigDecimal.valueOf(denom), scale, roundingMode);
if ((i % 2) != 0) {
result = result.subtract(term);
} else {
result = result.add(term);
}
i++;
} while (term.compareTo(BigDecimal.ZERO) != 0);
return result;
}
}